Finite Group Databasebeta

← #11884104

Subgroups — #11884104

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3Dic6×#67C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592750C211yesmaximal, characteristic, complemented
6C3×#5050C211yesmaximal, characteristic, complemented
7#10591627C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591578C211yesmaximal, characteristic, complemented
10#10591172C211yesmaximal, characteristic, complemented
11#10591158C211yesmaximal, characteristic, complemented
12#10590603C211yesmaximal, characteristic, complemented
13#10590559C211yesmaximal, characteristic, complemented
14#10590515C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#83506—31nomaximal
17#80204—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C3×C4×#67C2211yescharacteristic
30C3×#895—21no—
31C3×#895C2211yescharacteristic
32C3×#894—21no—
33C3×#893C2211yescharacteristic
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36Dic3×#67—21no—
37#63964—21no—
38#63943—24no—
39#63887—21no—
40#63866C2211yescharacteristic, complemented
41#63856C2211yescharacteristic, complemented
42Dic3×Dic6C2211yescharacteristic, complemented
43#63839—21no—
44C2×#3716C2211yescharacteristic
45C2×#3716C2211yescharacteristic
46C2×#3715—24no—
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×#810C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#951—31no—
65Q8×#67—31no—
66C22×#215—31no—
67C22×#214—31no—
68C2×#918—31no—
69#5630D311yescharacteristic
70D4×Dic6—31no—
71C3×#451—31no—
72#5239—31no—
73#5218—31no—
74#5190—31no—
75#5187—31no—
76#5185—31no—
77#5060—31no—
78#5054—31no—
79#5051—31no—
80#5051—31no—
81#5051—61no—
82#5050D311yescharacteristic, complemented
83#5042—31no—
84#5040—31no—
85#5019—31no—
86#5018—31no—
87#5011—31no—
88#4818—31no—
89#4817—31no—
90#4812—31no—
91#4806—31no—
92#4731—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C3×#239—22no—
101C3×#239—41no—
102C2×C3×D12—22no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—22no—
113C2×C3×Dic6—21no—
114C2×C3×Dic6—41no—
115C2×C3×Dic6C2311yescharacteristic
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#3757—21no—
125#3756—22no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128C2×C3⋊(C3⋊C8)—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217D411yescharacteristic
132C3×#216—22no—
133C3×#216—41no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
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—41no—
151#3715—22no—
152#3715—22no—
153#3715—22no—
154#3715D414yescomplemented
155#3711—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C2×#239C2×D311yescharacteristic
161C2×D3×Q8—31no—
162C22×D12C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6C2×D311yescharacteristic
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C3×#124—31no—
168C3×#123—61no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8C2×D311yescharacteristic
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×#121—31no—
173C3×#121—61no—
174C3×#120—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C2×C3×C22⋊C4—61no—
178#951—64no—
179#947C2×D311yescharacteristic
180#946—31no—
181#946—61no—
182Q8×Dic3—31no—
183#944—31no—
184#944—61no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#216C2×D311yescharacteristic, complemented
189C2×#216C2×D311yescharacteristic, complemented
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—64no—
195D4×Dic3—61no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—64no—
203C4×#67—61no—
204C4×#67C2×D311yescharacteristic
205#924—31no—
206#924—31no—
207#924—31no—
208#924—61no—
209#924—61no—
210C2×#208—31no—
211C22×C3⋊C8—31no—
212C22×C3⋊C8—31no—
213C22×C3⋊C8—61no—
214#918—64no—
215C2×#204—31no—
216C2×#204—31no—
217C2×ΓL(1,𝔽25)—31no—
218#895—21no—
219#895C2×D311yescharacteristic
220#894—21no—
221#893C2×D311yescharacteristic
222#888—61no—
223#882—21no—
224D3×C22⋊C4—21no—
225#878—61no—
226#878—61no—
227#869—31no—
228C4×Dic6—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#832—31no—
236#832—31no—
237#830—31no—
238#830C2×D311yescharacteristic
239#821—31no—
240#821—31no—
241(C2×D3)⋊C8—31no—
242#815—31no—
243Dic3⋊C8—31no—
244#810—31no—
245#810—31no—
246#810—61no—
247#810C2×D311yescharacteristic, complemented
248#810C2×D311yescharacteristic, complemented
249#807—31no—
250#807—31no—
251#807—61no—
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—
271#634—21no—
272#634—21no—
273C3×#67—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×D12—42no—
