Finite Group Databasebeta

← #11889279

Subgroups — #11889279

Order 1152.

854 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2#10594003C211yesmaximal, characteristic
3#10592788C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590614C211yesmaximal, characteristic, complemented
6#10590608C211yesmaximal, characteristic, complemented
7#10590596C211yesmaximal, characteristic, complemented
8#10590592C211yesmaximal, characteristic, complemented
9#10590587C211yesmaximal, characteristic, complemented
10#10590577C211yesmaximal, characteristic, complemented
11#10590428C211yesmaximal, characteristic, complemented
12#10590425C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83665—31nomaximal
17#81078—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21#64084C2211yescharacteristic
22C3×#947—21no—
23C3×Q8×Dic3—21no—
24C3×#898—21no—
25C3×#898—21no—
26C3×#897C2211yescharacteristic
27C3×#897C2211yescharacteristic, complemented
28C3×#892C2211yescharacteristic
29C3×#892C2211yescharacteristic, complemented
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35#63909C2211yescharacteristic
36#63906—21no—
37#63890—21no—
38#63857C2211yescharacteristic
39C2×#3719C2211yescharacteristic, complemented
40C2×#3717C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63637C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48#63630C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#556—31no—
62#5732D311yescharacteristic, complemented
63#5554—31no—
64#5550—31no—
65C3×#476—31no—
66#5089—31no—
67#5089—31no—
68#5089—61no—
69#5084D311yescharacteristic, complemented
70#5052—31no—
71#5048—31no—
72#5047—31no—
73#5046—31no—
74#5028—31no—
75#5026—31no—
76#5018—31no—
77#5011—31no—
78#5003—31no—
79#5002—31no—
80#5001—31no—
81#4996—31no—
82#4868—31no—
83#4867—31no—
84#4866—31no—
85#4864—31no—
86#4845—31no—
87#4836—31no—
88#4783—31no—
89#4776—31no—
90#4772—31no—
91#4770—31no—
92C22×D32—21no—
93C2×C32×Q8—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3795—22no—
109#3795—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752—21no—
115#3752—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3719—41no—
140#3717—41no—
141#3715—22no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C3×C4⋊Q8—21no—
150C3×C4⋊Q8C2×D311yescharacteristic, complemented
151C3×C4⋊Q8C2×D311yescharacteristic, complemented
152C3×#126—61no—
153C3×#126—61no—
154C3×#124—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×#117—31no—
162C3×#117—31no—
163#947—21no—
164Q8×Dic3—21no—
165C2×#216—31no—
166C2×#215—31no—
167C2×#215—31no—
168#937—61no—
169C2×#214—31no—
170#930—31no—
171#930—61no—
172C2×(C2×D3)⋊C4—61no—
173#924—31no—
174C2×#208—31no—
175C22×C3⋊C8—31no—
176C2×Dic12—31no—
177C2×#204—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#898—21no—
181#898—21no—
182#897—31no—
183#897C2×D311yescharacteristic
184#897C2×D311yescharacteristic, complemented
185#895—31no—
186#894—61no—
187#892C2×D311yescharacteristic
188#892C2×D311yescharacteristic, complemented
189#886—61no—
190#884—61no—
191#882—61no—
192D3×C22⋊C4—61no—
193#875—31no—
194#875—31no—
195#875—61no—
196C4×D12C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198C4×Dic6C2×D311yescharacteristic, complemented
199C3×#106—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×#102—31no—
203C3×#102—31no—
204#835—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#816—31no—
212#810—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—61no—
219#810—61no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#809—61no—
228#809C2×D311yescharacteristic
229#809C2×D311yescharacteristic
230#808C2×D311yescharacteristic, complemented
231#808C2×D311yescharacteristic, complemented
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235#803—31no—
236#803—31no—
237#803—61no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—42no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254#634—21no—
255#634—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—41no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—81no—
273#625—42no—
274D3×Dic3—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—31no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—31no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8—41no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C22×Dic3—61no—
310#237—62no—
311#237—121no—
312D3×D4—62no—
313D3×D4—121no—
314#235—62no—
315#235—121no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12#6711yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#217—61no—
364#216—121no—
365#215—62no—
366#215—121no—
367#214—62no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4—121no—
382(C2×D3)⋊C4#6711yescharacteristic
383(C2×D3)⋊C4#6711yescharacteristic
384C4⋊Dic3—21no—
385C4⋊Dic3—21no—
386C4⋊Dic3—61no—
387C4⋊Dic3#6711yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395#208—121no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406#204—121no—
407ΓL(1,𝔽25)—121no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422D32—84no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—91no—
437C2×Q16—91no—
438C2×SD16—91no—
439C2×SD16—91no—
440C2×M16—91no—
441C22×C8—91no—
442C4⋊Q8D3211yescharacteristic, complemented
443#126—61no—
444#126—61no—
445#124—61no—
446#124—91no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—31no—
455C4×Q8—61no—
