Finite Group Databasebeta

← #11707329

Subgroups — #11707329

Order 768.

7694 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#41C211yesmaximal, characteristic, complemented
2#87275C212yesmaximal, complemented
3C2×#5827C212yesmaximal, complemented
4#86773C212yesmaximal, complemented
5#86744C212yesmaximal, complemented
6#86722C214yesmaximal, complemented
7#86685C216yesmaximal, complemented
8#86634C2112yesmaximal, complemented
9D4×#237C216yesmaximal, complemented
10#86225C213yesmaximal, complemented
11#86223C213yesmaximal, complemented
12#86027C216yesmaximal, complemented
13#86024C216yesmaximal, complemented
14C4×#1009C211yesmaximal, characteristic, complemented
15#85828C211yesmaximal, characteristic, complemented
16#85764C213yesmaximal, complemented
17C2×#5555C213yesmaximal, complemented
18#62985—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C2×#1009C2211yescharacteristic
21C22×#237C2216yescomplemented
22C3×#550C2211yescharacteristic, complemented
23C3×D4×Q8C2211yescharacteristic, complemented
24C3×#548C2212yescomplemented
25C3×#547C2213yescomplemented
26C3×#546C2216yescomplemented
27C3×D42C2213yescomplemented
28C3×#532C2213yescomplemented
29C3×#525C2216yescomplemented
30C3×C4×#41C2211yescharacteristic
31C2×C3×C4×D4C2213yescomplemented
32#5834C2214yescomplemented
33#5833C2216yescomplemented
34#5830C2216yescomplemented
35#5829C22112yescomplemented
36#5827C2212yes—
37#5827C2211yescharacteristic
38#5827C2216yescomplemented
39#5827C2216yescomplemented
40#5827C22112yescomplemented
41#5827C2214yescomplemented
42#5817C2214yescomplemented
43C2×Q8×Dic3C2214yescomplemented
44#5806C2216yescomplemented
45D4×#67C22112yescomplemented
46C2×D4×Dic3C22112yescomplemented
47#5791C2216yescomplemented
48C2×#930C2216yescomplemented
49C2×#926C2216yescomplemented
50C22×C4⋊Dic3C2216yescomplemented
51#5732C2216yescomplemented
52#5728C2216yescomplemented
53#5718C2216yescomplemented
54#5716C2216yescomplemented
55#5682C22112yescomplemented
56#5681C22112yescomplemented
57#5665C22124yescomplemented
58#5658C22124yescomplemented
59#5643C22112yescomplemented
60#5642C22112yescomplemented
61#5635C22112yescomplemented
62#5624C22112yescomplemented
63#5619C22112yescomplemented
64#5618C22112yescomplemented
65#5618C22112yescomplemented
66#5617C22112yescomplemented
67#5611C22112yescomplemented
68#5606C22112yescomplemented
69#5598C22112yescomplemented
70#5596C22112yescomplemented
71#5591C22124yescomplemented
72#5586C22124yescomplemented
73#5574C2212yescomplemented
74C4×#239C2212yescomplemented
75#5570C2212yescomplemented
76Q8×Dic6C2212yescomplemented
77#5565C2216yescomplemented
78#5565C22112yescomplemented
79#5563C2213yescomplemented
80#5563C2216yescomplemented
81#5557C2216yescomplemented
82#5555C2213yescomplemented
83#5555C22112yescomplemented
