Finite Group Databasebeta

← #25971783

Subgroups — #25971783

Order 11008.

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×#14583699C212yesmaximal, complemented
2D4×#10621898C212yesmaximal, complemented
3#19146263C212yesmaximal, complemented
4#19146253C212yesmaximal, complemented
5#19146243C212yesmaximal, complemented
6#19146231C214yesmaximal, complemented
7#19146217C212yesmaximal, complemented
8#19146207C212yesmaximal, complemented
9#19146197C212yesmaximal, complemented
10#19145023C211yesmaximal, characteristic, complemented
11#19144204C212yesmaximal, complemented
12#19144052C212yesmaximal, complemented
13#19143817C214yesmaximal, complemented
14C4×#13063347C211yesmaximal, characteristic, complemented
15C2×C43×#436C211yesmaximal, characteristic, complemented
16C22×#10621898C2214yescomplemented
17#14583699—216no—
18C2×#13063358C2214yescomplemented
19C2×#13063358C2214yescomplemented
20C2×#13063353C2214yescomplemented
21C2×#13063353C2214yescomplemented
22C2×#13063347C2211yescharacteristic
23C2×#13063347C2212yescomplemented
24C2×#13063347C2214yescomplemented
25C2×#13063347C2212yescomplemented
26#14583570C2212yes—
27D4×Dic86C2212yescomplemented
28#14583558C2214yescomplemented
29#14583554C2212yes—
30#14583550—22no—
31#14583545C2214yescomplemented
32#14583539—24no—
33D4×D172C2212yescomplemented
34D4×C22⋊D43—22no—
35#14583449C2212yescomplemented
36#14583446—22no—
37#14583410C2214yescomplemented
38#14583408—24no—
39C4×#10621898C2212yescomplemented
40C4×D4×D43—22no—
41#14583283C2212yescomplemented
42#14583283C2212yescomplemented
43#14583279C2211yescharacteristic, complemented
44#14583276C2211yescharacteristic, complemented
45#14583272C2212yescomplemented
46#14583157C2214yescomplemented
47#14583152C2214yescomplemented
48#14583145C2214yescomplemented
49#14583145C2214yescomplemented
50#14583122C2214yescomplemented
51#14583115C2214yescomplemented
52#14583110C2212yescomplemented
53#14583105C2212yescomplemented
54#14583100C2212yescomplemented
55#14583095C2212yescomplemented
56#14583063C2214yescomplemented
57#14583063C2214yescomplemented
58#14583057C2214yescomplemented
59#14583052C2214yescomplemented
60#14583046C2214yescomplemented
61#14583046C2214yescomplemented
62#14583040C2214yescomplemented
63#14583035C2214yescomplemented
64C4×Dic172C2211yescharacteristic, complemented
65C4×Dic172C2211yescharacteristic, complemented
66C4×#10621873C2212yescomplemented
67C4×#10621873C2212yescomplemented
68C4×D344C2211yescharacteristic, complemented
69C4×D344C2211yescharacteristic, complemented
70#14582937C2211yescharacteristic, complemented
71#14582896C2214yescomplemented
72#14582896C2212yescomplemented
73C22×M16×C43C2212yescomplemented
74C2×C4×D4×C43C2211yescharacteristic
75C43×#436C2212yescomplemented
76C43×#436C2212yescomplemented
77C43×#436C2212yescomplemented
78C43×#436C2212yescomplemented
79C2×C4⋊C8×C43C2211yescharacteristic, complemented
80C2×C22⋊C8×C43C2212yescomplemented
81C2×C4×C8×C43C2211yescharacteristic, complemented
82C2×#10621898—24no—
83C2×#10621898—24no—
84C2×#10621898—216no—
85C2×#10621898—48no—
86C2×#10621898C2314yes—
87C2×#10621898C2314yes—
88C2×#10621898C2314yes—
89C2×#10621898C2312yes—
90C22×Dic86C2314yes—
91C22×D172C2314yes—
92C22×C22⋊D43—24no—
93C2×D4×D43—22no—
94C22×C4×D43—24no—
