Finite Group Databasebeta

← #11889294

Subgroups — #11889294

Order 1152.

852 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×#5630C211yesmaximal, characteristic
2#10594841C211yesmaximal, characteristic, complemented
3#10592744C211yesmaximal, characteristic, complemented
4C3×#5052C211yesmaximal, characteristic, complemented
5#10591624C211yesmaximal, characteristic, complemented
6#10591597C211yesmaximal, characteristic, complemented
7#10591578C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10591169C211yesmaximal, characteristic, complemented
10#10591147C211yesmaximal, characteristic, complemented
11#10591086C211yesmaximal, characteristic, complemented
12#10590558C211yesmaximal, characteristic, complemented
13#10590514C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590449C211yesmaximal, characteristic, complemented
16#83497—31nomaximal
17#80914—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64135C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic, complemented
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C3×#895—21no—
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#893C2211yescharacteristic
31C3×#882—21no—
32C3×D3×C22⋊C4—21no—
33#63959—21no—
34#63956—21no—
35#63918C2211yescharacteristic, complemented
36#63862—21no—
37#63856C2211yescharacteristic, complemented
38Dic3×Dic6C2211yescharacteristic, complemented
39#63841C2211yescharacteristic, complemented
40#63838—21no—
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63657C2211yescharacteristic
47#63635C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5641—31no—
63#5630D311yescharacteristic
64#5542—31no—
65C3×#470—31no—
66#5239—31no—
67#5233—31no—
68#5218—31no—
69#5215—31no—
70#5187—31no—
71#5185—31no—
72#5131—31no—
73#5127—31no—
74#5055—31no—
75#5054—31no—
76#5052D311yescharacteristic, complemented
77#5046—31no—
78#5045—31no—
79#5045—31no—
80#5045—61no—
81#5041—31no—
82#5035—31no—
83#5018—31no—
84#5011—31no—
85#5008—31no—
86#4870—31no—
87#4866—31no—
88#4817—31no—
89#4807—31no—
90#4804—31no—
91#4794—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—22no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#216—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C3×#208—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3715—22no—
142#3715—41no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×M16—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C2×D311yescharacteristic
157C3×#121—31no—
158C3×#121—61no—
159C3×#120—61no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C22⋊C4—61no—
163#947C2×D311yescharacteristic
164#946—31no—
165Q8×Dic3—31no—
166C2×#216C2×D311yescharacteristic, complemented
167C2×#215—31no—
168C2×#215—31no—
169#936—61no—
170C2×#214—31no—
171C2×#214—31no—
172C4×#67C2×D311yescharacteristic
173#926—31no—
174#926—31no—
175#926—31no—
176#926—61no—
177#924—31no—
178#924C2×D311yescharacteristic
179C2×#208C2×D311yescharacteristic
180C22×C3⋊C8—31no—
181C2×D3×C8—31no—
182#898—61no—
183#895—21no—
184#895C2×D311yescharacteristic
185#894—21no—
186#893C2×D311yescharacteristic
187#892—31no—
188#888—31no—
189#887—61no—
190#887—61no—
191#885—61no—
192#882—21no—
193D3×C22⋊C4—21no—
194#879—61no—
195#879—61no—
196#879—61no—
197#869—31no—
198C4×Dic6—31no—
199C3×#106—31no—
200C3×#103—31no—
201C3×#103—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#835—61no—
208#835C2×D311yescharacteristic, complemented
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#830—31no—
216#830—31no—
217#830—31no—
218#830—61no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224#815—31no—
225Dic3⋊C8—31no—
226#810C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234#807—31no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C3×#67—41no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—42no—
265C3×D12—42no—
266C3×D12—81no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#627—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—31no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—31no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67#6711yescharacteristic
317#239—22no—
318#239—41no—
319C2×D12—22no—
320C2×D12—21no—
321C2×D12—21no—
322C2×D12—21no—
323C2×D12—41no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6C22×D311yescharacteristic
332C3×Q16—121no—
333C3×M16—121no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
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⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356#217—21no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—121no—
362#217#6711yescharacteristic
363#216—41no—
364#215—62no—
365#215—121no—
366#214—62no—
367#214—121no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4#6711yescharacteristic
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4#6711yescharacteristic
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—121no—
397C4×Dic3C22×D311yescharacteristic
398#208—41no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D3×C8—121no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—31no—
438C2×SD16—91no—
439C2×SD16—91no—
440C2×M16—31no—
441C22×C8—91no—
442C4⋊Q8—91no—
443#126—181no—
444#126—181no—
445#124—31no—
