Finite Group Databasebeta

← #35163455

Subgroups — #35163455

Order 20224.

2790 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099363C212yesmaximal, complemented
2D4×#11929624C212yesmaximal, complemented
3#23775068C212yesmaximal, complemented
4#23775058C212yesmaximal, complemented
5#23775048C212yesmaximal, complemented
6#23775036C214yesmaximal, complemented
7#23775022C212yesmaximal, complemented
8#23775012C212yesmaximal, complemented
9#23775002C212yesmaximal, complemented
10#23773828C211yesmaximal, characteristic, complemented
11#23773009C212yesmaximal, complemented
12#23772857C212yesmaximal, complemented
13#23772622C214yesmaximal, complemented
14C4×#14579183C211yesmaximal, characteristic, complemented
15C2×#436×C79C211yesmaximal, characteristic, complemented
16C22×#11929624C2214yescomplemented
17#19099363—216no—
18C2×#14579194C2214yescomplemented
19C2×#14579194C2214yescomplemented
20C2×#14579189C2214yescomplemented
21C2×#14579189C2214yescomplemented
22C2×#14579183C2211yescharacteristic
23C2×#14579183C2212yescomplemented
24C2×#14579183C2214yescomplemented
25C2×#14579183C2212yescomplemented
26#19099234C2212yes—
27D4×Dic158C2212yescomplemented
28#19099222C2214yescomplemented
29#19099218C2212yes—
30#19099214—22no—
31#19099209C2214yescomplemented
32#19099203—24no—
33D4×D316C2212yescomplemented
34D4×C22⋊D79—22no—
35#19099113C2212yescomplemented
36#19099110—22no—
37#19099074C2214yescomplemented
38#19099072—24no—
39C4×#11929624C2212yescomplemented
40C4×D4×D79—22no—
41#19098947C2212yescomplemented
42#19098947C2212yescomplemented
43#19098943C2211yescharacteristic, complemented
44#19098940C2211yescharacteristic, complemented
45#19098936C2212yescomplemented
46#19098821C2214yescomplemented
47#19098816C2214yescomplemented
48#19098809C2214yescomplemented
49#19098809C2214yescomplemented
50#19098786C2214yescomplemented
51#19098779C2214yescomplemented
52#19098774C2212yescomplemented
53#19098769C2212yescomplemented
54#19098764C2212yescomplemented
55#19098759C2212yescomplemented
56#19098727C2214yescomplemented
57#19098727C2214yescomplemented
58#19098721C2214yescomplemented
59#19098716C2214yescomplemented
60#19098710C2214yescomplemented
61#19098710C2214yescomplemented
62#19098704C2214yescomplemented
63#19098699C2214yescomplemented
64C4×Dic316C2211yescharacteristic, complemented
65C4×Dic316C2211yescharacteristic, complemented
66C4×#11929613C2212yescomplemented
67C4×#11929613C2212yescomplemented
68C4×D632C2211yescharacteristic, complemented
69C4×D632C2211yescharacteristic, complemented
70#19098601C2211yescharacteristic, complemented
71#19098560C2212yescomplemented
72#19098560C2214yescomplemented
73C22×M16×C79C2212yescomplemented
74C2×C4×D4×C79C2211yescharacteristic
75#436×C79C2212yescomplemented
76#436×C79C2212yescomplemented
77#436×C79C2212yescomplemented
78#436×C79C2212yescomplemented