95#13063358—216no—
96#13063358—216no—
97#13063353—216no—
98#13063353—216no—
99#13063347—216no—
100#13063347—28no—
101#13063347—44no—
102#13063347D418yescomplemented
103C2×Dic172C2314yes—
104C2×Dic172C2312yes—
105C2×Dic172C2312yes—
106C2×Dic172C2311yescharacteristic
107C2×#10621873C2314yes—
108C2×#10621873C2314yes—
109C2×#10621873C2314yes—
110C2×#10621873C2314yes—
111C2×#10621873C2312yes—
112C2×D344C2314yes—
113C2×D344C2312yes—
114C2×D344C2312yes—
115C2×D344C2311yescharacteristic
116#13063325C2312yes—
117#13063324—22no—
118#13063322C2312yes—
119#13063321—22no—
120#13063313C2314yes—
121#13063311—24no—
122#13063310—24no—
123#13063308—24no—
124#13063307—24no—
125#13063304C2314yes—
126#13063304C2314yes—
127#13063303—24no—
128#13063302—24no—
129#13063300—22no—
130#13063299—22no—
131#13063299—22no—
132#13063299C2314yes—
133#13063299C2314yes—
134#13063298—24no—
135#13063298—24no—
136#13063297—24no—
137#13063296—22no—
138#13063295—24no—
139#13063294—24no—
140#13063293—24no—
141C4×Dic86C2312yes—
142C4×Dic86C2312yes—
143C4×D172—22no—
144C4×D172—22no—
145C4×D172C2312yes—
146C4×D172C2312yes—
147D4×Dic43—22no—
148#13063287—22no—
149C4×C22⋊D43—24no—
150C4×C22⋊D43—22no—
151C4×C22⋊D43—22no—
152C4×C22⋊D43—24no—
153(C22⋊D43)⋊C4—24no—
154#13063284C2312yes—
155#13063282—22no—
156C4⋊C4×D43—22no—
157C22⋊C4×D43—24no—
158C42×D43—22no—
159#13063259C2311yescharacteristic
160#13063259C2311yescharacteristic
161#13063257C2312yes—
162#13063250C2312yes—
163#13063250C2314yes—
164#13063250C2312yes—
165#13063250C2314yes—
166#13063247C2312yes—
167#13063247C2314yes—
168#13063247C2312yes—
169#13063247C2314yes—
170C22×D4×C43D411yescharacteristic
171C23×C4×C43C2312yes—
172C2×M16×C43—28no—
173C2×M16×C43C2314yes—
174C2×M16×C43C2314yes—
175C22×C8×C43C2312yes—
176C22×C8×C43C2311yescharacteristic
177C22×C8×C43C2311yescharacteristic
178C4×D4×C43D412yes—
179C4×D4×C43D412yes—
180C4×D4×C43C2312yes—
181C4×D4×C43C2312yes—
182C2×C4⋊C4×C43D411yescharacteristic
183C2×C22⋊C4×C43D412yes—
184C2×C42×C43C2311yescharacteristic
185C4⋊C8×C43C2312yes—
186C4⋊C8×C43C2312yes—
187C22⋊C8×C43C2314yes—
188C22⋊C8×C43C2314yes—
189C4×C8×C43C2311yescharacteristic
190C4×C8×C43C2311yescharacteristic
191C4×C8×C43C2311yescharacteristic
192C4×C8×C43C2311yescharacteristic
193C24×C43C2×D412yes—
194C23×D43—24no—
195C2×D4×C43—42no—
196C2×D4×C43C2×D412yes—
197C2×D4×C43C2×D412yes—
198C22×C4×C43—24no—
199C22×C4×C43—24no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2×D414yes—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2414yes—
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—22no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—416no—
213C22×Dic43—24no—
214D4×D43—48no—
215#10621898—24no—
216#10621898—28no—
217#10621898—28no—
218#10621898—28no—
219#10621898—28no—
220#10621898—44no—
221#10621898—44no—
222#10621898—416no—
223#10621898—416no—
224#10621898C2×D418yescomplemented
225C2×D172—22no—
226C2×D172—24no—
227C2×D172—22no—
228C2×D172—28no—
229C2×D172—44no—
230C2×D172C2414yes—
231C2×D172C2412yes—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—22no—
238C2×C4×D43—416no—
239C2×Dic86—28no—
240C2×Dic86—24no—
241C2×Dic86—44no—
242C2×Dic86C2414yes—
243C2×Dic86C2412yes—
244M16×C43—28no—
245M16×C43—28no—
246C2×C8×C43—24no—
247C2×C8×C43—22no—
