Finite Group Databasebeta

← #11707351

Subgroups — #11707351

Order 768.

7894 conjugacy classes of subgroups.

The subgroup lattice has 936 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#87282C212yesmaximal, complemented
3#85896C214yesmaximal, complemented
4#85891C216yesmaximal, complemented
5#85886C212yesmaximal, complemented
6#85871C2112yesmaximal, complemented
7#85862C216yesmaximal, complemented
8#85853C212yesmaximal, complemented
9#85848C213yesmaximal, complemented
10#85846C211yesmaximal, characteristic, complemented
11#85845C212yesmaximal, complemented
12#85825C213yesmaximal, complemented
13#41×Dic6C211yesmaximal, characteristic, complemented
14#85790C216yesmaximal, complemented
15#85788C213yesmaximal, complemented
16D4×#235C216yesmaximal, complemented
17C2×#5553C213yesmaximal, complemented
18#62986—31nomaximal, Sylow
19C2×C3×H(5,𝔽2)C2211yescharacteristic
20C2×#1009C2212yes—
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#5834C2214yescomplemented
34#5832C2216yescomplemented
35#5830C2216yescomplemented
36Dic3×#41C2212yes—
37#5805C2216yescomplemented
38C2×#940C2216yescomplemented
39D4×#67C22112yescomplemented
40D4×#67C22112yescomplemented
41#5791C22112yescomplemented
42C2×#930C2216yescomplemented
43#5585C2213yescomplemented
44#5585C2216yescomplemented
45#5577C2212yescomplemented
46#5577C2212yescomplemented
47#5574C2214yescomplemented
48C4×#239C2214yescomplemented
49#5570C2211yescharacteristic, complemented
50#5569C2212yescomplemented
51#5568C2216yescomplemented
52#5567C2211yescharacteristic, complemented
53Q8×Dic6C2211yescharacteristic, complemented
54#5565C2216yescomplemented
55#5563C2216yescomplemented
56#5562C22112yescomplemented
57#5562C22112yescomplemented
58#5560C22124yescomplemented
59#5559C22112yescomplemented
60#5559C2216yescomplemented
61#5558C22112yescomplemented
62#5553C2216yescomplemented
63#5553C2216yescomplemented
64#5553C2216yescomplemented
65#5553C2213yescomplemented
66#5553C2216yescomplemented
67#5553C22112yescomplemented
68#5553C22112yescomplemented
69#5552C2216yescomplemented
70#5551C2216yescomplemented
71#5550C22112yescomplemented
72#5550C22112yescomplemented
73D4×D12C2216yescomplemented
74D4×D12C2216yescomplemented
75#5548C22112yescomplemented
76#5548C22112yescomplemented
77#5547C22124yescomplemented
78#5545C22112yescomplemented
79C4×D3×D4C22112yescomplemented
80#5543C2213yescomplemented
81#5542C2213yescomplemented
82#5540C22112yescomplemented
83#5539C2216yescomplemented
84D4×Dic6C2213yescomplemented
85#5535C22112yescomplemented
86#5532C22112yescomplemented
87#5530C22112yescomplemented
88#5528C22112yescomplemented
89#5525C2216yescomplemented
90#5522C2216yescomplemented
