Finite Group Databasebeta

← #11707296

Subgroups — #11707296

Order 768.

7406 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3503C211yesmaximal, characteristic, complemented
2#87041C214yesmaximal, complemented
3#87018C212yesmaximal, complemented
4#87015C212yesmaximal, complemented
5#86949C2112yesmaximal, complemented
6#86761C216yesmaximal, complemented
7D3×D4×Q8C216yesmaximal, complemented
8#86599C216yesmaximal, complemented
9#86586C216yesmaximal, complemented
10#86280C213yesmaximal, complemented
11#86277C213yesmaximal, complemented
12#86215C213yesmaximal, complemented
13C2×#5727C213yesmaximal, complemented
14#85889C212yesmaximal, complemented
15#85886C212yesmaximal
16C4×#1009C211yesmaximal, characteristic
17#41×Dic6C211yesmaximal, characteristic, complemented
18Q8×H(5,𝔽2)—31nomaximal, Sylow
19C2×#1009C2211yescharacteristic
20C22×D3×Q8C2216yescomplemented
21C3×Q82C2212yescomplemented
22C3×#557C2212yescomplemented
23C3×#554C2216yescomplemented
24C3×D4×Q8C2216yescomplemented
25C3×#544C2216yescomplemented
26C3×#533C2213yescomplemented
27C2×C3×C4⋊Q8C2213yescomplemented
28C3×#520C2212yes—
29C3×C4×#41C2211yescharacteristic
30#5827C2211yescharacteristic
31Dic3×#41C2212yes—
32Q8×#67C22112yescomplemented
33C2×#946C2216yescomplemented
34#5730C22112yescomplemented
35#5730C2213yescomplemented
36#5730C2216yescomplemented
37#5729C22112yescomplemented
38#5729C22112yescomplemented
39#5728C2216yescomplemented
40#5727C22112yescomplemented
41#5727C22112yescomplemented
42#5727C2213yescomplemented
43#5727C2216yescomplemented
44#5727C22112yescomplemented
45#5727C2216yescomplemented
46#5727C2216yescomplemented
47D3×C4⋊Q8C22112yescomplemented
48D3×C4⋊Q8C2216yescomplemented
49#5722C2211yescharacteristic, complemented
50#5722C2216yescomplemented
51#5721C2213yescomplemented
52#5690C2216yescomplemented
53#5690C22112yescomplemented
54#5690C22112yescomplemented
55#5690C22112yescomplemented
56#5689C22112yescomplemented
57#5688C22112yescomplemented
58#5685C2216yescomplemented
59#5636C22112yescomplemented
60#5636C22124yescomplemented
61#5635C2216yescomplemented
62#5634C22112yescomplemented
63#5634C22124yescomplemented
64#5632C2216yescomplemented
65#5632C22124yescomplemented
66D3×C22⋊Q8C22112yescomplemented
67D3×C22⋊Q8C22124yescomplemented
68#5579C22112yescomplemented
69#5579C2216yescomplemented
70#5578C22112yescomplemented
71#5578C2216yescomplemented
72Q8×D12C2216yescomplemented
73#5574C2212yes—
74#5574C2214yes—
75C4×#239C2214yes—
76C4×#239C2212yes—
77C4×D3×Q8C2216yescomplemented
78#5570C2211yescharacteristic, complemented
79#5569C2212yescomplemented
80#5569C2214yescomplemented
81Q8×Dic6C2214yescomplemented
