Finite Group Databasebeta

← C2×#23766481 #34447900

Subgroups — C2×#23766481 #34447900

Order 20224.

3094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579138C211yesmaximal, characteristic
2#23766481C2116yesmaximal, direct product factor
3C2×#19098468C211yesmaximal, characteristic, complemented
4C2×#19098467C211yesmaximal, characteristic, complemented
5C2×#19098448C211yesmaximal, characteristic, complemented
6C2×#19098445C211yesmaximal, characteristic, complemented
7C2×#19098444C211yesmaximal, characteristic, complemented
8C2×#19098444C211yesmaximal, characteristic, complemented
9C2×#19098435C211yesmaximal, characteristic
10C2×C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
11C2×#19098414C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic79C211yesmaximal, characteristic
13C2×C22⋊C4×Dic79C211yesmaximal, characteristic
14C2×C4×C22⋊Dic79C211yesmaximal, characteristic
15C22×C79⋊#95C211yesmaximal, characteristic
16C2×#385×C79C211yesmaximal, characteristic
17C23×Dic158C2211yescharacteristic
18C24×Dic79C2211yescharacteristic
19C24×Dic79C2211yescharacteristic
20C2×#14579138C4116yescomplemented
21C2×#14579138C2218yes—
22C22×C4⋊Dic79C2211yescharacteristic
23C22×Dic79⋊C4C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×Dic79⋊C4C2211yescharacteristic
27C22×C22⋊Dic79C2211yescharacteristic
28C22×C22⋊Dic79C2211yescharacteristic
29C22×C4×Dic79C2211yescharacteristic
30C22×C4×Dic79C2211yescharacteristic
31C22×C4×Dic79C2211yescharacteristic
32C22×C4×Dic79C2211yescharacteristic
33C22×C4×Dic79C2211yescharacteristic
34C22×C4×Dic79C2211yescharacteristic
35#19098468C2218yescomplemented
36#19098467C2218yescomplemented
37#19098448C2218yescomplemented
38#19098445C2218yescomplemented
39#19098444C2218yescomplemented
40#19098444C2218yescomplemented
41#19098435C2218yes—
42C4⋊C4×Dic79C2218yescomplemented
43#19098414C2218yescomplemented
44C22⋊C4×Dic79C2218yes—
45C22⋊C4×Dic79C2218yes—
46C4×C22⋊Dic79C2218yes—
47C2×C79⋊#95C2211yescharacteristic
48C2×C79⋊#95C2211yescharacteristic
49C2×C79⋊#95C2211yescharacteristic
50C2×C79⋊#95C2211yescharacteristic
51C2×C79⋊#95C2211yescharacteristic
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2218yes—
59C2×C79⋊#95C2211yescharacteristic
60C24×C4×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63C22×C22⋊C4×C79C2211yescharacteristic
64C22×C22⋊C4×C79C2211yescharacteristic
65#385×C79C2218yes—
66C2×#95×C79C2211yescharacteristic
67C2×#95×C79C2211yescharacteristic
68C22×Dic158—42no—
69C22×Dic158—42no—
70C22×Dic158C2×C418yescomplemented
71C22×Dic158C2314yes—
72C23×Dic79—24no—
73C23×Dic79—24no—
74C23×Dic79—42no—
75C23×Dic79—42no—
76C23×Dic79—42no—
77C23×Dic79C2×C418yes—
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2314yes—
