Finite Group Databasebeta

← #34451589

Subgroups — #34451589

Order 20224.

2586 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099074C211yesmaximal, characteristic
2#23766544C214yesmaximal, complemented
3#23766414C212yesmaximal, complemented
4#23766403C212yesmaximal, complemented
5#23766342C212yesmaximal, complemented
6#23766304C212yesmaximal, complemented
7#23766291C211yesmaximal, characteristic, complemented
8#23766283C211yesmaximal, characteristic, complemented
9#23766240C211yesmaximal, characteristic, complemented
10#23766231C211yesmaximal, characteristic, complemented
11#23766093C212yesmaximal, complemented
12#23766082C212yesmaximal, complemented
13#23766055C214yesmaximal, complemented
14#23766040C212yesmaximal, complemented
15#23766029C212yesmaximal, complemented
16C2×#19098423C211yesmaximal, characteristic, complemented
17C79×#2280C211yesmaximal, characteristic, complemented
18C22×#11929624C2211yescharacteristic
19#19099074C4116yescomplemented
20C2×#14579144C2212yes—
21C2×#14579140C2211yescharacteristic
22C2×#14579140C2211yescharacteristic
23C2×#14579135C2211yescharacteristic
24C2×#14579135C2211yescharacteristic
25C2×#14579130C2212yes—
26C2×C4×Dic158C2212yescomplemented
27C2×C4×D316C2212yescomplemented
28C2×C4×C22⋊D79C2212yes—
29C2×C4×C22⋊D79C2212yes—
30C2×(C22⋊D79)⋊C4C2214yes—
31C2×#14579120C2211yescharacteristic
32C22×C4⋊Dic79C2212yes—
33C22×C22⋊Dic79C2212yes—
34#19098469C2212yescomplemented
35#19098465C2212yescomplemented
36#19098463C2214yes—
37#19098463C2214yes—
38#19098461C2212yescomplemented
39#19098461C2212yescomplemented
40#19098460C2214yescomplemented
41#19098458C2214yescomplemented
42#19098457C2214yes—
43#19098457C2214yes—
44#19098455C2214yescomplemented
45#19098453C2214yescomplemented
46#19098451C2214yes—
47#19098451C2214yes—
48#19098450C2214yescomplemented
49#19098444C2214yescomplemented
50#19098440C2214yes—
51#19098439C2214yes—
52#19098439C2214yes—
53#19098437C2214yescomplemented
54#19098435C2214yes—
55#19098434C2214yescomplemented
56#19098430C2212yescomplemented
57#19098427C2212yescomplemented
58#19098425C2212yescomplemented
59#19098423C2211yescharacteristic
60#19098423C2212yes—
61#19098423C2212yes—
62#19098423C2211yescharacteristic
63#19098423C2212yes—
64#19098422C2212yescomplemented
65C4×C4⋊Dic79C2212yescomplemented
66C4×C4⋊Dic79C2212yescomplemented
67#19098414C2212yescomplemented
68C22⋊C4×Dic79C2214yes—
69#19098410C2212yescomplemented
70#19098408C2212yescomplemented
71C2×C79⋊#95C2212yes—
72#95×D79C2212yescomplemented
73C24×C4×C79C2211yescharacteristic
74C2×#117×C79C2212yes—
75#381×C79C2211yescharacteristic
76#381×C79C2211yescharacteristic
77#380×C79C2212yes—
78#380×C79C2211yescharacteristic
79#380×C79C2211yescharacteristic
80#379×C79C2212yes—
81C4×C22⋊C4×C79C2211yescharacteristic
82C4×C22⋊C4×C79C2211yescharacteristic
83C4×C22⋊C4×C79C2212yes—
84C2×#11929624—44no—
85C2×#11929624C2×C418yescomplemented
86C22×Dic158C2311yescharacteristic
