Finite Group Databasebeta

← #11707317

Subgroups — #11707317

Order 768.

7686 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×#3480C211yesmaximal, characteristic, complemented
2#87054C216yesmaximal, complemented
3#87017C212yesmaximal, complemented
4#86990C216yesmaximal, complemented
5#86911C2112yesmaximal, complemented
6#86766C212yesmaximal, complemented
7D3×#548C214yesmaximal, complemented
8#86241C213yesmaximal, complemented
9#86225C213yesmaximal, complemented
10#86167C216yesmaximal, complemented
11#86163C216yesmaximal, complemented
12#85850C213yesmaximal, complemented
13#85844C212yesmaximal, complemented
14#41×D12C212yesmaximal, complemented
15C4×#1009C213yesmaximal, complemented
16C2×Q8×D12C211yesmaximal, characteristic, complemented
17#85802C211yesmaximal, characteristic, complemented
18#62984—31nomaximal, Sylow
19C2×#1009C2213yes—
20C2×D3×#41C2214yescomplemented
21C22×D3×Q8C2212yescomplemented
22C3×#559C2213yescomplemented
23C3×#557C2211yescharacteristic, complemented
24C3×#556C2213yescomplemented
25C3×#553C2216yescomplemented
26C3×#550C2211yescharacteristic, complemented
27C3×#548C2212yescomplemented
28C3×#532C2213yescomplemented
29C3×#529C2216yescomplemented
30C3×C4×#41C2213yescomplemented
31C3×C4×#41C2212yescomplemented
32C2×C3×C4×Q8C2211yescharacteristic, complemented
33#5833C2216yescomplemented
34#5831C2214yescomplemented
35#5827C2213yescomplemented
36#5817C2212yescomplemented
37#5728C2216yescomplemented
38#5726C2216yescomplemented
39#5717C2216yescomplemented
40#5716C2216yescomplemented
41#5707C22124yescomplemented
42#5705C22124yescomplemented
43#5694C22112yescomplemented
44#5691C22112yescomplemented
45#5682C22112yescomplemented
46#5677C22112yescomplemented
47#5676C22112yescomplemented
48D3×#124C22112yescomplemented
49#5658C22124yescomplemented
50#5657C22124yescomplemented
51#5633C22112yescomplemented
52D3×C22⋊Q8C22112yescomplemented
53#5618C22112yescomplemented
54#5612C22112yescomplemented
55#5606C22112yescomplemented
56#5605C22112yescomplemented
57D3×#121C22112yescomplemented
58#5598C22112yescomplemented
59#5585C2213yescomplemented
60#5584C2216yescomplemented
61#5584C2213yescomplemented
62#5580C2216yescomplemented
63#5579C2216yescomplemented
64#5577C2211yescharacteristic, complemented
65#5576C2214yescomplemented
66Q8×D12C2216yescomplemented
67Q8×D12C2212yescomplemented
68Q8×D12C2216yescomplemented
69Q8×D12C2212yescomplemented
70#5574C2216yescomplemented
71C4×#239C2216yescomplemented
72C4×#239C2212yescomplemented
73C4×D3×Q8C2214yescomplemented
74#5570C2211yescharacteristic, complemented
75#5565C22112yescomplemented
76#5563C2216yescomplemented
77#5563C2216yescomplemented
78#5557C22112yescomplemented
79#5555C2216yescomplemented
80#5554C22112yescomplemented
81#5552C22112yescomplemented
82#5551C2216yescomplemented