84#5555C2216yescomplemented
85#5555C22112yescomplemented
86#5555C2216yescomplemented
87#5555C2216yescomplemented
88#5545C2216yescomplemented
89C4×D3×D4C2216yescomplemented
90#5543C2211yescharacteristic, complemented
91#5543C2216yescomplemented
92#5543C2216yescomplemented
93#5542C2213yescomplemented
94#5541C2216yescomplemented
95#5538C22112yescomplemented
96D4×Dic6C2216yescomplemented
97C4×#237C2216yescomplemented
98#5523C2213yescomplemented
99#5521C2213yescomplemented
100#5519C2216yescomplemented
101#5513C2216yescomplemented
102C2×#897C2216yescomplemented
103#5495C22112yescomplemented
104C2×#886C22112yescomplemented
105C4×#235C2213yescomplemented
106C2×C4×D12C2213yescomplemented
107#5470C2213yescomplemented
108C2×#869C2213yescomplemented
109#3522—34no—
110#3520—36no—
111#3517—32no—
112#3513—312no—
113#3511—33no—
114#3506—33no—
115#3503—31no—
116#3494—36no—
117#3492—36no—
118#3488—32no—
119#3482—32no—
120#3475—33no—
121D4×#41—36no—
122D4×#41D311yescharacteristic, complemented
123C2×#547—33no—
124C4×H(5,𝔽2)—31no—
125C2×#520—32no—
126C2×C3×#41—216no—
127C2×C3×#41C2316yes—
128C2×C3×#41C2316yes—
129C2×C3×#41C2312yes—
130C2×C3×#41C2311yescharacteristic
131C22×C3×Q8C2312yes—
132C22×C3×D4C2313yes—
133C22×C3×D4C2316yes—
134C23×C3×C4C2316yes—
135C22×#67C23112yes—
136C23×Dic3C23112yes—
137#1009—28no—
138C2×#239C2312yes—
139C2×#237—424no—
140C2×#237C2316yes—
141C2×#237C23112yes—
142C2×#237C23124yes—
143C2×D3×D4C2316yes—
144C2×#235C2313yes—
145C22×D12C2313yes—
146C22×C4×D3C2316yes—
147C22×Dic6C2316yes—
148C3×C4⋊Q8C2313yes—
149C3×#127C2313yes—
150C3×#124C2316yes—
151C3×#123C23112yes—
152C3×C22⋊Q8C2316yes—
153C3×C22⋊Q8C2316yes—
154C3×#121C2316yes—
155C3×#121C2316yes—
156C3×#121C2316yes—
157C3×#121C2316yes—
158C3×#120C23112yes—
159C3×C4×Q8C2311yescharacteristic
160C3×C4×Q8C2311yescharacteristic
161C3×C4×D4C2313yes—
162C3×C4×D4C2313yes—
163C3×C4×D4C2316yes—
164C3×C4×D4C2316yes—
165C3×C4×D4C2313yes—
166C3×C4×D4C2313yes—
167C3×C4×D4C2311yescharacteristic
168C3×C4×D4C2316yes—
169C3×C4×D4C2313yes—
170C3×#117C2313yes—
171C2×C3×C4⋊C4C2313yes—
172C2×C3×C22⋊C4C2316yes—
173C2×C3×C42C2313yes—
174#953C23112yes—
175C2×#217C23112yes—
176#947C23112yes—
177#946C23112yes—
178Q8×Dic3C23112yes—
179Q8×Dic3C23112yes—
180Q8×Dic3C2312yes—
181Q8×Dic3C2314yes—
182#940C23112yes—
183#939C23124yes—
184#939C23124yes—
185#939C23112yes—
186#938C23112yes—
187#938C23112yes—
188#938C2316yes—
189#937C23124yes—
190#936C2316yes—
191#935C23112yes—
192D4×Dic3C23124yes—
193D4×Dic3C23124yes—
194D4×Dic3C23112yes—
195D4×Dic3C23112yes—
196D4×Dic3C23112yes—
197D4×Dic3C2312yes—
198D4×Dic3C23112yes—
199D4×Dic3C2316yes—
200#930C23112yes—
201#930C2316yes—
202#930C23112yes—
203#930C23112yes—
204#930C2316yes—
205#929C23112yes—
206C4×#67C23112yes—
207C4×#67C23112yes—
208C4×#67C2316yes—
209C4×#67C2316yes—
