Finite Group Databasebeta

← #35197338

Subgroups — #35197338

Order 20224.

10962 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579209C211yesmaximal, characteristic, complemented
2C2×2−1+4×D79C211yesmaximal, characteristic, complemented
3#23777170C218yesmaximal, complemented
4#23777168C218yesmaximal, complemented
5#23777059C211yesmaximal, characteristic, complemented
6#23777057C218yesmaximal, complemented
7#23777055C211yesmaximal, characteristic, complemented
8#23777054C216yesmaximal, complemented
9#23777051C211yesmaximal, characteristic, complemented
10#23777050C218yesmaximal, complemented
11#23777049C216yesmaximal, complemented
12#23776732C216yesmaximal, complemented
13#23776730C216yesmaximal, complemented
14#519×D79C211yesmaximal, characteristic, complemented
15C79×#3486C211yesmaximal, characteristic, complemented
16C2×#14579209—216no—
17C2×#14579209C2218yes—
18C2×#14579209C2211yescharacteristic
19C2×#14579209C2218yescomplemented
20C2×#14579209C2214yescomplemented
21C2×#14579208C2216yes—
22C2×#14579208C2214yescomplemented
232−1+4×D79—216no—
24C22×#11929625C2213yes—
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929624C2213yes—
27C22×#11929624C2213yescomplemented
28C2×#41×D79C2216yes—
29C2×#41×D79C2214yescomplemented
30C22×Q8×D79C2211yescharacteristic
31C22×Q8×D79C2213yescomplemented
32C22×Q8×D79C2214yescomplemented
33#19099235C2218yescomplemented
34#19099234C22124yescomplemented
35#19099232C2218yescomplemented
36#19099231C22124yescomplemented
37#19099228C22124yescomplemented
38Q8×C22⋊D79C2218yescomplemented
39#19099226C22124yescomplemented
40#19099225C2218yescomplemented
41#19099224C2218yescomplemented
42#19099224C2218yescomplemented
43#19099223C22124yescomplemented
44#19099223C22124yescomplemented
45#19099222C22124yescomplemented
46#19099221C22124yescomplemented
47#19099143C22124yescomplemented
48#19099143C22112yescomplemented
49#19099142C22112yescomplemented
50#19099138C22112yescomplemented
51#19099137C2216yescomplemented
52#19099136C22112yescomplemented
53#19099135C22112yescomplemented
54#19099132C2216yescomplemented
55#19099131C22112yescomplemented
56#19099129C22112yescomplemented
57#19099128C22112yescomplemented
58#19099127C2216yescomplemented
59#19099124C22112yes—
60#19099123C2214yes—
61#19099114C22112yescomplemented
62#19099112C22112yescomplemented
63#19099110C22124yescomplemented
64#19099076C22124yescomplemented
65#19099075C2216yescomplemented
66#19099074C2216yescomplemented
67#19099072C22124yescomplemented
68#19099071C22124yescomplemented
69#19099070C2216yescomplemented
70#19099041C2211yescharacteristic, complemented
71#19099040C2216yescomplemented
72#19099039C2218yescomplemented
73C4×Q8×D79C2218yescomplemented
74#117×D79C2216yes—
75C2×2−1+4×C79C2211yescharacteristic
76C23×Q8×C79C2211yescharacteristic, complemented
