Finite Group Databasebeta

← #11884289

Subgroups — #11884289

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
1C3×#5554C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic, complemented
3C2×#63932C211yesmaximal, characteristic, complemented
4#10593895C211yesmaximal, characteristic, complemented
5#10592718C211yesmaximal, characteristic, complemented
6C3×#5014C211yesmaximal, characteristic, complemented
7#10591463C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10590614C211yesmaximal, characteristic, complemented
10#10590613C211yesmaximal, characteristic, complemented
11#10590587C211yesmaximal, characteristic, complemented
12#10590578C211yesmaximal, characteristic, complemented
13#10590372C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83503—31nomaximal
17#79879—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25#64078C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C2×C3×(C2×D3)⋊C4—21no—
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#886—21no—
32C3×#882—21no—
33C3×#875C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic, complemented
36#63933—24no—
37#63932—24no—
38#63908—21no—
39#63891—21no—
40#63891—21no—
41D3×C4⋊Dic3—21no—
42#63857C2211yescharacteristic
43#63857C2211yescharacteristic, complemented
44C2×#3719C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#809C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65C2×#932—31no—
66C2×#912—31no—
67C2×#911—31no—
68#5555—31no—
69#5554D311yescharacteristic, complemented
70#5551—31no—
71C3×#442—31no—
72#5239—31no—
73#5218—31no—
74#5060—31no—
75#5057—31no—
76#5052—31no—
77#5047—31no—
78#5041—31no—
79#5037—31no—
80#5019—31no—
81#5019—31no—
82#5019—61no—
83#5016—31no—
84#5014D311yescharacteristic, complemented
85#5011—31no—
86#4867—31no—
87#4864—31no—
88#4783—31no—
89#4783—31no—
90#4781—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—41no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12—21no—
107C2×C3×D12D411yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#625—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3795—22no—
119#3795—22no—
120#3795—41no—
121#3795—41no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124C32×C42C2311yescharacteristic
125#3754—22no—
126#3754—22no—
127C4⋊(C3⋊Dic3)—21no—
128C4⋊(C3⋊Dic3)—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#213D414yescomplemented
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3D411yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3719—22no—
149#3719—41no—
150#3716—22no—
151#3716—41no—
152#3715—22no—
153#3713—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#237C2×D311yescharacteristic
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×C3×D8—31no—
166C3×#124—31no—
167C3×#123—61no—
168C3×C22⋊Q8—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#120—61no—
172C3×C4×D4—21no—
173C3×C4×D4—31no—
174C3×C4×D4—31no—
175C3×C4×D4C2×D311yescharacteristic
176C3×C4×D4C2×D311yescharacteristic
177C2×C3×C22⋊C4—61no—
178#950—64no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#215—31no—
182#938—61no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—61no—
191C2×#214—61no—
192#932—64no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213C2×D311yescharacteristic
196#930—21no—
197#930—61no—
198C2×(C2×D3)⋊C4—21no—
199C2×C4⋊Dic3—61no—
200#924—31no—
201#924—31no—
202C2×#208—31no—
203C22×C3⋊C8—31no—
204#912—64no—
205#911—64no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#897—31no—
213#897—31no—
214#897C2×D311yescharacteristic
215#895C2×D311yescharacteristic
216D3×C4⋊C4—61no—
217#886—21no—
218#886—61no—
219#886—61no—
220#883—61no—
221#883—61no—
222#882—21no—
223#875C2×D311yescharacteristic
224C4×D12C2×D311yescharacteristic
225C4×D12C2×D311yescharacteristic, complemented
226#869—31no—
227#869—31no—
228#869—61no—
229C3×#106—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#97—31no—
233#835—31no—
234#832—31no—
235#832C2×D311yescharacteristic
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#810—31no—
241#810—31no—
242#810—31no—
243#810—31no—
244#810—31no—
245#810—61no—
246#810—61no—
247#809—31no—
248#809C2×D311yescharacteristic, complemented
249#808C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—61no—
253#803C2×D311yescharacteristic, complemented
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×D4—21no—
263C32×D4C2×D412yes—
264C2×C32×C4—21no—
265C2×C32×C4—81no—
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271#634—21no—
272#634—21no—
273#634—21no—
274#634—21no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—41no—
286C3×D12—81no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#625—42no—
296#625—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—31no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—31no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—31no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—62no—
330C2×C3×D4—61no—
331C2×C3×D4—121no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—41no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—21no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350#237—22no—
351#237—41no—
352#237—62no—
353#237—62no—
354#237—121no—
355#237—121no—
356D3×D4—22no—
357D3×D4—41no—
358#235—62no—
359#235—62no—
360#235—121no—
361#235—121no—
362C2×D12—21no—
363C2×D12#6711yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
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×D8—34no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
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#216—62no—
403#216—121no—
404#215—62no—
405#214—62no—
406#214—62no—
407#214—62no—
408#214—62no—
409#214—62no—
410#214—62no—
411#214—122no—
412#214—122no—
413#214—121no—
414#213—62no—
415#213—62no—
416#213D1214yescomplemented
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4#6711yescharacteristic
425(C2×D3)⋊C4#6711yescharacteristic
426C4⋊Dic3—21no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—121no—
434C4⋊Dic3—121no—
435C4⋊Dic3#6711yescharacteristic
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439#208—62no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—62no—
450Dic12—121no—
451#204—62no—
452#204—121no—
453ΓL(1,𝔽25)—62no—
454D3×C8—62no—
455C22×C32—22no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32C22×D411yescharacteristic
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—
471C2×C3×D3—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—31no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—91no—