82Q8×Dic6C2211yescharacteristic, complemented
83#5545C2216yes—
84#5545C22112yes—
85C4×D3×D4C2216yes—
86C4×D3×D4C22112yes—
87#5543C2213yescomplemented
88#5539C2216yescomplemented
89#5539C22112yescomplemented
90D4×Dic6C2213yescomplemented
91D4×Dic6C22112yescomplemented
92#5523C2213yes—
93#5522C2216yes—
94#5521C2216yes—
95#5521C2213yes—
96#5519C2216yescomplemented
97#5517C2216yescomplemented
98#5517C2216yescomplemented
99#5511C22112yescomplemented
100C2×#896C22112yescomplemented
101#5504C2216yes—
102C2×#893C2216yes—
103#5500C2216yescomplemented
104C2×#888C2216yescomplemented
105C4×#235C2213yes—
106C2×C4×D12C2213yes—
107#5470C2213yescomplemented
108C2×C4×Dic6C2213yescomplemented
109#3503—34no—
110#3503—32no—
111#3503—36no—
112#3503—33no—
113#3503—32no—
114#3503D311yescharacteristic, complemented
115#3501—312no—
116#3501—36no—
117#3501—36no—
118#3501—33no—
119Q8×#41—32no—
120Q8×#41—33no—
121Q8×#41—31no—
122C2×D4×Q8—36no—
123C2×D4×Q8—33no—
124C4×H(5,𝔽2)—32no—
125C4×H(5,𝔽2)—31no—
126C2×C3×#41C2311yescharacteristic
127C22×C3×Q8C2316yes—
128#1009Q8116yescomplemented
129C2×#239C2312yes—
130C2×D3×Q8—424no—
131C2×D3×Q8C2316yes—
132C2×D3×Q8C23124yes—
133C2×D3×Q8C23112yes—
134C2×D3×D4C2316yes—
135C2×#235C2313yes—
136C22×D12C2313yes—
137C22×C4×D3C2316yes—
138C22×C4×D3C23112yes—
139C22×Dic6C2313yes—
140C22×Dic6C23112yes—
141C3×C4⋊Q8C23112yes—
142C3×C4⋊Q8C2316yes—
143C3×C4⋊Q8C2313yes—
144C3×C4⋊Q8C2316yes—
145C3×C4⋊Q8C2311yescharacteristic
146C3×C4⋊Q8C2316yes—
147C3×#125C2316yes—
148C3×#125C23112yes—
149C3×C22⋊Q8C23124yes—
150C3×C22⋊Q8C2316yes—
151C3×C22⋊Q8C2316yes—
152C3×C4×Q8C2311yescharacteristic
153C3×C4×Q8C2314yes—
154C3×C4×Q8C2316yes—
155C3×C4×Q8C2311yescharacteristic
156C3×C4×Q8C2316yes—
157C3×C4×D4C23112yes—
158C3×C4×D4C2313yes—
159C3×C4×D4C2313yes—
160C3×#117C2313yes—
161C3×#117C2316yes—
162C2×C3×C4⋊C4C2316yes—
163C2×C3×C4⋊C4C2316yes—
164C2×C3×C42C2313yes—
165#946C23112yes—
166#946C23124yes—
167#946C23124yes—
168#946C2316yes—
169#946C23112yes—
170Q8×Dic3C2316yes—
171Q8×Dic3C2312yes—
172Q8×Dic3C2312yes—
173Q8×Dic3C2312yes—
174#944C23124yes—
175#944C2316yes—
176#944C2314yes—
177D4×Dic3C2316yes—
178D4×Dic3C2316yes—
179D4×Dic3C2316yes—
180C4×#67C2316yes—
181C4×#67C23124yes—
182C4×#67C2316yes—
183C2×(C2×D3)⋊C4C2316yes—
184C2×(C2×D3)⋊C4C23112yes—
185#926C2316yes—
186#926C2313yes—
187C2×C4⋊Dic3C2313yes—
188C2×C4⋊Dic3C2313yes—
189#924C2316yes—
190#924C23124yes—
191#924C2316yes—
192C2×Dic3⋊C4C2316yes—
193C2×Dic3⋊C4C23112yes—
194C2×C4×Dic3C2316yes—
195#897C23124yes—
196#897C2316yes—
197#897C23112yes—
198#897C23112yes—
199#896C23124yes—
200#896C23124yes—
201#896C23112yes—
202#896C23124yes—
203#896C23112yes—
204#896C23124yes—
