Finite Group Databasebeta

← #34454113

Subgroups — #34454113

Order 20224.

2224 conjugacy classes of subgroups.

The subgroup lattice has 1512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23766566C211yesmaximal, characteristic, complemented
2#23766557C211yesmaximal, characteristic, complemented
3#23766548C211yesmaximal, characteristic, complemented
4#23766500C211yesmaximal, characteristic, complemented
5#23766485C211yesmaximal, characteristic, complemented
6#23766475C211yesmaximal, characteristic, complemented
7#23766475C211yesmaximal, characteristic, complemented
8#23766452C211yesmaximal, characteristic, complemented
9#23766452C211yesmaximal, characteristic, complemented
10#23766442C211yesmaximal, characteristic, complemented
11#23766431C211yesmaximal, characteristic, complemented
12#23766431C211yesmaximal, characteristic, complemented
13#23766396C211yesmaximal, characteristic, complemented
14#23766396C211yesmaximal, characteristic, complemented
15#23766396C211yesmaximal, characteristic, complemented
16#23766215C211yesmaximal, characteristic, complemented
17#23766215C211yesmaximal, characteristic, complemented
18#23766206C211yesmaximal, characteristic, complemented
19#23766194C211yesmaximal, characteristic, complemented
20#23766194C211yesmaximal, characteristic, complemented
21#23766194C211yesmaximal, characteristic, complemented
22#23766135C211yesmaximal, characteristic, complemented
23#23766135C211yesmaximal, characteristic, complemented
24#23766105C211yesmaximal, characteristic, complemented
25#23766095C211yesmaximal, characteristic, complemented
26#23766095C211yesmaximal, characteristic, complemented
27#23766084C211yesmaximal, characteristic, complemented
28C22⋊Q8×Dic79C211yesmaximal, characteristic, complemented
29#123×Dic79C211yesmaximal, characteristic, complemented
30#121×Dic79C211yesmaximal, characteristic, complemented
31C2×#562×C79C211yesmaximal, characteristic
32C2×Q8×Dic79C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×D4×Dic79C2211yescharacteristic
35C2×D4×Dic79C2211yescharacteristic
36C2×D4×Dic79C2211yescharacteristic
37C2×D4×Dic79C2211yescharacteristic
38C2×D4×Dic79C2211yescharacteristic
39C2×D4×Dic79C2211yescharacteristic
40C2×#14579120C2211yescharacteristic
41C2×#14579120C2211yescharacteristic
42C2×#14579120C2211yescharacteristic
43C22×C4×Dic79C2211yescharacteristic
44#19098470C2211yescharacteristic
45#19098470C2211yescharacteristic
46#19098470C2211yescharacteristic
47#19098470C2211yescharacteristic
48#19098470C2211yescharacteristic
49#19098470C2211yescharacteristic
50#19098466C2211yescharacteristic
51#19098466C2211yescharacteristic
52#19098466C2211yescharacteristic
53#19098466C2211yescharacteristic
54#19098466C2211yescharacteristic
55#19098466C2211yescharacteristic
56#19098462C2211yescharacteristic
57#19098462C2211yescharacteristic
58#19098462C2211yescharacteristic
59#19098462C2211yescharacteristic
60#19098462C2211yescharacteristic
61#19098462C2211yescharacteristic
62#19098462C2211yescharacteristic
63#19098462C2211yescharacteristic
64#19098462C2211yescharacteristic
65#19098462C2211yescharacteristic
66#19098456C2211yescharacteristic
67#19098456C2211yescharacteristic
68#19098456C2211yescharacteristic
69#19098456C2211yescharacteristic
70#19098456C2211yescharacteristic
71#19098456C2211yescharacteristic
72#19098456C2211yescharacteristic
73#19098456C2211yescharacteristic
74#19098456C2211yescharacteristic
75#19098456C2211yescharacteristic
76#19098456C2211yescharacteristic
77#19098456C2211yescharacteristic
78#19098456C2211yescharacteristic
79#19098456C2211yescharacteristic
80#19098456C2211yescharacteristic
81#19098456C2211yescharacteristic
82#19098456C2211yescharacteristic
83#19098456C2211yescharacteristic
84#19098456C2211yescharacteristic
85#19098456C2211yescharacteristic
86#19098456C2211yescharacteristic
87#19098456C2211yescharacteristic
88#19098456C2211yescharacteristic
89#19098456C2211yescharacteristic
90#19098449C2211yescharacteristic
91#19098449C2211yescharacteristic
92#19098449C2211yescharacteristic
93#19098449C2211yescharacteristic
94#19098449C2211yescharacteristic
95#19098449C2211yescharacteristic
96#19098449C2211yescharacteristic
97#19098449C2211yescharacteristic
98#19098449C2211yescharacteristic
99#19098449C2211yescharacteristic
100#19098449C2211yescharacteristic
101#19098449C2211yescharacteristic
102#19098449C2211yescharacteristic
103#19098449C2211yescharacteristic
104#19098449C2211yescharacteristic
105#19098449C2211yescharacteristic
106#19098449C2211yescharacteristic
107#19098449C2211yescharacteristic
108#19098449C2211yescharacteristic
109#19098449C2211yescharacteristic
110#19098443C2211yescharacteristic
111#19098443C2211yescharacteristic
112#19098443C2211yescharacteristic
