Finite Group Databasebeta

← #35168212

Subgroups — #35168212

Order 20224.

1870 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
1#23777201C211yesmaximal, characteristic, complemented
2#23776147C214yesmaximal, complemented
3#23776114C212yesmaximal, complemented
4#23776103C212yesmaximal, complemented
5#23776056C214yesmaximal, complemented
6#23776045C212yesmaximal, complemented
7#23776031C212yesmaximal, complemented
8#23773754C212yesmaximal, complemented
9#23773722C211yesmaximal, characteristic, complemented
10#23773251C212yesmaximal, complemented
11#23773197C211yesmaximal, characteristic, complemented
12#23772899C212yesmaximal, complemented
13#23772860C211yesmaximal, characteristic, complemented
14#23772335C211yesmaximal, characteristic, complemented
15#23772228C212yesmaximal, complemented
16C2×C4×#11929609C211yesmaximal, characteristic, complemented
17C79×#3506C211yesmaximal, characteristic, complemented
18C2×#14579186C2212yes—
19C22×#11929609C2211yescharacteristic
20#19099274—21no—
21#19099273C2212yescomplemented
22#19099273C2214yescomplemented
23#19099269—22no—
24Q8×D316C2212yescomplemented
25#19099228—21no—
26#19099191C2212yes—
27#19099188—22no—
28#19099120C2211yescharacteristic
29C22⋊Q8×D79—22no—
30#19099037C2212yes—
31C2×C4×D316C2211yescharacteristic
32#19098927C2214yescomplemented
33#19098922C2214yescomplemented
34#19098917C2212yescomplemented
35#19098917C2212yescomplemented
36#19098917C2214yescomplemented
37#19098913C2211yescharacteristic, complemented
38#19098913C2211yescharacteristic, complemented
39#19098909C2211yescharacteristic, complemented
40#19098909C2211yescharacteristic, complemented
41#19098909C2214yescomplemented
42#19098870C2214yescomplemented
43#19098863C2214yescomplemented
44#19098863C2214yescomplemented
45#19098858C2214yescomplemented
46#19098853C2212yescomplemented
47#19098843C2212yescomplemented
48#19098843C2214yescomplemented
49#19098775C2214yes—
50#19098775C2214yes—
51#19098775C2214yescomplemented
52#19098765C2212yescomplemented
53#19098755C2214yes—
54#19098755C2214yes—
55#19098755C2212yescomplemented
56#19098694C2212yescomplemented
57#19098694C2212yescomplemented
58Q8×C79⋊C8C2212yescomplemented
59Q8×C79⋊C8C2212yescomplemented
60#19098673C2214yescomplemented
61#19098661C2214yescomplemented
62C4×#11929611C2214yescomplemented
63C4×#11929609C2212yes—
64C4×#11929609C2212yes—
65C4×#11929609C2212yes—
66C4×#11929609C2212yes—
67C4×#11929609C2214yescomplemented
68#19098603C2212yes—
69C2×#14579094C2211yescharacteristic
70#19098590C2212yes—
71#19098587C2211yescharacteristic
72#19098568C2212yes—
73#19098564C2212yes—
74#19098559C2212yes—
75#19098559C2212yes—
76C2×#14579082C2211yescharacteristic
77C2×#14579081C2211yescharacteristic