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2311yescharacteristic
83C23×Dic79C2311yescharacteristic
84C23×Dic79C2311yescharacteristic
85C23×Dic79C2311yescharacteristic
86C23×Dic79C2311yescharacteristic
87C23×Dic79C2314yes—
88#14579138C2×C4164yescomplemented
89C2×C4⋊Dic79C2×C418yescomplemented
90C2×C4⋊Dic79C2314yes—
91C2×Dic79⋊C4—24no—
92C2×Dic79⋊C4—42no—
93C2×Dic79⋊C4C2×C418yescomplemented
94C2×Dic79⋊C4C2×C418yescomplemented
95C2×Dic79⋊C4C2314yes—
96C2×Dic79⋊C4C2314yes—
97C2×Dic79⋊C4C2314yes—
98C2×Dic79⋊C4C2314yes—
99C2×C22⋊Dic79C2×C418yes—
100C2×C22⋊Dic79Q818yescomplemented
101C2×C22⋊Dic79C2314yes—
102C2×C22⋊Dic79C2314yes—
103C2×C4×Dic79—24no—
104C2×C4×Dic79—24no—
105C2×C4×Dic79—42no—
106C2×C4×Dic79—42no—
107C2×C4×Dic79—42no—
108C2×C4×Dic79—42no—
109C2×C4×Dic79C2314yes—
110C2×C4×Dic79C2314yes—
111C2×C4×Dic79C2314yes—
112C2×C4×Dic79C2314yes—
113C2×C4×Dic79C2314yes—
114C2×C4×Dic79C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127C25×C79C2311yescharacteristic
128C23×C4×C79—24no—
129C23×C4×C79—24no—
130C23×C4×C79—42no—
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2314yes—
135C23×C4×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137C23×C4×C79C2311yescharacteristic
138C2×C4⋊C4×C79—24no—
139C2×C4⋊C4×C79—42no—
140C2×C4⋊C4×C79C2314yes—
141C2×C4⋊C4×C79C2314yes—
142C2×C22⋊C4×C79—24no—
143C2×C22⋊C4×C79C2×C418yes—
144C2×C22⋊C4×C79C2314yes—
145C2×C22⋊C4×C79C2314yes—
146#95×C79C2314yes—
147#95×C79C2314yes—
148C2×Dic158—416no—
149C2×Dic158—44no—
150C2×Dic158—44no—
151C2×Dic158C22×C4116yescomplemented
152C22×Dic79—28no—
153C22×Dic79—22no—
154C22×Dic79—22no—
155C22×Dic79—22no—
156C22×Dic79—22no—
157C22×Dic79—22no—
158C22×Dic79—22no—
159C22×Dic79—28no—
160C22×Dic79—22no—
161C22×Dic79—22no—
162C22×Dic79—22no—
163C22×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—416no—
172C22×Dic79—44no—
173C22×Dic79—44no—
174C22×Dic79—44no—
175C22×Dic79—416no—
176C22×Dic79C22×C414yes—
177C22×Dic79C22×C414yes—
178C22×Dic79C22×C414yes—
179C22×Dic79C22×C414yes—
180C22×Dic79C22×C4116yes—
181C22×Dic79C2×Q814yes—
182C22×Dic79C2×Q814yes—
183C22×Dic79#4114yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C22×Dic79C2412yes—
187C22×Dic79C2412yes—
188C22×Dic79C2412yes—
189C22×Dic79C2412yes—
190C22×Dic79C2412yes—
191C22×Dic79C2412yes—
192C4⋊Dic79C22×C4116yescomplemented
193Dic79⋊C4—28no—
194Dic79⋊C4—44no—
195Dic79⋊C4C22×C4116yescomplemented
196Dic79⋊C4C22×C4116yescomplemented
197C22⋊Dic79C22×C4116yes—
198C22⋊Dic79C2×Q8116yescomplemented
199C4×Dic79—28no—
200C4×Dic79—28no—
201C4×Dic79—44no—
202C4×Dic79—44no—
203C4×Dic79—44no—
204C4×Dic79—44no—
205C24×C79—22no—
206C24×C79—22no—
207C24×C79—22no—
208C24×C79—22no—
209C24×C79C22×C414yes—
210C24×C79C2×Q814yes—