113#19098443C2211yescharacteristic
114#19098443C2211yescharacteristic
115#19098443C2211yescharacteristic
116#19098443C2211yescharacteristic
117#19098443C2211yescharacteristic
118#19098443C2211yescharacteristic
119#19098443C2211yescharacteristic
120#19098443C2211yescharacteristic
121#19098443C2211yescharacteristic
122#19098438C2211yescharacteristic
123#19098438C2211yescharacteristic
124#19098438C2211yescharacteristic
125#19098438C2211yescharacteristic
126#19098438C2211yescharacteristic
127#19098438C2211yescharacteristic
128#19098438C2211yescharacteristic
129#19098438C2211yescharacteristic
130#19098438C2211yescharacteristic
131#19098438C2211yescharacteristic
132#19098438C2211yescharacteristic
133#19098438C2211yescharacteristic
134#19098431C2211yescharacteristic
135#19098426C2211yescharacteristic
136#19098423C2211yescharacteristic
137#19098423C2211yescharacteristic
138#19098423C2211yescharacteristic
139#19098423C2211yescharacteristic
140#19098423C2211yescharacteristic
141C4⋊C4×Dic79C2211yescharacteristic
142C4⋊C4×Dic79C2211yescharacteristic
143C4⋊C4×Dic79C2211yescharacteristic
144C4⋊C4×Dic79C2211yescharacteristic
145C4⋊C4×Dic79C2211yescharacteristic
146C4⋊C4×Dic79C2211yescharacteristic
147C4⋊C4×Dic79C2211yescharacteristic
148C4⋊C4×Dic79C2211yescharacteristic
149C4⋊C4×Dic79C2211yescharacteristic
150C4⋊C4×Dic79C2211yescharacteristic
151C4×C4⋊Dic79C2211yescharacteristic
152C4×C4⋊Dic79C2211yescharacteristic
153C4×C4⋊Dic79C2211yescharacteristic
154C22⋊C4×Dic79C2211yescharacteristic
155C22⋊C4×Dic79C2211yescharacteristic
156C22⋊C4×Dic79C2211yescharacteristic
157C22⋊C4×Dic79C2211yescharacteristic
158C22⋊C4×Dic79C2211yescharacteristic
159C22⋊C4×Dic79C2211yescharacteristic
160C22⋊C4×Dic79C2211yescharacteristic
161C22⋊C4×Dic79C2211yescharacteristic
162C22⋊C4×Dic79C2211yescharacteristic
163C22⋊C4×Dic79C2211yescharacteristic
164C22⋊C4×Dic79C2211yescharacteristic
165C22⋊C4×Dic79C2211yescharacteristic
166C4×C22⋊Dic79C2211yescharacteristic
167C4×C22⋊Dic79C2211yescharacteristic
168C4×C22⋊Dic79C2211yescharacteristic
169C2×C79⋊#95C2211yescharacteristic
170C2×C79⋊#95C2211yescharacteristic
171C2×C79⋊#95C2211yescharacteristic
172#562×C79C4116yescomplemented
173C2×#125×C79C2211yescharacteristic
174C2×#124×C79C2211yescharacteristic
175C2×#124×C79C2211yescharacteristic
176C2×#123×C79C2211yescharacteristic
177C2×#123×C79C2211yescharacteristic
178C2×#123×C79C2211yescharacteristic
179C2×#123×C79C2211yescharacteristic
180C2×C22⋊Q8×C79C2211yescharacteristic
181C2×C22⋊Q8×C79C2211yescharacteristic
182C2×C22⋊Q8×C79C2211yescharacteristic
183C2×C22⋊Q8×C79C2211yescharacteristic
184C2×#121×C79C2211yescharacteristic
185C2×#121×C79C2211yescharacteristic
186C2×#121×C79C2211yescharacteristic
187C2×#121×C79C2211yescharacteristic
188C23×Dic79C2311yescharacteristic
189C23×Dic79C2311yescharacteristic
190C23×Dic79C2311yescharacteristic
191C23×Dic79C2311yescharacteristic
192C23×Dic79C2311yescharacteristic
193C23×Dic79C2311yescharacteristic
194C23×Dic79C2311yescharacteristic
195C23×Dic79C2311yescharacteristic
196Q8×Dic79—42no—
197Q8×Dic79—42no—
198D4×Dic79—42no—
199D4×Dic79—42no—
200D4×Dic79—42no—
201D4×Dic79—42no—
202D4×Dic79—42no—
203D4×Dic79—42no—
204#14579120—42no—
205#14579120—42no—
206#14579120—42no—
207C2×C4⋊Dic79C2311yescharacteristic
208C2×C4⋊Dic79C2311yescharacteristic
209C2×C4⋊Dic79C2311yescharacteristic
210C2×C4⋊Dic79C2311yescharacteristic
211C2×C4⋊Dic79C2311yescharacteristic
212C2×C4⋊Dic79C2311yescharacteristic
213C2×C4⋊Dic79C2311yescharacteristic
214C2×C4⋊Dic79C2311yescharacteristic
215C2×C4⋊Dic79C2311yescharacteristic
216C2×C4⋊Dic79C2311yescharacteristic
217C2×C4⋊Dic79C2311yescharacteristic
218C2×C4⋊Dic79C2311yescharacteristic
219C2×C4⋊Dic79C2311yescharacteristic
220C2×C4⋊Dic79C2311yescharacteristic
221C2×C4⋊Dic79C2311yescharacteristic
222C2×C4⋊Dic79C2311yescharacteristic
223C2×C4⋊Dic79C2311yescharacteristic
224C2×C4⋊Dic79C2311yescharacteristic
225C2×C4⋊Dic79C2311yescharacteristic
226C2×C4⋊Dic79C2311yescharacteristic
227C2×C4⋊Dic79C2311yescharacteristic
228C2×C4⋊Dic79C2311yescharacteristic
229C2×C22⋊Dic79C2311yescharacteristic
230C2×C22⋊Dic79C2311yescharacteristic
231C2×C22⋊Dic79C2311yescharacteristic
232C2×C22⋊Dic79C2311yescharacteristic
233C2×C22⋊Dic79C2311yescharacteristic
234C2×C22⋊Dic79C2311yescharacteristic
235C2×C22⋊Dic79C2311yescharacteristic
236C2×C22⋊Dic79C2311yescharacteristic
237C2×C22⋊Dic79C2311yescharacteristic
238C2×C22⋊Dic79C2311yescharacteristic
239C2×C22⋊Dic79C2311yescharacteristic
240C2×C22⋊Dic79C2311yescharacteristic
241C2×C22⋊Dic79C2311yescharacteristic
242C2×C22⋊Dic79C2311yescharacteristic
243C2×C22⋊Dic79C2311yescharacteristic
244C2×C22⋊Dic79C2311yescharacteristic
245C2×C22⋊Dic79C2311yescharacteristic
246C2×C22⋊Dic79C2311yescharacteristic