77D4×Q8×C79C2218yescomplemented
78#548×C79C2218yescomplemented
79#536×C79C2216yescomplemented
80#525×C79C2216yescomplemented
81#519×C79C2211yescharacteristic, complemented
82#14579209—28no—
83#14579209—232no—
84#14579209—264no—
85#14579209—264no—
86#14579208—248no—
87#14579208—232no—
88C2×#11929625—28no—
89C2×#11929625—224no—
90C2×#11929625C23112yes—
91C2×#11929625C2314yes—
92C2×#11929625C2318yes—
93C2×#11929625C23112yes—
94C2×#11929625C2316yes—
95C2×#11929624—224no—
96C2×#11929624—224no—
97C2×#11929624C23112yes—
98C2×#11929624C2316yes—
99C2×#11929624C23112yes—
100C2×#11929624C23112yes—
101C2×#11929624C23124yes—
102C2×#11929624C23112yes—
103C2×#11929623C23112yes—
104C2×#11929623C23112yes—
105C2×#11929623C2316yes—
106#41×D79—232no—
107#41×D79—248no—
108C22×Dic158C23112yes—
109C22×Dic158C2313yes—
110C22×Dic158C2313yes—
111C2×Q8×D79—224no—
112C2×Q8×D79—232no—
113C2×Q8×D79D4116yescomplemented
114C2×Q8×D79C2316yes—
115C2×Q8×D79C23112yes—
116C2×Q8×D79C2314yes—
117C2×Q8×D79C23124yes—
118C2×Q8×D79C2314yes—
119C2×Q8×D79C2314yes—
120C22×D316C2313yes—
121C22×D316C2313yes—
122C22×C22⋊D79C2311yescharacteristic
123C22×C22⋊D79C2313yes—
124C2×D4×D79C2314yes—
125C2×D4×D79C2316yes—
126C22×C4×D79C2313yes—
127C22×C4×D79C2316yes—
128C22×C4×D79C23112yes—
129C22×C4×D79C2313yes—
130#14579160C23124yes—
131#14579159C23112yes—
132#14579158C23112yes—
133#14579157C23112yes—
134#14579157C23124yes—
135#14579150C23112yes—
136#14579150C23112yes—
137#14579149C23112yes—
138#14579147C23124yes—
139#14579147C23124yes—
140#14579146C23124yes—
141#14579145C2314yes—
142#14579144C23112yes—
143#14579143C2318yes—
144#14579142C2314yes—
145#14579141C23112yes—
146#14579140C23112yes—
147#14579139C23148yes—
148#14579139C23124yes—
149#14579138C23124yes—
150#14579137C23112yes—
151#14579137C23124yes—
152#14579136C23124yes—
153#14579136C23112yes—
154#14579136C23124yes—
155#14579135C23124yes—
156#14579135C23112yes—
157#14579134C23124yes—
158#14579134C2318yes—
159#14579134C23148yes—
160#14579134C23124yes—
161#14579133C23124yes—
162#14579132C2318yes—
163#14579132C23112yes—
164#14579131C23112yes—
165#14579131C23124yes—
166#14579130C2314yes—
167#14579129C23112yes—
168#14579129C2318yes—
169Q8×Dic79C2318yes—
170C4×Dic158C23124yes—
171#14579126C23124yes—
172C4×D316C23124yes—
173#14579123C23148yes—
174C4×C22⋊D79C23124yes—
175C4×C22⋊D79C23124yes—
176(C22⋊D79)⋊C4C23148yes—
177#14579120C2316yes—
178#14579119C23112yes—
179#14579118C23112yes—
180#14579117C23112yes—
181C4⋊C4×D79C23112yes—
182C22⋊C4×D79C2314yes—
183C42×D79C23112yes—
1842−1+4×C79—28no—
185C2×#41×C79C2316yes—
186C2×#41×C79C2314yes—
187C22×Q8×C79—28no—
188C22×Q8×C79C2313yes—
189C22×Q8×C79C2318yes—
190C22×Q8×C79C2314yes—
191C22×Q8×C79C2311yescharacteristic
192C23×C4×C79C2313yes—
193C4⋊Q8×C79C23112yes—
194#124×C79C23112yes—
195#123×C79C23112yes—
