Finite Group Databasebeta

← #11884348

Subgroups — #11884348

Order 1152.

1060 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63806C211yesmaximal, characteristic, complemented
2C2×#63795C211yesmaximal, characteristic, complemented
3#10594007C211yesmaximal, characteristic, complemented
4#10593895C211yesmaximal, characteristic, complemented
5#10592540C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4836C211yesmaximal, characteristic, complemented
8#10590970C211yesmaximal, characteristic, complemented
9#10590962C211yesmaximal, characteristic, complemented
10#10590960C211yesmaximal, characteristic, complemented
11#10590946C211yesmaximal, characteristic, complemented
12#10590849C211yesmaximal, characteristic, complemented
13#10590825C211yesmaximal, characteristic, complemented
14#10590372C211yesmaximal, characteristic, complemented
15#10590346C211yesmaximal, characteristic, complemented
16#80567—31nomaximal
17#79496—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25#64078C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#875C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33#63922—21no—
34#63921—21no—
35#63912—21no—
36#63908—21no—
37#63908C2211yescharacteristic
38#63891—21no—
39#63891—21no—
40D3×C4⋊Dic3—21no—
41#63857C2211yescharacteristic
42#63857C2211yescharacteristic, complemented
43#63856C2211yescharacteristic
44#63854—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50#63806—24no—
51#63795—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#803C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63563C2211yescharacteristic, complemented
63C2×#916—31no—
64C2×#911—31no—
65C2×#908—31no—
66C2×#904—31no—
67#5676—31no—
68#5555—31no—
69#5551—31no—
70#5550—31no—
71C3×#463—31no—
72C3×#435—31no—
73#5173—31no—
74#5158—31no—
75#5137—31no—
76#5114—31no—
77#5060—31no—
78#5014—31no—
79#4844D311yescharacteristic, complemented
80#4841—31no—
81#4841—31no—
82#4841—61no—
83#4836D311yescharacteristic, complemented
84#4816—31no—
85#4808—31no—
86#4778—31no—
87#4776—31no—
88#4734—31no—
89#4733—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4711—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116#3799—22no—
117#3799—41no—
118#3795—22no—
119#3795—22no—
120#3795—41no—
121#3795—41no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124C32×C42C2311yescharacteristic
125#3752—21no—
126C4⋊(C3⋊Dic3)—21no—
127C4⋊(C3⋊Dic3)—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3744—22no—
130#3744—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—22no—
141C3×#204—22no—
142C3×ΓL(1,𝔽25)—22no—
143C3×D3×C8—22no—
144#3724—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3719—22no—
152#3719—41no—
153#3716—22no—
154#3716—41no—
155#3714D414yescomplemented
156#3267—91noSylow
157C2×#239—31no—
158C2×#237—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×#124—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#946—31no—
173C2×#216—31no—
174C2×#216—31no—
175#938—31no—
176#938—61no—
177#937—61no—
178C2×#214—31no—
179C2×#214—31no—
180C2×#213—31no—
181#930—31no—
182#930—61no—
183C2×C4⋊Dic3—61no—
184#924—31no—
185#924—31no—
186#924—31no—
187#916—64no—
188#911—64no—
189#908—64no—
190C2×Dic12—31no—
191C2×Dic12—31no—
192#904—64no—
193C2×D24—31no—
194C2×D24C2×D311yescharacteristic
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—61no—
202C2×#204—61no—
203C2×#204C2×D311yescharacteristic, complemented
204C2×ΓL(1,𝔽25)C2×D311yescharacteristic
205C2×D3×C8C2×D311yescharacteristic, complemented
206#897—31no—
207#897—31no—
208#894—61no—
209D3×C4⋊C4—61no—
210#886—61no—
211#886—61no—
212#884—61no—
213#884—61no—
214#883—61no—
215#883—61no—
216#883—61no—
217#882—61no—
218D3×C22⋊C4—61no—
219D3×C22⋊C4—61no—
220#875C2×D311yescharacteristic
221C4×D12—31no—
222C4×D12—31no—
223C4×D12—61no—
224C4×D12C2×D311yescharacteristic
225C4×D12C2×D311yescharacteristic, complemented
226#869—31no—
227#869—31no—
228#869—61no—
229C3×C4⋊C8—21no—
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×#103—31no—
233C3×#102—31no—
234C3×C22⋊C8—31no—
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821C2×D311yescharacteristic
241(C2×D3)⋊C8C2×D311yescharacteristic
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#817—31no—
244#816—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—61no—
249#816—61no—
250#816C2×D311yescharacteristic, complemented
251#809—31no—
252#808—31no—