248C2×C8×C43C2×D414yescomplemented
249C2×C8×C43C2411yescharacteristic
250C2×C8×C43C2411yescharacteristic
251C2×C8×C43C2414yes—
252C2×C8×C43C2411yescharacteristic
253C2×C8×C43C2411yescharacteristic
254C4⋊C4×C43C2×D412yes—
255C4⋊C4×C43C2×D412yes—
256C22⋊C4×C43C2×D414yes—
257C22⋊C4×C43C2×D414yes—
258C42×C43C2×D411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2411yescharacteristic
261C42×C43C2411yescharacteristic
262C22⋊Dic43—24no—
263C22⋊Dic43—22no—
264C22⋊Dic43—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—22no—
268(C2×D43)⋊C4—22no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271C4⋊Dic43—22no—
272C4⋊Dic43—22no—
273C4⋊Dic43C2412yes—
274C4⋊Dic43C2412yes—
275Dic43⋊C4—24no—
276Dic43⋊C4—22no—
277Dic43⋊C4—22no—
278Dic43⋊C4—24no—
279C4×Dic43—22no—
280C4×Dic43—22no—
281C4×Dic43—22no—
282Dic172—28no—
283Dic172—24no—
284Dic172—42no—
285Dic172C2×D414yescomplemented
286D344—28no—
287D344—24no—
288D344—42no—
289D344C2×D414yescomplemented
290#10621873—28no—
291#10621873—28no—
292#10621873—28no—
293#10621873—44no—
294#10621873C2×D418yescomplemented
295C23×C43—24no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43C22×D414yes—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—24no—
302C22×D43—48no—
303C22×D43—48no—
304C22×D43—84no—
305D4×C43—24no—
306D4×C43—42no—
307C2×C4×C43—24no—
308C2×C4×C43—28no—
309C2×C4×C43—22no—
310C2×C4×C43—24no—
311C2×C4×C43—24no—
312C2×C4×C43—41no—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C22×D414yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43H(5,𝔽2)12yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—28no—
323C22⋊D43—48no—
324C22⋊D43—48no—
325C22⋊D43—48no—
326C22⋊D43—48no—
327C22⋊D43—84no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—24no—
332C2×Dic43—48no—
333D172—24no—
334D172—22no—
335D172—24no—
336D172—48no—
337D172—44no—
338D172—82no—
339D172C22×D414yes—
340C4×D43—28no—
341C4×D43—48no—
342C4×D43—48no—
343C4×D43—48no—
344C4×D43—44no—
345C4×D43—82no—
346Dic86—22no—
347Dic86—24no—
348Dic86—24no—
349Dic86—48no—
350Dic86C22×D414yes—
351C8×C43—24no—
352C8×C43—21no—
353C8×C43—21no—
354C8×C43C22×D412yes—
355C8×C43C22×D412yes—
356#61038—431nomaximal, Sylow
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—24no—
360C22×C43—24no—
361C22×C43—24no—
362C22×C43—84no—
363C22×C43D4212yes—
364C22×C43C23×D411yescharacteristic
365C2×D43—24no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—44no—
369C2×D43—44no—
370C2×D43—44no—
371C2×D43—816no—
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—24no—
375C4×C43—21no—
376C4×C43D4212yes—
377C4×C43#57512yescomplemented
378C4×C43C23×D411yescharacteristic
379C4×C43C2×H(5,𝔽2)11yescharacteristic
380Dic43—24no—
381Dic43—42no—
382Dic43—44no—
383Dic43—42no—
384C2×#575—432no—
385D4×#41—432no—
386#3278—432no—
387#3277—432no—
388#3276—432no—
389#3275—434no—
390#3274—432no—
391#3273—432no—
392#3272—432no—
393#3147—431no—
394#3054—432no—
395#3035—432no—
396#3002—434no—
397C4×#135—431no—
398C2×#436D4311yescharacteristic, complemented
399C2×C43—22no—
400C2×C43—44no—
401C2×C43C2×D4211yescharacteristic
402C2×C43C2×#57511yescharacteristic
403C2×C43#358411yescharacteristic
404D43—44no—
405D43—84no—
406C22×#41—434no—
407#575—8616no—
408C2×#137—434no—
409C2×#137—434no—
410C2×AGL(1,ℤ/8)—434no—
