Finite Group Databasebeta

← #11889277

Subgroups — #11889277

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2#10594007C211yesmaximal, characteristic
3#10592783C211yesmaximal, characteristic, complemented
4C3×#5089C211yesmaximal, characteristic, complemented
5#10590616C211yesmaximal, characteristic, complemented
6#10590610C211yesmaximal, characteristic, complemented
7#10590596C211yesmaximal, characteristic, complemented
8#10590592C211yesmaximal, characteristic, complemented
9#10590520C211yesmaximal, characteristic, complemented
10#10590519C211yesmaximal, characteristic, complemented
11#10590505C211yesmaximal, characteristic, complemented
12#10590501C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83665—31nomaximal
17#81698—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#947—21no—
23C3×Q8×Dic3—21no—
24C3×#898—21no—
25C3×#898—21no—
26C3×#897C2211yescharacteristic
27C3×#897C2211yescharacteristic, complemented
28C3×#892C2211yescharacteristic
29C3×#892C2211yescharacteristic, complemented
30C3×#875C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63922—21no—
34#63921—21no—
35#63912—21no—
36#63908C2211yescharacteristic
37#63856C2211yescharacteristic
38#63854—21no—
39C2×#3718C2211yescharacteristic, complemented
40C2×#3717C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, 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#5676—31no—
64#5550—31no—
65C3×#489—31no—
66#5089D311yescharacteristic, complemented
67#5084—31no—
68#5084—31no—
69#5084—61no—
70#5054—31no—
71#5052—31no—
72#5048—31no—
73#5047—31no—
74#5046—31no—
75#5028—31no—
76#5026—31no—
77#5011—31no—
78#5003—31no—
79#5002—31no—
80#5001—31no—
81#4996—31no—
82#4816—31no—
83#4814—31no—
84#4808—31no—
85#4804—31no—
86#4784—31no—
87#4778—31no—
88#4776—31no—
89#4770—31no—
90#4710—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×Q8—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3799—22no—
109#3799—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
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)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3D411yescharacteristic
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
136#3724—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3718—41no—
140#3717—22no—
141#3715—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C2×#239—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—31no—
155C3×#124—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—61no—
160C3×C4×D4—31no—
161C3×#117—31no—
162C3×#117—31no—
163#947—21no—
164#946—31no—
165Q8×Dic3—21no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#215—31no—
169C2×#215—31no—
170#938—31no—
171#937—61no—
172C2×#214—31no—
173#930—31no—
174#924—31no—
175C2×#208—31no—
176C22×C3⋊C8—31no—
177C2×#204—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#898—21no—
181#898—21no—
182#897C2×D311yescharacteristic
183#897C2×D311yescharacteristic, complemented
184#894—61no—
185#892C2×D311yescharacteristic
186#892C2×D311yescharacteristic, complemented
187#884—61no—
188#884—61no—
189#883—61no—
190#882—61no—
191D3×C22⋊C4—61no—
192D3×C22⋊C4—61no—
193#875C2×D311yescharacteristic
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198C4×Dic6C2×D311yescharacteristic, complemented
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#97—31no—
204#835—31no—
205#835—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#818—31no—
213#816—31no—
214#810—31no—
215#810C2×D311yescharacteristic, complemented
216#810C2×D311yescharacteristic, complemented
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—61no—
224#809—61no—
225#809C2×D311yescharacteristic
226#809C2×D311yescharacteristic
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#808—61no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic, complemented
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)#4112yes—
254C4×C3⋊D3—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—41no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—42no—
273#625—81no—
274#624—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—31no—
282#485—91no—
283#482—91no—
284#476—91no—
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—31no—
300C2×C3×Q8—41no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309#239—62no—
310#239—121no—
311D3×D4—62no—
312D3×D4—121no—
313#235—62no—
314#235—121no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—62no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—121no—
322C2×D12#6711yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—121no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
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—41no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
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#217—61no—
365#216—121no—
366#216—121no—
367#215—62no—
368#215—121no—
369#214—121no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
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#6711yescharacteristic
382(C2×D3)⋊C4#6711yescharacteristic
383C4⋊Dic3—21no—
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3#6711yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396#208—121no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—62no—