79C2×C4⋊C8×C79C2211yescharacteristic, complemented
80C2×C22⋊C8×C79C2212yescomplemented
81C2×C4×C8×C79C2211yescharacteristic, complemented
82C2×#11929624—24no—
83C2×#11929624—24no—
84C2×#11929624—216no—
85C2×#11929624—48no—
86C2×#11929624C2314yes—
87C2×#11929624C2314yes—
88C2×#11929624C2314yes—
89C2×#11929624C2312yes—
90C22×Dic158C2314yes—
91C22×D316C2314yes—
92C22×C22⋊D79—24no—
93C2×D4×D79—22no—
94C22×C4×D79—24no—
95#14579194—216no—
96#14579194—216no—
97#14579189—216no—
98#14579189—216no—
99#14579183—28no—
100#14579183—216no—
101#14579183—44no—
102#14579183D418yescomplemented
103C2×Dic316C2312yes—
104C2×Dic316C2314yes—
105C2×Dic316C2312yes—
106C2×Dic316C2311yescharacteristic
107C2×#11929613C2314yes—
108C2×#11929613C2314yes—
109C2×#11929613C2314yes—
110C2×#11929613C2314yes—
111C2×#11929613C2312yes—
112C2×D632C2312yes—
113C2×D632C2314yes—
114C2×D632C2312yes—
115C2×D632C2311yescharacteristic
116#14579161C2312yes—
117#14579160—22no—
118#14579158C2312yes—
119#14579157—22no—
120#14579149C2314yes—
121#14579147—24no—
122#14579146—24no—
123#14579144—24no—
124#14579143—24no—
125#14579140C2314yes—
126#14579140C2314yes—
127#14579139—24no—
128#14579138—24no—
129#14579136—22no—
130#14579135—22no—
131#14579135—22no—
132#14579135C2314yes—
133#14579135C2314yes—
134#14579134—24no—
135#14579134—24no—
136#14579133—24no—
137#14579132—22no—
138#14579131—24no—
139#14579130—24no—
140#14579129—24no—
141C4×Dic158C2312yes—
142C4×Dic158C2312yes—
143C4×D316—22no—
144C4×D316—22no—
145C4×D316C2312yes—
146C4×D316C2312yes—
147D4×Dic79—22no—
148#14579123—22no—
149C4×C22⋊D79—22no—
150C4×C22⋊D79—22no—
151C4×C22⋊D79—24no—
152C4×C22⋊D79—24no—
153(C22⋊D79)⋊C4—24no—
154#14579120C2312yes—
155#14579118—22no—
156C4⋊C4×D79—22no—
157C22⋊C4×D79—24no—
158C42×D79—22no—
159#14579095C2311yescharacteristic
160#14579095C2311yescharacteristic
161#14579093C2312yes—
162#14579086C2312yes—
163#14579086C2312yes—
164#14579086C2314yes—
165#14579086C2314yes—
166#14579083C2312yes—
167#14579083C2312yes—
168#14579083C2314yes—
169#14579083C2314yes—
170C22×D4×C79D411yescharacteristic
171C23×C4×C79C2312yes—
172C2×M16×C79—28no—
173C2×M16×C79C2314yes—
174C2×M16×C79C2314yes—
175C22×C8×C79C2312yes—
176C22×C8×C79C2311yescharacteristic
177C22×C8×C79C2311yescharacteristic
178C4×D4×C79D412yes—
179C4×D4×C79D412yes—
180C4×D4×C79C2312yes—
181C4×D4×C79C2312yes—
182C2×C4⋊C4×C79D411yescharacteristic
183C2×C22⋊C4×C79D412yes—
184C2×C42×C79C2311yescharacteristic
185C4⋊C8×C79C2312yes—
186C4⋊C8×C79C2312yes—
187C22⋊C8×C79C2314yes—
188C22⋊C8×C79C2314yes—
189C4×C8×C79C2311yescharacteristic
190C4×C8×C79C2311yescharacteristic
191C4×C8×C79C2311yescharacteristic
192C4×C8×C79C2311yescharacteristic
193C23×D79—24no—
194#11929624—24no—
195#11929624—28no—
196#11929624—28no—
197#11929624—28no—
198#11929624—28no—
199#11929624—416no—
200#11929624—44no—
201#11929624—44no—
202#11929624—416no—
