Finite Group Databasebeta

← #11878846

Subgroups — #11878846

Order 1152.

1070 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595374C211yesmaximal, characteristic, complemented
2#10595300C211yesmaximal, characteristic
3#10592868C211yesmaximal, characteristic, complemented
4C3×#5175C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591618C211yesmaximal, characteristic, complemented
8#10591617C211yesmaximal, characteristic, complemented
9#10591487C211yesmaximal, characteristic, complemented
10#10591467C211yesmaximal, characteristic, complemented
11#10591438C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590878C211yesmaximal, characteristic, complemented
14#10590799C211yesmaximal, characteristic, complemented
15#10590643C211yesmaximal, characteristic, complemented
16#81766—31nomaximal
17#80387—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×#3811—21no—
21C2×#3802C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic
24C2×#3755C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic
30C3×#940C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#204C2211yescharacteristic, complemented
33#63979—21no—
34#63979—21no—
35#63918C2211yescharacteristic, complemented
36#63911C2211yescharacteristic
37#63911C2211yescharacteristic
38#63895—21no—
39C4×#624C2211yescharacteristic
40#63871C2211yescharacteristic
41#63846—21no—
42Dic3×Dic6C2211yescharacteristic, complemented
43#63837—21no—
44#63836—21no—
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47#63659C2211yescharacteristic, complemented
48#63648C2211yescharacteristic, complemented
49#63647C2211yescharacteristic
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5728—31no—
62D3×#127—31no—
63D3×#127—31no—
64#5578—31no—
65C3×#492—31no—
66C3×#460—31no—
67#5175—31no—
68#5175D311yescharacteristic, complemented
69#5169—31no—
70#5169—31no—
71#5169—31no—
72#5169—31no—
73#5169—31no—
74#5169—31no—
75#5169—61no—
76#5163—31no—
77#5163—31no—
78#5163—31no—
79#5163D311yescharacteristic, complemented
80#5085—31no—
81#5075—31no—
82#5070—31no—
83#5027—31no—
84#4848—31no—
85#4833—31no—
86#4776—31no—
87#4776—31no—
88#4760—31no—
89#4760—31no—
90#4694—31no—
91#4685—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97D4×C3⋊D3—41no—
98D4×C3⋊D3—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108#3811—44no—
109#3811—44no—
110C2×#627—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#624D411yescharacteristic
117C2×#624D411yescharacteristic
118#3802—41no—
119#3802—41no—
120C32×SD16—41no—
121C2×C32×C8C2311yescharacteristic
122#3755—41no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#215—41no—
128C3×#215—41no—
129C3×#214—41no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—41no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144Dic32—21no—
145Dic32D411yescharacteristic
146Dic32D411yescharacteristic
147#3717—41no—
148#3715—41no—
149#3208—91noSylow
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C2×D3×D4—31no—
153C2×D3×D4—31no—
154C2×D3×D4—61no—
155C2×D3×D4—61no—
156C2×D3×D4—61no—
157C2×D3×D4—61no—
158C2×D3×D4—61no—
159C2×C3×SD16—21no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16C2×D311yescharacteristic, complemented
165C2×C3×SD16C2×D311yescharacteristic, complemented
166C3×C4⋊Q8—31no—
167C3×#127—31no—
168C3×#127—31no—
169C3×C4×Q8—31no—
170#946—31no—
171#946—31no—
172#946—31no—
173#946—61no—
174Q8×Dic3—31no—
175Q8×Dic3C2×D311yescharacteristic, complemented
176#944C2×D311yescharacteristic, complemented
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—61no—
182C2×#215C2×D311yescharacteristic, complemented
183C2×#215C2×D311yescharacteristic, complemented
184#940—31no—
185#940—31no—
186#940—61no—
187#940—61no—
188#940—61no—
189#940—61no—
190#940C2×D311yescharacteristic
191#940C2×D311yescharacteristic
192C2×#214—31no—
193C2×#214C2×D311yescharacteristic, complemented
194C2×#204—31no—
195C2×#204C2×D311yescharacteristic, complemented
196#897—31no—