210C2×(C2×D3)⋊C4C23112yes—
211C2×(C2×D3)⋊C4C2316yes—
212#926C23112yes—
213#926C23112yes—
214#926C2316yes—
215#926C2313yes—
216#926C2316yes—
217#926C2316yes—
218C2×C4⋊Dic3C23112yes—
219C2×C4⋊Dic3C23112yes—
220C2×C4⋊Dic3C23112yes—
221C2×C4⋊Dic3C2316yes—
222C2×C4⋊Dic3C2316yes—
223C2×C4⋊Dic3C2313yes—
224C2×C4⋊Dic3C2316yes—
225C2×C4⋊Dic3C23112yes—
226C2×C4⋊Dic3C2312yes—
227#924C2316yes—
228#924C2316yes—
229#924C2312yes—
230#924C2316yes—
231C2×C4×Dic3C23112yes—
232#898C23124yes—
233#898C23112yes—
234#897C23124yes—
235#897C23112yes—
236#897C2316yes—
237#893C2316yes—
238#893C2316yes—
239#892C2316yes—
240#892C23112yes—
241#892C2316yes—
242D3×C4⋊C4C2316yes—
243#890C23112yes—
244#890C23112yes—
245#890C2312yes—
246#889C23112yes—
247#888C23112yes—
248#887C2316yes—
249#886C23124yes—
250#886C23124yes—
251#886C23124yes—
252#886C23112yes—
253#885C23124yes—
254#885C23112yes—
255#883C23124yes—
256#883C23112yes—
257#67⋊C4C23124yes—
258#67⋊C4C23112yes—
259#67⋊C4C23112yes—
260D3×C22⋊C4C23112yes—
261#879C23112yes—
262#879C23112yes—
263#878C23124yes—
264#878C23124yes—
265#878C2314yes—
266#877C23112yes—
267C4×D12C2316yes—
268C4×D12C2316yes—
269C4×D12C2313yes—
270C4×D12C2316yes—
271C4×D12C2313yes—
272#872C2316yes—
273C42×D3C2316yes—
274#870C2316yes—
275#869C2316yes—
276#869C2316yes—
277#869C2313yes—
278#869C2316yes—
279#869C2311yescharacteristic
280C4×Dic6C2316yes—
281C4×Dic6C2316yes—
282C4×Dic6C2311yescharacteristic
283C4×Dic6C2313yes—
284C2×H(5,𝔽2)—31no—
285C22×#41—36no—
286C22×#41C2×D312yes—
287#559—312no—
288Q82—32no—
289#557—32no—
290#556—36no—
291#556—33no—
292#555—33no—
293#555—36no—
294#554—312no—
295#554—31no—
296#554—36no—
297#554—36no—
298#553—312no—
299#553—312no—
300#553—36no—
301#553—312no—
302#552—312no—
303#552—36no—
304#552—36no—
305#551—324no—
306#551—312no—
307#550—34no—
308#550—36no—
309#550C2×D311yescharacteristic, complemented
310D4×Q8—36no—
311D4×Q8C2×D311yescharacteristic, complemented
312#548—34no—
313#548—312no—
314#548C2×D312yescomplemented
315#547—312no—
316#547—33no—
317#547—36no—
318#547—312no—
319#547—36no—
320#547—312no—
321#547—36no—
322#547C2×D313yescomplemented
323#546—312no—
324#546—36no—
325#546—324no—
326#546C2×D316yescomplemented
327D42—312no—
328D42C2×D313yescomplemented
329#544—36no—
330#542—312no—
331#542—312no—
332#540—312no—
333#539—324no—
334#538—312no—
335#537—36no—
336#535—36no—
337#533—36no—
338#533—33no—
339#532—36no—
340#532—312no—
341#532C2×D313yescomplemented
342C2×C4⋊Q8—33no—
343#529—312no—
344#529—312no—
345#529—36no—
346#525—36no—
347#525—312no—
348#525—324no—
349#525C2×D316yescomplemented
350C2×#123—312no—
351C2×C22⋊Q8—36no—
352C2×#121—36no—
353#520—31no—
354#520—32no—
355#520—36no—
356#520—36no—
357#520—312no—
358#520—34no—
359#520—32no—
360#520—33no—
361#518—36no—
362#518—33no—
363C4×#41—32no—
