Finite Group Databasebeta

← #11707352

Subgroups — #11707352

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×#3498C211yesmaximal, characteristic, complemented
2#87282C212yesmaximal, complemented
3Dic3×H(5,𝔽2)C212yesmaximal, complemented
4#86773C212yesmaximal, complemented
5#86772C214yesmaximal, complemented
6#86768C212yesmaximal, complemented
7#86612C216yesmaximal, complemented
8#86611C2112yesmaximal, complemented
9D4×#237C216yesmaximal, complemented
10#86319C216yesmaximal, complemented
11#86318C216yesmaximal, complemented
12#86223C213yesmaximal, complemented
13#86220C213yesmaximal, complemented
14#86190C213yesmaximal, complemented
15C2×#5718C213yesmaximal, complemented
16C4×#1009C211yesmaximal, characteristic, complemented
17#41×Dic6C211yesmaximal, characteristic, complemented
18#62986—31nomaximal, Sylow
19C2×C3×H(5,𝔽2)C2212yes—
20C2×#1009C2211yescharacteristic
21C22×#237C2216yescomplemented
22C3×#550C2212yescomplemented
23C3×#550C2212yescomplemented
24C3×D42C2216yescomplemented
25C3×D42C2216yescomplemented
26C3×#535C2216yescomplemented
27C3×#532C2213yescomplemented
28C2×C3×#127C2213yescomplemented
29C3×C4×#41C2211yescharacteristic
30#5834C2214yescomplemented
31#5834C2214yescomplemented
32#5832C2216yescomplemented
33#5830C2216yescomplemented
34#5827C2211yescharacteristic
35#5827C2216yescomplemented
36#5827C2214yescomplemented
37Dic3×#41C2212yes—
38Dic3×#41C2216yescomplemented
39Dic3×#41C2214yescomplemented
40#5806C22112yescomplemented
41#5806C22112yescomplemented
42#5805C2216yescomplemented
43C2×#940C2216yescomplemented
44C2×#939C22112yescomplemented
45D4×#67C22112yescomplemented
46D4×#67C22112yescomplemented
47C2×#938C2216yescomplemented
48#5798C2216yescomplemented
49#5798C22112yescomplemented
50C2×D4×Dic3C2216yescomplemented
51C2×D4×Dic3C22112yescomplemented
52#5732C2213yescomplemented
53#5721C2211yescharacteristic, complemented
54#5719C22112yescomplemented
55#5718C22112yescomplemented
56#5718C2216yescomplemented
57#5718C2216yescomplemented
58#5718C22112yescomplemented
59#5718C2216yescomplemented
60#5718C2213yescomplemented
61#5718C2216yescomplemented
62#5716C2216yescomplemented
63#5716C2216yescomplemented
64#5713C2216yescomplemented
65#5713C2213yescomplemented
66#5681C22112yescomplemented
67#5681C2216yescomplemented
68#5671C2216yescomplemented
69#5619C22112yescomplemented
70#5619C22112yescomplemented
71#5618C22112yescomplemented
72#5618C2216yescomplemented
73#5617C22112yescomplemented
74#5616C22112yescomplemented
75#5614C22112yescomplemented
76#5611C22112yescomplemented
77#5606C22112yescomplemented
78#5601C22112yescomplemented
79#5598C2216yescomplemented
80#5596C22112yescomplemented
81#5596C22112yescomplemented
