Finite Group Databasebeta

← #11707341

Subgroups — #11707341

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×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#87285C212yesmaximal, complemented
3#85908C214yesmaximal, complemented
4#85902C216yesmaximal, complemented
5D3×#520C212yesmaximal, complemented
6#85870C2112yesmaximal, complemented
7#85869C216yesmaximal, complemented
8#85853C212yesmaximal, complemented
9#85850C213yesmaximal, complemented
10#85844C212yesmaximal, complemented
11#85840C213yesmaximal, complemented
12#41×D12C211yesmaximal, characteristic, complemented
13#85828C211yesmaximal, characteristic, complemented
14#85788C213yesmaximal, complemented
15D4×#235C216yesmaximal, complemented
16C2×#5551C213yesmaximal, complemented
17#85767C216yesmaximal, complemented
18#62985—31nomaximal, Sylow
19C2×C3×H(5,𝔽2)C2211yescharacteristic
20C2×D3×#41C2212yes—
21C22×#235C2216yescomplemented
22C3×#520C2211yescharacteristic
23C3×#520C2213yescomplemented
24C3×#520C2212yescomplemented
25C3×#518C2213yescomplemented
26C3×#518C2216yescomplemented
27C3×C4×#41C2211yescharacteristic
28C3×C4×#41C2213yescomplemented
29C3×C4×#41C2212yescomplemented
30C2×C3×C4×D4C2216yescomplemented
31C2×C3×C4×D4C2213yescomplemented
32#5834C2214yescomplemented
33#5833C2216yescomplemented
34#5831C2214yescomplemented
35#5828C2216yescomplemented
36#5827C2212yes—
37#5806C22112yescomplemented
38#5805C2216yescomplemented
39D4×#67C22112yescomplemented
40C2×#938C2216yescomplemented
41#5791C22112yescomplemented
42C2×#924C2216yescomplemented
43#5584C2213yescomplemented
44#5581C2216yescomplemented
45#5579C2211yescharacteristic, complemented
46#5579C2216yescomplemented
47#5577C2211yescharacteristic, complemented
48#5576C2212yescomplemented
49Q8×D12C2211yescharacteristic, complemented
50#5574C2214yescomplemented
51C4×D3×Q8C2214yescomplemented
52#5570C2212yescomplemented
53Q8×Dic6C2212yescomplemented
54#5565C22112yescomplemented
55#5564C22124yescomplemented
56#5563C2213yescomplemented
57#5563C2216yescomplemented
58#5562C22112yescomplemented
59#5561C22112yescomplemented
60#5559C22112yescomplemented
61#5558C22112yescomplemented
62#5558C2216yescomplemented
63#5557C22112yescomplemented
64#5556C22112yescomplemented
65#5555C2213yescomplemented
66#5554C2216yescomplemented
67#5553C2216yescomplemented
68#5552C22112yescomplemented
69#5551C2216yescomplemented
70#5551C2213yescomplemented
71#5551C2216yescomplemented
72#5551C2216yescomplemented
73#5551C22112yescomplemented
74#5551C22112yescomplemented
75#5550C2216yescomplemented
76D4×D12C2213yescomplemented
77#5548C22112yescomplemented
78#5547C22124yescomplemented
79#5546C22112yescomplemented
80C4×D3×D4C22112yescomplemented
81#5543C2216yescomplemented
82#5542C2216yescomplemented