407ΓL(1,𝔽25)—121no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—22no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
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—31no—
446#124—61no—
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—91no—
458#117—31no—
459#117—31no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—31no—
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—31no—
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—61no—
498C3×Q8—61no—
499C3×Q8—82no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—121no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—122no—
528#67—122no—
529#67—241no—
530#67—241no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—21no—
540D12—21no—
541D12—32no—
542D12—32no—
543D12—41no—
544D12—62no—
545D12—61no—
546D12—61no—
547D12—121no—
548D12—122no—
549D12—122no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—242no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563C3×C8—61no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—21no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8—121no—
573C2×C32#54611yescharacteristic
574C2×C32#57511yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—42no—
577C3×D3—41no—
578C3×D3—41no—
579C3×D3—81no—
580C24—181no—
581#41—182no—
582#41—361no—
583C2×Q8—21no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4—182no—
591C2×D4—181no—
592C2×D4—181no—
593C2×D4—361no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—361no—
599SD16—182no—
600SD16—361no—
601M16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—91no—
606C2×C8—361no—
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—61no—
629C42—61no—
630C42—61no—
631C42C2×D3211yescharacteristic
632C22×C3—21no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C22×#6711yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—122no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—241no—
661C2×D3—241no—
662C2×D3—244no—
663C2×D3—244no—
664C3×C4—22no—
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—61no—
677C3×C4—61no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4D3×#4111yescharacteristic
684C3×C4D3×#4111yescharacteristic
685C3×C4#100911yescharacteristic
686C3×C4#100911yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695C32#331111yescharacteristic, complemented, Sylow
696C23—31no—
697C23—31no—
698C23—61no—
699C23—181no—
700C23—362no—
701C23—362no—
702C23—721no—
703Q8—42no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—61no—
708D4—61no—
709D4—61no—
710D4—92no—
711D4—121no—
712D4—181no—
713D4—362no—
714D4—362no—
715D4—721no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—181no—
728C2×C4—362no—
729C2×C4—721no—
730C2×C4D3×#6711yescharacteristic
731C2×C4D3×#6711yescharacteristic
732C2×C4C22×D3211yescharacteristic
733C8—61no—
734C8—61no—
735C8—181no—
736C8—181no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—121no—
741C2×C3—121no—
742C2×C3—241no—
743C2×C3#567611yescharacteristic
744C2×C3#577311yescharacteristic
745C2×C3#577811yescharacteristic
746C2×C3#582211yescharacteristic
747C2×C3#582911yescharacteristic
748C2×C3#583711yescharacteristic
749D3—41no—
750D3—41no—
751D3—81no—
752D3—122no—
753D3—122no—
754D3—242no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—182no—
765C22—361no—
766C22—361no—
767C22—724no—
768C22C2×D3×#6711yescharacteristic
769C4—21no—
770C4—21no—
771C4—41no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—361no—
779C4#6431911yescharacteristic
780C4#6432011yescharacteristic
781C3—21no—
782C3#8169811yescharacteristic, complemented
783C3#8366511yescharacteristic, complemented
784C2—121no—
785C2—121no—
786C2—241no—
787C2—362no—
788C2#1059509511yescharacteristic
789C2#1059531911yescharacteristic
790C2#1059542811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594007C2
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. #10592783C2semidirect
4. C3×#5089C2semidirect
5. #10590616C2semidirect
6. #10590610C2semidirect
7. #10590596C2semidirect
8. #10590592C2semidirect
9. #10590520C2semidirect
10. #10590519C2semidirect
11. #10590505C2semidirect
12. #10590501C2semidirect
13. #10590362C2semidirect
14. #10590326C2semidirect
15. #10590267C2semidirect
20. C32×C4⋊Q8C22semidirect
27. C3×#897C22semidirect
29. C3×#892C22semidirect
32. C3×C4×Dic6C22semidirect
39. C2×#3718C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63635C22semidirect
47. #63635C22semidirect
48. C4⋊(C3⋊(C3⋊C8))C22semidirect
49. C3×#810C22semidirect
50. C3×#810C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5732D3semidirect
66. #5089D3semidirect
150. C3×C4⋊Q8C2×D3semidirect
151. C3×C4⋊Q8C2×D3semidirect
183. #897C2×D3semidirect
186. #892C2×D3semidirect
198. C4×Dic6C2×D3semidirect
215. #810C2×D3semidirect
216. #810C2×D3semidirect
237. #803C2×D3semidirect
442. C4⋊Q8D32semidirect
695. C32#3311semidirect
782. C3#81698semidirect
783. C3#83665semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105940072
#105927832
C3×#50892
#105906162
#105906102
#105905962
#105905922
#105905202
#105905192
#105905052
#105905012
#105903622
#105903262
#105902672
#836653
#816983