197#897—61no—
198#896—61no—
199#892—61no—
200#890—61no—
201#889—61no—
202#888—31no—
203#887—61no—
204#874—31no—
205#874—31no—
206#872—61no—
207C42×D3—31no—
208C42×D3—31no—
209#869—31no—
210C4×Dic6—31no—
211C4×Dic6—61no—
212C3×C4⋊C8—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×C4×C8—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—61no—
222#832C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—61no—
229#821C2×D311yescharacteristic, complemented
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—61no—
235Dic3⋊C8—31no—
236Dic3⋊C8C2×D311yescharacteristic, complemented
237C8×Dic3—31no—
238C8×Dic3C2×D311yescharacteristic, complemented
239#809—31no—
240#809—31no—
241C4⋊(C3⋊C8)—31no—
242C4×C3⋊C8—31no—
243C23×C32—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—42no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—42no—
248C22×C3⋊D3C2×D411yescharacteristic
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C2×D32—42no—
252C2×D32—42no—
253C2×D32—42no—
254C32×Q8—21no—
255C32×Q8—21no—
256C32×D4—21no—
257C32×D4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2411yescharacteristic
260#638—42no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—21no—
267C3×#67—42no—
268C3×#67—42no—
269C3×#67—42no—
270C3×#67—42no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283#627—42no—
284#626—42no—
285#626—42no—
286#626—42no—
287#626—42no—
288#625—42no—
289#624—22no—
290#624SD1614yescomplemented
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295#533—91no—
296C2×#127—91no—
297#492—31no—
298#492—91no—
299#486—91no—
300#486—91no—
301#460—31no—
302#460—91no—
303#460—91no—
304#460—91no—
305#450—91no—
306#450—91no—
307#450—91no—
308#450—91no—
309#431—91no—
310C23×D3—61no—
311C23×D3—61no—
312C23×D3—61no—
313C23×D3—61no—
314C23×D3—121no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×D4—21no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—21no—
331C2×#67—21no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—121no—
341D3×D4—124no—
342D3×D4—124no—
343D3×D4—121no—
344D3×D4—121no—
345D3×D4—121no—
346D3×D4—121no—
347D3×D4—121no—
348D3×D4—121no—
349D3×D4—121no—
350D3×D4—121no—
351D3×D4—124no—
352D3×D4—124no—
353D3×D4—122no—
354D3×D4—122no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—61no—
371C2×Dic6—61no—
372C2×Dic6—61no—
373C2×Dic6C22×D311yescharacteristic
374C3×SD16—41no—
375C3×SD16—41no—
376C3×SD16—42no—
377C3×SD16—121no—
378C3×SD16—121no—
379C3×SD16—121no—
380C3×SD16—121no—
381C2×C3×C8—21no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C3×C4⋊C4—31no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C42—31no—
391C3×C42—31no—
392C3×C42—61no—
393#215—41no—
394#215—41no—
395#215—121no—
396#215—121no—
397#215—121no—
398#215—121no—
399#215—122no—
400#214—41no—
401#214—121no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—121no—
407C4⋊Dic3—21no—
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3—61no—
414C4⋊Dic3C22×D311yescharacteristic
415Dic3⋊C4—21no—
416Dic3⋊C4—21no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—121no—
423C4×Dic3—21no—
424C4×Dic3—31no—
425C4×Dic3—31no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3C22×D311yescharacteristic
431C4×Dic3C22×D311yescharacteristic
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437#204—41no—
438#204—121no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3—41no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—84no—
449C2×C3⋊D3C2×SD1612yes—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456D32—84no—
457C32×C4—41no—
458C32×C4H(5,𝔽2)11yescharacteristic
459C32×C4H(5,𝔽2)11yescharacteristic
460C3⋊Dic3—21no—
461C3⋊Dic3—41no—
462C3×Dic3—21no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3C2×SD1612yes—
466C3×Dic3C2×SD1612yes—
467C3×Dic3AGL(1,ℤ/8)12yes—
468C22×D4—91no—
469C22×D4—91no—
470C22×D4—181no—
471C22×D4—181no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16D3211yescharacteristic, complemented