364C4×#41—36no—
365C4×#41—33no—
366C4×#41C2×D311yescharacteristic
367C2×C4×Q8—34no—
368C2×C4×D4—312no—
369C2×C4×D4—36no—
370C2×C4×D4—33no—
371C2×C4×D4C2×D313yescomplemented
372C2×#117—36no—
373C22×C4⋊C4—36no—
374C24×C3C2416yes—
375C23×D3C2416yes—
376C3×#41—28no—
377C3×#41—224no—
378C3×#41—224no—
379C3×#41#4118yescomplemented
380C2×C3×Q8—28no—
381C2×C3×Q8C2416yes—
382C2×C3×Q8C2411yescharacteristic
383C2×C3×D4—224no—
384C2×C3×D4—212no—
385C2×C3×D4C24112yes—
386C2×C3×D4C2416yes—
387C2×C3×D4C2416yes—
388C2×C3×D4C2413yes—
389C2×C3×D4C2416yes—
390C2×C3×D4C2413yes—
391C2×C3×D4C2411yescharacteristic
392C22×C3×C4—224no—
393C22×C3×C4C2416yes—
394C22×C3×C4C2413yes—
395C22×C3×C4C2412yes—
396C22×C3×C4C2416yes—
397C22×C3×C4C2416yes—
398C22×C3×C4C2416yes—
399C22×C3×C4C2413yes—
400C22×C3×C4C2413yes—
401C2×#67—424no—
402C2×#67C2416yes—
403C2×#67C24112yes—
404C2×#67C24112yes—
405C2×#67C24124yes—
406C22×Dic3—424no—
407C22×Dic3C24112yes—
408C22×Dic3C24112yes—
409C22×Dic3C2414yes—
410C22×Dic3C24124yes—
411C22×Dic3C2416yes—
412#239—28no—
413#237—224no—
414#237—424no—
415#237—448no—
416D3×D4—224no—
417#235—212no—
418C2×D12—212no—
419C2×D12C2413yes—
420C2×D12C2416yes—
421C2×C4×D3—412no—
422C2×C4×D3C2416yes—
423C2×C4×D3C2416yes—
424C2×C4×D3C2416yes—
425C2×C4×D3C24112yes—
426C2×Dic6—412no—
427C2×Dic6C2411yescharacteristic
428C2×Dic6C2416yes—
429C2×Dic6C2412yes—
430C2×Dic6C24112yes—
431C3×C4⋊C4C2413yes—
432C3×C4⋊C4C2413yes—
433C3×C4⋊C4C2416yes—
434C3×C4⋊C4C2413yes—
435C3×C4⋊C4C2416yes—
436C3×C4⋊C4C2411yescharacteristic
437C3×C22⋊C4C2416yes—
438C3×C22⋊C4C2416yes—
439C3×C22⋊C4C24112yes—
440C3×C22⋊C4C2412yes—
441C3×C22⋊C4C2416yes—
442C3×C22⋊C4C2416yes—
443C3×C42C2413yes—
444C3×C42C2413yes—
445C3×C42C2411yescharacteristic
446C3×C42C2413yes—
447#217C2414yes—
448#217C24112yes—
449#217C24112yes—
450#217C24112yes—
451#217C24112yes—
452#217C2416yes—
453(C2×D3)⋊C4C2416yes—
454(C2×D3)⋊C4C2416yes—
455(C2×D3)⋊C4C24112yes—
456(C2×D3)⋊C4C24112yes—
457(C2×D3)⋊C4C24124yes—
458(C2×D3)⋊C4C24112yes—
459C4⋊Dic3C2412yes—
460C4⋊Dic3C2416yes—
461C4⋊Dic3C2413yes—
462C4⋊Dic3C2411yescharacteristic
463C4⋊Dic3C2416yes—
464C4⋊Dic3C24112yes—
465C4⋊Dic3C24112yes—
466C4⋊Dic3C2412yes—
467C4⋊Dic3C2416yes—
468C4⋊Dic3C2414yes—
469C4⋊Dic3C24124yes—
470C4⋊Dic3C24112yes—
471Dic3⋊C4C24112yes—
472Dic3⋊C4C24112yes—
473Dic3⋊C4C2412yes—
474Dic3⋊C4C2416yes—
475Dic3⋊C4C24112yes—
476Dic3⋊C4C2414yes—
477C4×Dic3C24112yes—
478C4×Dic3C2412yes—
479C4×Dic3C2416yes—
480C4×Dic3C2416yes—
481C4×Dic3C24112yes—
482C4×Dic3C24112yes—
483H(5,𝔽2)—68no—
484C2×#41—216no—
485C2×#41—32no—
486C2×#41—36no—
487C2×#41—324no—
488C2×#41—312no—
489C2×#41—33no—
490C2×#41—1224no—
491C2×#41C22×D316yes—
492C2×#41C22×D316yes—
493C2×#41C22×D312yes—
494C2×#41C22×D311yescharacteristic
495C22×Q8—36no—
496C22×Q8C22×D312yes—
497C22×D4—312no—