78#19098519C2212yes—
79C2×C4×C79⋊C8C2211yescharacteristic
80#559×C79C2214yescomplemented
81#556×C79C2212yescomplemented
82#555×C79—21no—
83#553×C79—22no—
84#550×C79C2212yescomplemented
85#547×C79—21no—
86#538×C79—22no—
87#535×C79C2212yes—
88#533×C79C2211yescharacteristic
89#532×C79C2211yescharacteristic
90#525×C79—22no—
91#520×C79C2212yes—
92C2×C4×D4×C79C2211yescharacteristic
93C2×Q8×D79—22no—
94C22×D316C2311yescharacteristic
95C22×C4×D79—21no—
96#14579186—28no—
97C2×#11929611C2314yes—
98C2×#11929609—24no—
99C2×#11929609C2312yes—
100C2×#11929609C2312yes—
101C2×#11929609C2314yes—
102C2×#11929608C2312yes—
103C22×C79⋊C8C2311yescharacteristic
104C22×C79⋊C8C2311yescharacteristic
105#14579161C2311yescharacteristic
106#14579161C2311yescharacteristic
107#14579161C2314yes—
108#14579160—22no—
109#14579153C2312yes—
110#14579153C2314yes—
111#14579152—22no—
112#14579141—24no—
113#14579141—22no—
114#14579140—21no—
115#14579140—21no—
116#14579139—24no—
117#14579139—24no—
118#14579139—24no—
119#14579138—24no—
120#14579137—24no—
121#14579137—22no—
122C4×Dic158—21no—
123C4×Dic158—21no—
124C4×D316—21no—
125C4×D316—21no—
126C4×D316C2312yes—
127C4×D316C2312yes—
128C4×D316C2314yes—
129C4×D316C2314yes—
130#14579123—22no—
131#14579123—22no—
132#14579120C2312yes—
133C2×C4⋊Dic79C2311yescharacteristic
134C4⋊C4×D79—24no—
135C4⋊C4×D79—22no—
136C2×(C2×D79)⋊C4—21no—
137C22⋊C4×D79—24no—
138#14579094C2312yes—
139#14579094C2312yes—
140#14579094C2314yes—
141#14579092C2314yes—
142C4⋊(C79⋊C8)C2314yes—
143C4⋊(C79⋊C8)C2314yes—
144C4⋊(C79⋊C8)C2312yes—
145C4⋊(C79⋊C8)C2312yes—
146#14579085C2312yes—
147#14579085C2312yes—
148#14579085C2312yes—
149#14579085C2312yes—
150#14579085C2314yes—
151#14579082C2312yes—
152#14579082C2312yes—
153#14579082C2312yes—
154#14579082C2312yes—
155#14579082C2312yes—
156#14579082C2312yes—
157#14579082C2314yes—
158#14579082C2314yes—
159#14579082C2314yes—
160#14579081C2312yes—
161#14579081C2312yes—
162#14579072C2314yes—
163C4×C79⋊C8C2311yescharacteristic
164C4×C79⋊C8C2311yescharacteristic
165C4×C79⋊C8C2311yescharacteristic
166C4×C79⋊C8C2311yescharacteristic
167C4×C79⋊C8C2314yes—
168C2×#41×C79—22no—
169C2×#41×C79C2312yes—
170C22×D4×C79C2311yescharacteristic
171C23×C4×C79—21no—
172C4⋊Q8×C79D411yescharacteristic
173C4⋊Q8×C79D411yescharacteristic
174C4⋊Q8×C79C2311yescharacteristic
175#127×C79C2311yescharacteristic
176#127×C79C2314yes—
177#126×C79—24no—
178#125×C79D412yes—
179#124×C79—24no—
180#124×C79C2312yes—
181#124×C79C2314yes—
182#123×C79—24no—
183#123×C79—24no—
184C22⋊Q8×C79—22no—
185C22⋊Q8×C79D412yes—
186C22⋊Q8×C79D412yes—
187#121×C79—21no—
188#121×C79—21no—
189#121×C79—22no—
190#121×C79—22no—
191#121×C79—22no—
192#121×C79—24no—
193#120×C79—24no—
194C4×Q8×C79C2314yes—