480C4⋊Q8—31no—
481C4⋊Q8—91no—
482#127—31no—
483#127—31no—
484#127—91no—
485#127—91no—
486#127—181no—
487#127—181no—
488#125—181no—
489C22⋊Q8—91no—
490C22⋊Q8—91no—
491C22⋊Q8—181no—
492C4×Q8—31no—
493C4×Q8—91no—
494C4×Q8—181no—
495#117—181no—
496C2×C42—91no—
497C4⋊C8—31no—
498C4⋊C8—91no—
499#102—31no—
500#102—31no—
501#102—91no—
502#102—91no—
503#102—91no—
504#102—91no—
505#102—91no—
506#102—91no—
507C22⋊C8—91no—
508C22⋊C8—91no—
509C4×C8—31no—
510C4×C8—91no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—41no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—31no—
519C22×D3—31no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—121no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3—122no—
530C22×D3—122no—
531C22×D3—122no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—124no—
537C22×D3—242no—
538C22×D3—242no—
539C3×Q8—21no—
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—41no—
544C3×Q8—41no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×D4—22no—
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—41no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—122no—
558C3×D4—122no—
559C3×D4—122no—
560C3×D4—122no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—42no—
574#67—42no—
575#67—42no—
576#67—42no—
577#67—122no—
578#67—122no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—124no—
583#67—122no—
584#67—122no—
585#67—122no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3D3×D411yescharacteristic
595C2×Dic3D3×D411yescharacteristic
596C2×Dic3D3×D411yescharacteristic
597C2×Dic3D3×D411yescharacteristic
598D12—21no—
599D12—21no—
600D12—21no—
601D12—21no—
602D12—62no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12—122no—
609D12—122no—
610D12—122no—
611D12—122no—
612C4×D3—34no—
613C4×D3—34no—
614C4×D3—62no—
615C4×D3—61no—
616C4×D3—61no—
617C4×D3—61no—
618C4×D3—61no—
619C4×D3—62no—
620C4×D3—121no—
621C4×D3—121no—
622Dic6—21no—
623Dic6—21no—
624Dic6—122no—
625Dic6—122no—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—41no—
629C3×C8—61no—
630C3×C8—61no—
631C3⋊C8—21no—
632C3⋊C8—21no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—121no—
636C2×C32—81no—
637C2×C32#53511yescharacteristic
638C2×C32C22×SD1611yescharacteristic
639C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
640C3⋊D3—22no—
641C3⋊D3—81no—
642C3×D3—81no—
643C3×D3—81no—
644C24—181no—
645C24—181no—
646C2×Q8—31no—
647C2×Q8—181no—
648C2×Q8C2×D3211yescharacteristic
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4—91no—
656C2×D4—181no—
657C2×D4—181no—
658C2×D4—181no—
659C2×D4—181no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—364no—
663C2×D4—361no—
664C2×D4—361no—
665C2×D4—361no—
666C2×D4—361no—
667C2×D4—364no—
668C2×D4C2×D3211yescharacteristic
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—91no—
672SD16—41no—
673SD16—121no—
674SD16—121no—
675SD16—121no—
676SD16—121no—
677SD16—361no—
678SD16—361no—
679SD16—361no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—91no—
683C2×C8C2×D3211yescharacteristic
684C4⋊C4—31no—
685C4⋊C4—61no—
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—91no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C22⋊C4—181no—
694C22⋊C4—181no—
695C42—31no—
696C42—31no—
697C42—61no—
698C42—91no—
699C42—91no—
700C42—181no—
701C22×C3—21no—
702C22×C3—42no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C2×D3—32no—
720C2×D3—32no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—41no—
727C2×D3—62no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—122no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—241no—
742C2×D3—241no—
743C2×D3—244no—
744C2×D3—244no—
745C2×D3—244no—
746C2×D3—244no—
747C2×D3—248no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—32no—
751C3×C4—32no—
752C3×C4—32no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—61no—
756C3×C4—81no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4#100411yescharacteristic
