Finite Group Databasebeta

← #11884102

Subgroups — #11884102

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3#10594915C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5#10592749C211yesmaximal, characteristic, complemented
6C3×#5051C211yesmaximal, characteristic, complemented
7#10591627C211yesmaximal, characteristic, complemented
8#10591599C211yesmaximal, characteristic, complemented
9#10591577C211yesmaximal, characteristic, complemented
10#10591169C211yesmaximal, characteristic, complemented
11#10591155C211yesmaximal, characteristic, complemented
12#10590603C211yesmaximal, characteristic, complemented
13#10590590C211yesmaximal, characteristic, complemented
14#10590588C211yesmaximal, characteristic, complemented
15#10590559C211yesmaximal, characteristic, complemented
16#83506—31nomaximal
17#80771—31nomaximal
18C22×#634C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3756C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic, complemented
27C3×C4×#67C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#895—21no—
31C3×#895C2211yescharacteristic
32C3×#894—21no—
33C3×#893C2211yescharacteristic
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36#63982—21no—
37#67⋊Dic3—21no—
38#63943—24no—
39#63896—21no—
40#63866C2211yescharacteristic, complemented
41#63857C2211yescharacteristic, complemented
42#63844C2211yescharacteristic, complemented
43#63840—21no—
44C2×#3716—24no—
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic, complemented
52#63657C2211yescharacteristic
53#63637C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#951—31no—
65C22×#214—31no—
66C2×#918—31no—
67C22×#204—31no—
68#5632—31no—
69#5630D311yescharacteristic
70D4×Dic6—31no—
71C3×#467—31no—
72#5239—31no—
73#5218—31no—
74#5190—31no—
75#5111—31no—
76#5060—31no—
77#5054—31no—
78#5051D311yescharacteristic, complemented
79#5050—31no—
80#5050—31no—
81#5050—61no—
82#5046—31no—
83#5042—31no—
84#5040—31no—
85#5019—31no—
86#5018—31no—
87#5011—31no—
88#4889—31no—
89#4886—31no—
90#4818—31no—
91#4808—31no—
92#4806—31no—
93#4798—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×#634—22no—
99C2×#634—21no—
100C2×#634—41no—
101C2×#634C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67D411yescharacteristic
104C3×#239—22no—
105C3×#239—41no—
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×D3×Dic3—21no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3756—22no—
125#3756—41no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×#216—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3716—22no—
150#3716—22no—
151#3716—22no—
152#3716D414yescomplemented
153#3715—22no—
154#3715—41no—
155#3711—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239C2×D311yescharacteristic
160C2×D3×Q8—31no—
161C22×D12C2×D311yescharacteristic
162C22×Dic6—31no—
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—61no—
166C2×C3×Q16—31no—
167C22×C3×C8—31no—
168C3×#124—31no—
169C3×#123—61no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8C2×D311yescharacteristic
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×#121—31no—
175C3×#121—61no—
176C3×#120—61no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C2×C3×C22⋊C4—61no—
180#951—64no—
181#947C2×D311yescharacteristic
182#944—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#216—61no—
189C2×#216C2×D311yescharacteristic, complemented
190C2×#215—31no—
191C2×#215—31no—
192D4×Dic3—61no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—64no—
200C4×#67C2×D311yescharacteristic
201#924—31no—
202#924C2×D311yescharacteristic
203C2×#208—31no—
204C22×C3⋊C8C2×D311yescharacteristic
205#918—64no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—64no—
211C2×ΓL(1,𝔽25)—31no—
212#897—31no—
213#896—61no—
214#895—21no—
215#895C2×D311yescharacteristic
216#894—21no—
217#893C2×D311yescharacteristic
218#888—61no—
219#888—61no—
220#887—31no—
221#882—21no—
222#67⋊C4—61no—
223D3×C22⋊C4—21no—
224#878—61no—
225#878—61no—
226#878—61no—
227#869—31no—
228C4×Dic6—31no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#103—31no—
232#835C2×D311yescharacteristic, complemented
233#832—31no—
234#832—31no—
235#830—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239(C2×D3)⋊C8—31no—
240#815—31no—
241Dic3⋊C8—31no—
242#810—31no—
243#810—31no—
244#810—31no—
245#810—31no—
246#810—61no—
247#810—61no—
248#810C2×D311yescharacteristic, complemented
249#809—31no—
250#809—31no—
251#807C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—42no—
272#634—21no—
273#634—21no—
274#634—21no—
275#634—42no—
276#634C2×D412yes—