203#11929624C2×D418yescomplemented
204C2×Dic158—28no—
205C2×Dic158—24no—
206C2×Dic158—44no—
207C2×Dic158C2414yes—
208C2×Dic158C2412yes—
209C2×D316—28no—
210C2×D316—24no—
211C2×D316—22no—
212C2×D316—22no—
213C2×D316—44no—
214C2×D316C2414yes—
215C2×D316C2412yes—
216C2×C22⋊D79—22no—
217C2×C22⋊D79—24no—
218C2×C22⋊D79—24no—
219C2×C22⋊D79—24no—
220C2×C22⋊D79—24no—
221C2×C22⋊D79—24no—
222C2×C22⋊D79—416no—
223D4×D79—48no—
224C22×Dic79—24no—
225C2×C4×D79—22no—
226C2×C4×D79—24no—
227C2×C4×D79—24no—
228C2×C4×D79—24no—
229C2×C4×D79—22no—
230C2×C4×D79—22no—
231C2×C4×D79—416no—
232Dic316—28no—
233Dic316—24no—
234Dic316—42no—
235Dic316C2×D414yescomplemented
236#11929613—28no—
237#11929613—28no—
238#11929613—28no—
239#11929613—44no—
240#11929613C2×D418yescomplemented
241D632—28no—
242D632—24no—
243D632—42no—
244D632C2×D414yescomplemented
245C4⋊Dic79—22no—
246C4⋊Dic79—22no—
247C4⋊Dic79C2412yes—
248C4⋊Dic79C2412yes—
249Dic79⋊C4—24no—
250Dic79⋊C4—22no—
251Dic79⋊C4—22no—
252Dic79⋊C4—24no—
253C22⋊Dic79—24no—
254C22⋊Dic79—22no—
255C22⋊Dic79—24no—
256(C2×D79)⋊C4—24no—
257(C2×D79)⋊C4—24no—
258(C2×D79)⋊C4—22no—
259(C2×D79)⋊C4—22no—
260(C2×D79)⋊C4—24no—
261(C2×D79)⋊C4—24no—
262C4×Dic79—22no—
263C4×Dic79—22no—
264C4×Dic79—22no—
265C24×C79C2×D412yes—
266C2×D4×C79—42no—
267C2×D4×C79C2×D412yes—
268C2×D4×C79C2×D412yes—
269C22×C4×C79—24no—
270C22×C4×C79—24no—
271C22×C4×C79C2×D412yes—
272C22×C4×C79C2×D414yes—
273C22×C4×C79C2×D411yescharacteristic
274C22×C4×C79C2×D411yescharacteristic
275C22×C4×C79C2414yes—
276C22×C4×C79C2411yescharacteristic
277M16×C79—28no—
278M16×C79—28no—
279C2×C8×C79—24no—
280C2×C8×C79—22no—
281C2×C8×C79C2×D414yescomplemented
282C2×C8×C79C2411yescharacteristic
283C2×C8×C79C2411yescharacteristic
284C2×C8×C79C2414yes—
285C2×C8×C79C2411yescharacteristic
286C2×C8×C79C2411yescharacteristic
287C4⋊C4×C79C2×D412yes—
288C4⋊C4×C79C2×D412yes—
289C22⋊C4×C79C2×D414yes—
290C22⋊C4×C79C2×D414yes—
291C42×C79C2×D411yescharacteristic
292C42×C79C2×D411yescharacteristic
293C42×C79C2411yescharacteristic
294C42×C79C2411yescharacteristic
295C23×C79—24no—
296C23×C79—42no—
297C23×C79—42no—
298C23×C79C22×D414yes—
299C23×C79C22×D411yescharacteristic
300C22×D79—22no—
301C22×D79—24no—
302C22×D79—48no—
303C22×D79—48no—
304C22×D79—84no—
305D4×C79—24no—
306D4×C79—42no—
307C2×C4×C79—24no—
308C2×C4×C79—28no—
309C2×C4×C79—22no—
310C2×C4×C79—24no—
311C2×C4×C79—24no—
312C2×C4×C79—41no—
313C2×C4×C79C22×D412yes—
314C2×C4×C79C22×D411yescharacteristic
315C2×C4×C79C22×D411yescharacteristic
316C2×C4×C79C22×D411yescharacteristic
317C2×C4×C79C22×D414yes—
318C2×C4×C79C22×D411yescharacteristic
319C2×C4×C79C22×D411yescharacteristic
320C2×C4×C79H(5,𝔽2)12yes—
321C2×C4×C79C2511yescharacteristic
322C22⋊D79—28no—
323C22⋊D79—48no—
324C22⋊D79—48no—
325C22⋊D79—48no—
326C22⋊D79—48no—
327C22⋊D79—84no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—24no—
