Finite Group Databasebeta

← #34502131

Subgroups — #34502131

Order 20224.

2184 conjugacy classes of subgroups.

The subgroup lattice has 1632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099146C211yesmaximal, characteristic, complemented
2C2×#19099093C211yesmaximal, characteristic, complemented
3#23771732C211yesmaximal, characteristic, complemented
4#23771723C211yesmaximal, characteristic, complemented
5#23770361C211yesmaximal, characteristic, complemented
6#23770338C211yesmaximal, characteristic, complemented
7#23770140C211yesmaximal, characteristic, complemented
8#23770101C211yesmaximal, characteristic, complemented
9#23770071C211yesmaximal, characteristic, complemented
10#23770041C211yesmaximal, characteristic, complemented
11#23770011C211yesmaximal, characteristic, complemented
12#23769962C211yesmaximal, characteristic, complemented
13#23769849C211yesmaximal, characteristic, complemented
14#23769789C211yesmaximal, characteristic, complemented
15#23769764C211yesmaximal, characteristic, complemented
16#23769720C211yesmaximal, characteristic, complemented
17#23769679C211yesmaximal, characteristic, complemented
18#23769679C211yesmaximal, characteristic, complemented
19#23769649C211yesmaximal, characteristic, complemented
20#23769624C211yesmaximal, characteristic, complemented
21#23769287C211yesmaximal, characteristic, complemented
22#23769241C211yesmaximal, characteristic, complemented
23#23769081C211yesmaximal, characteristic, complemented
24#23769038C211yesmaximal, characteristic, complemented
25#23768991C211yesmaximal, characteristic, complemented
26#23768987C211yesmaximal, characteristic, complemented
27#23768380C211yesmaximal, characteristic, complemented
28#23768292C211yesmaximal, characteristic, complemented
29#23767698C211yesmaximal, characteristic, complemented
30#23767676C211yesmaximal, characteristic, complemented
31C79×#2319C211yesmaximal, characteristic, complemented
32#19099146—28no—
33C2×#14579161C2211yescharacteristic, complemented
34#19099093—28no—
35C2×#14579156C2211yescharacteristic
36C2×#14579156C2211yescharacteristic, complemented
37C2×#14579155C2211yescharacteristic
38C2×#14579154C2211yescharacteristic
39C2×#14579151C2211yescharacteristic, complemented
40C2×#14579149C2211yescharacteristic
41C2×#14579149C2211yescharacteristic
42C2×#14579147C2211yescharacteristic
43C2×#14579147C2211yescharacteristic
44C2×#14579146C2211yescharacteristic
45C2×#14579145C2211yescharacteristic
46C2×#14579145C2211yescharacteristic
47C2×#14579145C2211yescharacteristic, complemented
48C2×#14579145C2211yescharacteristic, complemented
49C2×#14579144C2211yescharacteristic
50C2×#14579142C2211yescharacteristic
51C2×#14579138C2211yescharacteristic
52C2×#14579138C2211yescharacteristic, complemented
53C2×#14579135C2211yescharacteristic
54C2×#14579134C2211yescharacteristic
55C2×#14579133C2211yescharacteristic
56C2×#14579133C2211yescharacteristic
57C2×#14579131C2211yescharacteristic
58C2×#14579131C2211yescharacteristic
59C2×#14579129C2211yescharacteristic
60C2×C4×Dic158C2211yescharacteristic, complemented
61C2×C4×C22⋊D79C2211yescharacteristic
62C2×C4×C22⋊D79C2211yescharacteristic
63C2×C4×C22⋊D79C2211yescharacteristic, complemented
64C2×#14579120C2211yescharacteristic
65C2×#14579118C2211yescharacteristic, complemented
66C22×(C2×D79)⋊C4C2211yescharacteristic
67C22×C4×Dic79C2211yescharacteristic, complemented
68#19098503C2211yescharacteristic, complemented
69#19098503C2211yescharacteristic, complemented
70#19098500C2211yescharacteristic
71#19098500C2211yescharacteristic
72#19098500C2211yescharacteristic
73#19098500C2211yescharacteristic, complemented
74#19098493C2211yescharacteristic, complemented
75#19098493C2211yescharacteristic, complemented
76#19098490C2211yescharacteristic
77#19098490C2211yescharacteristic
78#19098488C2211yescharacteristic
79#19098488C2211yescharacteristic
80#19098488C2211yescharacteristic
81#19098488C2211yescharacteristic, complemented
82#19098485C2211yescharacteristic
83#19098485C2211yescharacteristic
84#19098485C2211yescharacteristic
85#19098485C2211yescharacteristic
86#19098485C2211yescharacteristic
87#19098485C2211yescharacteristic
88#19098485C2211yescharacteristic, complemented
89#19098485C2211yescharacteristic, complemented
90#19098485C2211yescharacteristic, complemented
91#19098485C2211yescharacteristic, complemented
92#19098484C2211yescharacteristic, complemented
93#19098484C2211yescharacteristic, complemented
94#19098481C2211yescharacteristic
95#19098481C2211yescharacteristic
96#19098480C2211yescharacteristic
97#19098480C2211yescharacteristic
98#19098480C2211yescharacteristic
99#19098480C2211yescharacteristic
100#19098479C2211yescharacteristic
101#19098479C2211yescharacteristic
102#19098479C2211yescharacteristic
103#19098479C2211yescharacteristic
104#19098479C2211yescharacteristic
105#19098479C2211yescharacteristic
106#19098479C2211yescharacteristic, complemented
107#19098479C2211yescharacteristic, complemented
108#19098476C2211yescharacteristic
109#19098476C2211yescharacteristic, complemented
110#19098473C2211yescharacteristic