196C22⋊Q8×C79C23112yes—
197C22⋊Q8×C79C23124yes—
198#121×C79C23112yes—
199#120×C79C2314yes—
200C4×Q8×C79C2318yes—
201C4×D4×C79C23124yes—
202#117×C79C2316yes—
203C23×D79C2413yes—
204C23×D79C2414yes—
205C23×D79C2411yescharacteristic
206#11929625—224no—
207#11929625—248no—
208#11929625—248no—
209#11929625—216no—
210#11929625—232no—
211#11929624—248no—
212#11929624—248no—
213#11929624—248no—
214#11929624—248no—
215#11929624—296no—
216#11929624—224no—
217#11929623—248no—
218#11929623—224no—
219#11929623—248no—
220C2×Dic158—212no—
221C2×Dic158—248no—
222C2×Dic158C2×D4124yes—
223C2×Dic158C24112yes—
224C2×Dic158C24112yes—
225C2×Dic158C2416yes—
226C2×Dic158C24112yes—
227Q8×D79—224no—
228Q8×D79—248no—
229Q8×D79—296no—
230Q8×D79—216no—
231Q8×D79C2×D4132yes—
232Q8×D79C2×D4132yes—
233C2×D316—212no—
234C2×D316—212no—
235C2×D316C2414yes—
236C2×D316C2416yes—
237C2×D316C2416yes—
238C2×D316C2416yes—
239C2×D316C24112yes—
240C2×D316C24124yes—
241C2×C22⋊D79—212no—
242C2×C22⋊D79—24no—
243C2×C22⋊D79C2414yes—
244C2×C22⋊D79C2414yes—
245C2×C22⋊D79C24112yes—
246C2×C22⋊D79C2412yes—
247C2×C22⋊D79C2412yes—
248C2×C22⋊D79C24112yes—
249C2×C22⋊D79C24124yes—
250C2×C22⋊D79C2418yes—
251D4×D79—224no—
252D4×D79—216no—
253C22×Dic79C2411yescharacteristic
254C22×Dic79C24112yes—
255C22×Dic79C2413yes—
256C2×C4×D79—224no—
257C2×C4×D79—248no—
258C2×C4×D79—212no—
259C2×C4×D79C2×D4124yes—
260C2×C4×D79C2414yes—
261C2×C4×D79C24112yes—
262C2×C4×D79C24112yes—
263C2×C4×D79C24124yes—
264C2×C4×D79C24112yes—
265C2×C4×D79C2418yes—
266C2×C4×D79C2416yes—
267C2×C4×D79C2416yes—
268C4⋊Dic79C24112yes—
269C4⋊Dic79C2418yes—
270Dic79⋊C4C24124yes—
271Dic79⋊C4C24124yes—
272Dic79⋊C4C2418yes—
273C22⋊Dic79C2414yes—
274C22⋊Dic79C2418yes—
275C22⋊Dic79C2418yes—
276(C2×D79)⋊C4C2418yes—
277(C2×D79)⋊C4C24124yes—
278(C2×D79)⋊C4C24124yes—
279(C2×D79)⋊C4C24124yes—
280(C2×D79)⋊C4C2418yes—
281C4×Dic79C24124yes—
282C4×Dic79C24112yes—
283C24×C79C2411yescharacteristic
284#41×C79—216no—
285#41×C79—224no—
286C2×Q8×C79—216no—
287C2×Q8×C79—232no—
288C2×Q8×C79—212no—
289C2×Q8×C79C2×D418yes—
290C2×Q8×C79C2416yes—
291C2×Q8×C79C24112yes—
292C2×Q8×C79C2414yes—
293C2×D4×C79C2414yes—
294C2×D4×C79C2416yes—
295C2×D4×C79C2418yes—
296C22×C4×C79—212no—
297C22×C4×C79C24112yes—
298C22×C4×C79C2413yes—
299C22×C4×C79C24112yes—
300C22×C4×C79C2413yes—
301C4⋊C4×C79C24112yes—
302C4⋊C4×C79C24124yes—
303C22⋊C4×C79C2414yes—
304C22⋊C4×C79C2418yes—
305C22⋊C4×C79C24124yes—
306C42×C79C24112yes—
307C23×C79—22no—
308C23×C79—42no—
309C23×C79C2512yes—
310C23×C79C2514yes—
311C23×C79C2511yescharacteristic
312C22×D79—26no—
313C22×D79—28no—
314C22×D79—42no—
315C22×D79—48no—
316C22×D79—46no—
317C22×D79C22×D414yes—
318C22×D79C2514yes—
319C22×D79C2516yes—
320C22×D79C2511yescharacteristic
321C22×D79C2511yescharacteristic
322Q8×C79—212no—
323Q8×C79—224no—
324Q8×C79C22×D4116yes—
