Finite Group Databasebeta

← #34495644

Subgroups — #34495644

Order 20224.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099150C211yesmaximal, characteristic, complemented
2C2×#19099146C211yesmaximal, characteristic, complemented
3#23771681C211yesmaximal, characteristic, complemented
4#23771679C211yesmaximal, characteristic, complemented
5#23770308C211yesmaximal, characteristic, complemented
6#23770217C211yesmaximal, characteristic, complemented
7#23770212C211yesmaximal, characteristic, complemented
8#23770173C211yesmaximal, characteristic, complemented
9#23769942C211yesmaximal, characteristic, complemented
10#23769935C211yesmaximal, characteristic, complemented
11#23769912C211yesmaximal, characteristic, complemented
12#23769882C211yesmaximal, characteristic, complemented
13#23769881C211yesmaximal, characteristic, complemented
14#23769708C211yesmaximal, characteristic, complemented
15#23769698C211yesmaximal, characteristic, complemented
16#23769690C211yesmaximal, characteristic, complemented
17#23769658C211yesmaximal, characteristic, complemented
18#23769657C211yesmaximal, characteristic, complemented
19#23769642C211yesmaximal, characteristic, complemented
20#23769632C211yesmaximal, characteristic, complemented
21#23769140C211yesmaximal, characteristic, complemented
22#23769136C211yesmaximal, characteristic, complemented
23#23768584C211yesmaximal, characteristic, complemented
24#23768576C211yesmaximal, characteristic, complemented
25#23768362C211yesmaximal, characteristic, complemented
26#23768358C211yesmaximal, characteristic, complemented
27#23766848C211yesmaximal, characteristic, complemented
28#23766845C211yesmaximal, characteristic, complemented
29#23766837C211yesmaximal, characteristic, complemented
30C2×#19098434C211yesmaximal, characteristic, complemented
31C79×#2416C211yesmaximal, characteristic, complemented
32C23×C4×D79C2211yescharacteristic
33#19099150—28no—
34#19099146—28no—
35C2×#14579156C2211yescharacteristic
36C2×#14579156C2211yescharacteristic
37C2×#14579156C2211yescharacteristic
38C2×#14579155C2211yescharacteristic
39C2×#14579149C2211yescharacteristic
40C2×#14579147C2211yescharacteristic
41C2×#14579147C2211yescharacteristic
42C2×#14579147C2211yescharacteristic
43C2×#14579146C2211yescharacteristic
44C2×#14579145C2211yescharacteristic
45C2×#14579145C2211yescharacteristic
46C2×#14579144C2211yescharacteristic
47C2×#14579141C2211yescharacteristic, complemented
48C2×#14579140C2211yescharacteristic
49C2×#14579138C2211yescharacteristic
50C2×#14579138C2211yescharacteristic, complemented
51C2×#14579135C2211yescharacteristic
52C2×#14579134C2211yescharacteristic
53C2×#14579134C2211yescharacteristic
54C2×#14579134C2211yescharacteristic
55C2×#14579133C2211yescharacteristic
56C2×#14579133C2211yescharacteristic
57C2×#14579133C2211yescharacteristic
58C2×#14579133C2211yescharacteristic
59C2×#14579133C2211yescharacteristic
60C2×#14579133C2211yescharacteristic, complemented
61C2×#14579132C2211yescharacteristic
62C2×#14579132C2211yescharacteristic
63C2×#14579131C2211yescharacteristic
64C2×#14579129C2211yescharacteristic
65C2×#14579129C2211yescharacteristic
66C2×#14579129C2211yescharacteristic
67C2×D4×Dic79C2211yescharacteristic
68C2×D4×Dic79C2211yescharacteristic
69C2×C4×C22⋊D79C2211yescharacteristic
70C22×Dic79⋊C4C2211yescharacteristic
71C22×(C2×D79)⋊C4C2211yescharacteristic
72C22×(C2×D79)⋊C4C2211yescharacteristic
73#19098505C2211yescharacteristic, complemented
74#19098502C2211yescharacteristic, complemented
75#19098499C2211yescharacteristic, complemented
76#19098499C2211yescharacteristic, complemented
77#19098497C2211yescharacteristic, complemented
78#19098496C2211yescharacteristic, complemented
79#19098495C2211yescharacteristic, complemented
80#19098494C2211yescharacteristic, complemented
81#19098493C2211yescharacteristic, complemented
82#19098493C2211yescharacteristic, complemented
83#19098492C2211yescharacteristic
84#19098492C2211yescharacteristic
85#19098491C2211yescharacteristic, complemented
86#19098489C2211yescharacteristic
87#19098489C2211yescharacteristic
88#19098489C2211yescharacteristic, complemented
89#19098486C2211yescharacteristic, complemented
90#19098486C2211yescharacteristic, complemented
91#19098486C2211yescharacteristic, complemented
92#19098485C2211yescharacteristic, complemented
93#19098485C2211yescharacteristic, complemented
94#19098485C2211yescharacteristic, complemented
95#19098484C2211yescharacteristic, complemented
96#19098483C2211yescharacteristic, complemented
97#19098481C2211yescharacteristic
98#19098481C2211yescharacteristic
99#19098479C2211yescharacteristic
100#19098479C2211yescharacteristic
101#19098479C2211yescharacteristic
102#19098479C2211yescharacteristic
103#19098479C2211yescharacteristic, complemented
104#19098478C2211yescharacteristic
105#19098478C2211yescharacteristic
106#19098478C2211yescharacteristic, complemented
107#19098477C2211yescharacteristic, complemented
108#19098477C2211yescharacteristic, complemented
109#19098475C2211yescharacteristic, complemented
110#19098475C2211yescharacteristic, complemented
111#19098472C2211yescharacteristic
112#19098472C2211yescharacteristic
113#19098471C2211yescharacteristic
114#19098471C2211yescharacteristic
115#19098471C2211yescharacteristic, complemented
116#19098471C2211yescharacteristic, complemented
117#19098468C2211yescharacteristic, complemented
118#19098467C2211yescharacteristic, complemented
119#19098463C2211yescharacteristic, complemented
120#19098462C2211yescharacteristic, complemented