285C3×D12—81no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3—81no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—42no—
295C3×Dic6C2×D412yes—
296#627—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—31no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—31no—
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×Q8—31no—
324C2×C3×Q8—62no—
325C2×C3×Q8—61no—
326C2×C3×Q8—121no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—121no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67#6711yescharacteristic
345C22×Dic3—21no—
346C22×Dic3—61no—
347#239—22no—
348#239—41no—
349D3×Q8—62no—
350D3×Q8—121no—
351C2×D12—22no—
352C2×D12—21no—
353C2×D12—21no—
354C2×D12—21no—
355C2×D12—41no—
356C2×D12C22×D311yescharacteristic
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—61no—
361C2×C4×D3C22×D311yescharacteristic
362C2×Dic6—22no—
363C2×Dic6—21no—
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—41no—
367C2×Dic6—61no—
368C2×Dic6—62no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—121no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×Q16—62no—
375C3×Q16—121no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—41no—
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C4⋊C4C22×D311yescharacteristic
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—41no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—31no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—121no—
399#217#6711yescharacteristic
400#216—22no—
401#216—41no—
402#216—62no—
403#216—62no—
404#216—122no—
405#215—34no—
406#215—62no—
407#215—62no—
408#215—62no—
409#214—34no—
410#214—62no—
411#214—62no—
412#214—62no—
413#214—62no—
414#214—121no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4#6711yescharacteristic
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—121no—
435Dic3⋊C4#6711yescharacteristic
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3C22×D311yescharacteristic
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⋊C8—62no—
448C2×C3⋊C8—122no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451#204—62no—
452#204—121no—
453ΓL(1,𝔽25)—62no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32#13712yescomplemented
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—84no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—31no—
482C22×Q8—91no—
483C22×D4—31no—
484#137—184no—
485C2×Q16—31no—
486C2×Q16—31no—
487C2×Q16—91no—
488C2×SD16—91no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—91no—
496C22×C8—91no—
497C4⋊Q8—91no—
498C4⋊Q8—181no—
499#124—31no—
500#123—61no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503C22⋊Q8—181no—
504C22⋊Q8—181no—
505C22⋊Q8D3211yescharacteristic
506#121—31no—
507#121—61no—
508#120—61no—
509C4×Q8—91no—
510C4×D4—31no—
511C4×D4—31no—
512C4×D4—181no—
513C2×C22⋊C4—61no—
514#107—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—31no—
518#103—91no—
519#103—91no—
520#102—91no—
521#102—91no—
522C22⋊C8—31no—
523C22⋊C8—91no—
524#97—91no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—122no—
530C23×C3—122no—
531C23×C3—241no—
532C23×C3D3×D411yescharacteristic
533C23×C3C2×#6711yescharacteristic
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—81no—
539C22×D3C2×#6711yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—32no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—122no—
551C3×D4—32no—
552C3×D4—62no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—122no—
557C3×D4—122no—
558C3×D4—241no—
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—21no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—122no—
581C2×C3×C4—122no—
582C2×C3×C4—241no—
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4C2×#6711yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—22no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—42no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—122no—
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—21no—
616Dic6—42no—
617Dic6—61no—
618Dic6—61no—
619Dic6—61no—
620Dic6—61no—
621Dic6—121no—
622Dic6—121no—
623Dic6—122no—
624Dic6—122no—
625Dic6D3×D412yes—
626C3×C8—61no—
627C3×C8—61no—
628C3⋊C8—21no—
629C3⋊C8—21no—
630C3⋊C8—32no—
631C3⋊C8—32no—
632C3⋊C8—62no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—121no—
636C2×C32—22no—
637C2×C32D4211yescharacteristic
638C2×C32C2×#13711yescharacteristic
639C2×C32#57711yescharacteristic
640C3×D3—41no—
641C3×D3—42no—
642C3×D3—81no—
643C24—61no—
644#41—62no—
645#41—121no—
646C2×Q8—31no—
647C2×Q8—31no—