82#5593C22124yescomplemented
83#5591C22124yescomplemented
84#5591C22124yescomplemented
85#5586C22124yescomplemented
86#5574C2212yescomplemented
87C4×#239C2212yescomplemented
88#5570C2211yescharacteristic, complemented
89#5569C2212yescomplemented
90Q8×Dic6C2211yescharacteristic, complemented
91#5565C22112yescomplemented
92#5563C2216yescomplemented
93#5557C2216yescomplemented
94#5555C2216yescomplemented
95#5545C2216yescomplemented
96C4×D3×D4C2216yescomplemented
97#5543C2213yescomplemented
98#5539C2216yescomplemented
99#5538C22112yescomplemented
100D4×Dic6C2213yescomplemented
101C4×#237C2216yescomplemented
102#5523C2213yescomplemented
103#5521C2213yescomplemented
104#5517C2216yescomplemented
105C4×#235C2213yescomplemented
106C2×C4×D12C2213yescomplemented
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#3498D311yescharacteristic, complemented
119#3483—32no—
120#3480—33no—
121Q8×#41—31no—
122D4×#41—36no—
123C2×#550—33no—
124C4×H(5,𝔽2)—32no—
125C4×H(5,𝔽2)—31no—
126C3×H(5,𝔽2)—216no—
127C2×C3×#41C2316yes—
128C2×C3×#41C2314yes—
129C2×C3×#41C2311yescharacteristic
130C22×C3×D4C23112yes—
131C22×C3×D4C2316yes—
132C22×C3×D4C2316yes—
133C22×C3×D4C2316yes—
134C22×#67C23112yes—
135C22×#67C23112yes—
136C23×Dic3C23112yes—
137#1009—28no—
138C2×#239C2312yes—
139C2×#237—424no—
140C2×#237C2316yes—
141C2×#237C23112yes—
142C2×#237C23124yes—
143C2×#237C23112yes—
144C2×D3×D4C2316yes—
145C2×#235C2313yes—
146C22×D12C2313yes—
147C22×C4×D3C2316yes—
148C22×Dic6C2313yes—
149C3×C4⋊Q8C2311yescharacteristic
150C3×#127C2313yes—
151C3×#127C2316yes—
152C3×#127C2316yes—
153C3×#127C2316yes—
154C3×#124C2316yes—
155C3×#121C23112yes—
156C3×#121C23112yes—
157C3×#121C2316yes—
158C3×#121C2316yes—
159C3×#120C23124yes—
160C3×C4×Q8C2311yescharacteristic
161C3×C4×Q8C2311yescharacteristic
162C3×C4×D4C2316yes—
163C3×C4×D4C2313yes—
164C3×C4×D4C2316yes—
165C3×C4×D4C2313yes—
166C3×#117C2313yes—
167C2×C3×C42C2313yes—
168#953C23124yes—
169C2×#217C23112yes—
170C2×#217C23124yes—
171#947C2316yes—
172Q8×Dic3C2316yes—
173Q8×Dic3C2312yes—
174Q8×Dic3C2312yes—
175Q8×Dic3C2312yes—
176Q8×Dic3C2312yes—
177#944C2312yes—
178#940C2316yes—
179#940C23112yes—
180#940C23112yes—
181#940C23112yes—
182#939C23112yes—
183#939C23124yes—
184#939C23124yes—
185#939C23124yes—
186#939C23124yes—
187#939C23112yes—
188#939C23112yes—
189#938C23112yes—
190#938C23112yes—
191#938C23112yes—
192#938C23112yes—
193#938C2316yes—
194#938C23124yes—
195#937C23124yes—
196#936C2316yes—
197#936C2316yes—
198#936C23112yes—
199#935C23112yes—
200#935C23124yes—
201D4×Dic3C2316yes—
202D4×Dic3C23112yes—
203D4×Dic3C2316yes—
204D4×Dic3C2316yes—
205D4×Dic3C23112yes—
206D4×Dic3C23112yes—
207D4×Dic3C23112yes—
208D4×Dic3C23112yes—
209D4×Dic3C23112yes—