91#5521C2216yescomplemented
92#5517C2216yescomplemented
93#5514C22112yescomplemented
94#5507C22112yescomplemented
95#5504C2216yescomplemented
96C2×#893C2216yescomplemented
97#5494C22112yescomplemented
98#5490C22124yescomplemented
99#5490C22124yescomplemented
100C2×#884C22112yescomplemented
101#5479C2216yescomplemented
102#5477C2216yescomplemented
103#5477C2213yescomplemented
104#5477C2216yescomplemented
105C2×#874C2213yescomplemented
106C4×#235C2216yescomplemented
107#5470C2213yescomplemented
108C2×C4×Dic6C2213yescomplemented
109#3519—312no—
110#3519—36no—
111#3517—34no—
112#3517—32no—
113#3508—36no—
114#3508—33no—
115#3506—36no—
116#3506—33no—
117#3498—32no—
118#3498—31no—
119#3483—32no—
120#3480—33no—
121Q8×#41—31no—
122D4×#41—36no—
123C2×#550—33no—
124C4×H(5,𝔽2)—32no—
125C4×H(5,𝔽2)D311yescharacteristic, complemented
126C3×H(5,𝔽2)—28no—
127C2×C3×#41C2313yes—
128C2×C3×#41C2312yes—
129C2×C3×#41C2311yescharacteristic
130C22×C3×D4C2316yes—
131C22×C3×D4C2313yes—
132C23×C3×C4C2316yes—
133C22×#67C23112yes—
134C22×#67C23112yes—
135#1009—216no—
136C2×#239C2314yes—
137C2×D3×D4C23112yes—
138C2×#235—424no—
139C2×#235C2316yes—
140C2×#235C2316yes—
141C2×#235C23112yes—
142C2×#235C23124yes—
143C2×#235C23112yes—
144C22×D12C2316yes—
145C22×D12C2316yes—
146C22×D12C2316yes—
147C22×C4×D3C23112yes—
148C22×Dic6C2313yes—
149C3×C4×Q8C2311yescharacteristic
150C3×C4×Q8C2311yescharacteristic
151C3×C4×Q8C2313yes—
152C3×C4×Q8C2311yescharacteristic
153C3×C4×Q8C2312yes—
154C3×C4×D4C2313yes—
155C3×C4×D4C2313yes—
156C3×C4×D4C2316yes—
157C3×C4×D4C2313yes—
158C3×C4×D4C2316yes—
159C3×C4×D4C23112yes—
160C3×C4×D4C2316yes—
161C3×C4×D4C2316yes—
162C3×C4×D4C2316yes—
163C3×C4×D4C2316yes—
164C3×C4×D4C2316yes—
165C3×C4×D4C2316yes—
166C3×C4×D4C2313yes—
167C3×#117C2313yes—
168C3×#117C2313yes—
169C3×#117C2316yes—
170C3×#117C2316yes—
171C2×C3×C4⋊C4C2313yes—
172C2×C3×C4⋊C4C2316yes—
173C2×C3×C22⋊C4C2316yes—
174C2×C3×C22⋊C4C23112yes—
175C2×C3×C42C2313yes—
176C2×C3×C42C2316yes—
177#953C23124yes—
178#947C2316yes—
179Q8×Dic3C2312yes—
180Q8×Dic3C2312yes—
181#944C2312yes—
182#940C23112yes—
183#940C23112yes—
184#940C2316yes—
185#940C23112yes—
186#939C23112yes—
187#939C23112yes—
188#938C23112yes—
189#938C23112yes—
190#937C23124yes—
191#936C2316yes—
192D4×Dic3C2316yes—
193D4×Dic3C2316yes—
194#930C23112yes—
195#930C2316yes—
196#930C23112yes—
197#930C23112yes—
198#930C23112yes—
199#930C2316yes—
200#930C2316yes—
201#930C23124yes—
202#929C23112yes—
203#929C23124yes—
204C4×#67C23112yes—
205C4×#67C23112yes—
206C4×#67C23112yes—
207C4×#67C23124yes—
208C4×#67C23124yes—
209C2×(C2×D3)⋊C4C23112yes—
210#926C2316yes—
211#926C2316yes—
212C2×C4⋊Dic3C2313yes—
213#924C2316yes—
214#924C2316yes—
