Finite Group Databasebeta

← #11707746

Subgroups — #11707746

Order 768.

7900 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3483C211yesmaximal, characteristic, complemented
2#87043C212yesmaximal, complemented
3#86966C2112yesmaximal, complemented
4#86964C216yesmaximal, complemented
5#86787C216yesmaximal, complemented
6D3×#550C212yesmaximal, complemented
7#86769C214yesmaximal, complemented
8#86251C213yesmaximal, complemented
9#86249C216yesmaximal, complemented
10#86242C213yesmaximal, complemented
11#86241C216yesmaximal, complemented
12#85853C212yesmaximal, complemented
13#85848C213yesmaximal, complemented
14#85846C211yesmaximal, characteristic, complemented
15#85844C211yesmaximal, characteristic, complemented
16#85843C213yesmaximal, complemented
17#41×D12C212yesmaximal, complemented
18#63014—31nomaximal, Sylow
19C2×#1009C2212yescomplemented
20C2×#1009C2216yescomplemented
21C2×D3×#41C2214yescomplemented
22C3×Q82C2211yescharacteristic, complemented
23C3×#555C2213yescomplemented
24C3×#555C2216yescomplemented
25C3×#550C2213yescomplemented
26C3×#550C2212yescomplemented
27C3×#550C2211yescharacteristic, complemented
28C3×#532C2216yescomplemented
29C3×#532C2213yescomplemented
30C3×C4×#41C2212yescomplemented
31C3×C4×#41C2213yescomplemented
32C3×C4×#41C2211yescharacteristic, complemented
33#5834C2214yescomplemented
34#5833C22112yescomplemented
35#5831C2212yescomplemented
36#5830C2216yescomplemented
37#5830C2216yescomplemented
38#5829C2216yescomplemented
39#5733C22112yescomplemented
40#5730C2216yescomplemented
41#5726C22112yescomplemented
42#5725C2216yescomplemented
43#5718C2216yescomplemented
44#5717C22112yescomplemented
45#5715C22112yescomplemented
46D3×#127C2216yescomplemented
47#5684C22112yescomplemented
48#5678C22124yescomplemented
49#5676C22124yescomplemented
50#5674C22112yescomplemented
51#5620C22124yescomplemented
52#5619C22112yescomplemented
53#5612C22112yescomplemented
54#5609C22112yescomplemented
55#5609C22112yescomplemented
56#5608C22112yescomplemented
57#5605C22124yescomplemented
58D3×#121C22112yescomplemented
59D3×#121C22112yescomplemented
60#5599C22112yescomplemented
61#5585C2216yescomplemented
62#5585C2213yescomplemented
63#5580C2216yescomplemented
64#5579C2211yescharacteristic, complemented
65#5577C2212yescomplemented
66#5577C2212yescomplemented
67#5576C2214yescomplemented
68Q8×D12C2211yescharacteristic, complemented
69#5574C2214yescomplemented
70C4×D3×Q8C2212yescomplemented
71#5570C2211yescharacteristic, complemented
72#5565C2216yescomplemented
73#5562C22112yescomplemented
74#5557C2216yescomplemented
75#5555C2216yescomplemented
76#5554C22112yescomplemented
77#5553C2216yescomplemented
78#5553C2216yescomplemented
79#5553C2216yescomplemented
80#5551C2213yescomplemented
81#5551C2216yescomplemented
82#5550C2216yescomplemented