205#896C23124yes—
206#896C23112yes—
207#893C2316yes—
208#893C2316yes—
209#893C2316yes—
210#893C23112yes—
211#893C23112yes—
212#893C23112yes—
213#893C2316yes—
214#892C2316yes—
215#892C23112yes—
216D3×C4⋊C4C2316yes—
217D3×C4⋊C4C23112yes—
218D3×C4⋊C4C23124yes—
219D3×C4⋊C4C23112yes—
220D3×C4⋊C4C23112yes—
221D3×C4⋊C4C2316yes—
222#890C2316yes—
223#890C2316yes—
224#890C2316yes—
225#890C23112yes—
226#890C2316yes—
227#889C23112yes—
228#889C23112yes—
229#889C23112yes—
230#888C23112yes—
231#888C23112yes—
232#888C2312yes—
233#888C2316yes—
234#888C2316yes—
235#888C23112yes—
236#888C23112yes—
237#888C2312yes—
238#888C23112yes—
239#888C23112yes—
240#888C2316yes—
241#887C2312yes—
242#887C23112yes—
243#887C23112yes—
244#887C2312yes—
245#887C2316yes—
246#67⋊C4C23112yes—
247#67⋊C4C23112yes—
248#67⋊C4C23112yes—
249D3×C22⋊C4C23124yes—
250D3×C22⋊C4C23112yes—
251#878C23112yes—
252#878C23124yes—
253#878C23112yes—
254#878C23112yes—
255#878C23112yes—
256C4×D12C2316yes—
257C4×D12C2313yes—
258C4×D12C23112yes—
259C4×D12C23112yes—
260C4×D12C2313yes—
261C4×D12C2316yes—
262C4×D12C2316yes—
263#872C23112yes—
264#872C2316yes—
265C42×D3C23112yes—
266C42×D3C2316yes—
267#870C23112yes—
268#870C2316yes—
269#869C23112yes—
270#869C2313yes—
271#869C2313yes—
272C4×Dic6C2313yes—
273C4×Dic6C2316yes—
274C4×Dic6C2316yes—
275C4×Dic6C23112yes—
276C4×Dic6C23112yes—
277C4×Dic6C2311yescharacteristic
278C4×Dic6C2313yes—
279C4×Dic6C2311yescharacteristic
280C4×Dic6C2313yes—
281C4×Dic6C2316yes—
282C4×Dic6C2313yes—
283C2×H(5,𝔽2)—31no—
284C23×Q8—36no—
285Q82—31no—
286Q82—36no—
287Q82—31no—
288Q82—34no—
289Q82C2×D312yescomplemented
290#557—33no—
291#557—36no—
292#557—34no—
293#557—32no—
294#557—31no—
295#557C2×D312yescomplemented
296#554—33no—
297#554—312no—
298#554—36no—
299#554—312no—
300#554—36no—
301#554—312no—
302#554—312no—
303#554—36no—
304#554—312no—
305#554—324no—
306#554—36no—
307#554—312no—
308#554—36no—
309#554—33no—
310#554—312no—
311#554—312no—
312#554C2×D316yescomplemented
313D4×Q8—312no—
314D4×Q8—36no—
315D4×Q8—33no—
316D4×Q8—312no—
317D4×Q8—312no—
318D4×Q8—312no—
319D4×Q8—36no—
320D4×Q8—36no—
321D4×Q8—36no—
322D4×Q8—324no—
323D4×Q8—36no—
324D4×Q8—33no—
325D4×Q8—312no—
326D4×Q8C2×D316yescomplemented
327#544—312no—
328#544—312no—
329#544—312no—
330#544—36no—
331#544—36no—
332#544C2×D316yescomplemented
333#543—324no—
334#543—312no—
335#533—36no—
336#533—312no—
337#533—312no—
338#533—36no—
339#533—36no—
340#533—36no—
341#533—33no—
342#533C2×D313yescomplemented
343C2×C4⋊Q8—36no—
344C2×C4⋊Q8—312no—
345C2×C4⋊Q8—36no—
346C2×C4⋊Q8C2×D313yescomplemented
347C2×C22⋊Q8—36no—
348C2×C22⋊Q8—312no—
349C2×C22⋊Q8—324no—
350C2×C22⋊Q8—312no—
351#520—31no—
352#520—34no—