211C24×C79#4114yes—
212C24×C79C2412yes—
213C24×C79C2411yescharacteristic
214C22×C4×C79—22no—
215C22×C4×C79—22no—
216C22×C4×C79—22no—
217C22×C4×C79—22no—
218C22×C4×C79—22no—
219C22×C4×C79—22no—
220C22×C4×C79—22no—
221C22×C4×C79—22no—
222C22×C4×C79—22no—
223C22×C4×C79—28no—
224C22×C4×C79—22no—
225C22×C4×C79—22no—
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79—28no—
231C22×C4×C79—44no—
232C22×C4×C79—416no—
233C22×C4×C79C22×C414yes—
234C22×C4×C79C22×C414yes—
235C22×C4×C79#4114yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C22×C4×C79C2412yes—
241C22×C4×C79C2412yes—
242C4⋊C4×C79—28no—
243C4⋊C4×C79—44no—
244C22⋊C4×C79—28no—
245C22⋊C4×C79C22×C4116yes—
246C23×C79—28no—
247C23×C79—28no—
248C23×C79—28no—
249C23×C79—28no—
250C23×C79—28no—
251C23×C79—28no—
252C23×C79—22no—
253C23×C79—22no—
254C23×C79—22no—
255C23×C79—22no—
256C23×C79C4×Q8116yes—
257C23×C79C23×C414yes—
258C23×C79C23×C412yes—
259C23×C79C22×Q814yes—
260C23×C79C22×Q812yes—
261C23×C79C2×#4112yes—
262C23×C79C2×#4114yes—
263C23×C79C2×#4112yes—
264C23×C79C2×#4112yes—
265C23×C79H(5,𝔽2)12yes—
266C23×C79H(5,𝔽2)12yes—
267C23×C79C2511yescharacteristic
268C2×C4×C79—28no—
269C2×C4×C79—28no—
270C2×C4×C79—28no—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—22no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—416no—
287C2×C4×C79—44no—
288C2×C4×C79—44no—
289C2×C4×C79—44no—
290C2×C4×C79C23×C414yes—
291C2×C4×C79C23×C414yes—
292C2×C4×C79C2×#4114yes—
293C2×Dic79—28no—
294C2×Dic79—28no—
295C2×Dic79—28no—
296C2×Dic79—28no—
297C2×Dic79—28no—
298C2×Dic79—28no—
299C2×Dic79—28no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—416no—
318C2×Dic79—416no—
319C2×Dic79—44no—
320C2×Dic79C23×C414yes—
321C2×Dic79C23×C414yes—
322C2×Dic79C23×C414yes—
323C2×Dic79C23×C414yes—
324C2×Dic79C22×Q814yes—
325C2×Dic79C22×Q814yes—
326C2×Dic79C2×#4114yes—
327Dic158—416no—
328C22×C79—232no—
329C22×C79—24no—
330C22×C79—24no—
331C22×C79—24no—
332C22×C79—24no—
333C22×C79—24no—
334C22×C79—24no—
335C22×C79C2×C4×Q818yes—
336C22×C79C2×C4×Q814yes—
337C22×C79C4×#4114yes—
338C22×C79#51814yes—
339C22×C79#55114yes—
340C22×C79#55114yes—
341C22×C79#55414yes—
342C22×C79#55414yes—
343C22×C79C24×C411yescharacteristic
344C22×C79C23×Q811yescharacteristic
345C22×C79C22×#4111yescharacteristic
346C22×C79C22×#4111yescharacteristic
347C22×C79C22×#4111yescharacteristic
348C22×C79C2×H(5,𝔽2)11yescharacteristic
349C22×C79C2×H(5,𝔽2)11yescharacteristic
350C4×C79—24no—
351C4×C79—24no—
352C4×C79—24no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79—42no—
356Dic79—24no—
357Dic79—24no—
358Dic79—24no—
359Dic79—24no—
360Dic79—24no—
361Dic79—24no—
362Dic79—24no—
363Dic79—42no—
364C2×#2368—791nomaximal, Sylow
365C2×C79—28no—
366C2×C79#236818yescomplemented