411C2×AGL(1,ℤ/8)—434no—
412C2×#135—431no—
413C2×#135—432no—
414C2×#135—434no—
415C2×#135—432no—
416C22×M16C2×D4312yescomplemented
417#550—432no—
418D4×Q8—432no—
419#548—434no—
420#547—432no—
421#547—862no—
422#546—434no—
423#546—864no—
424D42—432no—
425D42—862no—
426#532—432no—
427#532—862no—
428#525—434no—
429#525—864no—
430C4×#41—432no—
431C2×C4×D4—862no—
432C2×C4×D4C2×D4311yescharacteristic
433#495—432no—
434#495—432no—
435#494—431no—
436#493—431no—
437#492—432no—
438#470—434no—
439#469—434no—
440#468—434no—
441#468—434no—
442#464—434no—
443#463—434no—
444#462—432no—
445#461—432no—
446#460—432no—
447#459—432no—
448#452—434no—
449#452—434no—
450#451—434no—
451#450—434no—
452#449—434no—
453#449—434no—
454#448—434no—
455#447—434no—
456C4×Q16—431no—
457C4×Q16—431no—
458C4×SD16—432no—
459C4×SD16—432no—
460C4×D8—431no—
461C4×D8—431no—
462#436C2×D4312yescomplemented
463#436C2×D4312yescomplemented
464#436C2×D4312yescomplemented
465#436C2×D4312yescomplemented
466#427—431no—
467C2×C4⋊C8C2×D4311yescharacteristic, complemented
468#416—432no—
469#416—434no—
470C2×C22⋊C8C2×D4312yescomplemented
471C2×C4×C8C2×D4311yescharacteristic, complemented
472C43#6103811yescharacteristic, complemented, Sylow
473C2×#41—432no—
474C2×#41—434no—
475C2×#41—434no—
476C2×#41—434no—
477C2×#41—8616no—
478C2×#41—864no—
479C2×#41—864no—
480C2×#41—1728no—
481C22×Q8—434no—
482C22×D4—434no—
483C22×D4—864no—
484C22×D4—862no—
485C22×D4D17211yescharacteristic
486C23×C4—864no—
487C23×C4C22×D4312yes—
488#137—8616no—
489#137—8616no—
490AGL(1,ℤ/8)—8616no—
491AGL(1,ℤ/8)—8616no—
492#135—438no—
493#135—8616no—
494#135—868no—
495#135—1724no—
496C2×Q16—431no—
497C2×Q16—434no—
498C2×Q16—432no—
499C2×Q16—432no—
500C2×SD16—432no—
501C2×SD16—434no—
502C2×SD16—434no—
503C2×SD16—434no—
504C2×SD16—434no—
505C2×D8—431no—
506C2×D8—434no—
507C2×D8—432no—
508C2×D8—432no—
509C2×M16—28no—
510C2×M16C22×D4314yes—
511C2×M16C22×D4314yes—
512C22×C8C22×D4312yes—
513C22×C8C22×D4311yescharacteristic
514C22×C8C22×D4311yescharacteristic
515C4⋊Q8—432no—
516C4⋊Q8—862no—
517#127—432no—
518#127—862no—
519#124—434no—
520#124—864no—
521#123—864no—
522#123—864no—
523#123—864no—
524C22⋊Q8—434no—
525C22⋊Q8—434no—
526C22⋊Q8—864no—
527C22⋊Q8—864no—
528#121—434no—
529#121—434no—
530#121—864no—
531#121—862no—
532#121—862no—
533#121—862no—
534#121—862no—
535#121—864no—
536#121—864no—
537#120—864no—
538#120—864no—
539#120—864no—
540C4×Q8—432no—
541C4×Q8—432no—
542C4×D4—432no—
543C4×D4—432no—
544C4×D4—862no—
545C4×D4—864no—
546C4×D4—862no—
547C4×D4—862no—
548C4×D4—864no—
549C4×D4—862no—
550C4×D4—864no—
551C4×D4—862no—
552C4×D4—862no—
553C4×D4D17212yes—
554C4×D4D17212yes—
555C4×D4C22×D4312yes—
556C4×D4C22×D4312yes—
557#117—432no—
558#117—862no—
559C2×C4⋊C4—862no—
560C2×C4⋊C4D17211yescharacteristic
561C2×C22⋊C4—864no—
562C2×C22⋊C4D17212yes—
563C2×C42—862no—
564C2×C42C22×D4311yescharacteristic
565#107—431no—
566#107—431no—
567#106—432no—
568C4⋊C8C22×D4312yes—
569C4⋊C8C22×D4312yes—
570#103—432no—
571#103—432no—
572#103—434no—
573#103—434no—
574#102—432no—
575#102—432no—
576#102—434no—
577#102—434no—
578C22⋊C8C22×D4314yes—
579C22⋊C8C22×D4314yes—
580C4×C8C22×D4311yescharacteristic
581C4×C8C22×D4311yescharacteristic
582C4×C8C22×D4311yescharacteristic
583C4×C8C22×D4311yescharacteristic