210D4×Dic3C2316yes—
211D4×Dic3C2316yes—
212D4×Dic3C2316yes—
213D4×Dic3C23112yes—
214D4×Dic3C23124yes—
215D4×Dic3C23112yes—
216#930C23112yes—
217#930C23112yes—
218C4×#67C2316yes—
219C4×#67C2316yes—
220C4×#67C23112yes—
221C4×#67C23112yes—
222C2×(C2×D3)⋊C4C2316yes—
223#926C2316yes—
224#926C2313yes—
225#926C23112yes—
226#926C23112yes—
227C2×C4⋊Dic3C2313yes—
228C2×C4⋊Dic3C2313yes—
229C2×C4⋊Dic3C23112yes—
230#924C2316yes—
231#924C2316yes—
232C2×Dic3⋊C4C2316yes—
233C2×C4×Dic3C2316yes—
234C2×C4×Dic3C23112yes—
235#898C23112yes—
236#897C2316yes—
237#893C2316yes—
238#893C2316yes—
239#892C2316yes—
240#892C2316yes—
241D3×C4⋊C4C2316yes—
242#890C2312yes—
243#890C2316yes—
244#890C2316yes—
245#889C2314yes—
246#888C2316yes—
247#888C2316yes—
248#887C2312yes—
249#886C23112yes—
250#886C23124yes—
251#885C23112yes—
252#885C23124yes—
253#883C23112yes—
254#883C23124yes—
255#67⋊C4C23112yes—
256#67⋊C4C23124yes—
257#67⋊C4C23112yes—
258D3×C22⋊C4C23112yes—
259#879C23112yes—
260#879C23112yes—
261#878C23112yes—
262#878C23112yes—
263#878C23112yes—
264#877C23112yes—
265C4×D12C2316yes—
266C4×D12C2313yes—
267C4×D12C2313yes—
268C4×D12C2316yes—
269C4×D12C2316yes—
270#872C2316yes—
271C42×D3C2316yes—
272#870C2316yes—
273#869C2313yes—
274#869C2313yes—
275C4×Dic6C2313yes—
276C4×Dic6C2316yes—
277C4×Dic6C2316yes—
278C4×Dic6C2311yescharacteristic
279C4×Dic6C2313yes—
280C4×Dic6C2311yescharacteristic
281C4×Dic6C2313yes—
282C4×Dic6C2316yes—
283C4×Dic6C2313yes—
284C2×H(5,𝔽2)—31no—
285C2×H(5,𝔽2)C2×D312yes—
286C22×#41—36no—
287#559—33no—
288#559—36no—
289#559—36no—
290#559—312no—
291Q82—31no—
292#557—31no—
293#557—32no—
294#557—31no—
295#556—33no—
296#556—36no—
297#555—312no—
298#555—36no—
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—33no—
309#550—36no—
310#550—312no—
311#550—36no—
312#550—312no—
313#550—36no—
314#550—36no—
315#550C2×D312yescomplemented
316#550C2×D312yescomplemented
317D4×Q8—33no—
318#548—36no—
319#547—312no—
320#547—36no—
321#546—312no—
322#546—312no—
323#546—324no—
324#546—324no—
325D42—312no—
326D42—312no—
327D42C2×D316yescomplemented
328D42C2×D316yescomplemented
329#540—312no—
330#540—312no—
331#540—312no—
332#538—312no—
333#538—324no—
334#535—36no—
335#535—36no—
336#535C2×D316yescomplemented
337#533—36no—
338#533—33no—
339#532—36no—
340#532—36no—
341#532—36no—
342#532—312no—
343#532—312no—
344#532C2×D313yescomplemented
345C2×#127—36no—
346C2×#127C2×D313yescomplemented
347#529—312no—
348#529—36no—
349#525—312no—
350#525—324no—
351C2×#121—36no—
352C2×#121—312no—
353#520—31no—
354#520—36no—
355#520—34no—
356#520—32no—
357#520—33no—
358#518—36no—
359#518—312no—
360#518—36no—
361#518—33no—
362C4×#41—32no—
363C4×#41—36no—
364C4×#41—34no—