498C22×D4—36no—
499C22×D4—33no—
500C22×D4C22×D316yes—
501C22×D4C22×D313yes—
502C23×C4—312no—
503C23×C4—36no—
504C23×C4C22×D316yes—
505C4⋊Q8—312no—
506C4⋊Q8—33no—
507C4⋊Q8—36no—
508C4⋊Q8—36no—
509C4⋊Q8—36no—
510C4⋊Q8—31no—
511C4⋊Q8C22×D313yes—
512#127—312no—
513#127C22×D313yes—
514#126—324no—
515#126—312no—
516#126—312no—
517#126—312no—
518#125—32no—
519#125—312no—
520#125—312no—
521#125—312no—
522#125—36no—
523#124—312no—
524#124—36no—
525#124—312no—
526#124—324no—
527#124C22×D316yes—
528#123—312no—
529#123—312no—
530#123—312no—
531#123—324no—
532#123—324no—
533#123—324no—
534#123—324no—
535#123—312no—
536#123C22×D3112yes—
537C22⋊Q8—312no—
538C22⋊Q8—32no—
539C22⋊Q8—36no—
540C22⋊Q8—36no—
541C22⋊Q8—36no—
542C22⋊Q8—36no—
543C22⋊Q8—312no—
544C22⋊Q8—324no—
545C22⋊Q8—324no—
546C22⋊Q8—324no—
547C22⋊Q8—34no—
548C22⋊Q8C22×D316yes—
549C22⋊Q8C22×D316yes—
550#121—36no—
551#121—324no—
552#121—324no—
553#121—312no—
554#121—312no—
555#121—312no—
556#121—36no—
557#121—312no—
558#121—312no—
559#121—312no—
560#121—36no—
561#121C22×D316yes—
562#121C22×D316yes—
563#121C22×D316yes—
564#121C22×D316yes—
565#120—312no—
566#120—324no—
567#120C22×D3112yes—
568C4×Q8—32no—
569C4×Q8—312no—
570C4×Q8—34no—
571C4×Q8—312no—
572C4×Q8—36no—
573C4×Q8—31no—
574C4×Q8—33no—
575C4×Q8—36no—
576C4×Q8—36no—
577C4×Q8C22×D311yescharacteristic
578C4×Q8C22×D311yescharacteristic
579C4×D4—36no—
580C4×D4—324no—
581C4×D4—312no—
582C4×D4—312no—
583C4×D4—324no—
584C4×D4—312no—
585C4×D4—32no—
586C4×D4—312no—
587C4×D4—36no—
588C4×D4—36no—
589C4×D4—312no—
590C4×D4—312no—
591C4×D4—36no—
592C4×D4—36no—
593C4×D4—312no—
594C4×D4—312no—
595C4×D4—324no—
596C4×D4—33no—
597C4×D4—36no—
598C4×D4—36no—
599C4×D4—36no—
600C4×D4—33no—
601C4×D4C22×D313yes—
602C4×D4C22×D311yescharacteristic
603C4×D4C22×D313yes—
604C4×D4C22×D316yes—
605C4×D4C22×D316yes—
606C4×D4C22×D313yes—
607C4×D4C22×D313yes—
608C4×D4C22×D313yes—
609C4×D4C22×D316yes—
610#117—33no—
611#117—36no—
612#117—312no—
613#117—312no—
614#117—36no—
615#117—36no—
616#117—36no—
617#117—36no—
618#117—312no—
619#117—312no—
620#117—36no—
621#117C22×D313yes—
622C2×C4⋊C4—36no—
623C2×C4⋊C4—33no—
624C2×C4⋊C4—312no—
625C2×C4⋊C4—36no—
626C2×C4⋊C4—312no—
627C2×C4⋊C4—312no—
628C2×C4⋊C4—312no—
629C2×C4⋊C4—32no—
630C2×C4⋊C4—36no—
631C2×C4⋊C4—36no—
632C2×C4⋊C4C22×D313yes—
633C2×C22⋊C4—312no—
634C2×C22⋊C4—36no—
635C2×C22⋊C4—312no—
636C2×C22⋊C4—312no—
637C2×C22⋊C4C22×D316yes—
638C2×C42—312no—
639C2×C42—36no—
640C2×C42C22×D313yes—
641C23×C3—212no—
642C23×C3—212no—
643C23×C3—46no—
644C23×C3C2516yes—
645C23×C3C2513yes—
646C23×C3C2512yes—
647C22×D3—212no—
648C22×D3—46no—
649C22×D3—46no—
650C22×D3C2516yes—
651C3×Q8—212no—
652C3×Q8C2×#4114yescomplemented
653C3×D4—224no—
654C3×D4—212no—
655C3×D4—212no—
656C3×D4—26no—
657C3×D4—46no—
658C3×D4C2×#41112yescomplemented