490C2×Q16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—91no—
501#124—31no—
502#123—61no—
503#123—181no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—31no—
509#121—61no—
510#121—181no—
511#120—61no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4D3211yescharacteristic
515C2×C4⋊C4—181no—
516C2×C22⋊C4—61no—
517#106—31no—
518C4⋊C8—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—31no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—122no—
537C23×C3—241no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—81no—
543C22×D3C2×#6711yescharacteristic
544C22×D3C2×#6711yescharacteristic
545C3×Q8—61no—
546C3×Q8—61no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—22no—
550C3×D4—32no—
551C3×D4—41no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—121no—
556C3×D4—122no—
557C3×D4—122no—
558C3×D4—241no—
559C3×D4C2×D1212yes—
560C3×D4D3×D412yes—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—81no—
576C2×C3×C4—81no—
577C2×C3×C4—82no—
578C2×C3×C4—122no—
579C2×C3×C4—122no—
580C2×C3×C4D3×D411yescharacteristic
581C2×C3×C4D3×D411yescharacteristic
582C2×C3×C4C2×#6711yescharacteristic
583C2×C3×C4C2×#6711yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586#67—42no—
587#67—42no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—42no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—122no—
602C2×Dic3—122no—
603C2×Dic3C2×#6711yescharacteristic
604C2×Dic3C2×#6711yescharacteristic
605D12—21no—
606D12—21no—
607D12—21no—
608D12—41no—
609D12—81no—
610D12C2×D1212yes—
611C4×D3—21no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—21no—
615C4×D3—42no—
616C4×D3—122no—
617C4×D3—122no—
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—32no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C3⋊C8—121no—
641C3⋊C8C2×D1212yes—
642C2×C32—42no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3×D3—41no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—81no—
650C24—61no—
651#41—62no—
652#41—121no—
653#41—182no—
654#41—182no—
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—61no—
664C2×D4—61no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—121no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4C2×D3211yescharacteristic
671C22×C4—21no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—182no—
679Q16—361no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—34no—
686D8—182no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—91no—
692C2×C8—182no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4C2×D3211yescharacteristic
701C22⋊C4—21no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42C2×D3211yescharacteristic
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—62no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—244no—
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C22×#6711yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—22no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—84no—
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—41no—
759C3×C4—41no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—81no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4C22×D1211yescharacteristic
766C3×C4C2×D3×D411yescharacteristic
767C3×C4#100411yescharacteristic
768C3×C4#100911yescharacteristic
769Dic3—21no—
770Dic3—21no—
771Dic3—41no—
772Dic3—41no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—241no—
778Dic3—241no—
779C32#326711yescharacteristic, complemented, Sylow
780C23—21no—
781C23—31no—
782C23—31no—
783C23—61no—
784C23—61no—
785C23—122no—
786C23—122no—
787C23—241no—
788Q8—61no—
789Q8—61no—
790Q8—181no—
791Q8—181no—
792Q8—181no—
793Q8—181no—
794D4—21no—
795D4—32no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—121no—
800D4—122no—
801D4—122no—
802D4—241no—
803D4—362no—
804D4—362no—
805D4D3×D1212yes—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—81no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4D3×#6711yescharacteristic
823C2×C4D3×#6711yescharacteristic
824C2×C4C22×D3211yescharacteristic
825C8—32no—
826C8—61no—
827C8—181no—
828C8—181no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—82no—
835C2×C3—121no—
836C2×C3—121no—
837C2×C3—122no—
838C2×C3—241no—
839C2×C3D4×D1211yescharacteristic
840C2×C3#577311yescharacteristic
841C2×C3#577511yescharacteristic
842C2×C3D4×#6711yescharacteristic
843C2×C3#582211yescharacteristic
844C2×C3#583611yescharacteristic
845D3—42no—
846D3—41no—
847D3—41no—
848D3—81no—
849C22—22no—
850C22—41no—
851C22—41no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—62no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—244no—
865C22C2×D3×#6711yescharacteristic
866C4—21no—
867C4—21no—
868C4—41no—
869C4—61no—
870C4—61no—
871C4—121no—
872C4—121no—
873C4—361no—
874C4—361no—
875C4C2×D3×D1211yescharacteristic
876C4#6430711yescharacteristic
877C3—21no—
878C3#7987911yescharacteristic, complemented
879C3#8350311yescharacteristic, complemented
880C2—42no—
881C2—121no—
882C2—121no—
883C2—122no—
884C2—241no—
885C2D12×#6711yescharacteristic
886C2#1059510611yescharacteristic
887C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5554C2semidirect
2. C2×#63933C2semidirect
3. C2×#63932C2semidirect
4. #10593895C2semidirect
5. #10592718C2semidirect
6. C3×#5014C2semidirect
7. #10591463C2semidirect
8. #10591459C2semidirect
9. #10590614C2semidirect
10. #10590613C2semidirect
11. #10590587C2semidirect
12. #10590578C2semidirect
13. #10590372C2semidirect
14. #10590348C2semidirect
15. #10590326C2semidirect
21. C2×#3795C22semidirect
25. #64078C22semidirect
35. C3×C4×D12C22semidirect
43. #63857C22semidirect
44. C2×#3719C22semidirect
45. C2×#3719C22semidirect
48. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63637C22semidirect
53. #63637C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
56. C3×#809C22semidirect
57. C3×#808C22semidirect
58. C3×#803C22semidirect
59. #63565C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. #5554D3semidirect
84. #5014D3semidirect
131. C3×#213D4semidirect
225. C4×D12C2×D3semidirect
248. #809C2×D3semidirect
249. #808C2×D3semidirect
253. #803C2×D3semidirect
416. #213D12semidirect
779. C32#3267semidirect
878. C3#79879semidirect
879. C3#83503semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
C2×#639332
C2×#639322
#105938952
#105927182
C3×#50142
#105914632
#105914592
#105906142
#105906132
#105905872
#105905782
#105903722
#105903482
#105903262
#835033
#798793