215#924C2316yes—
216C2×Dic3⋊C4C2316yes—
217C2×C4×Dic3C2316yes—
218#898C23112yes—
219#896C23112yes—
220#895C23112yes—
221#895C23112yes—
222#894C23124yes—
223#894C23112yes—
224#893C2316yes—
225#893C23112yes—
226#893C23112yes—
227#893C23112yes—
228#893C2316yes—
229#892C23112yes—
230D3×C4⋊C4C23112yes—
231#890C2316yes—
232#890C2316yes—
233#889C2314yes—
234#888C2316yes—
235#888C2316yes—
236#887C2316yes—
237#887C2312yes—
238#885C23112yes—
239#885C23124yes—
240#884C23112yes—
241#884C23124yes—
242#884C23124yes—
243#884C23124yes—
244#884C23124yes—
245#883C23112yes—
246#883C23124yes—
247#882C23124yes—
248#67⋊C4C23112yes—
249#67⋊C4C23112yes—
250D3×C22⋊C4C23124yes—
251#879C23112yes—
252#878C23112yes—
253#878C23112yes—
254#876C23112yes—
255#875C2316yes—
256#875C2316yes—
257#875C23112yes—
258#874C2313yes—
259#874C2316yes—
260#874C2316yes—
261#874C2316yes—
262C4×D12C2316yes—
263C4×D12C2316yes—
264C4×D12C23112yes—
265C4×D12C23112yes—
266C4×D12C2316yes—
267C4×D12C23112yes—
268#872C23112yes—
269#872C23112yes—
270C42×D3C23112yes—
271#870C2316yes—
272#870C2312yes—
273#869C2313yes—
274#869C2313yes—
275#869C2311yescharacteristic
276C4×Dic6C2311yescharacteristic
277C4×Dic6C2313yes—
278C4×Dic6C2313yes—
279C4×Dic6C2313yes—
280C4×Dic6C2316yes—
281C4×Dic6C2316yes—
282C4×Dic6C2316yes—
283C4×Dic6C2312yes—
284C2×H(5,𝔽2)—32no—
285C2×H(5,𝔽2)C2×D311yescharacteristic
286C22×#41—36no—
287#559—33no—
288#559—36no—
289#559—36no—
290#559—312no—
291Q82—31no—
292#557—32no—
293#557—31no—
294#557—31no—
295#556—36no—
296#556—33no—
297#555—36no—
298#555—312no—
299#554—36no—
300#554—33no—
301#553—312no—
302#553—36no—
303#553—312no—
304#553—312no—
305#553—312no—
306#550—34no—
307#550—34no—
308#550—32no—
309#550—32no—
310#550—33no—
311#550—36no—
312#550—312no—
313#550—36no—
314#550—312no—
315#550—36no—
316#550—36no—
317D4×Q8—33no—
318#548—36no—
319#547—36no—
320#547—312no—
321#546—312no—
322#546—312no—
323#546—324no—
324#546—324no—
325D42—312no—
326D42—312no—
327D42—36no—
328D42—36no—
329#540—312no—
330#540—312no—
331#540—312no—
332#538—324no—
333#538—312no—
334#535—36no—
335#535—36no—
336#535—36no—
337#533—36no—
338#533—33no—
339#532—36no—
340#532—312no—
341#532—312no—
342#532—36no—
343#532—33no—
344#532—36no—
345C2×#127—36no—
346C2×#127—33no—
347#529—312no—
348#529—36no—
349#525—312no—
350#525—324no—
351C2×#121—36no—
352C2×#121—312no—
353#520—34no—
354#520—36no—
355#520C2×D311yescharacteristic
356#520C2×D313yescomplemented
357#520C2×D312yescomplemented
358#518—312no—
359#518—36no—
360#518C2×D313yescomplemented
361#518C2×D316yescomplemented
362C4×#41—32no—
363C4×#41—34no—
364C4×#41—36no—
365C4×#41—36no—
366C4×#41C2×D311yescharacteristic
367C4×#41C2×D313yescomplemented