111#19098473C2211yescharacteristic
112#19098472C2211yescharacteristic
113#19098472C2211yescharacteristic
114#19098472C2211yescharacteristic
115#19098472C2211yescharacteristic, complemented
116#19098469C2211yescharacteristic, complemented
117#19098465C2211yescharacteristic
118#19098465C2211yescharacteristic
119#19098465C2211yescharacteristic
120#19098465C2211yescharacteristic, complemented
121#19098464C2211yescharacteristic
122#19098464C2211yescharacteristic
123#19098462C2211yescharacteristic, complemented
124#19098462C2211yescharacteristic, complemented
125#19098462C2211yescharacteristic, complemented
126#19098462C2211yescharacteristic, complemented
127#19098461C2211yescharacteristic, complemented
128#19098461C2211yescharacteristic, complemented
129#19098461C2211yescharacteristic, complemented
130#19098455C2211yescharacteristic
131#19098455C2211yescharacteristic
132#19098455C2211yescharacteristic
133#19098455C2211yescharacteristic
134#19098455C2211yescharacteristic
135#19098455C2211yescharacteristic
136#19098455C2211yescharacteristic
137#19098455C2211yescharacteristic
138#19098455C2211yescharacteristic, complemented
139#19098455C2211yescharacteristic, complemented
140#19098455C2211yescharacteristic, complemented
141#19098455C2211yescharacteristic, complemented
142#19098454C2211yescharacteristic
143#19098454C2211yescharacteristic
144#19098454C2211yescharacteristic
145#19098454C2211yescharacteristic
146#19098454C2211yescharacteristic, complemented
147#19098454C2211yescharacteristic, complemented
148#19098448C2211yescharacteristic, complemented
149#19098448C2211yescharacteristic, complemented
150#19098448C2211yescharacteristic, complemented
151#19098448C2211yescharacteristic, complemented
152#19098448C2211yescharacteristic, complemented
153#19098448C2211yescharacteristic, complemented
154#19098441C2211yescharacteristic
155#19098441C2211yescharacteristic
156#19098441C2211yescharacteristic, complemented
157#19098441C2211yescharacteristic, complemented
158#19098440C2211yescharacteristic
159#19098440C2211yescharacteristic
160#19098440C2211yescharacteristic
161#19098440C2211yescharacteristic, complemented
162#19098438C2211yescharacteristic
163#19098438C2211yescharacteristic
164#19098438C2211yescharacteristic, complemented
165#19098438C2211yescharacteristic, complemented
166#19098437C2211yescharacteristic, complemented
167#19098437C2211yescharacteristic, complemented
168#19098424C2211yescharacteristic
169#19098420C2211yescharacteristic, complemented
170#19098420C2211yescharacteristic, complemented
171#19098418C2211yescharacteristic
172#19098418C2211yescharacteristic
173#19098418C2211yescharacteristic
174C2×C4×D4×C79C2211yescharacteristic
175#390×C79C2211yescharacteristic
176#390×C79C2211yescharacteristic
177#389×C79C2211yescharacteristic, complemented
178#389×C79C2211yescharacteristic, complemented
179#388×C79C2211yescharacteristic
180#388×C79C2211yescharacteristic
181#388×C79C2211yescharacteristic, complemented
182#388×C79C2211yescharacteristic, complemented
183#381×C79C2211yescharacteristic
184#381×C79C2211yescharacteristic, complemented
185#380×C79C2211yescharacteristic
186#380×C79C2211yescharacteristic, complemented
187C4×C4⋊C4×C79C2211yescharacteristic, complemented
188#376×C79C2211yescharacteristic, complemented
189C24×D79C2311yescharacteristic
190C22×Dic158C2311yescharacteristic
191C22×Dic158C2311yescharacteristic
192C22×D316C2311yescharacteristic
193C22×D316C2311yescharacteristic
194C22×D316C2311yescharacteristic
195C22×D316C2311yescharacteristic
196C22×D316C2311yescharacteristic
197C22×C22⋊D79C2311yescharacteristic
198C22×C22⋊D79C2311yescharacteristic
199C22×C22⋊D79C2311yescharacteristic
200C22×C22⋊D79C2311yescharacteristic
201C22×C22⋊D79C2311yescharacteristic
202C22×C22⋊D79C2311yescharacteristic
203C23×Dic79C2311yescharacteristic
204C23×Dic79C2311yescharacteristic
205C23×Dic79C2311yescharacteristic
206C22×C4×D79C2311yescharacteristic
207C22×C4×D79C2311yescharacteristic
208#14579161—42no—
209#14579156—24no—
210#14579156—24no—
211#14579155—24no—
212#14579154—24no—
213#14579151—24no—
214#14579149—24no—
215#14579149—42no—
216#14579147—24no—
217#14579147—24no—
218#14579146—24no—
219#14579145—24no—
220#14579145—42no—
221#14579145—42no—
222#14579145—42no—
223#14579144—24no—
224#14579142—24no—
225#14579138—24no—
226#14579138—24no—
227#14579135—24no—
228#14579134—24no—
229#14579133—24no—
230#14579133—24no—
231#14579131—24no—
232#14579131—42no—
233#14579129—24no—
234C4×Dic158—24no—
235C4×C22⋊D79—24no—
236C4×C22⋊D79—24no—
237C4×C22⋊D79—24no—
238#14579120—24no—
239#14579118—24no—
240C2×C4⋊Dic79C2311yescharacteristic
241C2×C4⋊Dic79C2311yescharacteristic
242C2×C4⋊Dic79C2311yescharacteristic
243C2×C4⋊Dic79C2311yescharacteristic
244C2×C4⋊Dic79C2311yescharacteristic
245C2×C4⋊Dic79C2311yescharacteristic
246C2×C4⋊Dic79C2311yescharacteristic
247C2×C4⋊Dic79C2311yescharacteristic
248C2×C4⋊Dic79C2311yescharacteristic
249C2×C4⋊Dic79C2311yescharacteristic
250C2×C4⋊Dic79C2311yescharacteristic
251C2×C4⋊Dic79C2311yescharacteristic
252C2×C4⋊Dic79C2311yescharacteristic
253C2×C4⋊Dic79C2311yescharacteristic