87C22×D316C2311yescharacteristic
88C22×C22⋊D79C2312yes—
89C22×C22⋊D79C2312yes—
90C22×C22⋊D79C2312yes—
91C23×Dic79C2314yes—
92C22×C4×D79C2314yes—
93C22×C4×D79C2312yes—
94#14579144C2×C4116yescomplemented
95#14579140C2×C418yescomplemented
96#14579140C2×C418yescomplemented
97#14579135C2×C418yes—
98#14579135C2×C418yescomplemented
99#14579130C2×C4116yescomplemented
100C4×Dic158—44no—
101C4×D316—44no—
102C4×C22⋊D79C2×C4116yescomplemented
103C4×C22⋊D79C2×C4116yescomplemented
104(C22⋊D79)⋊C4—48no—
105#14579120C2×C418yescomplemented
106C2×C4⋊Dic79—44no—
107C2×C4⋊Dic79C2312yes—
108C2×C4⋊Dic79C2312yes—
109C2×C4⋊Dic79C2314yes—
110C2×C4⋊Dic79C2311yescharacteristic
111C2×C4⋊Dic79C2311yescharacteristic
112C2×Dic79⋊C4C2314yes—
113C2×Dic79⋊C4C2314yes—
114C2×Dic79⋊C4C2314yes—
115C2×Dic79⋊C4C2312yes—
116C2×Dic79⋊C4C2312yes—
117C2×C22⋊Dic79—44no—
118C2×C22⋊Dic79C2312yes—
119C2×C22⋊Dic79C2314yes—
120C2×C22⋊Dic79C2312yes—
121C2×C22⋊Dic79C2312yes—
122C2×C22⋊Dic79C2312yes—
123C2×C22⋊Dic79C2312yes—
124C2×(C2×D79)⋊C4C2314yes—
125C2×(C2×D79)⋊C4C2314yes—
126C2×(C2×D79)⋊C4C2314yes—
127C2×(C2×D79)⋊C4C2312yes—
128C2×(C2×D79)⋊C4C2312yes—
129C2×C4×Dic79C2314yes—
130C2×C4×Dic79C2314yes—
131C2×C4×Dic79C2314yes—
132C2×C4×Dic79C2312yes—
133C79⋊#95C2312yes—
134C79⋊#95C2314yes—
135C79⋊#95C2312yes—
136C79⋊#95C2314yes—
137C79⋊#95C2314yes—
138C79⋊#95C2314yes—
139C79⋊#95C2314yes—
140C79⋊#95C2314yes—
141C79⋊#95C2314yes—
142C25×C79C2311yescharacteristic
143C23×C4×C79—44no—
144C23×C4×C79C2×C418yescomplemented
145C23×C4×C79C2311yescharacteristic
146C23×C4×C79C2311yescharacteristic
147C23×C4×C79C2311yescharacteristic
148C23×C4×C79C2311yescharacteristic
149C23×C4×C79C2311yescharacteristic
150C23×C4×C79C2311yescharacteristic
151#117×C79—44no—
152C2×C4⋊C4×C79C2312yes—
153C2×C4⋊C4×C79C2312yes—
154C2×C22⋊C4×C79C2312yes—
155C2×C22⋊C4×C79C2312yes—
156C2×C22⋊C4×C79C2312yes—
157C2×C22⋊C4×C79C2312yes—
158C2×C22⋊C4×C79C2312yes—
159C2×C22⋊C4×C79C2312yes—
160C2×C42×C79C2312yes—
161C2×C42×C79C2312yes—
162#95×C79C2311yescharacteristic
163#95×C79C2311yescharacteristic
164#95×C79C2311yescharacteristic
165#95×C79C2311yescharacteristic
166#95×C79C2312yes—
167#95×C79C2312yes—
168C23×D79C2412yes—
169#11929624—416no—
170C2×Dic158—24no—
171C2×Dic158C22×C414yes—
172C2×D316—24no—
173C2×D316C22×C414yes—
174C2×C22⋊D79—24no—
175C2×C22⋊D79—24no—
176C2×C22⋊D79—44no—
177C2×C22⋊D79—44no—
178C2×C22⋊D79C22×C418yes—
179C2×C22⋊D79C22×C418yes—
180C2×C22⋊D79C22×C418yes—
181C22×Dic79—28no—
182C22×Dic79—44no—
183C22×Dic79—44no—
184C22×Dic79C2414yes—
185C22×Dic79C2414yes—
186C22×Dic79C2412yes—
187C22×Dic79C2412yes—
188C22×Dic79C2412yes—
189C2×C4×D79—44no—
190C2×C4×D79—44no—
191C2×C4×D79—44no—
192C2×C4×D79—44no—
193C2×C4×D79C22×C418yes—
194C4⋊Dic79—24no—
195C4⋊Dic79—24no—
196C4⋊Dic79—44no—
197C4⋊Dic79C22×C414yes—
198C4⋊Dic79C22×C414yes—
199Dic79⋊C4—44no—
200Dic79⋊C4—44no—
201Dic79⋊C4—44no—
202Dic79⋊C4C22×C418yes—
203Dic79⋊C4C22×C418yes—
204C22⋊Dic79—42no—
205C22⋊Dic79—44no—
