Finite Group Databasebeta

← #11707759

Subgroups — #11707759

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×#3482C211yesmaximal, characteristic, complemented
2#87023C212yesmaximal, complemented
3#87009C216yesmaximal, complemented
4#86846C2112yesmaximal, complemented
5D4×#239C212yesmaximal, complemented
6#86713C214yesmaximal, complemented
7#86702C216yesmaximal, complemented
8#86288C213yesmaximal, complemented
9#86261C213yesmaximal, complemented
10#86172C216yesmaximal, complemented
11#86166C216yesmaximal, complemented
12#85846C213yesmaximal, complemented
13#85846C211yesmaximal, characteristic, complemented
14#85845C211yesmaximal, characteristic, complemented
15#85843C213yesmaximal, complemented
16#85821C212yesmaximal, complemented
17C2×#5577C212yesmaximal, complemented
18#63014—31nomaximal, Sylow
19C2×#1009C2216yescomplemented
20C2×#1009C2212yescomplemented
21C22×#239C2214yescomplemented
22C3×#557C2211yescharacteristic, complemented
23C3×#556C2213yescomplemented
24C3×#552C2216yescomplemented
25C3×D4×Q8C2211yescharacteristic, complemented
26C3×#548C2212yescomplemented
27C3×#547C2213yescomplemented
28C3×#533C2213yescomplemented
29C3×#529C2216yescomplemented
30C3×C4×#41C2213yescomplemented
31C3×C4×#41C2211yescharacteristic, complemented
32C2×C3×C4×Q8C2212yescomplemented
33#5834C2212yescomplemented
34#5829C2216yescomplemented
35#5817C2214yescomplemented
36#5726C2216yescomplemented
37#5726C2216yescomplemented
38#5725C2216yescomplemented
39#5725C2216yescomplemented
40#5711C22124yescomplemented
41#5704C22124yescomplemented
42#5700C22112yescomplemented
43#5697C22112yescomplemented
44#5697C22112yescomplemented
45#5695C22112yescomplemented
46#5676C22112yescomplemented
47#5674C22112yescomplemented
48#5654C22124yescomplemented
49#5653C22124yescomplemented
50#5630C22112yescomplemented
51#5630C22112yescomplemented
52#5630C22112yescomplemented
53#5629C22112yescomplemented
54#5629C22112yescomplemented
55#5627C22112yescomplemented
56#5609C22112yescomplemented
57D3×#121C22112yescomplemented
58#5585C2216yescomplemented
59#5585C2213yescomplemented
60#5582C22112yescomplemented
61#5580C2216yescomplemented
62#5579C2213yescomplemented
63#5579C2216yescomplemented
64#5577C2216yescomplemented
65#5577C2216yescomplemented
66#5577C2211yescharacteristic, complemented
67#5577C2212yescomplemented
68#5577C22112yescomplemented
69#5577C2216yescomplemented
70#5577C2214yescomplemented
71#5577C2212yescomplemented
72#5577C2216yescomplemented
73#5574C2214yescomplemented
74C4×#239C2212yescomplemented
75Q8×Dic6C2211yescharacteristic, complemented
76#5565C2216yescomplemented
77#5563C2213yescomplemented
78#5553C2213yescomplemented
79#5550C2216yescomplemented
80D4×D12C22112yescomplemented
81D4×D12C2213yescomplemented