253#803C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)C2×D412yes—
270C4×C3⋊D3—81no—
271#634—21no—
272#634—21no—
273#634—21no—
274#634—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—41no—
283C3×D12C2×D412yes—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293#625—42no—
294#625—42no—
295#625—81no—
296#624—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C32×C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—31no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—31no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×Q8—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337#239—62no—
338#239—121no—
339#237—62no—
340#237—62no—
341#237—121no—
342#237—121no—
343D3×D4—62no—
344D3×D4—121no—
345#235—62no—
346#235—62no—
347#235—62no—
348#235—121no—
349#235—121no—
350#235—121no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—121no—
358C2×D12D1211yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—121no—
369C2×C4×D3C22×D311yescharacteristic
370C2×C4×D3C22×D311yescharacteristic
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—62no—
379C3×D8—62no—
380C3×M16—62no—
381C2×C3×C8—21no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—62no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C42—21no—
398C3×C42C22×D311yescharacteristic
399C3×C42C22×D311yescharacteristic
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#216—62no—
405#216—121no—
406#214—62no—
407#214—121no—
408#213—34no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4D1211yescharacteristic
420(C2×D3)⋊C4D1211yescharacteristic
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—121no—
431C4⋊Dic3—121no—
432C4⋊Dic3D1211yescharacteristic
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D311yescharacteristic
440Dic12—62no—
441Dic12—121no—
442D24—22no—
443D24—34no—
444#204—22no—
445#204—62no—
446#204—62no—
447#204—62no—
448#204—62no—
449#204—62no—
450#204—122no—
451#204—122no—
452#204—121no—
453ΓL(1,𝔽25)—22no—
454D3×C8—22no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—22no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—91no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—91no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—31no—
499C22×C8—31no—
500C4⋊Q8—91no—
501#124—31no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—91no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8D3211yescharacteristic, complemented
519#103—31no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—91no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—31no—
527#97—31no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—61no—
531C23×C3—61no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—241no—
542C22×D3—241no—
543C22×D3C2×D1211yescharacteristic
544C22×D3C2×D1211yescharacteristic
545C3×Q8—61no—
546C3×Q8—61no—
547C3×D4—32no—
548C3×D4—61no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—121no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—122no—
564C2×C3×C4C2×D1211yescharacteristic
565C2×C3×C4C2×D1211yescharacteristic
566C2×C3×C4D3×D411yescharacteristic
567C2×C3×C4D3×D411yescharacteristic
568C2×C3×C4C23×D311yescharacteristic
569C2×C3×C4C23×D311yescharacteristic
570#67—122no—
571#67—122no—
572#67—122no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—241no—
577#67—241no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—122no—
590C2×Dic3—122no—
591C2×Dic3C2×D1211yescharacteristic
592C2×Dic3C2×D1211yescharacteristic
593D12—21no—
594D12—21no—
595D12—21no—
596D12—32no—
597D12—32no—
598D12—41no—
599D12—62no—
600D12—61no—
601D12—61no—
602D12—121no—
603D12—122no—
604D12—122no—
605D12D3×D412yes—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—42no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—122no—
615C4×D3—241no—
616C4×D3—241no—
617C4×D3—242no—
618Dic6—21no—
619Dic6—21no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—121no—
629Dic6—121no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—32no—
637C3×C8—41no—
638C3×C8—41no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8D3×D412yes—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3⋊D3—42no—
646C3×D3—41no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—81no—
650C24—181no—
651#41—182no—
652#41—182no—
653#41—182no—
654#41—361no—
655#41—361no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—91no—
659C2×Q8—91no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—91no—