332C2×Dic79—48no—
333D316—24no—
334D316—22no—
335D316—24no—
336D316—48no—
337D316—44no—
338D316—82no—
339D316C22×D414yes—
340C4×D79—28no—
341C4×D79—48no—
342C4×D79—48no—
343C4×D79—48no—
344C4×D79—44no—
345C4×D79—82no—
346Dic158—22no—
347Dic158—24no—
348Dic158—24no—
349Dic158—48no—
350Dic158C22×D414yes—
351C8×C79—24no—
352C8×C79—21no—
353C8×C79—21no—
354C8×C79C22×D412yes—
355C8×C79C22×D412yes—
356C22×C79—21no—
357C22×C79—21no—
358C22×C79—24no—
359C22×C79—24no—
360C22×C79—24no—
361C22×C79—84no—
362C22×C79D4212yes—
363C22×C79C23×D411yescharacteristic
364C2×D79—24no—
365C2×D79—42no—
366C2×D79—42no—
367C2×D79—44no—
368C2×D79—44no—
369C2×D79—44no—
370C2×D79—816no—
371C4×C79—21no—
372C4×C79—21no—
373C4×C79—24no—
374C4×C79—21no—
375C4×C79D4212yes—
376C4×C79#57512yescomplemented
377C4×C79C23×D411yescharacteristic
378C4×C79C2×H(5,𝔽2)11yescharacteristic
379Dic79—24no—
380Dic79—42no—
381Dic79—44no—
382Dic79—42no—
383#61038—791nomaximal, Sylow
384C2×C79—22no—
385C2×C79—44no—
386C2×C79C2×D4211yescharacteristic
387C2×C79C2×#57511yescharacteristic
388C2×C79#358411yescharacteristic
389D79—44no—
390D79—84no—
391C2×#575—792no—
392D4×#41—792no—
393#3278—792no—
394#3277—792no—
395#3276—792no—
396#3275—794no—
397#3274—792no—
398#3273—792no—
399#3272—792no—
400#3147—791no—
401#3054—792no—
402#3035—792no—
403#3002—794no—
404C4×#135—791no—
405C2×#436D7911yescharacteristic, complemented
406C79#6103811yescharacteristic, complemented, Sylow
407C22×#41—794no—
408#575—15816no—
409C2×#137—794no—
410C2×#137—794no—
411C2×AGL(1,ℤ/8)—794no—
412C2×AGL(1,ℤ/8)—794no—
413C2×#135—792no—
414C2×#135—791no—
415C2×#135—792no—
416C2×#135—794no—
417C22×M16C2×D7912yescomplemented
418#550—792no—
419D4×Q8—792no—
420#548—794no—
421#547—792no—
422#547—1582no—
423#546—794no—
424#546—1584no—
425D42—792no—
426D42—1582no—
427#532—792no—
428#532—1582no—
429#525—794no—
430#525—1584no—
431C4×#41—792no—
432C2×C4×D4—1582no—
433C2×C4×D4C2×D7911yescharacteristic
434#495—792no—
435#495—792no—
436#494—791no—
437#493—791no—
438#492—792no—
439#470—794no—
440#469—794no—
441#468—794no—
442#468—794no—
443#464—794no—
444#463—794no—
445#462—792no—
446#461—792no—
447#460—792no—
448#459—792no—
449#452—794no—
450#452—794no—
451#451—794no—
452#450—794no—
453#449—794no—
454#449—794no—
455#448—794no—
456#447—794no—
457C4×Q16—791no—
458C4×Q16—791no—
459C4×SD16—792no—
460C4×SD16—792no—
461C4×D8—791no—
462C4×D8—791no—
463#436C2×D7912yescomplemented
464#436C2×D7912yescomplemented
465#436C2×D7912yescomplemented
466#436C2×D7912yescomplemented
467#427—791no—
468C2×C4⋊C8C2×D7911yescharacteristic, complemented
469#416—792no—
470#416—794no—
471C2×C22⋊C8C2×D7912yescomplemented
472C2×C4×C8C2×D7911yescharacteristic, complemented
473C2×#41—3168no—
474C2×#41—794no—
475C2×#41—794no—
476C2×#41—792no—
477C2×#41—794no—
478C2×#41—15816no—
479C2×#41—1584no—
480C2×#41—1584no—