206C22⋊Dic79—42no—
207C22⋊Dic79C22×C418yes—
208C22⋊Dic79C22×C418yes—
209C22⋊Dic79C22×C418yes—
210(C2×D79)⋊C4—44no—
211(C2×D79)⋊C4—44no—
212(C2×D79)⋊C4—44no—
213(C2×D79)⋊C4C22×C418yes—
214(C2×D79)⋊C4C22×C418yes—
215C4×Dic79—44no—
216C4×Dic79—44no—
217C4×Dic79—44no—
218C4×Dic79C22×C418yes—
219C24×C79—22no—
220C24×C79—22no—
221C24×C79—42no—
222C24×C79—42no—
223C24×C79C22×C414yes—
224C24×C79C2411yescharacteristic
225C24×C79C2411yescharacteristic
226C24×C79C2411yescharacteristic
227C22×C4×C79—24no—
228C22×C4×C79—24no—
229C22×C4×C79—24no—
230C22×C4×C79—416no—
231C22×C4×C79—42no—
232C22×C4×C79—42no—
233C22×C4×C79—42no—
234C22×C4×C79C22×C414yes—
235C22×C4×C79C22×C414yes—
236C22×C4×C79C22×C414yes—
237C22×C4×C79C22×C414yes—
238C22×C4×C79C22×C414yes—
239C22×C4×C79C22×C414yes—
240C22×C4×C79C2412yes—
241C22×C4×C79C2412yes—
242C22×C4×C79C2412yes—
243C22×C4×C79C2412yes—
244C22×C4×C79C2411yescharacteristic
245C22×C4×C79C2411yescharacteristic
246C22×C4×C79C2411yescharacteristic
247C22×C4×C79C2411yescharacteristic
248C4⋊C4×C79—42no—
249C4⋊C4×C79—42no—
250C22⋊C4×C79—24no—
251C22⋊C4×C79—24no—
252C22⋊C4×C79—42no—
253C22⋊C4×C79—42no—
254C22⋊C4×C79—42no—
255C22⋊C4×C79—42no—
256C42×C79—24no—
257C42×C79—24no—
258C23×C79—22no—
259C23×C79—22no—
260C23×C79—28no—
261C23×C79—21no—
262C23×C79—21no—
263C23×C79—22no—
264C23×C79—22no—
265C23×C79—21no—
266C23×C79—21no—
267C23×C79—22no—
268C23×C79—22no—
269C23×C79—44no—
270C23×C79—44no—
271C23×C79—48no—
272C23×C79—48no—
273C23×C79C23×C412yes—
274C23×C79C23×C412yes—
275C23×C79C23×C412yes—
276C23×C79H(5,𝔽2)12yes—
277C23×C792−1+412yes—
278C23×C79C2511yescharacteristic
279C22×D79—22no—
280C22×D79—24no—
281C22×D79—22no—
282C22×D79—24no—
283C22×D79C23×C414yes—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—28no—
288C2×C4×C79—28no—
289C2×C4×C79—28no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—44no—
303C2×C4×C79—44no—
304C2×C4×C79—44no—
305C2×C4×C79C23×C412yes—
306C2×C4×C79C23×C412yes—
307C2×C4×C79C23×C412yes—
308C2×C4×C79C23×C412yes—
309C2×C4×C79H(5,𝔽2)14yes—
310C22⋊D79—216no—
311C22⋊D79—48no—
312C22⋊D79—48no—
313C2×Dic79—22no—
314C2×Dic79—24no—
315C2×Dic79—22no—
316C2×Dic79—24no—
317C2×Dic79—24no—
318C2×Dic79—24no—
319C2×Dic79—24no—
320C2×Dic79—24no—
321C2×Dic79—24no—
322C2×Dic79—24no—
323C2×Dic79—88no—
324C2×Dic79C23×C414yes—
325C2×Dic79C23×C414yes—
326C2×Dic79C23×C414yes—
327D316—28no—
328C4×D79—48no—
329C4×D79—88no—
330Dic158—28no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—24no—
334C22×C79—24no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—416no—
342C22×C79—42no—
343C22×C79—42no—
344C22×C79—42no—
345C22×C79—42no—
346C22×C79#52014yes—
347C22×C79C24×C411yescharacteristic
348C22×C79C2×H(5,𝔽2)12yes—
349C22×C79C2×H(5,𝔽2)11yescharacteristic
350C22×C79C2×2−1+411yescharacteristic
351C22×C79#58512yes—
352C2×D79—24no—
353C2×D79—24no—
354C2×D79—24no—
355C2×D79—44no—
356C2×D79—44no—
357C4×C79—22no—
358C4×C79—22no—
359C4×C79—22no—
360C4×C79—42no—