254C2×C4⋊Dic79C2311yescharacteristic
255C2×C4⋊Dic79C2311yescharacteristic
256C2×C4⋊Dic79C2311yescharacteristic
257C2×Dic79⋊C4C2311yescharacteristic
258C2×Dic79⋊C4C2311yescharacteristic
259C2×Dic79⋊C4C2311yescharacteristic
260C2×Dic79⋊C4C2311yescharacteristic
261C2×Dic79⋊C4C2311yescharacteristic
262C2×Dic79⋊C4C2311yescharacteristic
263C2×Dic79⋊C4C2311yescharacteristic
264C2×Dic79⋊C4C2311yescharacteristic
265C2×Dic79⋊C4C2311yescharacteristic
266C2×Dic79⋊C4C2311yescharacteristic
267C2×C22⋊Dic79C2311yescharacteristic
268C2×C22⋊Dic79C2311yescharacteristic
269C2×C22⋊Dic79C2311yescharacteristic
270C2×C22⋊Dic79C2311yescharacteristic
271C2×C22⋊Dic79C2311yescharacteristic
272C2×C22⋊Dic79C2311yescharacteristic
273C2×(C2×D79)⋊C4—24no—
274C2×(C2×D79)⋊C4C2311yescharacteristic
275C2×(C2×D79)⋊C4C2311yescharacteristic
276C2×(C2×D79)⋊C4C2311yescharacteristic
277C2×(C2×D79)⋊C4C2311yescharacteristic
278C2×(C2×D79)⋊C4C2311yescharacteristic
279C2×(C2×D79)⋊C4C2311yescharacteristic
280C2×(C2×D79)⋊C4C2311yescharacteristic
281C2×(C2×D79)⋊C4C2311yescharacteristic
282C2×(C2×D79)⋊C4C2311yescharacteristic
283C2×(C2×D79)⋊C4C2311yescharacteristic
284C2×(C2×D79)⋊C4C2311yescharacteristic
285C2×(C2×D79)⋊C4C2311yescharacteristic
286C2×(C2×D79)⋊C4C2311yescharacteristic
287C2×(C2×D79)⋊C4C2311yescharacteristic
288C2×(C2×D79)⋊C4C2311yescharacteristic
289C2×(C2×D79)⋊C4C2311yescharacteristic
290C2×(C2×D79)⋊C4C2311yescharacteristic
291C2×(C2×D79)⋊C4C2311yescharacteristic
292C2×(C2×D79)⋊C4C2311yescharacteristic
293C2×(C2×D79)⋊C4C2311yescharacteristic
294C2×(C2×D79)⋊C4C2311yescharacteristic
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×C4×Dic79—24no—
315C2×C4×Dic79C2311yescharacteristic
316C2×C4×Dic79C2311yescharacteristic
317C2×C4×Dic79C2311yescharacteristic
318C2×C4×Dic79C2311yescharacteristic
319C2×C4×Dic79C2311yescharacteristic
320C2×C4×Dic79C2311yescharacteristic
321C79⋊#95C2311yescharacteristic
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
343C22×D4×C79C2311yescharacteristic
344C23×C4×C79C2311yescharacteristic
345C23×C4×C79C2311yescharacteristic
346C4×D4×C79D418yescomplemented
347C2×C4⋊C4×C79C2311yescharacteristic
348C2×C4⋊C4×C79C2311yescharacteristic
349C2×C4⋊C4×C79C2311yescharacteristic
350C2×C4⋊C4×C79C2311yescharacteristic
351C2×C4⋊C4×C79C2311yescharacteristic
352C2×C4⋊C4×C79C2311yescharacteristic
353C2×C4⋊C4×C79C2311yescharacteristic
354C2×C22⋊C4×C79C2311yescharacteristic
355C2×C22⋊C4×C79C2311yescharacteristic
356C2×C22⋊C4×C79C2311yescharacteristic
357C2×C22⋊C4×C79C2311yescharacteristic
358C2×C22⋊C4×C79C2311yescharacteristic
359C2×C22⋊C4×C79C2311yescharacteristic
360C2×C22⋊C4×C79C2311yescharacteristic
361C2×C22⋊C4×C79C2311yescharacteristic
362C2×C22⋊C4×C79C2311yescharacteristic
363C2×C22⋊C4×C79C2311yescharacteristic
364C2×C42×C79C2311yescharacteristic
365C2×C42×C79C2311yescharacteristic
366C2×C42×C79C2311yescharacteristic
367C2×C42×C79C2311yescharacteristic
368C2×C42×C79C2311yescharacteristic
369#95×C79C2311yescharacteristic
370#95×C79C2311yescharacteristic
371#95×C79C2311yescharacteristic
372#95×C79C2311yescharacteristic
373#95×C79C2311yescharacteristic
374#95×C79C2311yescharacteristic
375#95×C79C2311yescharacteristic
376#95×C79C2311yescharacteristic
377#95×C79C2311yescharacteristic
378#95×C79C2311yescharacteristic
379C23×D79—22no—
380C23×D79—41no—
381C23×D79—41no—
382C23×D79—41no—
383C23×D79—41no—
384C23×D79—41no—
385C23×D79—41no—
386C23×D79C2411yescharacteristic
387C23×D79C2411yescharacteristic
388C23×D79C2411yescharacteristic
389C23×D79C2411yescharacteristic
390C2×Dic158—22no—
391C2×Dic158—22no—
392C2×Dic158—22no—
393C2×Dic158—41no—
394C2×Dic158—41no—
395C2×Dic158—41no—
396C2×D316—22no—
397C2×D316—22no—
398C2×D316—41no—
399C2×D316—41no—
400C2×D316—41no—
401C2×D316—41no—
402C2×D316—41no—
403C2×D316—41no—
404C2×D316—41no—
405C2×D316—41no—
406C2×D316—41no—
407C2×D316—41no—
408C2×D316—41no—
409C2×D316—41no—
410C2×D316—41no—
411C2×C22⋊D79—22no—
412C2×C22⋊D79—22no—
413C2×C22⋊D79—22no—
414C2×C22⋊D79—22no—
415C2×C22⋊D79—22no—
416C2×C22⋊D79—22no—
417C2×C22⋊D79—22no—
418C2×C22⋊D79—41no—
419C2×C22⋊D79—41no—
420C2×C22⋊D79—41no—
421C2×C22⋊D79—41no—
422C2×C22⋊D79—41no—
423C2×C22⋊D79—41no—
424C2×C22⋊D79—41no—
425C2×C22⋊D79—41no—
426C2×C22⋊D79—41no—
427C2×C22⋊D79—41no—
428C2×C22⋊D79—41no—
429C22×Dic79—22no—
430C22×Dic79—22no—
431C22×Dic79—22no—
432C22×Dic79—22no—
433C22×Dic79—41no—
434C22×Dic79—41no—
435C22×Dic79—41no—
436C22×Dic79—41no—
437C22×Dic79—41no—
438C22×Dic79C2411yescharacteristic
439C22×Dic79C2411yescharacteristic
440C22×Dic79C2411yescharacteristic
441C22×Dic79C2411yescharacteristic
442C22×Dic79C2411yescharacteristic
443C22×Dic79C2411yescharacteristic
444C22×Dic79C2411yescharacteristic
445C22×Dic79C2411yescharacteristic
446C22×Dic79C2411yescharacteristic
447C22×Dic79C2411yescharacteristic
448C22×Dic79C2411yescharacteristic
449C22×Dic79C2411yescharacteristic
450C2×C4×D79—22no—
451C2×C4×D79—22no—
452C2×C4×D79—41no—
453C2×C4×D79—41no—
454C2×C4×D79—41no—
455C2×C4×D79—41no—
456C4⋊Dic79—22no—
457C4⋊Dic79—22no—
458C4⋊Dic79—22no—
459C4⋊Dic79—22no—
460C4⋊Dic79—22no—
461C4⋊Dic79—22no—