368C4×#41C2×D312yescomplemented
369C2×C4×Q8—33no—
370C2×C4×D4—312no—
371C2×C4×D4—36no—
372C2×C4×D4C2×D313yescomplemented
373C2×C4×D4C2×D316yescomplemented
374C24×C3C2416yes—
375C23×D3C24112yes—
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×D4C2413yes—
384C2×C3×D4C2416yes—
385C2×C3×D4C2416yes—
386C2×C3×D4C2413yes—
387C22×C3×C4—412no—
388C22×C3×C4C2413yes—
389C22×C3×C4C2416yes—
390C22×C3×C4C2416yes—
391C22×C3×C4C2413yes—
392C22×C3×C4C2416yes—
393C22×C3×C4C2416yes—
394C22×C3×C4C24112yes—
395C22×C3×C4C2413yes—
396C2×#67—424no—
397C2×#67—812no—
398C2×#67C24112yes—
399C2×#67C24112yes—
400C2×#67C24112yes—
401C2×#67C24124yes—
402C2×#67C24124yes—
403C22×Dic3C2416yes—
404C22×Dic3C2416yes—
405#239—216no—
406D3×D4—248no—
407#235—224no—
408#235—224no—
409#235—448no—
410#235—424no—
411#235—812no—
412C2×D12—224no—
413C2×D12—412no—
414C2×D12—86no—
415C2×D12C2416yes—
416C2×D12C24112yes—
417C2×D12C2416yes—
418C2×D12C2416yes—
419C2×D12C24112yes—
420C2×D12C24112yes—
421C2×C4×D3—424no—
422C2×C4×D3C24112yes—
423C2×C4×D3C24112yes—
424C2×C4×D3C24112yes—
425C2×C4×D3C24124yes—
426C2×Dic6—212no—
427C2×Dic6C2413yes—
428C2×Dic6C2416yes—
429C2×Dic6C2412yes—
430C2×Dic6C2416yes—
431C2×Dic6C2411yescharacteristic
432C3×C4⋊C4C2413yes—
433C3×C4⋊C4C2411yescharacteristic
434C3×C4⋊C4C2413yes—
435C3×C4⋊C4C2413yes—
436C3×C4⋊C4C2412yes—
437C3×C4⋊C4C2416yes—
438C3×C4⋊C4C2416yes—
439C3×C22⋊C4C2416yes—
440C3×C22⋊C4C2416yes—
441C3×C22⋊C4C2416yes—
442C3×C22⋊C4C2416yes—
443C3×C22⋊C4C24112yes—
444C3×C42C2411yescharacteristic
445C3×C42C2413yes—
446C3×C42C2413yes—
447C3×C42C2413yes—
448C3×C42C2412yes—
449C3×C42C2416yes—
450C3×C42C2416yes—
451#217C24112yes—
452#217C24112yes—
453#217C24112yes—
454(C2×D3)⋊C4C24112yes—
455(C2×D3)⋊C4C24112yes—
456(C2×D3)⋊C4C24112yes—
457(C2×D3)⋊C4C24112yes—
458(C2×D3)⋊C4C24112yes—
459(C2×D3)⋊C4C24124yes—
460(C2×D3)⋊C4C24112yes—
461C4⋊Dic3C2411yescharacteristic
462C4⋊Dic3C2413yes—
463C4⋊Dic3C2416yes—
464C4⋊Dic3C2412yes—
465C4⋊Dic3C2416yes—
466C4⋊Dic3C2416yes—
467C4⋊Dic3C2416yes—
468C4⋊Dic3C2412yes—
469Dic3⋊C4C2412yes—
470Dic3⋊C4C2416yes—
471Dic3⋊C4C2416yes—
472Dic3⋊C4C2416yes—
473Dic3⋊C4C24112yes—
474Dic3⋊C4C2414yes—
475Dic3⋊C4C2414yes—
476Dic3⋊C4C2414yes—
477Dic3⋊C4C24112yes—
478C4×Dic3C2412yes—
479C4×Dic3C2416yes—
480C4×Dic3C2416yes—
481C4×Dic3C2416yes—
482C4×Dic3C2414yes—
483C4×Dic3C24112yes—
484H(5,𝔽2)—28no—
485H(5,𝔽2)—616no—
486C2×#41—34no—
487C2×#41—36no—
488C2×#41—36no—
489C2×#41—324no—
490C2×#41—312no—
491C2×#41—312no—
492C2×#41—1224no—
493C2×#41C22×D313yes—
494C2×#41C22×D312yes—
495C2×#41C22×D311yescharacteristic
496C22×Q8—33no—
497C22×D4—312no—
498C22×D4—312no—
499C22×D4—312no—
500C22×D4—36no—
501C22×D4—36no—