277C3×#67—22no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×D12—42no—
288C3×D12—81no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—81no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#627—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—31no—
306#497—91no—
307#468—91no—
308#467—31no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—62no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—121no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67#6711yescharacteristic
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—121no—
344#239—22no—
345#239—41no—
346D3×Q8—62no—
347D3×Q8—121no—
348C2×D12—22no—
349C2×D12—21no—
350C2×D12—21no—
351C2×D12—21no—
352C2×D12—41no—
353C2×D12C22×D311yescharacteristic
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—21no—
357C2×C4×D3—61no—
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—61no—
364C2×Dic6—61no—
365C2×Dic6—62no—
366C2×Dic6—62no—
367C2×Dic6—62no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—61no—
372C2×Dic6—122no—
373C2×Dic6—121no—
374C2×Dic6—121no—
375C2×Dic6—121no—
376C2×Dic6—121no—
377C2×Dic6—122no—
378C2×Dic6C22×D311yescharacteristic
379C3×Q16—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—62no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—41no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—31no—
403#217—21no—
404#217—61no—
405#217#6711yescharacteristic
406#216—22no—
407#216—62no—
408#216—62no—
409#216—122no—
410#216—121no—
411#216—121no—
412#216—122no—
413#215—62no—
414#215—121no—
415#214—34no—
416#214—62no—
417#214—62no—
418#214—62no—
419#214—62no—
420#214—121no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4#6711yescharacteristic
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—21no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4#6711yescharacteristic
438C4×Dic3—61no—
439C4×Dic3—61no—
440C4×Dic3C22×D311yescharacteristic
441#208—62no—
442C2×C3⋊C8—22no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451#204—34no—
452#204—62no—
453#204—62no—
454#204—62no—
455ΓL(1,𝔽25)—62no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32#13712yescomplemented
459C22×C32C22×D411yescharacteristic
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—84no—
470C32×C4—21no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—22no—
476C3⋊Dic3—41no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C22×Q8—91no—
484C22×Q8—91no—
485C22×D4—31no—
486#137—184no—
487C2×Q16—31no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—91no—
498C22×C8—31no—
499C4⋊Q8—91no—
500C4⋊Q8—181no—
501#124—31no—
502#123—61no—
503C22⋊Q8—31no—
504C22⋊Q8—91no—
505C22⋊Q8—181no—
506C22⋊Q8—181no—
507C22⋊Q8D3211yescharacteristic
508#121—31no—
509#121—61no—
510#120—61no—
511C4×Q8—91no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—181no—
515C2×C22⋊C4—61no—
516#107—31no—
517C4⋊C8—91no—
518#103—31no—
519#103—31no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524C22⋊C8—91no—
525C22⋊C8—91no—
526#97—91no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C23×C3—241no—
534C23×C3D3×D411yescharacteristic
535C23×C3C2×#6711yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—81no—
541C22×D3C2×#6711yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—41no—
547C3×Q8—41no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—32no—
551C3×D4—62no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—122no—
556C3×D4—122no—
557C3×D4—241no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—122no—
580C2×C3×C4—241no—
581C2×C3×C4D3×D411yescharacteristic
582C2×C3×C4C2×#6711yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—22no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—122no—
595C2×Dic3—122no—
596C2×Dic3—122no—
597C2×Dic3—124no—
598C2×Dic3C2×#6711yescharacteristic
599C2×Dic3C2×#6711yescharacteristic
600C2×Dic3C2×#6711yescharacteristic
601D12—21no—
602D12—21no—
603D12—21no—
604D12—42no—
605D12—42no—
606D12—81no—
607D12D3×D412yes—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—42no—
611C4×D3—81no—
612C4×D3—122no—
613Dic6—21no—
614Dic6—21no—
615Dic6—32no—
616Dic6—32no—
617Dic6—62no—
618Dic6—61no—
619Dic6—61no—
620Dic6—62no—
621Dic6—61no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—121no—
626Dic6—121no—
627Dic6—122no—
628Dic6—122no—
629Dic6—122no—
630Dic6—122no—
631Dic6—124no—
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⋊C8D3×D412yes—
642C2×C32—22no—
643C2×C32D4211yescharacteristic
644C2×C32C2×#13711yescharacteristic
645C2×C32#57711yescharacteristic
646C3×D3—41no—
647C3×D3—42no—
648C3×D3—81no—
649C24—61no—