83#5551C2216yescomplemented
84#5550C22112yescomplemented
85D4×D12C2216yescomplemented
86#5545C2216yescomplemented
87#5545C22112yescomplemented
88C4×D3×D4C22112yescomplemented
89C4×D3×D4C2216yescomplemented
90#5543C2216yescomplemented
91#5542C2216yescomplemented
92#5534C22112yescomplemented
93#5529C22112yescomplemented
94#5524C22112yescomplemented
95#5523C2213yescomplemented
96#5523C2216yescomplemented
97#5521C2211yescharacteristic
98#5521C2216yescomplemented
99#5514C2216yescomplemented
100C2×#897C2216yescomplemented
101#5477C2213yescomplemented
102#5477C2216yescomplemented
103C4×#235C2213yescomplemented
104C4×#235C2216yescomplemented
105C2×C4×D12C2213yes—
106C2×C4×D12C2216yescomplemented
107#5470C2216yescomplemented
108C2×#869C2213yescomplemented
109#3520—36no—
110#3520—36no—
111#3514—36no—
112#3514—36no—
113#3511—33no—
114#3511—33no—
115#3505—312no—
116#3496—33no—
117#3482—32no—
118#3482—32no—
119#3480—31no—
120#3480D311yescharacteristic, complemented
121D4×#41—32no—
122D4×#41—32no—
123C2×D4×Q8—31no—
124C2×#548—34no—
125C4×H(5,𝔽2)—33no—
126C2×C3×#41C2312yes—
127C2×C3×#41C2313yes—
128C22×C3×Q8C2311yescharacteristic
129#1009—224no—
130D3×#41—416no—
131C2×#239C2316yes—
132C2×#239C2312yes—
133C2×D3×Q8—48no—
134C2×D3×Q8C2314yes—
135C2×D3×Q8C23112yes—
136C2×#237C23112yes—
137C2×D3×D4C2316yes—
138C2×D3×D4C23112yes—
139C2×D3×D4C23112yes—
140C2×#235C2313yes—
141C2×#235C2316yes—
142C2×#235C23112yes—
143C22×D12C2316yes—
144C22×D12C2311yescharacteristic
145C22×C4×D3C2316yes—
146C22×C4×D3C23112yes—
147C22×Dic6C2316yes—
148C3×C4⋊Q8C2313yes—
149C3×#127C2313yes—
150C3×#126C23112yes—
151C3×#125C2316yes—
152C3×#124C2316yes—
153C3×#124C2316yes—
154C3×#123C23112yes—
155C3×C22⋊Q8C2316yes—
156C3×#121C2316yes—
157C3×#121C2316yes—
158C3×#121C2316yes—
159C3×C4×Q8C2313yes—
160C3×C4×Q8C2313yes—
161C3×C4×Q8C2311yescharacteristic
162C3×C4×Q8C2312yes—
163C3×C4×Q8C2311yescharacteristic
164C3×C4×Q8C2313yes—
165C3×C4×Q8C2313yes—
166C3×C4×D4C2313yes—
167C3×C4×D4C2316yes—
168C3×C4×D4C2316yes—
169C3×C4×D4C2316yes—
170C3×C4×D4C2313yes—
171C3×C4×D4C2316yes—
172C3×C4×D4C2316yes—
173C3×#117C2311yescharacteristic
174C3×#117C2316yes—
175C3×#117C2316yes—
176C2×C3×C4⋊C4C2313yes—
177C2×C3×C42C2313yes—
178C2×C3×C42C2316yes—
179#947C2316yes—
180#946C23112yes—
181#946C2316yes—
182Q8×Dic3C2316yes—
183Q8×Dic3C2312yes—
184#939C23124yes—
185#938C23112yes—
186#938C23112yes—
187#938C23112yes—
188#937C23124yes—
189#936C23112yes—
190D4×Dic3C23112yes—
191D4×Dic3C2316yes—
192D4×Dic3C23112yes—
193#930C23112yes—
194#930C2316yes—
195#930C2316yes—
196#930C23112yes—
197C4×#67C23112yes—
198C4×#67C23112yes—
199C4×#67C2316yes—
200C4×#67C2316yes—
201C2×(C2×D3)⋊C4C23112yes—
202C2×(C2×D3)⋊C4C2316yes—
203#926C23112yes—
204#926C2311yescharacteristic
205#926C2316yes—
206C2×C4⋊Dic3C2313yes—
207C2×C4⋊Dic3C2316yes—
