Finite Group Databasebeta

← #72313810

Subgroups — #72313810

Order 1024.

10480 conjugacy classes of subgroups.

The subgroup lattice has 1450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7669845C212yesmaximal, complemented
2#7620704C214yesmaximal, complemented
3#7618079C214yesmaximal, complemented
4#7616331C211yesmaximal, characteristic, complemented
5#7615382C212yesmaximal, complemented
6#7614034C211yesmaximal, characteristic, complemented
7#7613013C218yesmaximal, complemented
8#7605741C212yesmaximal, complemented
9#7598756C212yesmaximal, complemented
10#7590412C214yesmaximal, complemented
11#7533713C214yesmaximal, complemented
12#7511824C214yesmaximal, complemented
13#6469636C212yesmaximal, complemented
14#6467316C214yesmaximal, complemented
15#6466642C214yesmaximal, complemented
16#6447455C218yesmaximal, complemented
17D4×#442C214yesmaximal, complemented
18#6373996C212yesmaximal, complemented
19#6373906C211yesmaximal, characteristic, complemented
20C2×D4×D8C2214yes—
21C2×#3176C2212yes—
22C2×#2970C2212yescomplemented
23C22×#442C2214yescomplemented
24#52292—24no—
25#52244—24no—
26#45380C2214yescomplemented
27#45377C2214yescomplemented
28#45375C2212yes—
29#45362C2214yescomplemented
30#45355C2212yes—
31#45257C2218yescomplemented
32#44881C2218yescomplemented
33#44656—24no—
34#44241—24no—
35#43800—24no—
36#43372—24no—
37#34963C2214yescomplemented
38#34956—24no—
39#34935C2214yescomplemented
40#34917C2218yescomplemented
41#34655—24no—
42#34547C2211yescharacteristic
43C4×D42C2218yescomplemented
44C4×#540C2214yescomplemented
45#32659C2218yescomplemented
46#32554C2218yescomplemented
47#32468C2214yescomplemented
48#32002C2218yescomplemented
49#31996C2218yescomplemented
50#31681C2214yescomplemented
51#31680C2214yescomplemented
52#31064C2214yes—
53#30400C2218yescomplemented
54#30396C2218yescomplemented
55#29542C2218yescomplemented
56#29295C2212yescomplemented
57#28854C2218yescomplemented
58#28853C2218yescomplemented
59#28834C2214yescomplemented
60#28707C2214yescomplemented
61#28536C2214yescomplemented
62#28292C2214yescomplemented
63#28276C2218yescomplemented
64#28259C2212yes—
65#28237C2218yescomplemented
66#28225C2214yes—
67#28197C2218yescomplemented
68#28152C2218yescomplemented
69#28107C2214yescomplemented
70#28104C2214yescomplemented
71#28097C2214yescomplemented
72#28094C2214yescomplemented
73#27845C2218yescomplemented
74#27733C2218yescomplemented
75#27663C2214yescomplemented
76#27658C2214yescomplemented
77#27641C2218yescomplemented
78#27525C2218yescomplemented
79#27520C2218yescomplemented
80#27097C2218yescomplemented
81#27096C2218yescomplemented
82#26657C2218yescomplemented
83#26656C2218yescomplemented
84#26541C2218yescomplemented
85#26310C2218yescomplemented
86#26118C2218yescomplemented
87#25891C2218yescomplemented
88#25342C2218yescomplemented
89#25330C2218yescomplemented
90#25042C2218yescomplemented
91#24977C2218yescomplemented
92#24897C2218yescomplemented
93#24893C2218yescomplemented
94#24823C2218yescomplemented
95#24272C2214yescomplemented
96#24267C2214yes—
97#24248C2218yes—
98#24162C2218yescomplemented
99#23764C2218yescomplemented
100#23761C2218yescomplemented
101#23708C2218yescomplemented
102#23708C2218yescomplemented
103#23188C2214yes—
104#23029C2218yescomplemented
105#23001C2218yescomplemented
106#22858C2218yescomplemented
107#22858C2218yescomplemented
108#22670C2214yescomplemented
109D4×#106C2214yescomplemented
110#22436C2218yescomplemented
111D4×#102C2218yescomplemented
112#21728C2212yescomplemented
113#21722C2212yescomplemented
114#21716C2211yescharacteristic, complemented
115#21716C2211yescharacteristic, complemented
116#21697C2212yes—
117#21690C2212yes—
118#21683C2211yescharacteristic
119#21683C2211yescharacteristic
120#21656C2214yescomplemented
121#21652C2214yescomplemented
122#21638C2212yescomplemented
123#21638C2212yescomplemented
124#21617C2218yescomplemented