82D4×D12C2216yescomplemented
83D4×D12C22112yescomplemented
84D4×D12C2216yescomplemented
85D4×D12C2216yescomplemented
86#5548C2216yescomplemented
87#5547C22112yescomplemented
88C4×D3×D4C2216yescomplemented
89#5543C2211yescharacteristic, complemented
90#5535C22112yescomplemented
91#5532C2216yescomplemented
92#5530C2216yescomplemented
93#5527C22112yescomplemented
94#5525C2216yescomplemented
95#5525C22112yescomplemented
96#5525C2216yescomplemented
97#5525C2216yescomplemented
98#5521C2216yescomplemented
99#5507C22112yescomplemented
100C2×#895C22112yescomplemented
101#5479C2216yescomplemented
102#5477C2213yescomplemented
103#5477C2213yescomplemented
104#5477C2216yescomplemented
105C2×#874C2216yescomplemented
106C2×#874C2213yescomplemented
107C4×#235C2213yescomplemented
108C2×C4×D12C2216yescomplemented
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#3483—31no—
122#3482D311yescharacteristic, complemented
123#3481—33no—
124D4×#41—32no—
125C2×#550—32no—
126C2×C3×#41C2313yes—
127C2×C3×#41C2311yescharacteristic
128C22×C3×Q8C2312yes—
129#1009—424no—
130#1009—48no—
131C2×#239—416no—
132C2×#239C2312yes—
133C2×#239C2314yes—
134C2×#239C23112yes—
135C2×#239C23112yes—
136C2×#239C23112yes—
137C2×D3×D4C2316yes—
138C2×D3×D4C23124yes—
139C2×D3×D4C23112yes—
140C2×#235C23112yes—
141C2×#235C2316yes—
142C2×#235C2316yes—
143C2×#235C2313yes—
144C22×D12C23112yes—
145C22×D12C23112yes—
146C22×D12C2316yes—
147C22×D12C2316yes—
148C22×D12C2316yes—
149C22×D12C2316yes—
150C22×C4×D3C23112yes—
151C3×C4⋊Q8C2313yes—
152C3×C4⋊Q8C2313yes—
153C3×#126C23112yes—
154C3×#125C2316yes—
155C3×#125C2316yes—
156C3×#124C2316yes—
157C3×#123C23112yes—
158C3×C22⋊Q8C2316yes—
159C3×C22⋊Q8C2316yes—
160C3×C22⋊Q8C2316yes—
161C3×#121C2316yes—
162C3×C4×Q8C2311yescharacteristic
163C3×C4×Q8C2311yescharacteristic
164C3×C4×Q8C2312yes—
165C3×C4×Q8C2316yes—
166C3×C4×Q8C2313yes—
167C3×C4×Q8C2313yes—
168C3×C4×Q8C2316yes—
169C3×C4×D4C2311yescharacteristic
170C3×C4×D4C2313yes—
171C3×C4×D4C2316yes—
172C3×C4×D4C2313yes—
173C3×C4×D4C2316yes—
174C3×C4×D4C2313yes—
175C3×#117C2316yes—
176C3×#117C2316yes—
177C3×#117C2313yes—
178C3×#117C2313yes—
179C2×C3×C4⋊C4C2316yes—
180C2×C3×C42C2316yes—
181C2×C3×C42C2313yes—
182#947C23112yes—
183#947C2316yes—
184#946C23112yes—
185#946C2316yes—
186Q8×Dic3C2312yes—
187#940C2316yes—
188#939C23112yes—
189#938C2316yes—
190#937C23112yes—
191D4×Dic3C2312yes—
192#930C2316yes—
193#930C23112yes—
194#930C2316yes—
195#930C2316yes—
196#930C2316yes—
197#930C2316yes—
198#929C23112yes—
199C4×#67C2316yes—
200C4×#67C2316yes—
201C4×#67C23112yes—
202C2×(C2×D3)⋊C4C23112yes—
203#926C2313yes—
204C2×C4⋊Dic3C2312yes—
205#924C2312yes—
206#898C23112yes—
207#896C23124yes—
208#896C23112yes—
209#895C23112yes—
210#895C23124yes—
211#895C23124yes—