121#19098460C2211yescharacteristic, complemented
122#19098458C2211yescharacteristic, complemented
123#19098457C2211yescharacteristic, complemented
124#19098453C2211yescharacteristic, complemented
125#19098451C2211yescharacteristic, complemented
126#19098451C2211yescharacteristic, complemented
127#19098450C2211yescharacteristic, complemented
128#19098447C2211yescharacteristic, complemented
129#19098447C2211yescharacteristic, complemented
130#19098446C2211yescharacteristic, complemented
131#19098443C2211yescharacteristic
132#19098443C2211yescharacteristic
133#19098443C2211yescharacteristic
134#19098443C2211yescharacteristic
135#19098443C2211yescharacteristic, complemented
136#19098442C2211yescharacteristic
137#19098442C2211yescharacteristic
138#19098441C2211yescharacteristic
139#19098441C2211yescharacteristic
140#19098440C2211yescharacteristic, complemented
141#19098439C2211yescharacteristic
142#19098439C2211yescharacteristic
143#19098439C2211yescharacteristic
144#19098439C2211yescharacteristic
145#19098439C2211yescharacteristic
146#19098439C2211yescharacteristic
147#19098439C2211yescharacteristic, complemented
148#19098439C2211yescharacteristic, complemented
149#19098438C2211yescharacteristic, complemented
150#19098436C2211yescharacteristic, complemented
151#19098436C2211yescharacteristic, complemented
152#19098435C2211yescharacteristic, complemented
153#19098434C2211yescharacteristic
154#19098434C2211yescharacteristic
155#19098434C2211yescharacteristic
156#19098434C2211yescharacteristic
157#19098434C2211yescharacteristic
158#19098434C2211yescharacteristic
159#19098434C2211yescharacteristic
160#19098434C2211yescharacteristic
161#19098423C2211yescharacteristic
162#19098423C2211yescharacteristic
163#19098422C2211yescharacteristic
164#19098422C2211yescharacteristic
165#19098421C2211yescharacteristic
166#19098421C2211yescharacteristic
167#19098421C2211yescharacteristic, complemented
168#19098421C2211yescharacteristic, complemented
169#19098420C2211yescharacteristic
170#19098420C2211yescharacteristic
171#19098420C2211yescharacteristic, complemented
172C2×C79⋊#95C2211yescharacteristic
173C2×C79⋊#95C2211yescharacteristic
174C2×#121×C79C2211yescharacteristic
175C2×#121×C79C2211yescharacteristic
176C2×#121×C79C2211yescharacteristic
177C2×#121×C79C2211yescharacteristic, complemented
178C2×C4×D4×C79C2211yescharacteristic
179C22×C4⋊C4×C79C2211yescharacteristic
180#396×C79C2211yescharacteristic, complemented
181#396×C79C2211yescharacteristic, complemented
182#394×C79C2211yescharacteristic, complemented
183#394×C79C2211yescharacteristic, complemented
184#390×C79C2211yescharacteristic, complemented
185#389×C79C2211yescharacteristic, complemented
186#386×C79C2211yescharacteristic
187#386×C79C2211yescharacteristic
188#380×C79C2211yescharacteristic, complemented
189C24×D79C2311yescharacteristic
190C22×Dic158C2311yescharacteristic
191C22×Dic158C2311yescharacteristic
192C22×D316C2311yescharacteristic
193C22×D316C2311yescharacteristic
194C22×C22⋊D79C2311yescharacteristic
195C22×C22⋊D79C2311yescharacteristic
196C22×C22⋊D79C2311yescharacteristic
197C22×C22⋊D79C2311yescharacteristic
198C22×C22⋊D79C2311yescharacteristic
199C22×C22⋊D79C2311yescharacteristic
200C22×C22⋊D79C2311yescharacteristic
201C22×C22⋊D79C2311yescharacteristic
202C22×C22⋊D79C2311yescharacteristic
203C22×C22⋊D79C2311yescharacteristic
204C23×Dic79C2311yescharacteristic
205C23×Dic79C2311yescharacteristic
206C23×Dic79C2311yescharacteristic
207C23×Dic79C2311yescharacteristic
208C23×Dic79C2311yescharacteristic
209C22×C4×D79—42no—
210C22×C4×D79—42no—
211C22×C4×D79—42no—
212C22×C4×D79C2311yescharacteristic
213C22×C4×D79C2311yescharacteristic
214C22×C4×D79C2311yescharacteristic
215C22×C4×D79C2311yescharacteristic
216C22×C4×D79C2311yescharacteristic
217#14579156—24no—
218#14579156—24no—
219#14579156—24no—
220#14579155—24no—
221#14579149—24no—
222#14579147—24no—
223#14579147—24no—
224#14579147—24no—
225#14579146—24no—
226#14579145—24no—
227#14579145—24no—
228#14579144—24no—
229#14579141—42no—
230#14579140—24no—
231#14579138—24no—
232#14579138—42no—
233#14579135—24no—
234#14579134—24no—
235#14579134—42no—
236#14579134—42no—
237#14579133—24no—
238#14579133—24no—
239#14579133—24no—
240#14579133—42no—
241#14579133—42no—
242#14579133—42no—
243#14579132—42no—
244#14579132—42no—
245#14579131—24no—
246#14579129—24no—
247#14579129—24no—
248#14579129—24no—
249D4×Dic79—24no—
250D4×Dic79—24no—
251C4×C22⋊D79—24no—
252C2×C4⋊Dic79C2311yescharacteristic
253C2×C4⋊Dic79C2311yescharacteristic
254C2×C4⋊Dic79C2311yescharacteristic
255C2×C4⋊Dic79C2311yescharacteristic
256C2×C4⋊Dic79C2311yescharacteristic
257C2×C4⋊Dic79C2311yescharacteristic
258C2×C4⋊Dic79C2311yescharacteristic
259C2×C4⋊Dic79C2311yescharacteristic
260C2×Dic79⋊C4—42no—
261C2×Dic79⋊C4C2311yescharacteristic
262C2×Dic79⋊C4C2311yescharacteristic
263C2×Dic79⋊C4C2311yescharacteristic
264C2×Dic79⋊C4C2311yescharacteristic
265C2×Dic79⋊C4C2311yescharacteristic
266C2×Dic79⋊C4C2311yescharacteristic
267C2×Dic79⋊C4C2311yescharacteristic
268C2×Dic79⋊C4C2311yescharacteristic
269C2×Dic79⋊C4C2311yescharacteristic
270C2×Dic79⋊C4C2311yescharacteristic
271C2×Dic79⋊C4C2311yescharacteristic
272C2×Dic79⋊C4C2311yescharacteristic
273C2×Dic79⋊C4C2311yescharacteristic
274C2×Dic79⋊C4C2311yescharacteristic
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C2311yescharacteristic
277C2×C22⋊Dic79C2311yescharacteristic
278C2×C22⋊Dic79C2311yescharacteristic
279C2×C22⋊Dic79C2311yescharacteristic
280C2×C22⋊Dic79C2311yescharacteristic
281C2×C22⋊Dic79C2311yescharacteristic