208C2×C4⋊Dic3C2316yes—
209#924C23112yes—
210#924C23112yes—
211#898C23124yes—
212#898C23112yes—
213#897C23124yes—
214#897C23112yes—
215#897C23112yes—
216#897C23112yes—
217#896C23124yes—
218#895C23112yes—
219#895C2316yes—
220#894C23112yes—
221#894C23124yes—
222#893C23112yes—
223#893C23112yes—
224#893C2316yes—
225#893C2312yes—
226#893C2312yes—
227#892C23112yes—
228#892C23112yes—
229#892C2316yes—
230#892C2316yes—
231D3×C4⋊C4C23112yes—
232D3×C4⋊C4C23112yes—
233D3×C4⋊C4C2316yes—
234#890C23112yes—
235#890C2316yes—
236#887C23112yes—
237#886C23124yes—
238#885C23124yes—
239#885C23124yes—
240#884C23124yes—
241#883C23124yes—
242#883C23124yes—
243#882C23124yes—
244#67⋊C4C23112yes—
245#67⋊C4C23112yes—
246#67⋊C4C23112yes—
247D3×C22⋊C4C23112yes—
248D3×C22⋊C4C23124yes—
249D3×C22⋊C4C23112yes—
250D3×C22⋊C4C2314yes—
251#879C23124yes—
252#878C23124yes—
253#875C23112yes—
254#875C2316yes—
255#874C2313yes—
256C4×D12C2316yes—
257C4×D12C2316yes—
258C4×D12C23112yes—
259C4×D12C23112yes—
260C4×D12C23112yes—
261C4×D12C2316yes—
262C4×D12C2316yes—
263C4×D12C2316yes—
264C4×D12C2316yes—
265C4×D12C2312yes—
266C4×D12C2313yes—
267C4×D12C2316yes—
268C4×D12C2312yes—
269C4×D12C2313yes—
270#872C2316yes—
271#872C23112yes—
272C42×D3C23112yes—
273C42×D3C2316yes—
274#870C23112yes—
275#869C2316yes—
276#869C2316yes—
277#869C2316yes—
278#869C2316yes—
279#869C2313yes—
280C4×Dic6C23112yes—
281C4×Dic6C2316yes—
282C4×Dic6C2313yes—
283C4×Dic6C2313yes—
284C2×H(5,𝔽2)—33no—
285C22×#41—34no—
286C23×Q8—32no—
287#559—33no—
288#559C2×D313yescomplemented
289#557—31no—
290#557C2×D311yescharacteristic, complemented
291#556—33no—
292#556—36no—
293#556—36no—
294#556C2×D313yescomplemented
295#555—36no—
296#555—36no—
297#554—36no—
298#554—36no—
299#553—312no—
300#553—312no—
301#553—36no—
302#553C2×D316yescomplemented
303#552—312no—
304#552—312no—
305#551—324no—
306#551—324no—
307#550—31no—
308#550C2×D311yescharacteristic, complemented
309D4×Q8—32no—
310D4×Q8—32no—
311D4×Q8—36no—
312D4×Q8—36no—
313#548—34no—
314#548—32no—
315#548—312no—
316#548—312no—
317#548—312no—
318#548—34no—
319#548—312no—
320#548C2×D312yescomplemented
321#547—36no—
322#547—36no—
323#547—36no—
324#547—36no—
325#546—312no—
326#546—312no—
327#546—312no—
328#546—312no—
329D42—36no—
330D42—36no—
331#542—312no—
332#542—312no—
333#539—324no—
334#538—324no—
335#537—36no—
336#534—312no—
337#533—36no—
338#533—36no—
339#532—36no—
340#532—36no—
341#532—33no—
342#532C2×D313yescomplemented
343C2×C4⋊Q8—33no—
344#529—312no—
345#529—36no—
346#529—312no—
347#529C2×D316yescomplemented
348C2×#124—312no—
349#525—312no—
350#525—312no—
351C2×C22⋊Q8—312no—
352C2×C22⋊Q8—36no—
353C2×#121—312no—
354#520—33no—
355#520—36no—
356#520—33no—
357#520—36no—
358#518—312no—
359#518—36no—
360#518—31no—
361#518—36no—
362C4×#41—36no—
363C4×#41—32no—
364C4×#41—33no—