353#520—32no—
354#520—33no—
355#520—36no—
356#520C2×D312yes—
357#518—36no—
358#518—312no—
359#518—36no—
360#518—33no—
361C4×#41—32no—
362C4×#41—34no—
363C4×#41—32no—
364C4×#41—36no—
365C4×#41—33no—
366C4×#41C2×D311yescharacteristic
367C2×C4×Q8—36no—
368C2×C4×Q8—33no—
369C2×C4×D4—312no—
370C2×C4×D4—36no—
371C2×C4×D4—36no—
372C2×C4×D4—33no—
373C23×D3C2416yes—
374C3×#41C2×Q818yescomplemented
375C2×C3×Q8—412no—
376C2×C3×Q8C2416yes—
377C2×C3×Q8C2412yes—
378C2×C3×Q8C24112yes—
379C2×C3×Q8C2411yescharacteristic
380C2×C3×D4C2413yes—
381C22×C3×C4C2413yes—
382C22×C3×C4C2413yes—
383C22×C3×C4C24112yes—
384C22×C3×C4C2413yes—
385C2×#67C2416yes—
386C22×Dic3C2416yes—
387C22×Dic3C2416yes—
388C22×Dic3C2416yes—
389#239C2×Q8116yescomplemented
390D3×Q8—224no—
391D3×Q8—448no—
392D3×Q8—424no—
393D3×D4C2×Q8148yescomplemented
394#235C2×Q8124yescomplemented
395C2×D12C2×Q8124yescomplemented
396C2×D12C2416yes—
397C2×D12C2413yes—
398C2×C4×D3—424no—
399C2×C4×D3—412no—
400C2×C4×D3C2416yes—
401C2×C4×D3C24112yes—
402C2×C4×D3C24112yes—
403C2×C4×D3C2416yes—
404C2×C4×D3C24112yes—
405C2×C4×D3C24124yes—
406C2×C4×D3C2416yes—
407C2×Dic6—212no—
408C2×Dic6—424no—
409C2×Dic6C2413yes—
410C2×Dic6C2416yes—
411C2×Dic6C24112yes—
412C2×Dic6C2414yes—
413C2×Dic6C2416yes—
414C2×Dic6C24124yes—
415C2×Dic6C2411yescharacteristic
416C2×Dic6C2411yescharacteristic
417C3×C4⋊C4C2416yes—
418C3×C4⋊C4C2412yes—
419C3×C4⋊C4C2412yes—
420C3×C4⋊C4C24112yes—
421C3×C4⋊C4C24112yes—
422C3×C4⋊C4C24112yes—
423C3×C4⋊C4C2413yes—
424C3×C4⋊C4C2413yes—
425C3×C4⋊C4C24112yes—
426C3×C4⋊C4C2416yes—
427C3×C22⋊C4C2416yes—
428C3×C22⋊C4C24112yes—
429C3×C42C2411yescharacteristic
430C3×C42C2413yes—
431C3×C42C2413yes—
432C3×C42C24112yes—
433C3×C42C2413yes—
434#217C24112yes—
435#217C2416yes—
436(C2×D3)⋊C4C2416yes—
437(C2×D3)⋊C4C24112yes—
438(C2×D3)⋊C4C2416yes—
439(C2×D3)⋊C4C24112yes—
440(C2×D3)⋊C4C24112yes—
441(C2×D3)⋊C4C24124yes—
442C4⋊Dic3C2411yescharacteristic
443C4⋊Dic3C2413yes—
444C4⋊Dic3C2416yes—
445C4⋊Dic3C24112yes—
446C4⋊Dic3C2416yes—
447C4⋊Dic3C2413yes—
448C4⋊Dic3C2411yescharacteristic
449C4⋊Dic3C24112yes—
450C4⋊Dic3C2416yes—
451C4⋊Dic3C2416yes—
452C4⋊Dic3C2416yes—
453Dic3⋊C4C2412yes—
454Dic3⋊C4C2414yes—
455Dic3⋊C4C2416yes—
456Dic3⋊C4C2416yes—
457Dic3⋊C4C2416yes—
458Dic3⋊C4C24112yes—
459Dic3⋊C4C24112yes—
460Dic3⋊C4C2412yes—
461Dic3⋊C4C2416yes—
462Dic3⋊C4C24112yes—
463Dic3⋊C4C24112yes—
464Dic3⋊C4C24124yes—
465Dic3⋊C4C2414yes—
466Dic3⋊C4C24112yes—
467C4×Dic3C2416yes—
468C4×Dic3C2416yes—
469C4×Dic3C2416yes—
470C4×Dic3C2412yes—
471C4×Dic3C2416yes—
472C4×Dic3C2412yes—
473C4×Dic3C2416yes—
474C4×Dic3C2414yes—
475C4×Dic3C24112yes—
476H(5,𝔽2)—316no—
477C2×#41—32no—
478C2×#41—33no—