446#124—181no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8D3211yescharacteristic
451#121—31no—
452#121—61no—
453#120—61no—
454C4×Q8—91no—
455C4×Q8—181no—
456C4×D4—31no—
457C4×D4—31no—
458#117—91no—
459#117—91no—
460C2×C22⋊C4—61no—
461#107—91no—
462#106—31no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477#97—91no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—122no—
483C23×C3—122no—
484C23×C3—241no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—81no—
492C22×D3C2×#6711yescharacteristic
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×D4—32no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4—122no—
507C3×D4—121no—
508C3×D4—241no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4—241no—
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—41no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3C2×#6711yescharacteristic
546C2×Dic3C2×#6711yescharacteristic
547C2×Dic3C2×#6711yescharacteristic
548D12—21no—
549D12—21no—
550D12—21no—
551D12—42no—
552D12—42no—
553D12—81no—
554D12#23712yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—81no—
559Dic6—21no—
560Dic6—21no—
561Dic6—122no—
562Dic6—122no—
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—41no—
574C2×C32#54611yescharacteristic
575C2×C32#57511yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—41no—
578C3×D3—42no—
579C3×D3—81no—
580C24—61no—
581#41—62no—
582#41—121no—
583C2×Q8—31no—
584C2×Q8—181no—
585C2×Q8C2×D3211yescharacteristic
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—62no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—121no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4C2×D3211yescharacteristic
598Q16—121no—
599SD16—182no—
600SD16—361no—
601M16—121no—
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—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—21no—
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—
628C42—31no—
629C42—181no—
630C42—181no—
631C42—181no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—62no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C22×#6711yescharacteristic
654C2×D3—21no—
655C2×D3—22no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—84no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—81no—
677C3×C4—81no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4C2×#23711yescharacteristic
681C3×C4#100411yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4D3×#4111yescharacteristic
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695C32#331111yescharacteristic, complemented, Sylow
696C23—31no—
697C23—61no—
698C23—61no—
699C23—122no—
700C23—122no—
701C23—241no—
702C23D3×#6711yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—61no—
706Q8—61no—
707Q8—362no—
708D4—32no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—122no—
713D4—122no—
714D4—121no—
715D4—241no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—122no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—241no—
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—41no—
741C2×C3—41no—
742C2×C3—81no—
743C2×C3—121no—
744C2×C3—122no—
745C2×C3—241no—
746C2×C3#561011yescharacteristic
747C2×C3#577711yescharacteristic
748C2×C3#577811yescharacteristic
749C2×C3#580611yescharacteristic
750C2×C3#582211yescharacteristic
751C2×C3#583611yescharacteristic
752D3—41no—
753D3—42no—
754D3—81no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—61no—
759C22—62no—
760C22—61no—
761C22—61no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—244no—
768C22C2×D3×#6711yescharacteristic
769C4—21no—
770C4—41no—
771C4—41no—
772C4—61no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—361no—
778C4—361no—
779C4D3×#23711yescharacteristic
780C4#6431311yescharacteristic
781C3—21no—
782C3#8091411yescharacteristic, complemented
783C3#8349711yescharacteristic, complemented
784C2—41no—
785C2—121no—
786C2—122no—
787C2—241no—
788C2#1059515011yescharacteristic
789C2#1059531711yescharacteristic
790C2#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#3311
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. #10594841C2semidirect
3. #10592744C2semidirect
4. C3×#5052C2semidirect
5. #10591624C2semidirect
6. #10591597C2semidirect
7. #10591578C2semidirect
8. #10591556C2semidirect
9. #10591169C2semidirect
10. #10591147C2semidirect
11. #10591086C2semidirect
12. #10590558C2semidirect
13. #10590514C2semidirect
14. #10590478C2semidirect
15. #10590449C2semidirect
23. C2×C3×#216C22semidirect
35. #63918C22semidirect
37. #63856C22semidirect
38. Dic3×Dic6C22semidirect
39. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63662C22semidirect
47. #63635C22semidirect
48. #63634C22semidirect
49. C3×#835C22semidirect
50. C3×#810C22semidirect
51. C3×#808C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
76. #5052D3semidirect
166. C2×#216C2×D3semidirect
208. #835C2×D3semidirect
226. #810C2×D3semidirect
232. #808C2×D3semidirect
695. C32#3311semidirect
782. C3#80914semidirect
783. C3#83497semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
#105948412
#105927442
C3×#50522
#105916242
#105915972
#105915782
#105915562
#105911692
#105911472
#105910862
#105905582
#105905142
#105904782
#105904492
#834973
#809143