83#5541C2216yescomplemented
84D4×Dic6C2216yescomplemented
85#5534C22112yescomplemented
86#5530C22112yescomplemented
87#5529C22112yescomplemented
88#5528C22112yescomplemented
89#5524C2216yescomplemented
90#5523C2216yescomplemented
91D3×#117C2216yescomplemented
92#5519C2216yescomplemented
93#5511C22112yescomplemented
94#5507C22112yescomplemented
95#5504C2216yescomplemented
96C2×D3×C4⋊C4C2216yescomplemented
97#5495C22124yescomplemented
98#5494C22112yescomplemented
99#5490C22124yescomplemented
100C2×#883C22112yescomplemented
101#5479C2216yescomplemented
102#5477C2216yescomplemented
103#5477C2213yescomplemented
104C4×#235C2216yescomplemented
105C2×C4×D12C2213yescomplemented
106#5470C2216yescomplemented
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—31no—
122D4×#41—36no—
123C2×#547—33no—
124C4×H(5,𝔽2)D311yescharacteristic, complemented
125C2×#520—32no—
126C3×H(5,𝔽2)—28no—
127C2×C3×#41C2313yes—
128C2×C3×#41C2312yes—
129C2×C3×#41C2311yescharacteristic
130C22×C3×D4C2313yes—
131C22×C3×D4C2316yes—
132C23×C3×C4C2316yes—
133C22×#67C23112yes—
134D3×#41—216no—
135C2×#239C2312yes—
136C2×D3×Q8C2312yes—
137C2×#237C2316yes—
138C2×D3×D4C2316yes—
139C2×#235—424no—
140C2×#235C2316yes—
141C2×#235C2316yes—
142C2×#235C23112yes—
143C2×#235C23124yes—
144C22×D12C2313yes—
145C22×C4×D3C2316yes—
146C22×C4×D3C23112yes—
147C22×Dic6C2316yes—
148C3×C4×Q8C2311yescharacteristic
149C3×C4×Q8C2311yescharacteristic
150C3×C4×Q8C2312yes—
151C3×C4×Q8C2313yes—
152C3×C4×Q8C2311yescharacteristic
153C3×C4×D4C2313yes—
154C3×C4×D4C2316yes—
155C3×C4×D4C2316yes—
156C3×C4×D4C2313yes—
157C3×C4×D4C2316yes—
158C3×C4×D4C23112yes—
159C3×C4×D4C2316yes—
160C3×C4×D4C2313yes—
161C3×C4×D4C2316yes—
162C3×C4×D4C2316yes—
163C3×C4×D4C2316yes—
164C3×C4×D4C2316yes—
165C3×C4×D4C2313yes—
166C3×#117C2313yes—
167C3×#117C2313yes—
168C3×#117C2316yes—
169C3×#117C2316yes—
170C2×C3×C4⋊C4C2313yes—
171C2×C3×C4⋊C4C2316yes—
172C2×C3×C22⋊C4C2316yes—
173C2×C3×C22⋊C4C23112yes—
174C2×C3×C42C2313yes—
175C2×C3×C42C2316yes—
176#953C23124yes—
177C2×#217C23112yes—
178#946C2312yes—
179#946C2316yes—
180Q8×Dic3C2314yes—
181#940C23112yes—
182#939C23124yes—
183#938C2316yes—
184#938C23112yes—
185#938C23112yes—
186#938C23112yes—
187#938C2316yes—
188#937C23112yes—
189#936C23112yes—
190#935C23112yes—
191D4×Dic3C23112yes—
192#930C23112yes—
193#930C2316yes—
194#930C23112yes—
195#930C2316yes—
196#930C2316yes—
197#929C23112yes—
198#929C23124yes—
199C4×#67C23112yes—
200C4×#67C23112yes—
201C4×#67C23112yes—
202C4×#67C23124yes—
203C4×#67C23124yes—
204C2×(C2×D3)⋊C4C2316yes—
205#926C23112yes—
206#926C2316yes—
207#926C2316yes—
208C2×C4⋊Dic3C2316yes—
209C2×C4⋊Dic3C2316yes—
210C2×C4⋊Dic3C2313yes—
211#924C2316yes—
212#924C23112yes—
213#924C23112yes—
214#924C2316yes—
215#924C2316yes—
216#924C23124yes—