648C2×Q8—62no—
649C2×Q8—61no—
650C2×Q8—91no—
651C2×Q8—121no—
652C2×Q8—181no—
653C2×Q8—182no—
654C2×Q8—361no—
655C2×Q8C2×D3211yescharacteristic
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—121no—
664C22×C4—31no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—181no—
669C22×C4C2×D3211yescharacteristic
670Q16—62no—
671Q16—121no—
672Q16—182no—
673SD16—94no—
674SD16—182no—
675SD16—182no—
676SD16—182no—
677SD16—182no—
678SD16—361no—
679M16—182no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—91no—
683C2×C8—91no—
684C2×C8—182no—
685C4⋊C4—21no—
686C4⋊C4—31no—
687C4⋊C4—91no—
688C4⋊C4—181no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4C2×D3211yescharacteristic
694C22⋊C4—21no—
695C22⋊C4—31no—
696C22⋊C4—31no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—31no—
704C42—181no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—22no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3#91812yescomplemented
724C22×C3#95112yescomplemented
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C22×#6711yescharacteristic
727C2×D3—21no—
728C2×D3—22no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—84no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4—62no—
749C3×C4—61no—
750C3×C4—81no—
751C3×C4—81no—
752C3×C4—121no—
753C3×C4C2×D3×D411yescharacteristic
754C3×C4C2×D3×D411yescharacteristic
755C3×C4#100411yescharacteristic
756C3×C4#100411yescharacteristic
757Dic3—21no—
758Dic3—21no—
759Dic3—21no—
760Dic3—22no—
761Dic3—41no—
762Dic3—121no—
763Dic3—121no—
764Dic3—121no—
765Dic3—121no—
766Dic3—241no—
767Dic3—241no—
768C32#326611yescharacteristic, complemented, Sylow
769C23—31no—
770C23—61no—
771C23—61no—
772C23—122no—
773C23—122no—
774C23—241no—
775C23D3×#6711yescharacteristic
776Q8—21no—
777Q8—21no—
778Q8—32no—
779Q8—61no—
780Q8—61no—
781Q8—61no—
782Q8—122no—
783Q8—181no—
784Q8—181no—
785Q8—362no—
786D4—32no—
787D4—62no—
788D4—61no—
789D4—61no—
790D4—61no—
791D4—122no—
792D4—122no—
793D4—241no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—241no—
810C2×C4—362no—
811C2×C4D3×#6711yescharacteristic
812C2×C4C22×D3211yescharacteristic
813C8—61no—
814C8—61no—
815C8—92no—
816C8—181no—
817C2×C3—22no—
818C2×C3—22no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—42no—
823C2×C3—121no—
824C2×C3—122no—
825C2×C3—241no—
826C2×C3#559011yescharacteristic
827C2×C3C2×#91811yescharacteristic
828C2×C3#577811yescharacteristic
829C2×C3D4×#6711yescharacteristic
830C2×C3C2×#95111yescharacteristic
831C2×C3#583611yescharacteristic
832D3—41no—
833D3—42no—
834D3—81no—
835C22—21no—
836C22—21no—
837C22—61no—
838C22—61no—
839C22—62no—
840C22—61no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—244no—
847C22#6394312yescomplemented
848C22C2×D3×#6711yescharacteristic
849C4—21no—
850C4—41no—
851C4—41no—
852C4—61no—
853C4—61no—
854C4—62no—
855C4—61no—
856C4—121no—
857C4—361no—
858C4—361no—
859C4D32×D411yescharacteristic
860C4#6431311yescharacteristic
861C3—21no—
862C3#8020411yescharacteristic, complemented
863C3#8350611yescharacteristic, complemented
864C2—22no—
865C2—121no—
866C2—122no—
867C2—241no—
868C2#1059528711yescharacteristic
869C2C2×#6394311yescharacteristic
870C2#1059546411yescharacteristic
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. Dic6×#67C2semidirect
4. C22×#3715C2semidirect
5. #10592750C2semidirect
6. C3×#5050C2semidirect
7. #10591627C2semidirect
8. #10591597C2semidirect
9. #10591578C2semidirect
10. #10591172C2semidirect
11. #10591158C2semidirect
12. #10590603C2semidirect
13. #10590559C2semidirect
14. #10590515C2semidirect
15. #10590478C2semidirect
21. C2×D3×Dic6C22semidirect
23. C2×#3756C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#216C22semidirect
40. #63866C22semidirect
41. #63856C22semidirect
42. Dic3×Dic6C22semidirect
51. C2×#3711C22semidirect
52. #63662C22semidirect
53. #63637C22semidirect
54. #63634C22semidirect
56. C3×#810C22semidirect
57. C3×#810C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
82. #5050D3semidirect
154. #3715D4semidirect
188. C2×#216C2×D3semidirect
189. C2×#216C2×D3semidirect
247. #810C2×D3semidirect
248. #810C2×D3semidirect
456. C22×C32#137semidirect
723. C22×C3#918semidirect
724. C22×C3#951semidirect
768. C32#3266semidirect
847. C22#63943semidirect
862. C3#80204semidirect
863. 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
Dic6×#672
C22×#37152
#105927502
C3×#50502
#105916272
#105915972
#105915782
#105911722
#105911582
#105906032
#105905592
#105905152
#105904782
#835063
#802043