502C22×D4—36no—
503C22×D4C22×D313yes—
504C22×D4C22×D316yes—
505C23×C4—312no—
506C23×C4C22×D316yes—
507C4⋊Q8—32no—
508C4⋊Q8—36no—
509C4⋊Q8—36no—
510C4⋊Q8—31no—
511C4⋊Q8—33no—
512C4⋊Q8—33no—
513#127—36no—
514#127—312no—
515#127—312no—
516#127—312no—
517#127—33no—
518#127—36no—
519#127—36no—
520#127—36no—
521#126—312no—
522#126—312no—
523#126—312no—
524#125—34no—
525#125—36no—
526#125—36no—
527#125—32no—
528#125—36no—
529#124—36no—
530#124—36no—
531#124—312no—
532#124—324no—
533#124—36no—
534#124—36no—
535#124—312no—
536#123—324no—
537#123—312no—
538#123—324no—
539#123—312no—
540#123—324no—
541#123—312no—
542C22⋊Q8—36no—
543C22⋊Q8—36no—
544C22⋊Q8—36no—
545C22⋊Q8—312no—
546C22⋊Q8—312no—
547C22⋊Q8—312no—
548#121—312no—
549#121—312no—
550#121—312no—
551#121—312no—
552#121—36no—
553#121—312no—
554#121—324no—
555#121—36no—
556#121—312no—
557#121—312no—
558#121—36no—
559#121—312no—
560#121—312no—
561#121—312no—
562#121—312no—
563#121—324no—
564#121—324no—
565#121—324no—
566#121—324no—
567#120—324no—
568#120—324no—
569#120—324no—
570C4×Q8—32no—
571C4×Q8—32no—
572C4×Q8—32no—
573C4×Q8—36no—
574C4×Q8—31no—
575C4×Q8—33no—
576C4×Q8—36no—
577C4×Q8—33no—
578C4×Q8—36no—
579C4×Q8—33no—
580C4×Q8—32no—
581C4×Q8—36no—
582C4×Q8C22×D312yes—
583C4×Q8C22×D311yescharacteristic
584C4×Q8C22×D311yescharacteristic
585C4×Q8C22×D311yescharacteristic
586C4×Q8C22×D313yes—
587C4×D4—36no—
588C4×D4—36no—
589C4×D4—324no—
590C4×D4—312no—
591C4×D4—312no—
592C4×D4—324no—
593C4×D4—312no—
594C4×D4—312no—
595C4×D4—36no—
596C4×D4—312no—
597C4×D4—312no—
598C4×D4—36no—
599C4×D4—312no—
600C4×D4—312no—
601C4×D4—312no—
602C4×D4—312no—
603C4×D4—36no—
604C4×D4—36no—
605C4×D4—312no—
606C4×D4—36no—
607C4×D4C22×D316yes—
608C4×D4C22×D313yes—
609C4×D4C22×D316yes—
610C4×D4C22×D316yes—
611C4×D4C22×D313yes—
612C4×D4C22×D3112yes—
613C4×D4C22×D316yes—
614C4×D4C22×D316yes—
615C4×D4C22×D316yes—
616C4×D4C22×D313yes—
617C4×D4C22×D316yes—
618C4×D4C22×D316yes—
619C4×D4C22×D313yes—
620#117—36no—
621#117—36no—
622#117—312no—
623#117—312no—
624#117—312no—
625#117C22×D313yes—
626#117C22×D313yes—
627#117C22×D316yes—
628#117C22×D316yes—
629C2×C4⋊C4—36no—
630C2×C4⋊C4—33no—
631C2×C4⋊C4—312no—
632C2×C4⋊C4C22×D313yes—
633C2×C4⋊C4C22×D316yes—
634C2×C22⋊C4—312no—
635C2×C22⋊C4—324no—
636C2×C22⋊C4C22×D316yes—
637C2×C22⋊C4C22×D3112yes—
638C2×C42—36no—
639C2×C42—312no—
640C2×C42C22×D313yes—
641C2×C42C22×D316yes—
642C23×C3—212no—
643C23×C3—46no—
644C23×C3—46no—
645C23×C3C2516yes—
646C23×C3C2513yes—
647C22×D3—224no—
648C22×D3—412no—
649C22×D3—412no—
650C22×D3C25112yes—
651C3×Q8—22no—
652C3×Q8C2×#4114yescomplemented
653C3×D4—212no—
654C3×D4—26no—
655C3×D4—212no—
656C3×D4C2×#41112yescomplemented