361C4×C79—42no—
362C4×C79—42no—
363C4×C79—42no—
364C4×C79#51814yes—
365Dic79—24no—
366Dic79—24no—
367Dic79—24no—
368Dic79—44no—
369Dic79—44no—
370#34404—791nomaximal, Sylow
371C2×C79—24no—
372C2×C79—42no—
373C2×C79—42no—
374C2×C79C2×#51811yescharacteristic
375C2×C79C2×#52011yescharacteristic
376C2×C79#342811yescharacteristic
377C2×C79#354112yes—
378C2×C79#354212yes—
379D79—44no—
380C2×#525—791no—
381#2376—794no—
382#2361—792no—
383#2360—792no—
384#2353—792no—
385#2349—792no—
386#2347—791no—
387#2346—791no—
388#2341—791no—
389#2339—791no—
390#2324—792no—
391#2323—792no—
392#2321—794no—
393#2319—792no—
394#2318—792no—
395#2280D7911yescharacteristic, complemented
396C2×#380—791no—
397C79#3440411yescharacteristic, complemented, Sylow
398C22×#41—791no—
399C24×C4C2×D7911yescharacteristic
400#525—7916no—
401C2×#123—792no—
402C2×C22⋊Q8—791no—
403C2×C22⋊Q8—791no—
404C2×#121—791no—
405C2×#121—791no—
406C2×#120—792no—
407C2×C4×Q8—792no—
408C2×C4×D4—792no—
409C2×C4×D4—792no—
410C2×C4×D4—794no—
411C2×C4×D4—792no—
412C2×#117—791no—
413C2×#117C2×D7912yes—
414C22×C4⋊C4—792no—
415C22×C22⋊C4—792no—
416#391—792no—
417#390—794no—
418#390—794no—
419#390—792no—
420#389—794no—
421#389—792no—
422#389—792no—
423#389—794no—
424#388—794no—
425#388—794no—
426#388—794no—
427#388—794no—
428#388—794no—
429#388—794no—
430#387—794no—
431#387—794no—
432#386—794no—
433#386—794no—
434#386—794no—
435#385—794no—
436#385—794no—
437#385—794no—
438#383—792no—
439#382—792no—
440#381—792no—
441#381C2×D7911yescharacteristic
442#381C2×D7911yescharacteristic
443#380—792no—
444#380—792no—
445#380—791no—
446#380—791no—
447#380—792no—
448#380—792no—
449#380C2×D7911yescharacteristic
450#380C2×D7911yescharacteristic
451#380C2×D7912yes—
452#379C2×D7912yes—
453C4×C4⋊C4—792no—
454C4×C4⋊C4—792no—
455C4×C4⋊C4—792no—
456C4×C22⋊C4—794no—
457C4×C22⋊C4—792no—
458C4×C22⋊C4C2×D7911yescharacteristic
459C4×C22⋊C4C2×D7911yescharacteristic
460C4×C22⋊C4C2×D7912yes—
461#376—792no—
462C2×#95—792no—
463C2×#95—792no—
464C25C22×D7911yescharacteristic
465C2×#41—3164no—
466C2×#41—798no—
467C22×Q8—791no—
468C22×D4—792no—
469C22×D4—792no—
470C22×D4—792no—
471C22×D4—791no—
472C23×C4—44no—
473C23×C4—794no—
474C23×C4—792no—
475C23×C4—794no—
476C23×C4C4×D7918yescomplemented
477C23×C4C22×D7911yescharacteristic
478C23×C4C22×D7911yescharacteristic
479C23×C4C22×D7911yescharacteristic
480C23×C4C22×D7911yescharacteristic
481C23×C4C22×D7911yescharacteristic
482C23×C4C22×D7911yescharacteristic
483#123—7916no—
484C22⋊Q8—798no—
485C22⋊Q8—798no—
486#121—798no—
487#121—798no—
488#120—7916no—
489C4×Q8—3164no—
490C4×D4—3164no—
491C4×D4—3168no—
492C4×D4—7916no—
493C4×D4—7916no—
494#117—44no—
495#117—798no—
496C2×C4⋊C4—3164no—
497C2×C4⋊C4—794no—
498C2×C4⋊C4—794no—
499C2×C4⋊C4—794no—
500C2×C4⋊C4—794no—
501C2×C4⋊C4—791no—
502C2×C4⋊C4—791no—
503C2×C4⋊C4—792no—
504C2×C4⋊C4—792no—
505C2×C4⋊C4—792no—
506C2×C4⋊C4—792no—
507C2×C4⋊C4C22×D7912yes—
508C2×C4⋊C4C22×D7912yes—