212#895C23124yes—
213#895C23112yes—
214#895C23112yes—
215#895C23124yes—
216#895C23112yes—
217#895C23112yes—
218#895C23112yes—
219#895C2316yes—
220#895C23112yes—
221#895C2316yes—
222#894C23124yes—
223#894C23124yes—
224#894C23112yes—
225#894C23112yes—
226#894C23124yes—
227#893C23112yes—
228#893C2316yes—
229#893C23112yes—
230#893C23112yes—
231#893C2316yes—
232#892C2316yes—
233D3×C4⋊C4C23112yes—
234D3×C4⋊C4C2316yes—
235#890C2312yes—
236#888C2316yes—
237#885C23112yes—
238#884C23112yes—
239#884C23124yes—
240#884C23124yes—
241#884C23112yes—
242#883C23112yes—
243#882C23124yes—
244#882C23124yes—
245#882C23124yes—
246#882C23124yes—
247#882C23112yes—
248#67⋊C4C23112yes—
249D3×C22⋊C4C23112yes—
250D3×C22⋊C4C23124yes—
251#878C2314yes—
252#876C23112yes—
253#875C2316yes—
254#875C2316yes—
255#875C23112yes—
256#875C2316yes—
257#874C23112yes—
258#874C2316yes—
259#874C23112yes—
260#874C2316yes—
261#874C2316yes—
262#874C2313yes—
263#874C2313yes—
264#874C23112yes—
265C4×D12C23112yes—
266C4×D12C23112yes—
267C4×D12C23112yes—
268C4×D12C2316yes—
269C4×D12C2316yes—
270C4×D12C2313yes—
271C4×D12C2316yes—
272C4×D12C2316yes—
273C4×D12C2316yes—
274C4×D12C2313yes—
275C4×D12C23112yes—
276#872C23112yes—
277#872C2316yes—
278C42×D3C2316yes—
279#870C2316yes—
280#869C2311yescharacteristic
281#869C2313yes—
282C4×Dic6C2311yescharacteristic
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—
291Q82—31no—
292#557C2×D311yescharacteristic, complemented
293#556C2×D313yescomplemented
294#555—33no—
295#555—36no—
296#554—33no—
297#554—36no—
298#554—31no—
299#553—312no—
300#553—36no—
301#553—36no—
302#552C2×D316yescomplemented
303#551—312no—
304#550—32no—
305#550—31no—
306#550—34no—
307#550—32no—
308#550—36no—
309#550—312no—
310#550—36no—
311#550—32no—
312#550—36no—
313#550—36no—
314#550—33no—
315D4×Q8C2×D311yescharacteristic, complemented
316#548—34no—
317#548C2×D312yescomplemented
318#547—36no—
319#547—36no—
320#547—312no—
321#547C2×D313yescomplemented
322#546—36no—
323#546—312no—
324#546—324no—
325#546—312no—
326#546—312no—
327#546—312no—
328#546—36no—
329D42—312no—
330D42—36no—
331D42—33no—
332D42—312no—
333D42—36no—
334D42—36no—
335D42—312no—
336#542—312no—
337#540—312no—
338#540—312no—
339#540—312no—
340#538—324no—
341#537—312no—
342#537—312no—
343#535—312no—
344#535—312no—
345#535—36no—
346#535—36no—
347#535—36no—
348#534—324no—
349#533C2×D313yescomplemented
350#532—36no—
351#532—36no—
352#532—36no—
353#532—33no—
354#532—33no—
355#532—36no—
356C2×#127—36no—
357C2×#127—33no—
358#529—36no—
359#529—36no—
360#529C2×D316yescomplemented
361#525—312no—
362#525—312no—
363C2×#121—312no—
364C2×#121—312no—
365#520—34no—
366#518—36no—
367C4×#41—32no—
368C4×#41—33no—
369C4×#41C2×D313yescomplemented
370C4×#41C2×D311yescharacteristic, complemented