481C22×Q8—794no—
482C22×D4—794no—
483C22×D4—1584no—
484C22×D4—1582no—
485C22×D4D31611yescharacteristic
486C23×C4—1584no—
487C23×C4C22×D7912yes—
488#137—15816no—
489#137—15816no—
490AGL(1,ℤ/8)—15816no—
491AGL(1,ℤ/8)—15816no—
492#135—3164no—
493#135—798no—
494#135—15816no—
495#135—1588no—
496C2×Q16—792no—
497C2×Q16—791no—
498C2×Q16—794no—
499C2×Q16—792no—
500C2×SD16—794no—
501C2×SD16—792no—
502C2×SD16—794no—
503C2×SD16—794no—
504C2×SD16—794no—
505C2×D8—792no—
506C2×D8—791no—
507C2×D8—794no—
508C2×D8—792no—
509C2×M16—28no—
510C2×M16C22×D7914yes—
511C2×M16C22×D7914yes—
512C22×C8C22×D7912yes—
513C22×C8C22×D7911yescharacteristic
514C22×C8C22×D7911yescharacteristic
515C4⋊Q8—792no—
516C4⋊Q8—1582no—
517#127—792no—
518#127—1582no—
519#124—794no—
520#124—1584no—
521#123—1584no—
522#123—1584no—
523#123—1584no—
524C22⋊Q8—794no—
525C22⋊Q8—794no—
526C22⋊Q8—1584no—
527C22⋊Q8—1584no—
528#121—794no—
529#121—794no—
530#121—1584no—
531#121—1582no—
532#121—1582no—
533#121—1582no—
534#121—1582no—
535#121—1584no—
536#121—1584no—
537#120—1584no—
538#120—1584no—
539#120—1584no—
540C4×Q8—792no—
541C4×Q8—792no—
542C4×D4—792no—
543C4×D4—792no—
544C4×D4—1582no—
545C4×D4—1584no—
546C4×D4—1582no—
547C4×D4—1582no—
548C4×D4—1584no—
549C4×D4—1582no—
550C4×D4—1584no—
551C4×D4—1582no—
552C4×D4—1582no—
553C4×D4D31612yes—
554C4×D4D31612yes—
555C4×D4C22×D7912yes—
556C4×D4C22×D7912yes—
557#117—792no—
558#117—1582no—
559C2×C4⋊C4—1582no—
560C2×C4⋊C4D31611yescharacteristic
561C2×C22⋊C4—1584no—
562C2×C22⋊C4D31612yes—
563C2×C42—1582no—
564C2×C42C22×D7911yescharacteristic
565#107—791no—
566#107—791no—
567#106—792no—
568C4⋊C8C22×D7912yes—
569C4⋊C8C22×D7912yes—
570#103—792no—
571#103—792no—
572#103—794no—
573#103—794no—
574#102—792no—
575#102—792no—
576#102—794no—
577#102—794no—
578C22⋊C8C22×D7914yes—
579C22⋊C8C22×D7914yes—
580C4×C8C22×D7911yescharacteristic
581C4×C8C22×D7911yescharacteristic
582C4×C8C22×D7911yescharacteristic
583C4×C8C22×D7911yescharacteristic
584C24—1584no—
585C24C2×D31612yes—
586#41—31616no—
587#41—3164no—
588#41—3164no—
589#41—31616no—
590#41—798no—
591#41—1588no—
592#41—1588no—
593#41—1588no—
594#41—1588no—
595#41—1584no—
596C2×Q8—3164no—
597C2×Q8—792no—
598C2×Q8—794no—
599C2×Q8—1588no—
600C2×Q8—1584no—
601C2×D4—42no—
602C2×D4—3164no—
603C2×D4—3168no—
604C2×D4—31616no—
605C2×D4—792no—
606C2×D4—794no—
607C2×D4—1588no—
608C2×D4—1584no—
609C2×D4—1584no—
610C2×D4—1584no—
611C2×D4—1584no—
612C2×D4—1584no—
613C2×D4—1582no—
614C2×D4—1582no—
615C2×D4—1584no—
616C2×D4—1582no—
617C2×D4C2×D31612yes—
618C2×D4C2×D31612yes—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—31616no—
622C22×C4—1584no—
623C22×C4—1582no—
624C22×C4—1584no—
625C22×C4—1584no—
626C22×C4—1584no—
627C22×C4—1582no—
628C22×C4—1582no—
629C22×C4C2×D31611yescharacteristic
630C22×C4C2×D31612yes—
631C22×C4C2×D31614yes—
632C22×C4C2×D31611yescharacteristic