247C2×C22⋊Dic79C2311yescharacteristic
248C2×C22⋊Dic79C2311yescharacteristic
249C2×C22⋊Dic79C2311yescharacteristic
250C2×C22⋊Dic79C2311yescharacteristic
251C2×C22⋊Dic79C2311yescharacteristic
252C2×C22⋊Dic79C2311yescharacteristic
253C2×C4×Dic79—42no—
254C2×C4×Dic79C2311yescharacteristic
255C2×C4×Dic79C2311yescharacteristic
256C2×C4×Dic79C2311yescharacteristic
257C2×C4×Dic79C2311yescharacteristic
258C2×C4×Dic79C2311yescharacteristic
259C2×C4×Dic79C2311yescharacteristic
260C2×C4×Dic79C2311yescharacteristic
261C2×C4×Dic79C2311yescharacteristic
262C2×C4×Dic79C2311yescharacteristic
263C2×C4×Dic79C2311yescharacteristic
264C2×C4×Dic79C2311yescharacteristic
265C2×C4×Dic79C2311yescharacteristic
266C2×C4×Dic79C2311yescharacteristic
267C2×C4×Dic79C2311yescharacteristic
268C2×C4×Dic79C2311yescharacteristic
269C2×C4×Dic79C2311yescharacteristic
270C2×C4×Dic79C2311yescharacteristic
271C2×C4×Dic79C2311yescharacteristic
272C2×C4×Dic79C2311yescharacteristic
273C2×C4×Dic79C2311yescharacteristic
274C2×C4×Dic79C2311yescharacteristic
275C2×C4×Dic79C2311yescharacteristic
276C79⋊#95C2311yescharacteristic
277C79⋊#95C2311yescharacteristic
278C79⋊#95C2311yescharacteristic
279C79⋊#95C2311yescharacteristic
280C79⋊#95C2311yescharacteristic
281C79⋊#95C2311yescharacteristic
282C79⋊#95C2311yescharacteristic
283C79⋊#95C2311yescharacteristic
284C79⋊#95C2311yescharacteristic
285C79⋊#95C2311yescharacteristic
286C79⋊#95C2311yescharacteristic
287C79⋊#95C2311yescharacteristic
288C79⋊#95C2311yescharacteristic
289C79⋊#95C2311yescharacteristic
290C79⋊#95C2311yescharacteristic
291C79⋊#95C2311yescharacteristic
292C79⋊#95C2311yescharacteristic
293C79⋊#95C2311yescharacteristic
294C79⋊#95C2311yescharacteristic
295C79⋊#95C2311yescharacteristic
296C79⋊#95C2311yescharacteristic
297C79⋊#95C2311yescharacteristic
298C79⋊#95C2311yescharacteristic
299C79⋊#95C2311yescharacteristic
300C79⋊#95C2311yescharacteristic
301C79⋊#95C2311yescharacteristic
302C79⋊#95C2311yescharacteristic
303C79⋊#95C2311yescharacteristic
304C79⋊#95C2311yescharacteristic
305C79⋊#95C2311yescharacteristic
306C79⋊#95C2311yescharacteristic
307C79⋊#95C2311yescharacteristic
308C79⋊#95C2311yescharacteristic
309C79⋊#95C2311yescharacteristic
310C79⋊#95C2311yescharacteristic
311C79⋊#95C2311yescharacteristic
312C79⋊#95C2311yescharacteristic
313C79⋊#95C2311yescharacteristic
314C79⋊#95C2311yescharacteristic
315C79⋊#95C2311yescharacteristic
316C79⋊#95C2311yescharacteristic
317C79⋊#95C2311yescharacteristic
318C79⋊#95C2311yescharacteristic
319C79⋊#95C2311yescharacteristic
320C22×Q8×C79C2311yescharacteristic
321C22×Q8×C79C2311yescharacteristic
322C22×D4×C79C2311yescharacteristic
323C22×D4×C79C2311yescharacteristic
324C22×D4×C79C2311yescharacteristic
325C22×D4×C79C2311yescharacteristic
326C22×D4×C79C2311yescharacteristic
327C22×D4×C79C2311yescharacteristic
328C23×C4×C79C2311yescharacteristic
329C23×C4×C79C2311yescharacteristic
330C23×C4×C79C2311yescharacteristic
331C23×C4×C79C2311yescharacteristic
332#125×C79C2×C418yescomplemented
333#124×C79C2×C418yescomplemented
334#124×C79C2×C418yescomplemented
335#123×C79C2×C418yescomplemented
336#123×C79C2×C418yescomplemented
337#123×C79C2×C418yescomplemented
338#123×C79C2×C418yescomplemented
339C22⋊Q8×C79C2×C418yescomplemented
340C22⋊Q8×C79C2×C418yescomplemented
341C22⋊Q8×C79C2×C418yescomplemented
342C22⋊Q8×C79C2×C418yescomplemented
343#121×C79C2×C418yescomplemented
344#121×C79C2×C418yescomplemented
345#121×C79C2×C418yescomplemented
346#121×C79C2×C418yescomplemented
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×C4⋊C4×C79C2311yescharacteristic
355C2×C4⋊C4×C79C2311yescharacteristic
356C2×C4⋊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×C22⋊C4×C79C2311yescharacteristic
365C2×C22⋊C4×C79C2311yescharacteristic
366C2×C22⋊C4×C79C2311yescharacteristic
367C2×C22⋊C4×C79C2311yescharacteristic
368C2×C22⋊C4×C79C2311yescharacteristic
369C2×C42×C79C2311yescharacteristic
370C22×Dic79—22no—
371C22×Dic79—22no—
372C22×Dic79—22no—
373C22×Dic79—22no—
374C22×Dic79—22no—
375C22×Dic79—22no—
376C22×Dic79—41no—
377C22×Dic79—41no—
378C22×Dic79—41no—
379C22×Dic79—41no—
380C22×Dic79—41no—
381C22×Dic79—41no—
382C22×Dic79—41no—
383C22×Dic79—41no—
384C22×Dic79—41no—
385C22×Dic79—41no—
386C22×Dic79—41no—
387C22×Dic79—41no—
388C22×Dic79—41no—
389C22×Dic79—41no—
390C22×Dic79—41no—
391C22×Dic79—41no—
392C22×Dic79—41no—
393C22×Dic79—41no—
394C22×Dic79C2411yescharacteristic
395C22×Dic79C2411yescharacteristic
396C22×Dic79C2411yescharacteristic
397C22×Dic79C2411yescharacteristic
398C22×Dic79C2411yescharacteristic
399C22×Dic79C2411yescharacteristic
400C22×Dic79C2411yescharacteristic
401C22×Dic79C2411yescharacteristic
402C22×Dic79C2411yescharacteristic
403C22×Dic79C2411yescharacteristic
404C22×Dic79C2411yescharacteristic