462C4⋊Dic79—22no—
463C4⋊Dic79—41no—
464C4⋊Dic79—41no—
465C4⋊Dic79—41no—
466C4⋊Dic79—41no—
467C4⋊Dic79—41no—
468C4⋊Dic79—41no—
469C4⋊Dic79—41no—
470C4⋊Dic79—41no—
471C4⋊Dic79—41no—
472C4⋊Dic79—41no—
473Dic79⋊C4—22no—
474Dic79⋊C4—22no—
475Dic79⋊C4—22no—
476Dic79⋊C4—22no—
477Dic79⋊C4—22no—
478Dic79⋊C4—22no—
479Dic79⋊C4—22no—
480Dic79⋊C4—22no—
481Dic79⋊C4—22no—
482Dic79⋊C4—22no—
483C22⋊Dic79—22no—
484C22⋊Dic79—22no—
485C22⋊Dic79—22no—
486C22⋊Dic79—22no—
487C22⋊Dic79—22no—
488C22⋊Dic79—22no—
489(C2×D79)⋊C4—22no—
490(C2×D79)⋊C4—22no—
491(C2×D79)⋊C4—22no—
492(C2×D79)⋊C4—22no—
493(C2×D79)⋊C4—22no—
494(C2×D79)⋊C4—22no—
495(C2×D79)⋊C4—22no—
496(C2×D79)⋊C4—22no—
497(C2×D79)⋊C4—22no—
498(C2×D79)⋊C4—22no—
499(C2×D79)⋊C4—22no—
500(C2×D79)⋊C4—22no—
501(C2×D79)⋊C4—22no—
502(C2×D79)⋊C4—22no—
503(C2×D79)⋊C4—22no—
504(C2×D79)⋊C4—22no—
505(C2×D79)⋊C4—22no—
506(C2×D79)⋊C4—41no—
507(C2×D79)⋊C4—41no—
508(C2×D79)⋊C4—41no—
509(C2×D79)⋊C4—41no—
510(C2×D79)⋊C4—41no—
511(C2×D79)⋊C4—41no—
512(C2×D79)⋊C4—41no—
513(C2×D79)⋊C4—41no—
514(C2×D79)⋊C4—41no—
515(C2×D79)⋊C4—41no—
516(C2×D79)⋊C4—41no—
517(C2×D79)⋊C4—41no—
518(C2×D79)⋊C4—41no—
519(C2×D79)⋊C4—41no—
520(C2×D79)⋊C4—41no—
521(C2×D79)⋊C4—41no—
522(C2×D79)⋊C4—41no—
523(C2×D79)⋊C4—41no—
524(C2×D79)⋊C4—41no—
525(C2×D79)⋊C4—41no—
526(C2×D79)⋊C4—41no—
527(C2×D79)⋊C4—41no—
528(C2×D79)⋊C4—41no—
529C4×Dic79—22no—
530C4×Dic79—22no—
531C4×Dic79—22no—
532C4×Dic79—22no—
533C4×Dic79—22no—
534C4×Dic79—22no—
535C24×C79C2411yescharacteristic
536C24×C79C2411yescharacteristic
537C2×D4×C79—41no—
538C2×D4×C79—41no—
539C2×D4×C79C2×D414yes—
540C22×C4×C79—41no—
541C22×C4×C79—41no—
542C22×C4×C79—41no—
543C22×C4×C79—41no—
544C22×C4×C79C2×D414yes—
545C22×C4×C79C2×D414yes—
546C22×C4×C79C2411yescharacteristic
547C22×C4×C79C2411yescharacteristic
548C22×C4×C79C2411yescharacteristic
549C22×C4×C79C2411yescharacteristic
550C22×C4×C79C2411yescharacteristic
551C22×C4×C79C2411yescharacteristic
552C22×C4×C79C2411yescharacteristic
553C22×C4×C79C2411yescharacteristic
554C22×C4×C79C2411yescharacteristic
555C22×C4×C79C2411yescharacteristic
556C22×C4×C79C2411yescharacteristic
557C22×C4×C79C2411yescharacteristic
558C22×C4×C79C2411yescharacteristic
559C4⋊C4×C79—41no—
560C4⋊C4×C79—41no—
561C4⋊C4×C79—41no—
562C4⋊C4×C79—41no—
563C4⋊C4×C79—41no—
564C4⋊C4×C79—41no—
565C4⋊C4×C79C2×D414yes—
566C22⋊C4×C79—41no—
567C22⋊C4×C79—41no—
568C22⋊C4×C79—41no—
569C22⋊C4×C79—41no—
570C22⋊C4×C79—41no—
571C22⋊C4×C79—41no—
572C22⋊C4×C79—41no—
573C22⋊C4×C79—41no—
574C22⋊C4×C79C2×D414yes—
575C22⋊C4×C79C2×D414yes—
576C42×C79—41no—
577C42×C79—41no—
578C42×C79—41no—
579C42×C79—41no—
580C42×C79C2×D414yes—
581C23×C79—21no—
582C23×C79—21no—
583C23×C79—21no—
584C23×C79—21no—
585C23×C79—21no—
586C23×C79—21no—
587C23×C79—21no—
588C23×C79—21no—
589C23×C79—21no—
590C23×C79—21no—
591C23×C79—21no—
592C23×C79—21no—
593C23×C79C22×D412yes—
594C23×C79C22×D412yes—
595C23×C79C2511yescharacteristic
596C22×D79—21no—
597C22×D79—21no—
598C22×D79—21no—
599C22×D79—21no—
600C22×D79—21no—
601C22×D79—21no—
602C22×D79—21no—
603C22×D79—21no—
604C22×D79—21no—
605C22×D79—21no—
606C22×D79—21no—
607C22×D79—21no—
608C22×D79—21no—
609C22×D79—21no—
610C22×D79—21no—
611C22×D79—21no—
612C22×D79—21no—
613C22×D79—21no—
614C22×D79—21no—
615C22×D79—21no—
616C22×D79—21no—
617C22×D79—21no—
618C22×D79—21no—
619C22×D79—21no—
620C22×D79—21no—
621C22×D79—21no—
622C22×D79—21no—
623C22×D79—21no—
624C22×D79—44no—
625C22×D79—82no—
626C22×D79—82no—
627C22×D79—82no—
628C22×D79—82no—
629C22×D79—82no—
630C22×D79—82no—
631D4×C79—44no—
632C2×C4×C79—21no—
633C2×C4×C79—21no—
634C2×C4×C79—21no—
635C2×C4×C79—21no—
636C2×C4×C79—21no—
637C2×C4×C79—21no—
638C2×C4×C79—21no—
639C2×C4×C79—21no—
640C2×C4×C79—21no—
641C2×C4×C79—21no—
642C2×C4×C79—21no—
643C2×C4×C79—21no—
644C2×C4×C79—21no—
645C2×C4×C79—21no—
646C2×C4×C79—21no—
647C2×C4×C79—21no—
648C2×C4×C79—21no—
649C2×C4×C79—21no—
650C2×C4×C79—21no—
651C2×C4×C79—21no—
652C2×C4×C79—21no—
653C2×C4×C79—21no—
654C2×C4×C79—21no—
655C2×C4×C79—21no—
656C2×C4×C79—21no—
657C2×C4×C79—21no—
658C2×C4×C79—21no—
659C2×C4×C79—21no—
660C2×C4×C79—21no—
661C2×C4×C79—21no—
662C2×C4×C79—21no—
663C2×C4×C79—21no—
664C2×C4×C79—21no—
665C2×C4×C79—21no—
666C2×C4×C79—44no—
667C2×C4×C79—44no—
668C2×C4×C79C22×D412yes—
669C2×C4×C79C22×D412yes—
670C2×C4×C79C22×D412yes—
671C2×C4×C79C22×D412yes—
672C2×C4×C79C22×D412yes—
673C22⋊D79—44no—
674C22⋊D79—44no—
675C22⋊D79—44no—
676C22⋊D79—82no—
677C22⋊D79—82no—
678C22⋊D79—82no—
679C2×Dic79—21no—
680C2×Dic79—21no—
681C2×Dic79—21no—
682C2×Dic79—21no—
683C2×Dic79—21no—
684C2×Dic79—21no—
685C2×Dic79—21no—
686C2×Dic79—21no—
687C2×Dic79—21no—
688C2×Dic79—21no—
689C2×Dic79—21no—
690C2×Dic79—21no—
691C2×Dic79—21no—
692C2×Dic79—21no—
693C2×Dic79—21no—
694C2×Dic79—21no—
695C2×Dic79—21no—
696C2×Dic79—21no—
697C2×Dic79—21no—
698C2×Dic79—21no—
699C2×Dic79—21no—
700C2×Dic79—21no—
701C2×Dic79—21no—
702C2×Dic79—21no—
703C2×Dic79—21no—
704C2×Dic79—21no—
705C2×Dic79—21no—
706C2×Dic79—21no—
707C2×Dic79—21no—
708C2×Dic79—21no—
709C2×Dic79—21no—
710C2×Dic79—21no—
711C2×Dic79—21no—
712C2×Dic79—21no—
713C2×Dic79—21no—
714C2×Dic79—44no—