659C3×D4H(5,𝔽2)14yescomplemented
660C2×C3×C4—212no—
661C2×C3×C4—24no—
662C2×C3×C4—212no—
663C2×C3×C4—212no—
664C2×C3×C4—212no—
665C2×C3×C4—26no—
666C2×C3×C4—43no—
667C2×C3×C4C2×#41112yescomplemented
668C2×C3×C4C2516yes—
669C2×C3×C4C2513yes—
670C2×C3×C4C2513yes—
671C2×C3×C4C2512yes—
672C2×C3×C4C2511yescharacteristic
673C2×C3×C4C2513yes—
674C2×C3×C4C2511yescharacteristic
675C2×C3×C4C2511yescharacteristic
676#67—212no—
677#67—224no—
678#67—424no—
679#67—412no—
680C2×Dic3—224no—
681C2×Dic3—412no—
682C2×Dic3—46no—
683C2×Dic3—424no—
684C2×Dic3—44no—
685C2×Dic3C2512yes—
686C2×Dic3C2514yes—
687C2×Dic3C2512yes—
688C2×Dic3C2516yes—
689C2×Dic3C25112yes—
690D12—26no—
691D12—212no—
692C4×D3—212no—
693C4×D3—212no—
694C4×D3—412no—
695C4×D3—46no—
696Dic6—22no—
697Dic6—212no—
698Dic6—412no—
699Dic6—42no—
700C24—36no—
701C24C23×D316yes—
702#41—28no—
703#41—224no—
704#41—224no—
705#41—68no—
706#41—624no—
707#41—612no—
708#41—1248no—
709#41—1224no—
710#41#23718yescomplemented
711C2×Q8—28no—
712C2×Q8—31no—
713C2×Q8—36no—
714C2×Q8—32no—
715C2×Q8—312no—
716C2×Q8—1212no—
717C2×Q8C23×D316yes—
718C2×Q8C23×D311yescharacteristic
719C2×D4—224no—
720C2×D4—212no—
721C2×D4—36no—
722C2×D4—312no—
723C2×D4—312no—
724C2×D4—324no—
725C2×D4—33no—
726C2×D4—36no—
727C2×D4—624no—
728C2×D4—612no—
729C2×D4—1224no—
730C2×D4C23×D3112yes—
731C2×D4C23×D316yes—
732C2×D4C23×D316yes—
733C2×D4C23×D313yes—
734C2×D4C23×D316yes—
735C2×D4C23×D313yes—
736C2×D4C23×D311yescharacteristic
737C22×C4—224no—
738C22×C4—312no—
739C22×C4—34no—
740C22×C4—36no—
741C22×C4—312no—
742C22×C4—324no—
743C22×C4—36no—
744C22×C4—36no—
745C22×C4—36no—
746C22×C4—312no—
747C22×C4—1212no—
748C22×C4—1224no—
749C22×C4C23×D316yes—
750C22×C4C23×D313yes—
751C22×C4C23×D316yes—
752C22×C4C23×D312yes—
753C22×C4C23×D316yes—
754C22×C4C23×D316yes—
755C22×C4C23×D313yes—
756C22×C4C23×D313yes—
757C4⋊C4—33no—
758C4⋊C4—36no—
759C4⋊C4—36no—
760C4⋊C4—312no—
761C4⋊C4—312no—
762C4⋊C4—324no—
763C4⋊C4—31no—
764C4⋊C4—36no—
765C4⋊C4—36no—
766C4⋊C4—32no—
767C4⋊C4—34no—
768C4⋊C4—312no—
769C4⋊C4—32no—
770C4⋊C4—32no—
771C4⋊C4—312no—
772C4⋊C4—312no—
773C4⋊C4—34no—
774C4⋊C4—312no—
775C4⋊C4C23×D313yes—
776C4⋊C4C23×D311yescharacteristic
777C4⋊C4C23×D313yes—
778C4⋊C4C23×D316yes—
779C4⋊C4C23×D313yes—
780C4⋊C4C23×D316yes—
781C22⋊C4—36no—
782C22⋊C4—312no—
783C22⋊C4—312no—
784C22⋊C4—312no—
785C22⋊C4—34no—
786C22⋊C4—312no—
787C22⋊C4—312no—
788C22⋊C4—36no—
789C22⋊C4—36no—
790C22⋊C4—312no—
791C22⋊C4—324no—
792C22⋊C4—312no—
793C22⋊C4C23×D316yes—
794C22⋊C4C23×D312yes—
795C22⋊C4C23×D316yes—
796C22⋊C4C23×D316yes—
797C22⋊C4C23×D316yes—
798C22⋊C4C23×D3112yes—
799C42—36no—
800C42—32no—
801C42—36no—
802C42—312no—
803C42—312no—
804C42—312no—
805C42C23×D313yes—
806C42C23×D311yescharacteristic
807C42C23×D313yes—
808C42C23×D313yes—
809C22×C3—22no—