405C22×Dic79C2411yescharacteristic
406C22×Dic79C2411yescharacteristic
407C22×Dic79C2411yescharacteristic
408C22×Dic79C2411yescharacteristic
409C22×Dic79C2411yescharacteristic
410C4⋊Dic79—22no—
411C4⋊Dic79—22no—
412C4⋊Dic79—22no—
413C4⋊Dic79—22no—
414C4⋊Dic79—22no—
415C4⋊Dic79—22no—
416C4⋊Dic79—41no—
417C4⋊Dic79—41no—
418C4⋊Dic79—41no—
419C4⋊Dic79—41no—
420C4⋊Dic79—41no—
421C4⋊Dic79—41no—
422C4⋊Dic79—41no—
423C4⋊Dic79—41no—
424C4⋊Dic79—41no—
425C4⋊Dic79—41no—
426C4⋊Dic79—41no—
427C4⋊Dic79—41no—
428C4⋊Dic79—41no—
429C4⋊Dic79—41no—
430C4⋊Dic79—41no—
431C4⋊Dic79—41no—
432C22⋊Dic79—22no—
433C22⋊Dic79—22no—
434C22⋊Dic79—22no—
435C22⋊Dic79—22no—
436C22⋊Dic79—22no—
437C22⋊Dic79—22no—
438C22⋊Dic79—41no—
439C22⋊Dic79—41no—
440C22⋊Dic79—41no—
441C22⋊Dic79—41no—
442C22⋊Dic79—41no—
443C22⋊Dic79—41no—
444C22⋊Dic79—41no—
445C22⋊Dic79—41no—
446C22⋊Dic79—41no—
447C22⋊Dic79—41no—
448C22⋊Dic79—41no—
449C22⋊Dic79—41no—
450C22⋊Dic79—41no—
451C22⋊Dic79—41no—
452C22⋊Dic79—41no—
453C22⋊Dic79—41no—
454C22⋊Dic79—41no—
455C22⋊Dic79—41no—
456C4×Dic79—22no—
457C4×Dic79—22no—
458C4×Dic79—22no—
459C4×Dic79—22no—
460C4×Dic79—22no—
461C4×Dic79—41no—
462C4×Dic79—41no—
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—
473C4×Dic79—41no—
474C4×Dic79—41no—
475C4×Dic79—41no—
476C4×Dic79—41no—
477C4×Dic79—41no—
478C24×C79C2411yescharacteristic
479C24×C79C2411yescharacteristic
480C24×C79C2411yescharacteristic
481C24×C79C2411yescharacteristic
482C2×Q8×C79—41no—
483C2×Q8×C79—41no—
484C2×Q8×C79—41no—
485C2×Q8×C79—41no—
486C2×Q8×C79C22×C414yes—
487C2×Q8×C79C22×C414yes—
488C2×D4×C79—41no—
489C2×D4×C79—41no—
490C2×D4×C79—41no—
491C2×D4×C79—41no—
492C2×D4×C79—41no—
493C2×D4×C79—41no—
494C2×D4×C79—41no—
495C2×D4×C79—41no—
496C2×D4×C79—41no—
497C2×D4×C79—41no—
498C2×D4×C79—41no—
499C2×D4×C79—41no—
500C2×D4×C79C22×C414yes—
501C2×D4×C79C22×C414yes—
502C2×D4×C79C22×C414yes—
503C2×D4×C79C22×C414yes—
504C2×D4×C79C22×C414yes—
505C2×D4×C79C22×C414yes—
506C22×C4×C79—41no—
507C22×C4×C79—41no—
508C22×C4×C79—41no—
509C22×C4×C79—41no—
510C22×C4×C79—41no—
511C22×C4×C79—41no—
512C22×C4×C79—41no—
513C22×C4×C79—41no—
514C22×C4×C79C22×C414yes—
515C22×C4×C79C22×C414yes—
516C22×C4×C79C22×C414yes—
517C22×C4×C79C22×C414yes—
518C22×C4×C79C2411yescharacteristic
519C22×C4×C79C2411yescharacteristic
520C22×C4×C79C2411yescharacteristic
521C22×C4×C79C2411yescharacteristic
522C22×C4×C79C2411yescharacteristic
523C22×C4×C79C2411yescharacteristic
524C22×C4×C79C2411yescharacteristic
525C22×C4×C79C2411yescharacteristic
526C22×C4×C79C2411yescharacteristic
527C22×C4×C79C2411yescharacteristic
528C22×C4×C79C2411yescharacteristic
529C4⋊C4×C79C22×C414yes—
530C4⋊C4×C79C22×C414yes—
531C4⋊C4×C79C22×C414yes—
532C4⋊C4×C79C22×C414yes—
533C4⋊C4×C79C22×C414yes—
534C4⋊C4×C79C22×C414yes—
535C4⋊C4×C79C22×C414yes—
536C4⋊C4×C79C22×C414yes—
537C4⋊C4×C79C22×C414yes—
538C4⋊C4×C79C22×C414yes—
539C22⋊C4×C79C22×C414yes—
540C22⋊C4×C79C22×C414yes—
541C22⋊C4×C79C22×C414yes—
542C22⋊C4×C79C22×C414yes—
543C22⋊C4×C79C22×C414yes—
544C22⋊C4×C79C22×C414yes—
545C22⋊C4×C79C22×C414yes—
546C22⋊C4×C79C22×C414yes—
547C22⋊C4×C79C22×C414yes—
548C22⋊C4×C79C22×C414yes—
549C22⋊C4×C79C22×C414yes—
550C22⋊C4×C79C22×C414yes—
551C42×C79C22×C414yes—
552C23×C79—21no—
553C23×C79—21no—
554C23×C79—21no—
555C23×C79—21no—
556C23×C79—21no—
557C23×C79—21no—
558C23×C79—21no—
559C23×C79—21no—
560C23×C79—21no—
561C23×C79—21no—
562C23×C79—21no—
563C23×C79—21no—
564C23×C79—21no—
565C23×C79—21no—
566C23×C79—21no—
567C23×C79—21no—
568C23×C79—21no—
569C23×C79—21no—
570C23×C79—21no—
571C23×C79—21no—
572C23×C79—21no—
573C23×C79—21no—
574C23×C79—21no—
575C23×C79—21no—
576C23×C79C23×C412yes—
577C23×C79C23×C412yes—
578C23×C79C23×C412yes—
579C23×C79C23×C412yes—
580C23×C79C2511yescharacteristic
581Q8×C79—44no—
582Q8×C79—44no—
583D4×C79—44no—
584D4×C79—44no—
585D4×C79—44no—
586D4×C79—44no—
587D4×C79—44no—
588D4×C79—44no—
589C2×C4×C79—21no—
590C2×C4×C79—21no—
591C2×C4×C79—21no—
592C2×C4×C79—21no—
593C2×C4×C79—21no—
594C2×C4×C79—21no—
595C2×C4×C79—21no—
596C2×C4×C79—21no—
597C2×C4×C79—21no—
598C2×C4×C79—21no—
599C2×C4×C79—21no—
600C2×C4×C79—21no—
601C2×C4×C79—21no—
602C2×C4×C79—21no—
603C2×C4×C79—21no—
604C2×C4×C79—21no—
605C2×C4×C79—21no—
606C2×C4×C79—21no—
607C2×C4×C79—21no—
608C2×C4×C79—21no—
609C2×C4×C79—21no—
610C2×C4×C79—21no—
611C2×C4×C79—44no—
612C2×C4×C79—44no—
613C2×C4×C79—44no—
614C2×C4×C79—44no—
615C2×C4×C79C23×C412yes—
616C2×C4×C79C23×C412yes—
617C2×C4×C79C23×C412yes—
618C2×C4×C79C23×C412yes—
619C2×C4×C79C23×C412yes—
620C2×C4×C79C23×C412yes—
621C2×C4×C79C23×C412yes—
622C2×C4×C79C23×C412yes—
623C2×C4×C79C23×C412yes—
624C2×C4×C79C23×C412yes—
625C2×C4×C79C23×C412yes—
626C2×Dic79—21no—
627C2×Dic79—21no—
628C2×Dic79—21no—
629C2×Dic79—21no—
630C2×Dic79—21no—
631C2×Dic79—21no—
632C2×Dic79—21no—