195C4×Q8×C79C2312yes—
196C4×Q8×C79C2312yes—
197C4×D4×C79—24no—
198C4×D4×C79—24no—
199C4×D4×C79—21no—
200C4×D4×C79—21no—
201C4×D4×C79—21no—
202C4×D4×C79—21no—
203C4×D4×C79C2312yes—
204C4×D4×C79C2312yes—
205C4×D4×C79C2314yes—
206#117×C79—22no—
207#117×C79—22no—
208#117×C79C2312yes—
209C2×C4⋊C4×C79—22no—
210C2×C4⋊C4×C79C2311yescharacteristic
211C2×C22⋊C4×C79—21no—
212C2×C42×C79C2311yescharacteristic
213C23×D79—21no—
214C2×Dic158—21no—
215C2×Dic158—24no—
216C2×Dic158—21no—
217Q8×D79—84no—
218C2×D316—21no—
219C2×D316—22no—
220C2×D316#4114yescomplemented
221C2×D316C2412yes—
222C22×Dic79—21no—
223C2×C4×D79—22no—
224C2×C4×D79—24no—
225C2×C4×D79—24no—
226C2×C4×D79—22no—
227C2×C4×D79—82no—
228#11929611—28no—
229#11929609—24no—
230#11929609—24no—
231#11929609—28no—
232#11929608—24no—
233C2×C79⋊C8—22no—
234C2×C79⋊C8—22no—
235C2×C79⋊C8C2411yescharacteristic
236C2×C79⋊C8C2411yescharacteristic
237C2×C79⋊C8C2411yescharacteristic
238C2×C79⋊C8C2411yescharacteristic
239C2×C79⋊C8C2414yes—
240C4⋊Dic79—21no—
241C4⋊Dic79—24no—
242C4⋊Dic79—21no—
243C4⋊Dic79—21no—
244C4⋊Dic79C2412yes—
245C4⋊Dic79C2412yes—
246C4⋊Dic79C2412yes—
247Dic79⋊C4—22no—
248Dic79⋊C4—24no—
249Dic79⋊C4—24no—
250Dic79⋊C4—22no—
251C22⋊Dic79—22no—
252(C2×D79)⋊C4—24no—
253(C2×D79)⋊C4—24no—
254(C2×D79)⋊C4—22no—
255(C2×D79)⋊C4—22no—
256C4×Dic79—22no—
257C24×C79—21no—
258#41×C79—24no—
259#41×C79—24no—
260#41×C79—84no—
261C2×Q8×C79C2×D412yes—
262C2×Q8×C79C2×D412yes—
263C2×Q8×C79C2412yes—
264C2×D4×C79—22no—
265C2×D4×C79—21no—
266C2×D4×C79—21no—
267C2×D4×C79—24no—
268C2×D4×C79—21no—
269C2×D4×C79—24no—
270C2×D4×C79—22no—
271C2×D4×C79—22no—
272C2×D4×C79C2412yes—
273C2×D4×C79C2412yes—
274C22×C4×C79—21no—
275C22×C4×C79—22no—
276C22×C4×C79—22no—
277C22×C4×C79—24no—
278C22×C4×C79—22no—
279C22×C4×C79—82no—
280C22×C4×C79C2×D411yescharacteristic
281C22×C4×C79C2×D411yescharacteristic
282C22×C4×C79C2411yescharacteristic
283C4⋊C4×C79—21no—
284C4⋊C4×C79—24no—
285C4⋊C4×C79—21no—
286C4⋊C4×C79—21no—
287C4⋊C4×C79C2×D412yes—
288C4⋊C4×C79C2×D412yes—
289C4⋊C4×C79C2×D412yes—
290C4⋊C4×C79C2×D414yes—
291C4⋊C4×C79C2×D414yes—
292C4⋊C4×C79C2×D412yes—
293C4⋊C4×C79C2412yes—
294C22⋊C4×C79—22no—
295C22⋊C4×C79—22no—
296C22⋊C4×C79—24no—
297C22⋊C4×C79—24no—
298C22⋊C4×C79—22no—
299C22⋊C4×C79—24no—
300C22⋊C4×C79—22no—
301C22⋊C4×C79C2×D414yes—
302C42×C79—24no—
303C42×C79C2×D411yescharacteristic
304C42×C79C2×D411yescharacteristic
305C42×C79C2411yescharacteristic
306C42×C79C2411yescharacteristic
307C42×C79C2414yes—
308C23×C79—22no—
309C23×C79—22no—
310C23×C79—42no—
311C23×C79—81no—
312C23×C79—81no—
313C23×C79C22×D411yescharacteristic
314C22×D79—22no—
315C22×D79—24no—
316C22×D79—81no—
317C22×D79—81no—
318Q8×C79—24no—
319Q8×C79—22no—
320Q8×C79—22no—
321Q8×C79—42no—