371C2×C4×Q8C2×D312yescomplemented
372C2×C4×D4—36no—
373C2×C4×D4—36no—
374C23×D3C24112yes—
375C23×D3C24112yes—
376C3×#41—24no—
377C3×#41—212no—
378C2×C3×Q8—28no—
379C2×C3×Q8C2416yes—
380C2×C3×Q8C2413yes—
381C2×C3×Q8C2411yescharacteristic
382C2×C3×D4C2416yes—
383C2×C3×D4C2413yes—
384C2×C3×D4C2411yescharacteristic
385C22×C3×C4C2412yes—
386C22×C3×C4C2413yes—
387C22×C3×C4C2416yes—
388C22×C3×C4C2416yes—
389C22×C3×C4C2413yes—
390C22×C3×C4C2413yes—
391C2×#67C24112yes—
392C2×#67C2416yes—
393C2×#67C24112yes—
394C2×#67C24112yes—
395C22×Dic3C2414yes—
396#239—28no—
397#239—216no—
398#239—424no—
399#239—424no—
400#239—424no—
401D3×D4—224no—
402D3×D4—424no—
403D3×D4—448no—
404#235—46no—
405#235—412no—
406#235—412no—
407#235—424no—
408C2×D12—412no—
409C2×D12—412no—
410C2×D12—424no—
411C2×D12—412no—
412C2×D12—412no—
413C2×D12—424no—
414C2×D12C2413yes—
415C2×D12C2416yes—
416C2×D12C2416yes—
417C2×D12C2416yes—
418C2×D12C24112yes—
419C2×D12C24112yes—
420C2×D12C2416yes—
421C2×D12C24112yes—
422C2×D12C2416yes—
423C2×D12C24112yes—
424C2×D12C24124yes—
425C2×D12C24124yes—
426C2×C4×D3—424no—
427C2×C4×D3C2416yes—
428C2×C4×D3C2416yes—
429C2×C4×D3C24112yes—
430C2×C4×D3C2416yes—
431C2×C4×D3C24112yes—
432C2×C4×D3C24112yes—
433C2×C4×D3C24124yes—
434C2×Dic6C2411yescharacteristic
435C2×Dic6C2412yes—
436C2×Dic6C2416yes—
437C3×C4⋊C4C2413yes—
438C3×C4⋊C4C2411yescharacteristic
439C3×C4⋊C4C2416yes—
440C3×C4⋊C4C2413yes—
441C3×C4⋊C4C2413yes—
442C3×C4⋊C4C2416yes—
443C3×C4⋊C4C2416yes—
444C3×C4⋊C4C24112yes—
445C3×C4⋊C4C2416yes—
446C3×C4⋊C4C2416yes—
447C3×C22⋊C4C2412yes—
448C3×C22⋊C4C2416yes—
449C3×C22⋊C4C24112yes—
450C3×C22⋊C4C2416yes—
451C3×C22⋊C4C2416yes—
452C3×C42C2411yescharacteristic
453C3×C42C2413yes—
454C3×C42C2416yes—
455C3×C42C2413yes—
456C3×C42C2416yes—
457C3×C42C2413yes—
458C3×C42C2416yes—
459#217C2414yes—
460#217C2416yes—
461(C2×D3)⋊C4C2416yes—
462(C2×D3)⋊C4C24112yes—
463(C2×D3)⋊C4C2416yes—
464(C2×D3)⋊C4C24112yes—
465(C2×D3)⋊C4C24112yes—
466(C2×D3)⋊C4C24112yes—
467(C2×D3)⋊C4C24112yes—
468(C2×D3)⋊C4C24112yes—
469(C2×D3)⋊C4C24124yes—
470(C2×D3)⋊C4C24112yes—
471(C2×D3)⋊C4C24112yes—
472C4⋊Dic3C2413yes—
473C4⋊Dic3C2411yescharacteristic
474C4⋊Dic3C2412yes—
475C4⋊Dic3C2416yes—
476C4⋊Dic3C2412yes—
477C4⋊Dic3C2414yes—
478Dic3⋊C4C2412yes—
479Dic3⋊C4C2416yes—
480Dic3⋊C4C24112yes—
481Dic3⋊C4C24112yes—
482Dic3⋊C4C2414yes—
483C4×Dic3C2412yes—
484C4×Dic3C2416yes—
485C4×Dic3C2416yes—
486H(5,𝔽2)—1224no—
487H(5,𝔽2)—128no—
488C2×#41—32no—
489C2×#41—34no—
490C2×#41—312no—
491C2×#41—312no—
492C2×#41—312no—
493C2×#41—33no—
494C2×#41—36no—
495C2×#41—36no—
496C2×#41—312no—
497C2×#41—1216no—
498C2×#41C22×D313yes—
499C2×#41C22×D311yescharacteristic
500C22×Q8C22×D312yes—
501C22×D4—36no—
502C22×D4—324no—
503C22×D4—312no—