810C22×C3—23no—
811C22×C3—22no—
812C22×C3—23no—
813C22×C3—26no—
814C22×C3—26no—
815C22×C3—26no—
816C22×C3—424no—
817C22×C3C22×#4116yes—
818C22×C3C2×H(5,𝔽2)14yes—
819C22×C3C2611yescharacteristic
820C2×D3—26no—
821C2×D3—26no—
822C2×D3—26no—
823C2×D3—812no—
824C3×C4—22no—
825C3×C4—26no—
826C3×C4—23no—
827C3×C4—21no—
828C3×C4—23no—
829C3×C4C22×#4112yes—
830C3×C4C22×#4116yes—
831C3×C4C2×H(5,𝔽2)12yes—
832Dic3—22no—
833Dic3—212no—
834Dic3—26no—
835Dic3—24no—
836Dic3—22no—
837C23—212no—
838C23—212no—
839C23—36no—
840C23—46no—
841C23—612no—
842C23—126no—
843C23—126no—
844C23C24×D316yes—
845C23C24×D313yes—
846C23C24×D312yes—
847Q8—212no—
848Q8—62no—
849Q8—612no—
850Q8—1212no—
851Q8—122no—
852Q8C2×#23714yescomplemented
853D4—224no—
854D4—212no—
855D4—212no—
856D4—26no—
857D4—46no—
858D4—612no—
859D4—624no—
860D4—66no—
861D4—612no—
862D4—1224no—
863D4—1212no—
864D4C2×#237112yescomplemented
865D4#100914yescomplemented
866C2×C4—212no—
867C2×C4—24no—
868C2×C4—212no—
869C2×C4—212no—
870C2×C4—212no—
871C2×C4—26no—
872C2×C4—32no—
873C2×C4—34no—
874C2×C4—32no—
875C2×C4—36no—
876C2×C4—312no—
877C2×C4—43no—
878C2×C4—624no—
879C2×C4—612no—
880C2×C4—612no—
881C2×C4—1212no—
882C2×C4—126no—
883C2×C4—126no—
884C2×C4—1212no—
885C2×C4—1224no—
886C2×C4—124no—
887C2×C4C2×#237112yescomplemented
888C2×C4C24×D316yes—
889C2×C4C24×D313yes—
890C2×C4C24×D311yescharacteristic
891C2×C4C24×D313yes—
892C2×C4C24×D312yes—
893C2×C4C24×D313yes—
894C2×C4C24×D311yescharacteristic
895C2×C4C24×D311yescharacteristic
896C2×C3—26no—
897C2×C3—24no—
898C2×C3—46no—
899C2×C3C23×#4111yescharacteristic
900C2×C3C22×H(5,𝔽2)11yescharacteristic
901C2×C32−1+611yescharacteristic
902D3—46no—
903C22—22no—
904C22—23no—
905C22—23no—
906C22—22no—
907C22—26no—
908C22—26no—
909C22—26no—
910C22—424no—
911C22—66no—
912C22—66no—
913C22—66no—
914C22—2412no—
915C22C22×#23716yes—
916C22C2×#100914yes—
917C22C25×D311yescharacteristic
918C4—22no—
919C4—26no—
920C4—23no—
921C4—21no—
922C4—23no—
923C4—62no—
924C4—66no—
925C4—612no—
926C4—62no—
927C4—64no—
928C4C22×#23712yes—
929C4C22×#23716yes—
930C4C2×#100912yes—
931C3#6298511yescharacteristic, complemented, Sylow
932C2—24no—
933C2—26no—
934C2—46no—
935C2—126no—
936C2C23×#23711yescharacteristic
937C2C22×#100911yescharacteristic
938C2#8757211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×D4×#41C2
hypercenterD4×#41D3
hypocenterC3#62985
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C3×D4×#41C2semidirect
2. #87275C2semidirect
3. C2×#5827C2semidirect
4. #86773C2semidirect
5. #86744C2semidirect
6. #86722C2semidirect
7. #86685C2semidirect
8. #86634C2semidirect
9. D4×#237C2semidirect
10. #86225C2semidirect
11. #86223C2semidirect
12. #86027C2semidirect
13. #86024C2semidirect
14. C4×#1009C2semidirect
15. #85828C2semidirect
16. #85764C2semidirect