217C2×Dic3⋊C4C23112yes—
218#898C23112yes—
219#897C2316yes—
220#897C2316yes—
221#896C23124yes—
222#896C2314yes—
223#895C2316yes—
224#895C2316yes—
225#894C23112yes—
226#893C23112yes—
227#892C2316yes—
228#892C2316yes—
229D3×C4⋊C4C2316yes—
230D3×C4⋊C4C23112yes—
231D3×C4⋊C4C23112yes—
232D3×C4⋊C4C23112yes—
233D3×C4⋊C4C2312yes—
234#890C23112yes—
235#889C23112yes—
236#888C23112yes—
237#887C23112yes—
238#886C23112yes—
239#885C23124yes—
240#885C23112yes—
241#884C23112yes—
242#884C23124yes—
243#883C23112yes—
244#883C23124yes—
245#883C23124yes—
246#883C23124yes—
247#882C23112yes—
248#67⋊C4C23124yes—
249D3×C22⋊C4C23112yes—
250#879C23124yes—
251#879C23112yes—
252#878C23124yes—
253#877C23112yes—
254#876C23112yes—
255#875C2316yes—
256#875C2316yes—
257#874C2313yes—
258C4×D12C2311yescharacteristic
259C4×D12C2313yes—
260C4×D12C2313yes—
261C4×D12C2313yes—
262C4×D12C2316yes—
263C4×D12C2316yes—
264C4×D12C2312yes—
265C4×D12C23112yes—
266C4×D12C2316yes—
267C4×D12C23112yes—
268#872C23112yes—
269#872C23112yes—
270C42×D3C23112yes—
271#870C2316yes—
272#870C23112yes—
273#870C2312yes—
274#869C2313yes—
275#869C2316yes—
276#869C2316yes—
277#869C2316yes—
278#869C2311yescharacteristic
279#869C2313yes—
280C4×Dic6C2316yes—
281C4×Dic6C2316yes—
282C4×Dic6C23112yes—
283C4×Dic6C2316yes—
284C2×H(5,𝔽2)C2×D311yescharacteristic
285C22×#41—32no—
286C22×#41—36no—
287#559—312no—
288Q82—32no—
289#557—32no—
290#556—33no—
291#556—36no—
292#555—33no—
293#555—36no—
294#554—31no—
295#554—36no—
296#554—36no—
297#554—312no—
298#553—36no—
299#553—312no—
300#553—312no—
301#553—312no—
302#552—36no—
303#552—36no—
304#552—312no—
305#551—312no—
306#551—324no—
307#550—34no—
308#550—31no—
309#550—36no—
310D4×Q8—31no—
311D4×Q8—36no—
312#548—34no—
313#548—32no—
314#548—312no—
315#547—33no—
316#547—36no—
317#547—312no—
318#547—36no—
319#547—312no—
320#547—36no—
321#547—33no—
322#547—312no—
323#546—312no—
324#546—36no—
325#546—36no—
326#546—324no—
327D42—312no—
328D42—33no—
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—33no—
338#533—36no—
339#532—312no—
340#532—33no—
341#532—36no—
342C2×C4⋊Q8—33no—
343#529—312no—
344#529—312no—
345#529—36no—
346#525—36no—
347#525—312no—
348#525—324no—
349#525—36no—
350C2×#123—312no—
351C2×C22⋊Q8—36no—
352C2×#121—36no—
353#520—32no—
354#520—34no—
355#520—312no—
356#520—36no—
357#520—36no—
358#520C2×D311yescharacteristic
359#520C2×D313yescomplemented
360#520C2×D312yescomplemented
361#518C2×D313yescomplemented
362#518C2×D316yescomplemented
363C4×#41—36no—
364C4×#41C2×D311yescharacteristic
365C4×#41C2×D313yescomplemented
366C4×#41C2×D312yescomplemented
367C2×C4×Q8—34no—
368C2×C4×D4—312no—
369C2×C4×D4—33no—
370C2×C4×D4C2×D313yescomplemented
371C2×C4×D4C2×D316yescomplemented
372C2×#117—36no—
373C22×C4⋊C4—36no—