664C2×D4—181no—
665C2×D4—182no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—182no—
679Q16—361no—
680SD16—62no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—62no—
686D8—94no—
687M16—62no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8C2×D3211yescharacteristic
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—91no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42C2×D3211yescharacteristic
712C22×C3—21no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—62no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3C22×D1211yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—22no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—62no—
740C2×D3—62no—
741C2×D3—122no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—244no—
749C2×D3—244no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4C2×D3×D411yescharacteristic
763C3×C4C2×D3×D411yescharacteristic
764C3×C4#100911yescharacteristic
765C3×C4#100911yescharacteristic
766Dic3—21no—
767Dic3—21no—
768Dic3—41no—
769Dic3—41no—
770Dic3—121no—
771Dic3—121no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—241no—
777Dic3—241no—
778Dic3—241no—
779C32#326711yescharacteristic, complemented, Sylow
780C23—31no—
781C23—31no—
782C23—61no—
783C23—61no—
784C23—181no—
785C23—362no—
786C23—362no—
787C23—721no—
788Q8—61no—
789Q8—61no—
790Q8—181no—
791Q8—181no—
792Q8—181no—
793Q8—181no—
794D4—32no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—92no—
799D4—121no—
800D4—181no—
801D4—362no—
802D4—362no—
803D4—362no—
804D4—362no—
805D4—721no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—122no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—362no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4—721no—
822C2×C4D3×D1211yescharacteristic
823C2×C4D3×D1211yescharacteristic
824C2×C4C22×D3211yescharacteristic
825C8—21no—
826C8—21no—
827C8—32no—
828C8—61no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—122no—
833C2×C3—121no—
834C2×C3—121no—
835C2×C3—241no—
836C2×C3D4×D1211yescharacteristic
837C2×C3#560911yescharacteristic
838C2×C3#574811yescharacteristic
839C2×C3#575111yescharacteristic
840C2×C3#577011yescharacteristic
841C2×C3#577311yescharacteristic
842D3—41no—
843D3—41no—
844D3—42no—
845D3—81no—
846D3—122no—
847D3—122no—
848D3—242no—
849C22—61no—
850C22—61no—
851C22—62no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—182no—
862C22—361no—
863C22—361no—
864C22—724no—
865C22C2×D3×D1211yescharacteristic
866C4—21no—
867C4—21no—
868C4—61no—
869C4—61no—
870C4—121no—
871C4—121no—
872C4—361no—
873C4—361no—
874C4—361no—
875C4D32×D411yescharacteristic
876C4#6432011yescharacteristic
877C3—21no—
878C3#7949611yescharacteristic, complemented
879C3#8056711yescharacteristic, complemented
880C2—121no—
881C2—121no—
882C2—122no—
883C2—241no—
884C2—362no—
885C2#1059462111yescharacteristic
886C2#1059467911yescharacteristic
887C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63806C2semidirect
2. C2×#63795C2semidirect
3. #10594007C2semidirect
4. #10593895C2semidirect
5. #10592540C2semidirect
6. C3×#4844C2semidirect
7. C3×#4836C2semidirect
8. #10590970C2semidirect
9. #10590962C2semidirect
10. #10590960C2semidirect
11. #10590946C2semidirect
12. #10590849C2semidirect
13. #10590825C2semidirect
14. #10590372C2semidirect
15. #10590346C2semidirect
21. C2×#3795C22semidirect
25. #64078C22semidirect
27. C2×C3×#204C22semidirect
29. C2×C3×D3×C8C22semidirect
32. C3×C4×D12C22semidirect
42. #63857C22semidirect
45. C2×#3719C22semidirect
46. C2×#3719C22semidirect
52. C32×C4⋊C8C22semidirect
53. #63643C22semidirect
54. #63643C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#803C22semidirect
60. #63573C22semidirect
62. #63563C22semidirect
79. #4844D3semidirect
83. #4836D3semidirect
155. #3714D4semidirect
203. C2×#204C2×D3semidirect
205. C2×D3×C8C2×D3semidirect
225. C4×D12C2×D3semidirect
230. C3×C4⋊C8C2×D3semidirect
231. C3×C4⋊C8C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
250. #816C2×D3semidirect
253. #803C2×D3semidirect
518. C4⋊C8D32semidirect
779. C32#3267semidirect
878. C3#79496semidirect
879. C3#80567semidirect

Maximal subgroups

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

subgroupindex
C2×#638062
C2×#637952
#105940072
#105938952
#105925402
C3×#48442
C3×#48362
#105909702
#105909622
#105909602
#105909462
#105908492
#105908252
#105903722
#105903462
#805673
#794963