282C2×C22⋊Dic79C2311yescharacteristic
283C2×C22⋊Dic79C2311yescharacteristic
284C2×C22⋊Dic79C2311yescharacteristic
285C2×C22⋊Dic79C2311yescharacteristic
286C2×C22⋊Dic79C2311yescharacteristic
287C2×C22⋊Dic79C2311yescharacteristic
288C2×C22⋊Dic79C2311yescharacteristic
289C2×C22⋊Dic79C2311yescharacteristic
290C2×C22⋊Dic79C2311yescharacteristic
291C2×C22⋊Dic79C2311yescharacteristic
292C2×C22⋊Dic79C2311yescharacteristic
293C2×(C2×D79)⋊C4—42no—
294C2×(C2×D79)⋊C4D418yescomplemented
295C2×(C2×D79)⋊C4C2311yescharacteristic
296C2×(C2×D79)⋊C4C2311yescharacteristic
297C2×(C2×D79)⋊C4C2311yescharacteristic
298C2×(C2×D79)⋊C4C2311yescharacteristic
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2311yescharacteristic
301C2×(C2×D79)⋊C4C2311yescharacteristic
302C2×(C2×D79)⋊C4C2311yescharacteristic
303C2×(C2×D79)⋊C4C2311yescharacteristic
304C2×(C2×D79)⋊C4C2311yescharacteristic
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C2311yescharacteristic
307C2×(C2×D79)⋊C4C2311yescharacteristic
308C2×(C2×D79)⋊C4C2311yescharacteristic
309C2×(C2×D79)⋊C4C2311yescharacteristic
310C2×(C2×D79)⋊C4C2311yescharacteristic
311C2×(C2×D79)⋊C4C2311yescharacteristic
312C2×(C2×D79)⋊C4C2311yescharacteristic
313C2×(C2×D79)⋊C4C2311yescharacteristic
314C2×(C2×D79)⋊C4C2311yescharacteristic
315C2×(C2×D79)⋊C4C2311yescharacteristic
316C2×(C2×D79)⋊C4C2311yescharacteristic
317C2×(C2×D79)⋊C4C2311yescharacteristic
318C2×(C2×D79)⋊C4C2311yescharacteristic
319C2×C4×Dic79C2311yescharacteristic
320C2×C4×Dic79C2311yescharacteristic
321C2×C4×Dic79C2311yescharacteristic
322C79⋊#95C2311yescharacteristic
323C79⋊#95C2311yescharacteristic
324C79⋊#95C2311yescharacteristic
325C79⋊#95C2311yescharacteristic
326C79⋊#95C2311yescharacteristic
327C79⋊#95C2311yescharacteristic
328C79⋊#95C2311yescharacteristic
329C79⋊#95C2311yescharacteristic
330C79⋊#95C2311yescharacteristic
331C79⋊#95C2311yescharacteristic
332C79⋊#95C2311yescharacteristic
333C79⋊#95C2311yescharacteristic
334C79⋊#95C2311yescharacteristic
335C79⋊#95C2311yescharacteristic
336C79⋊#95C2311yescharacteristic
337C79⋊#95C2311yescharacteristic
338C79⋊#95C2311yescharacteristic
339C79⋊#95C2311yescharacteristic
340C79⋊#95C2311yescharacteristic
341C79⋊#95C2311yescharacteristic
342C79⋊#95C2311yescharacteristic
343C79⋊#95C2311yescharacteristic
344C79⋊#95C2311yescharacteristic
345C79⋊#95C2311yescharacteristic
346C79⋊#95C2311yescharacteristic
347C79⋊#95C2311yescharacteristic
348C79⋊#95C2311yescharacteristic
349C79⋊#95C2311yescharacteristic
350C22×D4×C79C2311yescharacteristic
351C22×D4×C79C2311yescharacteristic
352C22×D4×C79C2311yescharacteristic
353C22×D4×C79C2311yescharacteristic
354C22×D4×C79C2311yescharacteristic
355C22×D4×C79C2311yescharacteristic
356C23×C4×C79C2311yescharacteristic
357C23×C4×C79C2311yescharacteristic
358C23×C4×C79C2311yescharacteristic
359C23×C4×C79C2311yescharacteristic
360#121×C79—24no—
361#121×C79—42no—
362#121×C79—42no—
363#121×C79—42no—
364C4×D4×C79—24no—
365C2×C4⋊C4×C79—42no—
366C2×C4⋊C4×C79C2311yescharacteristic
367C2×C4⋊C4×C79C2311yescharacteristic
368C2×C4⋊C4×C79C2311yescharacteristic
369C2×C4⋊C4×C79C2311yescharacteristic
370C2×C4⋊C4×C79C2311yescharacteristic
371C2×C4⋊C4×C79C2311yescharacteristic
372C2×C4⋊C4×C79C2311yescharacteristic
373C2×C4⋊C4×C79C2311yescharacteristic
374C2×C22⋊C4×C79C2311yescharacteristic
375C2×C22⋊C4×C79C2311yescharacteristic
376C2×C22⋊C4×C79C2311yescharacteristic
377C2×C22⋊C4×C79C2311yescharacteristic
378C2×C22⋊C4×C79C2311yescharacteristic
379C2×C22⋊C4×C79C2311yescharacteristic
380C2×C22⋊C4×C79C2311yescharacteristic
381C2×C22⋊C4×C79C2311yescharacteristic
382C2×C22⋊C4×C79C2311yescharacteristic
383C2×C22⋊C4×C79C2311yescharacteristic
384C2×C22⋊C4×C79C2311yescharacteristic
385C2×C22⋊C4×C79C2311yescharacteristic
386C2×C42×C79C2311yescharacteristic
387#95×C79C2311yescharacteristic
388#95×C79C2311yescharacteristic
389#95×C79C2311yescharacteristic
390#95×C79C2311yescharacteristic
391C23×D79—22no—
392C23×D79—22no—
393C23×D79—41no—
394C23×D79—41no—
395C23×D79—41no—
396C23×D79—41no—
397C23×D79C2×D414yes—
398C23×D79C2411yescharacteristic
399C23×D79C2411yescharacteristic
400C23×D79C2411yescharacteristic
401C2×Dic158—22no—
402C2×Dic158—22no—
403C2×Dic158—41no—
404C2×Dic158—41no—
405C2×Dic158—41no—
406C2×Dic158—41no—
407C2×D316—22no—
408C2×D316—22no—
409C2×D316—41no—
410C2×D316—41no—
411C2×D316—41no—
412C2×D316—41no—
413C2×C22⋊D79—22no—
414C2×C22⋊D79—22no—
415C2×C22⋊D79—22no—
416C2×C22⋊D79—22no—
417C2×C22⋊D79—22no—
418C2×C22⋊D79—22no—
419C2×C22⋊D79—22no—
420C2×C22⋊D79—22no—
421C2×C22⋊D79—22no—
422C2×C22⋊D79—22no—
423C2×C22⋊D79—22no—
424C2×C22⋊D79—41no—
425C2×C22⋊D79—41no—
426C2×C22⋊D79—41no—
427C2×C22⋊D79—41no—
428C2×C22⋊D79—41no—
429C2×C22⋊D79—41no—
430C2×C22⋊D79—41no—
431C2×C22⋊D79—41no—
432C2×C22⋊D79—41no—
433C2×C22⋊D79—41no—
434C2×C22⋊D79—41no—
435C2×C22⋊D79—41no—
436C2×C22⋊D79—41no—
437C2×C22⋊D79—41no—
438C2×C22⋊D79—41no—
439C2×C22⋊D79—41no—
440C2×C22⋊D79—41no—
441C2×C22⋊D79—41no—
442C2×C22⋊D79—41no—
443C22×Dic79—22no—
444C22×Dic79—22no—
445C22×Dic79—22no—
446C22×Dic79—22no—
447C22×Dic79—22no—
448C22×Dic79—41no—
449C22×Dic79—41no—
450C22×Dic79—41no—
451C22×Dic79—41no—
452C22×Dic79—41no—
453C22×Dic79—41no—
454C22×Dic79—41no—
455C22×Dic79—41no—
456C22×Dic79—41no—
457C22×Dic79C2×D414yes—
458C22×Dic79C2411yescharacteristic
459C22×Dic79C2411yescharacteristic
460C22×Dic79C2411yescharacteristic
461C22×Dic79C2411yescharacteristic
462C22×Dic79C2411yescharacteristic
463C22×Dic79C2411yescharacteristic
464C22×Dic79C2411yescharacteristic
465C22×Dic79C2411yescharacteristic
466C22×Dic79C2411yescharacteristic