365C4×#41—32no—
366C4×#41—36no—
367C4×#41—33no—
368C4×#41C2×D311yescharacteristic
369C2×C4×Q8—33no—
370C2×C4×D4—36no—
371C2×C4×D4—312no—
372C2×C4×D4—36no—
373C2×C4×D4—33no—
374C24×C3C24112yes—
375C23×D3C2416yes—
376C3×#41—216no—
377C3×#41—224no—
378C3×#41#4118yescomplemented
379C2×C3×Q8C2412yes—
380C2×C3×Q8C2411yescharacteristic
381C2×C3×D4—248no—
382C2×C3×D4—224no—
383C2×C3×D4—412no—
384C2×C3×D4—86no—
385C2×C3×D4C2416yes—
386C2×C3×D4C24112yes—
387C2×C3×D4C24112yes—
388C2×C3×D4C2416yes—
389C2×C3×D4C24112yes—
390C2×C3×D4C24112yes—
391C2×C3×D4C2416yes—
392C2×C3×D4C2413yes—
393C22×C3×C4C24112yes—
394C22×C3×C4C2413yes—
395C22×C3×C4C2413yes—
396C22×C3×C4C2413yes—
397C2×#67—424no—
398C2×#67—812no—
399C2×#67C2416yes—
400C2×#67C24112yes—
401C2×#67C24124yes—
402C2×#67C24112yes—
403C2×#67C24124yes—
404C22×Dic3—424no—
405C22×Dic3C24112yes—
406C22×Dic3C2416yes—
407C22×Dic3C2416yes—
408C22×Dic3C2416yes—
409C22×Dic3C24112yes—
410C22×Dic3C24124yes—
411#239—28no—
412#237—224no—
413#237—424no—
414#237—448no—
415#237—812no—
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—212no—
427C2×Dic6C2411yescharacteristic
428C2×Dic6C2413yes—
429C2×Dic6C2416yes—
430C2×Dic6C2416yes—
431C2×Dic6C2411yescharacteristic
432C3×C4⋊C4C2412yes—
433C3×C4⋊C4C2413yes—
434C3×C4⋊C4C2413yes—
435C3×C4⋊C4C2412yes—
436C3×C22⋊C4C24112yes—
437C3×C22⋊C4C2416yes—
438C3×C22⋊C4C24112yes—
439C3×C42C2411yescharacteristic
440C3×C42C2413yes—
441C3×C42C2413yes—
442C3×C42C2413yes—
443#217C24112yes—
444#217C24112yes—
445#217C24112yes—
446#217C24112yes—
447#217C2416yes—
448#217C24112yes—
449#217C24124yes—
450(C2×D3)⋊C4C2416yes—
451(C2×D3)⋊C4C2416yes—
452(C2×D3)⋊C4C24112yes—
453(C2×D3)⋊C4C24112yes—
454(C2×D3)⋊C4C24112yes—
455C4⋊Dic3C2411yescharacteristic
456C4⋊Dic3C2413yes—
457C4⋊Dic3C2416yes—
458C4⋊Dic3C2416yes—
459C4⋊Dic3C2413yes—
460C4⋊Dic3C2411yescharacteristic
461C4⋊Dic3C2416yes—
462C4⋊Dic3C2416yes—
463C4⋊Dic3C2416yes—
464C4⋊Dic3C24112yes—
465C4⋊Dic3C2414yes—
466Dic3⋊C4C2412yes—
467Dic3⋊C4C2416yes—
468Dic3⋊C4C2416yes—
469Dic3⋊C4C2416yes—
470Dic3⋊C4C24112yes—
471Dic3⋊C4C2412yes—
472Dic3⋊C4C2416yes—
473Dic3⋊C4C2414yes—
474Dic3⋊C4C2414yes—
475C4×Dic3C2412yes—
476C4×Dic3C2416yes—
477C4×Dic3C2416yes—
478C4×Dic3C2416yes—
479C4×Dic3C2412yes—
480C4×Dic3C2416yes—
481C4×Dic3C2416yes—
482C4×Dic3C24112yes—
483C4×Dic3C2414yes—
484H(5,𝔽2)—216no—
485H(5,𝔽2)—68no—
486C2×#41—32no—
487C2×#41—36no—
488C2×#41—324no—
489C2×#41—312no—
490C2×#41—312no—
491C2×#41—33no—
492C2×#41—1224no—
493C2×#41C22×D316yes—
494C2×#41C22×D314yes—
495C2×#41C22×D311yescharacteristic
496C22×Q8—33no—
497C22×D4—312no—
498C22×D4—312no—
499C22×D4—36no—
500C22×D4—33no—
501C22×D4C22×D316yes—
502C22×D4C22×D3112yes—
503C22×D4C22×D316yes—