479C2×#41C22×D311yescharacteristic
480C22×Q8—36no—
481C22×Q8—324no—
482C22×Q8—312no—
483C22×Q8—33no—
484C22×Q8—312no—
485C22×Q8—1224no—
486C22×Q8C22×D316yes—
487C22×D4—36no—
488C22×D4—33no—
489C23×C4—312no—
490C23×C4—36no—
491C4⋊Q8—36no—
492C4⋊Q8—324no—
493C4⋊Q8—34no—
494C4⋊Q8—312no—
495C4⋊Q8—36no—
496C4⋊Q8—312no—
497C4⋊Q8—36no—
498C4⋊Q8—312no—
499C4⋊Q8—312no—
500C4⋊Q8—312no—
501C4⋊Q8—312no—
502C4⋊Q8—36no—
503C4⋊Q8—32no—
504C4⋊Q8—32no—
505C4⋊Q8—33no—
506C4⋊Q8—312no—
507C4⋊Q8—33no—
508C4⋊Q8C22×D316yes—
509C4⋊Q8C22×D3112yes—
510C4⋊Q8C22×D313yes—
511C4⋊Q8C22×D316yes—
512C4⋊Q8C22×D316yes—
513C4⋊Q8C22×D311yescharacteristic
514#125—312no—
515#125—312no—
516#125—312no—
517#125—36no—
518#125—36no—
519#125—36no—
520#125—312no—
521#125—36no—
522#125—312no—
523#125—36no—
524#125C22×D3112yes—
525#125C22×D316yes—
526C22⋊Q8—36no—
527C22⋊Q8—312no—
528C22⋊Q8—324no—
529C22⋊Q8—324no—
530C22⋊Q8—312no—
531C22⋊Q8—36no—
532C22⋊Q8—324no—
533C22⋊Q8—36no—
534C22⋊Q8—312no—
535C22⋊Q8—324no—
536C22⋊Q8—312no—
537C22⋊Q8—36no—
538C22⋊Q8—324no—
539C22⋊Q8—324no—
540C22⋊Q8—324no—
541C22⋊Q8—324no—
542C22⋊Q8—324no—
543C22⋊Q8—312no—
544C22⋊Q8—312no—
545C22⋊Q8—312no—
546C22⋊Q8—312no—
547C22⋊Q8—312no—
548C22⋊Q8—324no—
549C22⋊Q8—312no—
550C22⋊Q8—312no—
551C22⋊Q8C22×D316yes—
552C22⋊Q8C22×D3124yes—
553C22⋊Q8C22×D316yes—
554C4×Q8—36no—
555C4×Q8—32no—
556C4×Q8—32no—
557C4×Q8—32no—
558C4×Q8—32no—
559C4×Q8—312no—
560C4×Q8—32no—
561C4×Q8—36no—
562C4×Q8—312no—
563C4×Q8—33no—
564C4×Q8—31no—
565C4×Q8—312no—
566C4×Q8—36no—
567C4×Q8—36no—
568C4×Q8—33no—
569C4×Q8—33no—
570C4×Q8—31no—
571C4×Q8—33no—
572C4×Q8—312no—
573C4×Q8—36no—
574C4×Q8C22×D316yes—
575C4×Q8C22×D311yescharacteristic
576C4×Q8C22×D314yes—
577C4×Q8C22×D311yescharacteristic
578C4×Q8C22×D316yes—
579C4×D4—36no—
580C4×D4—36no—
581C4×D4—36no—
582C4×D4—36no—
583C4×D4—324no—
584C4×D4—36no—
585C4×D4—312no—
586C4×D4—36no—
587C4×D4—36no—
588C4×D4—312no—
589C4×D4—312no—
590C4×D4—36no—
591C4×D4—36no—
592C4×D4—312no—
593C4×D4—312no—
594C4×D4—312no—
595C4×D4—36no—
596C4×D4—33no—
597C4×D4—312no—
598C4×D4—36no—
599C4×D4—36no—
600C4×D4—312no—
601C4×D4—33no—
602C4×D4C22×D313yes—
603C4×D4C22×D3112yes—
604C4×D4C22×D313yes—
605#117—36no—
606#117—33no—
607#117—36no—
608#117—312no—
609#117—312no—
610#117—36no—
611#117C22×D316yes—
612#117C22×D313yes—
613C2×C4⋊C4—33no—
614C2×C4⋊C4—36no—
615C2×C4⋊C4—33no—
616C2×C4⋊C4—312no—
617C2×C4⋊C4—36no—
618C2×C4⋊C4—312no—
619C2×C4⋊C4—312no—
620C2×C4⋊C4—36no—
621C2×C4⋊C4—324no—
622C2×C4⋊C4—312no—
623C2×C4⋊C4C22×D316yes—
624C2×C4⋊C4C22×D316yes—
625C2×C22⋊C4—312no—
626C2×C22⋊C4—36no—
627C2×C22⋊C4—324no—
628C2×C22⋊C4—312no—
629C2×C42—36no—
630C2×C42—312no—
631C2×C42—36no—