367C2×C79C22×C4×Q811yescharacteristic
368C2×C79C2×C4×#4111yescharacteristic
369C2×C79C2×#51811yescharacteristic
370C2×C79C2×#55111yescharacteristic
371C2×C79C2×#55111yescharacteristic
372C2×C79C2×#55411yescharacteristic
373C2×C79C2×#55411yescharacteristic
374C22×C22⋊Q8—791no—
375#2368—7916no—
376C2×#391—791no—
377C2×#391—791no—
378C2×#387—791no—
379C2×#387—791no—
380C2×#387—791no—
381C2×#387—791no—
382C2×#385—791no—
383C2×#385D7911yescharacteristic
384C2×C4×C4⋊C4—791no—
385C2×C4×C4⋊C4—791no—
386C2×C4×C22⋊C4—791no—
387C2×C4×C22⋊C4—791no—
388C2×C4×C22⋊C4—791no—
389C22×#95—791no—
390C79C2×#236811yescharacteristic, complemented, Sylow
391C23×Q8—791no—
392C24×C4—791no—
393C24×C4—791no—
394C24×C4C2×D7911yescharacteristic
395C2×C22⋊Q8—798no—
396C2×C22⋊Q8—7916no—
397C22×C4⋊C4—791no—
398C22×C4⋊C4—791no—
399C22×C4⋊C4—791no—
400C22×C4⋊C4—791no—
401C22×C4⋊C4—791no—
402C22×C4⋊C4C2×D7911yescharacteristic
403C22×C4⋊C4C2×D7911yescharacteristic
404C22×C22⋊C4—791no—
405C22×C22⋊C4—791no—
406C22×C22⋊C4C2×D7911yescharacteristic
407C22×C22⋊C4C2×D7911yescharacteristic
408C22×C42—791no—
409C22×C42—791no—
410C22×C42—791no—
411C22×C42—791no—
412C22×C42—791no—
413C22×C42—791no—
414#391—798no—
415#391—798no—
416#387—798no—
417#387—798no—
418#387—798no—
419#387—798no—
420#385—798no—
421#385C2×D7918yes—
422C4×C4⋊C4—798no—
423C4×C4⋊C4—798no—
424C4×C22⋊C4—798no—
425C4×C22⋊C4—798no—
426C4×C22⋊C4—798no—
427C2×#95—798no—
428C2×#95—791no—
429C2×#95—791no—
430C2×#95—791no—
431C2×#95—791no—
432C2×#95—791no—
433C2×#95—791no—
434C2×#95—791no—
435C2×#95—791no—
436C2×#95—791no—
437C2×#95—791no—
438C2×#95—791no—
439C2×#95—791no—
440C2×#95C2×D7911yescharacteristic
441C2×#95C2×D7911yescharacteristic
442C25C22×D7911yescharacteristic
443C22×Q8—3162no—
444C22×Q8—3162no—
445C22×Q8—798no—
446C22×Q8—794no—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—42no—
450C23×C4—3162no—
451C23×C4—3162no—
452C23×C4—3162no—
453C23×C4—798no—
454C23×C4—794no—
455C23×C4—794no—
456C23×C4—791no—
457C23×C4—791no—
458C23×C4—791no—
459C23×C4—791no—
460C23×C4—791no—
461C23×C4—791no—
462C23×C4—791no—
463C23×C4—791no—
464C23×C4—1584no—
465C23×C4—1584no—
466C23×C4C22×D7911yescharacteristic
467C23×C4C22×D7911yescharacteristic
468C23×C4C22×D7911yescharacteristic
469C23×C4C22×D7914yes—
470C23×C4C22×D7911yescharacteristic
471C23×C4C22×D7911yescharacteristic
472C23×C4C22×D7911yescharacteristic
473C22⋊Q8—7964no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—3162no—
477C2×C4⋊C4—794no—
478C2×C4⋊C4—798no—
479C2×C4⋊C4—798no—
480C2×C4⋊C4—798no—
481C2×C4⋊C4—794no—
482C2×C4⋊C4—794no—
483C2×C4⋊C4—794no—
484C2×C4⋊C4—794no—
485C2×C4⋊C4—1584no—
486C2×C4⋊C4C22×D7914yes—
487C2×C4⋊C4C22×D7914yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—798no—