374C24×C3C2416yes—
375C23×D3C2416yes—
376C3×#41—28no—
377C3×#41—212no—
378C3×#41#4118yescomplemented
379C2×C3×Q8C2411yescharacteristic
380C2×C3×Q8C2411yescharacteristic
381C2×C3×D4—224no—
382C2×C3×D4—212no—
383C2×C3×D4C2416yes—
384C2×C3×D4C2416yes—
385C2×C3×D4C2413yes—
386C2×C3×D4C2413yes—
387C22×C3×C4—412no—
388C22×C3×C4C2416yes—
389C22×C3×C4C2413yes—
390C22×C3×C4C2416yes—
391C22×C3×C4C2416yes—
392C22×C3×C4C2413yes—
393C22×C3×C4C24112yes—
394C22×C3×C4C2416yes—
395C22×C3×C4C2413yes—
396C2×#67—424no—
397C2×#67C24112yes—
398C2×#67C24112yes—
399C2×#67C24124yes—
400C2×#67C24112yes—
401C22×Dic3C2416yes—
402C22×Dic3C24112yes—
403#239—28no—
404D3×Q8—28no—
405#237—224no—
406D3×D4—224no—
407#235—224no—
408#235—224no—
409#235—424no—
410#235—448no—
411C2×D12—212no—
412C2×D12C2413yes—
413C2×D12C2416yes—
414C2×D12C2416yes—
415C2×D12C2416yes—
416C2×D12C2411yescharacteristic
417C2×C4×D3—224no—
418C2×C4×D3—424no—
419C2×C4×D3C2416yes—
420C2×C4×D3C24112yes—
421C2×C4×D3C2416yes—
422C2×C4×D3C2412yes—
423C2×C4×D3C2416yes—
424C2×C4×D3C2414yes—
425C2×C4×D3C24124yes—
426C2×Dic6—412no—
427C2×Dic6C2416yes—
428C2×Dic6C2416yes—
429C2×Dic6C2412yes—
430C2×Dic6C24112yes—
431C3×C4⋊C4C2416yes—
432C3×C4⋊C4C2413yes—
433C3×C4⋊C4C2416yes—
434C3×C4⋊C4C2413yes—
435C3×C4⋊C4C2413yes—
436C3×C4⋊C4C2411yescharacteristic
437C3×C4⋊C4C2412yes—
438C3×C22⋊C4C2416yes—
439C3×C22⋊C4C2416yes—
440C3×C22⋊C4C24112yes—
441C3×C22⋊C4C2416yes—
442C3×C22⋊C4C2416yes—
443C3×C42C2412yes—
444C3×C42C2413yes—
445C3×C42C2413yes—
446C3×C42C2416yes—
447C3×C42C2411yescharacteristic
448C3×C42C2413yes—
449C3×C42C2416yes—
450#217C24112yes—
451#217C24112yes—
452#217C24112yes—
453#217C24124yes—
454(C2×D3)⋊C4C2414yes—
455(C2×D3)⋊C4C2416yes—
456(C2×D3)⋊C4C24112yes—
457(C2×D3)⋊C4C24112yes—
458(C2×D3)⋊C4C2412yes—
459(C2×D3)⋊C4C2416yes—
460(C2×D3)⋊C4C24112yes—
461(C2×D3)⋊C4C2416yes—
462(C2×D3)⋊C4C24112yes—
463C4⋊Dic3C2412yes—
464C4⋊Dic3C2413yes—
465C4⋊Dic3C2416yes—
466C4⋊Dic3C24112yes—
467C4⋊Dic3C2416yes—
468C4⋊Dic3C24112yes—
469C4⋊Dic3C2412yes—
470C4⋊Dic3C2416yes—
471C4⋊Dic3C2411yescharacteristic
472C4⋊Dic3C2416yes—
473Dic3⋊C4C24112yes—
474Dic3⋊C4C24112yes—
475Dic3⋊C4C24112yes—
476Dic3⋊C4C24124yes—
477Dic3⋊C4C2414yes—
478Dic3⋊C4C2414yes—
479Dic3⋊C4C24112yes—
480C4×Dic3C24112yes—
481C4×Dic3C24112yes—
482C4×Dic3C24112yes—
483H(5,𝔽2)—28no—
484C2×#41—32no—
485C2×#41—36no—
486C2×#41—36no—
487C2×#41—36no—
488C2×#41—324no—
489C2×#41—312no—
490C2×#41—616no—
491C2×#41—1224no—
492C2×#41C22×D313yes—
493C2×#41C22×D312yes—
494C2×#41C22×D311yescharacteristic
495C22×Q8—32no—
496C22×Q8—36no—
497C22×D4—312no—
498C22×D4—36no—
499C22×D4—33no—
500C22×D4C22×D313yes—
501C22×D4C22×D316yes—
502C23×C4—36no—
503C23×C4—312no—
504C23×C4C22×D316yes—
505C4⋊Q8—312no—
506C4⋊Q8—33no—
507C4⋊Q8—36no—