125#21538C2214yescomplemented
126#21536C2214yescomplemented
127#21529C2214yescomplemented
128#21526C2214yescomplemented
129#21526C2218yescomplemented
130#21503C2218yescomplemented
131#21492C2214yescomplemented
132#21492C2214yescomplemented
133#21452C2218yescomplemented
134#21452C2218yescomplemented
135#21414C2214yescomplemented
136#21379C2212yescomplemented
137#21290C2214yescomplemented
138#21284C2214yescomplemented
139#21271C2214yescomplemented
140#20823C2214yescomplemented
141#20820C2212yescomplemented
142#20811C2211yescharacteristic, complemented
143#20739C2214yescomplemented
144#20738C2214yescomplemented
145C4×#442C2214yescomplemented
146C4×#442C2214yescomplemented
147D4×#97C2214yescomplemented
148#20331C2211yescharacteristic, complemented
149C23×D8C2314yes—
150C2×D42C2318yes—
151C2×#540C2314yes—
152C2×#525—24no—
153C2×C4×#41C2312yes—
154C22×C4×D4—28no—
155C22×C4×D4C2314yes—
156C22×C4×D4C2314yes—
157D4×D8—232no—
158#3176—216no—
159C2×#499C2312yes—
160C2×#493C2312yes—
161C2×#490C2314yes—
162C2×#478C2318yes—
163C2×#469C2314yes—
164C2×#466C2314yes—
165C2×#466C2318yes—
166C2×#459C2318yes—
167C2×#447C2318yes—
168C2×#447C2318yes—
169#2970—48no—
170C2×#446C2312yes—
171C2×#446C2312yes—
172C2×#442—416no—
173C2×#442C2314yes—
174C2×#442C2314yes—
175C2×#442C2314yes—
176C2×#442C2314yes—
177C2×#442C2318yes—
178C2×#442C2318yes—
179C2×#442C2318yes—
180C2×C4×D8C2314yes—
181C2×C4×D8C2314yes—
182C2×#435C2314yes—
183C2×#435C2314yes—
184C2×C8×D4C2314yes—
185C2×C8×D4C2312yes—
186C2×C8×D4C2314yes—
187C2×C8×D4C2312yes—
188C2×#432C2314yes—
189C2×#432C2312yes—
190C22×#106C2314yes—
191C22×#102C2314yes—
192C22×#102C2314yes—
193C2×#405C2312yes—
194C2×#405C2312yes—
195C2×C4×M16C2311yescharacteristic
196C22×#97C2314yes—
197C22×#97C2311yescharacteristic
198#2807—24no—
199#2796—28no—
200#2787—28no—
201#2784—28no—
202#2780—28no—
203#2778—28no—
204#2771—24no—
205#2760—24no—
206#2750—28no—
207#2750—28no—
208#2746—28no—
209#2736—24no—
210#2735—24no—
211#2708—28no—
212#2697—28no—
213#2693—24no—
214#2688—28no—
215#2678—28no—
216#2668—24no—
217#2668—24no—
218#2600—24no—
219#2600—28no—
220#2600—24no—
221#2598—24no—
222#2598—24no—
223#2580C2318yes—
224#2579—28no—
225#2579—28no—
226#2578—28no—
227#2576—28no—
228#2570C2318yes—
229#2566C2318yes—
230#2562C2318yes—
231#2538C2318yes—
232#2537C2318yes—
233#2536—24no—
234#2535—24no—
235#2535C2318yes—
236#2535C2318yes—
237#2534—28no—
238#2534—28no—
239#2534—24no—
240#2534—24no—
241#2515—28no—
242#2497C2318yes—
243#2494C2318yes—
244#2487C2314yes—
245#2487C2314yes—
246#2486C2314yes—
247#2486C2314yes—
248#2483—24no—
249#2482—24no—
250#2463—24no—
251#2457—28no—
252#2456—28no—
253#2455—24no—
254#2449—28no—
255#2443—28no—
256#2437—24no—
257#2424—28no—
258#2422C2318yes—
259#2420C2318yes—
260#2418—28no—
261#2410—28no—
262#2408C2314yes—
263#2408C2314yes—
264#2408C2314yes—
265#2408C2314yes—
266#2405—28no—
267#2404—24no—
268#2403—24no—
269#2403—24no—
270#2401—28no—
271#2399C2311yescharacteristic
272#2398—24no—
273#2398C2312yes—
274#2397—24no—
275#2397C2311yescharacteristic
276#2396D414yes—
277#2395D414yes—
278#2392—28no—
279#2392—24no—
280#2392—24no—
281#2392D414yes—
282#2392C2314yes—
283#2388D414yes—
284#2366C2318yes—
285#2361—28no—
286#2361C2318yes—
287#2361C2318yes—
288#2358—28no—
289#2358—28no—
290D4×C4⋊C4C2318yes—
291D4×C4⋊C4C2318yes—
292D4×C22⋊C4—28no—
293D4×C22⋊C4C2318yes—
294D4×C22⋊C4C2318yes—
295#2335—28no—
296#2333—28no—
297#2330C2314yes—
298#2328C2314yes—
299#2324C2318yes—
300#2319C2318yes—
301#2314C2314yes—
302C4×#127C2314yes—
303C4×#125C2314yes—
304C4×#123—28no—
305C4×#123—28no—
306C4×#121—28no—
307C4×#121—28no—
308C4×#121C2318yes—
309C4×#121C2318yes—
310C4×#121C2318yes—
311C4×#120—28no—
312C4×#120—28no—
313C4×#120—24no—
314C4×#120—24no—
315#2290—28no—
316#2285C2314yes—
317#2283C2314yes—
318#2280—24no—
319C42×D4C2314yes—
320C42×D4C2318yes—
321C4×#117C2311yescharacteristic