504C22×D4C22×D316yes—
505C23×C4—312no—
506C23×C4—36no—
507C4⋊Q8—32no—
508C4⋊Q8—36no—
509C4⋊Q8—36no—
510C4⋊Q8—33no—
511C4⋊Q8—33no—
512C4⋊Q8C22×D311yescharacteristic
513#127—36no—
514#127—312no—
515#127—312no—
516#127—312no—
517#127C22×D313yes—
518#127C22×D316yes—
519#127C22×D316yes—
520#127C22×D316yes—
521#126—312no—
522#126—312no—
523#126—312no—
524#125—34no—
525#125—32no—
526#125—36no—
527#125—36no—
528#125—36no—
529#124—36no—
530#124—36no—
531#124—36no—
532#124—312no—
533#124—312no—
534#124—324no—
535#124C22×D316yes—
536#123—324no—
537#123—312no—
538#123—324no—
539#123—324no—
540#123—312no—
541#123—312no—
542C22⋊Q8—36no—
543C22⋊Q8—36no—
544C22⋊Q8—36no—
545C22⋊Q8—312no—
546C22⋊Q8—312no—
547C22⋊Q8—312no—
548#121—36no—
549#121—312no—
550#121—312no—
551#121—324no—
552#121—324no—
553#121—324no—
554#121—324no—
555#121—312no—
556#121—312no—
557#121—312no—
558#121—312no—
559#121—312no—
560#121—324no—
561#121—312no—
562#121—312no—
563#121C22×D316yes—
564#121C22×D3112yes—
565#121C22×D3112yes—
566#121C22×D316yes—
567#120—324no—
568#120—324no—
569#120C22×D3124yes—
570C4×Q8—32no—
571C4×Q8—32no—
572C4×Q8—32no—
573C4×Q8—32no—
574C4×Q8—36no—
575C4×Q8—32no—
576C4×Q8—31no—
577C4×Q8—33no—
578C4×Q8—36no—
579C4×Q8—33no—
580C4×Q8—36no—
581C4×Q8—33no—
582C4×Q8—31no—
583C4×Q8—33no—
584C4×Q8—36no—
585C4×Q8C22×D311yescharacteristic
586C4×Q8C22×D311yescharacteristic
587C4×D4—36no—
588C4×D4—36no—
589C4×D4—312no—
590C4×D4—312no—
591C4×D4—36no—
592C4×D4—324no—
593C4×D4—312no—
594C4×D4—312no—
595C4×D4—312no—
596C4×D4—312no—
597C4×D4—36no—
598C4×D4—312no—
599C4×D4—36no—
600C4×D4—36no—
601C4×D4—312no—
602C4×D4—36no—
603C4×D4—36no—
604C4×D4—312no—
605C4×D4—312no—
606C4×D4—36no—
607C4×D4—36no—
608C4×D4—312no—
609C4×D4—312no—
610C4×D4—324no—
611C4×D4—36no—
612C4×D4—33no—
613C4×D4—36no—
614C4×D4—36no—
615C4×D4—33no—
616C4×D4C22×D313yes—
617C4×D4C22×D316yes—
618C4×D4C22×D313yes—
619C4×D4C22×D316yes—
620#117—33no—
621#117—312no—
622#117—36no—
623#117—312no—
624#117—36no—
625#117—36no—
626#117—312no—
627#117—36no—
628#117C22×D313yes—
629C2×C4⋊C4—33no—
630C2×C4⋊C4—312no—
631C2×C4⋊C4—36no—
632C2×C4⋊C4—33no—
633C2×C4⋊C4—36no—
634C2×C22⋊C4—312no—
635C2×C22⋊C4—324no—
636C2×C22⋊C4—36no—
637C2×C22⋊C4—312no—
638C2×C42—36no—
639C2×C42—312no—
640C2×C42—36no—
641C2×C42C22×D313yes—
642C23×C3—224no—
643C23×C3—412no—
644C23×C3—412no—
645C23×C3C25112yes—
646C23×C3C2513yes—
647C22×D3—212no—
648C22×D3—46no—
649C22×D3—46no—
650C22×D3C2516yes—
651C3×Q8—24no—
652C3×Q8C2×#4114yescomplemented
653C3×D4—224no—
654C3×D4—212no—
655C3×D4—224no—
656C3×D4—212no—
657C3×D4—412no—
658C3×D4—412no—
659C3×D4—46no—
660C3×D4C2×#41112yescomplemented
661C2×C3×C4—224no—
662C2×C3×C4—26no—
663C2×C3×C4—43no—