365C4×#41—36no—
366C4×#41C2×D313yescomplemented
367C4×#41C2×D312yescomplemented
368C2×C4×Q8—34no—
369C2×C4×Q8C2×D311yescharacteristic, complemented
370C2×C4×D4—312no—
371C2×C4×D4—36no—
372C2×C4×D4—33no—
373C2×C4×D4—36no—
374C23×D3C24112yes—
375C23×D3C2412yes—
376C3×#41—28no—
377C3×#41—212no—
378C2×C3×Q8—24no—
379C2×C3×Q8C2413yes—
380C2×C3×Q8C2413yes—
381C2×C3×Q8C2411yescharacteristic
382C2×C3×D4C2413yes—
383C2×C3×D4C2416yes—
384C2×C3×D4C2416yes—
385C2×C3×D4C2416yes—
386C22×C3×C4C2416yes—
387C22×C3×C4C2416yes—
388C22×C3×C4C2413yes—
389C22×C3×C4C2413yes—
390C22×C3×C4C2416yes—
391C22×C3×C4C2411yescharacteristic
392C2×#67C24112yes—
393C2×#67C2416yes—
394C2×#67C24124yes—
395C22×Dic3C24112yes—
396C22×Dic3C2416yes—
397#239—28no—
398#239—224no—
399D3×Q8—216no—
400D3×Q8—424no—
401#237—424no—
402D3×D4—248no—
403D3×D4—224no—
404D3×D4—424no—
405#235—212no—
406#235—224no—
407#235—424no—
408C2×D12—224no—
409C2×D12#4118yescomplemented
410C2×D12C2413yes—
411C2×D12C24112yes—
412C2×D12C2416yes—
413C2×D12C2416yes—
414C2×D12C2412yes—
415C2×D12C2412yes—
416C2×C4×D3—412no—
417C2×C4×D3—424no—
418C2×C4×D3C2416yes—
419C2×C4×D3C24112yes—
420C2×C4×D3C24112yes—
421C2×C4×D3C2416yes—
422C2×C4×D3C2414yes—
423C2×C4×D3C2416yes—
424C2×C4×D3C2414yes—
425C2×C4×D3C24112yes—
426C2×C4×D3C24112yes—
427C2×Dic6—412no—
428C2×Dic6C2413yes—
429C2×Dic6C24112yes—
430C2×Dic6C24112yes—
431C3×C4⋊C4C2416yes—
432C3×C4⋊C4C2416yes—
433C3×C4⋊C4C2413yes—
434C3×C4⋊C4C2411yescharacteristic
435C3×C4⋊C4C2416yes—
436C3×C4⋊C4C2411yescharacteristic
437C3×C4⋊C4C2413yes—
438C3×C4⋊C4C2416yes—
439C3×C4⋊C4C2416yes—
440C3×C22⋊C4C24112yes—
441C3×C22⋊C4C24112yes—
442C3×C22⋊C4C2412yes—
443C3×C22⋊C4C2416yes—
444C3×C22⋊C4C2416yes—
445C3×C42C2412yes—
446C3×C42C2416yes—
447C3×C42C2413yes—
448C3×C42C2413yes—
449C3×C42C2413yes—
450C3×C42C2413yes—
451C3×C42C2416yes—
452#217C24124yes—
453#217C24112yes—
454#217C2412yes—
455(C2×D3)⋊C4C2414yes—
456(C2×D3)⋊C4C24112yes—
457(C2×D3)⋊C4C2416yes—
458(C2×D3)⋊C4C2416yes—
459(C2×D3)⋊C4C2414yes—
460(C2×D3)⋊C4C24112yes—
461(C2×D3)⋊C4C24112yes—
462(C2×D3)⋊C4C24112yes—
463(C2×D3)⋊C4C24124yes—
464(C2×D3)⋊C4C24112yes—
465C4⋊Dic3C2411yescharacteristic
466C4⋊Dic3C2411yescharacteristic
467C4⋊Dic3C2416yes—
468C4⋊Dic3C2416yes—
469C4⋊Dic3C2416yes—
470C4⋊Dic3C24112yes—
471C4⋊Dic3C24112yes—
472C4⋊Dic3C2416yes—
473C4⋊Dic3C24112yes—
474Dic3⋊C4C24112yes—
475Dic3⋊C4C24124yes—
476Dic3⋊C4C2416yes—
477Dic3⋊C4C2416yes—
478C4×Dic3C24112yes—
479C4×Dic3C2416yes—
480C4×Dic3C2416yes—
481C4×Dic3C2412yes—
482C4×Dic3C24112yes—
483H(5,𝔽2)—624no—
484C2×#41—36no—
485C2×#41—32no—
486C2×#41—312no—
487C2×#41—33no—
488C2×#41—36no—
489C2×#41—312no—
490C2×#41—1216no—
491C2×#41C22×D313yes—
492C2×#41C22×D312yes—
493C22×Q8—34no—
494C22×Q8—312no—
495C22×Q8—36no—
496C22×Q8—128no—
497C22×Q8C22×D311yescharacteristic
498C22×D4—312no—