633C2×Dic79—21no—
634C2×Dic79—21no—
635C2×Dic79—21no—
636C2×Dic79—21no—
637C2×Dic79—21no—
638C2×Dic79—21no—
639C2×Dic79—21no—
640C2×Dic79—21no—
641C2×Dic79—21no—
642C2×Dic79—21no—
643C2×Dic79—21no—
644C2×Dic79—21no—
645C2×Dic79—21no—
646C2×Dic79—21no—
647C2×Dic79—21no—
648C2×Dic79—21no—
649C2×Dic79—21no—
650C2×Dic79—21no—
651C2×Dic79—21no—
652C2×Dic79—21no—
653C2×Dic79—21no—
654C2×Dic79—21no—
655C2×Dic79—21no—
656C2×Dic79—21no—
657C2×Dic79—21no—
658C2×Dic79—21no—
659C2×Dic79—21no—
660C2×Dic79—21no—
661C2×Dic79—21no—
662C2×Dic79—21no—
663C2×Dic79—21no—
664C2×Dic79—21no—
665C2×Dic79—21no—
666C2×Dic79—21no—
667C2×Dic79—21no—
668C2×Dic79—21no—
669C2×Dic79—21no—
670C2×Dic79—21no—
671C2×Dic79—44no—
672C2×Dic79—44no—
673C2×Dic79—82no—
674C2×Dic79—82no—
675C2×Dic79—82no—
676C2×Dic79—82no—
677C2×Dic79—82no—
678C2×Dic79—82no—
679C2×Dic79H(5,𝔽2)12yes—
680C2×Dic79H(5,𝔽2)12yes—
681C2×Dic792−1+412yes—
682C22×C79—22no—
683C22×C79—22no—
684C22×C79—22no—
685C22×C79—22no—
686C22×C79—22no—
687C22×C79—22no—
688C22×C79—22no—
689C22×C79—22no—
690C22×C79—22no—
691C22×C79—22no—
692C22×C79—22no—
693C22×C79—22no—
694C22×C79—41no—
695C22×C79—41no—
696C22×C79—41no—
697C22×C79—41no—
698C22×C79—41no—
699C22×C79—41no—
700C22×C79—41no—
701C22×C79—41no—
702C22×C79—41no—
703C22×C79—41no—
704C22×C79—41no—
705C22×C79—41no—
706C22×C79—41no—
707C22×C79—41no—
708C22×C79—41no—
709C22×C79—41no—
710C22×C79C24×C411yescharacteristic
711C22×C79C2×H(5,𝔽2)11yescharacteristic
712C22×C79C2×H(5,𝔽2)11yescharacteristic
713C22×C79C2×2−1+411yescharacteristic
714C22×C79#58511yescharacteristic
715C22×C79#58511yescharacteristic
716C22×C79#58511yescharacteristic
717C4×C79—22no—
718C4×C79—22no—
719C4×C79—22no—
720C4×C79—22no—
721C4×C79—22no—
722C4×C79—22no—
723C4×C79—22no—
724C4×C79—22no—
725C4×C79—22no—
726C4×C79—22no—
727C4×C79—22no—
728Dic79—22no—
729Dic79—22no—
730Dic79—22no—
731Dic79—41no—
732Dic79—41no—
733Dic79—41no—
734Dic79—41no—
735Dic79—41no—
736Dic79—41no—
737Dic79—41no—
738Dic79—41no—
739Dic79—41no—
740Dic79—41no—
741Dic79—41no—
742Dic79—41no—
743Dic79—41no—
744#34513—791nomaximal, Sylow
745C2×C79—42no—
746C2×C79—42no—
747C2×C79—42no—
748C2×C79—42no—
749C2×C79C4×H(5,𝔽2)11yescharacteristic
750C2×C79C4×H(5,𝔽2)11yescharacteristic
751C2×C79C4×2−1+411yescharacteristic
752C2×C79#353311yescharacteristic
753C2×C79#353611yescharacteristic
754C2×C79#356211yescharacteristic
755C2×C79#356511yescharacteristic
756C2×#562D7911yescharacteristic
757#2378—791no—
758#2377—791no—
759#2376—791no—
760#2370—791no—
761#2368—791no—
762#2367—791no—
763#2367—791no—
764#2364—791no—
765#2364—791no—
766#2363—791no—
767#2362—791no—
768#2362—791no—
769#2359—791no—
770#2359—791no—
771#2359—791no—
772#2337—791no—
773#2337—791no—
774#2336—791no—
775#2335—791no—
776#2335—791no—
777#2335—791no—
778#2329—791no—
779#2329—791no—
780#2325—791no—
781#2324—791no—
782#2324—791no—
783#2323—791no—
784C4×C22⋊Q8—791no—
785C4×#123—791no—
786C4×#121—791no—
787C79#3451311yescharacteristic, complemented, Sylow
788#562Dic79116yescomplemented
789C2×#125C2×D7911yescharacteristic
790C2×#124C2×D7911yescharacteristic
791C2×#124C2×D7911yescharacteristic
792C2×#123C2×D7911yescharacteristic
793C2×#123C2×D7911yescharacteristic
794C2×#123C2×D7911yescharacteristic
795C2×#123C2×D7911yescharacteristic
796C2×C22⋊Q8C2×D7911yescharacteristic
797C2×C22⋊Q8C2×D7911yescharacteristic
798C2×C22⋊Q8C2×D7911yescharacteristic
799C2×C22⋊Q8C2×D7911yescharacteristic
800C2×#121C2×D7911yescharacteristic
801C2×#121C2×D7911yescharacteristic
802C2×#121C2×D7911yescharacteristic
803C2×#121C2×D7911yescharacteristic
804C2×C4×Q8—791no—
805C2×C4×Q8—791no—
806C2×C4×D4—791no—
807C2×C4×D4—791no—
808C2×C4×D4—791no—
809C2×C4×D4—791no—
810C2×C4×D4—791no—
811C2×C4×D4—791no—
812C2×#117—791no—
813C2×#117—791no—
814C2×#117—791no—
815C22×C42—791no—
816#391—791no—
817#391—791no—
818#391—791no—
819#391—791no—
820#391—791no—
821#391—791no—
822#390—791no—
823#390—791no—
824#390—791no—
825#390—791no—
826#390—791no—
827#390—791no—
828#389—791no—
829#389—791no—
830#389—791no—
831#389—791no—
832#389—791no—
833#389—791no—
834#389—791no—
835#389—791no—
836#389—791no—
837#389—791no—
838#388—791no—
839#388—791no—
840#388—791no—
841#388—791no—
842#388—791no—
843#388—791no—
844#388—791no—
845#388—791no—
846#388—791no—
847#388—791no—
848#388—791no—
849#388—791no—
850#388—791no—
851#388—791no—
852#388—791no—
853#388—791no—
854#388—791no—
855#388—791no—
856#388—791no—
857#388—791no—
858#388—791no—
859#388—791no—
860#388—791no—
861#388—791no—
862#387—791no—
863#387—791no—
864#387—791no—
865#387—791no—
866#387—791no—
867#387—791no—
868#387—791no—
869#387—791no—
870#387—791no—
871#387—791no—
872#387—791no—
873#387—791no—
874#387—791no—
875#387—791no—
876#387—791no—
877#387—791no—
878#387—791no—