509C2×C22⋊C4—3164no—
510C2×C22⋊C4—792no—
511C2×C22⋊C4—794no—
512C2×C22⋊C4—792no—
513C2×C22⋊C4—794no—
514C2×C22⋊C4—794no—
515C2×C22⋊C4—794no—
516C2×C22⋊C4—792no—
517C2×C22⋊C4—792no—
518C2×C22⋊C4—792no—
519C2×C22⋊C4—792no—
520C2×C22⋊C4—792no—
521C2×C22⋊C4C22×D7912yes—
522C2×C22⋊C4C22×D7912yes—
523C2×C22⋊C4C22×D7912yes—
524C2×C22⋊C4C22×D7912yes—
525C2×C22⋊C4C22×D7912yes—
526C2×C22⋊C4C22×D7912yes—
527C2×C42—794no—
528C2×C42—794no—
529C2×C42—794no—
530C2×C42—792no—
531C2×C42C22×D7912yes—
532C2×C42C22×D7912yes—
533#95—792no—
534#95—792no—
535#95—794no—
536#95—794no—
537#95—794no—
538#95—794no—
539#95—794no—
540#95—794no—
541#95—794no—
542#95C22×D7911yescharacteristic
543#95C22×D7911yescharacteristic
544#95C22×D7911yescharacteristic
545#95C22×D7911yescharacteristic
546#95C22×D7912yes—
547#95C22×D7912yes—
548C24—22no—
549C24—22no—
550C24—42no—
551C24—42no—
552C24—792no—
553C24C2×C4×D7914yes—
554C24C23×D7911yescharacteristic
555C24C23×D7911yescharacteristic
556C24C23×D7911yescharacteristic
557#41—31616no—
558C2×Q8—794no—
559C2×Q8—1584no—
560C2×D4—3164no—
561C2×D4—3164no—
562C2×D4—798no—
563C2×D4—798no—
564C2×D4—798no—
565C2×D4—794no—
566C2×D4—1584no—
567C2×D4—1584no—
568C2×D4—1584no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—416no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—3164no—
577C22×C4—3164no—
578C22×C4—3164no—
579C22×C4—3164no—
580C22×C4—3164no—
581C22×C4—3164no—
582C22×C4—798no—
583C22×C4—792no—
584C22×C4—792no—
585C22×C4—792no—
586C22×C4—794no—
587C22×C4—794no—
588C22×C4—1588no—
589C22×C4C2×C4×D7914yes—
590C22×C4C2×C4×D7914yes—
591C22×C4C2×C4×D7914yes—
592C22×C4C2×C4×D7914yes—
593C22×C4C2×C4×D7914yes—
594C22×C4C2×C4×D7914yes—
595C22×C4C23×D7912yes—
596C22×C4C23×D7912yes—
597C22×C4C23×D7912yes—
598C22×C4C23×D7912yes—
599C22×C4C23×D7911yescharacteristic
600C22×C4C23×D7911yescharacteristic
601C22×C4C23×D7911yescharacteristic
602C22×C4C23×D7911yescharacteristic
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—3164no—
606C4⋊C4—3164no—
607C4⋊C4—3164no—
608C4⋊C4—3164no—
609C4⋊C4—798no—
610C4⋊C4—798no—
611C4⋊C4—794no—
612C4⋊C4—794no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—3164no—
622C22⋊C4—3164no—
623C22⋊C4—3164no—
624C22⋊C4—3162no—
625C22⋊C4—3164no—
626C22⋊C4—3162no—
627C22⋊C4—798no—
628C22⋊C4—798no—
629C22⋊C4—798no—
630C22⋊C4—798no—
631C22⋊C4—798no—
632C42—24no—
633C42—24no—
634C42—3164no—
635C42—3164no—
636C42—3164no—
637C42—798no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—22no—
648C23—28no—
649C23—44no—
650C23—44no—
651C23—48no—
652C23—48no—
653C23—794no—
654C23—1584no—
655C23—1582no—
656C23—1582no—
657C23—1584no—
658C23C22×C4×D7912yes—
659C23C22×C4×D7912yes—
660C23C22×C4×D7912yes—
661C23#1457920712yes—
662C23#1457920812yes—
663C23C24×D7911yescharacteristic
664Q8—1588no—
665D4—3168no—
666D4—3168no—
667D4—15816no—
668D4—1588no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—3168no—
691C2×C4—794no—
692C2×C4—794no—
693C2×C4—794no—
694C2×C4—6328no—