83#5550C22112yescomplemented
84#5550C22112yescomplemented
85D4×D12C2216yescomplemented
86D4×D12C2216yescomplemented
87D4×D12C2213yescomplemented
88D4×D12C2216yescomplemented
89#5547C22112yescomplemented
90C4×D3×D4C2216yescomplemented
91#5543C2213yescomplemented
92#5542C2213yescomplemented
93#5535C22112yescomplemented
94#5530C2216yescomplemented
95#5530C22112yescomplemented
96#5529C2216yescomplemented
97#5527C22112yescomplemented
98#5525C2216yescomplemented
99#5524C22112yescomplemented
100#5521C2216yescomplemented
101#5479C2216yescomplemented
102#5477C2216yescomplemented
103#5477C2213yescomplemented
104#5477C2216yescomplemented
105C2×#874C2213yescomplemented
106C4×#235C2213yescomplemented
107C2×C4×D12C2216yescomplemented
108#5470C2213yescomplemented
109#3548—33no—
110#3546—36no—
111#3543—36no—
112#3542—312no—
113#3522—32no—
114#3519—36no—
115#3517—32no—
116#3508—33no—
117#3498—33no—
118#3498—31no—
119#3496—36no—
120#3488—34no—
121#3483D311yescharacteristic, complemented
122#3482—31no—
123#3481—33no—
124D4×#41—32no—
125C2×#550—32no—
126C2×C3×#41C2312yes—
127C2×C3×#41C2311yescharacteristic
128C2×C3×#41C2316yes—
129C2×C3×#41C2313yes—
130#1009—424no—
131#1009—48no—
132D3×#41—416no—
133C2×#239C2314yes—
134C2×#239C23112yes—
135C2×D3×Q8C2312yes—
136C2×#237C23112yes—
137C2×D3×D4C23112yes—
138C2×D3×D4C23124yes—
139C2×D3×D4C23112yes—
140C2×D3×D4C23112yes—
141C2×D3×D4C2316yes—
142C2×#235C2313yes—
143C2×#235C23112yes—
144C2×#235C2316yes—
145C2×#235C23112yes—
146C22×D12C2316yes—
147C22×D12C2316yes—
148C22×D12C2316yes—
149C22×D12C2316yes—
150C22×C4×D3C23112yes—
151C3×C4⋊Q8C2313yes—
152C3×C4⋊Q8C2316yes—
153C3×#127C2313yes—
154C3×#127C2316yes—
155C3×#124C2316yes—
156C3×#124C23112yes—
157C3×#121C2316yes—
158C3×#121C2316yes—
159C3×#121C23112yes—
160C3×#121C2316yes—
161C3×#121C2316yes—
162C3×C4×Q8C2311yescharacteristic
163C3×C4×Q8C2312yes—
164C3×C4×Q8C2313yes—
165C3×C4×Q8C2311yescharacteristic
166C3×C4×Q8C2311yescharacteristic
167C3×C4×D4C2313yes—
168C3×C4×D4C2313yes—
169C3×C4×D4C2313yes—
170C3×C4×D4C2316yes—
171C3×C4×D4C2313yes—
172C3×C4×D4C2316yes—
173C3×C4×D4C2316yes—
174C3×C4×D4C2316yes—
175C3×#117C2313yes—
176C3×#117C2316yes—
177C3×#117C2313yes—
178C3×#117C2316yes—
179C2×C3×C42C2313yes—
180C2×C3×C42C2316yes—
181#947C23112yes—
182#947C2316yes—
183#946C23124yes—
184#946C2312yes—
185Q8×Dic3C2312yes—
186#940C23112yes—
187#940C23112yes—
188#940C23112yes—
189#939C23124yes—
190#939C23124yes—
191#939C23112yes—
192#938C23124yes—
193#938C2316yes—
194#938C23112yes—
195#937C23124yes—
196#937C23124yes—
197#937C23112yes—
198#936C2316yes—
199D4×Dic3C2316yes—
200#930C2316yes—
201#930C23112yes—
202#930C23112yes—
203#930C23112yes—
204#930C2316yes—
205#930C23112yes—
206#930C2316yes—
207#929C23112yes—
208C4×#67C2316yes—
209C4×#67C2316yes—
210C4×#67C23112yes—