467C22×Dic79C2411yescharacteristic
468C22×Dic79C2411yescharacteristic
469C22×Dic79C2411yescharacteristic
470C22×Dic79C2411yescharacteristic
471C2×C4×D79—22no—
472C2×C4×D79—22no—
473C2×C4×D79—22no—
474C2×C4×D79—22no—
475C2×C4×D79—22no—
476C2×C4×D79—41no—
477C2×C4×D79—41no—
478C2×C4×D79—41no—
479C2×C4×D79—41no—
480C2×C4×D79—41no—
481C2×C4×D79—41no—
482C2×C4×D79—41no—
483C2×C4×D79—41no—
484C2×C4×D79—41no—
485C2×C4×D79—41no—
486C2×C4×D79—416no—
487C4⋊Dic79—22no—
488C4⋊Dic79—22no—
489C4⋊Dic79—22no—
490C4⋊Dic79—22no—
491C4⋊Dic79—22no—
492C4⋊Dic79—41no—
493C4⋊Dic79—41no—
494C4⋊Dic79—41no—
495Dic79⋊C4—22no—
496Dic79⋊C4—22no—
497Dic79⋊C4—22no—
498Dic79⋊C4—22no—
499Dic79⋊C4—22no—
500Dic79⋊C4—22no—
501Dic79⋊C4—22no—
502Dic79⋊C4—22no—
503Dic79⋊C4—22no—
504Dic79⋊C4—41no—
505Dic79⋊C4—41no—
506Dic79⋊C4—41no—
507Dic79⋊C4—41no—
508Dic79⋊C4—41no—
509Dic79⋊C4—41no—
510Dic79⋊C4—41no—
511C22⋊Dic79—22no—
512C22⋊Dic79—22no—
513C22⋊Dic79—22no—
514C22⋊Dic79—22no—
515C22⋊Dic79—22no—
516C22⋊Dic79—22no—
517C22⋊Dic79—22no—
518C22⋊Dic79—22no—
519C22⋊Dic79—41no—
520C22⋊Dic79—41no—
521C22⋊Dic79—41no—
522C22⋊Dic79—41no—
523C22⋊Dic79—41no—
524C22⋊Dic79—41no—
525C22⋊Dic79—41no—
526C22⋊Dic79—41no—
527(C2×D79)⋊C4—22no—
528(C2×D79)⋊C4—22no—
529(C2×D79)⋊C4—22no—
530(C2×D79)⋊C4—22no—
531(C2×D79)⋊C4—22no—
532(C2×D79)⋊C4—22no—
533(C2×D79)⋊C4—22no—
534(C2×D79)⋊C4—22no—
535(C2×D79)⋊C4—22no—
536(C2×D79)⋊C4—22no—
537(C2×D79)⋊C4—22no—
538(C2×D79)⋊C4—41no—
539(C2×D79)⋊C4—41no—
540(C2×D79)⋊C4—41no—
541(C2×D79)⋊C4—41no—
542(C2×D79)⋊C4—41no—
543(C2×D79)⋊C4—41no—
544(C2×D79)⋊C4—41no—
545(C2×D79)⋊C4—41no—
546(C2×D79)⋊C4—41no—
547(C2×D79)⋊C4C2×D414yes—
548(C2×D79)⋊C4C2×D414yes—
549(C2×D79)⋊C4C2×D414yes—
550(C2×D79)⋊C4C2×D414yes—
551C4×Dic79—22no—
552C4×Dic79—22no—
553C4×Dic79—22no—
554C24×C79C2411yescharacteristic
555C24×C79C2411yescharacteristic
556C24×C79C2411yescharacteristic
557C24×C79C2411yescharacteristic
558C2×D4×C79—22no—
559C2×D4×C79—22no—
560C2×D4×C79—22no—
561C2×D4×C79—22no—
562C2×D4×C79—22no—
563C2×D4×C79—22no—
564C2×D4×C79—22no—
565C2×D4×C79—22no—
566C2×D4×C79—22no—
567C2×D4×C79—22no—
568C2×D4×C79—22no—
569C2×D4×C79—41no—
570C2×D4×C79—41no—
571C2×D4×C79—41no—
572C2×D4×C79—41no—
573C2×D4×C79—41no—
574C2×D4×C79—41no—
575C2×D4×C79—41no—
576C22×C4×C79—22no—
577C22×C4×C79—22no—
578C22×C4×C79—22no—
579C22×C4×C79—22no—
580C22×C4×C79—41no—
581C22×C4×C79—41no—
582C22×C4×C79—41no—
583C22×C4×C79—41no—
584C22×C4×C79—41no—
585C22×C4×C79—41no—
586C22×C4×C79—41no—
587C22×C4×C79C2×D414yes—
588C22×C4×C79C2411yescharacteristic
589C22×C4×C79C2411yescharacteristic
590C22×C4×C79C2411yescharacteristic
591C22×C4×C79C2411yescharacteristic
592C22×C4×C79C2411yescharacteristic
593C22×C4×C79C2411yescharacteristic
594C22×C4×C79C2411yescharacteristic
595C22×C4×C79C2411yescharacteristic
596C22×C4×C79C2411yescharacteristic
597C22×C4×C79C2411yescharacteristic
598C22×C4×C79C2411yescharacteristic
599C4⋊C4×C79—22no—
600C4⋊C4×C79—22no—
601C4⋊C4×C79—22no—
602C4⋊C4×C79—22no—
603C4⋊C4×C79—41no—
604C4⋊C4×C79—41no—
605C4⋊C4×C79—41no—
606C4⋊C4×C79—41no—
607C22⋊C4×C79—22no—
608C22⋊C4×C79—22no—
609C22⋊C4×C79—22no—
610C22⋊C4×C79—22no—
611C22⋊C4×C79—22no—
612C22⋊C4×C79—41no—
613C22⋊C4×C79—41no—
614C22⋊C4×C79—41no—
615C22⋊C4×C79—41no—
616C22⋊C4×C79—41no—
617C22⋊C4×C79—41no—
618C22⋊C4×C79—41no—
619C42×C79—22no—
620C23×C79—21no—
621C23×C79—21no—
622C23×C79—21no—
623C23×C79—21no—
624C23×C79—21no—
625C23×C79—21no—
626C23×C79—21no—
627C23×C79—21no—
628C23×C79—21no—
629C23×C79—21no—
630C23×C79—21no—
631C23×C79—21no—
632C23×C79—21no—
633C23×C79—21no—
634C23×C79—21no—
635C23×C79—21no—
636C23×C79—21no—
637C23×C79—21no—
638C23×C79—21no—
639C23×C79—21no—
640C23×C79—21no—
641C23×C79—21no—
642C23×C79—21no—
643C23×C79—21no—
644C23×C79—21no—
645C23×C79C22×D412yes—
646C23×C79H(5,𝔽2)12yes—
647C23×C792−1+412yes—
648C23×C79C2511yescharacteristic
649C22×D79—28no—
650C22×D79—21no—
651C22×D79—21no—
652C22×D79—21no—
653C22×D79—21no—
654C22×D79—21no—
655C22×D79—21no—
656C22×D79—21no—
657C22×D79—21no—
658C22×D79—21no—
659C22×D79—21no—
660C22×D79—21no—
661C22×D79—21no—
662C22×D79—21no—
663C22×D79—21no—
664C22×D79—21no—
665C22×D79—21no—
666C22×D79—21no—
667C22×D79—21no—
668C22×D79—21no—
669C22×D79—44no—
670C22×D79—44no—
671C22×D79—44no—
672C22×D79—44no—
673C22×D79—44no—
674C22×D79—44no—
675C22×D79C22×D412yes—
676C22×D79C22×D412yes—
677D4×C79—44no—
678D4×C79—44no—
679D4×C79—44no—
680D4×C79—82no—
681D4×C79—82no—
682D4×C79—82no—
683C2×C4×C79—21no—
684C2×C4×C79—21no—
685C2×C4×C79—21no—
686C2×C4×C79—21no—
687C2×C4×C79—21no—
688C2×C4×C79—21no—
689C2×C4×C79—21no—
690C2×C4×C79—21no—
691C2×C4×C79—21no—
692C2×C4×C79—21no—
693C2×C4×C79—21no—
694C2×C4×C79—21no—
695C2×C4×C79—21no—
696C2×C4×C79—21no—
697C2×C4×C79—21no—
698C2×C4×C79—21no—
699C2×C4×C79—21no—
700C2×C4×C79—21no—
701C2×C4×C79—21no—
702C2×C4×C79—21no—
703C2×C4×C79—21no—
704C2×C4×C79—21no—
705C2×C4×C79—21no—
706C2×C4×C79—21no—
707C2×C4×C79—21no—
708C2×C4×C79—21no—
709C2×C4×C79—21no—
710C2×C4×C79—21no—
711C2×C4×C79—21no—
712C2×C4×C79—21no—
713C2×C4×C79—44no—
714C2×C4×C79—44no—
715C2×C4×C79—82no—
716C2×C4×C79—82no—
717C2×C4×C79C22×D412yes—
718C2×C4×C79C22×D412yes—
719C2×C4×C79H(5,𝔽2)12yes—
720C22⋊D79—44no—
721C22⋊D79—82no—
722C22⋊D79—82no—
723C22⋊D79—82no—
724C22⋊D79—82no—
725C22⋊D79—82no—
726C22⋊D79—82no—
727C22⋊D79—82no—
728C22⋊D79—82no—
729C22⋊D79—82no—
730C2×Dic79—21no—
731C2×Dic79—21no—
732C2×Dic79—21no—
733C2×Dic79—21no—
734C2×Dic79—21no—
735C2×Dic79—21no—
736C2×Dic79—21no—
737C2×Dic79—21no—
738C2×Dic79—21no—
739C2×Dic79—21no—
740C2×Dic79—21no—