695C2×C4—6328no—
696C2×C4—1584no—
697C2×C4—1584no—
698C2×C4—1584no—
699C2×C4—1584no—
700C2×C4—1584no—
701C2×C4—1584no—
702C2×C4—1584no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1584no—
706C2×C4C22×C4×D7912yes—
707C2×C4C22×C4×D7912yes—
708C2×C4C22×C4×D7912yes—
709C2×C4C22×C4×D7912yes—
710C2×C4#1457920614yes—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—24no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—3164no—
727C22—3164no—
728C22—1584no—
729C22—1584no—
730C22—1584no—
731C22#1909904314yes—
732C22C23×C4×D7911yescharacteristic
733C22C2×#1457920612yes—
734C22C2×#1457920711yescharacteristic
735C22C2×#1457920811yescharacteristic
736C22#1909939912yes—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—3164no—
745C4—3164no—
746C4—1584no—
747C4—1584no—
748C4—1584no—
749C4#1909903614yes—
750C2—24no—
751C2—42no—
752C2—42no—
753C2—3164no—
754C2C2×#1909903611yescharacteristic
755C2C2×#1909904311yescharacteristic
756C2#2377660111yescharacteristic
757C2#2377769312yes—
758C2#2377771612yes—
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2280C2
socle, cosocleC23×C79C25
prime radicalC2×#19099074C2
hypercenter#2280D79
hypocenterC79#34404
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #23766544C2semidirect
3. #23766414C2semidirect
4. #23766403C2semidirect
5. #23766342C2semidirect
6. #23766304C2semidirect
7. #23766291C2semidirect
8. #23766283C2semidirect
9. #23766240C2semidirect
10. #23766231C2semidirect
11. #23766093C2semidirect
12. #23766082C2semidirect
13. #23766055C2semidirect
14. #23766040C2semidirect
15. #23766029C2semidirect
16. C2×#19098423C2semidirect
17. C79×#2280C2semidirect
19. #19099074C4semidirect
26. C2×C4×Dic158C22semidirect
27. C2×C4×D316C22semidirect
34. #19098469C22semidirect
35. #19098465C22semidirect
38. #19098461C22semidirect
39. #19098461C22semidirect
40. #19098460C22semidirect
41. #19098458C22semidirect
44. #19098455C22semidirect
45. #19098453C22semidirect
48. #19098450C22semidirect
49. #19098444C22semidirect
53. #19098437C22semidirect
55. #19098434C22semidirect
56. #19098430C22semidirect
57. #19098427C22semidirect
58. #19098425C22semidirect
64. #19098422C22semidirect
65. C4×C4⋊Dic79C22semidirect
66. C4×C4⋊Dic79C22semidirect
67. #19098414C22semidirect
69. #19098410C22semidirect
70. #19098408C22semidirect
72. #95×D79C22semidirect
85. C2×#11929624C2×C4semidirect
94. #14579144C2×C4semidirect
95. #14579140C2×C4semidirect
96. #14579140C2×C4semidirect
98. #14579135C2×C4semidirect
99. #14579130C2×C4semidirect
102. C4×C22⋊D79C2×C4semidirect
103. C4×C22⋊D79C2×C4semidirect
105. #14579120C2×C4semidirect
144. C23×C4×C79C2×C4semidirect
395. #2280D79semidirect
397. C79#34404semidirect
476. C23×C4C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190990742
#237665442
#237664142
#237664032
#237663422
#237663042
#237662912
#237662832
#237662402
#237662312
#237660932
#237660822
#237660552
#237660402
#237660292
C2×#190984232
C79×#22802
#3440479