211C2×(C2×D3)⋊C4C23112yes—
212#926C2316yes—
213#926C2313yes—
214C2×C4⋊Dic3C2316yes—
215#924C2316yes—
216#924C2316yes—
217#924C2316yes—
218#898C23112yes—
219#897C23112yes—
220#897C2316yes—
221#896C2314yes—
222#895C2316yes—
223#895C23112yes—
224#895C23112yes—
225#895C23112yes—
226#894C23112yes—
227#894C23124yes—
228#894C23112yes—
229#893C23112yes—
230#893C23112yes—
231#893C2316yes—
232D3×C4⋊C4C2316yes—
233D3×C4⋊C4C23112yes—
234D3×C4⋊C4C2312yes—
235#890C2316yes—
236#890C2316yes—
237#887C2316yes—
238#886C23124yes—
239#884C23124yes—
240#884C23124yes—
241#884C23112yes—
242#884C23124yes—
243#883C23112yes—
244#883C23124yes—
245#883C23112yes—
246#882C23112yes—
247#882C23124yes—
248#882C23124yes—
249#67⋊C4C23112yes—
250D3×C22⋊C4C23112yes—
251D3×C22⋊C4C23124yes—
252#879C23112yes—
253#878C23112yes—
254#876C23112yes—
255#875C2316yes—
256#875C23112yes—
257#875C2316yes—
258#874C2316yes—
259#874C2316yes—
260#874C2313yes—
261#874C2316yes—
262C4×D12C23112yes—
263C4×D12C23112yes—
264C4×D12C23112yes—
265C4×D12C23112yes—
266C4×D12C23112yes—
267C4×D12C2316yes—
268C4×D12C2312yes—
269C4×D12C2313yes—
270C4×D12C2316yes—
271C4×D12C2316yes—
272C4×D12C2311yescharacteristic
273#872C2316yes—
274#872C23112yes—
275C42×D3C2316yes—
276#870C2316yes—
277#870C2312yes—
278#869C2313yes—
279#869C2313yes—
280#869C2311yescharacteristic
281C4×Dic6C2316yes—
282C4×Dic6C2313yes—
283C4×Dic6C2313yes—
284C2×H(5,𝔽2)—32no—
285C2×H(5,𝔽2)—36no—
286C22×#41—34no—
287#562—312no—
288#560—324no—
289#559—33no—
290#559—36no—
291Q82C2×D311yescharacteristic, complemented
292#557—31no—
293#556—33no—
294#555C2×D313yescomplemented
295#555C2×D316yescomplemented
296#554—36no—
297#554—31no—
298#554—33no—
299#553—36no—
300#553—36no—
301#553—312no—
302#552—36no—
303#551—312no—
304#550—34no—
305#550—36no—
306#550—312no—
307#550—32no—
308#550—32no—
309#550—36no—
310#550—36no—
311#550—36no—
312#550C2×D311yescharacteristic, complemented
313#550C2×D312yescomplemented
314#550C2×D313yescomplemented
315D4×Q8—31no—
316#548—32no—
317#548—34no—
318#547—312no—
319#547—36no—
320#547—33no—
321#547—36no—
322#546—36no—
323#546—324no—
324#546—312no—
325#546—312no—
326#546—36no—
327#546—312no—
328#546—312no—
329D42—312no—
330D42—312no—
331D42—312no—
332D42—36no—
333D42—33no—
334D42—36no—
335D42—36no—
336#542—312no—
337#540—312no—
338#540—312no—
339#540—312no—
340#538—324no—
341#537—312no—
342#537—312no—
343#535—36no—
344#535—36no—
345#535—312no—
346#535—312no—
347#535—36no—
348#534—324no—
349#533—33no—
350#532—36no—
351#532—36no—
352#532—33no—
353#532—36no—
354#532C2×D316yescomplemented
355#532C2×D313yescomplemented
356C2×#127—36no—
357C2×#127—33no—
358#529—36no—
359#529—36no—
360#529—36no—
361#525—312no—
362#525—312no—
363C2×#121—312no—
364C2×#121—312no—
365#520—34no—
366#518—36no—
367C4×#41—33no—