741C2×Dic79—21no—
742C2×Dic79—21no—
743C2×Dic79—21no—
744C2×Dic79—21no—
745C2×Dic79—21no—
746C2×Dic79—21no—
747C2×Dic79—21no—
748C2×Dic79—21no—
749C2×Dic79—21no—
750C2×Dic79—21no—
751C2×Dic79—21no—
752C2×Dic79—21no—
753C2×Dic79—21no—
754C2×Dic79—21no—
755C2×Dic79—21no—
756C2×Dic79—21no—
757C2×Dic79—21no—
758C2×Dic79—21no—
759C2×Dic79—21no—
760C2×Dic79—21no—
761C2×Dic79—21no—
762C2×Dic79—21no—
763C2×Dic79—21no—
764C2×Dic79—21no—
765C2×Dic79—21no—
766C2×Dic79—44no—
767C2×Dic79—44no—
768C2×Dic79—82no—
769C2×Dic79—82no—
770C2×Dic79—82no—
771C2×Dic79C22×D412yes—
772C2×Dic79C22×D412yes—
773C2×Dic79H(5,𝔽2)12yes—
774D316—82no—
775D316—82no—
776C4×D79—44no—
777C4×D79—44no—
778C4×D79—44no—
779C4×D79—44no—
780C4×D79—82no—
781Dic158—82no—
782Dic158—82no—
783C22×C79—22no—
784C22×C79—22no—
785C22×C79—22no—
786C22×C79—22no—
787C22×C79—22no—
788C22×C79—22no—
789C22×C79—41no—
790C22×C79—41no—
791C22×C79—41no—
792C22×C79—41no—
793C22×C79—41no—
794C22×C79—41no—
795C22×C79—41no—
796C22×C79—41no—
797C22×C79—41no—
798C22×C79—41no—
799C22×C79—41no—
800C22×C79—41no—
801C22×C79—41no—
802C22×C79—41no—
803C22×C79—41no—
804C22×C79—41no—
805C22×C79—41no—
806C22×C79—41no—
807C22×C79—41no—
808C22×C79—41no—
809C22×C79—41no—
810C22×C79#53714yes—
811C22×C79C23×D411yescharacteristic
812C22×C79C2×H(5,𝔽2)11yescharacteristic
813C22×C79C2×H(5,𝔽2)11yescharacteristic
814C22×C79C2×H(5,𝔽2)11yescharacteristic
815C22×C79C2×2−1+411yescharacteristic
816C22×C79#58511yescharacteristic
817C22×C79#58511yescharacteristic
818C2×D79—22no—
819C2×D79—22no—
820C2×D79—22no—
821C2×D79—22no—
822C2×D79—22no—
823C2×D79—22no—
824C2×D79—416no—
825C2×D79—41no—
826C2×D79—41no—
827C2×D79—41no—
828C2×D79—41no—
829C2×D79—41no—
830C2×D79—41no—
831C2×D79—41no—
832C2×D79—41no—
833C2×D79—41no—
834C2×D79—41no—
835C2×D79—41no—
836C2×D79—41no—
837C2×D79—41no—
838C2×D79—41no—
839C2×D79—41no—
840C4×C79—22no—
841C4×C79—22no—
842C4×C79—22no—
843C4×C79—41no—
844C4×C79—41no—
845C4×C79—41no—
846C4×C79—41no—
847C4×C79—41no—
848C4×C79—41no—
849C4×C79—41no—
850C4×C79—41no—
851Dic79—22no—
852Dic79—22no—
853Dic79—22no—
854Dic79—41no—
855Dic79—41no—
856Dic79—41no—
857Dic79—41no—
858Dic79—41no—
859Dic79—41no—
860Dic79—41no—
861Dic79—41no—
862Dic79—41no—
863Dic79—41no—
864#36738—791nomaximal, Sylow
865C2×C79—24no—
866C2×C79—81no—
867C2×C79—81no—
868C2×C79—81no—
869C2×C79C2×#53711yescharacteristic
870C2×C79#349611yescharacteristic
871C2×C79#349611yescharacteristic
872C2×C79#353211yescharacteristic
873C2×C79#353311yescharacteristic
874C2×C79#354111yescharacteristic
875C2×C79#354111yescharacteristic
876D79—42no—
877D79—42no—
878D79—81no—
879C2×#538—791no—
880C2×#538—791no—
881#2847—791no—
882#2847—791no—
883#2722—791no—
884#2715—791no—
885#2715—791no—
886#2712—791no—
887#2695—791no—
888#2695—791no—
889#2693—791no—
890#2691—791no—
891#2691—791no—
892#2676—791no—
893#2676—791no—
894#2675—791no—
895#2672—791no—
896#2672—791no—
897#2671—791no—
898#2671—791no—
899#2617—791no—
900#2617—791no—
901#2564—791no—
902#2564—791no—
903#2543—791no—
904#2543—791no—
905#2417—791no—
906#2417—791no—
907#2416—791no—
908#2416D7911yescharacteristic, complemented
909C2×#385—791no—
910C79#3673811yescharacteristic, complemented, Sylow
911C24×C4—791no—
912#538—1588no—
913#538—1588no—
914C2×#126—791no—
915C2×#126—791no—
916C2×#126—791no—
917C2×#126—791no—
918C2×#124—791no—
919C2×#124—791no—
920C2×#124—791no—
921C2×#124—791no—
922C2×#123—791no—
923C2×#123—791no—
924C2×#123—791no—
925C2×#123—791no—
926C2×C22⋊Q8—791no—
927C2×C22⋊Q8—791no—
928C2×C22⋊Q8—791no—
929C2×C22⋊Q8—791no—
930C2×#121—791no—
931C2×#121—791no—
932C2×#121—791no—
933C2×#121—791no—
934C2×#121—791no—
935C2×#121—791no—
936C2×#121—791no—
937C2×#121—791no—
938C2×#121—791no—
939C2×#121—791no—
940C2×#121—791no—
941C2×#121—791no—
942C2×#121C2×D7911yescharacteristic
943C2×#121C2×D7911yescharacteristic
944C2×#121C2×D7911yescharacteristic
945C2×#121C2×D7911yescharacteristic, complemented
946C2×#120—791no—
947C2×#120—791no—
948C2×#120—791no—
949C2×#120—791no—
950C2×C4×D4—791no—
951C2×C4×D4—791no—
952C2×C4×D4—791no—
953C2×C4×D4C2×D7911yescharacteristic
954C22×C4⋊C4—791no—
955C22×C4⋊C4C2×D7911yescharacteristic
956C22×C22⋊C4—791no—
957C22×C22⋊C4—791no—
958#400—791no—
959#400—791no—
960#399—791no—
961#399—791no—
962#398—791no—
963#398—791no—
964#398—791no—
965#398—791no—
966#398—791no—
967#398—791no—
968#397—791no—
969#397—791no—
970#397—791no—
971#397—791no—
972#397—791no—
973#397—791no—
974#396—791no—
975#396—791no—
976#396—791no—
977#396—791no—
978#396—791no—
979#396—791no—
980#396C2×D7911yescharacteristic, complemented
981#396C2×D7911yescharacteristic, complemented
982#395—791no—
983#395—791no—
984#394—791no—
985#394—791no—
986#394—791no—
987#394—791no—
988#394—791no—
989#394—791no—
990#394—791no—
991#394—791no—
992#394—791no—
993#394—791no—
994#394—791no—
995#394—791no—
996#394C2×D7911yescharacteristic, complemented
997#394C2×D7911yescharacteristic, complemented
998#393—791no—
999#393—791no—
1000#392—791no—
1001#392—791no—
1002#392—791no—
1003#392—791no—
1004#392—791no—
1005#392—791no—
1006#391—791no—
1007#391—791no—
1008#390—791no—
1009#390C2×D7911yescharacteristic, complemented
1010#389—791no—
1011#389—791no—
1012#389—791no—
1013#389C2×D7911yescharacteristic, complemented
1014#388—791no—
1015#388—791no—
1016#388—791no—
1017#388—791no—
1018#387—791no—
1019#387—791no—
1020#387—791no—
1021#387—791no—
1022#386—791no—
1023#386—791no—
1024#386—791no—
1025#386—791no—
1026#386—791no—
1027#386—791no—
1028#386—791no—
1029#386—791no—
1030#386—791no—
1031#386—791no—
1032#386—791no—