879#387—791no—
880#387—791no—
881#387—791no—
882#386—791no—
883#386—791no—
884#386—791no—
885#386—791no—
886#386—791no—
887#386—791no—
888#386—791no—
889#386—791no—
890#386—791no—
891#386—791no—
892#386—791no—
893#386—791no—
894#385—791no—
895#385—791no—
896#385—791no—
897#385—791no—
898#385—791no—
899#385—791no—
900#385—791no—
901#385—791no—
902#385—791no—
903#385—791no—
904#385—791no—
905#385—791no—
906#383—791no—
907#381—791no—
908#380—791no—
909#380—791no—
910#380—791no—
911#380—791no—
912#380—791no—
913C4×C4⋊C4—791no—
914C4×C4⋊C4—791no—
915C4×C4⋊C4—791no—
916C4×C4⋊C4—791no—
917C4×C4⋊C4—791no—
918C4×C4⋊C4—791no—
919C4×C4⋊C4—791no—
920C4×C4⋊C4—791no—
921C4×C4⋊C4—791no—
922C4×C4⋊C4—791no—
923C4×C4⋊C4—791no—
924C4×C4⋊C4—791no—
925C4×C4⋊C4—791no—
926C4×C22⋊C4—791no—
927C4×C22⋊C4—791no—
928C4×C22⋊C4—791no—
929C4×C22⋊C4—791no—
930C4×C22⋊C4—791no—
931C4×C22⋊C4—791no—
932C4×C22⋊C4—791no—
933C4×C22⋊C4—791no—
934C4×C22⋊C4—791no—
935C4×C22⋊C4—791no—
936C4×C22⋊C4—791no—
937C4×C22⋊C4—791no—
938C4×C22⋊C4—791no—
939C4×C22⋊C4—791no—
940C4×C22⋊C4—791no—
941C2×#95—791no—
942C2×#95—791no—
943C2×#95—791no—
944C22×Q8C22×D7911yescharacteristic
945C22×Q8C22×D7911yescharacteristic
946C22×D4C22×D7911yescharacteristic
947C22×D4C22×D7911yescharacteristic
948C22×D4C22×D7911yescharacteristic
949C22×D4C22×D7911yescharacteristic
950C22×D4C22×D7911yescharacteristic
951C22×D4C22×D7911yescharacteristic
952C23×C4—791no—
953C23×C4—791no—
954C23×C4—791no—
955C23×C4—791no—
956C23×C4—791no—
957C23×C4—791no—
958C23×C4—791no—
959C23×C4—791no—
960C23×C4C22×D7911yescharacteristic
961C23×C4C22×D7911yescharacteristic
962C23×C4C22×D7911yescharacteristic
963C23×C4C22×D7911yescharacteristic
964#125C2×Dic7918yescomplemented
965#124C2×Dic7918yescomplemented
966#124C2×Dic7918yescomplemented
967#123C2×Dic7918yescomplemented
968#123C2×Dic7918yescomplemented
969#123C2×Dic7918yescomplemented
970#123C2×Dic7918yescomplemented
971C22⋊Q8C2×Dic7918yescomplemented
972C22⋊Q8C2×Dic7918yescomplemented
973C22⋊Q8C2×Dic7918yescomplemented
974C22⋊Q8C2×Dic7918yescomplemented
975#121C2×Dic7918yescomplemented
976#121C2×Dic7918yescomplemented
977#121C2×Dic7918yescomplemented
978#121C2×Dic7918yescomplemented
979C4×Q8—3162no—
980C4×Q8—3162no—
981C4×D4—3162no—
982C4×D4—3162no—
983C4×D4—3162no—
984C4×D4—3162no—
985C4×D4—3162no—
986C4×D4—3162no—
987#117—3162no—
988#117—3162no—
989#117—3162no—
990C2×C4⋊C4—791no—
991C2×C4⋊C4—791no—
992C2×C4⋊C4—791no—
993C2×C4⋊C4—791no—
994C2×C4⋊C4—791no—
995C2×C4⋊C4—791no—
996C2×C4⋊C4—791no—
997C2×C4⋊C4—791no—
998C2×C4⋊C4—791no—
999C2×C4⋊C4—791no—
1000C2×C4⋊C4—791no—
1001C2×C4⋊C4—791no—
1002C2×C4⋊C4—791no—
1003C2×C4⋊C4—791no—
1004C2×C4⋊C4—791no—
1005C2×C4⋊C4—791no—
1006C2×C4⋊C4—791no—
1007C2×C4⋊C4—791no—
1008C2×C4⋊C4—791no—
1009C2×C4⋊C4—791no—
1010C2×C4⋊C4—791no—
1011C2×C4⋊C4—791no—
1012C2×C4⋊C4C22×D7911yescharacteristic
1013C2×C4⋊C4C22×D7911yescharacteristic
1014C2×C4⋊C4C22×D7911yescharacteristic
1015C2×C4⋊C4C22×D7911yescharacteristic
1016C2×C4⋊C4C22×D7911yescharacteristic
1017C2×C4⋊C4C22×D7911yescharacteristic
1018C2×C4⋊C4C22×D7911yescharacteristic
1019C2×C4⋊C4C22×D7911yescharacteristic
1020C2×C4⋊C4C22×D7911yescharacteristic
1021C2×C4⋊C4C22×D7911yescharacteristic
1022C2×C22⋊C4—791no—
1023C2×C22⋊C4—791no—
1024C2×C22⋊C4—791no—
1025C2×C22⋊C4—791no—
1026C2×C22⋊C4—791no—
1027C2×C22⋊C4—791no—
1028C2×C22⋊C4—791no—
1029C2×C22⋊C4—791no—
1030C2×C22⋊C4—791no—
1031C2×C22⋊C4—791no—
1032C2×C22⋊C4—791no—
1033C2×C22⋊C4—791no—
1034C2×C22⋊C4—791no—
1035C2×C22⋊C4—791no—
1036C2×C22⋊C4—791no—
1037C2×C22⋊C4—791no—
1038C2×C22⋊C4—791no—
1039C2×C22⋊C4—791no—
1040C2×C22⋊C4—791no—
1041C2×C22⋊C4—791no—
1042C2×C22⋊C4—791no—
1043C2×C22⋊C4—791no—
1044C2×C22⋊C4—791no—
1045C2×C22⋊C4—791no—
1046C2×C22⋊C4C22×D7911yescharacteristic
1047C2×C22⋊C4C22×D7911yescharacteristic
1048C2×C22⋊C4C22×D7911yescharacteristic
1049C2×C22⋊C4C22×D7911yescharacteristic
1050C2×C22⋊C4C22×D7911yescharacteristic
1051C2×C22⋊C4C22×D7911yescharacteristic
1052C2×C22⋊C4C22×D7911yescharacteristic
1053C2×C22⋊C4C22×D7911yescharacteristic
1054C2×C22⋊C4C22×D7911yescharacteristic
1055C2×C22⋊C4C22×D7911yescharacteristic
1056C2×C22⋊C4C22×D7911yescharacteristic
1057C2×C22⋊C4C22×D7911yescharacteristic
1058C2×C42—3162no—
1059C2×C42—791no—
1060C2×C42—791no—
1061C2×C42—791no—
1062C2×C42—791no—
1063C2×C42—791no—
1064C2×C42—791no—
1065C2×C42—791no—
1066C2×C42—791no—
1067C2×C42—791no—
1068C2×C42—791no—
1069C2×C42—791no—
1070C2×C42—791no—
1071C2×C42—791no—
1072C2×C42—791no—
1073C2×C42—791no—
1074C2×C42—791no—
1075C2×C42—791no—
1076C2×C42—791no—
1077C2×C42—791no—
1078C2×C42—791no—
1079C2×C42—791no—
1080C2×C42—791no—
1081C2×C42C22×D7911yescharacteristic
1082#95—791no—
1083#95—791no—
1084#95—791no—
1085#95—791no—
1086#95—791no—
1087#95—791no—
