Finite Group Databasebeta

← #11887255

Subgroups — #11887255

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596021C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591187C211yesmaximal, characteristic, complemented
5#10591184C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#10591177C211yesmaximal, characteristic, complemented
8#10591136C211yesmaximal, characteristic, complemented
9#10591124C211yesmaximal, characteristic, complemented
10#10591105C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590368C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590293C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#79440—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64146—21no—
22#64139C2211yescharacteristic
23#64133C2211yescharacteristic
24#64103—21no—
25#64093—21no—
26C22⋊C4×C3⋊D3—21no—
27#64084C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C3×#935—21no—
30C3×#926C2211yescharacteristic, complemented
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic, complemented
34C22×C3×C3⋊C8C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#889—21no—
37C3×#879—21no—
38C3×#877—21no—
39C3×#870C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#830C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×C4×C3⋊C8C2211yescharacteristic, complemented
48#63575C2211yescharacteristic, complemented
49#63573C2211yescharacteristic, complemented
50#63573C2211yescharacteristic, complemented
51#63567C2211yescharacteristic, complemented
52#63567C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61C3×#552—31no—
62#5550—31no—
63#5550—31no—
64#5550—61no—
65#5541D311yescharacteristic, complemented
66C3×C8×D4—31no—
67#5116—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5068—31no—
72#5066—31no—
73#5051—31no—
74#5048—31no—
75#5047—31no—
76#5046—31no—
77#5028—31no—
78C4×#215—31no—
79D4×C3⋊C8D311yescharacteristic, complemented
80#5003—31no—
81#5002—31no—
82#4971—31no—
83C2×#809—31no—
84#4847—31no—
85#4845—31no—
86#4737—31no—
87#4733—31no—
88#4731—31no—
89#4721—31no—
90#4697—31no—
91C4×#204—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C22×C3×Dic3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×C4⋊C4D411yescharacteristic
111C32×C22⋊C4D411yescharacteristic
112C32×C22⋊C4D411yescharacteristic
113C32×C42C2311yescharacteristic
114#3757—21no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C2×C3×C3⋊C8—41no—
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3719—41no—
142#3717—22no—
143#3717—41no—
144#3296—91noSylow
145C2×#235—31no—
146C2×#235—31no—
147C2×#235—61no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—61no—
151C22×C3×C8—31no—
152C22×C3×C8—31no—
153C3×#126—61no—
154C3×#125—31no—
155C3×#125—61no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4C2×D311yescharacteristic
162C3×C4×D4C2×D311yescharacteristic
163C3×#117—31no—
164C3×#117—61no—
165C2×C3×C4⋊C4—31no—
166C2×#216—31no—
167C2×#215—31no—
168C2×#215—31no—
169#937—62no—
170#937—61no—
171#937—61no—
172#935—21no—
173#930—31no—
174#930—31no—
175#930—61no—
176#926C2×D311yescharacteristic, complemented
177C2×C4⋊Dic3C2×D311yescharacteristic
178#924—31no—
179#924—31no—
180#924—61no—
181#924C2×D311yescharacteristic
182#924C2×D311yescharacteristic, complemented
183C22×C3⋊C8C2×D311yescharacteristic
184C22×C3⋊C8C2×D311yescharacteristic, complemented
185C2×Dic12—31no—
186C2×#204—31no—
187C2×#204—31no—
188#894—62no—
189#894—61no—
190#894—61no—
191#889—21no—
192#884—62no—
193#884—61no—
194#884—61no—
195D3×C22⋊C4—62no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#879—21no—
199#877—21no—
200#875—31no—
201#875—31no—
202#875—61no—
203C4×D12—31no—
204C4×D12—31no—
205C4×D12—61no—
206#870C2×D311yescharacteristic, complemented
207C4×Dic6C2×D311yescharacteristic, complemented
208C3×C4⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×C4×C8—31no—
212#835—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic, complemented
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#818—31no—
222#817—31no—
223#817—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#808—31no—
238#808—31no—
239#807—31no—
240C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
241C4×C3⋊C8C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—42no—
248C22×C3⋊D3—81no—
249C32×D4—22no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259#638—42no—
260#638—81no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—42no—
267C4⋊(C3⋊D3)#4112yes—
268C4×C3⋊D3—42no—
269C4×C3⋊D3—81no—
270#634—21no—
271#634—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#552—31no—
284#546—91no—
285#488—91no—
286#483—91no—
287#482—91no—
288#478—91no—
289#467—91no—
290#465—91no—