657C2×C3×C4—212no—
658C2×C3×C4—26no—
659C2×C3×C4—212no—
660C2×C3×C4—46no—
661C2×C3×C4—43no—
662C2×C3×C4—412no—
663C2×C3×C4—46no—
664C2×C3×C4C2×#41112yescomplemented
665C2×C3×C4C2512yes—
666C2×C3×C4C2516yes—
667C2×C3×C4C2511yescharacteristic
668C2×C3×C4C2513yes—
669C2×C3×C4C2513yes—
670C2×C3×C4C2512yes—
671C2×C3×C4C2511yescharacteristic
672C2×C3×C4C2513yes—
673C2×C3×C4C2511yescharacteristic
674#67—224no—
675#67—224no—
676#67—424no—
677#67—424no—
678#67—412no—
679C2×Dic3—212no—
680C2×Dic3—46no—
681C2×Dic3C2512yes—
682C2×Dic3C2514yes—
683C2×Dic3C2516yes—
684C2×Dic3C2516yes—
685C2×Dic3C2512yes—
686D12—212no—
687D12—224no—
688D12—212no—
689D12—412no—
690D12—46no—
691D12—412no—
692C4×D3—224no—
693C4×D3—224no—
694C4×D3—424no—
695C4×D3—412no—
696Dic6—24no—
697Dic6—26no—
698Dic6—212no—
699Dic6—46no—
700Dic6H(5,𝔽2)14yescomplemented
701C24—312no—
702C24C23×D316yes—
703#41—28no—
704#41—212no—
705#41—624no—
706#41—616no—
707#41—624no—
708#41—1224no—
709#41—1248no—
710#41—2412no—
711#41#23518yescomplemented
712C2×Q8—31no—
713C2×Q8—32no—
714C2×Q8—36no—
715C2×Q8—33no—
716C2×Q8—36no—
717C2×Q8—612no—
718C2×Q8C23×D311yescharacteristic
719C2×Q8C23×D311yescharacteristic
720C2×D4—224no—
721C2×D4—212no—
722C2×D4—312no—
723C2×D4—312no—
724C2×D4—324no—
725C2×D4—312no—
726C2×D4—324no—
727C2×D4—312no—
728C2×D4—36no—
729C2×D4—36no—
730C2×D4—312no—
731C2×D4—36no—
732C2×D4—312no—
733C2×D4—648no—
734C2×D4—624no—
735C2×D4—1212no—
736C2×D4—1224no—
737C2×D4—246no—
738C2×D4—2412no—
739C2×D4C23×D316yes—
740C2×D4C23×D316yes—
741C2×D4C23×D313yes—
742C2×D4C23×D313yes—
743C22×C4—36no—
744C22×C4—36no—
745C22×C4—312no—
746C22×C4—312no—
747C22×C4—312no—
748C22×C4—324no—
749C22×C4—412no—
750C22×C4—1224no—
751C22×C4C23×D313yes—
752C22×C4C23×D316yes—
753C22×C4C23×D316yes—
754C22×C4C23×D313yes—
755C22×C4C23×D316yes—
756C22×C4C23×D316yes—
757C22×C4C23×D3112yes—
758C22×C4C23×D313yes—
759C4⋊C4—32no—
760C4⋊C4—31no—
761C4⋊C4—36no—
762C4⋊C4—312no—
763C4⋊C4—36no—
764C4⋊C4—33no—
765C4⋊C4—36no—
766C4⋊C4—36no—
767C4⋊C4—36no—
768C4⋊C4—36no—
769C4⋊C4—34no—
770C4⋊C4—32no—
771C4⋊C4—34no—
772C4⋊C4—34no—
773C4⋊C4—32no—
774C4⋊C4—312no—
775C4⋊C4—36no—
776C4⋊C4C23×D316yes—
777C4⋊C4C23×D313yes—
778C4⋊C4C23×D313yes—
779C4⋊C4C23×D316yes—
780C4⋊C4C23×D311yescharacteristic
781C4⋊C4C23×D313yes—
782C4⋊C4C23×D312yes—
783C22⋊C4—312no—
784C22⋊C4—312no—
785C22⋊C4—312no—
786C22⋊C4—312no—
787C22⋊C4—324no—
788C22⋊C4—312no—
789C22⋊C4—312no—
790C22⋊C4—312no—
791C22⋊C4—312no—
792C22⋊C4—312no—
793C22⋊C4C23×D316yes—
794C22⋊C4C23×D316yes—
795C22⋊C4C23×D316yes—
796C22⋊C4C23×D316yes—
797C22⋊C4C23×D3112yes—
798C42—34no—
799C42—36no—
800C42—32no—
801C42—312no—
802C42—36no—
803C42—36no—
804C42C23×D316yes—