322#2101C2318yes—
323#2099C2318yes—
324#2093C2318yes—
325#2092C2318yes—
326#2088C2318yes—
327#2088C2318yes—
328#2085C2318yes—
329#2084C2318yes—
330#2077C2318yes—
331#2077C2318yes—
332#2077C2318yes—
333#2076C2318yes—
334#2076C2318yes—
335#2075C2318yes—
336#2073C2318yes—
337#2071C2318yes—
338#2067C2318yes—
339#2067C2318yes—
340#2065C2318yes—
341#2065C2318yes—
342#2054C2318yes—
343#2054C2318yes—
344#2034C2318yes—
345#2034C2318yes—
346#2034C2318yes—
347#2034C2318yes—
348#2034C2318yes—
349#2033C2318yes—
350#2033C2318yes—
351#2033C2318yes—
352#1999C2318yes—
353#1999C2318yes—
354#1992C2314yes—
355#1991C2314yes—
356#1989C2318yes—
357#1985C2312yes—
358#1985C2312yes—
359#1982C2318yes—
360#1972C2314yes—
361#1972C2318yes—
362#1972C2314yes—
363#1972C2314yes—
364#1970C2314yes—
365#1961C2314yes—
366#1957C2314yes—
367#1955C2314yes—
368#1955C2314yes—
369#1955C2312yes—
370#1955C2312yes—
371#1949C2318yes—
372#1948C2318yes—
373#1944C2314yes—
374#1943C2318yes—
375#1943C2314yes—
376#1943C2314yes—
377#1941C2314yes—
378#1940C2314yes—
379#1940C2314yes—
380#1936C2318yes—
381#1936C2318yes—
382#1936C2318yes—
383#1934C2318yes—
384#1934C2318yes—
385#1934C2318yes—
386#1926C2318yes—
387#1926C2318yes—
388#1923C2318yes—
389#1923C2318yes—
390#1920C2318yes—
391#1918C2318yes—
392#1895C2318yes—
393#1893C2318yes—
394#1893C2318yes—
395#1893C2318yes—
396#1879C2318yes—
397#1879C2318yes—
398#1879C2318yes—
399#1879C2318yes—
400#1879C2318yes—
401#1879C2318yes—
402#1874C2318yes—
403#1874C2318yes—
404#1869C2318yes—
405#1864C2318yes—
406#1864C2318yes—
407#1864C2318yes—
408#1864C2318yes—
409#1864C2318yes—
410#1862C2318yes—
411#1853C2318yes—
412#1853C2318yes—
413#1847C2318yes—
414#1846C2312yes—
415#1844C2312yes—
416#1843C2311yescharacteristic
417#1843C2311yescharacteristic
418#1836C2314yes—
419#1836C2318yes—
420#1832C2312yes—
421#1824C2314yes—
422#1824C2314yes—
423#1823C2314yes—
424#1823C2314yes—
425#1809C2314yes—
426#1808C2314yes—
427#1808C2314yes—
428#1807C2314yes—
429#1807C2318yes—
430#1807C2314yes—
431#1807C2314yes—
432#1804C2318yes—
433#1804C2318yes—
434#1804C2318yes—
435#1802C2318yes—
436#1802C2318yes—
437#1802C2318yes—
438#1798C2314yes—
439#1786C2314yes—
440#1786C2314yes—
441#1786C2314yes—
442#1786C2314yes—
443#1786C2318yes—
444#1786C2318yes—
445#1776C2314yes—
446#1776C2314yes—
447#1776C2314yes—
448#1776C2314yes—
449#1776C2318yes—
450C4×#106C2314yes—
451C4×#106C2314yes—
452#1770C2314yes—
453#1770C2314yes—
454#1767C2314yes—
455#1762C2318yes—
456#1762C2318yes—
457#1762C2318yes—
458#1762C2318yes—
459#1762C2318yes—
460#1762C2318yes—
461C4×#102C2318yes—
462C4×#102C2318yes—
463#1752C2318yes—
464#1752C2318yes—
465#1749C2318yes—
466#1726C2311yescharacteristic
467#1726C2311yescharacteristic
468#1726C2311yescharacteristic
469#1726C2311yescharacteristic
470C4×#97C2312yes—
471C4×#97C2312yes—
472C22×#41C2×D412yes—
473C23×D4—28no—
474C23×D4C2414yes—
475C23×D4C2414yes—
476C24×C4—24no—
477C24×C4—24no—
478C22×D8—232no—
479C22×D8—48no—
480C22×D8C2418yes—
481C22×D8C2414yes—
482C22×D8C2414yes—
483C22×M16C2411yescharacteristic
484C22×M16C2411yescharacteristic
485C23×C8C2414yes—
486C23×C8C2412yes—
487C23×C8C2414yes—
488D42—232no—
489D42—416no—
490#540—216no—
491#540—48no—
492C2×#127C2414yes—
493C2×#125C2414yes—
494#525—816no—
495C2×#123—24no—
496C2×#123—24no—
497C2×#123—28no—
498C2×#123—28no—
499C2×C22⋊Q8—28no—
500C2×#121—28no—
501C2×#121—28no—
502C2×#121—28no—
503C2×#121C2418yes—
504C2×#121C2418yes—
505C2×#121C2418yes—
506C2×#120—24no—
507C2×#120—24no—
508C2×#120—24no—
509C2×#120—24no—
510C2×#120—28no—
511C2×#120—28no—
512C4×#41—44no—
513C4×#41—44no—
514C2×C4×Q8C2×D412yes—
515C2×C4×Q8C2412yes—
516C2×C4×D4—28no—
517C2×C4×D4—28no—
518C2×C4×D4—28no—
519C2×C4×D4—28no—
520C2×C4×D4—28no—
521C2×C4×D4—28no—
522C2×C4×D4—28no—
523C2×C4×D4—28no—
524C2×C4×D4—24no—
525C2×C4×D4—24no—
526C2×C4×D4—24no—
527C2×C4×D4—24no—
528C2×C4×D4—48no—