490C2×C22⋊C4—798no—
491C2×C22⋊C4—794no—
492C2×C22⋊C4—794no—
493C2×C22⋊C4C4×D7918yes—
494C2×C22⋊C4C22×D7914yes—
495C2×C22⋊C4C22×D7914yes—
496C2×C42—3162no—
497C2×C42—3162no—
498C2×C42—3162no—
499C2×C42—3162no—
500C2×C42—794no—
501C2×C42—794no—
502C2×C42—794no—
503C2×C42—794no—
504C2×C42—794no—
505C2×C42—794no—
506C2×C42—1584no—
507C2×C42—1584no—
508#95—794no—
509#95—794no—
510#95—794no—
511#95—794no—
512#95—794no—
513#95—794no—
514#95—794no—
515#95—794no—
516#95—794no—
517#95—794no—
518#95—794no—
519#95—794no—
520#95C22×D7914yes—
521#95C22×D7914yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24C2×C4×D7914yes—
527C24Q8×D7914yes—
528C24#1192962314yes—
529C24C23×D7912yes—
530C24C23×D7911yescharacteristic
531C2×Q8—3164no—
532C2×Q8—3164no—
533C2×Q8—31616no—
534C2×Q8—7916no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—28no—
552C22×C4—44no—
553C22×C4—416no—
554C22×C4—31616no—
555C22×C4—3164no—
556C22×C4—3164no—
557C22×C4—3164no—
558C22×C4—31616no—
559C22×C4—7916no—
560C22×C4—794no—
561C22×C4—794no—
562C22×C4—794no—
563C22×C4—792no—
564C22×C4—792no—
565C22×C4—792no—
566C22×C4—792no—
567C22×C4—792no—
568C22×C4—792no—
569C22×C4—792no—
570C22×C4—794no—
571C22×C4—794no—
572C22×C4—794no—
573C22×C4—794no—
574C22×C4—792no—
575C22×C4—1588no—
576C22×C4—1582no—
577C22×C4—1582no—
578C22×C4—1588no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4—1582no—
582C22×C4—1582no—
583C22×C4—1582no—
584C22×C4—1582no—
585C22×C4—1582no—
586C22×C4—1582no—
587C22×C4—1582no—
588C22×C4—1582no—
589C22×C4—1582no—
590C22×C4—1582no—
591C22×C4—1582no—
592C22×C4—1582no—
593C22×C4—1582no—
594C22×C4C2×C4×D7914yes—
595C22×C4C2×C4×D7914yes—
596C22×C4#1192962314yes—
597C22×C4C23×D7912yes—
598C22×C4C23×D7912yes—
599C22×C4C23×D7912yes—
600C22×C4C23×D7912yes—
601C22×C4C23×D7912yes—
602C22×C4C23×D7912yes—
603C4⋊C4—28no—
604C4⋊C4—44no—
605C4⋊C4—3164no—
606C4⋊C4—7916no—
607C4⋊C4—7916no—
608C4⋊C4—7916no—
609C4⋊C4—1588no—
610C22⋊C4—28no—
611C22⋊C4—7916no—
612C22⋊C4—7916no—
613C22⋊C4C2×C4×D79116yes—
614C42—3164no—
615C42—3164no—
616C42—3164no—
617C42—3164no—
618C42—1588no—
619C42—1588no—
620C23—22no—
621C23—22no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—22no—
629C23—22no—
630C23#14579126116yes—
631C23C22×C4×D7914yes—
632C23C22×C4×D7912yes—
633C23C2×Q8×D7914yes—
634C23C2×Q8×D7912yes—
635C23#41×D7912yes—
636C23C2×#1192962314yes—
637C23C2×#1192962312yes—
638C23C2×#1192962312yes—
639C23#1457920612yes—
640C23#1457920712yes—
641C23C24×D7911yescharacteristic
642Q8—31616no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—416no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—3164no—
666C2×C4—31616no—
667C2×C4—31616no—
668C2×C4—794no—
669C2×C4—794no—