760C3×C4#100411yescharacteristic
761C3×C4#100411yescharacteristic
762C3×C4#100911yescharacteristic
763Dic3—21no—
764Dic3—41no—
765Dic3—41no—
766Dic3—61no—
767Dic3—61no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—241no—
772Dic3D3×SD1612yes—
773Dic3D3×SD1612yes—
774Dic3#91412yes—
775C32#320811yescharacteristic, complemented, Sylow
776C23—21no—
777C23—61no—
778C23—61no—
779C23—91no—
780C23—181no—
781C23—362no—
782C23—362no—
783C23—362no—
784C23—362no—
785C23—362no—
786C23—362no—
787Q8—21no—
788Q8—21no—
789Q8—61no—
790Q8—61no—
791Q8—362no—
792D4—21no—
793D4—21no—
794D4—61no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—122no—
799D4—122no—
800D4—122no—
801D4—122no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—362no—
808D4—362no—
809D4—362no—
810C2×C4—21no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—31no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—94no—
818C2×C4—91no—
819C2×C4—182no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—181no—
823C2×C4C22×D3211yescharacteristic
824C8—21no—
825C8—61no—
826C8—61no—
827C8—181no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—82no—
832C2×C3—81no—
833C2×C3—81no—
834C2×C3—241no—
835C2×C3—241no—
836C2×C3#560711yescharacteristic
837C2×C3#571511yescharacteristic
838C2×C3C2×D3×SD1611yescharacteristic
839C2×C3C2×D3×SD1611yescharacteristic
840C2×C3C2×#91411yescharacteristic
841C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
842D3—62no—
843D3—62no—
844D3—81no—
845D3—81no—
846D3—122no—
847D3—242no—
848D3—241no—
849D3—241no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—92no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—181no—
861C22—181no—
862C22—361no—
863C22—361no—
864C22—361no—
865C22—724no—
866C22—724no—
867C22D32×D411yescharacteristic
868C4—32no—
869C4—32no—
870C4—32no—
871C4—41no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4—361no—
877C4#6431411yescharacteristic
878C4#6433011yescharacteristic
879C3—21no—
880C3#8038711yescharacteristic, complemented
881C3#8176611yescharacteristic, complemented
882C2—81no—
883C2—182no—
884C2—241no—
885C2—241no—
886C2—721no—
887C2D32×SD1611yescharacteristic
888C2D3×#91411yescharacteristic
889C2#1059529911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595300C2
hypercenterC2×SD16D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595374C2semidirect
3. #10592868C2semidirect
4. C3×#5175C2semidirect
5. C3×#5163C2semidirect
6. #10591652C2semidirect
7. #10591618C2semidirect
8. #10591617C2semidirect
9. #10591487C2semidirect
10. #10591467C2semidirect
11. #10591438C2semidirect
12. #10590943C2semidirect
13. #10590878C2semidirect
14. #10590799C2semidirect
15. #10590643C2semidirect
22. C2×C32×SD16C22semidirect
24. C2×#3755C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C3×#944C22semidirect
27. C2×C3×#215C22semidirect
28. C2×C3×#215C22semidirect
31. C2×C3×#214C22semidirect
32. C2×C3×#204C22semidirect
35. #63918C22semidirect
42. Dic3×Dic6C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
47. #63659C22semidirect
48. #63648C22semidirect
50. C3×#832C22semidirect
51. C3×#821C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
68. #5175D3semidirect
79. #5163D3semidirect
164. C2×C3×SD16C2×D3semidirect
165. C2×C3×SD16C2×D3semidirect
175. Q8×Dic3C2×D3semidirect
176. #944C2×D3semidirect
182. C2×#215C2×D3semidirect
183. C2×#215C2×D3semidirect
193. C2×#214C2×D3semidirect
195. C2×#204C2×D3semidirect
222. #832C2×D3semidirect
229. #821C2×D3semidirect
236. Dic3⋊C8C2×D3semidirect
238. C8×Dic3C2×D3semidirect
290. #624SD16semidirect
479. C2×SD16D32semidirect
775. C32#3208semidirect
880. C3#80387semidirect
881. C3#81766semidirect

Maximal subgroups

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

subgroupindex
#105953742
#105953002
#105928682
C3×#51752
C3×#51632
#105916522
#105916182
#105916172
#105914872
#105914672
#105914382
#105909432
#105908782
#105907992
#105906432
#817663
#803873