368C4×#41C2×D312yescomplemented
369C4×#41C2×D313yescomplemented
370C4×#41C2×D311yescharacteristic, complemented
371C2×C4×Q8—32no—
372C2×C4×D4—36no—
373C2×C4×D4—36no—
374C23×D3C24112yes—
375C23×D3C24112yes—
376C3×#41—28no—
377C3×#41—24no—
378C3×#41—412no—
379C3×#41—46no—
380C2×C3×Q8C2411yescharacteristic
381C2×C3×Q8C2416yes—
382C2×C3×Q8C2411yescharacteristic
383C2×C3×D4C2413yes—
384C2×C3×D4C2413yes—
385C2×C3×D4C2416yes—
386C2×C3×D4C2416yes—
387C2×C3×D4C24112yes—
388C2×C3×D4C2416yes—
389C22×C3×C4C2413yes—
390C22×C3×C4C2413yes—
391C22×C3×C4C2416yes—
392C22×C3×C4C2413yes—
393C22×C3×C4C2416yes—
394C22×C3×C4C2416yes—
395C2×#67C2416yes—
396C2×#67C24112yes—
397C2×#67C24112yes—
398C2×#67C24124yes—
399C2×#67C24124yes—
400C22×Dic3C24112yes—
401#239—216no—
402#239—424no—
403D3×Q8—28no—
404#237—424no—
405D3×D4—412no—
406D3×D4—424no—
407D3×D4—424no—
408D3×D4—424no—
409D3×D4—448no—
410#235—212no—
411#235—424no—
412#235—424no—
413#235—412no—
414C2×D12—224no—
415C2×D12—412no—
416C2×D12—412no—
417C2×D12—412no—
418C2×D12C2416yes—
419C2×D12C24112yes—
420C2×D12C2416yes—
421C2×D12C24112yes—
422C2×D12C24112yes—
423C2×D12C2416yes—
424C2×D12C24112yes—
425C2×D12C2411yescharacteristic
426C2×C4×D3—424no—
427C2×C4×D3C2412yes—
428C2×C4×D3C2416yes—
429C2×C4×D3C2416yes—
430C2×C4×D3C24112yes—
431C2×C4×D3C2414yes—
432C2×C4×D3C24112yes—
433C2×C4×D3C24124yes—
434C2×Dic6C2413yes—
435C2×Dic6C2416yes—
436C2×Dic6C2412yes—
437C3×C4⋊C4C2413yes—
438C3×C4⋊C4C2413yes—
439C3×C4⋊C4C2413yes—
440C3×C4⋊C4C2411yescharacteristic
441C3×C4⋊C4C2416yes—
442C3×C4⋊C4C2412yes—
443C3×C4⋊C4C2416yes—
444C3×C22⋊C4C2416yes—
445C3×C22⋊C4C2416yes—
446C3×C22⋊C4C2416yes—
447C3×C22⋊C4C2416yes—
448C3×C22⋊C4C24112yes—
449C3×C42C2411yescharacteristic
450C3×C42C2413yes—
451C3×C42C2413yes—
452C3×C42C2413yes—
453C3×C42C2412yes—
454C3×C42C2416yes—
455C3×C42C2416yes—
456#217C24112yes—
457#217C2416yes—
458#217C24112yes—
459(C2×D3)⋊C4C2412yes—
460(C2×D3)⋊C4C2416yes—
461(C2×D3)⋊C4C24112yes—
462(C2×D3)⋊C4C24112yes—
463(C2×D3)⋊C4C2414yes—
464(C2×D3)⋊C4C24112yes—
465(C2×D3)⋊C4C24112yes—
466(C2×D3)⋊C4C24112yes—
467(C2×D3)⋊C4C24112yes—
468(C2×D3)⋊C4C24124yes—
469C4⋊Dic3C2411yescharacteristic
470C4⋊Dic3C2413yes—
471C4⋊Dic3C2416yes—
472C4⋊Dic3C2412yes—
473C4⋊Dic3C2416yes—
474C4⋊Dic3C2416yes—
475C4⋊Dic3C2412yes—
476C4⋊Dic3C24112yes—
477Dic3⋊C4C2416yes—
478Dic3⋊C4C24112yes—
479Dic3⋊C4C2416yes—
480Dic3⋊C4C2414yes—
481Dic3⋊C4C2414yes—
482Dic3⋊C4C24112yes—
483C4×Dic3C2416yes—
484C4×Dic3C2416yes—
485C4×Dic3C2416yes—
486H(5,𝔽2)—1224no—
487H(5,𝔽2)—128no—
488C2×#41—34no—
489C2×#41—312no—
490C2×#41—312no—
491C2×#41—33no—
492C2×#41—36no—
493C2×#41—312no—
494C2×#41—312no—
495C2×#41—1216no—
496C2×#41C22×D311yescharacteristic
497C2×#41C22×D312yes—
498C2×#41C22×D313yes—
499C2×#41C22×D316yes—
500C22×Q8—32no—
501C22×D4—36no—
502C22×D4—312no—
