Finite Group Databasebeta

← #11878852

Subgroups — #11878852

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#10595300C211yesmaximal, characteristic
2#10594397C211yesmaximal, characteristic, complemented
3#10592475C211yesmaximal, characteristic, complemented
4C3×#4762C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591490C211yesmaximal, characteristic, complemented
7#10591467C211yesmaximal, characteristic, complemented
8#10591439C211yesmaximal, characteristic, complemented
9#10590943C211yesmaximal, characteristic, complemented
10#10590879C211yesmaximal, characteristic, complemented
11#10590877C211yesmaximal, characteristic, complemented
12#10590643C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590549C211yesmaximal, characteristic, complemented
15#10590548C211yesmaximal, characteristic, complemented
16#81568—31nomaximal
17#80387—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×#3811—21no—
21C2×#3802C2211yescharacteristic
22C2×#3754C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic, complemented
24#64106C2211yescharacteristic
25C3×#940C2211yescharacteristic
26C3×#940C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#888C2211yescharacteristic, complemented
30C3×#887C2211yescharacteristic, complemented
31#63979—21no—
32#63979—21no—
33#63911C2211yescharacteristic
34#63911C2211yescharacteristic
35#63888—21no—
36C4×#624C2211yescharacteristic
37#63871C2211yescharacteristic
38#63866C2211yescharacteristic, complemented
39#63845—21no—
40#63844C2211yescharacteristic, complemented
41Dic3×Dic6—21no—
42#63836—21no—
43C2×#3717C2211yescharacteristic, complemented
44C2×#3716C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic, complemented
48#63647C2211yescharacteristic
49#63636C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5728—31no—
62D3×#127—31no—
63D3×#127—31no—
64#5578—31no—
65C3×#486—31no—
66C3×#460—31no—
67#5175—31no—
68#5175—31no—
69#5169—31no—
70#5169—31no—
71#5088—31no—
72#5076—31no—
73#5075—31no—
74#5027—31no—
75#4848—31no—
76#4833—31no—
77#4776—31no—
78#4776—31no—
79#4776—31no—
80#4776—31no—
81#4776—31no—
82#4776—31no—
83#4776—61no—
84#4762—31no—
85#4762—31no—
86#4762—31no—
87#4762D311yescharacteristic, complemented
88#4760—31no—
89#4760D311yescharacteristic, complemented
90#4693—31no—
91#4685—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—41no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109#3811—44no—
110#3811—44no—
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—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3754—41no—
123#3752—21no—
124C4⋊(C3⋊Dic3)—21no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744—41no—
127C3×#214—41no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—41no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142Dic32—21no—
143Dic32D411yescharacteristic
144Dic32D411yescharacteristic
145#3717—41no—
146#3716—41no—
147#3716—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—31no—
160C2×C3×SD16—31no—
161C3×C4⋊Q8—31no—
162C3×#127—31no—
163C3×#127—31no—
164C3×C4×Q8—31no—
165#946—31no—
166#946—61no—
167Q8×Dic3—61no—
168#944—31no—
169C2×#215—31no—
170C2×#215—31no—
171#940—31no—
172#940—31no—
173#940—61no—
174#940—61no—
175#940—61no—
176#940—61no—
177#940C2×D311yescharacteristic
178#940C2×D311yescharacteristic
179C2×#214—31no—
180C2×#214—31no—
181C2×#214—31no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—61no—
185C2×#214C2×D311yescharacteristic, complemented
186C2×#204—31no—
187C2×#204—31no—
188C2×#204—31no—
189C2×#204—31no—
190C2×#204—31no—
191C2×#204—61no—
192C2×#204C2×D311yescharacteristic, complemented
193#897—31no—
194#897—31no—
195#897—31no—
196#897—61no—
197#896—61no—
198#892—61no—
199#890—61no—
200#889—61no—
201#888C2×D311yescharacteristic, complemented
202#887—31no—
203#887C2×D311yescharacteristic, complemented
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—21no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102C2×D311yescharacteristic, complemented
219C3×#102C2×D311yescharacteristic, complemented
220C3×C4×C8—31no—
221#832—31no—
222#832C2×D311yescharacteristic, complemented
223#821—31no—
224#821C2×D311yescharacteristic, complemented
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—61no—
230Dic3⋊C8—31no—
231Dic3⋊C8C2×D311yescharacteristic, complemented
232C8×Dic3—31no—
233C8×Dic3C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#809—61no—
239#809C2×D311yescharacteristic, complemented
240#809C2×D311yescharacteristic, complemented
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×D4—21no—
255C32×D4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2411yescharacteristic
258#638—42no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3C2×D411yescharacteristic
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—21no—
265#634—21no—
266#634—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—
283C3×Dic6—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—91no—
298#492—91no—
299#486—31no—
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—31no—
316C2×C3×Q8—61no—
317C2×C3×D4—21no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C22×D311yescharacteristic
326C2×#67—21no—
327C2×#67—21no—
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—121no—
339D3×D4—124no—
340D3×D4—124no—
341D3×D4—121no—
342D3×D4—121no—
343D3×D4—121no—
344D3×D4—121no—
345D3×D4—121no—
346D3×D4—121no—
347D3×D4—121no—
348D3×D4—121no—
349D3×D4—124no—
350D3×D4—124no—
351D3×D4—122no—
352D3×D4—122no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—61no—
369C2×Dic6—21no—
370C2×Dic6—31no—
371C2×Dic6—31no—