499C22×D4—36no—
500C22×D4—312no—
501C22×D4—31no—
502C22×D4—36no—
503C23×C4—36no—
504C23×C4—312no—
505C4⋊Q8—36no—
506C4⋊Q8—36no—
507C4⋊Q8—36no—
508C4⋊Q8—36no—
509C4⋊Q8—33no—
510C4⋊Q8C22×D313yes—
511#127—33no—
512#127C22×D313yes—
513#126—324no—
514#126—312no—
515#126—324no—
516#126C22×D3112yes—
517#125—36no—
518#125—312no—
519#125—312no—
520#125C22×D316yes—
521#124—36no—
522#124—312no—
523#124—324no—
524#124—324no—
525#124—312no—
526#124—36no—
527#124C22×D316yes—
528#124C22×D316yes—
529#123—324no—
530#123—312no—
531#123—324no—
532#123—324no—
533#123—324no—
534#123C22×D3112yes—
535C22⋊Q8—36no—
536C22⋊Q8—312no—
537C22⋊Q8—312no—
538C22⋊Q8—312no—
539C22⋊Q8—312no—
540C22⋊Q8—312no—
541C22⋊Q8—312no—
542C22⋊Q8—324no—
543C22⋊Q8—324no—
544C22⋊Q8—324no—
545C22⋊Q8C22×D316yes—
546#121—312no—
547#121—324no—
548#121—312no—
549#121—312no—
550#121—36no—
551#121—36no—
552#121—312no—
553#121—312no—
554#121—312no—
555#121—36no—
556#121—324no—
557#121C22×D316yes—
558#121C22×D316yes—
559#121C22×D316yes—
560#120—324no—
561#120—324no—
562C4×Q8—32no—
563C4×Q8—36no—
564C4×Q8—312no—
565C4×Q8—312no—
566C4×Q8—33no—
567C4×Q8—36no—
568C4×Q8—33no—
569C4×Q8C22×D312yes—
570C4×Q8C22×D311yescharacteristic
571C4×Q8C22×D311yescharacteristic
572C4×Q8C22×D313yes—
573C4×Q8C22×D313yes—
574C4×Q8C22×D313yes—
575C4×Q8C22×D313yes—
576C4×D4—36no—
577C4×D4—312no—
578C4×D4—312no—
579C4×D4—312no—
580C4×D4—36no—
581C4×D4—312no—
582C4×D4—36no—
583C4×D4—32no—
584C4×D4—312no—
585C4×D4—32no—
586C4×D4—312no—
587C4×D4—36no—
588C4×D4—312no—
589C4×D4—312no—
590C4×D4—312no—
591C4×D4—32no—
592C4×D4—36no—
593C4×D4—36no—
594C4×D4—312no—
595C4×D4—33no—
596C4×D4—312no—
597C4×D4—36no—
598C4×D4—36no—
599C4×D4—36no—
600C4×D4—32no—
601C4×D4—33no—
602C4×D4—36no—
603C4×D4—312no—
604C4×D4—36no—
605C4×D4C22×D313yes—
606C4×D4C22×D316yes—
607C4×D4C22×D316yes—
608C4×D4C22×D313yes—
609C4×D4C22×D316yes—
610C4×D4C22×D316yes—
611C4×D4C22×D316yes—
612#117—31no—
613#117—36no—
614#117—312no—
615#117—312no—
616#117—36no—
617#117—36no—
618#117—312no—
619#117—36no—
620#117—312no—
621#117C22×D311yescharacteristic
622#117C22×D316yes—
623#117C22×D316yes—
624C2×C4⋊C4—33no—
625C2×C4⋊C4—36no—
626C2×C4⋊C4—36no—
627C2×C4⋊C4—312no—
628C2×C4⋊C4—36no—
629C2×C4⋊C4—312no—
630C2×C4⋊C4C22×D313yes—
631C2×C22⋊C4—36no—
632C2×C22⋊C4—312no—
633C2×C22⋊C4—34no—
634C2×C22⋊C4—312no—
635C2×C22⋊C4—312no—
636C2×C22⋊C4—324no—
637C2×C42—312no—
638C2×C42—36no—
639C2×C42C22×D313yes—
640C2×C42C22×D316yes—
641C23×C3C2516yes—
642C23×C3C2511yescharacteristic
643C22×D3—224no—
644C22×D3—42no—
645C22×D3—42no—
646C22×D3—412no—
647C22×D3—412no—
648C22×D3C2×#4118yescomplemented
649C22×D3C2516yes—
650C22×D3C2514yes—
651C3×Q8—26no—
652C3×Q8—26no—
653C3×Q8H(5,𝔽2)14yescomplemented
654C3×D4—212no—
655C3×D4—26no—
656C3×D4—212no—
657C3×D4—46no—
658C2×C3×C4—212no—