664C2×C3×C4C2×#41112yescomplemented
665C2×C3×C4C2514yes—
666C2×C3×C4C2513yes—
667C2×C3×C4C2511yescharacteristic
668C2×C3×C4C2513yes—
669C2×C3×C4C2511yescharacteristic
670C2×C3×C4C2513yes—
671C2×C3×C4C2511yescharacteristic
672#67—212no—
673#67—224no—
674#67—424no—
675#67—424no—
676#67—412no—
677C2×Dic3—212no—
678C2×Dic3—224no—
679C2×Dic3—46no—
680C2×Dic3—424no—
681C2×Dic3—412no—
682C2×Dic3—46no—
683C2×Dic3C2512yes—
684C2×Dic3C2512yes—
685C2×Dic3C2512yes—
686C2×Dic3C2516yes—
687C2×Dic3C2516yes—
688C2×Dic3C2516yes—
689C2×Dic3C2512yes—
690D12—26no—
691D12—212no—
692C4×D3—212no—
693C4×D3—212no—
694C4×D3—412no—
695C4×D3—46no—
696Dic6—22no—
697Dic6—26no—
698Dic6—212no—
699Dic6—46no—
700Dic6H(5,𝔽2)14yescomplemented
701C24—36no—
702C24C23×D3112yes—
703#41—216no—
704#41—224no—
705#41—624no—
706#41—68no—
707#41—612no—
708#41—1224no—
709#41—1248no—
710#41—2412no—
711#41#23718yescomplemented
712C2×Q8—31no—
713C2×Q8—31no—
714C2×Q8—36no—
715C2×Q8—33no—
716C2×Q8—36no—
717C2×Q8—612no—
718C2×Q8C23×D312yes—
719C2×Q8C23×D311yescharacteristic
720C2×D4—248no—
721C2×D4—224no—
722C2×D4—36no—
723C2×D4—312no—
724C2×D4—324no—
725C2×D4—312no—
726C2×D4—324no—
727C2×D4—36no—
728C2×D4—33no—
729C2×D4—412no—
730C2×D4—624no—
731C2×D4—612no—
732C2×D4—86no—
733C2×D4—1224no—
734C2×D4—2412no—
735C2×D4C23×D3112yes—
736C2×D4C23×D3112yes—
737C2×D4C23×D316yes—
738C2×D4C23×D316yes—
739C2×D4C23×D3112yes—
740C2×D4C23×D316yes—
741C2×D4C23×D3112yes—
742C2×D4C23×D313yes—
743C22×C4—36no—
744C22×C4—312no—
745C22×C4—36no—
746C22×C4—312no—
747C22×C4—36no—
748C22×C4—324no—
749C22×C4—36no—
750C22×C4—36no—
751C22×C4—36no—
752C22×C4—312no—
753C22×C4—1212no—
754C22×C4—1224no—
755C22×C4C23×D3112yes—
756C22×C4C23×D313yes—
757C22×C4C23×D313yes—
758C22×C4C23×D313yes—
759C4⋊C4—36no—
760C4⋊C4—32no—
761C4⋊C4—31no—
762C4⋊C4—33no—
763C4⋊C4—36no—
764C4⋊C4—36no—
765C4⋊C4—312no—
766C4⋊C4—36no—
767C4⋊C4—33no—
768C4⋊C4—36no—
769C4⋊C4—36no—
770C4⋊C4—36no—
771C4⋊C4—31no—
772C4⋊C4—36no—
773C4⋊C4—34no—
774C4⋊C4—32no—
775C4⋊C4—34no—
776C4⋊C4—34no—
777C4⋊C4—312no—
778C4⋊C4—36no—
779C4⋊C4C23×D313yes—
780C4⋊C4C23×D312yes—
781C4⋊C4C23×D313yes—
782C4⋊C4C23×D312yes—
783C22⋊C4—36no—
784C22⋊C4—312no—
785C22⋊C4—312no—
786C22⋊C4—312no—
787C22⋊C4—324no—
788C22⋊C4—312no—
789C22⋊C4—312no—
790C22⋊C4—36no—
791C22⋊C4—36no—
792C22⋊C4—312no—
793C22⋊C4—312no—
794C22⋊C4—312no—
795C22⋊C4C23×D316yes—
796C22⋊C4C23×D3112yes—
797C22⋊C4C23×D3112yes—
798C42—36no—
799C42—34no—
800C42—32no—
801C42—36no—
802C42—32no—
803C42—36no—
804C42—312no—
805C42—36no—
806C42—36no—
807C42C23×D313yes—
808C42C23×D311yescharacteristic
809C42C23×D313yes—
810C42C23×D313yes—
811C22×C3—23no—
812C22×C3—23no—
813C22×C3—212no—
814C22×C3—212no—
815C22×C3—212no—