1088#95—791no—
1089#95—791no—
1090#95—791no—
1091#95—791no—
1092#95—791no—
1093#95—791no—
1094#95—791no—
1095#95—791no—
1096#95—791no—
1097#95—791no—
1098#95—791no—
1099#95—791no—
1100#95—791no—
1101#95—791no—
1102#95—791no—
1103#95—791no—
1104#95—791no—
1105#95—791no—
1106#95—791no—
1107#95—791no—
1108#95—791no—
1109#95—791no—
1110#95—791no—
1111#95—791no—
1112#95—791no—
1113#95—791no—
1114#95—791no—
1115#95—791no—
1116#95—791no—
1117#95—791no—
1118#95—791no—
1119#95—791no—
1120#95—791no—
1121#95—791no—
1122#95—791no—
1123#95—791no—
1124#95—791no—
1125#95—791no—
1126C24C23×D7911yescharacteristic
1127C24C23×D7911yescharacteristic
1128C24C23×D7911yescharacteristic
1129C24C23×D7911yescharacteristic
1130C2×Q8—41no—
1131C2×Q8—41no—
1132C2×Q8—41no—
1133C2×Q8—41no—
1134C2×Q8C22×Dic7914yes—
1135C2×Q8C22×Dic7914yes—
1136C2×D4—41no—
1137C2×D4—41no—
1138C2×D4—41no—
1139C2×D4—41no—
1140C2×D4—41no—
1141C2×D4—41no—
1142C2×D4—41no—
1143C2×D4—41no—
1144C2×D4—41no—
1145C2×D4—41no—
1146C2×D4—41no—
1147C2×D4—41no—
1148C2×D4C22×Dic7914yes—
1149C2×D4C22×Dic7914yes—
1150C2×D4C22×Dic7914yes—
1151C2×D4C22×Dic7914yes—
1152C2×D4C22×Dic7914yes—
1153C2×D4C22×Dic7914yes—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—3161no—
1163C22×C4—3161no—
1164C22×C4—3161no—
1165C22×C4—3161no—
1166C22×C4—3161no—
1167C22×C4—3161no—
1168C22×C4—3161no—
1169C22×C4—3161no—
1170C22×C4—3161no—
1171C22×C4—3161no—
1172C22×C4—3161no—
1173C22×C4—3161no—
1174C22×C4—3161no—
1175C22×C4—3161no—
1176C22×C4—3161no—
1177C22×C4—3161no—
1178C22×C4—3161no—
1179C22×C4—3161no—
1180C22×C4—791no—
1181C22×C4—791no—
1182C22×C4—791no—
1183C22×C4—791no—
1184C22×C4—791no—
1185C22×C4—791no—
1186C22×C4—791no—
1187C22×C4—791no—
1188C22×C4—791no—
1189C22×C4—791no—
1190C22×C4—791no—
1191C22×C4—791no—
1192C22×C4—791no—
1193C22×C4—791no—
1194C22×C4—791no—
1195C22×C4—791no—
1196C22×C4—1582no—
1197C22×C4—1582no—
1198C22×C4—1582no—
1199C22×C4—1582no—
1200C22×C4—1582no—
1201C22×C4—1582no—
1202C22×C4C22×Dic7914yes—
1203C22×C4C22×Dic7914yes—
1204C22×C4C22×Dic7914yes—
1205C22×C4C22×Dic7914yes—
1206C22×C4C23×D7911yescharacteristic
1207C22×C4C23×D7911yescharacteristic
1208C22×C4C23×D7911yescharacteristic
1209C22×C4C23×D7911yescharacteristic
1210C22×C4C23×D7911yescharacteristic
1211C22×C4C23×D7911yescharacteristic
1212C22×C4C23×D7911yescharacteristic
1213C22×C4C23×D7911yescharacteristic
1214C22×C4C23×D7911yescharacteristic
1215C22×C4C23×D7911yescharacteristic
1216C22×C4C23×D7911yescharacteristic
1217C4⋊C4—3161no—
1218C4⋊C4—3161no—
1219C4⋊C4—3161no—
1220C4⋊C4—3161no—
1221C4⋊C4—3161no—
1222C4⋊C4—3161no—
1223C4⋊C4—3161no—
1224C4⋊C4—3161no—
1225C4⋊C4—3161no—
1226C4⋊C4—3161no—
1227C4⋊C4—3161no—
1228C4⋊C4—3161no—
1229C4⋊C4—3161no—
1230C4⋊C4—3161no—
1231C4⋊C4—3161no—
1232C4⋊C4—3161no—
1233C4⋊C4—1582no—
1234C4⋊C4—1582no—
1235C4⋊C4—1582no—
1236C4⋊C4—1582no—
1237C4⋊C4—1582no—
1238C4⋊C4—1582no—
1239C4⋊C4C22×Dic7914yes—
1240C4⋊C4C22×Dic7914yes—
1241C4⋊C4C22×Dic7914yes—
1242C4⋊C4C22×Dic7914yes—
1243C4⋊C4C22×Dic7914yes—
1244C4⋊C4C22×Dic7914yes—
1245C4⋊C4C22×Dic7914yes—
1246C4⋊C4C22×Dic7914yes—
1247C4⋊C4C22×Dic7914yes—
1248C4⋊C4C22×Dic7914yes—
1249C22⋊C4—3161no—
1250C22⋊C4—3161no—
1251C22⋊C4—3161no—
1252C22⋊C4—3161no—
1253C22⋊C4—3161no—
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—3161no—
1264C22⋊C4—3161no—
1265C22⋊C4—3161no—
1266C22⋊C4—3161no—
1267C22⋊C4—1582no—
1268C22⋊C4—1582no—
1269C22⋊C4—1582no—
1270C22⋊C4—1582no—
1271C22⋊C4—1582no—
1272C22⋊C4—1582no—
1273C22⋊C4C22×Dic7914yes—
1274C22⋊C4C22×Dic7914yes—
1275C22⋊C4C22×Dic7914yes—
1276C22⋊C4C22×Dic7914yes—
1277C22⋊C4C22×Dic7914yes—
1278C22⋊C4C22×Dic7914yes—
1279C22⋊C4C22×Dic7914yes—
1280C22⋊C4C22×Dic7914yes—
1281C22⋊C4C22×Dic7914yes—
1282C22⋊C4C22×Dic7914yes—
1283C22⋊C4C22×Dic7914yes—
1284C22⋊C4C22×Dic7914yes—
1285C42—3161no—
1286C42—3161no—
1287C42—3161no—
1288C42—3161no—
1289C42—3161no—
1290C42—3161no—
1291C42—3161no—
1292C42—3161no—
1293C42—3161no—
1294C42—3161no—
1295C42—3161no—
1296C42—3161no—
1297C42—3161no—
1298C42—3161no—
1299C42—3161no—
1300C42—3161no—
1301C42—3161no—
1302C42—1582no—
1303C42—1582no—
1304C42—1582no—
1305C42—1582no—
1306C42—1582no—
1307C42C22×Dic7914yes—
1308C23—21no—
1309C23—21no—
1310C23—21no—
1311C23—21no—
1312C23—21no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23C23×Dic7912yes—
1333C23C23×Dic7912yes—
1334C23C23×Dic7912yes—
1335C23C23×Dic7912yes—
1336C23C24×D7911yescharacteristic
1337Q8—44no—
1338Q8—44no—
1339D4—44no—
1340D4—44no—
1341D4—44no—
1342D4—44no—
1343D4—44no—
1344D4—44no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—44no—
1368C2×C4—44no—
1369C2×C4—44no—
1370C2×C4—44no—
1371C2×C4—3164no—
1372C2×C4—3164no—
1373C2×C4—792no—
1374C2×C4—792no—
1375C2×C4—792no—
1376C2×C4—6322no—
1377C2×C4—6322no—
1378C2×C4—6322no—