322D4×C79—22no—
323D4×C79—22no—
324D4×C79—22no—
325D4×C79—22no—
326D4×C79—44no—
327D4×C79—42no—
328D4×C79—42no—
329D4×C79—81no—
330D4×C79—84no—
331D4×C79—84no—
332C2×C4×C79—22no—
333C2×C4×C79—22no—
334C2×C4×C79—22no—
335C2×C4×C79—41no—
336C2×C4×C79—44no—
337C2×C4×C79—44no—
338C2×C4×C79—82no—
339C2×C4×C79—84no—
340C2×C4×C79—81no—
341C2×C4×C79C22×D411yescharacteristic
342C2×C4×C79C22×D411yescharacteristic
343C2×C4×C79C22×D414yes—
344C2×C4×C79C22×D414yes—
345C2×C4×C79C22×D411yescharacteristic
346C2×C4×C79C22×D411yescharacteristic
347C2×C4×C79C22×D411yescharacteristic
348C2×C4×C79C2×#4112yes—
349C2×C4×C792−1+412yes—
350C2×C4×C79C2511yescharacteristic
351C2×Dic79—22no—
352C2×Dic79—22no—
353C2×Dic79—22no—
354C2×Dic79—81no—
355D316—24no—
356D316—22no—
357D316C2×#4114yes—
358C4×D79—44no—
359C4×D79—84no—
360C4×D79—82no—
361C4×D79—84no—
362Dic158—42no—
363Dic158—84no—
364Dic158—81no—
365C79⋊C8—21no—
366C79⋊C8—21no—
367C79⋊C8—24no—
368C79⋊C8—21no—
369C79⋊C8—21no—
370C22×C79—21no—
371C22×C79—21no—
372C22×C79—42no—
373C22×C79—42no—
374C22×C79—42no—
375C22×C79—42no—
376C22×C79—42no—
377C22×C79—42no—
378C22×C79—84no—
379C22×C79#54812yes—
380C22×C79C23×D411yescharacteristic
381C2×D79—24no—
382C2×D79—42no—
383C2×D79—42no—
384C2×D79—84no—
385C4×C79—21no—
386C4×C79—21no—
387C4×C79—24no—
388C4×C79—21no—
389C4×C79—24no—
390C4×C79—42no—
391C4×C79—42no—
392C4×C79#54812yes—
393C4×C79#57612yes—
394C4×C79C22×#4111yescharacteristic
395C4×C79C2×2−1+411yescharacteristic
396Dic79—42no—
397Dic79—42no—
398Dic79—42no—
399#61325—791nomaximal, Sylow
400C2×C79—22no—
401C2×C79—82no—
402C2×C79—82no—
403C2×C79C2×#54811yescharacteristic
404C2×C79C2×#57611yescharacteristic
405C2×C79#358411yescharacteristic
406D79—44no—
407#3506D7911yescharacteristic, complemented
408#3501—791no—
409#3370—794no—
410#3367—792no—
411#3366—792no—
412#3361—794no—
413#3360—792no—
414#3358—792no—
415#3136—792no—
416#3131—791no—
417#3083—792no—
418#3077—791no—
419#3041—792no—
420#3036—791no—
421#2960—791no—
422#2946—792no—
423C2×C4×D8—791no—
424C79#6132511yescharacteristic, complemented, Sylow
425C2×AGL(1,ℤ/8)—792no—
426C22×D8—791no—
427#559C2×D7914yescomplemented
428#556C2×D7912yescomplemented
429#555—21no—
430#554—792no—
431#554—794no—
432#554—1581no—
433#554—1582no—
434#553—22no—
435#550C2×D7912yescomplemented
436D4×Q8—792no—
437D4×Q8—1581no—
438#547—21no—
439#544—792no—
440#543—1582no—
441#538—22no—
442#535C2×D7912yes—
443#533—791no—
444#533C2×D7911yescharacteristic
445#532C2×D7911yescharacteristic
446#525—22no—
447C2×C22⋊Q8—1582no—
448#520C2×D7912yes—
449#518—792no—
450C2×C4×D4—791no—
451C2×C4×D4C2×D7911yescharacteristic
452#490—794no—
453#489—794no—
454#488—794no—
455#488—792no—
456#488—792no—
457#487—791no—