715C2×Dic79—44no—
716C2×Dic79—82no—
717C2×Dic79H(5,𝔽2)12yes—
718D316—82no—
719D316—82no—
720D316—82no—
721D316—82no—
722D316—82no—
723C4×D79—44no—
724C4×D79—82no—
725Dic158—44no—
726Dic158—82no—
727C22×C79—22no—
728C22×C79—22no—
729C22×C79—22no—
730C22×C79—22no—
731C22×C79—22no—
732C22×C79—22no—
733C22×C79—41no—
734C22×C79—41no—
735C22×C79—41no—
736C22×C79—41no—
737C22×C79—41no—
738C22×C79—41no—
739C22×C79—41no—
740C22×C79—41no—
741C22×C79C23×D411yescharacteristic
742C22×C79C2×H(5,𝔽2)11yescharacteristic
743C22×C79#58511yescharacteristic
744C22×C79#58511yescharacteristic
745C22×C79#58511yescharacteristic
746C22×C79#58511yescharacteristic
747C22×C79#58511yescharacteristic
748C2×D79—41no—
749C2×D79—41no—
750C2×D79—41no—
751C2×D79—41no—
752C2×D79—41no—
753C2×D79—41no—
754C2×D79—41no—
755C2×D79—41no—
756C2×D79—41no—
757C2×D79—41no—
758C2×D79—41no—
759C2×D79—41no—
760C2×D79—41no—
761C2×D79—41no—
762C2×D79—41no—
763C2×D79—41no—
764C2×D79—41no—
765C2×D79—41no—
766C2×D79—41no—
767C2×D79—41no—
768C2×D79—41no—
769C2×D79—41no—
770C2×D79—41no—
771C2×D79—41no—
772C2×D79—41no—
773C2×D79—41no—
774C2×D79—41no—
775C2×D79—41no—
776C2×D79—88no—
777C4×C79—22no—
778C4×C79—22no—
779C4×C79—22no—
780C4×C79—22no—
781C4×C79—22no—
782C4×C79—41no—
783C4×C79—41no—
784C4×C79—41no—
785C4×C79—41no—
786C4×C79—41no—
787C4×C79—41no—
788C4×C79—41no—
789C4×C79—41no—
790Dic79—22no—
791Dic79—41no—
792Dic79—41no—
793Dic79—41no—
794Dic79—41no—
795Dic79—41no—
796Dic79—41no—
797Dic79—41no—
798Dic79—41no—
799Dic79—41no—
800Dic79—41no—
801Dic79—41no—
802#36973—791nomaximal, Sylow
803C2×C79—42no—
804C2×C79—42no—
805C2×C79#344911yescharacteristic
806C2×C79#348511yescharacteristic
807C2×C79#348811yescharacteristic
808C2×C79#355111yescharacteristic
809C2×C79#356211yescharacteristic
810C2×C79#356611yescharacteristic
811C2×C79#356811yescharacteristic
812D79—81no—
813D79—81no—
814D79—81no—
815D79—81no—
816C2×#538—791no—
817C2×#529—791no—
818#2854—791no—
819#2853—791no—
820#2727—791no—
821#2725—791no—
822#2710—791no—
823#2707—791no—
824#2705—791no—
825#2703—791no—
826#2701—791no—
827#2697—791no—
828#2689—791no—
829#2685—791no—
830#2682—791no—
831#2678—791no—
832#2674—791no—
833#2674—791no—
834#2672—791no—
835#2670—791no—
836#2635—791no—
837#2630—791no—
838#2610—791no—
839#2604—791no—
840#2601—791no—
841#2600—791no—
842#2545—791no—
843#2534—791no—
844#2485—791no—
845#2482—791no—
846#2319D7911yescharacteristic, complemented
847C79#3697311yescharacteristic, complemented, Sylow
848#538—1588no—
849C2×C4⋊Q8—791no—
850#529—1588no—
851C2×#126—791no—
852C2×#126—791no—
853C2×#126—791no—
854C2×#126—791no—
855C2×#125—791no—
856C2×#124—791no—
857C2×#124—791no—
858C2×#124—791no—
859C2×#124—791no—
860C2×#123—791no—
861C2×#123—791no—
862C2×#123—791no—
863C2×#123—791no—
864C2×#123—791no—
865C2×#123—791no—
866C2×#123—791no—
867C2×C22⋊Q8—791no—
868C2×C22⋊Q8—791no—
869C2×#121—791no—
870C2×#121—791no—
871C2×#121—791no—
872C2×#121—791no—
873C2×#120—791no—
874C2×#120—791no—
875C2×#120—791no—
876C2×C4×Q8—791no—
877C2×C4×D4—791no—
878C2×C4×D4—791no—
879C2×C4×D4—791no—
880C2×C4×D4C2×D7911yescharacteristic
881C2×#117—791no—
882C2×#117—791no—
883C22×C22⋊C4—791no—
884C22×C42—791no—
885#400—791no—
886#400—791no—
887#399—791no—
888#399—791no—
889#399—791no—
890#399—791no—
891#398—791no—
892#398—791no—
893#397—791no—
894#397—791no—
895#397—791no—
896#397—791no—
897#397—791no—
898#397—791no—
899#396—791no—
900#396—791no—
901#396—791no—
902#396—791no—
903#396—791no—
904#396—791no—
905#396—791no—
906#396—791no—
907#396—791no—
908#396—791no—
909#395—791no—
910#395—791no—
911#394—791no—
912#394—791no—
913#394—791no—
914#394—791no—
915#394—791no—
916#394—791no—
917#394—791no—
918#394—791no—
919#394—791no—
920#394—791no—
921#394—791no—
922#394—791no—
923#394—791no—
924#394—791no—
925#393—791no—
926#393—791no—
927#392—791no—
928#392—791no—
929#392—791no—
930#392—791no—
931#392—791no—
932#392—791no—
933#391—791no—
934#390—791no—
935#390—791no—
936#390—791no—
937#390—791no—
938#390—791no—
939#390—791no—
940#390C2×D7911yescharacteristic
941#390C2×D7911yescharacteristic
942#389—791no—
943#389—791no—
944#389—791no—
945#389—791no—
946#389—791no—
947#389—791no—
948#389—791no—
949#389C2×D7911yescharacteristic, complemented
950#389C2×D7911yescharacteristic, complemented
951#388—791no—
952#388—791no—
953#388—791no—
954#388—791no—
955#388—791no—
956#388—791no—
957#388—791no—
958#388—791no—
959#388—791no—
960#388—791no—
961#388—791no—
962#388—791no—
963#388—791no—
964#388—791no—
965#388—791no—
966#388—791no—
967#388—791no—
968#388—791no—
969#388C2×D7911yescharacteristic
970#388C2×D7911yescharacteristic
971#388C2×D7911yescharacteristic, complemented
972#388C2×D7911yescharacteristic, complemented
973#387—791no—
974#387—791no—
975#387—791no—
976#387—791no—
977#387—791no—
978#387—791no—
979#386—791no—
980#386—791no—
981#386—791no—
982#386—791no—
983#386—791no—
984#386—791no—
985#386—791no—
986#386—791no—
987#385—791no—
988#385—791no—
989#385—791no—
990#385—791no—
991#385—791no—
992#385—791no—
993#381—791no—
994#381C2×D7911yescharacteristic
995#381C2×D7911yescharacteristic, complemented