632C2×C42C22×D313yes—
633C23×C3C2513yes—
634C22×D3—46no—
635C22×D3—46no—
636C22×D3C22×Q8124yescomplemented
637C22×D3C2516yes—
638C3×Q8—212no—
639C3×Q8—412no—
640C3×Q8—42no—
641C3×Q8C22×Q814yescomplemented
642C3×D4C22×Q8112yescomplemented
643C2×C3×C4—26no—
644C2×C3×C4—412no—
645C2×C3×C4—43no—
646C2×C3×C4C22×Q8112yescomplemented
647C2×C3×C4C2513yes—
648C2×C3×C4C2514yes—
649C2×C3×C4C25112yes—
650C2×C3×C4C2511yescharacteristic
651C2×C3×C4C2513yes—
652C2×C3×C4C2511yescharacteristic
653C2×C3×C4C2513yes—
654C2×C3×C4C2511yescharacteristic
655#67C22×Q8124yescomplemented
656C2×Dic3—212no—
657C2×Dic3—46no—
658C2×Dic3—46no—
659C2×Dic3C2512yes—
660C2×Dic3C2516yes—
661C2×Dic3C2512yes—
662C2×Dic3C2516yes—
663C2×Dic3C2516yes—
664C2×Dic3C2512yes—
665C2×Dic3C2512yes—
666D12C22×Q8112yescomplemented
667D12C22×Q8124yescomplemented
668C4×D3—212no—
669C4×D3—224no—
670C4×D3—412no—
671C4×D3—424no—
672C4×D3—46no—
673C4×D3—412no—
674C4×D3C22×Q8124yescomplemented
675Dic6—26no—
676Dic6—212no—
677Dic6—224no—
678Dic6—424no—
679Dic6—44no—
680Dic6—46no—
681Dic6C22×Q814yescomplemented
682Dic6H(5,𝔽2)14yescomplemented
683C24—36no—
684#41—316no—
685#41—324no—
686#41D3×Q818yescomplemented
687C2×Q8—31no—
688C2×Q8—31no—
689C2×Q8—312no—
690C2×Q8—36no—
691C2×Q8—33no—
692C2×Q8—36no—
693C2×Q8—34no—
694C2×Q8—324no—
695C2×Q8—412no—
696C2×Q8—612no—
697C2×Q8—624no—
698C2×Q8—1224no—
699C2×Q8—1224no—
700C2×Q8—1248no—
701C2×Q8C23×D316yes—
702C2×Q8C23×D312yes—
703C2×Q8C23×D3112yes—
704C2×Q8C23×D311yescharacteristic
705C2×D4—36no—
706C2×D4—348no—
707C2×D4—324no—
708C2×D4—33no—
709C2×D4—36no—
710C2×D4C23×D313yes—
711C22×C4—36no—
712C22×C4—36no—
713C22×C4—36no—
714C22×C4—36no—
715C22×C4—312no—
716C22×C4—36no—
717C22×C4—36no—
718C22×C4—312no—
719C22×C4—324no—
720C22×C4—312no—
721C22×C4—1212no—
722C22×C4—1224no—
723C22×C4C23×D313yes—
724C22×C4C23×D313yes—
725C22×C4C23×D3112yes—
726C22×C4C23×D313yes—
727C4⋊C4—36no—
728C4⋊C4—34no—
729C4⋊C4—32no—
730C4⋊C4—31no—
731C4⋊C4—33no—
732C4⋊C4—312no—
733C4⋊C4—36no—
734C4⋊C4—33no—
735C4⋊C4—36no—
736C4⋊C4—36no—
737C4⋊C4—312no—
738C4⋊C4—324no—
739C4⋊C4—312no—
740C4⋊C4—312no—
741C4⋊C4—36no—
742C4⋊C4—312no—
743C4⋊C4—36no—
744C4⋊C4—312no—
745C4⋊C4—36no—
746C4⋊C4—312no—
747C4⋊C4—36no—
748C4⋊C4—34no—
749C4⋊C4—32no—
750C4⋊C4—31no—
751C4⋊C4—36no—
752C4⋊C4C23×D312yes—
753C4⋊C4C23×D313yes—
754C4⋊C4C23×D3112yes—
755C4⋊C4C23×D3112yes—
756C4⋊C4C23×D3112yes—
757C4⋊C4C23×D3112yes—
758C4⋊C4C23×D316yes—
759C4⋊C4C23×D316yes—
760C4⋊C4C23×D313yes—
761C4⋊C4C23×D312yes—
762C22⋊C4—312no—
763C22⋊C4—36no—
764C22⋊C4—312no—
765C22⋊C4—324no—
766C22⋊C4—36no—
767C22⋊C4—312no—
768C22⋊C4—312no—
769C22⋊C4—36no—
770C22⋊C4C23×D316yes—
771C22⋊C4C23×D3112yes—