456C4×D4—31no—
457C4×D4—31no—
458#117—31no—
459#117—31no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—31no—
463#106—31no—
464C4⋊C8—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477#97—91no—
478C23×C3—31no—
479C23×C3—31no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—122no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3C2×#6711yescharacteristic
492C22×D3C2×#6711yescharacteristic
493C3×Q8—42no—
494C3×Q8—42no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—82no—
498C3×D4—32no—
499C3×D4—61no—
500C3×D4—121no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—241no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—122no—
527#67—122no—
528#67—122no—
529#67—241no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—21no—
540D12—41no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—61no—
545D12—121no—
546D12—121no—
547D12—122no—
548D12—241no—
549D12#23912yes—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—81no—
555C4×D3—122no—
556Dic6—21no—
557Dic6—21no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—121no—
563Dic6—121no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8—121no—
574C2×C32#54611yescharacteristic
575C2×C32#57511yescharacteristic
576C2×C32#57711yescharacteristic
577C3⋊D3—81no—
578C3×D3—41no—
579C3×D3—42no—
580C3×D3—41no—
581C24—181no—
582#41—182no—
583#41—361no—
584C2×Q8—21no—
585C2×Q8—31no—
586C2×Q8—91no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—181no—
593C2×D4—181no—
594C2×D4—361no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—181no—
599Q16—361no—
600SD16—182no—
601SD16—361no—
602M16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—91no—
607C2×C8—361no—
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—61no—
630C42—61no—
631C42—61no—
632C42C2×D3211yescharacteristic
633C22×C3—21no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—62no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C22×#6711yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—241no—
661C2×D3—241no—
662C2×D3—241no—
663C2×D3—244no—
664C2×D3—244no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C2×#23911yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4#100911yescharacteristic
687C3×C4#100911yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696C32#331111yescharacteristic, complemented, Sylow
697C23—31no—
698C23—31no—
699C23—61no—
700C23—181no—
701C23—362no—
702C23—362no—
703C23—721no—
704Q8—42no—
705Q8—61no—
706Q8—61no—
707Q8—181no—
708Q8—181no—
709D4—32no—
710D4—61no—
711D4—121no—
712D4—181no—
713D4—181no—
714D4—362no—
715D4—362no—
716D4—721no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—181no—
729C2×C4—241no—
730C2×C4—362no—
731C2×C4D3×#6711yescharacteristic
732C2×C4D3×#6711yescharacteristic
733C2×C4C22×D3211yescharacteristic
734C8—61no—
735C8—61no—
736C8—181no—
737C8—181no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—121no—
742C2×C3—121no—
743C2×C3—122no—
744C2×C3#563011yescharacteristic
745C2×C3#576211yescharacteristic
746C2×C3#577311yescharacteristic
747C2×C3#582211yescharacteristic
748C2×C3#582911yescharacteristic
749C2×C3#583711yescharacteristic
750D3—42no—
751D3—41no—
752D3—41no—
753D3—241no—
754D3—241no—
755D3—481no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—62no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—361no—
766C22—361no—
767C22—361no—
768C22—724no—
769C22C2×D3×#6711yescharacteristic
770C4—21no—
771C4—21no—
772C4—41no—
773C4—41no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—361no—
780C4D3×#23911yescharacteristic
781C4#6432011yescharacteristic
782C3—21no—
783C3#8107811yescharacteristic, complemented
784C3#8366511yescharacteristic, complemented
785C2—121no—
786C2—121no—
787C2—122no—
788C2—721no—
789C2#1059509511yescharacteristic
790C2#1059531811yescharacteristic
791C2#1059542711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594003C2
hypercenterC4⋊Q8D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5732C2semidirect
3. #10592788C2semidirect
4. C3×#5084C2semidirect
5. #10590614C2semidirect
6. #10590608C2semidirect
7. #10590596C2semidirect
8. #10590592C2semidirect
9. #10590587C2semidirect
10. #10590577C2semidirect
11. #10590428C2semidirect
12. #10590425C2semidirect
13. #10590368C2semidirect
14. #10590358C2semidirect
15. #10590330C2semidirect
20. C32×C4⋊Q8C22semidirect
27. C3×#897C22semidirect
29. C3×#892C22semidirect
32. C3×C4×Dic6C22semidirect
39. C2×#3719C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63637C22semidirect
45. #63637C22semidirect
48. #63630C22semidirect
51. C3×#808C22semidirect
52. C3×#808C22semidirect
53. C3×C4⋊(C3⋊C8)C22semidirect
54. #63576C22semidirect
55. #63567C22semidirect
56. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5732D3semidirect
69. #5084D3semidirect
150. C3×C4⋊Q8C2×D3semidirect
151. C3×C4⋊Q8C2×D3semidirect
184. #897C2×D3semidirect
188. #892C2×D3semidirect
198. C4×Dic6C2×D3semidirect
230. #808C2×D3semidirect
231. #808C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
442. C4⋊Q8D32semidirect
696. C32#3311semidirect
783. C3#81078semidirect
784. C3#83665semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105940032
#105927882
C3×#50842
#105906142
#105906082
#105905962
#105905922
#105905872
#105905772
#105904282
#105904252
#105903682
#105903582
#105903302
#836653
#810783