291#464—91no—
292#452—91no—
293#450—91no—
294C4×SD16—91no—
295C8×D4—31no—
296#416—91no—
297C2×#102—91no—
298C23×D3—62no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4D1211yescharacteristic
304C2×C3×D4#6711yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—61no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—62no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—62no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—21no—
319#235—62no—
320#235—62no—
321#235—122no—
322#235—121no—
323#235—121no—
324#235—122no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—62no—
333C2×D12—62no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—122no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12—122no—
340C2×C4×D3—62no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—62no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—61no—
349C2×Dic6C22×D311yescharacteristic
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—121no—
355C2×C3×C8—121no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4D1211yescharacteristic
367C3×C4⋊C4#6711yescharacteristic
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4D1211yescharacteristic
374C3×C22⋊C4D1211yescharacteristic
375C3×C22⋊C4#6711yescharacteristic
376C3×C22⋊C4#6711yescharacteristic
377C3×C42—21no—
378C3×C42—61no—
379C3×C42—61no—
380C3×C42C22×D311yescharacteristic
381C3×C42C22×D311yescharacteristic
382#217—21no—
383#217—21no—
384#217—21no—
385#217—62no—
386#217—61no—
387#217—61no—
388#216—121no—
389#215—62no—
390#215—121no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403C4⋊Dic3—21no—
404C4⋊Dic3—31no—
405C4⋊Dic3—31no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414Dic3⋊C4—21no—
415Dic3⋊C4—62no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418C4×Dic3—21no—
419C4×Dic3—21no—
420C2×C3⋊C8—41no—
421C2×C3⋊C8—41no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426Dic12—121no—
427#204—62no—
428#204—121no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32#13512yes—
435C22×C32C22×D411yescharacteristic
436C2×C3⋊D3—22no—
437C2×C3⋊D3—41no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—84no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4C2×#4111yescharacteristic
448C32×C4H(5,𝔽2)11yescharacteristic
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—91no—
456C22×D4—91no—
457C2×Q16—91no—
458C2×SD16—91no—
459C2×SD16—91no—
460C22×C8—31no—
461C22×C8—31no—
462#126—61no—
463#125—31no—
464#125—61no—
465#124—91no—
466#123—61no—
467#123—181no—
468C22⋊Q8—31no—
469C22⋊Q8—31no—
470C22⋊Q8—91no—
471#121—91no—
472#121—181no—
473#120—181no—
474C4×Q8—31no—
475C4×D4—91no—
476C4×D4D3211yescharacteristic
477#117—31no—
478#117—61no—
479C2×C4⋊C4—31no—
480C2×C22⋊C4—181no—
481#107—91no—
482#106—91no—
483#106—91no—
484C4⋊C8—31no—
485#103—91no—
486#103—91no—
487#103—91no—
488#103—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495C22⋊C8—31no—
496C22⋊C8—31no—
497C4×C8—31no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3C2×D1211yescharacteristic
501C23×C3C2×D1211yescharacteristic
502C23×C3C2×#6711yescharacteristic
503C23×C3C2×#6711yescharacteristic
504C22×D3—62no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—62no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—124no—
513C22×D3—124no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—242no—
519C3×Q8—61no—
520C3×Q8—61no—
521C3×D4—22no—
522C3×D4—22no—
523C3×D4—42no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—122no—
546C2×C3×C4C2×D1211yescharacteristic
547C2×C3×C4C2×D1211yescharacteristic
548C2×C3×C4C2×D1211yescharacteristic
549C2×C3×C4C2×D1211yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C2×#6711yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—122no—
557#67—122no—
558#67—124no—
559#67—241no—
560#67—241no—
561#67—242no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—42no—
567C2×Dic3—62no—
568C2×Dic3—62no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573D12—32no—
574D12—32no—
575D12—62no—
576D12—62no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—61no—
581D12—61no—
582D12—61no—
583D12—121no—
584D12—121no—
585D12—122no—
586D12—122no—
587D12—124no—
588C4×D3—122no—
589C4×D3—122no—
590C4×D3—124no—
591C4×D3—241no—
592C4×D3—241no—
593C4×D3—242no—
594Dic6—21no—
595Dic6—21no—
596Dic6—61no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—121no—
601Dic6—121no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3×C8—61no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C2×C32—22no—
611C2×C32—41no—
612C2×C32#54611yescharacteristic
613C2×C32C2×#13511yescharacteristic
614C2×C32#57711yescharacteristic
615C3⋊D3—42no—
616C3⋊D3—81no—
617C24—181no—
618#41—182no—