529C2×C4×D4—48no—
530C2×C4×D4—48no—
531C2×C4×D4—48no—
532C2×C4×D4—832no—
533C2×C4×D4C2×D418yes—
534C2×C4×D4C2×D414yes—
535C2×C4×D4C2×D412yes—
536C2×C4×D4C2418yes—
537C2×C4×D4C2418yes—
538C2×C4×D4C2418yes—
539C2×C4×D4C2418yes—
540C2×C4×D4C2418yes—
541C2×C4×D4C2414yes—
542C2×C4×D4C2414yes—
543C2×C4×D4C2412yes—
544C2×#117—24no—
545C2×#117C2×D412yes—
546C2×#117C2×D414yes—
547C2×#117C2412yes—
548C22×C4⋊C4—28no—
549C22×C4⋊C4C2414yes—
550C22×C4⋊C4C2414yes—
551C22×C22⋊C4—24no—
552C22×C22⋊C4—24no—
553C22×C22⋊C4—28no—
554C22×C22⋊C4—28no—
555C22×C42—28no—
556C22×C42C2411yescharacteristic
557C22×C42C2414yes—
558#499—28no—
559#493#41116yescomplemented
560#490—216no—
561#478—416no—
562#469—216no—
563#466—216no—
564#466—232no—
565#459—232no—
566#447—232no—
567#447—232no—
568#446—44no—
569#446—44no—
570#442—216no—
571#442—216no—
572#442—416no—
573#442—416no—
574#442—416no—
575#442—48no—
576#442—48no—
577C4×D8—216no—
578C4×D8—216no—
579#435—48no—
580#435—48no—
581C8×D4—216no—
582C8×D4—48no—
583C8×D4—44no—
584C8×D4—44no—
585#432—44no—
586#432—48no—
587C2×#107C2414yes—
588C2×#107C2414yes—
589C2×#107C2418yes—
590C2×#106—48no—
591C2×#106C2414yes—
592C2×#106C2414yes—
593C2×#106C2418yes—
594C2×#106C2414yes—
595C2×#106C2414yes—
596C2×#106C2418yes—
597C2×C4⋊C8C2414yes—
598C2×C4⋊C8C2414yes—
599C2×C4⋊C8C2412yes—
600C2×C4⋊C8C2414yes—
601C2×C4⋊C8C2414yes—
602C2×C4⋊C8C2412yes—
603C2×#102—48no—
604C2×#102—48no—
605C2×#102C2418yes—
606C2×#102C2418yes—
607C2×#102C2418yes—
608C2×#102C2418yes—
609C2×#102C2418yes—
610C2×#102C2418yes—
611C2×#102C2418yes—
612C2×#102C2418yes—
613C2×#102C2418yes—
614C2×#102C2418yes—
615C2×#102C2418yes—
616C2×#102C2418yes—
617C2×C22⋊C8C2418yes—
618C2×C22⋊C8C2414yes—
619C2×C22⋊C8C2418yes—
620C2×C22⋊C8C2414yes—
621C2×C22⋊C8C2414yes—
622#405—28no—
623#405—44no—
624C4×M16—24no—
625C2×#97—216no—
626C2×#97—42no—
627C2×#97C2414yes—
628C2×#97C2412yes—
629C2×#97C2414yes—
630C2×#97C2414yes—
631C2×#97C2412yes—
632C2×#97C2411yescharacteristic
633C2×#97C2412yes—
634C2×#97C2412yes—
635C2×#97C2411yescharacteristic
636C2×#97C2411yescharacteristic
637C2×#97C2412yes—
638C2×#97C2411yescharacteristic
639C2×C4×C8C2411yescharacteristic
640C2×C4×C8C2411yescharacteristic
641C2×C4×C8C2412yes—
642C2×C4×C8C2412yes—
643C2×C4×C8C2412yes—
644C2×C4×C8C2412yes—
645#401—28no—
646#400—28no—
647#400—28no—
648#400—24no—
649#400—24no—
650#400—28no—
651#400C2×D414yes—
652#399—28no—
653#399—24no—
654#399—24no—
655#399C2×D414yes—
656#398—28no—
657#398—24no—
658#398—24no—
659#398C2×D414yes—
660#398C2×D414yes—
661#397—28no—
662#397—28no—
663#397—28no—
664#397—24no—
665#397—24no—
666#397—28no—
667#397—28no—
668#397C2×D414yes—
669#397C2×D414yes—
670#396—28no—
671#396—28no—
672#396—28no—
673#396—28no—
674#396—28no—
675#396C2×D418yes—
676#395C2×D414yes—
677#394—28no—
678#394—24no—
679#394—24no—
680#394—24no—
681#394—24no—
682#394—28no—
683#394—28no—
684#394—28no—
685#394—28no—
686#394C2×D414yes—
687#394C2×D414yes—
688#394C2×D418yes—
689#393—28no—
690#393C2×D414yes—
691#392—28no—
692#392—28no—
693#392—24no—
694#392—24no—
695#392—24no—
696#392—24no—
697#392C2×D414yes—
698#392C2×D414yes—
699#390—28no—
700#390—28no—
701#390—28no—
702#390C2418yes—
703#390C2418yes—
704#390C2418yes—
705#390C2418yes—
706#389—28no—
707#389—28no—
708#389C2418yes—
709#389C2418yes—
710#389C2418yes—
711#389C2418yes—
712#388—28no—
713#388—28no—
714#388—28no—
715#388—28no—
716#388—28no—
717#388—28no—
718#388—28no—
719#388—28no—
720#388—28no—
721#388—28no—
722#388—28no—
723#388—28no—
724#388—28no—
725#387—28no—
726#387—28no—
727#387—28no—
728#387—28no—
729#387—28no—
730#387—28no—
731#387—28no—
732#386—24no—
733#386—24no—
734#386—28no—
735#386—28no—
736#386—28no—
737#386—28no—
738#386—28no—
739#386—28no—
740#386—28no—
741#386—28no—
742#386—28no—
743#386—28no—
744#386—28no—
745#386—28no—
746#386—28no—
747#386—28no—
748#386—28no—
749#386—28no—
750#386—28no—
751#386—28no—