996#380—791no—
997#380—791no—
998#380C2×D7911yescharacteristic
999#380C2×D7911yescharacteristic, complemented
1000#379—791no—
1001#379—791no—
1002#379—791no—
1003C4×C4⋊C4C2×D7911yescharacteristic, complemented
1004#376C2×D7911yescharacteristic, complemented
1005C25—791no—
1006C22×Q8—791no—
1007C22×Q8—791no—
1008C22×D4—791no—
1009C22×D4—791no—
1010C22×D4—791no—
1011C22×D4—791no—
1012C22×D4—791no—
1013C22×D4—791no—
1014C22×D4—791no—
1015C22×D4—791no—
1016C22×D4—791no—
1017C22×D4—791no—
1018C22×D4—791no—
1019C22×D4C22×D7911yescharacteristic
1020C23×C4—791no—
1021C23×C4—791no—
1022C23×C4—791no—
1023C23×C4—791no—
1024C23×C4—791no—
1025C23×C4C22×D7911yescharacteristic
1026C23×C4C22×D7911yescharacteristic
1027C4⋊Q8—3162no—
1028#126—1584no—
1029#126—1584no—
1030#126—1584no—
1031#126—1584no—
1032#125—1584no—
1033#124—3162no—
1034#124—1584no—
1035#124—1584no—
1036#124—1584no—
1037#123—3162no—
1038#123—3162no—
1039#123—3162no—
1040#123—1584no—
1041#123—1584no—
1042#123—1584no—
1043#123—1584no—
1044C22⋊Q8—1584no—
1045C22⋊Q8—1584no—
1046#121—1584no—
1047#121—1584no—
1048#121—1584no—
1049#121—1584no—
1050#120—3162no—
1051#120—1584no—
1052#120—1584no—
1053C4×Q8—1584no—
1054C4×D4—1584no—
1055C4×D4—1584no—
1056C4×D4—1584no—
1057C4×D4D31618yescomplemented
1058#117—1584no—
1059#117—1584no—
1060C2×C4⋊C4—791no—
1061C2×C4⋊C4—791no—
1062C2×C4⋊C4—791no—
1063C2×C4⋊C4—791no—
1064C2×C4⋊C4—791no—
1065C2×C4⋊C4—791no—
1066C2×C4⋊C4—791no—
1067C2×C4⋊C4—791no—
1068C2×C4⋊C4—791no—
1069C2×C4⋊C4—791no—
1070C2×C4⋊C4—791no—
1071C2×C4⋊C4—791no—
1072C2×C4⋊C4—791no—
1073C2×C4⋊C4—791no—
1074C2×C4⋊C4—791no—
1075C2×C4⋊C4—791no—
1076C2×C4⋊C4—791no—
1077C2×C4⋊C4—791no—
1078C2×C4⋊C4—791no—
1079C2×C4⋊C4—791no—
1080C2×C4⋊C4—791no—
1081C2×C4⋊C4—791no—
1082C2×C4⋊C4—791no—
1083C2×C4⋊C4—791no—
1084C2×C4⋊C4—791no—
1085C2×C4⋊C4—791no—
1086C2×C4⋊C4—791no—
1087C2×C4⋊C4C22×D7911yescharacteristic
1088C2×C4⋊C4C22×D7911yescharacteristic
1089C2×C4⋊C4C22×D7911yescharacteristic
1090C2×C4⋊C4C22×D7911yescharacteristic
1091C2×C4⋊C4C22×D7911yescharacteristic
1092C2×C4⋊C4C22×D7911yescharacteristic
1093C2×C4⋊C4C22×D7911yescharacteristic
1094C2×C22⋊C4—791no—
1095C2×C22⋊C4—791no—
1096C2×C22⋊C4—791no—
1097C2×C22⋊C4—791no—
1098C2×C22⋊C4—791no—
1099C2×C22⋊C4—791no—
1100C2×C22⋊C4—791no—
1101C2×C22⋊C4—791no—
1102C2×C22⋊C4—791no—
1103C2×C22⋊C4—791no—
1104C2×C22⋊C4—791no—
1105C2×C22⋊C4—791no—
1106C2×C22⋊C4—791no—
1107C2×C22⋊C4—791no—
1108C2×C22⋊C4—791no—
1109C2×C22⋊C4—791no—
1110C2×C22⋊C4—791no—
1111C2×C22⋊C4—791no—
1112C2×C22⋊C4—791no—
1113C2×C22⋊C4—791no—
1114C2×C22⋊C4—791no—
1115C2×C22⋊C4—791no—
1116C2×C22⋊C4—791no—
1117C2×C22⋊C4—791no—
1118C2×C22⋊C4—791no—
1119C2×C22⋊C4—791no—
1120C2×C22⋊C4—791no—
1121C2×C22⋊C4—791no—
1122C2×C22⋊C4—791no—
1123C2×C22⋊C4—791no—
1124C2×C22⋊C4—791no—
1125C2×C22⋊C4—791no—
1126C2×C22⋊C4—791no—
1127C2×C22⋊C4—791no—
1128C2×C22⋊C4—791no—
1129C2×C22⋊C4—791no—
1130C2×C22⋊C4—791no—
1131C2×C22⋊C4—791no—
1132C2×C22⋊C4—791no—
1133C2×C22⋊C4—791no—
1134C2×C22⋊C4—791no—
1135C2×C22⋊C4—791no—
1136C2×C22⋊C4—791no—
1137C2×C22⋊C4—791no—
1138C2×C22⋊C4—791no—
1139C2×C22⋊C4—791no—
1140C2×C22⋊C4—1584no—
1141C2×C22⋊C4C22×D7911yescharacteristic
1142C2×C22⋊C4C22×D7911yescharacteristic
1143C2×C22⋊C4C22×D7911yescharacteristic
1144C2×C22⋊C4C22×D7911yescharacteristic
1145C2×C22⋊C4C22×D7911yescharacteristic
1146C2×C22⋊C4C22×D7911yescharacteristic
1147C2×C22⋊C4C22×D7911yescharacteristic
1148C2×C22⋊C4C22×D7911yescharacteristic
1149C2×C22⋊C4C22×D7911yescharacteristic
1150C2×C22⋊C4C22×D7911yescharacteristic
1151C2×C42—791no—
1152C2×C42—791no—
1153C2×C42—791no—
1154C2×C42—791no—
1155C2×C42—791no—
1156C2×C42—791no—
1157C2×C42—1584no—
1158C2×C42C22×D7911yescharacteristic
1159C2×C42C22×D7911yescharacteristic
1160C2×C42C22×D7911yescharacteristic
1161C2×C42C22×D7911yescharacteristic
1162C2×C42C22×D7911yescharacteristic
1163#95—791no—
1164#95—791no—
1165#95—791no—
1166#95—791no—
1167#95—791no—
1168#95—791no—
1169#95—791no—
1170#95—791no—
1171#95—791no—
1172#95—791no—
1173#95—791no—
1174#95—791no—
1175#95—791no—
1176#95—791no—
1177#95—791no—
1178#95—791no—
1179#95—791no—
1180#95—791no—
1181#95—791no—
1182#95—791no—
1183#95—791no—
1184#95—791no—
1185#95C22×D7911yescharacteristic
1186#95C22×D7911yescharacteristic
1187#95C22×D7911yescharacteristic
1188#95C22×D7911yescharacteristic
1189#95C22×D7911yescharacteristic
1190#95C22×D7911yescharacteristic
1191#95C22×D7911yescharacteristic
1192#95C22×D7911yescharacteristic
1193#95C22×D7911yescharacteristic
1194#95C22×D7911yescharacteristic
1195C24—3161no—
1196C24—3161no—
1197C24—3161no—
1198C24—3161no—
1199C24—3161no—
1200C24—3161no—
1201C24—791no—
1202C24—791no—
1203C24—791no—
1204C24—791no—
1205C24—1582no—
1206C24C23×D7911yescharacteristic
1207C24C23×D7911yescharacteristic
1208C2×Q8—3161no—
1209C2×Q8—3161no—
1210C2×Q8—3161no—
1211C2×Q8—1582no—
1212C2×Q8—1582no—
1213C2×Q8—1582no—
1214C2×D4—41no—
1215C2×D4—41no—
1216C2×D4—3161no—
1217C2×D4—3161no—
1218C2×D4—3161no—
1219C2×D4—3161no—
1220C2×D4—3161no—
1221C2×D4—3161no—
1222C2×D4—3161no—
1223C2×D4—3161no—
1224C2×D4—3161no—
1225C2×D4—3161no—