504C22×D4—36no—
505C22×D4—36no—
506C22×D4—312no—
507C22×D4—312no—
508C22×D4—36no—
509C22×D4—36no—
510C23×C4—312no—
511C4⋊Q8—36no—
512C4⋊Q8—31no—
513C4⋊Q8—33no—
514C4⋊Q8C22×D313yes—
515C4⋊Q8C22×D313yes—
516#127—36no—
517#127—36no—
518#127—33no—
519#127—33no—
520#127—36no—
521#127—36no—
522#127—312no—
523#127—312no—
524#127—312no—
525#126—312no—
526#126—312no—
527#126C22×D3112yes—
528#125—32no—
529#125—36no—
530#125C22×D316yes—
531#125C22×D316yes—
532#124—36no—
533#124—312no—
534#124—312no—
535#124—36no—
536#124—312no—
537#124—36no—
538#124—36no—
539#124C22×D316yes—
540#123—312no—
541#123—324no—
542#123—312no—
543#123—312no—
544#123—324no—
545#123—324no—
546#123—312no—
547#123C22×D3112yes—
548C22⋊Q8—312no—
549C22⋊Q8—36no—
550C22⋊Q8—32no—
551C22⋊Q8—312no—
552C22⋊Q8—324no—
553C22⋊Q8—34no—
554C22⋊Q8C22×D316yes—
555C22⋊Q8C22×D316yes—
556C22⋊Q8C22×D316yes—
557#121—312no—
558#121—36no—
559#121—312no—
560#121—36no—
561#121—36no—
562#121—36no—
563#121—36no—
564#121—36no—
565#121—312no—
566#121—36no—
567#121—324no—
568#121—312no—
569#121—312no—
570#121—324no—
571#121—312no—
572#121—36no—
573#121—312no—
574#121—312no—
575#121—312no—
576#121—324no—
577#121—324no—
578#121—324no—
579#121—312no—
580#121—312no—
581#121—324no—
582#121C22×D316yes—
583#120—312no—
584#120—324no—
585#120—312no—
586#120—324no—
587#120—324no—
588#120—324no—
589C4×Q8—32no—
590C4×Q8—31no—
591C4×Q8—33no—
592C4×Q8C22×D311yescharacteristic
593C4×Q8C22×D312yes—
594C4×Q8C22×D316yes—
595C4×Q8C22×D316yes—
596C4×Q8C22×D311yescharacteristic
597C4×Q8C22×D313yes—
598C4×Q8C22×D313yes—
599C4×D4—32no—
600C4×D4—312no—
601C4×D4—36no—
602C4×D4—36no—
603C4×D4—36no—
604C4×D4—36no—
605C4×D4—312no—
606C4×D4—312no—
607C4×D4—312no—
608C4×D4—312no—
609C4×D4—33no—
610C4×D4—36no—
611C4×D4—312no—
612C4×D4—36no—
613C4×D4—36no—
614C4×D4—312no—
615C4×D4—36no—
616C4×D4—36no—
617C4×D4—33no—
618C4×D4—312no—
619C4×D4—312no—
620C4×D4C22×D313yes—
621C4×D4C22×D311yescharacteristic
622C4×D4C22×D316yes—
623C4×D4C22×D316yes—
624C4×D4C22×D313yes—
625C4×D4C22×D313yes—
626#117—33no—
627#117—36no—
628#117—36no—
629#117—312no—
630#117C22×D316yes—
631#117C22×D313yes—
632#117C22×D313yes—
633#117C22×D316yes—
634C2×C4⋊C4—32no—
635C2×C4⋊C4—36no—
636C2×C4⋊C4—312no—
637C2×C4⋊C4C22×D316yes—
638C2×C22⋊C4—312no—
639C2×C22⋊C4—312no—
640C2×C22⋊C4—324no—
641C2×C42—36no—
642C2×C42C22×D316yes—
643C2×C42C22×D313yes—
644C23×C3C2513yes—
645C23×C3C2512yes—
646C22×D3—224no—
647C22×D3—412no—
648C22×D3—412no—
649C22×D3—412no—
650C22×D3—412no—
651C22×D3—412no—
652C22×D3C25112yes—
653C22×D3C2516yes—
654C3×Q8—212no—
655C3×Q8—26no—
656C3×Q8H(5,𝔽2)14yescomplemented
657C3×D4—212no—
658C3×D4—26no—
659C3×D4H(5,𝔽2)14yescomplemented
660C2×C3×C4—212no—
661C2×C3×C4—212no—
662C2×C3×C4—26no—
663C2×C3×C4—26no—