752#386—28no—
753#385—28no—
754#385—28no—
755#385—28no—
756#385—24no—
757#385—28no—
758#385—28no—
759#385—24no—
760#385—28no—
761#385—28no—
762#385—28no—
763#385—28no—
764#385—28no—
765#385—28no—
766#385—28no—
767#384C2414yes—
768#384C2418yes—
769#383—24no—
770#382—24no—
771#382C2414yes—
772#382C2418yes—
773#381—24no—
774#381—24no—
775#381—24no—
776#381—28no—
777#381—28no—
778#380—24no—
779#380—28no—
780#380—28no—
781#380—28no—
782#380—28no—
783#380C2414yes—
784#380C2414yes—
785#380C2418yes—
786#380C2418yes—
787#380C2418yes—
788#380C2414yes—
789#380C2414yes—
790#379—28no—
791#379—28no—
792#379—24no—
793#379—24no—
794#379—24no—
795#379—24no—
796C4×C4⋊C4—28no—
797C4×C4⋊C4—24no—
798C4×C4⋊C4C2×D414yes—
799C4×C4⋊C4C2×D418yes—
800C4×C4⋊C4C2418yes—
801C4×C4⋊C4C2418yes—
802C4×C4⋊C4C2418yes—
803C4×C4⋊C4C2414yes—
804C4×C22⋊C4—24no—
805C4×C22⋊C4—28no—
806C4×C22⋊C4—28no—
807C4×C22⋊C4—28no—
808C4×C22⋊C4—28no—
809C4×C22⋊C4—28no—
810C4×C22⋊C4—28no—
811C4×C22⋊C4C2×D418yes—
812C4×C22⋊C4C2×D418yes—
813C4×C22⋊C4C2×D414yes—
814C4×C22⋊C4C2418yes—
815#376—24no—
816#376C2411yescharacteristic
817#376C2411yescharacteristic
818C43C2412yes—
819#340C2418yes—
820#340C2418yes—
821#340C2418yes—
822#340C2418yes—
823#340C2418yes—
824#340C2418yes—
825#340C2418yes—
826#340C2418yes—
827#340C2418yes—
828#340C2418yes—
829#340C2418yes—
830#340C2418yes—
831#336C2418yes—
832#336C2418yes—
833#336C2418yes—
834C25—24no—
835C25—24no—
836C2×#41—44no—
837C2×#41—48no—
838C22×Q8C22×D412yes—
839C22×D4—216no—
840C22×D4—216no—
841C22×D4—28no—
842C22×D4—28no—
843C22×D4—28no—
844C22×D4—28no—
845C22×D4—24no—
846C22×D4—24no—
847C22×D4—44no—
848C22×D4—44no—
849C22×D4—48no—
850C22×D4—48no—
851C22×D4—44no—
852C22×D4—44no—
853C22×D4—432no—
854C22×D4—816no—
855C22×D4—816no—
856C22×D4C22×D414yes—
857C22×D4C22×D412yes—
858C22×D4C22×D414yes—
859C22×D4C2518yes—
860C23×C4—24no—
861C23×C4—24no—
862C23×C4—28no—
863C23×C4—28no—
864C23×C4—28no—
865C23×C4—28no—
866C23×C4—28no—
867C23×C4—416no—
868C23×C4—88no—
869C23×C4—88no—
870C23×C4—816no—
871C23×C4—88no—
872C23×C4C22×D414yes—
873C23×C4C22×D414yes—
874C23×C4C22×D412yes—
875C23×C4C2514yes—
876C23×C4C2511yescharacteristic
877C2×D8—216no—
878C2×D8—216no—
879C2×D8—28no—
880C2×D8—28no—
881C2×D8—48no—
882C2×D8—44no—
883C2×D8—44no—
884C2×D8—464no—
885C2×D8C2×#41116yes—
886C2×D8C2×#41116yes—
887C2×M16—24no—
888C2×M16—22no—
889C2×M16—22no—
890C2×M16—42no—
891C22×C8—216no—
892C22×C8—24no—
893C22×C8—28no—
894C22×C8—28no—
895C22×C8—42no—
896C22×C8—42no—
897C22×C8—48no—
898C22×C8C2514yes—
899C22×C8C2512yes—
900C22×C8C2514yes—
901C22×C8C2511yescharacteristic
902C22×C8C2511yescharacteristic
903C22×C8C2512yes—
904C22×C8C2511yescharacteristic
905C22×C8C2511yescharacteristic
906#127—28no—
907#127C2×#41116yes—
908#125—28no—
909#125—28no—
910#123—432no—
911#123—816no—
912#123—88no—
913#123—88no—
914C22⋊Q8—816no—
915#121—216no—
916#121—216no—
917#121—216no—
918#121—432no—
919#121—48no—
920#121—48no—
921#121—48no—
922#121—432no—
923#121—816no—
924#120—432no—
925#120—432no—
926#120—88no—
927#120—88no—
928#120—88no—
929#120—88no—
930C4×Q8—44no—
931C4×Q8—42no—
932C4×Q8—42no—
933C4×D4—216no—
934C4×D4—28no—
935C4×D4—216no—
936C4×D4—216no—
937C4×D4—28no—
938C4×D4—216no—
939C4×D4—216no—
940C4×D4—48no—
941C4×D4—44no—
942C4×D4—48no—
943C4×D4—42no—
944C4×D4—44no—
945C4×D4—42no—
946C4×D4—44no—
947C4×D4—48no—
948C4×D4—48no—
949C4×D4—48no—
950C4×D4—48no—
951C4×D4—416no—
952C4×D4—432no—
953C4×D4—88no—
954C4×D4—88no—
955C4×D4—88no—
956C4×D4—88no—
957C4×D4—816no—
958C4×D4—816no—
959C4×D4—816no—
960C4×D4—816no—
961C4×D4—816no—
962C4×D4—816no—
963C4×D4—816no—
964#117—24no—
965#117—24no—
966#117—48no—
967#117—44no—
968#117—88no—
969C2×C4⋊C4—28no—
970C2×C4⋊C4—28no—
971C2×C4⋊C4—28no—
972C2×C4⋊C4—28no—
973C2×C4⋊C4—24no—
974C2×C4⋊C4—24no—
975C2×C4⋊C4—28no—
976C2×C4⋊C4—28no—
977C2×C4⋊C4—28no—
978C2×C4⋊C4—28no—
979C2×C4⋊C4—44no—