458#487—791no—
459#486—791no—
460#486—794no—
461#486—791no—
462#479—794no—
463#478—794no—
464#478—794no—
465#477—794no—
466#476—792no—
467#474—792no—
468#474—794no—
469#463—794no—
470#463—794no—
471#463—794no—
472#461—792no—
473#459—792no—
474#459—794no—
475#459—794no—
476#446—792no—
477#446—792no—
478C8×Q8—792no—
479C8×Q8—792no—
480#442—794no—
481#440—794no—
482C4×SD16—794no—
483C4×D8—792no—
484C4×D8—792no—
485C4×D8—792no—
486C4×D8—792no—
487C4×D8—794no—
488#428—792no—
489C2×#107—791no—
490#424—792no—
491#423—791no—
492#418—792no—
493#417—792no—
494#416—792no—
495#416—792no—
496C2×#102—791no—
497C2×#102—791no—
498#405—792no—
499C2×C4×C8—791no—
500C2×#41—22no—
501C2×#41C22×D7912yes—
502C22×Q8—1582no—
503C22×D4—791no—
504C22×D4C22×D7911yescharacteristic
505C23×C4—21no—
506C23×C4—1581no—
507AGL(1,ℤ/8)—1588no—
508C2×SD16—794no—
509C2×D8—792no—
510C2×D8—792no—
511C2×D8—794no—
512C2×D8—1584no—
513C2×M16—792no—
514C22×C8—791no—
515C22×C8—791no—
516C4⋊Q8—791no—
517C4⋊Q8—791no—
518C4⋊Q8—794no—
519C4⋊Q8—1582no—
520C4⋊Q8C22⋊D7911yescharacteristic
521C4⋊Q8C22⋊D7911yescharacteristic
522C4⋊Q8C22×D7911yescharacteristic
523#127C22×D7911yescharacteristic
524#127C22×D7914yes—
525#126—24no—
526#125—792no—
527#125—794no—
528#125—1582no—
529#125C22⋊D7912yes—
530#124—24no—
531#124C22×D7912yes—
532#124C22×D7914yes—
533#123—24no—
534#123—24no—
535C22⋊Q8—22no—
536C22⋊Q8—1582no—
537C22⋊Q8—1584no—
538C22⋊Q8—1581no—
539C22⋊Q8—1581no—
540C22⋊Q8—1582no—
541C22⋊Q8—1584no—
542C22⋊Q8—1584no—
543C22⋊Q8—1584no—
544C22⋊Q8—1584no—
545C22⋊Q8—1584no—
546C22⋊Q8C22⋊D7912yes—
547C22⋊Q8C22⋊D7912yes—
548#121—21no—
549#121—21no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—24no—
554#120—24no—
555C4×Q8—1581no—
556C4×Q8—1581no—
557C4×Q8C22×D7914yes—
558C4×Q8C22×D7912yes—
559C4×Q8C22×D7912yes—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—792no—
567C4×D4—792no—
568C4×D4—794no—
569C4×D4—794no—
570C4×D4—1582no—
571C4×D4—1582no—
572C4×D4—1581no—
573C4×D4—1581no—
574C4×D4C22×D7912yes—
575C4×D4C22×D7912yes—
576C4×D4C22×D7914yes—
577#117—22no—
578#117—22no—
579#117—792no—
580#117C22×D7912yes—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—791no—
583C2×C4⋊C4—1584no—
584C2×C4⋊C4—1582no—
585C2×C4⋊C4C22×D7911yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—1581no—
588C2×C22⋊C4—1584no—
589C2×C42C22×D7911yescharacteristic
590#107—792no—
591#107—792no—
592#107—794no—
593#106—794no—
594C4⋊C8—792no—
595C4⋊C8—792no—
596C4⋊C8—794no—
597C4⋊C8—794no—
598#103—792no—
599#103—792no—
600#103—792no—
601#103—792no—
602#103—794no—
603#102—792no—
604#102—792no—
605#102—792no—
606#102—792no—
607#102—792no—
608#102—792no—
609#102—794no—
610#102—794no—
611#102—794no—
612#102—792no—
613#102—792no—
614#97—794no—