584C24—864no—
585C24C2×D17212yes—
586#41—438no—
587#41—868no—
588#41—868no—
589#41—864no—
590#41—868no—
591#41—868no—
592#41—17216no—
593#41—1724no—
594#41—1724no—
595#41—17216no—
596C2×Q8—432no—
597C2×Q8—434no—
598C2×Q8—868no—
599C2×Q8—864no—
600C2×Q8—1724no—
601C2×D4—42no—
602C2×D4—432no—
603C2×D4—434no—
604C2×D4—868no—
605C2×D4—862no—
606C2×D4—864no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—864no—
610C2×D4—864no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—864no—
614C2×D4—1724no—
615C2×D4—1728no—
616C2×D4—17216no—
617C2×D4C2×D17212yes—
618C2×D4C2×D17212yes—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—862no—
622C22×C4—864no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—864no—
626C22×C4—864no—
627C22×C4—864no—
628C22×C4—17216no—
629C22×C4C2×D17211yescharacteristic
630C22×C4C2×D17212yes—
631C22×C4C2×D17214yes—
632C22×C4C2×D17211yescharacteristic
633C22×C4C23×D4314yes—
634C22×C4C23×D4311yescharacteristic
635Q16—434no—
636Q16—868no—
637Q16—864no—
638Q16—1722no—
639SD16—438no—
640SD16—868no—
641SD16—868no—
642SD16—868no—
643SD16—1724no—
644D8—434no—
645D8—868no—
646D8—864no—
647D8—1722no—
648M16—28no—
649M16—28no—
650C2×C8—24no—
651C2×C8—22no—
652C2×C8D4×D4314yescomplemented
653C2×C8C23×D4311yescharacteristic
654C2×C8C23×D4311yescharacteristic
655C2×C8C23×D4314yes—
656C2×C8C23×D4311yescharacteristic
657C2×C8C23×D4311yescharacteristic
658C4⋊C4—432no—
659C4⋊C4—432no—
660C4⋊C4—862no—
661C4⋊C4—864no—
662C4⋊C4—862no—
663C4⋊C4—862no—
664C4⋊C4—864no—
665C4⋊C4—862no—
666C4⋊C4C2×D17212yes—
667C4⋊C4C2×D17212yes—
668C22⋊C4—864no—
669C22⋊C4—862no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—862no—
674C22⋊C4—862no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4C2×D17214yes—
678C22⋊C4C2×D17214yes—
679C42—862no—
680C42—862no—
681C42—862no—
682C42C2×D17211yescharacteristic
683C42C2×D17211yescharacteristic
684C42C23×D4311yescharacteristic
685C42C23×D4311yescharacteristic
686C23—24no—
687C23—42no—
688C23—42no—
689C23—862no—
690C23—864no—
691C23—3444no—
692C23—1728no—
693C23—1728no—
694C23C22×D17214yes—
695C23C22×D17211yescharacteristic
696Q8—434no—
697Q8—862no—
698Q8—864no—
699Q8—864no—
700Q8—1728no—
701D4—24no—
702D4—42no—
703D4—434no—
704D4—868no—
705D4—864no—
706D4—862no—
707D4—864no—
708D4—3442no—
709D4—3444no—
710D4—1728no—
711D4—1728no—
712D4—1728no—
713D4—1728no—
714D4—1728no—
715D4—1724no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—41no—
722C2×C4—862no—
723C2×C4—868no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—864no—
727C2×C4—3442no—
728C2×C4—1728no—
729C2×C4—1728no—
730C2×C4—1728no—
731C2×C4—1724no—
732C2×C4—1728no—
733C2×C4C2×D4×D4312yes—
734C2×C4C22×D17211yescharacteristic
735C2×C4C22×D17211yescharacteristic
736C2×C4C22×D17211yescharacteristic
737C2×C4C22×D17214yes—
738C2×C4C22×D17211yescharacteristic
739C2×C4C22×D17211yescharacteristic
740C2×C4#1306337112yes—
741C2×C4C24×D4311yescharacteristic
742C8—24no—
743C8—21no—
744C8—21no—
745C8C2×D4×D4312yes—
746C8C2×D4×D4312yes—
747C22—21no—
748C22—21no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—84no—
753C22—864no—
754C22—34416no—
755C22—1724no—
756C22—1724no—
757C22—1724no—
758C22—1722no—
759C22—1722no—
760C22D4×D17212yes—
761C22C23×D17211yescharacteristic