772C42—34no—
773C42—32no—
774C42—32no—
775C42—36no—
776C42—312no—
777C42—36no—
778C42—36no—
779C42—36no—
780C42—36no—
781C42C23×D313yes—
782C42C23×D3112yes—
783C42C23×D311yescharacteristic
784C42C23×D313yes—
785C42C23×D313yes—
786C22×C3—23no—
787C22×C3—23no—
788C22×C3C23×Q816yes—
789C22×C3C2611yescharacteristic
790C2×D3—26no—
791C2×D3—26no—
792C2×D3—424no—
793C2×D3C23×Q8112yes—
794C3×C4—23no—
795C3×C4—212no—
796C3×C4—23no—
797C3×C4—24no—
798C3×C4—21no—
799C3×C4C23×Q812yes—
800C3×C4C23×Q816yes—
801C3×C4C2×H(5,𝔽2)12yes—
802Dic3—26no—
803Dic3—26no—
804Dic3—22no—
805Dic3—26no—
806Dic3—22no—
807Dic3C23×Q814yes—
808Dic3C2×H(5,𝔽2)14yes—
809C23—36no—
810C23—324no—
811C23—126no—
812C23—126no—
813C23C24×D313yes—
814Q8—212no—
815Q8—34no—
816Q8—34no—
817Q8—412no—
818Q8—42no—
819Q8—612no—
820Q8—624no—
821Q8—66no—
822Q8—1224no—
823Q8—126no—
824Q8—124no—
825Q8C2×D3×Q814yescomplemented
826D4—324no—
827D4—324no—
828D4—312no—
829D4C2×D3×Q8112yescomplemented
830C2×C4—26no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—324no—
834C2×C4—32no—
835C2×C4—36no—
836C2×C4—32no—
837C2×C4—36no—
838C2×C4—36no—
839C2×C4—412no—
840C2×C4—43no—
841C2×C4—624no—
842C2×C4—612no—
843C2×C4—612no—
844C2×C4—1212no—
845C2×C4—1224no—
846C2×C4—126no—
847C2×C4—1212no—
848C2×C4—126no—
849C2×C4—126no—
850C2×C4C2×D3×Q8112yescomplemented
851C2×C4C24×D313yes—
852C2×C4C24×D314yes—
853C2×C4C24×D3112yes—
854C2×C4C24×D311yescharacteristic
855C2×C4C24×D313yes—
856C2×C4C24×D311yescharacteristic
857C2×C4C24×D313yes—
858C2×C4C24×D311yescharacteristic
859C2×C3—26no—
860C2×C3C24×Q811yescharacteristic
861C2×C3C22×H(5,𝔽2)11yescharacteristic
862C2×C32−1+611yescharacteristic
863D3—212no—
864C22—23no—
865C22—23no—
866C22—312no—
867C22—66no—
868C22—66no—
869C22—1224no—
870C22C22×D3×Q816yes—
871C22C25×D311yescharacteristic
872C4—23no—
873C4—212no—
874C4—21no—
875C4—23no—
876C4—24no—
877C4—34no—
878C4—34no—
879C4—66no—
880C4—66no—
881C4—62no—
882C4—66no—
883C4—62no—
884C4C22×D3×Q816yes—
885C4C22×D3×Q812yes—
886C4D3×H(5,𝔽2)12yes—
887C3Q8×H(5,𝔽2)11yescharacteristic, complemented, Sylow
888C2—26no—
889C2—612no—
890C2C23×D3×Q811yescharacteristic
891C2C2×D3×H(5,𝔽2)11yescharacteristic
892C2#8757111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3503C2
prime radicalC2×#1009C22
hypercenter#3503D3
hypocenterC3Q8×H(5,𝔽2)
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. C3×#3503C2semidirect
2. #87041C2semidirect
3. #87018C2semidirect
4. #87015C2semidirect
5. #86949C2semidirect
6. #86761C2semidirect
7. D3×D4×Q8C2semidirect
8. #86599C2semidirect
9. #86586C2semidirect
10. #86280C2semidirect
11. #86277C2semidirect
12. #86215C2semidirect
13. C2×#5727C2semidirect