1033#386—791no—
1034#386—791no—
1035#386—791no—
1036#386—791no—
1037#386—791no—
1038#386—791no—
1039#386—791no—
1040#386C2×D7911yescharacteristic
1041#386C2×D7911yescharacteristic
1042#385—791no—
1043#385—791no—
1044#385—791no—
1045#385—791no—
1046#385—791no—
1047#385—791no—
1048#385—791no—
1049#385—791no—
1050#385—791no—
1051#385—791no—
1052#385—791no—
1053#385—791no—
1054#380—791no—
1055#380—791no—
1056#380—791no—
1057#380—791no—
1058#380—791no—
1059#380—791no—
1060#380—791no—
1061#380—791no—
1062#380—791no—
1063#380—791no—
1064#380—791no—
1065#380C2×D7911yescharacteristic, complemented
1066C2×#95—791no—
1067C2×#95—791no—
1068C25—791no—
1069C22×Q8—791no—
1070C22×Q8—791no—
1071C22×D4—791no—
1072C22×D4—791no—
1073C22×D4—791no—
1074C22×D4—791no—
1075C22×D4—791no—
1076C22×D4—791no—
1077C22×D4—791no—
1078C22×D4—791no—
1079C22×D4—791no—
1080C22×D4—791no—
1081C22×D4—791no—
1082C22×D4—791no—
1083C22×D4C22×D7911yescharacteristic
1084C22×D4C22×D7911yescharacteristic
1085C22×D4C22×D7911yescharacteristic
1086C22×D4C22×D7911yescharacteristic
1087C22×D4C22×D7911yescharacteristic
1088C22×D4C22×D7911yescharacteristic
1089C23×C4—3162no—
1090C23×C4—3162no—
1091C23×C4—3162no—
1092C23×C4—791no—
1093C23×C4—791no—
1094C23×C4—791no—
1095C23×C4—791no—
1096C23×C4—791no—
1097C23×C4—791no—
1098C23×C4—791no—
1099C23×C4—791no—
1100C23×C4—791no—
1101C23×C4—791no—
1102C23×C4C22×D7911yescharacteristic
1103C23×C4C22×D7911yescharacteristic
1104C23×C4C22×D7911yescharacteristic
1105C23×C4C22×D7911yescharacteristic
1106#126—1584no—
1107#126—1584no—
1108#126—1584no—
1109#126—1584no—
1110#124—1584no—
1111#124—1584no—
1112#124—1584no—
1113#124—1584no—
1114#123—1584no—
1115#123—1584no—
1116#123—1584no—
1117#123—1584no—
1118C22⋊Q8—3162no—
1119C22⋊Q8—3162no—
1120C22⋊Q8—1584no—
1121C22⋊Q8—1584no—
1122#121—24no—
1123#121—42no—
1124#121—42no—
1125#121—42no—
1126#121—3162no—
1127#121—3162no—
1128#121—3162no—
1129#121—3162no—
1130#121—3162no—
1131#121—3162no—
1132#121—3162no—
1133#121—1584no—
1134#121—1584no—
1135#121—1584no—
1136#121—1584no—
1137#121—1584no—
1138#120—1584no—
1139#120—1584no—
1140#120—1584no—
1141#120—1584no—
1142C4×D4—24no—
1143C4×D4—1584no—
1144C4×D4—1584no—
1145C4×D4—1584no—
1146C2×C4⋊C4—42no—
1147C2×C4⋊C4—3162no—
1148C2×C4⋊C4—791no—
1149C2×C4⋊C4—791no—
1150C2×C4⋊C4—791no—
1151C2×C4⋊C4—791no—
1152C2×C4⋊C4—791no—
1153C2×C4⋊C4—791no—
1154C2×C4⋊C4—791no—
1155C2×C4⋊C4—791no—
1156C2×C4⋊C4—791no—
1157C2×C4⋊C4—791no—
1158C2×C4⋊C4—791no—
1159C2×C4⋊C4—791no—
1160C2×C4⋊C4—791no—
1161C2×C4⋊C4—791no—
1162C2×C4⋊C4—791no—
1163C2×C4⋊C4—791no—
1164C2×C4⋊C4—791no—
1165C2×C4⋊C4—791no—
1166C2×C4⋊C4—791no—
1167C2×C4⋊C4—791no—
1168C2×C4⋊C4—791no—
1169C2×C4⋊C4—791no—
1170C2×C4⋊C4—791no—
1171C2×C4⋊C4—791no—
1172C2×C4⋊C4C22×D7911yescharacteristic
1173C2×C4⋊C4C22×D7911yescharacteristic
1174C2×C4⋊C4C22×D7911yescharacteristic
1175C2×C4⋊C4C22×D7911yescharacteristic
1176C2×C4⋊C4C22×D7911yescharacteristic
1177C2×C4⋊C4C22×D7911yescharacteristic
1178C2×C4⋊C4C22×D7911yescharacteristic
1179C2×C4⋊C4C22×D7911yescharacteristic
1180C2×C22⋊C4—3162no—
1181C2×C22⋊C4—791no—
1182C2×C22⋊C4—791no—
1183C2×C22⋊C4—791no—
1184C2×C22⋊C4—791no—
1185C2×C22⋊C4—791no—
1186C2×C22⋊C4—791no—
1187C2×C22⋊C4—791no—
1188C2×C22⋊C4—791no—
1189C2×C22⋊C4—791no—
1190C2×C22⋊C4—791no—
1191C2×C22⋊C4—791no—
1192C2×C22⋊C4—791no—
1193C2×C22⋊C4—791no—
1194C2×C22⋊C4—791no—
1195C2×C22⋊C4—791no—
1196C2×C22⋊C4—791no—
1197C2×C22⋊C4—791no—
1198C2×C22⋊C4—798no—
1199C2×C22⋊C4—791no—
1200C2×C22⋊C4—791no—
1201C2×C22⋊C4—791no—
1202C2×C22⋊C4—791no—
1203C2×C22⋊C4—791no—
1204C2×C22⋊C4—791no—
1205C2×C22⋊C4—791no—
1206C2×C22⋊C4—791no—
1207C2×C22⋊C4—791no—
1208C2×C22⋊C4—791no—
1209C2×C22⋊C4—791no—
1210C2×C22⋊C4—791no—
1211C2×C22⋊C4—791no—
1212C2×C22⋊C4—791no—
1213C2×C22⋊C4—791no—
1214C2×C22⋊C4—791no—
1215C2×C22⋊C4—791no—
1216C2×C22⋊C4—791no—
1217C2×C22⋊C4—791no—
1218C2×C22⋊C4—791no—
1219C2×C22⋊C4—791no—
1220C2×C22⋊C4—791no—
1221C2×C22⋊C4—791no—
1222C2×C22⋊C4C22×D7911yescharacteristic
1223C2×C22⋊C4C22×D7911yescharacteristic
1224C2×C22⋊C4C22×D7911yescharacteristic
1225C2×C22⋊C4C22×D7911yescharacteristic
1226C2×C22⋊C4C22×D7911yescharacteristic
1227C2×C22⋊C4C22×D7911yescharacteristic
1228C2×C22⋊C4C22×D7911yescharacteristic
1229C2×C22⋊C4C22×D7911yescharacteristic
1230C2×C22⋊C4C22×D7911yescharacteristic
1231C2×C22⋊C4C22×D7911yescharacteristic
1232C2×C22⋊C4C22×D7911yescharacteristic
1233C2×C22⋊C4C22×D7911yescharacteristic
1234C2×C42—791no—
1235C2×C42—791no—
1236C2×C42—791no—
1237C2×C42C22×D7911yescharacteristic
1238#95—791no—
1239#95—791no—
1240#95—791no—
1241#95—791no—
1242#95—791no—
1243#95—791no—
1244#95—791no—
1245#95—791no—
1246#95—791no—
1247#95—791no—
1248#95—791no—
1249#95—791no—
1250#95—791no—
1251#95—791no—
1252#95—791no—
1253#95—791no—
1254#95—791no—
1255#95—791no—
1256#95—791no—
1257#95—791no—
1258#95—791no—
1259#95—791no—
1260#95—791no—
1261#95—791no—
1262#95—791no—
1263#95—791no—
1264#95—791no—
1265#95—791no—
1266#95C22×D7911yescharacteristic
1267#95C22×D7911yescharacteristic
1268#95C22×D7911yescharacteristic
1269#95C22×D7911yescharacteristic
1270C24—3161no—
1271C24—3161no—
1272C24—3161no—
1273C24—3161no—
1274C24—794no—
1275C24—791no—
1276C24—791no—
1277C24—791no—
1278C24—1582no—
1279C24—1582no—
1280C24C23×D7911yescharacteristic
1281C24C23×D7911yescharacteristic
1282C24C23×D7911yescharacteristic
1283C24C23×D7911yescharacteristic
1284C2×Q8—3161no—
1285C2×Q8—3161no—
1286C2×Q8—3161no—
1287C2×Q8—3161no—
1288C2×Q8—1582no—
1289C2×Q8—1582no—
1290C2×D4—22no—
1291C2×D4—22no—
1292C2×D4—22no—
1293C2×D4—22no—
1294C2×D4—22no—