1226C2×D4—3161no—
1227C2×D4—3161no—
1228C2×D4—3161no—
1229C2×D4—3161no—
1230C2×D4—3161no—
1231C2×D4—3161no—
1232C2×D4—3161no—
1233C2×D4—3161no—
1234C2×D4—3161no—
1235C2×D4—3161no—
1236C2×D4—3161no—
1237C2×D4—3161no—
1238C2×D4—3161no—
1239C2×D4—3161no—
1240C2×D4—1582no—
1241C2×D4—1582no—
1242C2×D4—1582no—
1243C2×D4—1582no—
1244C2×D4—1582no—
1245C2×D4—1582no—
1246C2×D4—1582no—
1247C2×D4—1582no—
1248C2×D4—1582no—
1249C2×D4C2×D31614yes—
1250C22×C4—41no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—3161no—
1255C22×C4—3161no—
1256C22×C4—3161no—
1257C22×C4—3161no—
1258C22×C4—3161no—
1259C22×C4—3161no—
1260C22×C4—3161no—
1261C22×C4—3161no—
1262C22×C4—3161no—
1263C22×C4—791no—
1264C22×C4—791no—
1265C22×C4—791no—
1266C22×C4—791no—
1267C22×C4—791no—
1268C22×C4—791no—
1269C22×C4—791no—
1270C22×C4—791no—
1271C22×C4—791no—
1272C22×C4—791no—
1273C22×C4—791no—
1274C22×C4—791no—
1275C22×C4—1582no—
1276C22×C4—1582no—
1277C22×C4—1582no—
1278C22×C4—1582no—
1279C22×C4—1582no—
1280C22×C4—1582no—
1281C22×C4C2×D31614yes—
1282C22×C4C2×D31614yes—
1283C22×C4C23×D7911yescharacteristic
1284C22×C4C23×D7911yescharacteristic
1285C22×C4C23×D7911yescharacteristic
1286C22×C4C23×D7911yescharacteristic
1287C22×C4C23×D7911yescharacteristic
1288C22×C4C23×D7911yescharacteristic
1289C22×C4C23×D7911yescharacteristic
1290C22×C4C23×D7911yescharacteristic
1291C22×C4C23×D7911yescharacteristic
1292C22×C4C23×D7911yescharacteristic
1293C22×C4C23×D7911yescharacteristic
1294C22×C4C23×D7911yescharacteristic
1295C22×C4C23×D7911yescharacteristic
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—41no—
1300C4⋊C4—41no—
1301C4⋊C4—41no—
1302C4⋊C4—3161no—
1303C4⋊C4—3161no—
1304C4⋊C4—3161no—
1305C4⋊C4—3161no—
1306C4⋊C4—3161no—
1307C4⋊C4—3161no—
1308C4⋊C4—3161no—
1309C4⋊C4—3161no—
1310C4⋊C4—3161no—
1311C4⋊C4—3161no—
1312C4⋊C4—1582no—
1313C4⋊C4—1582no—
1314C4⋊C4—1582no—
1315C4⋊C4—1582no—
1316C4⋊C4—1582no—
1317C4⋊C4—1582no—
1318C4⋊C4—1582no—
1319C4⋊C4—1582no—
1320C4⋊C4—1582no—
1321C4⋊C4—1582no—
1322C4⋊C4—1582no—
1323C4⋊C4—1582no—
1324C4⋊C4—1582no—
1325C4⋊C4—1582no—
1326C4⋊C4—1582no—
1327C4⋊C4—1582no—
1328C4⋊C4—1582no—
1329C4⋊C4C2×D31614yes—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—3161no—
1339C22⋊C4—3161no—
1340C22⋊C4—3161no—
1341C22⋊C4—3161no—
1342C22⋊C4—3161no—
1343C22⋊C4—3161no—
1344C22⋊C4—3161no—
1345C22⋊C4—3161no—
1346C22⋊C4—3161no—
1347C22⋊C4—3161no—
1348C22⋊C4—3161no—
1349C22⋊C4—3161no—
1350C22⋊C4—3161no—
1351C22⋊C4—3161no—
1352C22⋊C4—3161no—
1353C22⋊C4—3161no—
1354C22⋊C4—3161no—
1355C22⋊C4—3161no—
1356C22⋊C4—3161no—
1357C22⋊C4—3161no—
1358C22⋊C4—3161no—
1359C22⋊C4—3161no—
1360C22⋊C4—3161no—
1361C22⋊C4—1582no—
1362C22⋊C4—1582no—
1363C22⋊C4—1582no—
1364C22⋊C4—1582no—
1365C22⋊C4—1582no—
1366C22⋊C4—1582no—
1367C22⋊C4—1582no—
1368C22⋊C4—1582no—
1369C22⋊C4—1582no—
1370C22⋊C4—1582no—
1371C22⋊C4—1582no—
1372C22⋊C4—1582no—
1373C22⋊C4—1582no—
1374C22⋊C4—1582no—
1375C22⋊C4—1582no—
1376C22⋊C4—1582no—
1377C22⋊C4—1582no—
1378C22⋊C4—1582no—
1379C22⋊C4—1582no—
1380C22⋊C4—1582no—
1381C22⋊C4—1582no—
1382C22⋊C4—1582no—
1383C22⋊C4—1582no—
1384C22⋊C4C2×D31614yes—
1385C22⋊C4C2×D31614yes—
1386C42—41no—
1387C42—41no—
1388C42—41no—
1389C42—41no—
1390C42—1582no—
1391C42—1582no—
1392C42—1582no—
1393C42—1582no—
1394C42—1582no—
1395C42—1582no—
1396C42C2×D31614yes—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—3164no—
1410C23—6322no—
1411C23—6322no—
1412C23—6322no—
1413C23—6322no—
1414C23—6322no—
1415C23—6322no—
1416C23—1581no—
1417C23—1581no—
1418C23—1581no—
1419C23—1581no—
1420C23—1581no—
1421C23—1581no—
1422C23—1581no—
1423C23—1581no—
1424C23—1581no—
1425C23—1581no—
1426C23—1581no—
1427C23—1581no—
1428C23—1581no—
1429C23—1581no—
1430C23—1581no—
1431C23—1581no—
1432C23—1581no—
1433C23—1581no—
1434C23—1581no—
1435C23—1581no—
1436C23—1581no—
1437C23—1581no—
1438C23—1581no—
1439C23—1581no—
1440C23—1581no—
1441C23—1581no—
1442C23—1581no—
1443C23—1581no—
1444C23C22×D31612yes—
1445C23C22×D31612yes—
1446C23C24×D7911yescharacteristic
1447Q8—3164no—
1448Q8—6322no—
1449D4—44no—
1450D4—3164no—
1451D4—3164no—
1452D4—3164no—
1453D4—6322no—
1454D4—6322no—
1455D4—6322no—
1456D4—6322no—
1457D4—6322no—
1458D4—6322no—
1459D4—6322no—
1460D4—6322no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—44no—
1496C2×C4—44no—
1497C2×C4—3164no—
1498C2×C4—3164no—
1499C2×C4—3164no—
1500C2×C4—792no—
1501C2×C4—6322no—
1502C2×C4—6322no—
1503C2×C4—1581no—
1504C2×C4—1581no—
1505C2×C4—1581no—
1506C2×C4—1581no—
1507C2×C4—1581no—
1508C2×C4—1581no—
1509C2×C4—1581no—
1510C2×C4—1581no—
1511C2×C4—1581no—
1512C2×C4—1581no—
1513C2×C4—1581no—
1514C2×C4—1581no—
1515C2×C4—1581no—
1516C2×C4—1581no—
1517C2×C4—1581no—
1518C2×C4—1581no—
1519C2×C4—1581no—
1520C2×C4—1581no—
1521C2×C4—1581no—
1522C2×C4—1581no—
1523C2×C4—1581no—
1524C2×C4—1581no—
1525C2×C4—1581no—
1526C2×C4—1581no—
1527C2×C4—1581no—
1528C2×C4—1581no—
1529C2×C4—1581no—
1530C2×C4—1581no—
1531C2×C4—1581no—
1532C2×C4—1581no—
1533C2×C4—1581no—
1534C2×C4—1581no—
1535C2×C4—1581no—
1536C2×C4—1581no—
1537C2×C4—1581no—
1538C2×C4C22×D31612yes—
1539C2×C4C22×D31612yes—
1540C2×C4C22×D31612yes—
1541C2×C4C22×D31612yes—