14. #85889C2semidirect
17. #41×Dic6C2semidirect
20. C22×D3×Q8C22semidirect
21. C3×Q82C22semidirect
22. C3×#557C22semidirect
23. C3×#554C22semidirect
24. C3×D4×Q8C22semidirect
25. C3×#544C22semidirect
26. C3×#533C22semidirect
27. C2×C3×C4⋊Q8C22semidirect
32. Q8×#67C22semidirect
33. C2×#946C22semidirect
34. #5730C22semidirect
35. #5730C22semidirect
36. #5730C22semidirect
37. #5729C22semidirect
38. #5729C22semidirect
39. #5728C22semidirect
40. #5727C22semidirect
41. #5727C22semidirect
42. #5727C22semidirect
43. #5727C22semidirect
44. #5727C22semidirect
45. #5727C22semidirect
46. #5727C22semidirect
47. D3×C4⋊Q8C22semidirect
48. D3×C4⋊Q8C22semidirect
49. #5722C22semidirect
50. #5722C22semidirect
51. #5721C22semidirect
52. #5690C22semidirect
53. #5690C22semidirect
54. #5690C22semidirect
55. #5690C22semidirect
56. #5689C22semidirect
57. #5688C22semidirect
58. #5685C22semidirect
59. #5636C22semidirect
60. #5636C22semidirect
61. #5635C22semidirect
62. #5634C22semidirect
63. #5634C22semidirect
64. #5632C22semidirect
65. #5632C22semidirect
66. D3×C22⋊Q8C22semidirect
67. D3×C22⋊Q8C22semidirect
68. #5579C22semidirect
69. #5579C22semidirect
70. #5578C22semidirect
71. #5578C22semidirect
72. Q8×D12C22semidirect
77. C4×D3×Q8C22semidirect
78. #5570C22semidirect
79. #5569C22semidirect
80. #5569C22semidirect
81. Q8×Dic6C22semidirect
82. Q8×Dic6C22semidirect
87. #5543C22semidirect
88. #5539C22semidirect
89. #5539C22semidirect
90. D4×Dic6C22semidirect
91. D4×Dic6C22semidirect
96. #5519C22semidirect
97. #5517C22semidirect
98. #5517C22semidirect
99. #5511C22semidirect
100. C2×#896C22semidirect
103. #5500C22semidirect
104. C2×#888C22semidirect
107. #5470C22semidirect
108. C2×C4×Dic6C22semidirect
114. #3503D3semidirect
128. #1009Q8semidirect
289. Q82C2×D3semidirect
295. #557C2×D3semidirect
312. #554C2×D3semidirect
326. D4×Q8C2×D3semidirect
332. #544C2×D3semidirect
342. #533C2×D3semidirect
346. C2×C4⋊Q8C2×D3semidirect
374. C3×#41C2×Q8semidirect
389. #239C2×Q8semidirect
393. D3×D4C2×Q8semidirect
394. #235C2×Q8semidirect
395. C2×D12C2×Q8semidirect
636. C22×D3C22×Q8semidirect
641. C3×Q8C22×Q8semidirect
642. C3×D4C22×Q8semidirect
646. C2×C3×C4C22×Q8semidirect
655. #67C22×Q8semidirect
666. D12C22×Q8semidirect
667. D12C22×Q8semidirect
674. C4×D3C22×Q8semidirect
681. Dic6C22×Q8semidirect
682. Dic6H(5,𝔽2)semidirect
686. #41D3×Q8semidirect
825. Q8C2×D3×Q8semidirect
829. D4C2×D3×Q8semidirect
850. C2×C4C2×D3×Q8semidirect
887. C3Q8×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C3×#35032
#870412
#870182
#870152
#869492
#867612
D3×D4×Q82
#865992
#865862
#862802
#862772
#862152
C2×#57272
#858892
#858862
C4×#10092
#41×Dic62
Q8×H(5,𝔽2)3