664C2×C3×C4—24no—
665C2×C3×C4—26no—
666C2×C3×C4C2513yes—
667C2×C3×C4C2512yes—
668C2×C3×C4C2511yescharacteristic
669C2×C3×C4C2513yes—
670C2×C3×C4C2516yes—
671C2×C3×C4C2516yes—
672C2×C3×C4C2513yes—
673C2×C3×C4C2511yescharacteristic
674C2×C3×C4C2511yescharacteristic
675#67—224no—
676#67—412no—
677#67—412no—
678#67—46no—
679C2×Dic3—44no—
680C2×Dic3C2512yes—
681C2×Dic3C2512yes—
682C2×Dic3C2516yes—
683C2×Dic3C2514yes—
684D12—212no—
685D12—224no—
686D12—212no—
687D12—212no—
688D12—26no—
689D12—46no—
690D12—46no—
691D12—412no—
692D12—412no—
693D12—412no—
694D12—424no—
695D12—424no—
696C4×D3—212no—
697C4×D3—224no—
698C4×D3—212no—
699C4×D3—412no—
700C4×D3—412no—
701C4×D3—46no—
702C4×D3—424no—
703Dic6—22no—
704Dic6—46no—
705Dic6—42no—
706C24—312no—
707C24—312no—
708#41—24no—
709#41—212no—
710#41—68no—
711#41—616no—
712#41—1212no—
713#41—1212no—
714#41—1224no—
715#41—126no—
716#41—1224no—
717#41—1224no—
718#41—1224no—
719C2×Q8—28no—
720C2×Q8—31no—
721C2×Q8—32no—
722C2×Q8—36no—
723C2×Q8C23×D316yes—
724C2×Q8C23×D313yes—
725C2×Q8C23×D311yescharacteristic
726C2×D4—312no—
727C2×D4—36no—
728C2×D4—312no—
729C2×D4—312no—
730C2×D4—36no—
731C2×D4—33no—
732C2×D4—36no—
733C2×D4—312no—
734C2×D4—36no—
735C2×D4—312no—
736C2×D4—312no—
737C2×D4—324no—
738C2×D4—36no—
739C2×D4—312no—
740C2×D4—324no—
741C2×D4—36no—
742C2×D4—624no—
743C2×D4—1224no—
744C2×D4—1212no—
745C2×D4—1212no—
746C2×D4—1212no—
747C2×D4—1212no—
748C2×D4—1224no—
749C2×D4—1224no—
750C2×D4—1248no—
751C2×D4C23×D316yes—
752C2×D4C23×D313yes—
753C2×D4C23×D311yescharacteristic
754C22×C4—34no—
755C22×C4—36no—
756C22×C4—36no—
757C22×C4—312no—
758C22×C4—36no—
759C22×C4—312no—
760C22×C4—324no—
761C22×C4—312no—
762C22×C4—1224no—
763C22×C4C23×D312yes—
764C22×C4C23×D316yes—
765C22×C4C23×D316yes—
766C22×C4C23×D313yes—
767C22×C4C23×D313yes—
768C22×C4C23×D313yes—
769C4⋊C4—32no—
770C4⋊C4—31no—
771C4⋊C4—36no—
772C4⋊C4—312no—
773C4⋊C4—32no—
774C4⋊C4—34no—
775C4⋊C4—312no—
776C4⋊C4—32no—
777C4⋊C4—34no—
778C4⋊C4—33no—
779C4⋊C4—36no—
780C4⋊C4C23×D316yes—
781C4⋊C4C23×D313yes—
782C4⋊C4C23×D313yes—
783C4⋊C4C23×D3112yes—
784C4⋊C4C23×D313yes—
785C4⋊C4C23×D311yescharacteristic
786C4⋊C4C23×D316yes—
787C4⋊C4C23×D316yes—
788C4⋊C4C23×D316yes—
789C4⋊C4C23×D316yes—
790C22⋊C4—36no—
791C22⋊C4—34no—
792C22⋊C4—312no—
793C22⋊C4—36no—
794C22⋊C4—312no—
795C22⋊C4—324no—
796C22⋊C4—312no—
797C22⋊C4—312no—
798C22⋊C4—312no—
799C22⋊C4—312no—
800C22⋊C4—312no—
801C22⋊C4—36no—
802C22⋊C4—312no—
803C22⋊C4C23×D316yes—
804C22⋊C4C23×D3112yes—
805C22⋊C4C23×D312yes—
806C22⋊C4C23×D316yes—
807C22⋊C4C23×D316yes—
808C42—32no—
809C42—36no—
810C42—36no—
811C42C23×D313yes—
812C42C23×D313yes—
813C42C23×D311yescharacteristic
814C42C23×D313yes—
815C42C23×D316yes—
816C42C23×D316yes—