508C4⋊Q8—36no—
509C4⋊Q8—36no—
510C4⋊Q8—33no—
511C4⋊Q8—31no—
512#127—312no—
513#127—33no—
514#126—312no—
515#126—324no—
516#126—312no—
517#126—312no—
518#125—312no—
519#125—312no—
520#125—32no—
521#125—312no—
522#125—36no—
523#124—312no—
524#124—312no—
525#124—324no—
526#124—36no—
527#124—36no—
528#123—312no—
529#123—324no—
530#123—312no—
531#123—312no—
532#123—312no—
533#123—324no—
534#123—324no—
535#123—324no—
536#123—312no—
537C22⋊Q8—32no—
538C22⋊Q8—36no—
539C22⋊Q8—36no—
540C22⋊Q8—312no—
541C22⋊Q8—324no—
542C22⋊Q8—36no—
543C22⋊Q8—312no—
544C22⋊Q8—36no—
545C22⋊Q8—36no—
546C22⋊Q8—324no—
547C22⋊Q8—36no—
548C22⋊Q8—34no—
549C22⋊Q8—324no—
550#121—36no—
551#121—312no—
552#121—312no—
553#121—312no—
554#121—36no—
555#121—324no—
556#121—36no—
557#121—36no—
558#121—312no—
559#121—36no—
560#121—312no—
561#121—36no—
562#121—36no—
563#121—324no—
564#121—312no—
565#120—324no—
566#120—312no—
567#120—312no—
568C4×Q8—34no—
569C4×Q8—312no—
570C4×Q8—312no—
571C4×Q8—36no—
572C4×Q8—36no—
573C4×Q8—36no—
574C4×Q8C22×D312yes—
575C4×Q8C22×D311yescharacteristic
576C4×Q8C22×D311yescharacteristic
577C4×Q8C22×D311yescharacteristic
578C4×Q8C22×D313yes—
579C4×D4—312no—
580C4×D4—324no—
581C4×D4—312no—
582C4×D4—312no—
583C4×D4—324no—
584C4×D4—312no—
585C4×D4—312no—
586C4×D4—324no—
587C4×D4—31no—
588C4×D4—33no—
589C4×D4—312no—
590C4×D4—36no—
591C4×D4—36no—
592C4×D4—33no—
593C4×D4—33no—
594C4×D4—32no—
595C4×D4—312no—
596C4×D4—36no—
597C4×D4C22×D316yes—
598C4×D4C22×D313yes—
599C4×D4C22×D316yes—
600C4×D4C22×D313yes—
601C4×D4C22×D316yes—
602C4×D4C22×D3112yes—
603C4×D4C22×D316yes—
604C4×D4C22×D316yes—
605C4×D4C22×D316yes—
606C4×D4C22×D313yes—
607C4×D4C22×D316yes—
608C4×D4C22×D316yes—
609C4×D4C22×D313yes—
610#117—36no—
611#117—36no—
612#117—312no—
613#117—36no—
614#117—36no—
615#117—312no—
616#117—312no—
617#117—312no—
618#117C22×D313yes—
619#117C22×D313yes—
620#117C22×D316yes—
621#117C22×D316yes—
622C2×C4⋊C4—36no—
623C2×C4⋊C4—312no—
624C2×C4⋊C4—33no—
625C2×C4⋊C4—36no—
626C2×C4⋊C4—36no—
627C2×C4⋊C4—312no—
628C2×C4⋊C4—312no—
629C2×C4⋊C4—312no—
630C2×C4⋊C4—32no—
631C2×C4⋊C4C22×D313yes—
632C2×C4⋊C4C22×D316yes—
633C2×C22⋊C4—312no—
634C2×C22⋊C4—36no—
635C2×C22⋊C4—312no—
636C2×C22⋊C4C22×D316yes—
637C2×C22⋊C4C22×D3112yes—
638C2×C42—312no—
639C2×C42C22×D313yes—
640C2×C42C22×D316yes—
641C23×C3—212no—
642C23×C3—46no—
643C23×C3—46no—
644C23×C3C2516yes—
645C23×C3C2513yes—
646C22×D3—212no—
647C22×D3—212no—
648C22×D3—46no—
649C22×D3C2516yes—
650C22×D3C2512yes—
651C3×Q8—22no—
652C3×Q8C2×#4114yescomplemented
653C3×D4—212no—
654C3×D4—212no—
655C3×D4—26no—
656C3×D4C2×#41112yescomplemented
657C2×C3×C4—212no—
658C2×C3×C4—26no—
659C2×C3×C4—212no—
660C2×C3×C4—46no—
661C2×C3×C4—412no—
662C2×C3×C4—43no—
663C2×C3×C4—46no—
664C2×C3×C4C2×#41112yescomplemented