633C22×C4C23×D7914yes—
634C22×C4C23×D7911yescharacteristic
635Q16—3162no—
636Q16—794no—
637Q16—1588no—
638Q16—1584no—
639SD16—3164no—
640SD16—798no—
641SD16—1588no—
642SD16—1588no—
643SD16—1588no—
644D8—3162no—
645D8—794no—
646D8—1588no—
647D8—1584no—
648M16—28no—
649M16—28no—
650C2×C8—22no—
651C2×C8—24no—
652C2×C8D4×D7914yescomplemented
653C2×C8C23×D7911yescharacteristic
654C2×C8C23×D7911yescharacteristic
655C2×C8C23×D7914yes—
656C2×C8C23×D7911yescharacteristic
657C2×C8C23×D7911yescharacteristic
658C4⋊C4—792no—
659C4⋊C4—792no—
660C4⋊C4—1584no—
661C4⋊C4—1582no—
662C4⋊C4—1582no—
663C4⋊C4—1584no—
664C4⋊C4—1582no—
665C4⋊C4—1582no—
666C4⋊C4C2×D31612yes—
667C4⋊C4C2×D31612yes—
668C22⋊C4—1584no—
669C22⋊C4—1582no—
670C22⋊C4—1584no—
671C22⋊C4—1584no—
672C22⋊C4—1584no—
673C22⋊C4—1582no—
674C22⋊C4—1582no—
675C22⋊C4—1584no—
676C22⋊C4—1584no—
677C22⋊C4C2×D31614yes—
678C22⋊C4C2×D31614yes—
679C42—1582no—
680C42—1582no—
681C42—1582no—
682C42C2×D31611yescharacteristic
683C42C2×D31611yescharacteristic
684C42C23×D7911yescharacteristic
685C42C23×D7911yescharacteristic
686C23—24no—
687C23—42no—
688C23—42no—
689C23—3168no—
690C23—3168no—
691C23—6324no—
692C23—1584no—
693C23—1582no—
694C23C22×D31614yes—
695C23C22×D31611yescharacteristic
696Q8—3168no—
697Q8—794no—
698Q8—1584no—
699Q8—1584no—
700Q8—1582no—
701D4—24no—
702D4—42no—
703D4—3168no—
704D4—3168no—
705D4—3168no—
706D4—3168no—
707D4—3168no—
708D4—3164no—
709D4—794no—
710D4—6322no—
711D4—6324no—
712D4—1588no—
713D4—1584no—
714D4—1582no—
715D4—1584no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—41no—
722C2×C4—3168no—
723C2×C4—3168no—
724C2×C4—3168no—
725C2×C4—3168no—
726C2×C4—3164no—
727C2×C4—6322no—
728C2×C4—1582no—
729C2×C4—1582no—
730C2×C4—1584no—
731C2×C4—1582no—
732C2×C4—1588no—
733C2×C4C2×D4×D7912yes—
734C2×C4C22×D31611yescharacteristic
735C2×C4C22×D31611yescharacteristic
736C2×C4C22×D31611yescharacteristic
737C2×C4C22×D31614yes—
738C2×C4C22×D31611yescharacteristic
739C2×C4C22×D31611yescharacteristic
740C2×C4#1457920712yes—
741C2×C4C24×D7911yescharacteristic
742C8—21no—
743C8—21no—
744C8—24no—
745C8C2×D4×D7912yes—
746C8C2×D4×D7912yes—
747C22—21no—
748C22—21no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—84no—
753C22—3162no—
754C22—3162no—
755C22—3164no—
756C22—3164no—
757C22—3164no—
758C22—63216no—
759C22—1584no—
760C22D4×D31612yes—
761C22C23×D31611yescharacteristic
762C4—24no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—3164no—
767C4—3162no—
768C4—3162no—
769C4—1584no—
770C4D4×D31612yes—
771C4#1909936312yescomplemented
772C4C22×D4×D7911yescharacteristic
773C4C2×#1457920711yescharacteristic
774C2—22no—
775C2—44no—
776C2—3164no—
777C2—6324no—
778C2C2×D4×D31611yescharacteristic
779C2C2×#1909936311yescharacteristic
780C2#2377817411yescharacteristic
subgroupG/H
centerC2×C4C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#436×C79C2