659C2×C3×C4—26no—
660C2×C3×C4—212no—
661C2×C3×C4—46no—
662C2×C3×C4—43no—
663C2×C3×C4C2×#4114yescomplemented
664C2×C3×C4C2512yes—
665C2×C3×C4C2516yes—
666C2×C3×C4C2513yes—
667C2×C3×C4C2512yes—
668C2×C3×C4C2513yes—
669C2×C3×C4C2513yes—
670C2×C3×C4C2511yescharacteristic
671C2×C3×C4C2511yescharacteristic
672C2×C3×C4C2513yes—
673#67—212no—
674#67—224no—
675#67—424no—
676C2×Dic3—46no—
677C2×Dic3—412no—
678C2×Dic3C2512yes—
679C2×Dic3C2516yes—
680C2×Dic3C2512yes—
681C2×Dic3C25112yes—
682D12—224no—
683D12—26no—
684D12—212no—
685D12—46no—
686D12C2×#4118yescomplemented
687D12C2×#4118yescomplemented
688C4×D3—224no—
689C4×D3—212no—
690C4×D3—224no—
691C4×D3—212no—
692C4×D3—44no—
693C4×D3—412no—
694C4×D3—412no—
695C4×D3—44no—
696C4×D3—46no—
697Dic6—26no—
698Dic6—224no—
699Dic6—412no—
700C24—32no—
701C24—312no—
702#41—28no—
703#41—212no—
704#41—624no—
705#41—624no—
706#41—68no—
707#41—612no—
708#41—1224no—
709#41—1224no—
710C2×Q8—24no—
711C2×Q8—33no—
712C2×Q8—312no—
713C2×Q8—312no—
714C2×Q8—616no—
715C2×Q8—1212no—
716C2×Q8—1224no—
717C2×Q8C23×D313yes—
718C2×Q8C23×D313yes—
719C2×Q8C23×D311yescharacteristic
720C2×D4—312no—
721C2×D4—36no—
722C2×D4—324no—
723C2×D4—38no—
724C2×D4—32no—
725C2×D4—32no—
726C2×D4—312no—
727C2×D4—33no—
728C2×D4—36no—
729C2×D4—36no—
730C2×D4—624no—
731C2×D4—624no—
732C2×D4—648no—
733C2×D4—1224no—
734C2×D4C23×D316yes—
735C2×D4C23×D313yes—
736C2×D4C23×D316yes—
737C2×D4C23×D316yes—
738C22×C4—36no—
739C22×C4—312no—
740C22×C4—312no—
741C22×C4—36no—
742C22×C4—312no—
743C22×C4—36no—
744C22×C4—34no—
745C22×C4—36no—
746C22×C4—312no—
747C22×C4—34no—
748C22×C4—312no—
749C22×C4—1212no—
750C22×C4—1224no—
751C22×C4C23×D316yes—
752C22×C4C23×D313yes—
753C22×C4C23×D316yes—
754C22×C4C23×D313yes—
755C22×C4C23×D316yes—
756C22×C4C23×D311yescharacteristic
757C4⋊C4—31no—
758C4⋊C4—36no—
759C4⋊C4—36no—
760C4⋊C4—36no—
761C4⋊C4—312no—
762C4⋊C4—312no—
763C4⋊C4—36no—
764C4⋊C4—312no—
765C4⋊C4—312no—
766C4⋊C4—324no—
767C4⋊C4—31no—
768C4⋊C4—36no—
769C4⋊C4—36no—
770C4⋊C4C23×D311yescharacteristic
771C4⋊C4C23×D316yes—
772C4⋊C4C23×D316yes—
773C4⋊C4C23×D313yes—
774C4⋊C4C23×D313yes—
775C4⋊C4C23×D316yes—
776C4⋊C4C23×D311yescharacteristic
777C4⋊C4C23×D316yes—
778C4⋊C4C23×D316yes—
779C22⋊C4—32no—
780C22⋊C4—312no—
781C22⋊C4—324no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—312no—
785C22⋊C4—312no—
786C22⋊C4—36no—
787C22⋊C4—312no—
788C22⋊C4—36no—
789C22⋊C4—312no—
790C22⋊C4—324no—
791C22⋊C4—312no—
792C22⋊C4C23×D312yes—
793C22⋊C4C23×D316yes—
794C22⋊C4C23×D316yes—
795C22⋊C4C23×D3112yes—
796C22⋊C4C23×D3112yes—
797C42—32no—
798C42—36no—
799C42—36no—
800C42—312no—
801C42—312no—
802C42C23×D313yes—
803C42C23×D316yes—
804C42C23×D312yes—
805C42C23×D313yes—
806C42C23×D316yes—
807C42C23×D313yes—
808C42C23×D313yes—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—26no—