665C2×C3×C4C2512yes—
666C2×C3×C4C2516yes—
667C2×C3×C4C2512yes—
668C2×C3×C4C2513yes—
669C2×C3×C4C2513yes—
670C2×C3×C4C2511yescharacteristic
671C2×C3×C4C2513yes—
672C2×C3×C4C2511yescharacteristic
673C2×C3×C4C2511yescharacteristic
674#67—224no—
675#67—224no—
676#67—424no—
677#67—412no—
678C2×Dic3—212no—
679C2×Dic3—412no—
680C2×Dic3C2514yes—
681C2×Dic3C2516yes—
682C2×Dic3C25112yes—
683C2×Dic3C2512yes—
684D12—212no—
685D12—212no—
686D12—26no—
687D12—46no—
688D12H(5,𝔽2)14yescomplemented
689C4×D3—224no—
690C4×D3—24no—
691C4×D3—212no—
692C4×D3—212no—
693C4×D3—212no—
694C4×D3—424no—
695C4×D3—44no—
696Dic6—212no—
697Dic6—212no—
698Dic6—412no—
699Dic6—42no—
700C24—36no—
701C24C23×D316yes—
702#41—28no—
703#41—212no—
704#41—624no—
705#41—68no—
706#41—624no—
707#41—624no—
708#41—1224no—
709#41—1248no—
710#41#23518yescomplemented
711C2×Q8—36no—
712C2×Q8—36no—
713C2×Q8—32no—
714C2×Q8—312no—
715C2×Q8—68no—
716C2×Q8—1212no—
717C2×Q8C23×D311yescharacteristic
718C2×Q8C23×D311yescharacteristic
719C2×D4—224no—
720C2×D4—212no—
721C2×D4—312no—
722C2×D4—312no—
723C2×D4—312no—
724C2×D4—324no—
725C2×D4—31no—
726C2×D4—36no—
727C2×D4—36no—
728C2×D4—33no—
729C2×D4—36no—
730C2×D4—612no—
731C2×D4—624no—
732C2×D4—1224no—
733C2×D4C23×D316yes—
734C2×D4C23×D313yes—
735C2×D4C23×D316yes—
736C2×D4C23×D313yes—
737C22×C4—36no—
738C22×C4—312no—
739C22×C4—36no—
740C22×C4—312no—
741C22×C4—32no—
742C22×C4—36no—
743C22×C4—36no—
744C22×C4—34no—
745C22×C4—324no—
746C22×C4—412no—
747C22×C4—624no—
748C22×C4—1224no—
749C22×C4C23×D313yes—
750C22×C4C23×D316yes—
751C22×C4C23×D316yes—
752C22×C4C23×D313yes—
753C22×C4C23×D316yes—
754C22×C4C23×D316yes—
755C22×C4C23×D3112yes—
756C22×C4C23×D313yes—
757C4⋊C4—36no—
758C4⋊C4—312no—
759C4⋊C4—31no—
760C4⋊C4—312no—
761C4⋊C4—324no—
762C4⋊C4—36no—
763C4⋊C4—32no—
764C4⋊C4—34no—
765C4⋊C4—33no—
766C4⋊C4—312no—
767C4⋊C4—36no—
768C4⋊C4—32no—
769C4⋊C4—36no—
770C4⋊C4—312no—
771C4⋊C4—312no—
772C4⋊C4—34no—
773C4⋊C4—312no—
774C4⋊C4C23×D313yes—
775C4⋊C4C23×D316yes—
776C4⋊C4C23×D311yescharacteristic
777C4⋊C4C23×D313yes—
778C4⋊C4C23×D316yes—
779C4⋊C4C23×D313yes—
780C4⋊C4C23×D312yes—
781C22⋊C4—312no—
782C22⋊C4—312no—
783C22⋊C4—324no—
784C22⋊C4—312no—
785C22⋊C4—32no—
786C22⋊C4—36no—
787C22⋊C4—312no—
788C22⋊C4—312no—
789C22⋊C4—36no—
790C22⋊C4—36no—
791C22⋊C4—34no—
792C22⋊C4—312no—
793C22⋊C4—312no—
794C22⋊C4C23×D316yes—
795C22⋊C4C23×D316yes—
796C22⋊C4C23×D3112yes—
797C22⋊C4C23×D316yes—
798C22⋊C4C23×D316yes—
799C42—312no—
800C42—312no—
801C42—312no—
802C42C23×D316yes—
803C42C23×D311yescharacteristic
804C42C23×D313yes—
805C42C23×D312yes—
806C42C23×D316yes—
807C42C23×D313yes—
808C42C23×D313yes—
809C22×C3—23no—
810C22×C3—23no—
811C22×C3—26no—
812C22×C3—26no—
813C22×C3—26no—
814C22×C3—812no—
815C22×C3C22×#4116yes—