805C42C23×D312yes—
806C42C23×D313yes—
807C42C23×D311yescharacteristic
808C42C23×D316yes—
809C42C23×D313yes—
810C42C23×D313yes—
811C22×C3—23no—
812C22×C3—23no—
813C22×C3—26no—
814C22×C3—26no—
815C22×C3—26no—
816C22×C3—812no—
817C22×C3C22×#4116yes—
818C22×C3C2611yescharacteristic
819C2×D3—212no—
820C2×D3—212no—
821C2×D3—212no—
822C2×D3—824no—
823C3×C4—22no—
824C3×C4—23no—
825C3×C4—26no—
826C3×C4—23no—
827C3×C4—22no—
828C3×C4—21no—
829C3×C4C22×#4112yes—
830C3×C4C22×#4116yes—
831C3×C4C2×H(5,𝔽2)12yes—
832Dic3—24no—
833Dic3—26no—
834Dic3—26no—
835Dic3—22no—
836Dic3C2×H(5,𝔽2)14yes—
837C23—212no—
838C23—312no—
839C23—46no—
840C23—46no—
841C23—624no—
842C23—1212no—
843C23—1212no—
844C23C24×D316yes—
845C23C24×D313yes—
846Q8—22no—
847Q8—34no—
848Q8—612no—
849Q8—64no—
850Q8—66no—
851Q8—126no—
852Q8C2×#23514yescomplemented
853D4—212no—
854D4—212no—
855D4—26no—
856D4—624no—
857D4—624no—
858D4—624no—
859D4—612no—
860D4—612no—
861D4—1212no—
862D4—126no—
863D4—1212no—
864D4—1224no—
865D4—1212no—
866D4—1224no—
867D4C2×#235112yescomplemented
868C2×C4—212no—
869C2×C4—26no—
870C2×C4—212no—
871C2×C4—32no—
872C2×C4—34no—
873C2×C4—36no—
874C2×C4—32no—
875C2×C4—36no—
876C2×C4—46no—
877C2×C4—412no—
878C2×C4—43no—
879C2×C4—46no—
880C2×C4—624no—
881C2×C4—612no—
882C2×C4—624no—
883C2×C4—1224no—
884C2×C4—1212no—
885C2×C4—126no—
886C2×C4C2×#235112yescomplemented
887C2×C4C24×D312yes—
888C2×C4C24×D316yes—
889C2×C4C24×D312yes—
890C2×C4C24×D313yes—
891C2×C4C24×D311yescharacteristic
892C2×C4C24×D313yes—
893C2×C4C24×D311yescharacteristic
894C2×C4C24×D313yes—
895C2×C4C24×D311yescharacteristic
896C2×C3—26no—
897C2×C3—46no—
898C2×C3C23×#4111yescharacteristic
899C2×C3C22×H(5,𝔽2)11yescharacteristic
900C2×C3H(7,𝔽2)11yescharacteristic
901D3—412no—
902C22—23no—
903C22—23no—
904C22—26no—
905C22—26no—
906C22—26no—
907C22—612no—
908C22—612no—
909C22—612no—
910C22—812no—
911C22—2424no—
912C22C22×#23516yes—
913C22C25×D311yescharacteristic
914C4—22no—
915C4—26no—
916C4—23no—
917C4—22no—
918C4—21no—
919C4—23no—
920C4—34no—
921C4—64no—
922C4—66no—
923C4—62no—
924C4—66no—
925C4C22×#23516yes—
926C4C22×#23512yes—
927C4D3×H(5,𝔽2)12yes—
928C3#6298611yescharacteristic, complemented, Sylow
929C2—26no—
930C2—46no—
931C2—1212no—
932C2C23×#23511yescharacteristic
933C2C2×D3×H(5,𝔽2)11yescharacteristic
934C2#8757411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×C4×H(5,𝔽2)C2
hypercenterC4×H(5,𝔽2)D3
hypocenterC3#62986
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. #87282C2semidirect
3. #85896C2semidirect
4. #85891C2semidirect
5. #85886C2semidirect
6. #85871C2semidirect
7. #85862C2semidirect
8. #85853C2semidirect
9. #85848C2semidirect
10. #85846C2semidirect
11. #85845C2semidirect