812C22×C3—26no—
813C22×C3—26no—
814C22×C3C22×#4112yes—
815C22×C3C2611yescharacteristic
816C2×D3—24no—
817C2×D3—24no—
818C2×D3—26no—
819C2×D3—26no—
820C2×D3—26no—
821C2×D3—48no—
822C2×D3—824no—
823C2×D3C22×#4118yes—
824C3×C4—26no—
825C3×C4—23no—
826C3×C4—22no—
827C3×C4—22no—
828C3×C4—23no—
829C3×C4—23no—
830C3×C4C22×#4112yes—
831C3×C4C22×#4112yes—
832C3×C4C2×H(5,𝔽2)16yes—
833Dic3—26no—
834Dic3—212no—
835Dic3—22no—
836Dic3—22no—
837C23—34no—
838C23—38no—
839C23—36no—
840C23—624no—
841C23—122no—
842C23—122no—
843C23—1212no—
844C23—1212no—
845C23C24×D316yes—
846C23C24×D311yescharacteristic
847Q8—26no—
848Q8—26no—
849Q8—66no—
850Q8—624no—
851Q8—1212no—
852Q8#100914yescomplemented
853D4—212no—
854D4—26no—
855D4—212no—
856D4—38no—
857D4—38no—
858D4—46no—
859D4—624no—
860D4—624no—
861D4—612no—
862D4—66no—
863D4—612no—
864D4—126no—
865D4—1224no—
866C2×C4—212no—
867C2×C4—26no—
868C2×C4—212no—
869C2×C4—32no—
870C2×C4—36no—
871C2×C4—32no—
872C2×C4—312no—
873C2×C4—46no—
874C2×C4—43no—
875C2×C4—624no—
876C2×C4—612no—
877C2×C4—624no—
878C2×C4—612no—
879C2×C4—124no—
880C2×C4—1212no—
881C2×C4—1212no—
882C2×C4—124no—
883C2×C4—126no—
884C2×C4—126no—
885C2×C4—1212no—
886C2×C4D3×#4114yescomplemented
887C2×C4C24×D312yes—
888C2×C4C24×D313yes—
889C2×C4C24×D316yes—
890C2×C4C24×D313yes—
891C2×C4C24×D312yes—
892C2×C4C24×D313yes—
893C2×C4C24×D311yescharacteristic
894C2×C4C24×D311yescharacteristic
895C2×C4C24×D313yes—
896C2×C3—22no—
897C2×C3—46no—
898C2×C3C23×#4111yescharacteristic
899C2×C3C22×H(5,𝔽2)11yescharacteristic
900C2×C32−1+611yescharacteristic
901D3—28no—
902D3—46no—
903C22—21no—
904C22—21no—
905C22—26no—
906C22—26no—
907C22—26no—
908C22—38no—
909C22—64no—
910C22—64no—
911C22—66no—
912C22—66no—
913C22—66no—
914C22—128no—
915C22—2424no—
916C22C2×D3×#4112yes—
917C22C25×D311yescharacteristic
918C4—26no—
919C4—22no—
920C4—23no—
921C4—22no—
922C4—23no—
923C4—23no—
924C4—66no—
925C4—62no—
926C4—612no—
927C4—62no—
928C4C2×D3×#4112yes—
929C4C2×D3×#4112yes—
930C4C2×#100916yes—
931C3#6298411yescharacteristic, complemented, Sylow
932C2—22no—
933C2—46no—
934C2—68no—
935C2—126no—
936C2C22×D3×#4111yescharacteristic
937C2C22×#100911yescharacteristic
938C2#8757211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3480C2
hypercenter#3480D3
hypocenterC3#62984
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. C3×#3480C2semidirect
2. #87054C2semidirect
3. #87017C2semidirect
4. #86990C2semidirect
5. #86911C2semidirect
6. #86766C2semidirect
7. D3×#548C2semidirect
8. #86241C2semidirect
9. #86225C2semidirect
10. #86167C2semidirect
11. #86163C2semidirect
12. #85850C2semidirect
13. #85844C2semidirect
14. #41×D12C2semidirect
15. C4×#1009C2semidirect
16. C2×Q8×D12C2semidirect
17. #85802C2semidirect
20. C2×D3×#41C22semidirect
21. C22×D3×Q8C22semidirect
22. C3×#559C22semidirect