325D4×C79—28no—
326D4×C79—212no—
327D4×C79—48no—
328C2×C4×C79—26no—
329C2×C4×C79—224no—
330C2×C4×C79—224no—
331C2×C4×C79C22×D4112yes—
332C2×C4×C79C2518yes—
333C2×C4×C79C2514yes—
334C2×C4×C79C2516yes—
335C2×C4×C79C2516yes—
336C22⋊D79—28no—
337C22⋊D79—28no—
338C22⋊D79—24no—
339C22⋊D79—24no—
340C22⋊D79—224no—
341C22⋊D79—224no—
342C22⋊D79—424no—
343C22⋊D79—48no—
344C2×Dic79—22no—
345C2×Dic79—224no—
346C2×Dic79C22×D4112yes—
347C2×Dic79C2518yes—
348C2×Dic79C2514yes—
349C2×Dic79C2512yes—
350C2×Dic79C2516yes—
351D316—28no—
352D316—212no—
353D316—212no—
354D316—212no—
355D316—224no—
356D316—424no—
357C4×D79—28no—
358C4×D79—224no—
359C4×D79—224no—
360C4×D79—224no—
361C4×D79—248no—
362C4×D79—48no—
363C4×D79C22×D4124yes—
364C4×D79C22×D4124yes—
365Dic158—212no—
366Dic158—224no—
367Dic158—224no—
368Dic158C22×D4148yes—
369C22×C79—22no—
370C22×C79—22no—
371C22×C79—24no—
372C22×C79—22no—
373C22×C79—28no—
374C22×C79—22no—
375C22×C79—44no—
376C22×C79C23×D412yes—
377C22×C79C2611yescharacteristic
378C2×D79—22no—
379C2×D79—22no—
380C2×D79—24no—
381C2×D79—26no—
382C2×D79—212no—
383C2×D79—28no—
384C2×D79—44no—
385C2×D79—416no—
386C2×D79—412no—
387C2×D79C23×D412yes—
388C2×D79C23×D412yes—
389C4×C79—24no—
390C4×C79—26no—
391C4×C79—28no—
392C4×C79C23×D4112yes—
393Dic79—22no—
394Dic79—24no—
395Dic79—28no—
396Dic79C23×D4112yes—
397#62848—791nomaximal, Sylow
398C2×C79—22no—
399C2×C79—44no—
400C2×C79—42no—
401C2×C79C24×D411yescharacteristic
402C2×C792−1+612yes—
403D79—22no—
404D79—22no—
405D79—44no—
406D79—46no—
407C22×2−1+4—791no—
408C22×2−1+4—791no—
409#3497—798no—
410#3497—798no—
411#3487—791no—
412#3487—798no—
413#3487—796no—
414#3487—791no—
415#3486—791no—
416#3486—798no—
417#3486—796no—
418#3486D7911yescharacteristic, complemented
419#3449—796no—
420#3449—796no—
421C2×#519—791no—
422C79#6284811yescharacteristic, complemented, Sylow
423C2×2−1+4—796no—
424C2×2−1+4—794no—
425C2×2−1+4—798no—
426C2×2−1+4—791no—
427C2×2−1+4—794no—
428C2×2−1+4—798no—
429C2×2−1+4—15816no—
430C2×2−1+4—15816no—
431C2×2−1+4C2×D7911yescharacteristic
432C22×#41—796no—
433C22×#41—794no—
434C22×#41—793no—
435C22×#41—791no—
436C22×#41—793no—
437C22×#41—793no—
438C23×Q8—791no—
439C23×Q8—794no—
440C23×Q8—793no—
441C23×Q8C2×D7911yescharacteristic, complemented
442#550—798no—
443#550—7924no—
444#550—798no—
445#550—7924no—
446D4×Q8—798no—
447D4×Q8—7924no—
448D4×Q8—7924no—
449D4×Q8C2×D7918yescomplemented
450#548—798no—
451#548—798no—
452#548—7924no—
453#548—7924no—
454#548—7924no—
455#548—798no—
456#548—7924no—
457#548C2×D7918yescomplemented
458#537—7924no—
459#537—7912no—
460#537—7912no—
461#536—796no—
462#536—7912no—
463#536—7912no—
464#536—7912no—
465#536C2×D7916yescomplemented
466#535—796no—
467#535—7912no—
468#535—7912no—
469#535—7912no—
470#535—796no—
471#534—7912no—
472#534—794no—
473#532—7912no—
474#532—7912no—