12. #85825C2semidirect
13. #41×Dic6C2semidirect
14. #85790C2semidirect
15. #85788C2semidirect
16. D4×#235C2semidirect
17. C2×#5553C2semidirect
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. #5834C22semidirect
34. #5832C22semidirect
35. #5830C22semidirect
37. #5805C22semidirect
38. C2×#940C22semidirect
39. D4×#67C22semidirect
40. D4×#67C22semidirect
41. #5791C22semidirect
42. C2×#930C22semidirect
43. #5585C22semidirect
44. #5585C22semidirect
45. #5577C22semidirect
46. #5577C22semidirect
47. #5574C22semidirect
48. C4×#239C22semidirect
49. #5570C22semidirect
50. #5569C22semidirect
51. #5568C22semidirect
52. #5567C22semidirect
53. Q8×Dic6C22semidirect
54. #5565C22semidirect
55. #5563C22semidirect
56. #5562C22semidirect
57. #5562C22semidirect
58. #5560C22semidirect
59. #5559C22semidirect
60. #5559C22semidirect
61. #5558C22semidirect
62. #5553C22semidirect
63. #5553C22semidirect
64. #5553C22semidirect
65. #5553C22semidirect
66. #5553C22semidirect
67. #5553C22semidirect
68. #5553C22semidirect
69. #5552C22semidirect
70. #5551C22semidirect
71. #5550C22semidirect
72. #5550C22semidirect
73. D4×D12C22semidirect
74. D4×D12C22semidirect
75. #5548C22semidirect
76. #5548C22semidirect
77. #5547C22semidirect
78. #5545C22semidirect
79. C4×D3×D4C22semidirect
80. #5543C22semidirect
81. #5542C22semidirect
82. #5540C22semidirect
83. #5539C22semidirect
84. D4×Dic6C22semidirect
85. #5535C22semidirect
86. #5532C22semidirect
87. #5530C22semidirect
88. #5528C22semidirect
89. #5525C22semidirect
90. #5522C22semidirect
91. #5521C22semidirect
92. #5517C22semidirect
93. #5514C22semidirect
94. #5507C22semidirect
95. #5504C22semidirect
96. C2×#893C22semidirect
97. #5494C22semidirect
98. #5490C22semidirect
99. #5490C22semidirect
100. C2×#884C22semidirect
101. #5479C22semidirect
102. #5477C22semidirect
103. #5477C22semidirect
104. #5477C22semidirect
105. C2×#874C22semidirect
106. C4×#235C22semidirect
107. #5470C22semidirect
108. C2×C4×Dic6C22semidirect
125. C4×H(5,𝔽2)D3semidirect
356. #520C2×D3semidirect
357. #520C2×D3semidirect
360. #518C2×D3semidirect
361. #518C2×D3semidirect
367. C4×#41C2×D3semidirect
368. C4×#41C2×D3semidirect
372. C2×C4×D4C2×D3semidirect
373. C2×C4×D4C2×D3semidirect
378. C3×#41#41semidirect
652. C3×Q8C2×#41semidirect
656. C3×D4C2×#41semidirect
664. C2×C3×C4C2×#41semidirect
700. Dic6H(5,𝔽2)semidirect
711. #41#235semidirect
852. Q8C2×#235semidirect
867. D4C2×#235semidirect
886. C2×C4C2×#235semidirect
928. C3#62986semidirect

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
#872822
#858962
#858912
#858862
#858712
#858622
#858532
#858482
#858462
#858452
#858252
#41×Dic62
#857902
#857882
D4×#2352
C2×#55532
#629863