1379C2×C4—6322no—
1380C2×C4—6322no—
1381C2×C4—6322no—
1382C2×C4—1581no—
1383C2×C4—1581no—
1384C2×C4—1581no—
1385C2×C4—1581no—
1386C2×C4—1581no—
1387C2×C4—1581no—
1388C2×C4—1581no—
1389C2×C4—1581no—
1390C2×C4—1581no—
1391C2×C4—1581no—
1392C2×C4—1581no—
1393C2×C4—1581no—
1394C2×C4—1581no—
1395C2×C4—1581no—
1396C2×C4—1581no—
1397C2×C4—1581no—
1398C2×C4—1581no—
1399C2×C4—1581no—
1400C2×C4—1581no—
1401C2×C4—1581no—
1402C2×C4—1581no—
1403C2×C4—1581no—
1404C2×C4—1581no—
1405C2×C4—1581no—
1406C2×C4—1581no—
1407C2×C4—1581no—
1408C2×C4—1581no—
1409C2×C4—1581no—
1410C2×C4—1581no—
1411C2×C4—1581no—
1412C2×C4—1581no—
1413C2×C4—1581no—
1414C2×C4—1581no—
1415C2×C4—1581no—
1416C2×C4—1581no—
1417C2×C4—1581no—
1418C2×C4—1581no—
1419C2×C4—1581no—
1420C2×C4—1581no—
1421C2×C4—1581no—
1422C2×C4—1581no—
1423C2×C4—1581no—
1424C2×C4—1581no—
1425C2×C4—1581no—
1426C2×C4—1581no—
1427C2×C4C23×Dic7912yes—
1428C2×C4C23×Dic7912yes—
1429C2×C4C23×Dic7912yes—
1430C2×C4C23×Dic7912yes—
1431C2×C4C23×Dic7912yes—
1432C2×C4C23×Dic7912yes—
1433C2×C4C23×Dic7912yes—
1434C2×C4C23×Dic7912yes—
1435C2×C4C23×Dic7912yes—
1436C2×C4C23×Dic7912yes—
1437C2×C4C23×Dic7912yes—
1438C22—22no—
1439C22—22no—
1440C22—22no—
1441C22—22no—
1442C22—22no—
1443C22—22no—
1444C22—22no—
1445C22—22no—
1446C22—22no—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—41no—
1451C22—41no—
1452C22—41no—
1453C22—41no—
1454C22—41no—
1455C22—41no—
1456C22—41no—
1457C22—41no—
1458C22—41no—
1459C22—41no—
1460C22—41no—
1461C22—41no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22C24×Dic7911yescharacteristic
1467C22H(5,𝔽2)×D7911yescharacteristic
1468C22H(5,𝔽2)×D7911yescharacteristic
1469C222−1+4×D7911yescharacteristic
1470C22#1909939811yescharacteristic
1471C22#1909939811yescharacteristic
1472C22#1909940011yescharacteristic
1473C4—22no—
1474C4—22no—
1475C4—22no—
1476C4—22no—
1477C4—22no—
1478C4—22no—
1479C4—22no—
1480C4—22no—
1481C4—22no—
1482C4—22no—
1483C4—22no—
1484C4—3161no—
1485C4—3161no—
1486C4—3161no—
1487C4—3161no—
1488C4—3161no—
1489C4—3161no—
1490C4—3161no—
1491C4—3161no—
1492C4—3161no—
1493C4—3161no—
1494C4—3161no—
1495C4—3161no—
1496C4—3161no—
1497C4—1582no—
1498C4—1582no—
1499C4—1582no—
1500C2—42no—
1501C2—42no—
1502C2—42no—
1503C2—42no—
1504C2H(5,𝔽2)×Dic7911yescharacteristic
1505C2H(5,𝔽2)×Dic7911yescharacteristic
1506C22−1+4×Dic7911yescharacteristic
1507C2#2377756211yescharacteristic
1508C2#2377761911yescharacteristic
1509C2#2377798511yescharacteristic
1510C2#2377803411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
Fitting, prime radicalC2×#562×C79C2
socle, cosocleC23×C79C25
hypercenterC2×#562D79
hypocenterC79#34513
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #23766566C2semidirect
2. #23766557C2semidirect
3. #23766548C2semidirect
4. #23766500C2semidirect
5. #23766485C2semidirect
6. #23766475C2semidirect
7. #23766475C2semidirect
8. #23766452C2semidirect
9. #23766452C2semidirect
10. #23766442C2semidirect
11. #23766431C2semidirect
12. #23766431C2semidirect
13. #23766396C2semidirect
14. #23766396C2semidirect
15. #23766396C2semidirect
16. #23766215C2semidirect
17. #23766215C2semidirect
18. #23766206C2semidirect
19. #23766194C2semidirect
20. #23766194C2semidirect
21. #23766194C2semidirect
22. #23766135C2semidirect
23. #23766135C2semidirect
24. #23766105C2semidirect
25. #23766095C2semidirect
26. #23766095C2semidirect
27. #23766084C2semidirect
28. C22⋊Q8×Dic79C2semidirect
29. #123×Dic79C2semidirect
30. #121×Dic79C2semidirect
172. #562×C79C4semidirect
332. #125×C79C2×C4semidirect
333. #124×C79C2×C4semidirect
334. #124×C79C2×C4semidirect
335. #123×C79C2×C4semidirect
336. #123×C79C2×C4semidirect
337. #123×C79C2×C4semidirect
338. #123×C79C2×C4semidirect
339. C22⋊Q8×C79C2×C4semidirect
340. C22⋊Q8×C79C2×C4semidirect
341. C22⋊Q8×C79C2×C4semidirect
342. C22⋊Q8×C79C2×C4semidirect
343. #121×C79C2×C4semidirect
344. #121×C79C2×C4semidirect
345. #121×C79C2×C4semidirect
346. #121×C79C2×C4semidirect
787. C79#34513semidirect
788. #562Dic79semidirect
964. #125C2×Dic79semidirect
965. #124C2×Dic79semidirect
966. #124C2×Dic79semidirect
967. #123C2×Dic79semidirect
968. #123C2×Dic79semidirect
969. #123C2×Dic79semidirect
970. #123C2×Dic79semidirect
971. C22⋊Q8C2×Dic79semidirect
972. C22⋊Q8C2×Dic79semidirect
973. C22⋊Q8C2×Dic79semidirect
974. C22⋊Q8C2×Dic79semidirect
975. #121C2×Dic79semidirect
976. #121C2×Dic79semidirect
977. #121C2×Dic79semidirect
978. #121C2×Dic79semidirect

Maximal subgroups

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

subgroupindex
#237665662
#237665572
#237665482
#237665002
#237664852
#237664752
#237664522
#237664422
#237664312
#237663962
#237662152
#237662062
#237661942
#237661352
#237661052
#237660952
#237660842
C22⋊Q8×Dic792
#123×Dic792
#121×Dic792
C2×#562×C792
#3451379