670C2×C4—794no—
671C2×C4—794no—
672C2×C4—794no—
673C2×C4—794no—
674C2×C4—794no—
675C2×C4—1582no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1588no—
688C2×C4—1588no—
689C2×C4—1588no—
690C2×C4—1588no—
691C2×C4—1588no—
692C2×C4—1588no—
693C2×C4—1588no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4C22×C4×D7914yes—
700C2×C4C22×C4×D7914yes—
701C2×C4C2×#1192962314yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—232no—
709C22C2×#1457912618yes—
710C22C2×#1457912614yes—
711C22C4×#1192962314yes—
712C22#1909903514yes—
713C22#1909923614yes—
714C22#1909924414yes—
715C22#1909926714yes—
716C22#1909927114yes—
717C22C23×C4×D7911yescharacteristic
718C22C22×Q8×D7911yescharacteristic
719C22C2×#41×D7911yescharacteristic
720C22C22×#1192962311yescharacteristic
721C22C22×#1192962311yescharacteristic
722C22C2×#1457920611yescharacteristic
723C22C2×#1457920711yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—3162no—
731C4—1584no—
732C4—1584no—
733C4—1584no—
734C4—1584no—
735C4—1584no—
736C4—1584no—
737C4—1584no—
738C2—28no—
739C2#2376648118yesdirect product factor
740C2C22×#1457912611yescharacteristic
741C2C2×C4×#1192962311yescharacteristic
742C2C2×#1909903511yescharacteristic
743C2C2×#1909923611yescharacteristic
744C2C2×#1909924411yescharacteristic
745C2C2×#1909926711yescharacteristic
746C2C2×#1909927111yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#385×C79C2
socleC24×C79C24
prime radicalC25×C79C23
cosocleC23×C79C25
hypercenterC2×#385D79
hypocenterC79C2×#2368
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #23766481C2direct (N × H)
3. C2×#19098468C2semidirect
4. C2×#19098467C2semidirect
5. C2×#19098448C2semidirect
6. C2×#19098445C2semidirect
7. C2×#19098444C2semidirect
8. C2×#19098444C2semidirect
10. C2×C4⋊C4×Dic79C2semidirect
11. C2×#19098414C2semidirect
20. C2×#14579138C4semidirect
35. #19098468C22semidirect
36. #19098467C22semidirect
37. #19098448C22semidirect
38. #19098445C22semidirect
39. #19098444C22semidirect
40. #19098444C22semidirect
42. C4⋊C4×Dic79C22semidirect
43. #19098414C22semidirect
70. C22×Dic158C2×C4semidirect
88. #14579138C2×C4semidirect
89. C2×C4⋊Dic79C2×C4semidirect
93. C2×Dic79⋊C4C2×C4semidirect
94. C2×Dic79⋊C4C2×C4semidirect
100. C2×C22⋊Dic79Q8semidirect
151. C2×Dic158C22×C4semidirect
192. C4⋊Dic79C22×C4semidirect
195. Dic79⋊C4C22×C4semidirect
196. Dic79⋊C4C22×C4semidirect
198. C22⋊Dic79C2×Q8semidirect
366. C2×C79#2368semidirect
390. C79C2×#2368semidirect
739. C2#23766481direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791382
#237664812
C2×#190984682
C2×#190984672
C2×#190984482
C2×#190984452
C2×#190984442
C2×#190984352
C2×C4⋊C4×Dic792
C2×#190984142
C2×C22⋊C4×Dic792
C2×C4×C22⋊Dic792
C22×C79⋊#952
C2×#385×C792
C2×#236879