816C22×C3—824no—
817C22×C3C22×#4116yes—
818C22×C3C2611yescharacteristic
819C2×D3—26no—
820C2×D3—26no—
821C2×D3—26no—
822C2×D3—812no—
823C3×C4—24no—
824C3×C4—23no—
825C3×C4—23no—
826C3×C4—21no—
827C3×C4C22×#4112yes—
828C3×C4C22×#4116yes—
829C3×C4C2×H(5,𝔽2)12yes—
830Dic3—22no—
831Dic3—26no—
832Dic3—26no—
833Dic3—26no—
834Dic3—22no—
835Dic3—22no—
836Dic3C2×H(5,𝔽2)14yes—
837C23—224no—
838C23—36no—
839C23—412no—
840C23—412no—
841C23—612no—
842C23—126no—
843C23—126no—
844C23C24×D3112yes—
845C23C24×D313yes—
846Q8—24no—
847Q8—34no—
848Q8—612no—
849Q8—62no—
850Q8—66no—
851Q8—126no—
852Q8C2×#23714yescomplemented
853D4—224no—
854D4—224no—
855D4—212no—
856D4—212no—
857D4—412no—
858D4—46no—
859D4—412no—
860D4—624no—
861D4—612no—
862D4—612no—
863D4—66no—
864D4—1224no—
865D4—1212no—
866D4—1224no—
867D4C2×#237112yescomplemented
868C2×C4—224no—
869C2×C4—26no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—36no—
874C2×C4—36no—
875C2×C4—32no—
876C2×C4—36no—
877C2×C4—43no—
878C2×C4—612no—
879C2×C4—624no—
880C2×C4—612no—
881C2×C4—612no—
882C2×C4—1212no—
883C2×C4—126no—
884C2×C4—126no—
885C2×C4—1224no—
886C2×C4—126no—
887C2×C4—1212no—
888C2×C4C2×#237112yescomplemented
889C2×C4C24×D314yes—
890C2×C4C24×D313yes—
891C2×C4C24×D311yescharacteristic
892C2×C4C24×D313yes—
893C2×C4C24×D311yescharacteristic
894C2×C4C24×D313yes—
895C2×C4C24×D311yescharacteristic
896C2×C3—26no—
897C2×C3—412no—
898C2×C3C23×#4111yescharacteristic
899C2×C3C22×H(5,𝔽2)11yescharacteristic
900C2×C3H(7,𝔽2)11yescharacteristic
901D3—46no—
902C22—23no—
903C22—23no—
904C22—212no—
905C22—212no—
906C22—212no—
907C22—66no—
908C22—66no—
909C22—66no—
910C22—824no—
911C22—2412no—
912C22C22×#23716yes—
913C22C25×D311yescharacteristic
914C4—24no—
915C4—23no—
916C4—21no—
917C4—23no—
918C4—34no—
919C4—62no—
920C4—66no—
921C4—66no—
922C4—62no—
923C4—62no—
924C4—66no—
925C4C22×#23716yes—
926C4C22×#23712yes—
927C4D3×H(5,𝔽2)12yes—
928C3#6298611yescharacteristic, complemented, Sylow
929C2—26no—
930C2—412no—
931C2—126no—
932C2C23×#23711yescharacteristic
933C2C2×D3×H(5,𝔽2)11yescharacteristic
934C2#8756811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3498C2
hypercenter#3498D3
hypocenterC3#62986
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. C3×#3498C2semidirect
2. #87282C2semidirect
3. Dic3×H(5,𝔽2)C2semidirect
4. #86773C2semidirect
5. #86772C2semidirect
6. #86768C2semidirect
7. #86612C2semidirect
8. #86611C2semidirect
9. D4×#237C2semidirect
10. #86319C2semidirect
11. #86318C2semidirect
12. #86223C2semidirect
13. #86220C2semidirect
14. #86190C2semidirect
15. C2×#5718C2semidirect
16. C4×#1009C2semidirect
17. #41×Dic6C2semidirect
21. C22×#237C22semidirect
22. C3×#550C22semidirect