1542C2×C4C22×D31612yes—
1543C22—22no—
1544C22—22no—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—3161no—
1558C22—3161no—
1559C22—3161no—
1560C22—3161no—
1561C22—3161no—
1562C22—3161no—
1563C22—3161no—
1564C22—3161no—
1565C22—3161no—
1566C22—3161no—
1567C22—3161no—
1568C22—3161no—
1569C22—3161no—
1570C22—3161no—
1571C22—3161no—
1572C22—3161no—
1573C22—3161no—
1574C22—3161no—
1575C22—3161no—
1576C22—3161no—
1577C22—3161no—
1578C22—3161no—
1579C22—3161no—
1580C22—3161no—
1581C22—3161no—
1582C22—3161no—
1583C22—3161no—
1584C22—3161no—
1585C22—6328no—
1586C22C23×D31611yescharacteristic
1587C22H(5,𝔽2)×D7911yescharacteristic
1588C22#1909939811yescharacteristic
1589C22#1909939811yescharacteristic
1590C22#1909939911yescharacteristic
1591C22#1909939911yescharacteristic
1592C22#1909940011yescharacteristic
1593C4—22no—
1594C4—22no—
1595C4—22no—
1596C4—22no—
1597C4—22no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—3161no—
1607C4—3161no—
1608C4—3161no—
1609C4—3161no—
1610C4—3161no—
1611C4—3161no—
1612C4—3161no—
1613C4—3161no—
1614C4—3161no—
1615C4—3161no—
1616C4—3161no—
1617C4—1582no—
1618C2—42no—
1619C2—42no—
1620C2—6321no—
1621C2—6321no—
1622C2—6321no—
1623C2—6321no—
1624C2#2377673311yescharacteristic
1625C2#2377704511yescharacteristic
1626C2#2377707011yescharacteristic
1627C2#2377782111yescharacteristic
1628C2#2377797911yescharacteristic
1629C2#2377808011yescharacteristic
1630C2#2377809211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutator, socle, cosocleC23×C79C25
FittingC79×#2319C2
hypercenter#2319D79
hypocenterC79#36973
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2319

Complements

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

NH ≅ G/Ntype
1. C2×#19099146C2semidirect
2. C2×#19099093C2semidirect
3. #23771732C2semidirect
4. #23771723C2semidirect
5. #23770361C2semidirect
6. #23770338C2semidirect
7. #23770140C2semidirect
8. #23770101C2semidirect
9. #23770071C2semidirect
10. #23770041C2semidirect
11. #23770011C2semidirect
12. #23769962C2semidirect
13. #23769849C2semidirect
14. #23769789C2semidirect
15. #23769764C2semidirect
16. #23769720C2semidirect
17. #23769679C2semidirect
18. #23769679C2semidirect
19. #23769649C2semidirect
20. #23769624C2semidirect
21. #23769287C2semidirect
22. #23769241C2semidirect
23. #23769081C2semidirect
24. #23769038C2semidirect
25. #23768991C2semidirect
26. #23768987C2semidirect
27. #23768380C2semidirect
28. #23768292C2semidirect
29. #23767698C2semidirect
30. #23767676C2semidirect
31. C79×#2319C2semidirect
33. C2×#14579161C22semidirect
36. C2×#14579156C22semidirect
39. C2×#14579151C22semidirect
47. C2×#14579145C22semidirect
48. C2×#14579145C22semidirect
52. C2×#14579138C22semidirect
60. C2×C4×Dic158C22semidirect
63. C2×C4×C22⋊D79C22semidirect
65. C2×#14579118C22semidirect
67. C22×C4×Dic79C22semidirect
68. #19098503C22semidirect
69. #19098503C22semidirect
73. #19098500C22semidirect
74. #19098493C22semidirect
75. #19098493C22semidirect
81. #19098488C22semidirect
88. #19098485C22semidirect
89. #19098485C22semidirect
90. #19098485C22semidirect
91. #19098485C22semidirect
92. #19098484C22semidirect
93. #19098484C22semidirect
106. #19098479C22semidirect
107. #19098479C22semidirect
109. #19098476C22semidirect
115. #19098472C22semidirect
116. #19098469C22semidirect
120. #19098465C22semidirect
123. #19098462C22semidirect
124. #19098462C22semidirect
125. #19098462C22semidirect
126. #19098462C22semidirect
127. #19098461C22semidirect
128. #19098461C22semidirect
129. #19098461C22semidirect
138. #19098455C22semidirect
139. #19098455C22semidirect
140. #19098455C22semidirect
141. #19098455C22semidirect
146. #19098454C22semidirect
147. #19098454C22semidirect
148. #19098448C22semidirect
149. #19098448C22semidirect
150. #19098448C22semidirect
151. #19098448C22semidirect
152. #19098448C22semidirect
153. #19098448C22semidirect
156. #19098441C22semidirect
157. #19098441C22semidirect
161. #19098440C22semidirect
164. #19098438C22semidirect
165. #19098438C22semidirect
166. #19098437C22semidirect
167. #19098437C22semidirect
169. #19098420C22semidirect
170. #19098420C22semidirect
177. #389×C79C22semidirect
178. #389×C79C22semidirect
181. #388×C79C22semidirect
182. #388×C79C22semidirect
184. #381×C79C22semidirect
186. #380×C79C22semidirect
187. C4×C4⋊C4×C79C22semidirect
188. #376×C79C22semidirect
346. C4×D4×C79D4semidirect
846. #2319D79semidirect
847. C79#36973semidirect
949. #389C2×D79semidirect
950. #389C2×D79semidirect
971. #388C2×D79semidirect
972. #388C2×D79semidirect
995. #381C2×D79semidirect
999. #380C2×D79semidirect
1003. C4×C4⋊C4C2×D79semidirect
1004. #376C2×D79semidirect
1057. C4×D4D316semidirect

Maximal subgroups

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

subgroupindex
C2×#190991462
C2×#190990932
#237717322
#237717232
#237703612
#237703382
#237701402
#237701012
#237700712
#237700412
#237700112
#237699622
#237698492
#237697892
#237697642
#237697202
#237696792
#237696492
#237696242
#237692872
#237692412
#237690812
#237690382
#237689912
#237689872
#237683802
#237682922
#237676982
#237676762
C79×#23192
#3697379