619#41—361no—
620C2×Q8—31no—
621C2×Q8—91no—
622C2×D4—91no—
623C2×D4—91no—
624C2×D4—182no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—181no—
628C2×D4—361no—
629C2×D4#62611yescharacteristic
630C22×C4—61no—
631C22×C4—181no—
632C22×C4—181no—
633C22×C4C2×D3211yescharacteristic
634C22×C4C2×D3211yescharacteristic
635Q16—361no—
636SD16—182no—
637SD16—361no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—121no—
643C2×C8—121no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—91no—
654C4⋊C4—181no—
655C4⋊C4#62611yescharacteristic
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4#62611yescharacteristic
665C22⋊C4#62611yescharacteristic
666C42—61no—
667C42—61no—
668C42C2×D3211yescharacteristic
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—22no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3#90412yes—
687C22×C3#95012yes—
688C22×C3C22×D1211yescharacteristic
689C22×C3C22×#6711yescharacteristic
690C2×D3—64no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—122no—
694C2×D3—122no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—244no—
709C2×D3—244no—
710C2×D3—248no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4#100411yescharacteristic
730C3×C4D3×#4111yescharacteristic
731C3×C4D3×#4111yescharacteristic
732C3×C4#100911yescharacteristic
733Dic3—41no—
734Dic3—41no—
735Dic3—41no—
736Dic3—41no—
737Dic3—122no—
738Dic3—122no—
739Dic3—121no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743C32#329611yescharacteristic, complemented, Sylow
744C23—181no—
745C23—181no—
746C23—362no—
747C23—362no—
748C23—721no—
749C23C2×#62611yescharacteristic
750C23C2×#62611yescharacteristic
751Q8—61no—
752Q8—61no—
753Q8—181no—
754Q8—181no—
755D4—22no—
756D4—92no—
757D4—181no—
758D4—181no—
759D4—181no—
760D4—362no—
761D4—362no—
762D4—721no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—122no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—362no—
775C2×C4—721no—
776C2×C4C2×#62611yescharacteristic
777C2×C4C2×#62611yescharacteristic
778C2×C4C2×#62611yescharacteristic
779C2×C4C2×#62611yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C8—61no—
782C8—61no—
783C8—61no—
784C8—61no—
785C2×C3—22no—
786C2×C3—22no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—42no—
791C2×C3—41no—
792C2×C3—41no—
793C2×C3—81no—
794C2×C3#555411yescharacteristic
795C2×C3C2×#90411yescharacteristic
796C2×C3#575111yescharacteristic
797C2×C3C2×#95011yescharacteristic
798C2×C3#582911yescharacteristic
799C2×C3#583711yescharacteristic
800D3—124no—
801D3—122no—
802D3—122no—
803D3—242no—
804D3—241no—
805D3—241no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—182no—
812C22—361no—
813C22—361no—
814C22—361no—
815C22—361no—
816C22—361no—
817C22—724no—
818C22#6382912yes—
819C22C22×#62611yescharacteristic
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4—121no—
828C4—361no—
829C4—361no—
830C4#6431211yescharacteristic
831C4#6431411yescharacteristic
832C3—21no—
833C3#7944011yescharacteristic, complemented
834C3#8359811yescharacteristic, complemented
835C2—22no—
836C2—41no—
837C2—362no—
838C2—721no—
839C2C2×#6382911yescharacteristic
840C2#1059525411yescharacteristic
841C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10596021C2
hypercenterC4×D4D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5541C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10591187C2semidirect
5. #10591184C2semidirect
6. #10591183C2semidirect
7. #10591177C2semidirect
8. #10591136C2semidirect
9. #10591124C2semidirect
10. #10591105C2semidirect
11. C2×#63564C2semidirect
12. #10590368C2semidirect
13. C4×#3717C2semidirect
14. #10590308C2semidirect
15. #10590293C2semidirect
30. C3×#926C22semidirect
33. C3×#924C22semidirect
35. C22×C3×C3⋊C8C22semidirect
39. C3×#870C22semidirect
40. C3×C4×Dic6C22semidirect
41. C2×#3719C22semidirect
45. C3×#830C22semidirect
46. C3×C4⋊(C3⋊C8)C22semidirect
47. C3×C4×C3⋊C8C22semidirect
48. #63575C22semidirect
49. #63573C22semidirect
50. #63573C22semidirect
51. #63567C22semidirect
52. #63567C22semidirect
53. #63567C22semidirect
54. #63566C22semidirect
65. #5541D3semidirect
79. D4×C3⋊C8D3semidirect
176. #926C2×D3semidirect
182. #924C2×D3semidirect
184. C22×C3⋊C8C2×D3semidirect
206. #870C2×D3semidirect
207. C4×Dic6C2×D3semidirect
214. #830C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
743. C32#3296semidirect
833. C3#79440semidirect
834. C3#83598semidirect

Maximal subgroups

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

subgroupindex
#105960212
C3×#55412
C3×D4×C3⋊C82
#105911872
#105911842
#105911832
#105911772
#105911362
#105911242
#105911052
C2×#635642
#105903682
C4×#37172
#105903082
#105902932
#835983
#794403