762C4—24no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—864no—
767C4—1724no—
768C4—1722no—
769C4—1722no—
770C4D4×D17212yes—
771C4#1458369912yescomplemented
772C4C22×D4×D4311yescharacteristic
773C4C2×#1306337111yescharacteristic
774C2—22no—
775C2—44no—
776C2—3444no—
777C2—1724no—
778C2C2×D4×D17211yescharacteristic
779C2C2×#1458369911yescharacteristic
780C2#1914936911yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#436C2
socleC22×C43C23×D4
hypercenterC2×#436D43
hypocenterC43#61038
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#14583699C2semidirect
2. D4×#10621898C2semidirect
3. #19146263C2semidirect
4. #19146253C2semidirect
5. #19146243C2semidirect
6. #19146231C2semidirect
7. #19146217C2semidirect
8. #19146207C2semidirect
9. #19146197C2semidirect
10. #19145023C2semidirect
11. #19144204C2semidirect
12. #19144052C2semidirect
13. #19143817C2semidirect
14. C4×#13063347C2semidirect
15. C2×C43×#436C2semidirect
16. C22×#10621898C22semidirect
18. C2×#13063358C22semidirect
19. C2×#13063358C22semidirect
20. C2×#13063353C22semidirect
21. C2×#13063353C22semidirect
23. C2×#13063347C22semidirect
24. C2×#13063347C22semidirect
25. C2×#13063347C22semidirect
27. D4×Dic86C22semidirect
28. #14583558C22semidirect
31. #14583545C22semidirect
33. D4×D172C22semidirect
35. #14583449C22semidirect
37. #14583410C22semidirect
39. C4×#10621898C22semidirect
41. #14583283C22semidirect
42. #14583283C22semidirect
43. #14583279C22semidirect
44. #14583276C22semidirect
45. #14583272C22semidirect
46. #14583157C22semidirect
47. #14583152C22semidirect
48. #14583145C22semidirect
49. #14583145C22semidirect
50. #14583122C22semidirect
51. #14583115C22semidirect
52. #14583110C22semidirect
53. #14583105C22semidirect
54. #14583100C22semidirect
55. #14583095C22semidirect
56. #14583063C22semidirect
57. #14583063C22semidirect
58. #14583057C22semidirect
59. #14583052C22semidirect
60. #14583046C22semidirect
61. #14583046C22semidirect
62. #14583040C22semidirect
63. #14583035C22semidirect
64. C4×Dic172C22semidirect
65. C4×Dic172C22semidirect
66. C4×#10621873C22semidirect
67. C4×#10621873C22semidirect
68. C4×D344C22semidirect
69. C4×D344C22semidirect
70. #14582937C22semidirect
71. #14582896C22semidirect
72. #14582896C22semidirect
73. C22×M16×C43C22semidirect
75. C43×#436C22semidirect
76. C43×#436C22semidirect
77. C43×#436C22semidirect
78. C43×#436C22semidirect
79. C2×C4⋊C8×C43C22semidirect
80. C2×C22⋊C8×C43C22semidirect
81. C2×C4×C8×C43C22semidirect
102. #13063347D4semidirect
224. #10621898C2×D4semidirect
248. C2×C8×C43C2×D4semidirect
285. Dic172C2×D4semidirect
289. D344C2×D4semidirect
294. #10621873C2×D4semidirect
377. C4×C43#575semidirect
398. C2×#436D43semidirect
416. C22×M16C2×D43semidirect
462. #436C2×D43semidirect
463. #436C2×D43semidirect
464. #436C2×D43semidirect
465. #436C2×D43semidirect
467. C2×C4⋊C8C2×D43semidirect
470. C2×C22⋊C8C2×D43semidirect
471. C2×C4×C8C2×D43semidirect
472. C43#61038semidirect
652. C2×C8D4×D43semidirect
771. C4#14583699semidirect

Maximal subgroups

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

subgroupindex
C2×#145836992
D4×#106218982
#191462632
#191462532
#191462432
#191462312
#191462172
#191462072
#191461972
#191450232
#191442042
#191440522
#191438172
C4×#130633472
C2×C43×#4362
#6103843