372C2×Dic6—61no—
373C2×Dic6C22×D311yescharacteristic
374C3×SD16—121no—
375C3×SD16—121no—
376C2×C3×C8—21no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C3×C4⋊C4—21no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C42—31no—
388C3×C42—31no—
389C3×C42—61no—
390#215—121no—
391#215—121no—
392#214—41no—
393#214—121no—
394#214—121no—
395#214—121no—
396#214—121no—
397#214—121no—
398#214—122no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—121no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—121no—
410C4⋊Dic3C22×D311yescharacteristic
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418C4×Dic3—21no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3C22×D311yescharacteristic
426C4×Dic3C22×D311yescharacteristic
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—61no—
430C2×C3⋊C8C22×D311yescharacteristic
431C2×C3⋊C8C22×D311yescharacteristic
432#204—41no—
433#204—121no—
434#204—121no—
435#204—122no—
436#204—121no—
437#204—121no—
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—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
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—31no—
502#102—31no—
503#102—91no—
504#102—91no—
505#102—91no—
506#102D3211yescharacteristic, complemented
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—61no—
540C3×Q8—61no—
541C3×Q8—122no—
542C3×D4—22no—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—41no—
548C3×D4—61no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—61no—
552C3×D4—122no—
553C3×D4—122no—
554C3×D4—122no—
555C3×D4—122no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568#67—42no—
569#67—42no—
570#67—42no—
571#67—42no—
572#67—122no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—122no—
577#67—124no—
578#67—122no—
579#67—122no—
580#67—122no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—121no—
589C2×Dic3D3×D411yescharacteristic
590C2×Dic3D3×D411yescharacteristic
591C2×Dic3D3×D411yescharacteristic
592C2×Dic3D3×D411yescharacteristic
593D12—21no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—62no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—121no—
603D12—122no—
604D12—122no—
605D12—122no—
606D12—122no—
607C4×D3—34no—
608C4×D3—34no—
609C4×D3—62no—
610C4×D3—61no—
611C4×D3—61no—
612C4×D3—61no—
613C4×D3—61no—
614C4×D3—62no—
615C4×D3—121no—
616C4×D3—121no—
617Dic6—21no—
618Dic6—21no—
619Dic6—42no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—121no—
625Dic6—121no—
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—61no—
648C2×Q8—91no—
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—121no—
673SD16—121no—
674SD16—361no—
675SD16—361no—
676SD16—361no—
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—181no—
688C4⋊C4—181no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4C2×D3211yescharacteristic
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#100911yescharacteristic
761C3×C4#100911yescharacteristic
762C3×C4#100911yescharacteristic
763Dic3—21no—
764Dic3—41no—
765Dic3—41no—
766Dic3—61no—
767Dic3—61no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—241no—
772Dic3#91112yes—
773Dic3D3×SD1612yes—
774Dic3D3×SD1612yes—
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—61no—
788Q8—61no—
789Q8—122no—
790Q8—181no—
791Q8—181no—
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#567411yescharacteristic
838C2×C3C2×#91111yescharacteristic
839C2×C3C2×D3×SD1611yescharacteristic
840C2×C3C2×D3×SD1611yescharacteristic
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#6430811yescharacteristic
878C4#6431411yescharacteristic
879C3—21no—
880C3#8038711yescharacteristic, complemented
881C3#8156811yescharacteristic, complemented
882C2—81no—
883C2—182no—
884C2—241no—
885C2—241no—
886C2—721no—
887C2#1059428711yescharacteristic
888C2D3×#91111yescharacteristic
889C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595300C2
hypercenter#102D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594397C2semidirect
3. #10592475C2semidirect
4. C3×#4762C2semidirect
5. C3×#4760C2semidirect
6. #10591490C2semidirect
7. #10591467C2semidirect
8. #10591439C2semidirect
9. #10590943C2semidirect
10. #10590879C2semidirect
11. #10590877C2semidirect
12. #10590643C2semidirect
13. #10590597C2semidirect
14. #10590549C2semidirect
15. #10590548C2semidirect
22. C2×#3754C22semidirect
23. C2×#3744C22semidirect
27. C2×C3×#214C22semidirect
28. C2×C3×#204C22semidirect
29. C3×#888C22semidirect
30. C3×#887C22semidirect
38. #63866C22semidirect
40. #63844C22semidirect
43. C2×#3717C22semidirect
44. C2×#3716C22semidirect
45. C2×#3716C22semidirect
46. C2×#3715C22semidirect
47. C32×#102C22semidirect
49. #63636C22semidirect
50. C3×#832C22semidirect
51. C3×#821C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#809C22semidirect
55. C3×#809C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
87. #4762D3semidirect
89. #4760D3semidirect
185. C2×#214C2×D3semidirect
192. C2×#204C2×D3semidirect
201. #888C2×D3semidirect
203. #887C2×D3semidirect
218. C3×#102C2×D3semidirect
219. C3×#102C2×D3semidirect
222. #832C2×D3semidirect
224. #821C2×D3semidirect
231. Dic3⋊C8C2×D3semidirect
233. C8×Dic3C2×D3semidirect
239. #809C2×D3semidirect
240. #809C2×D3semidirect
290. #624SD16semidirect
506. #102D32semidirect
775. C32#3208semidirect
880. C3#80387semidirect
881. C3#81568semidirect

Maximal subgroups

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

subgroupindex
#105953002
#105943972
#105924752
C3×#47622
C3×#47602
#105914902
#105914672
#105914392
#105909432
#105908792
#105908772
#105906432
#105905972
#105905492
#105905482
#815683
#803873