615C4×C8—791no—
616C4×C8—791no—
617C4×C8—791no—
618C4×C8—791no—
619C4×C8—794no—
620C24—21no—
621C24—1581no—
622#41—24no—
623#41—24no—
624#41—84no—
625C2×Q8—6324no—
626C2×Q8—1581no—
627C2×Q8—1581no—
628C2×Q8—1584no—
629C2×Q8C2×C22⋊D7912yes—
630C2×Q8C2×C22⋊D7912yes—
631C2×Q8C23×D7912yes—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—24no—
640C2×D4—794no—
641C2×D4—792no—
642C2×D4—1582no—
643C2×D4—1581no—
644C2×D4C23×D7912yes—
645C2×D4C23×D7912yes—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—24no—
650C22×C4—22no—
651C22×C4—82no—
652C22×C4—6322no—
653C22×C4—1582no—
654C22×C4—1581no—
655C22×C4—1584no—
656C22×C4—1584no—
657C22×C4—1582no—
658C22×C4C2×C22⋊D7911yescharacteristic
659C22×C4C2×C22⋊D7911yescharacteristic
660C22×C4C23×D7911yescharacteristic
661SD16—1588no—
662D8—1584no—
663D8—1584no—
664D8—1588no—
665M16—1584no—
666C2×C8—791no—
667C2×C8—791no—
668C2×C8—791no—
669C2×C8—791no—
670C2×C8—794no—
671C2×C8—1582no—
672C2×C8—1582no—
673C4⋊C4—21no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—792no—
678C4⋊C4—792no—
679C4⋊C4—792no—
680C4⋊C4—1582no—
681C4⋊C4—1584no—
682C4⋊C4—1584no—
683C4⋊C4—1582no—
684C4⋊C4—1581no—
685C4⋊C4—1581no—
686C4⋊C4—1584no—
687C4⋊C4—1581no—
688C4⋊C4C2×C22⋊D7912yes—
689C4⋊C4C2×C22⋊D7912yes—
690C4⋊C4C2×C22⋊D7914yes—
691C4⋊C4C2×C22⋊D7912yes—
692C4⋊C4C2×C22⋊D7914yes—
693C4⋊C4C2×C22⋊D7912yes—
694C4⋊C4C23×D7912yes—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—22no—
700C22⋊C4—24no—
701C22⋊C4—22no—
702C22⋊C4—1582no—
703C22⋊C4—1584no—
704C22⋊C4—1584no—
705C22⋊C4—1582no—
706C22⋊C4—1582no—
707C22⋊C4C2×C22⋊D7914yes—
708C42—24no—
709C42—1582no—
710C42C2×C22⋊D7911yescharacteristic
711C42C2×C22⋊D7911yescharacteristic
712C42C23×D7911yescharacteristic
713C42C23×D7911yescharacteristic
714C42C23×D7914yes—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—81no—
719C23—81no—
720C23—6321no—
721C23—6321no—
722C23—1582no—
723C23—1584no—
724C23C22×C22⋊D7911yescharacteristic
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—3162no—
730Q8—6324no—
731Q8—6321no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—42no—
738D4—42no—
739D4—81no—
740D4—84no—
741D4—84no—
742D4—794no—
743D4—1582no—
744D4—1584no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—41no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—82no—
752C2×C4—84no—
753C2×C4—81no—
754C2×C4—3164no—
755C2×C4—6322no—
756C2×C4—6324no—
757C2×C4—6324no—
758C2×C4—6321no—
759C2×C4—1582no—
760C2×C4—1582no—
761C2×C4—1582no—
762C2×C4C22×C22⋊D7914yes—
763C2×C4C22×C22⋊D7911yescharacteristic
764C2×C4C22×C22⋊D7911yescharacteristic
765C2×C4C22×C22⋊D7911yescharacteristic
766C2×C4C22×C22⋊D7914yes—
767C2×C4C22×C22⋊D7911yescharacteristic
768C2×C4C22×C22⋊D7911yescharacteristic