817C42C23×D316yes—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—23no—
821C22×C3—23no—
822C22×C3—23no—
823C22×C3C2×H(5,𝔽2)14yes—
824C22×C3C2611yescharacteristic
825C2×D3—26no—
826C2×D3—212no—
827C2×D3—26no—
828C2×D3—212no—
829C2×D3—26no—
830C2×D3—212no—
831C2×D3—824no—
832C2×D3—1612no—
833C3×C4—23no—
834C3×C4—21no—
835C3×C4—26no—
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—24no—
844Dic3—22no—
845Dic3—22no—
846C23—312no—
847C23—36no—
848C23—624no—
849C23—1212no—
850C23—1212no—
851C23—1212no—
852C23—1212no—
853C23—1212no—
854C23C24×D313yes—
855C23C24×D312yes—
856Q8—212no—
857Q8—26no—
858Q8—62no—
859Q8—122no—
860Q8—126no—
861Q8#100914yescomplemented
862D4—212no—
863D4—26no—
864D4—624no—
865D4—612no—
866D4—624no—
867D4—612no—
868D4—612no—
869D4—66no—
870D4—126no—
871D4—126no—
872D4—1212no—
873D4—1224no—
874D4—1224no—
875D4—1212no—
876D4—1212no—
877D4—1212no—
878D4—1212no—
879D4—126no—
880D4#100914yescomplemented
881C2×C4—212no—
882C2×C4—212no—
883C2×C4—26no—
884C2×C4—26no—
885C2×C4—24no—
886C2×C4—26no—
887C2×C4—32no—
888C2×C4—32no—
889C2×C4—36no—
890C2×C4—34no—
891C2×C4—612no—
892C2×C4—624no—
893C2×C4—612no—
894C2×C4—1212no—
895C2×C4—1212no—
896C2×C4—1224no—
897C2×C4—126no—
898C2×C4—124no—
899C2×C4C24×D313yes—
900C2×C4C24×D312yes—
901C2×C4C24×D311yescharacteristic
902C2×C4C24×D313yes—
903C2×C4C24×D316yes—
904C2×C4C24×D316yes—
905C2×C4C24×D313yes—
906C2×C4C24×D311yescharacteristic
907C2×C4C24×D311yescharacteristic
908C2×C3—24no—
909C2×C3—43no—
910C2×C3C22×H(5,𝔽2)11yescharacteristic
911C2×C3C22×H(5,𝔽2)11yescharacteristic
912C2×C3C2×#58511yescharacteristic
913D3—46no—
914D3—412no—
915C22—22no—
916C22—22no—
917C22—23no—
918C22—23no—
919C22—23no—
920C22—66no—
921C22—612no—
922C22—66no—
923C22—612no—
924C22—66no—
925C22—612no—
926C22—2424no—
927C22—4812no—
928C22C2×#100914yes—
929C22C25×D311yescharacteristic
930C4—23no—
931C4—21no—
932C4—26no—
933C4—26no—
934C4—23no—
935C4—22no—
936C4—62no—
937C4—64no—
938C4—66no—
939C4—62no—
940C4C2×#100916yes—
941C4C2×#100912yes—
942C4#596812yes—
943C3#6301411yescharacteristic, complemented, Sylow
944C2—24no—
945C2—43no—
946C2—126no—
947C2—1212no—
948C2C22×#100911yescharacteristic
949C2C22×#100911yescharacteristic
950C2C2×#596811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3482C2
hypercenter#3482D3
hypocenterC3#63014
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. C3×#3482C2semidirect
2. #87023C2semidirect
3. #87009C2semidirect
4. #86846C2semidirect
5. D4×#239C2semidirect
6. #86713C2semidirect
7. #86702C2semidirect
8. #86288C2semidirect
9. #86261C2semidirect
10. #86172C2semidirect
11. #86166C2semidirect
12. #85846C2semidirect
13. #85846C2semidirect
14. #85845C2semidirect
15. #85843C2semidirect
16. #85821C2semidirect
17. C2×#5577C2semidirect