980C2×C4⋊C4—44no—
981C2×C4⋊C4—44no—
982C2×C4⋊C4—44no—
983C2×C4⋊C4—816no—
984C2×C4⋊C4C22×D414yes—
985C2×C4⋊C4C22×D414yes—
986C2×C4⋊C4C22×D418yes—
987C2×C4⋊C4C22×D414yes—
988C2×C4⋊C4C22×D412yes—
989C2×C4⋊C4C22×D414yes—
990C2×C4⋊C4C22×D412yes—
991C2×C4⋊C4C2518yes—
992C2×C4⋊C4C2518yes—
993C2×C4⋊C4C2518yes—
994C2×C22⋊C4—28no—
995C2×C22⋊C4—24no—
996C2×C22⋊C4—28no—
997C2×C22⋊C4—28no—
998C2×C22⋊C4—28no—
999C2×C22⋊C4—28no—
1000C2×C22⋊C4—28no—
1001C2×C22⋊C4—28no—
1002C2×C22⋊C4—28no—
1003C2×C22⋊C4—28no—
1004C2×C22⋊C4—24no—
1005C2×C22⋊C4—24no—
1006C2×C22⋊C4—28no—
1007C2×C22⋊C4—24no—
1008C2×C22⋊C4—28no—
1009C2×C22⋊C4—28no—
1010C2×C22⋊C4—28no—
1011C2×C22⋊C4—28no—
1012C2×C22⋊C4—28no—
1013C2×C22⋊C4—28no—
1014C2×C22⋊C4—28no—
1015C2×C22⋊C4—28no—
1016C2×C22⋊C4—28no—
1017C2×C22⋊C4—816no—
1018C2×C22⋊C4—88no—
1019C2×C22⋊C4—88no—
1020C2×C22⋊C4—816no—
1021C2×C22⋊C4C22×D418yes—
1022C2×C22⋊C4C22×D414yes—
1023C2×C22⋊C4C22×D418yes—
1024C2×C22⋊C4C22×D418yes—
1025C2×C22⋊C4C22×D414yes—
1026C2×C22⋊C4C22×D414yes—
1027C2×C22⋊C4C22×D414yes—
1028C2×C42—28no—
1029C2×C42—22no—
1030C2×C42—28no—
1031C2×C42—22no—
1032C2×C42—28no—
1033C2×C42—28no—
1034C2×C42—28no—
1035C2×C42—816no—
1036C2×C42C22×D414yes—
1037C2×C42C22×D412yes—
1038C2×C42C22×D414yes—
1039C2×C42C22×D418yes—
1040C2×C42C2512yes—
1041C2×C42C2514yes—
1042C2×C42C2511yescharacteristic
1043C2×C42C2512yes—
1044C2×C42C2511yescharacteristic
1045#107—28no—
1046#107—28no—
1047#107—48no—
1048#106—28no—
1049#106—28no—
1050#106—48no—
1051#106—44no—
1052#106—44no—
1053#106—48no—
1054C4⋊C8—28no—
1055C4⋊C8—28no—
1056C4⋊C8—42no—
1057C4⋊C8—42no—
1058C4⋊C8—44no—
1059C4⋊C8—44no—
1060#102—216no—
1061#102—216no—
1062#102—216no—
1063#102—216no—
1064#102—216no—
1065#102—216no—
1066#102—48no—
1067#102—48no—
1068#102—48no—
1069#102—48no—
1070#102—48no—
1071#102—48no—
1072C22⋊C8—216no—
1073C22⋊C8—44no—
1074C22⋊C8—44no—
1075C22⋊C8—44no—
1076C22⋊C8—48no—
1077#97—24no—
1078#97—28no—
1079#97—28no—
1080#97—24no—
1081#97—28no—
1082#97—22no—
1083#97—24no—
1084#97—24no—
1085#97—41no—
1086#97—41no—
1087#97—42no—
1088#97H(5,𝔽2)14yes—
1089C4×C8—24no—
1090C4×C8—22no—
1091C4×C8—22no—
1092C4×C8—24no—
1093C4×C8—42no—
1094C4×C8C2×#4118yes—
1095#95—24no—
1096#95—24no—
1097#95—28no—
1098#95—28no—
1099#95—28no—
1100#95—28no—
1101#95—28no—
1102#95—28no—
1103#95—28no—
1104#95—28no—
1105#95—28no—
1106#95—28no—
1107#95—28no—
1108#95—24no—
1109#95—24no—
1110#95—28no—
1111#95—28no—
1112#95C22×D414yes—
1113#95C22×D414yes—
1114#95C22×D414yes—
1115#95C22×D414yes—
1116#95C22×D418yes—
1117#95C22×D418yes—
1118C24—28no—
1119C24—416no—
1120C24—416no—
1121C24—48no—
1122C24—48no—
1123C24—84no—
1124C24—84no—
1125C24—88no—
1126C24—88no—
1127C24—84no—
1128C24—84no—
1129C24C23×D411yescharacteristic
1130C24C23×D414yes—
1131#41—816no—
1132C2×Q8—42no—
1133C2×Q8—44no—
1134C2×D4—216no—
1135C2×D4—28no—
1136C2×D4—28no—
1137C2×D4—28no—
1138C2×D4—28no—
1139C2×D4—28no—
1140C2×D4—28no—
1141C2×D4—28no—
1142C2×D4—28no—
1143C2×D4—232no—
1144C2×D4—42no—
1145C2×D4—44no—
1146C2×D4—44no—
1147C2×D4—416no—
1148C2×D4—416no—
1149C2×D4—416no—
1150C2×D4—416no—
1151C2×D4—416no—
1152C2×D4—416no—
1153C2×D4—416no—
1154C2×D4—416no—
1155C2×D4—416no—
1156C2×D4—84no—
1157C2×D4—84no—
1158C2×D4—88no—
1159C2×D4—88no—
1160C2×D4—816no—
1161C2×D4—816no—
1162C2×D4—88no—
1163C2×D4—88no—
1164C2×D4—88no—
1165C2×D4—88no—
1166C2×D4—88no—
1167C2×D4—88no—
1168C2×D4—8128no—
1169C2×D4C22×#41116yes—
1170C22×C4—28no—
1171C22×C4—28no—
1172C22×C4—22no—
1173C22×C4—21no—
1174C22×C4—24no—
1175C22×C4—28no—
1176C22×C4—24no—
1177C22×C4—21no—
1178C22×C4—22no—
1179C22×C4—28no—
1180C22×C4—28no—
1181C22×C4—24no—
1182C22×C4—28no—
1183C22×C4—28no—
1184C22×C4—28no—
1185C22×C4—44no—
1186C22×C4—48no—
1187C22×C4—44no—
1188C22×C4—416no—
1189C22×C4—416no—
1190C22×C4—416no—
1191C22×C4—416no—
1192C22×C4—48no—
1193C22×C4—416no—
1194C22×C4—416no—
1195C22×C4—88no—
1196C22×C4—88no—
1197C22×C4—88no—