475#532—7924no—
476#525—796no—
477#525—796no—
478#525—7924no—
479#525—7924no—
480#525—7924no—
481#525—796no—
482#525C2×D7916yescomplemented
483#519—791no—
484#519—798no—
485#519—796no—
486#519C2×D7911yescharacteristic, complemented
487C2×C4×Q8—798no—
488C2×#117—796no—
4892−1+4—28no—
4902−1+4—15864no—
4912−1+4—15864no—
4922−1+4—15832no—
4932−1+4—15832no—
4942−1+4—15848no—
4952−1+4—1588no—
496C2×#41—7912no—
497C2×#41—796no—
498C2×#41—7912no—
499C2×#41—794no—
500C2×#41—798no—
501C2×#41—7912no—
502C2×#41—796no—
503C2×#41—7912no—
504C2×#41—7912no—
505C2×#41—796no—
506C2×#41—7912no—
507C2×#41—7912no—
508C2×#41—7912no—
509C2×#41—7924no—
510C2×#41—15824no—
511C2×#41—15824no—
512C2×#41—15824no—
513C2×#41—15848no—
514C2×#41—15832no—
515C2×#41—1588no—
516C2×#41C22×D7916yes—
517C2×#41C22×D7914yes—
518C22×Q8—28no—
519C22×Q8—7916no—
520C22×Q8—794no—
521C22×Q8—794no—
522C22×Q8—796no—
523C22×Q8—7912no—
524C22×Q8—7924no—
525C22×Q8—794no—
526C22×Q8—793no—
527C22×Q8—793no—
528C22×Q8—7912no—
529C22×Q8—15832no—
530C22×Q8—15824no—
531C22×Q8C22×D7913yes—
532C22×Q8C22×D7914yes—
533C22×Q8C22×D7918yes—
534C22×Q8C22×D7911yescharacteristic
535C22×D4—791no—
536C22×D4—793no—
537C22×D4—794no—
538C22×D4—796no—
539C22×D4—793no—
540C22×D4—793no—
541C23×C4—793no—
542C23×C4—796no—
543C23×C4—7912no—
544C23×C4—793no—
545C23×C4C22×D7913yes—
546C4⋊Q8—7912no—
547C4⋊Q8—7924no—
548C4⋊Q8C22×D79112yes—
549#127—7912no—
550#127—7924no—
551#127—7912no—
552#124—7912no—
553#124—7912no—
554#124—7924no—
555#124—7924no—
556#124—7912no—
557#124C22×D79112yes—
558#123—794no—
559#123—7912no—
560#123—7924no—
561#123—798no—
562#123—794no—
563#123C22×D79112yes—
564C22⋊Q8—7912no—
565C22⋊Q8—7924no—
566C22⋊Q8—7912no—
567C22⋊Q8—7948no—
568C22⋊Q8—7924no—
569C22⋊Q8—7912no—
570C22⋊Q8—7924no—
571C22⋊Q8C22×D79124yes—
572C22⋊Q8C22×D79112yes—
573#121—7912no—
574#121—7924no—
575#121—798no—
576#121—7924no—
577#121—7912no—
578#121—7924no—
579#121—7912no—
580#121—7924no—
581#121—7948no—
582#121—7924no—
583#121—7924no—
584#121—798no—
585#121C22×D79112yes—
586#120—794no—
587#120—7912no—
588#120—798no—
589#120—7924no—
590#120—7912no—
591#120C22×D7914yes—
592C4×Q8—798no—
593C4×Q8—7924no—
594C4×Q8—7924no—
595C4×Q8C22×D7918yes—
596C4×D4—7924no—
597C4×D4—7924no—
598C4×D4—7948no—
599C4×D4—7948no—
600C4×D4—7924no—
601C4×D4C22×D79124yes—
602#117—796no—
603#117—7912no—
604#117—7912no—
605#117—7912no—
606#117C22×D7916yes—
607C2×C4⋊C4—7912no—
608C2×C22⋊C4—794no—
609C2×C42—7912no—
610C24—791no—
611C24—794no—
612C24—793no—
613C24C23×D7911yescharacteristic
614#41—216no—
615#41—224no—
616#41—15848no—
617#41—15848no—
618#41—15848no—
619#41—15896no—
620#41—15848no—
621#41—15848no—
622#41—15824no—
623#41—15848no—
624#41—15848no—
625#41—15824no—
626#41—15848no—
627#41—15816no—
628#41—15832no—
629#41—15824no—
630C2×Q8—232no—