503C22×D4—312no—
504C22×D4—324no—
505C22×D4—312no—
506C22×D4—36no—
507C22×D4—36no—
508C22×D4—36no—
509C22×D4—36no—
510C23×C4—312no—
511C4⋊Q8—31no—
512C4⋊Q8—33no—
513C4⋊Q8—33no—
514C4⋊Q8C22×D313yes—
515C4⋊Q8C22×D316yes—
516#127—312no—
517#127—312no—
518#127—312no—
519#127—36no—
520#127—33no—
521#127—36no—
522#127—36no—
523#127C22×D313yes—
524#127C22×D316yes—
525#126—312no—
526#126—312no—
527#126—312no—
528#125—36no—
529#125—36no—
530#125—32no—
531#125—36no—
532#124—36no—
533#124—312no—
534#124—36no—
535#124—36no—
536#124—36no—
537#124—312no—
538#124C22×D316yes—
539#124C22×D3112yes—
540#123—312no—
541#123—312no—
542#123—312no—
543#123—324no—
544#123—312no—
545#123—324no—
546#123—312no—
547#123—324no—
548C22⋊Q8—32no—
549C22⋊Q8—324no—
550C22⋊Q8—36no—
551C22⋊Q8—36no—
552C22⋊Q8—36no—
553C22⋊Q8—34no—
554C22⋊Q8—36no—
555C22⋊Q8—312no—
556C22⋊Q8—312no—
557#121—36no—
558#121—324no—
559#121—324no—
560#121—312no—
561#121—312no—
562#121—324no—
563#121—312no—
564#121—36no—
565#121—312no—
566#121—312no—
567#121—312no—
568#121—36no—
569#121—36no—
570#121—312no—
571#121—312no—
572#121—312no—
573#121—36no—
574#121—312no—
575#121—324no—
576#121—324no—
577#121—324no—
578#121C22×D316yes—
579#121C22×D316yes—
580#121C22×D3112yes—
581#121C22×D316yes—
582#121C22×D316yes—
583#120—312no—
584#120—324no—
585#120—324no—
586#120—324no—
587#120—312no—
588#120—324no—
589C4×Q8—32no—
590C4×Q8—36no—
591C4×Q8—36no—
592C4×Q8—33no—
593C4×Q8—33no—
594C4×Q8C22×D311yescharacteristic
595C4×Q8C22×D311yescharacteristic
596C4×Q8C22×D311yescharacteristic
597C4×Q8C22×D312yes—
598C4×Q8C22×D313yes—
599C4×D4—36no—
600C4×D4—312no—
601C4×D4—36no—
602C4×D4—36no—
603C4×D4—36no—
604C4×D4—312no—
605C4×D4—312no—
606C4×D4—312no—
607C4×D4—32no—
608C4×D4—33no—
609C4×D4—312no—
610C4×D4—312no—
611C4×D4—36no—
612C4×D4—36no—
613C4×D4—36no—
614C4×D4—31no—
615C4×D4—312no—
616C4×D4—312no—
617C4×D4—312no—
618C4×D4C22×D313yes—
619C4×D4C22×D316yes—
620C4×D4C22×D313yes—
621C4×D4C22×D313yes—
622C4×D4C22×D316yes—
623C4×D4C22×D313yes—
624C4×D4C22×D316yes—
625C4×D4C22×D316yes—
626#117—33no—
627#117—36no—
628#117—36no—
629#117—312no—
630#117C22×D313yes—
631#117C22×D316yes—
632#117C22×D313yes—
633#117C22×D316yes—
634C2×C4⋊C4—36no—
635C2×C4⋊C4—32no—
636C2×C4⋊C4—36no—
637C2×C4⋊C4—312no—
638C2×C22⋊C4—312no—
639C2×C22⋊C4—312no—
640C2×C22⋊C4—324no—
641C2×C42—36no—
642C2×C42C22×D316yes—
643C2×C42C22×D313yes—
644C23×C3C2513yes—
645C23×C3C2516yes—
646C22×D3—224no—
647C22×D3—412no—
648C22×D3—412no—
649C22×D3—412no—
650C22×D3—412no—
651C22×D3—412no—
652C22×D3C25112yes—
653C22×D3C2512yes—
654C3×Q8—22no—
655C3×Q8—46no—
656C3×Q8H(5,𝔽2)14yescomplemented
657C3×D4—26no—
658C3×D4—212no—
659C3×D4—26no—
660C3×D4—46no—
661C3×D4—412no—
662C3×D4—46no—
663C2×C3×C4—212no—
664C2×C3×C4—212no—
665C2×C3×C4—26no—
666C2×C3×C4—26no—