23. C3×#557C22semidirect
24. C3×#556C22semidirect
25. C3×#553C22semidirect
26. C3×#550C22semidirect
27. C3×#548C22semidirect
28. C3×#532C22semidirect
29. C3×#529C22semidirect
30. C3×C4×#41C22semidirect
31. C3×C4×#41C22semidirect
32. C2×C3×C4×Q8C22semidirect
33. #5833C22semidirect
34. #5831C22semidirect
35. #5827C22semidirect
36. #5817C22semidirect
37. #5728C22semidirect
38. #5726C22semidirect
39. #5717C22semidirect
40. #5716C22semidirect
41. #5707C22semidirect
42. #5705C22semidirect
43. #5694C22semidirect
44. #5691C22semidirect
45. #5682C22semidirect
46. #5677C22semidirect
47. #5676C22semidirect
48. D3×#124C22semidirect
49. #5658C22semidirect
50. #5657C22semidirect
51. #5633C22semidirect
52. D3×C22⋊Q8C22semidirect
53. #5618C22semidirect
54. #5612C22semidirect
55. #5606C22semidirect
56. #5605C22semidirect
57. D3×#121C22semidirect
58. #5598C22semidirect
59. #5585C22semidirect
60. #5584C22semidirect
61. #5584C22semidirect
62. #5580C22semidirect
63. #5579C22semidirect
64. #5577C22semidirect
65. #5576C22semidirect
66. Q8×D12C22semidirect
67. Q8×D12C22semidirect
68. Q8×D12C22semidirect
69. Q8×D12C22semidirect
70. #5574C22semidirect
71. C4×#239C22semidirect
72. C4×#239C22semidirect
73. C4×D3×Q8C22semidirect
74. #5570C22semidirect
75. #5565C22semidirect
76. #5563C22semidirect
77. #5563C22semidirect
78. #5557C22semidirect
79. #5555C22semidirect
80. #5554C22semidirect
81. #5552C22semidirect
82. #5551C22semidirect
83. #5551C22semidirect
84. #5550C22semidirect
85. D4×D12C22semidirect
86. #5545C22semidirect
87. #5545C22semidirect
88. C4×D3×D4C22semidirect
89. C4×D3×D4C22semidirect
90. #5543C22semidirect
91. #5542C22semidirect
92. #5534C22semidirect
93. #5529C22semidirect
94. #5524C22semidirect
95. #5523C22semidirect
96. #5523C22semidirect
98. #5521C22semidirect
99. #5514C22semidirect
100. C2×#897C22semidirect
101. #5477C22semidirect
102. #5477C22semidirect
103. C4×#235C22semidirect
104. C4×#235C22semidirect
106. C2×C4×D12C22semidirect
107. #5470C22semidirect
108. C2×#869C22semidirect
120. #3480D3semidirect
288. #559C2×D3semidirect
290. #557C2×D3semidirect
294. #556C2×D3semidirect
302. #553C2×D3semidirect
308. #550C2×D3semidirect
320. #548C2×D3semidirect
342. #532C2×D3semidirect
347. #529C2×D3semidirect
366. C4×#41C2×D3semidirect
367. C4×#41C2×D3semidirect
369. C2×C4×Q8C2×D3semidirect
409. C2×D12#41semidirect
648. C22×D3C2×#41semidirect
653. C3×Q8H(5,𝔽2)semidirect
663. C2×C3×C4C2×#41semidirect
686. D12C2×#41semidirect
687. D12C2×#41semidirect
852. Q8#1009semidirect
886. C2×C4D3×#41semidirect
931. C3#62984semidirect

Maximal subgroups

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

subgroupindex
C3×#34802
#870542
#870172
#869902
#869112
#867662
D3×#5482
#862412
#862252
#861672
#861632
#858502
#858442
#41×D122
C4×#10092
C2×Q8×D122
#858022
#629843