631C2×Q8—216no—
632C2×Q8—212no—
633C2×Q8—7932no—
634C2×Q8—7932no—
635C2×Q8—7912no—
636C2×Q8—7912no—
637C2×Q8—7912no—
638C2×Q8—796no—
639C2×Q8—7924no—
640C2×Q8—15812no—
641C2×Q8—15848no—
642C2×Q8—15824no—
643C2×Q8—15896no—
644C2×Q8—15848no—
645C2×Q8—15816no—
646C2×Q8D4×D7918yes—
647C2×Q8C23×D7916yes—
648C2×Q8C23×D79112yes—
649C2×Q8C23×D7914yes—
650C2×D4—798no—
651C2×D4—7924no—
652C2×D4—792no—
653C2×D4—794no—
654C2×D4—792no—
655C2×D4—794no—
656C2×D4—7912no—
657C2×D4—7912no—
658C2×D4—7924no—
659C2×D4—796no—
660C2×D4—794no—
661C2×D4—796no—
662C2×D4—796no—
663C2×D4—7912no—
664C2×D4—15812no—
665C2×D4—15824no—
666C2×D4—15812no—
667C2×D4—15816no—
668C2×D4—1584no—
669C2×D4—15812no—
670C2×D4C23×D7914yes—
671C2×D4C23×D7916yes—
672C2×D4C23×D7918yes—
673C22×C4—212no—
674C22×C4—798no—
675C22×C4—793no—
676C22×C4—796no—
677C22×C4—796no—
678C22×C4—7924no—
679C22×C4—7912no—
680C22×C4—791no—
681C22×C4—7912no—
682C22×C4—7924no—
683C22×C4—7912no—
684C22×C4—7912no—
685C22×C4—794no—
686C22×C4—15824no—
687C22×C4—15848no—
688C22×C4—15812no—
689C22×C4C23×D79112yes—
690C22×C4C23×D79112yes—
691C22×C4C23×D7913yes—
692C22×C4C23×D7913yes—
693C4⋊C4—7924no—
694C4⋊C4—798no—
695C4⋊C4—7924no—
696C4⋊C4—7912no—
697C4⋊C4—798no—
698C4⋊C4C23×D79112yes—
699C4⋊C4C23×D79124yes—
700C22⋊C4—794no—
701C22⋊C4—798no—
702C22⋊C4—798no—
703C22⋊C4—798no—
704C22⋊C4—7924no—
705C22⋊C4—7924no—
706C22⋊C4—7924no—
707C22⋊C4—798no—
708C22⋊C4C23×D7914yes—
709C22⋊C4C23×D79124yes—
710C22⋊C4C23×D7918yes—
711C42—7924no—
712C42—7912no—
713C42C23×D79112yes—
714C23—22no—
715C23—42no—
716C23—3166no—
717C23—3162no—
718C23—3168no—
719C23—794no—
720C23—791no—
721C23—791no—
722C23—796no—
723C23—794no—
724C23—1588no—
725C23—1586no—
726C23C24×D7912yes—
727C23C24×D7914yes—
728C23C24×D7911yescharacteristic
729Q8—224no—
730Q8—212no—
731Q8—7948no—
732Q8—15824no—
733Q8—15824no—
734Q8—15812no—
735Q8C2×D4×D79116yes—
736D4—28no—
737D4—212no—
738D4—48no—
739D4—31624no—
740D4—31624no—
741D4—3168no—
742D4—1588no—
743D4—15812no—
744D4—15812no—
745D4—15824no—
746D4—15824no—
747D4—1584no—
748D4—1584no—
749D4—1588no—
750D4—1588no—
751D4—15812no—
752D4—15824no—
753C2×C4—26no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—3168no—
757C2×C4—796no—
758C2×C4—7912no—
759C2×C4—7924no—
760C2×C4—7924no—
761C2×C4—798no—
762C2×C4—792no—
763C2×C4—794no—
764C2×C4—15824no—
765C2×C4—15848no—
766C2×C4—1588no—
767C2×C4—15824no—
768C2×C4—1582no—
769C2×C4—15824no—
770C2×C4—15824no—
771C2×C4C2×D4×D79112yes—
772C2×C4C24×D7918yes—
773C2×C4C24×D7914yes—
774C2×C4C24×D7916yes—
775C2×C4C24×D7916yes—
776C22—22no—
777C22—22no—
778C22—24no—
779C22—22no—
780C22—28no—
781C22—22no—
782C22—44no—
783C22—31612no—
784C22—3164no—
785C22—31616no—
786C22—792no—
787C22—792no—
788C22—1586no—
789C22—1584no—
790C22—1588no—
791C22—15812no—
792C22—1582no—
793C22—1582no—