17. C2×#5555C2semidirect
21. C22×#237C22semidirect
22. C3×#550C22semidirect
23. C3×D4×Q8C22semidirect
24. C3×#548C22semidirect
25. C3×#547C22semidirect
26. C3×#546C22semidirect
27. C3×D42C22semidirect
28. C3×#532C22semidirect
29. C3×#525C22semidirect
31. C2×C3×C4×D4C22semidirect
32. #5834C22semidirect
33. #5833C22semidirect
34. #5830C22semidirect
35. #5829C22semidirect
38. #5827C22semidirect
39. #5827C22semidirect
40. #5827C22semidirect
41. #5827C22semidirect
42. #5817C22semidirect
43. C2×Q8×Dic3C22semidirect
44. #5806C22semidirect
45. D4×#67C22semidirect
46. C2×D4×Dic3C22semidirect
47. #5791C22semidirect
48. C2×#930C22semidirect
49. C2×#926C22semidirect
50. C22×C4⋊Dic3C22semidirect
51. #5732C22semidirect
52. #5728C22semidirect
53. #5718C22semidirect
54. #5716C22semidirect
55. #5682C22semidirect
56. #5681C22semidirect
57. #5665C22semidirect
58. #5658C22semidirect
59. #5643C22semidirect
60. #5642C22semidirect
61. #5635C22semidirect
62. #5624C22semidirect
63. #5619C22semidirect
64. #5618C22semidirect
65. #5618C22semidirect
66. #5617C22semidirect
67. #5611C22semidirect
68. #5606C22semidirect
69. #5598C22semidirect
70. #5596C22semidirect
71. #5591C22semidirect
72. #5586C22semidirect
73. #5574C22semidirect
74. C4×#239C22semidirect
75. #5570C22semidirect
76. Q8×Dic6C22semidirect
77. #5565C22semidirect
78. #5565C22semidirect
79. #5563C22semidirect
80. #5563C22semidirect
81. #5557C22semidirect
82. #5555C22semidirect
83. #5555C22semidirect
84. #5555C22semidirect
85. #5555C22semidirect
86. #5555C22semidirect
87. #5555C22semidirect
88. #5545C22semidirect
89. C4×D3×D4C22semidirect
90. #5543C22semidirect
91. #5543C22semidirect
92. #5543C22semidirect
93. #5542C22semidirect
94. #5541C22semidirect
95. #5538C22semidirect
96. D4×Dic6C22semidirect
97. C4×#237C22semidirect
98. #5523C22semidirect
99. #5521C22semidirect
100. #5519C22semidirect
101. #5513C22semidirect
102. C2×#897C22semidirect
103. #5495C22semidirect
104. C2×#886C22semidirect
105. C4×#235C22semidirect
106. C2×C4×D12C22semidirect
107. #5470C22semidirect
108. C2×#869C22semidirect
122. D4×#41D3semidirect
309. #550C2×D3semidirect
311. D4×Q8C2×D3semidirect
314. #548C2×D3semidirect
322. #547C2×D3semidirect
326. #546C2×D3semidirect
328. D42C2×D3semidirect
341. #532C2×D3semidirect
349. #525C2×D3semidirect
371. C2×C4×D4C2×D3semidirect
379. C3×#41#41semidirect
652. C3×Q8C2×#41semidirect
658. C3×D4C2×#41semidirect
659. C3×D4H(5,𝔽2)semidirect
667. C2×C3×C4C2×#41semidirect
710. #41#237semidirect
852. Q8C2×#237semidirect
864. D4C2×#237semidirect
865. D4#1009semidirect
887. C2×C4C2×#237semidirect
931. C3#62985semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#412
#872752
C2×#58272
#867732
#867442
#867222
#866852
#866342
D4×#2372
#862252
#862232
#860272
#860242
C4×#10092
#858282
#857642
C2×#55552
#629853