667C2×C3×C4—26no—
668C2×C3×C4—46no—
669C2×C3×C4C2513yes—
670C2×C3×C4C2511yescharacteristic
671C2×C3×C4C2513yes—
672C2×C3×C4C2516yes—
673C2×C3×C4C2512yes—
674C2×C3×C4C2512yes—
675C2×C3×C4C2513yes—
676C2×C3×C4C2511yescharacteristic
677C2×C3×C4C2511yescharacteristic
678#67—212no—
679#67—424no—
680#67—412no—
681#67—424no—
682#67—412no—
683C2×Dic3—412no—
684C2×Dic3C2512yes—
685C2×Dic3C2516yes—
686C2×Dic3C2516yes—
687C2×Dic3C2514yes—
688D12—224no—
689D12—212no—
690D12—224no—
691D12—212no—
692D12—46no—
693D12—412no—
694D12—412no—
695D12H(5,𝔽2)14yescomplemented
696C4×D3—212no—
697C4×D3—212no—
698C4×D3—224no—
699C4×D3—24no—
700C4×D3—44no—
701C4×D3—412no—
702C4×D3—424no—
703Dic6—26no—
704Dic6—212no—
705Dic6—42no—
706C24—312no—
707C24—312no—
708#41—28no—
709#41—24no—
710#41—412no—
711#41—46no—
712#41—612no—
713#41—616no—
714#41—1212no—
715#41—1224no—
716#41—1224no—
717#41—1224no—
718#41—1224no—
719C2×Q8—36no—
720C2×Q8—33no—
721C2×Q8—32no—
722C2×Q8—68no—
723C2×Q8C23×D311yescharacteristic
724C2×Q8C23×D316yes—
725C2×Q8C23×D311yescharacteristic
726C2×D4—36no—
727C2×D4—312no—
728C2×D4—312no—
729C2×D4—324no—
730C2×D4—324no—
731C2×D4—31no—
732C2×D4—36no—
733C2×D4—312no—
734C2×D4—312no—
735C2×D4—36no—
736C2×D4—312no—
737C2×D4—312no—
738C2×D4—36no—
739C2×D4—624no—
740C2×D4—1212no—
741C2×D4—1212no—
742C2×D4—1212no—
743C2×D4—1224no—
744C2×D4—1224no—
745C2×D4—1212no—
746C2×D4—1224no—
747C2×D4—1248no—
748C2×D4C23×D313yes—
749C2×D4C23×D313yes—
750C2×D4C23×D316yes—
751C2×D4C23×D316yes—
752C2×D4C23×D3112yes—
753C2×D4C23×D316yes—
754C22×C4—312no—
755C22×C4—32no—
756C22×C4—36no—
757C22×C4—36no—
758C22×C4—312no—
759C22×C4—34no—
760C22×C4—312no—
761C22×C4—324no—
762C22×C4—1224no—
763C22×C4C23×D316yes—
764C22×C4C23×D313yes—
765C22×C4C23×D313yes—
766C22×C4C23×D316yes—
767C22×C4C23×D313yes—
768C22×C4C23×D316yes—
769C4⋊C4—32no—
770C4⋊C4—36no—
771C4⋊C4—33no—
772C4⋊C4—312no—
773C4⋊C4—32no—
774C4⋊C4—34no—
775C4⋊C4—312no—
776C4⋊C4—312no—
777C4⋊C4—31no—
778C4⋊C4—34no—
779C4⋊C4—36no—
780C4⋊C4—36no—
781C4⋊C4—36no—
782C4⋊C4—36no—
783C4⋊C4C23×D311yescharacteristic
784C4⋊C4C23×D316yes—
785C4⋊C4C23×D313yes—
786C4⋊C4C23×D313yes—
787C4⋊C4C23×D312yes—
788C4⋊C4C23×D313yes—
789C4⋊C4C23×D316yes—
790C22⋊C4—312no—
791C22⋊C4—312no—
792C22⋊C4—36no—
793C22⋊C4—34no—
794C22⋊C4—312no—
795C22⋊C4—36no—
796C22⋊C4—312no—
797C22⋊C4—324no—
798C22⋊C4—312no—
799C22⋊C4—312no—
800C22⋊C4—32no—
801C22⋊C4—312no—
802C22⋊C4—312no—
803C22⋊C4C23×D316yes—
804C22⋊C4C23×D316yes—
805C22⋊C4C23×D316yes—
806C22⋊C4C23×D316yes—
807C22⋊C4C23×D3112yes—
808C42—36no—
809C42—36no—
810C42—36no—
811C42C23×D313yes—
812C42C23×D312yes—
813C42C23×D313yes—
814C42C23×D311yescharacteristic
815C42C23×D313yes—
816C42C23×D316yes—
817C42C23×D316yes—
818C22×C3—26no—
819C22×C3—23no—
820C22×C3—23no—
821C22×C3—26no—
822C22×C3—26no—
823C22×C3—23no—