794C22C22×D4×D7912yes—
795C22C25×D7911yescharacteristic
796C4—24no—
797C4—26no—
798C4—28no—
799C4—7912no—
800C4—1584no—
801C4—1582no—
802C4—1588no—
803C4C22×D4×D79112yes—
804C2—22no—
805C2—42no—
806C2—44no—
807C2—3166no—
808C2—3164no—
809C2—1582no—
810C2—1582no—
811C2C23×D4×D7911yescharacteristic
812C2#2377821212yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3486C2
hypercenter#3486D79
hypocenterC79#62848
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. C22×#14579209C2semidirect
2. C2×2−1+4×D79C2semidirect
3. #23777170C2semidirect
4. #23777168C2semidirect
5. #23777059C2semidirect
6. #23777057C2semidirect
7. #23777055C2semidirect
8. #23777054C2semidirect
9. #23777051C2semidirect
10. #23777050C2semidirect
11. #23777049C2semidirect
12. #23776732C2semidirect
13. #23776730C2semidirect
14. #519×D79C2semidirect
15. C79×#3486C2semidirect
19. C2×#14579209C22semidirect
20. C2×#14579209C22semidirect
22. C2×#14579208C22semidirect
25. C22×#11929625C22semidirect
27. C22×#11929624C22semidirect
29. C2×#41×D79C22semidirect
31. C22×Q8×D79C22semidirect
32. C22×Q8×D79C22semidirect
33. #19099235C22semidirect
34. #19099234C22semidirect
35. #19099232C22semidirect
36. #19099231C22semidirect
37. #19099228C22semidirect
38. Q8×C22⋊D79C22semidirect
39. #19099226C22semidirect
40. #19099225C22semidirect
41. #19099224C22semidirect
42. #19099224C22semidirect
43. #19099223C22semidirect
44. #19099223C22semidirect
45. #19099222C22semidirect
46. #19099221C22semidirect
47. #19099143C22semidirect
48. #19099143C22semidirect
49. #19099142C22semidirect
50. #19099138C22semidirect
51. #19099137C22semidirect
52. #19099136C22semidirect
53. #19099135C22semidirect
54. #19099132C22semidirect
55. #19099131C22semidirect
56. #19099129C22semidirect
57. #19099128C22semidirect
58. #19099127C22semidirect
61. #19099114C22semidirect
62. #19099112C22semidirect
63. #19099110C22semidirect
64. #19099076C22semidirect
65. #19099075C22semidirect
66. #19099074C22semidirect
67. #19099072C22semidirect
68. #19099071C22semidirect
69. #19099070C22semidirect
70. #19099041C22semidirect
71. #19099040C22semidirect
72. #19099039C22semidirect
73. C4×Q8×D79C22semidirect
76. C23×Q8×C79C22semidirect
77. D4×Q8×C79C22semidirect
78. #548×C79C22semidirect
79. #536×C79C22semidirect
80. #525×C79C22semidirect
81. #519×C79C22semidirect
113. C2×Q8×D79D4semidirect
418. #3486D79semidirect
422. C79#62848semidirect
441. C23×Q8C2×D79semidirect
449. D4×Q8C2×D79semidirect
457. #548C2×D79semidirect
465. #536C2×D79semidirect
482. #525C2×D79semidirect
486. #519C2×D79semidirect

Maximal subgroups

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

subgroupindex
C22×#145792092
C2×2−1+4×D792
#237771702
#237771682
#237770592
#237770572
#237770552
#237770542
#237770512
#237770502
#237770492
#237767322
#237767302
#519×D792
C79×#34862
#6284879