1198C22×C4—88no—
1199C22×C4—88no—
1200C22×C4—88no—
1201C22×C4—88no—
1202C22×C4—88no—
1203C22×C4—88no—
1204C22×C4—84no—
1205C22×C4—84no—
1206C22×C4—88no—
1207C22×C4—84no—
1208C22×C4—1632no—
1209C22×C4—1632no—
1210C22×C4C23×D414yes—
1211C22×C4C23×D411yescharacteristic
1212C22×C4C23×D414yes—
1213C22×C4C23×D412yes—
1214C22×C4C23×D414yes—
1215C22×C4C23×D414yes—
1216C22×C4C23×D414yes—
1217C22×C4C23×D412yes—
1218C22×C4C2611yescharacteristic
1219D8—232no—
1220D8—416no—
1221D8—432no—
1222M16—44no—
1223M16—44no—
1224C2×C8—22no—
1225C2×C8—22no—
1226C2×C8—22no—
1227C2×C8—22no—
1228C2×C8—22no—
1229C2×C8—28no—
1230C2×C8—21no—
1231C2×C8—21no—
1232C2×C8—24no—
1233C2×C8—24no—
1234C2×C8—22no—
1235C2×C8—22no—
1236C2×C8—22no—
1237C2×C8—28no—
1238C2×C8—48no—
1239C2×C8—416no—
1240C2×C8—88no—
1241C2×C8C22×#4114yes—
1242C2×C8C22×#4114yes—
1243C2×C8C2×H(5,𝔽2)12yes—
1244C2×C8C2×H(5,𝔽2)12yes—
1245C4⋊C4—28no—
1246C4⋊C4—28no—
1247C4⋊C4—28no—
1248C4⋊C4—28no—
1249C4⋊C4—28no—
1250C4⋊C4—28no—
1251C4⋊C4—28no—
1252C4⋊C4—28no—
1253C4⋊C4—48no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—416no—
1259C4⋊C4—416no—
1260C4⋊C4—84no—
1261C4⋊C4—84no—
1262C4⋊C4—88no—
1263C4⋊C4—88no—
1264C4⋊C4—88no—
1265C4⋊C4—88no—
1266C4⋊C4—88no—
1267C4⋊C4—88no—
1268C22⋊C4—216no—
1269C22⋊C4—28no—
1270C22⋊C4—216no—
1271C22⋊C4—48no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—416no—
1276C22⋊C4—416no—
1277C22⋊C4—416no—
1278C22⋊C4—416no—
1279C22⋊C4—416no—
1280C22⋊C4—416no—
1281C22⋊C4—48no—
1282C22⋊C4—416no—
1283C22⋊C4—416no—
1284C22⋊C4—88no—
1285C22⋊C4—88no—
1286C22⋊C4—88no—
1287C22⋊C4—88no—
1288C22⋊C4—88no—
1289C22⋊C4—88no—
1290C22⋊C4—88no—
1291C22⋊C4—88no—
1292C22⋊C4—88no—
1293C22⋊C4—88no—
1294C22⋊C4—84no—
1295C22⋊C4—84no—
1296C22⋊C4—88no—
1297C22⋊C4—84no—
1298C42—22no—
1299C42—21no—
1300C42—24no—
1301C42—22no—
1302C42—21no—
1303C42—24no—
1304C42—24no—
1305C42—28no—
1306C42—28no—
1307C42—48no—
1308C42—416no—
1309C42—88no—
1310C42—88no—
1311C42C22×#4114yes—
1312C42C2×H(5,𝔽2)12yes—
1313C42#58514yes—
1314C42#58512yes—
1315C23—24no—
1316C23—28no—
1317C23—24no—
1318C23—28no—
1319C23—21no—
1320C23—24no—
1321C23—22no—
1322C23—216no—
1323C23—48no—
1324C23—48no—
1325C23—48no—
1326C23—48no—
1327C23—48no—
1328C23—48no—
1329C23—832no—
1330C23—832no—
1331C23—816no—
1332C23—816no—
1333C23—168no—
1334C23—168no—
1335C23—1616no—
1336C23—1616no—
1337C23—168no—
1338C23—168no—
1339C23#358518yes—
1340C23C24×D411yescharacteristic
1341Q8—84no—
1342D4—232no—
1343D4—216no—
1344D4—216no—
1345D4—48no—
1346D4—48no—
1347D4—48no—
1348D4—832no—
1349D4—88no—
1350D4—816no—
1351D4—816no—
1352D4—832no—
1353D4—832no—
1354D4—1616no—
1355C2×C4—24no—
1356C2×C4—28no—
1357C2×C4—21no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—28no—
1363C2×C4—28no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—28no—
1369C2×C4—22no—
1370C2×C4—416no—
1371C2×C4—44no—
1372C2×C4—41no—
1373C2×C4—42no—
1374C2×C4—48no—
1375C2×C4—44no—
1376C2×C4—41no—
1377C2×C4—48no—
1378C2×C4—48no—
1379C2×C4—48no—
1380C2×C4—48no—
1381C2×C4—48no—
1382C2×C4—48no—
1383C2×C4—48no—
1384C2×C4—48no—
1385C2×C4—48no—
1386C2×C4—88no—
1387C2×C4—84no—
1388C2×C4—832no—
1389C2×C4—832no—
1390C2×C4—1616no—
1391C2×C4—1616no—
1392C2×C4—1616no—
1393C2×C4—168no—
1394C2×C4—168no—
1395C2×C4D4×#4118yes—
1396C2×C4#349614yes—
1397C2×C4C23×#4112yes—
1398C2×C4C22×H(5,𝔽2)11yescharacteristic
1399C2×C4C2×#58512yes—
1400C2×C4C2×#58511yescharacteristic
1401C8—22no—
1402C8—24no—
1403C8—44no—
1404C8—41no—
1405C8—42no—
1406C8—44no—
1407C8—41no—
1408C8#348114yes—
1409C22—216no—
1410C22—28no—
1411C22—48no—
1412C22—44no—
1413C22—44no—
1414C22—416no—
1415C22—416no—
1416C22—44no—
1417C22—41no—
1418C22—416no—
1419C22—42no—
1420C22—88no—
1421C22—88no—
1422C22—88no—
1423C22—88no—
1424C22—1632no—
1425C22—1632no—
1426C22C2×D4×#4112yes—
1427C22C2×#349611yescharacteristic
1428C22C2×#358514yes—
1429C4—28no—
1430C4—24no—
1431C4—44no—
1432C4—41no—