1295C2×D4—22no—
1296C2×D4—22no—
1297C2×D4—22no—
1298C2×D4—22no—
1299C2×D4—22no—
1300C2×D4—22no—
1301C2×D4—41no—
1302C2×D4—41no—
1303C2×D4—41no—
1304C2×D4—41no—
1305C2×D4—41no—
1306C2×D4—41no—
1307C2×D4—41no—
1308C2×D4—3161no—
1309C2×D4—3161no—
1310C2×D4—3161no—
1311C2×D4—3161no—
1312C2×D4—3161no—
1313C2×D4—3161no—
1314C2×D4—3161no—
1315C2×D4—3161no—
1316C2×D4—3161no—
1317C2×D4—3161no—
1318C2×D4—3161no—
1319C2×D4—3161no—
1320C2×D4—3161no—
1321C2×D4—3161no—
1322C2×D4—3161no—
1323C2×D4—3161no—
1324C2×D4—3161no—
1325C2×D4—3161no—
1326C2×D4—3161no—
1327C2×D4—3161no—
1328C2×D4—3161no—
1329C2×D4—3161no—
1330C2×D4—3161no—
1331C2×D4—1582no—
1332C2×D4—1582no—
1333C2×D4—1582no—
1334C2×D4—1582no—
1335C2×D4—1582no—
1336C2×D4—1582no—
1337C2×D4—1582no—
1338C2×D4—1582no—
1339C2×D4—1582no—
1340C2×D4—1582no—
1341C2×D4—1582no—
1342C2×D4—1582no—
1343C2×D4—1582no—
1344C22×C4—22no—
1345C22×C4—22no—
1346C22×C4—22no—
1347C22×C4—22no—
1348C22×C4—41no—
1349C22×C4—41no—
1350C22×C4—41no—
1351C22×C4—41no—
1352C22×C4—41no—
1353C22×C4—41no—
1354C22×C4—41no—
1355C22×C4—3161no—
1356C22×C4—3161no—
1357C22×C4—3161no—
1358C22×C4—3161no—
1359C22×C4—3161no—
1360C22×C4—3161no—
1361C22×C4—3161no—
1362C22×C4—3161no—
1363C22×C4—3161no—
1364C22×C4—3161no—
1365C22×C4—31616no—
1366C22×C4—3161no—
1367C22×C4—3161no—
1368C22×C4—3161no—
1369C22×C4—3161no—
1370C22×C4—3161no—
1371C22×C4—3161no—
1372C22×C4—3161no—
1373C22×C4—3161no—
1374C22×C4—3161no—
1375C22×C4—794no—
1376C22×C4—791no—
1377C22×C4—791no—
1378C22×C4—791no—
1379C22×C4—791no—
1380C22×C4—791no—
1381C22×C4—791no—
1382C22×C4—791no—
1383C22×C4—791no—
1384C22×C4—791no—
1385C22×C4—791no—
1386C22×C4—791no—
1387C22×C4—791no—
1388C22×C4—791no—
1389C22×C4—1582no—
1390C22×C4—1582no—
1391C22×C4—1582no—
1392C22×C4—1582no—
1393C22×C4—1582no—
1394C22×C4—1582no—
1395C22×C4—1582no—
1396C22×C4—1582no—
1397C22×C4—1582no—
1398C22×C4—1582no—
1399C22×C4D4×D7914yes—
1400C22×C4C23×D7911yescharacteristic
1401C22×C4C23×D7911yescharacteristic
1402C22×C4C23×D7911yescharacteristic
1403C22×C4C23×D7911yescharacteristic
1404C22×C4C23×D7911yescharacteristic
1405C22×C4C23×D7911yescharacteristic
1406C22×C4C23×D7911yescharacteristic
1407C22×C4C23×D7911yescharacteristic
1408C22×C4C23×D7911yescharacteristic
1409C22×C4C23×D7911yescharacteristic
1410C22×C4C23×D7911yescharacteristic
1411C4⋊C4—22no—
1412C4⋊C4—22no—
1413C4⋊C4—22no—
1414C4⋊C4—22no—
1415C4⋊C4—41no—
1416C4⋊C4—41no—
1417C4⋊C4—41no—
1418C4⋊C4—41no—
1419C4⋊C4—3161no—
1420C4⋊C4—3161no—
1421C4⋊C4—3161no—
1422C4⋊C4—3161no—
1423C4⋊C4—3161no—
1424C4⋊C4—3161no—
1425C4⋊C4—3161no—
1426C4⋊C4—3161no—
1427C4⋊C4—3161no—
1428C4⋊C4—3161no—
1429C4⋊C4—1582no—
1430C4⋊C4—1582no—
1431C4⋊C4—1582no—
1432C4⋊C4—1582no—
1433C4⋊C4—1582no—
1434C4⋊C4—1582no—
1435C4⋊C4—1582no—
1436C4⋊C4—1582no—
1437C4⋊C4—1582no—
1438C4⋊C4—1582no—
1439C4⋊C4—1582no—
1440C4⋊C4—1582no—
1441C4⋊C4—1582no—
1442C4⋊C4—1582no—
1443C22⋊C4—22no—
1444C22⋊C4—22no—
1445C22⋊C4—22no—
1446C22⋊C4—22no—
1447C22⋊C4—22no—
1448C22⋊C4—41no—
1449C22⋊C4—41no—
1450C22⋊C4—41no—
1451C22⋊C4—41no—
1452C22⋊C4—41no—
1453C22⋊C4—41no—
1454C22⋊C4—41no—
1455C22⋊C4—3161no—
1456C22⋊C4—3161no—
1457C22⋊C4—3161no—
1458C22⋊C4—3161no—
1459C22⋊C4—3161no—
1460C22⋊C4—3161no—
1461C22⋊C4—3161no—
1462C22⋊C4—3161no—
1463C22⋊C4—3161no—
1464C22⋊C4—3161no—
1465C22⋊C4—3161no—
1466C22⋊C4—3161no—
1467C22⋊C4—3161no—
1468C22⋊C4—3161no—
1469C22⋊C4—3161no—
1470C22⋊C4—3161no—
1471C22⋊C4—3161no—
1472C22⋊C4—794no—
1473C22⋊C4—794no—
1474C22⋊C4—794no—
1475C22⋊C4—794no—
1476C22⋊C4—1582no—
1477C22⋊C4—1582no—
1478C22⋊C4—1582no—
1479C22⋊C4—1582no—
1480C22⋊C4—1582no—
1481C22⋊C4—1582no—
1482C22⋊C4—1582no—
1483C22⋊C4—1582no—
1484C22⋊C4—1582no—
1485C22⋊C4—1582no—
1486C22⋊C4—1582no—
1487C22⋊C4—1582no—
1488C22⋊C4—1582no—
1489C22⋊C4—1582no—
1490C22⋊C4—1582no—
1491C22⋊C4—1582no—
1492C22⋊C4—1582no—
1493C22⋊C4—1582no—
1494C22⋊C4—1582no—
1495C42—22no—
1496C42—1582no—
1497C42—1582no—
1498C42—1582no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—21no—
1519C23—21no—
1520C23—21no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—3164no—
1525C23—3164no—
1526C23—3164no—
1527C23—3164no—
1528C23—3164no—
1529C23—3164no—
1530C23—792no—
1531C23—792no—
1532C23—1581no—
1533C23—1581no—
1534C23—1581no—
1535C23—1581no—
1536C23—1581no—
1537C23—1581no—
1538C23—1581no—
1539C23—1581no—
1540C23—1581no—
1541C23—1581no—
1542C23—1581no—
1543C23—1581no—
1544C23—1581no—
1545C23—1581no—
1546C23—1581no—
1547C23—1588no—
1548C23—1581no—
1549C23—1581no—
1550C23—1581no—
1551C23—1581no—
1552C23C2×D4×D7912yes—
1553C23#1457920612yes—
1554C23#1457920812yes—
1555C23C24×D7911yescharacteristic
1556Q8—6322no—
1557Q8—6322no—
1558D4—44no—
1559D4—44no—
1560D4—44no—
1561D4—82no—
1562D4—82no—
1563D4—82no—
1564D4—3164no—
1565D4—6322no—
1566D4—6322no—
1567D4—6322no—
1568D4—6322no—
1569D4—6322no—
1570D4—6322no—
1571D4—6322no—
1572D4—6322no—
1573D4—6322no—
1574D4—6322no—
1575D4—6322no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—44no—
1607C2×C4—44no—
1608C2×C4—82no—
1609C2×C4—82no—
1610C2×C4—3164no—
1611C2×C4—3164no—
1612C2×C4—3164no—
1613C2×C4—3164no—
1614C2×C4—3164no—
1615C2×C4—3164no—
1616C2×C4—792no—
1617C2×C4—792no—
1618C2×C4—792no—
1619C2×C4—6322no—
1620C2×C4—6322no—
1621C2×C4—6322no—
1622C2×C4—6322no—
1623C2×C4—1581no—
1624C2×C4—1581no—
1625C2×C4—1581no—
1626C2×C4—1581no—
1627C2×C4—1581no—
1628C2×C4—1581no—
1629C2×C4—1581no—
1630C2×C4—1581no—
1631C2×C4—1581no—
1632C2×C4—1581no—
1633C2×C4—1581no—
1634C2×C4—1581no—
1635C2×C4—1581no—
1636C2×C4—1581no—
1637C2×C4—1581no—
1638C2×C4—1581no—
1639C2×C4—1581no—