816C22×C3C2611yescharacteristic
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—26no—
820C2×D3—26no—
821C2×D3—26no—
822C2×D3—424no—
823C2×D3C2×H(5,𝔽2)14yes—
824C3×C4—22no—
825C3×C4—23no—
826C3×C4—26no—
827C3×C4—21no—
828C3×C4—22no—
829C3×C4—23no—
830C3×C4C22×#4116yes—
831C3×C4C22×#4112yes—
832C3×C4C2×H(5,𝔽2)12yes—
833Dic3—26no—
834Dic3—22no—
835Dic3—212no—
836Dic3—24no—
837C23—212no—
838C23—32no—
839C23—36no—
840C23—46no—
841C23—46no—
842C23—612no—
843C23—612no—
844C23—126no—
845C23C24×D316yes—
846C23C24×D313yes—
847Q8—22no—
848Q8—612no—
849Q8—612no—
850Q8—1212no—
851Q8—122no—
852Q8C2×#23514yescomplemented
853D4—212no—
854D4—212no—
855D4—26no—
856D4—34no—
857D4—612no—
858D4—624no—
859D4—624no—
860D4—612no—
861D4—66no—
862D4—126no—
863D4—1224no—
864D4—1212no—
865D4C2×#235112yescomplemented
866C2×C4—212no—
867C2×C4—26no—
868C2×C4—212no—
869C2×C4—34no—
870C2×C4—36no—
871C2×C4—312no—
872C2×C4—32no—
873C2×C4—46no—
874C2×C4—412no—
875C2×C4—46no—
876C2×C4—43no—
877C2×C4—624no—
878C2×C4—612no—
879C2×C4—64no—
880C2×C4—612no—
881C2×C4—612no—
882C2×C4—612no—
883C2×C4—1224no—
884C2×C4—124no—
885C2×C4—1212no—
886C2×C4C2×#235112yescomplemented
887C2×C4C24×D312yes—
888C2×C4C24×D316yes—
889C2×C4C24×D311yescharacteristic
890C2×C4C24×D312yes—
891C2×C4C24×D313yes—
892C2×C4C24×D313yes—
893C2×C4C24×D313yes—
894C2×C4C24×D311yescharacteristic
895C2×C4C24×D311yescharacteristic
896C2×C3—26no—
897C2×C3—46no—
898C2×C3C23×#4111yescharacteristic
899C2×C3C22×H(5,𝔽2)11yescharacteristic
900C2×C32−1+611yescharacteristic
901D3—24no—
902D3—46no—
903C22—23no—
904C22—23no—
905C22—26no—
906C22—26no—
907C22—26no—
908C22—34no—
909C22—62no—
910C22—62no—
911C22—66no—
912C22—66no—
913C22—66no—
914C22—812no—
915C22—1224no—
916C22C22×#23516yes—
917C22C25×D311yescharacteristic
918C4—22no—
919C4—26no—
920C4—23no—
921C4—22no—
922C4—23no—
923C4—21no—
924C4—62no—
925C4—66no—
926C4—612no—
927C4—64no—
928C4C22×#23516yes—
929C4C22×#23512yes—
930C4D3×H(5,𝔽2)12yes—
931C3#6298511yescharacteristic, complemented, Sylow
932C2—26no—
933C2—46no—
934C2—64no—
935C2—126no—
936C2C23×#23511yescharacteristic
937C2C2×D3×H(5,𝔽2)11yescharacteristic
938C2#8757211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×C4×H(5,𝔽2)C2
hypercenterC4×H(5,𝔽2)D3
hypocenterC3#62985
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C3×C4×H(5,𝔽2)C2semidirect
2. #87285C2semidirect
3. #85908C2semidirect
4. #85902C2semidirect
5. D3×#520C2semidirect
6. #85870C2semidirect
7. #85869C2semidirect
8. #85853C2semidirect
9. #85850C2semidirect
10. #85844C2semidirect
11. #85840C2semidirect
12. #41×D12C2semidirect
13. #85828C2semidirect
14. #85788C2semidirect
15. D4×#235C2semidirect
16. C2×#5551C2semidirect
17. #85767C2semidirect
21. C22×#235C22semidirect
23. C3×#520C22semidirect