23. C3×#550C22semidirect
24. C3×D42C22semidirect
25. C3×D42C22semidirect
26. C3×#535C22semidirect
27. C3×#532C22semidirect
28. C2×C3×#127C22semidirect
30. #5834C22semidirect
31. #5834C22semidirect
32. #5832C22semidirect
33. #5830C22semidirect
35. #5827C22semidirect
36. #5827C22semidirect
38. Dic3×#41C22semidirect
39. Dic3×#41C22semidirect
40. #5806C22semidirect
41. #5806C22semidirect
42. #5805C22semidirect
43. C2×#940C22semidirect
44. C2×#939C22semidirect
45. D4×#67C22semidirect
46. D4×#67C22semidirect
47. C2×#938C22semidirect
48. #5798C22semidirect
49. #5798C22semidirect
50. C2×D4×Dic3C22semidirect
51. C2×D4×Dic3C22semidirect
52. #5732C22semidirect
53. #5721C22semidirect
54. #5719C22semidirect
55. #5718C22semidirect
56. #5718C22semidirect
57. #5718C22semidirect
58. #5718C22semidirect
59. #5718C22semidirect
60. #5718C22semidirect
61. #5718C22semidirect
62. #5716C22semidirect
63. #5716C22semidirect
64. #5713C22semidirect
65. #5713C22semidirect
66. #5681C22semidirect
67. #5681C22semidirect
68. #5671C22semidirect
69. #5619C22semidirect
70. #5619C22semidirect
71. #5618C22semidirect
72. #5618C22semidirect
73. #5617C22semidirect
74. #5616C22semidirect
75. #5614C22semidirect
76. #5611C22semidirect
77. #5606C22semidirect
78. #5601C22semidirect
79. #5598C22semidirect
80. #5596C22semidirect
81. #5596C22semidirect
82. #5593C22semidirect
83. #5591C22semidirect
84. #5591C22semidirect
85. #5586C22semidirect
86. #5574C22semidirect
87. C4×#239C22semidirect
88. #5570C22semidirect
89. #5569C22semidirect
90. Q8×Dic6C22semidirect
91. #5565C22semidirect
92. #5563C22semidirect
93. #5557C22semidirect
94. #5555C22semidirect
95. #5545C22semidirect
96. C4×D3×D4C22semidirect
97. #5543C22semidirect
98. #5539C22semidirect
99. #5538C22semidirect
100. D4×Dic6C22semidirect
101. C4×#237C22semidirect
102. #5523C22semidirect
103. #5521C22semidirect
104. #5517C22semidirect
105. C4×#235C22semidirect
106. C2×C4×D12C22semidirect
107. #5470C22semidirect
108. C2×C4×Dic6C22semidirect
118. #3498D3semidirect
315. #550C2×D3semidirect
316. #550C2×D3semidirect
327. D42C2×D3semidirect
328. D42C2×D3semidirect
336. #535C2×D3semidirect
344. #532C2×D3semidirect
346. C2×#127C2×D3semidirect
378. C3×#41#41semidirect
652. C3×Q8C2×#41semidirect
660. C3×D4C2×#41semidirect
664. C2×C3×C4C2×#41semidirect
700. Dic6H(5,𝔽2)semidirect
711. #41#237semidirect
852. Q8C2×#237semidirect
867. D4C2×#237semidirect
888. C2×C4C2×#237semidirect
928. C3#62986semidirect

Maximal subgroups

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

subgroupindex
C3×#34982
#872822
Dic3×H(5,𝔽2)2
#867732
#867722
#867682
#866122
#866112
D4×#2372
#863192
#863182
#862232
#862202
#861902
C2×#57182
C4×#10092
#41×Dic62
#629863