1640C2×C4—1581no—
1641C2×C4—1581no—
1642C2×C4—1581no—
1643C2×C4—1581no—
1644C2×C4—1581no—
1645C2×C4—1581no—
1646C2×C4—1581no—
1647C2×C4—1581no—
1648C2×C4—1581no—
1649C2×C4—1581no—
1650C2×C4—1581no—
1651C2×C4—1581no—
1652C2×C4—1581no—
1653C2×C4—1581no—
1654C2×C4—1581no—
1655C2×C4—1581no—
1656C2×C4—1581no—
1657C2×C4—1581no—
1658C2×C4—1581no—
1659C2×C4C2×D4×D7912yes—
1660C2×C4C2×D4×D7912yes—
1661C2×C4#1457920612yes—
1662C22—22no—
1663C22—22no—
1664C22—22no—
1665C22—22no—
1666C22—22no—
1667C22—22no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22—41no—
1677C22—41no—
1678C22—41no—
1679C22—41no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—41no—
1687C22—41no—
1688C22—41no—
1689C22—31616no—
1690C22—3161no—
1691C22—3161no—
1692C22—3161no—
1693C22—3161no—
1694C22—3161no—
1695C22—3161no—
1696C22—3161no—
1697C22—3161no—
1698C22—3161no—
1699C22—3161no—
1700C22—3161no—
1701C22—3161no—
1702C22—3161no—
1703C22—3161no—
1704C22—3161no—
1705C22—1582no—
1706C22—1582no—
1707C22—1582no—
1708C22—1582no—
1709C22—1582no—
1710C22—1582no—
1711C22#1909914214yes—
1712C22C22×D4×D7911yescharacteristic
1713C22H(5,𝔽2)×D7911yescharacteristic
1714C22C2×#1457920611yescharacteristic
1715C22C2×#1457920611yescharacteristic
1716C22C2×#1457920811yescharacteristic
1717C22#1909939911yescharacteristic
1718C22#1909940011yescharacteristic
1719C4—22no—
1720C4—22no—
1721C4—22no—
1722C4—41no—
1723C4—41no—
1724C4—41no—
1725C4—41no—
1726C4—41no—
1727C4—41no—
1728C4—41no—
1729C4—41no—
1730C4—3161no—
1731C4—3161no—
1732C4—3161no—
1733C4—3161no—
1734C4—3161no—
1735C4—3161no—
1736C4—3161no—
1737C4—3161no—
1738C4—3161no—
1739C4—3161no—
1740C4—1582no—
1741C4—1582no—
1742C4—1582no—
1743C2—24no—
1744C2—81no—
1745C2—81no—
1746C2—81no—
1747C2—3162no—
1748C2—3162no—
1749C2—6321no—
1750C2C2×#1909914211yescharacteristic
1751C2#2377715711yescharacteristic
1752C2#2377716311yescharacteristic
1753C2#2377755011yescharacteristic
1754C2#2377757011yescharacteristic
1755C2#2377767811yescharacteristic
1756C2#2377767911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutator, socle, cosocleC23×C79C25
FittingC79×#2416C2
hypercenter#2416D79
hypocenterC79#36738
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2416

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19099150C2semidirect
2. C2×#19099146C2semidirect
3. #23771681C2semidirect
4. #23771679C2semidirect
5. #23770308C2semidirect
6. #23770217C2semidirect
7. #23770212C2semidirect
8. #23770173C2semidirect
9. #23769942C2semidirect
10. #23769935C2semidirect
11. #23769912C2semidirect
12. #23769882C2semidirect
13. #23769881C2semidirect
14. #23769708C2semidirect
15. #23769698C2semidirect
16. #23769690C2semidirect
17. #23769658C2semidirect
18. #23769657C2semidirect
19. #23769642C2semidirect
20. #23769632C2semidirect
21. #23769140C2semidirect
22. #23769136C2semidirect
23. #23768584C2semidirect
24. #23768576C2semidirect
25. #23768362C2semidirect
26. #23768358C2semidirect
27. #23766848C2semidirect
28. #23766845C2semidirect
29. #23766837C2semidirect
30. C2×#19098434C2semidirect
31. C79×#2416C2semidirect
47. C2×#14579141C22semidirect
50. C2×#14579138C22semidirect
60. C2×#14579133C22semidirect
73. #19098505C22semidirect
74. #19098502C22semidirect
75. #19098499C22semidirect
76. #19098499C22semidirect
77. #19098497C22semidirect
78. #19098496C22semidirect
79. #19098495C22semidirect
80. #19098494C22semidirect
81. #19098493C22semidirect
82. #19098493C22semidirect
85. #19098491C22semidirect
88. #19098489C22semidirect
89. #19098486C22semidirect
90. #19098486C22semidirect
91. #19098486C22semidirect
92. #19098485C22semidirect
93. #19098485C22semidirect
94. #19098485C22semidirect
95. #19098484C22semidirect
96. #19098483C22semidirect
103. #19098479C22semidirect
106. #19098478C22semidirect
107. #19098477C22semidirect
108. #19098477C22semidirect
109. #19098475C22semidirect
110. #19098475C22semidirect
115. #19098471C22semidirect
116. #19098471C22semidirect
117. #19098468C22semidirect
118. #19098467C22semidirect
119. #19098463C22semidirect
120. #19098462C22semidirect
121. #19098460C22semidirect
122. #19098458C22semidirect
123. #19098457C22semidirect
124. #19098453C22semidirect
125. #19098451C22semidirect
126. #19098451C22semidirect
127. #19098450C22semidirect
128. #19098447C22semidirect
129. #19098447C22semidirect
130. #19098446C22semidirect
135. #19098443C22semidirect
140. #19098440C22semidirect
147. #19098439C22semidirect
148. #19098439C22semidirect
149. #19098438C22semidirect
150. #19098436C22semidirect
151. #19098436C22semidirect
152. #19098435C22semidirect
167. #19098421C22semidirect
168. #19098421C22semidirect
171. #19098420C22semidirect
177. C2×#121×C79C22semidirect
180. #396×C79C22semidirect
181. #396×C79C22semidirect
182. #394×C79C22semidirect
183. #394×C79C22semidirect
184. #390×C79C22semidirect
185. #389×C79C22semidirect
188. #380×C79C22semidirect
294. C2×(C2×D79)⋊C4D4semidirect
908. #2416D79semidirect
910. C79#36738semidirect
945. C2×#121C2×D79semidirect
980. #396C2×D79semidirect
981. #396C2×D79semidirect
996. #394C2×D79semidirect
997. #394C2×D79semidirect
1009. #390C2×D79semidirect
1013. #389C2×D79semidirect
1065. #380C2×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#190991502
C2×#190991462
#237716812
#237716792
#237703082
#237702172
#237702122
#237701732
#237699422
#237699352
#237699122
#237698822
#237698812
#237697082
#237696982
#237696902
#237696582
#237696572
#237696422
#237696322
#237691402
#237691362
#237685842
#237685762
#237683622
#237683582
#237668482
#237668452
#237668372
C2×#190984342
C79×#24162
#3673879