824C22×C3C2611yescharacteristic
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—212no—
828C2×D3—212no—
829C2×D3—212no—
830C2×D3—824no—
831C2×D3—1612no—
832C2×D3C2×H(5,𝔽2)14yes—
833C3×C4—21no—
834C3×C4—23no—
835C3×C4—22no—
836C3×C4—26no—
837C3×C4—23no—
838C3×C4—22no—
839C3×C4C2×H(5,𝔽2)16yes—
840C3×C4C2×H(5,𝔽2)12yes—
841C3×C4#58512yes—
842Dic3—26no—
843Dic3—26no—
844Dic3—24no—
845Dic3—22no—
846C23—32no—
847C23—312no—
848C23—624no—
849C23—1212no—
850C23—1212no—
851C23—1212no—
852C23—1212no—
853C23—1212no—
854C23C24×D313yes—
855C23C24×D316yes—
856Q8—22no—
857Q8—46no—
858Q8—612no—
859Q8—66no—
860Q8—122no—
861Q8#100914yescomplemented
862D4—26no—
863D4—212no—
864D4—26no—
865D4—34no—
866D4—46no—
867D4—412no—
868D4—46no—
869D4—624no—
870D4—612no—
871D4—624no—
872D4—612no—
873D4—612no—
874D4—126no—
875D4—1212no—
876D4—1212no—
877D4—1212no—
878D4—1224no—
879D4—1224no—
880D4—1212no—
881C2×C4—212no—
882C2×C4—26no—
883C2×C4—26no—
884C2×C4—212no—
885C2×C4—26no—
886C2×C4—32no—
887C2×C4—36no—
888C2×C4—36no—
889C2×C4—34no—
890C2×C4—46no—
891C2×C4—612no—
892C2×C4—612no—
893C2×C4—624no—
894C2×C4—64no—
895C2×C4—124no—
896C2×C4—1212no—
897C2×C4—1224no—
898C2×C4—1212no—
899C2×C4C24×D313yes—
900C2×C4C24×D312yes—
901C2×C4C24×D313yes—
902C2×C4C24×D312yes—
903C2×C4C24×D311yescharacteristic
904C2×C4C24×D316yes—
905C2×C4C24×D313yes—
906C2×C4C24×D311yescharacteristic
907C2×C4C24×D311yescharacteristic
908C2×C3—46no—
909C2×C3—43no—
910C2×C3C22×H(5,𝔽2)11yescharacteristic
911C2×C3C22×H(5,𝔽2)11yescharacteristic
912C2×C3C2×#58511yescharacteristic
913D3—24no—
914D3—412no—
915C22—26no—
916C22—23no—
917C22—23no—
918C22—26no—
919C22—23no—
920C22—26no—
921C22—34no—
922C22—62no—
923C22—62no—
924C22—612no—
925C22—612no—
926C22—612no—
927C22—2424no—
928C22—4812no—
929C22C25×D311yescharacteristic
930C4—22no—
931C4—21no—
932C4—23no—
933C4—22no—
934C4—23no—
935C4—26no—
936C4—64no—
937C4—66no—
938C4—62no—
939C4—66no—
940C4C2×#100916yes—
941C4#596412yes—
942C4D3×H(5,𝔽2)12yes—
943C3#6301411yescharacteristic, complemented, Sylow
944C2—46no—
945C2—43no—
946C2—64no—
947C2—1212no—
948C2C22×#100911yescharacteristic
949C2C2×#596411yescharacteristic
950C2C2×D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3483C2
hypercenter#3483D3
hypocenterC3#63014
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3483

Complements

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

NH ≅ G/Ntype
1. C3×#3483C2semidirect
2. #87043C2semidirect
3. #86966C2semidirect
4. #86964C2semidirect
5. #86787C2semidirect
6. D3×#550C2semidirect
7. #86769C2semidirect
8. #86251C2semidirect
9. #86249C2semidirect
10. #86242C2semidirect
11. #86241C2semidirect
12. #85853C2semidirect
13. #85848C2semidirect
14. #85846C2semidirect
15. #85844C2semidirect
16. #85843C2semidirect
17. #41×D12C2semidirect