24. C3×#520C22semidirect
25. C3×#518C22semidirect
26. C3×#518C22semidirect
28. C3×C4×#41C22semidirect
29. C3×C4×#41C22semidirect
30. C2×C3×C4×D4C22semidirect
31. C2×C3×C4×D4C22semidirect
32. #5834C22semidirect
33. #5833C22semidirect
34. #5831C22semidirect
35. #5828C22semidirect
37. #5806C22semidirect
38. #5805C22semidirect
39. D4×#67C22semidirect
40. C2×#938C22semidirect
41. #5791C22semidirect
42. C2×#924C22semidirect
43. #5584C22semidirect
44. #5581C22semidirect
45. #5579C22semidirect
46. #5579C22semidirect
47. #5577C22semidirect
48. #5576C22semidirect
49. Q8×D12C22semidirect
50. #5574C22semidirect
51. C4×D3×Q8C22semidirect
52. #5570C22semidirect
53. Q8×Dic6C22semidirect
54. #5565C22semidirect
55. #5564C22semidirect
56. #5563C22semidirect
57. #5563C22semidirect
58. #5562C22semidirect
59. #5561C22semidirect
60. #5559C22semidirect
61. #5558C22semidirect
62. #5558C22semidirect
63. #5557C22semidirect
64. #5556C22semidirect
65. #5555C22semidirect
66. #5554C22semidirect
67. #5553C22semidirect
68. #5552C22semidirect
69. #5551C22semidirect
70. #5551C22semidirect
71. #5551C22semidirect
72. #5551C22semidirect
73. #5551C22semidirect
74. #5551C22semidirect
75. #5550C22semidirect
76. D4×D12C22semidirect
77. #5548C22semidirect
78. #5547C22semidirect
79. #5546C22semidirect
80. C4×D3×D4C22semidirect
81. #5543C22semidirect
82. #5542C22semidirect
83. #5541C22semidirect
84. D4×Dic6C22semidirect
85. #5534C22semidirect
86. #5530C22semidirect
87. #5529C22semidirect
88. #5528C22semidirect
89. #5524C22semidirect
90. #5523C22semidirect
91. D3×#117C22semidirect
92. #5519C22semidirect
93. #5511C22semidirect
94. #5507C22semidirect
95. #5504C22semidirect
96. C2×D3×C4⋊C4C22semidirect
97. #5495C22semidirect
98. #5494C22semidirect
99. #5490C22semidirect
100. C2×#883C22semidirect
101. #5479C22semidirect
102. #5477C22semidirect
103. #5477C22semidirect
104. C4×#235C22semidirect
105. C2×C4×D12C22semidirect
106. #5470C22semidirect
107. #5470C22semidirect
108. C2×#869C22semidirect
124. C4×H(5,𝔽2)D3semidirect
359. #520C2×D3semidirect
360. #520C2×D3semidirect
361. #518C2×D3semidirect
362. #518C2×D3semidirect
365. C4×#41C2×D3semidirect
366. C4×#41C2×D3semidirect
370. C2×C4×D4C2×D3semidirect
371. C2×C4×D4C2×D3semidirect
378. C3×#41#41semidirect
652. C3×Q8C2×#41semidirect
656. C3×D4C2×#41semidirect
664. C2×C3×C4C2×#41semidirect
688. D12H(5,𝔽2)semidirect
710. #41#235semidirect
852. Q8C2×#235semidirect
865. D4C2×#235semidirect
886. C2×C4C2×#235semidirect
931. C3#62985semidirect

Maximal subgroups

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

subgroupindex
C3×C4×H(5,𝔽2)2
#872852
#859082
#859022
D3×#5202
#858702
#858692
#858532
#858502
#858442
#858402
#41×D122
#858282
#857882
D4×#2352
C2×#55512
#857672
#629853