socleC22×C79C23×D4
hypercenterC2×#436D79
hypocenterC79#61038
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#19099363C2semidirect
2. D4×#11929624C2semidirect
3. #23775068C2semidirect
4. #23775058C2semidirect
5. #23775048C2semidirect
6. #23775036C2semidirect
7. #23775022C2semidirect
8. #23775012C2semidirect
9. #23775002C2semidirect
10. #23773828C2semidirect
11. #23773009C2semidirect
12. #23772857C2semidirect
13. #23772622C2semidirect
14. C4×#14579183C2semidirect
15. C2×#436×C79C2semidirect
16. C22×#11929624C22semidirect
18. C2×#14579194C22semidirect
19. C2×#14579194C22semidirect
20. C2×#14579189C22semidirect
21. C2×#14579189C22semidirect
23. C2×#14579183C22semidirect
24. C2×#14579183C22semidirect
25. C2×#14579183C22semidirect
27. D4×Dic158C22semidirect
28. #19099222C22semidirect
31. #19099209C22semidirect
33. D4×D316C22semidirect
35. #19099113C22semidirect
37. #19099074C22semidirect
39. C4×#11929624C22semidirect
41. #19098947C22semidirect
42. #19098947C22semidirect
43. #19098943C22semidirect
44. #19098940C22semidirect
45. #19098936C22semidirect
46. #19098821C22semidirect
47. #19098816C22semidirect
48. #19098809C22semidirect
49. #19098809C22semidirect
50. #19098786C22semidirect
51. #19098779C22semidirect
52. #19098774C22semidirect
53. #19098769C22semidirect
54. #19098764C22semidirect
55. #19098759C22semidirect
56. #19098727C22semidirect
57. #19098727C22semidirect
58. #19098721C22semidirect
59. #19098716C22semidirect
60. #19098710C22semidirect
61. #19098710C22semidirect
62. #19098704C22semidirect
63. #19098699C22semidirect
64. C4×Dic316C22semidirect
65. C4×Dic316C22semidirect
66. C4×#11929613C22semidirect
67. C4×#11929613C22semidirect
68. C4×D632C22semidirect
69. C4×D632C22semidirect
70. #19098601C22semidirect
71. #19098560C22semidirect
72. #19098560C22semidirect
73. C22×M16×C79C22semidirect
75. #436×C79C22semidirect
76. #436×C79C22semidirect
77. #436×C79C22semidirect
78. #436×C79C22semidirect
79. C2×C4⋊C8×C79C22semidirect
80. C2×C22⋊C8×C79C22semidirect
81. C2×C4×C8×C79C22semidirect
102. #14579183D4semidirect
203. #11929624C2×D4semidirect
235. Dic316C2×D4semidirect
240. #11929613C2×D4semidirect
244. D632C2×D4semidirect
281. C2×C8×C79C2×D4semidirect
376. C4×C79#575semidirect
405. C2×#436D79semidirect
406. C79#61038semidirect
417. C22×M16C2×D79semidirect
463. #436C2×D79semidirect
464. #436C2×D79semidirect
465. #436C2×D79semidirect
466. #436C2×D79semidirect
468. C2×C4⋊C8C2×D79semidirect
471. C2×C22⋊C8C2×D79semidirect
472. C2×C4×C8C2×D79semidirect
652. C2×C8D4×D79semidirect
771. C4#19099363semidirect

Maximal subgroups

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

subgroupindex
C2×#190993632
D4×#119296242
#237750682
#237750582
#237750482
#237750362
#237750222
#237750122
#237750022
#237738282
#237730092
#237728572
#237726222
C4×#145791832
C2×#436×C792
#6103879