769C2×C4#41×D7912yes—
770C2×C4#1457920812yes—
771C2×C4C24×D7911yescharacteristic
772C8—1581no—
773C8—1581no—
774C8—1581no—
775C8—1581no—
776C8—1584no—
777C22—21no—
778C22—21no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—3162no—
787C22—3162no—
788C22—6324no—
789C22—1584no—
790C22#1909922012yes—
791C22C23×C22⋊D7911yescharacteristic
792C4—21no—
793C4—24no—
794C4—21no—
795C4—21no—
796C4—24no—
797C4—42no—
798C4—42no—
799C4—3162no—
800C4—3162no—
801C4—3162no—
802C4#1909922012yes—
803C4#1909936612yes—
804C4C2×#41×D7911yescharacteristic
805C4C2×#1457920811yescharacteristic
806C2—22no—
807C2—82no—
808C2—82no—
809C2—3164no—
810C2C2×#1909922011yescharacteristic
811C2C2×#1909936611yescharacteristic
812C2#2377817111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC79×#3506C2
socleC22×C79C23×D4
hypercenter#3506D79
hypocenterC79#61325
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #533 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #23777201C2semidirect
2. #23776147C2semidirect
3. #23776114C2semidirect
4. #23776103C2semidirect
5. #23776056C2semidirect
6. #23776045C2semidirect
7. #23776031C2semidirect
8. #23773754C2semidirect
9. #23773722C2semidirect
10. #23773251C2semidirect
11. #23773197C2semidirect
12. #23772899C2semidirect
13. #23772860C2semidirect
14. #23772335C2semidirect
15. #23772228C2semidirect
16. C2×C4×#11929609C2semidirect
17. C79×#3506C2semidirect
21. #19099273C22semidirect
22. #19099273C22semidirect
24. Q8×D316C22semidirect
32. #19098927C22semidirect
33. #19098922C22semidirect
34. #19098917C22semidirect
35. #19098917C22semidirect
36. #19098917C22semidirect
37. #19098913C22semidirect
38. #19098913C22semidirect
39. #19098909C22semidirect
40. #19098909C22semidirect
41. #19098909C22semidirect
42. #19098870C22semidirect
43. #19098863C22semidirect
44. #19098863C22semidirect
45. #19098858C22semidirect
46. #19098853C22semidirect
47. #19098843C22semidirect
48. #19098843C22semidirect
51. #19098775C22semidirect
52. #19098765C22semidirect
55. #19098755C22semidirect
56. #19098694C22semidirect
57. #19098694C22semidirect
58. Q8×C79⋊C8C22semidirect
59. Q8×C79⋊C8C22semidirect
60. #19098673C22semidirect
61. #19098661C22semidirect
62. C4×#11929611C22semidirect
67. C4×#11929609C22semidirect
80. #559×C79C22semidirect
81. #556×C79C22semidirect
84. #550×C79C22semidirect
220. C2×D316#41semidirect
407. #3506D79semidirect
424. C79#61325semidirect
427. #559C2×D79semidirect
428. #556C2×D79semidirect
435. #550C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237772012
#237761472
#237761142
#237761032
#237760562
#237760452
#237760312
#237737542
#237737222
#237732512
#237731972
#237728992
#237728602
#237723352
#237722282
C2×C4×#119296092
C79×#35062
#6132579