1433C4—44no—
1434C4—44no—
1435C4—44no—
1436C4—42no—
1437C4—88no—
1438C4—88no—
1439C4—88no—
1440C4C2×#348111yescharacteristic
1441C4#6275911yescharacteristic
1442C4#6278112yes—
1443C2—48no—
1444C2—81no—
1445C2—816no—
1446C2#766698311yescharacteristic
1447C2#1057692814yes—
1448C2#1057766012yes—
subgroupG/H
center, socleC23C24×D4
commutator, Frattini, cosocleC22×C4C26
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #34547 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #7669845C2semidirect
2. #7620704C2semidirect
3. #7618079C2semidirect
4. #7616331C2semidirect
5. #7615382C2semidirect
6. #7614034C2semidirect
7. #7613013C2semidirect
8. #7605741C2semidirect
9. #7598756C2semidirect
10. #7590412C2semidirect
11. #7533713C2semidirect
12. #7511824C2semidirect
13. #6469636C2semidirect
14. #6467316C2semidirect
15. #6466642C2semidirect
16. #6447455C2semidirect
17. D4×#442C2semidirect
18. #6373996C2semidirect
19. #6373906C2semidirect
22. C2×#2970C22semidirect
23. C22×#442C22semidirect
26. #45380C22semidirect
27. #45377C22semidirect
29. #45362C22semidirect
31. #45257C22semidirect
32. #44881C22semidirect
37. #34963C22semidirect
39. #34935C22semidirect
40. #34917C22semidirect
43. C4×D42C22semidirect
44. C4×#540C22semidirect
45. #32659C22semidirect
46. #32554C22semidirect
47. #32468C22semidirect
48. #32002C22semidirect
49. #31996C22semidirect
50. #31681C22semidirect
51. #31680C22semidirect
53. #30400C22semidirect
54. #30396C22semidirect
55. #29542C22semidirect
56. #29295C22semidirect
57. #28854C22semidirect
58. #28853C22semidirect
59. #28834C22semidirect
60. #28707C22semidirect
61. #28536C22semidirect
62. #28292C22semidirect
63. #28276C22semidirect
65. #28237C22semidirect
67. #28197C22semidirect
68. #28152C22semidirect
69. #28107C22semidirect
70. #28104C22semidirect
71. #28097C22semidirect
72. #28094C22semidirect
73. #27845C22semidirect
74. #27733C22semidirect
75. #27663C22semidirect
76. #27658C22semidirect
77. #27641C22semidirect
78. #27525C22semidirect
79. #27520C22semidirect
80. #27097C22semidirect
81. #27096C22semidirect
82. #26657C22semidirect
83. #26656C22semidirect
84. #26541C22semidirect
85. #26310C22semidirect
86. #26118C22semidirect
87. #25891C22semidirect
88. #25342C22semidirect
89. #25330C22semidirect
90. #25042C22semidirect
91. #24977C22semidirect
92. #24897C22semidirect
93. #24893C22semidirect
94. #24823C22semidirect
95. #24272C22semidirect
98. #24162C22semidirect
99. #23764C22semidirect
100. #23761C22semidirect
101. #23708C22semidirect
102. #23708C22semidirect
104. #23029C22semidirect
105. #23001C22semidirect
106. #22858C22semidirect
107. #22858C22semidirect
108. #22670C22semidirect
109. D4×#106C22semidirect
110. #22436C22semidirect
111. D4×#102C22semidirect
112. #21728C22semidirect
113. #21722C22semidirect
114. #21716C22semidirect
115. #21716C22semidirect
120. #21656C22semidirect
121. #21652C22semidirect
122. #21638C22semidirect
123. #21638C22semidirect
124. #21617C22semidirect
125. #21538C22semidirect
126. #21536C22semidirect
127. #21529C22semidirect
128. #21526C22semidirect
129. #21526C22semidirect
130. #21503C22semidirect
131. #21492C22semidirect
132. #21492C22semidirect
133. #21452C22semidirect
134. #21452C22semidirect
135. #21414C22semidirect
136. #21379C22semidirect
137. #21290C22semidirect
138. #21284C22semidirect
139. #21271C22semidirect
140. #20823C22semidirect
141. #20820C22semidirect
142. #20811C22semidirect
143. #20739C22semidirect
144. #20738C22semidirect
145. C4×#442C22semidirect
146. C4×#442C22semidirect
147. D4×#97C22semidirect
148. #20331C22semidirect
559. #493#41semidirect

Maximal subgroups

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

subgroupindex
#76698452
#76207042
#76180792
#76163312
#76153822
#76140342
#76130132
#76057412
#75987562
#75904122
#75337132
#75118242
#64696362
#64673162
#64666422
#64474552
D4×#4422
#63739962
#63739062