19. C2×#1009C22semidirect
20. C2×#1009C22semidirect
21. C2×D3×#41C22semidirect
22. C3×Q82C22semidirect
23. C3×#555C22semidirect
24. C3×#555C22semidirect
25. C3×#550C22semidirect
26. C3×#550C22semidirect
27. C3×#550C22semidirect
28. C3×#532C22semidirect
29. C3×#532C22semidirect
30. C3×C4×#41C22semidirect
31. C3×C4×#41C22semidirect
32. C3×C4×#41C22semidirect
33. #5834C22semidirect
34. #5833C22semidirect
35. #5831C22semidirect
36. #5830C22semidirect
37. #5830C22semidirect
38. #5829C22semidirect
39. #5733C22semidirect
40. #5730C22semidirect
41. #5726C22semidirect
42. #5725C22semidirect
43. #5718C22semidirect
44. #5717C22semidirect
45. #5715C22semidirect
46. D3×#127C22semidirect
47. #5684C22semidirect
48. #5678C22semidirect
49. #5676C22semidirect
50. #5674C22semidirect
51. #5620C22semidirect
52. #5619C22semidirect
53. #5612C22semidirect
54. #5609C22semidirect
55. #5609C22semidirect
56. #5608C22semidirect
57. #5605C22semidirect
58. D3×#121C22semidirect
59. D3×#121C22semidirect
60. #5599C22semidirect
61. #5585C22semidirect
62. #5585C22semidirect
63. #5580C22semidirect
64. #5579C22semidirect
65. #5577C22semidirect
66. #5577C22semidirect
67. #5576C22semidirect
68. Q8×D12C22semidirect
69. #5574C22semidirect
70. C4×D3×Q8C22semidirect
71. #5570C22semidirect
72. #5565C22semidirect
73. #5562C22semidirect
74. #5557C22semidirect
75. #5555C22semidirect
76. #5554C22semidirect
77. #5553C22semidirect
78. #5553C22semidirect
79. #5553C22semidirect
80. #5551C22semidirect
81. #5551C22semidirect
82. #5550C22semidirect
83. #5550C22semidirect
84. #5550C22semidirect
85. D4×D12C22semidirect
86. D4×D12C22semidirect
87. D4×D12C22semidirect
88. D4×D12C22semidirect
89. #5547C22semidirect
90. C4×D3×D4C22semidirect
91. #5543C22semidirect
92. #5542C22semidirect
93. #5535C22semidirect
94. #5530C22semidirect
95. #5530C22semidirect
96. #5529C22semidirect
97. #5527C22semidirect
98. #5525C22semidirect
99. #5524C22semidirect
100. #5521C22semidirect
101. #5479C22semidirect
102. #5477C22semidirect
103. #5477C22semidirect
104. #5477C22semidirect
105. C2×#874C22semidirect
106. C4×#235C22semidirect
107. C2×C4×D12C22semidirect
108. #5470C22semidirect
121. #3483D3semidirect
291. Q82C2×D3semidirect
294. #555C2×D3semidirect
295. #555C2×D3semidirect
312. #550C2×D3semidirect
313. #550C2×D3semidirect
314. #550C2×D3semidirect
354. #532C2×D3semidirect
355. #532C2×D3semidirect
368. C4×#41C2×D3semidirect
369. C4×#41C2×D3semidirect
370. C4×#41C2×D3semidirect
656. C3×Q8H(5,𝔽2)semidirect
695. D12H(5,𝔽2)semidirect
861. Q8#1009semidirect
943. C3#63014semidirect

Maximal subgroups

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

subgroupindex
C3×#34832
#870432
#869662
#869642
#867872
D3×#5502
#867692
#862512
#862492
#862422
#862412
#858532
#858482
#858462
#858442
#858432
#41×D122
#630143