19. C2×#1009C22semidirect
20. C2×#1009C22semidirect
21. C22×#239C22semidirect
22. C3×#557C22semidirect
23. C3×#556C22semidirect
24. C3×#552C22semidirect
25. C3×D4×Q8C22semidirect
26. C3×#548C22semidirect
27. C3×#547C22semidirect
28. C3×#533C22semidirect
29. C3×#529C22semidirect
30. C3×C4×#41C22semidirect
31. C3×C4×#41C22semidirect
32. C2×C3×C4×Q8C22semidirect
33. #5834C22semidirect
34. #5829C22semidirect
35. #5817C22semidirect
36. #5726C22semidirect
37. #5726C22semidirect
38. #5725C22semidirect
39. #5725C22semidirect
40. #5711C22semidirect
41. #5704C22semidirect
42. #5700C22semidirect
43. #5697C22semidirect
44. #5697C22semidirect
45. #5695C22semidirect
46. #5676C22semidirect
47. #5674C22semidirect
48. #5654C22semidirect
49. #5653C22semidirect
50. #5630C22semidirect
51. #5630C22semidirect
52. #5630C22semidirect
53. #5629C22semidirect
54. #5629C22semidirect
55. #5627C22semidirect
56. #5609C22semidirect
57. D3×#121C22semidirect
58. #5585C22semidirect
59. #5585C22semidirect
60. #5582C22semidirect
61. #5580C22semidirect
62. #5579C22semidirect
63. #5579C22semidirect
64. #5577C22semidirect
65. #5577C22semidirect
66. #5577C22semidirect
67. #5577C22semidirect
68. #5577C22semidirect
69. #5577C22semidirect
70. #5577C22semidirect
71. #5577C22semidirect
72. #5577C22semidirect
73. #5574C22semidirect
74. C4×#239C22semidirect
75. Q8×Dic6C22semidirect
76. #5565C22semidirect
77. #5563C22semidirect
78. #5553C22semidirect
79. #5550C22semidirect
80. D4×D12C22semidirect
81. D4×D12C22semidirect
82. D4×D12C22semidirect
83. D4×D12C22semidirect
84. D4×D12C22semidirect
85. D4×D12C22semidirect
86. #5548C22semidirect
87. #5547C22semidirect
88. C4×D3×D4C22semidirect
89. #5543C22semidirect
90. #5535C22semidirect
91. #5532C22semidirect
92. #5530C22semidirect
93. #5527C22semidirect
94. #5525C22semidirect
95. #5525C22semidirect
96. #5525C22semidirect
97. #5525C22semidirect
98. #5521C22semidirect
99. #5507C22semidirect
100. C2×#895C22semidirect
101. #5479C22semidirect
102. #5477C22semidirect
103. #5477C22semidirect
104. #5477C22semidirect
105. C2×#874C22semidirect
106. C2×#874C22semidirect
107. C4×#235C22semidirect
108. C2×C4×D12C22semidirect
122. #3482D3semidirect
292. #557C2×D3semidirect
293. #556C2×D3semidirect
302. #552C2×D3semidirect
315. D4×Q8C2×D3semidirect
317. #548C2×D3semidirect
321. #547C2×D3semidirect
349. #533C2×D3semidirect
360. #529C2×D3semidirect
369. C4×#41C2×D3semidirect
370. C4×#41C2×D3semidirect
371. C2×C4×Q8C2×D3semidirect
656. C3×Q8H(5,𝔽2)semidirect
659. C3×D4H(5,𝔽2)semidirect
861. Q8#1009semidirect
880. D4#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×#34822
#870232
#870092
#868462
D4×#2392
#867132
#867022
#862882
#862612
#861722
#861662
#858462
#858452
#858432
#858212
C2×#55772
#630143