650#41—62no—
651#41—121no—
652C2×Q8—31no—
653C2×Q8—91no—
654C2×Q8—91no—
655C2×Q8—182no—
656C2×Q8—181no—
657C2×Q8—182no—
658C2×Q8—181no—
659C2×Q8—361no—
660C2×Q8—361no—
661C2×Q8C2×D3211yescharacteristic
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—121no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4C2×D3211yescharacteristic
676Q16—62no—
677Q16—182no—
678Q16—361no—
679SD16—94no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—62no—
689C2×C8—91no—
690C2×C8—91no—
691C4⋊C4—21no—
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4C2×D3211yescharacteristic
700C22⋊C4—21no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—181no—
709C42—31no—
710C42—181no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—22no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—62no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—244no—
729C22×C3#91812yescomplemented
730C22×C3#95112yescomplemented
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C22×#6711yescharacteristic
733C2×D3—21no—
734C2×D3—22no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—84no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—81no—
756C3×C4—81no—
757C3×C4—121no—
758C3×C4—121no—
759C3×C4C2×D3×D411yescharacteristic
760C3×C4C2×D3×D411yescharacteristic
761C3×C4#100411yescharacteristic
762C3×C4#100911yescharacteristic
763Dic3—21no—
764Dic3—21no—
765Dic3—21no—
766Dic3—41no—
767Dic3—41no—
768Dic3—62no—
769Dic3—62no—
770Dic3—122no—
771Dic3—122no—
772Dic3—121no—
773Dic3—121no—
774C32#326611yescharacteristic, complemented, Sylow
775C23—31no—
776C23—61no—
777C23—61no—
778C23—122no—
779C23—122no—
780C23—241no—
781C23D3×#6711yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—61no—
785Q8—61no—
786Q8—92no—
787Q8—181no—
788Q8—181no—
789Q8—181no—
790Q8—362no—
791Q8—362no—
792D4—32no—
793D4—62no—
794D4—61no—
795D4—61no—
796D4—61no—
797D4—122no—
798D4—122no—
799D4—241no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—122no—
812C2×C4—181no—
813C2×C4—181no—
814C2×C4—241no—
815C2×C4—362no—
816C2×C4—362no—
817C2×C4D3×#6711yescharacteristic
818C2×C4C22×D3211yescharacteristic
819C8—32no—
820C8—61no—
821C8—181no—
822C8—181no—
823C2×C3—22no—
824C2×C3—22no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—42no—
829C2×C3—121no—
830C2×C3—122no—
831C2×C3—241no—
832C2×C3#560911yescharacteristic
833C2×C3C2×#91811yescharacteristic
834C2×C3#577011yescharacteristic
835C2×C3D4×#6711yescharacteristic
836C2×C3C2×#95111yescharacteristic
837C2×C3#583611yescharacteristic
838D3—41no—
839D3—42no—
840D3—81no—
841C22—21no—
842C22—21no—
843C22—61no—
844C22—61no—
845C22—62no—
846C22—61no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—244no—
853C22#6394312yescomplemented
854C22C2×D3×#6711yescharacteristic
855C4—21no—
856C4—41no—
857C4—41no—
858C4—61no—
859C4—61no—
860C4—61no—
861C4—121no—
862C4—121no—
863C4—182no—
864C4—361no—
865C4D32×D411yescharacteristic
866C4#6431411yescharacteristic
867C3—21no—
868C3#8077111yescharacteristic, complemented
869C3#8350611yescharacteristic, complemented
870C2—22no—
871C2—121no—
872C2—122no—
873C2—241no—
874C2#1059529111yescharacteristic
875C2C2×#6394311yescharacteristic
876C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC3×#5630C2
hypercenterC22⋊Q8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63943C2semidirect
3. #10594915C2semidirect
4. C22×#3716C2semidirect
5. #10592749C2semidirect
6. C3×#5051C2semidirect
7. #10591627C2semidirect
8. #10591599C2semidirect
9. #10591577C2semidirect
10. #10591169C2semidirect
11. #10591155C2semidirect
12. #10590603C2semidirect
13. #10590590C2semidirect
14. #10590588C2semidirect
15. #10590559C2semidirect
21. C2×D3×Dic6C22semidirect
23. C2×#3756C22semidirect
24. C2×#3756C22semidirect
26. C2×C3×#216C22semidirect
40. #63866C22semidirect
41. #63857C22semidirect
42. #63844C22semidirect
51. C2×#3711C22semidirect
53. #63637C22semidirect
54. #63637C22semidirect
55. C3×#835C22semidirect
56. C3×#810C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
78. #5051D3semidirect
152. #3716D4semidirect
189. C2×#216C2×D3semidirect
232. #835C2×D3semidirect
248. #810C2×D3semidirect
251. #807C2×D3semidirect
458. C22×C32#137semidirect
729. C22×C3#918semidirect
730. C22×C3#951semidirect
774. C32#3266semidirect
853. C22#63943semidirect
868. C3#80771semidirect
869. C3#83506semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
C2×#639432
#105949152
C22×#37162
#105927492
C3×#50512
#105916272
#105915992
#105915772
#105911692
#105911552
#105906032
#105905902
#105905882
#105905592
#835063
#807713