Finite Group Databasebeta

← #11888687

Subgroups — #11888687

Order 1152.

848 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×#5726C211yesmaximal, characteristic, complemented
2#10593925C211yesmaximal, characteristic, complemented
3#10592782C211yesmaximal, characteristic, complemented
4C3×#5082C211yesmaximal, characteristic, complemented
5#10591589C211yesmaximal, characteristic, complemented
6#10591588C211yesmaximal, characteristic, complemented
7#10591588C211yesmaximal, characteristic, complemented
8#10591585C211yesmaximal, characteristic, complemented
9#10591559C211yesmaximal, characteristic, complemented
10#10591556C211yesmaximal, characteristic, complemented
11#10591550C211yesmaximal, characteristic, complemented
12#10591549C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83512—31nomaximal
17#81748—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#895—21no—
27C3×#894—21no—
28C3×#894—21no—
29C3×D3×C4⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×#870C2211yescharacteristic
33#63909C2211yescharacteristic
34#63909C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63886—21no—
37#63881—21no—
38#63853—21no—
39#63848—21no—
40#63841C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#803C2211yescharacteristic
52#63576C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#547—31no—
62#5726D311yescharacteristic, complemented
63#5695—31no—
64#5565—31no—
65C3×#491—31no—
66#5238—31no—
67#5238—31no—
68#5233—31no—
69#5232—31no—
70#5083—31no—
71#5083—31no—
72#5083—61no—
73#5082D311yescharacteristic, complemented
74#5066—31no—
75#5049—31no—
76#5048—31no—
77#5045—31no—
78#5043—31no—
79#5014—31no—
80#5011—31no—
81#5009—31no—
82#4815—31no—
83#4812—31no—
84#4810—31no—
85#4810—31no—
86#4807—31no—
87#4805—31no—
88#4804—31no—
89#4803—31no—
90#4711—31no—
91#4706—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C3×#239—22no—
97C3×#239—22no—
98C3×#239—41no—
99C3×#239—41no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×D3×Dic3—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3755—41no—
116#3755—41no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
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⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3714—22no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C2×D311yescharacteristic
148C2×#239C2×D311yescharacteristic
149C3×C4⋊Q8—21no—
150C3×C4⋊Q8C2×D311yescharacteristic
151C3×C4⋊Q8C2×D311yescharacteristic
152C3×#125—31no—
153C3×#123—61no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×#121—61no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C2×C3×C4⋊C4—61no—
161#946C2×D311yescharacteristic
162#946C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—61no—
168C2×#215—61no—
169#939—61no—
170C2×#213—31no—
171#930—31no—
172#930—31no—
173#926—31no—
174C2×C4⋊Dic3—31no—
175C2×#208—31no—
176C22×C3⋊C8—31no—
177C2×D24—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#898—61no—
181#898—61no—
182#895—21no—
183#895—31no—
184#895—31no—
185#895—61no—
186#894—21no—
187#894—21no—
188#894—61no—
189#893—61no—
190#892—31no—
191D3×C4⋊C4—21no—
192D3×C4⋊C4—31no—
193#883—61no—
194#67⋊C4—61no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200#870C2×D311yescharacteristic
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#97—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#835—61no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#835C2×D311yescharacteristic
216#832—31no—
217#832—31no—
218#832—31no—
219#830—31no—
220#830—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#817—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—21no—
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—
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—41no—
262C3×D12—42no—
263C3×D12—42no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272#626—42no—
273#626—81no—
274D3×Dic3—81no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—31no—
281#491—31no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—61no—
314C2×#67—61no—
315C22×Dic3—61no—
316#239—22no—
317#239—22no—
318#239—41no—
319#239—41no—
320C2×D12—21no—
321C2×D12—21no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12#6711yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—121no—
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—41no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—21no—
360C3×C42C22×D311yescharacteristic
361C3×C42C22×D311yescharacteristic
362#217—61no—
363#215—121no—
364#215—121no—
365#215—121no—
366#215—121no—
367#215—122no—
368#215—122no—
369#213—62no—
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#6711yescharacteristic
382(C2×D3)⋊C4#6711yescharacteristic
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3#6711yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398#208—121no—
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
408D24—62no—
409ΓL(1,𝔽25)—121no—
410D3×C8—121no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C2×#41—31no—
438C2×SD16—91no—
439C2×SD16—91no—
440C2×D8—91no—
441C2×M16—91no—
442C22×C8—91no—
443C4⋊Q8D3211yescharacteristic
444#126—181no—
445#125—31no—
446#123—61no—
447#123—61no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451#121—61no—
452#121—91no—
453#121—91no—
454#121—181no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—181no—
459#117—91no—
460C2×C4⋊C4—61no—
461C2×C4⋊C4—91no—
462#107—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478#97—31no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3C2×#6711yescharacteristic
487C22×D3C2×#6711yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—41no—
500C3×D4—32no—
501C3×D4—61no—
502C3×D4—121no—
503C3×D4—122no—
504C3×D4—122no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—122no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—122no—
533#67—241no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—241no—
541C2×Dic3C2×#6711yescharacteristic
542C2×Dic3C2×#6711yescharacteristic
543D12—21no—
544D12—41no—
545D12—42no—
546D12—42no—
547D12—62no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—121no—
553D12—122no—
554D12—241no—
555D12#23712yes—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—42no—
561C4×D3—42no—
562C4×D3—42no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—242no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—121no—
576C3⋊C8—121no—
577C2×C32#54611yescharacteristic
578C2×C32#57511yescharacteristic
579C2×C32#57711yescharacteristic
580C3⋊D3—81no—
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—42no—
584#41—62no—
585#41—62no—
586#41—121no—
587#41—121no—
588C2×Q8C2×D3211yescharacteristic
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—181no—
596C2×D4—181no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—181no—
603C22×C4—181no—
604SD16—361no—
605SD16—361no—
606D8—182no—
607M16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—91no—
612C2×C8—361no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C22⋊C4—31no—
626C22⋊C4—31no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—181no—
635C42C2×D3211yescharacteristic
636C22×C3—21no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—62no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C22×#6711yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—22no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—122no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—241no—
665C2×D3—241no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4C2×#23711yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#330711yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23—61no—
701C23—181no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—21no—
706D4—32no—
707D4—61no—
708D4—121no—
709D4—122no—
710D4—122no—
711D4—181no—
712D4—181no—
713D4—362no—
714D4—721no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4D3×#6711yescharacteristic
733C2×C4D3×#6711yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—61no—
736C8—61no—
737C8—181no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—121no—
743C2×C3—121no—
744C2×C3—122no—
745C2×C3#567611yescharacteristic
746C2×C3#577711yescharacteristic
747C2×C3#577811yescharacteristic
748C2×C3#580611yescharacteristic
749C2×C3#582211yescharacteristic
750C2×C3#583711yescharacteristic
751D3—41no—
752D3—41no—
753D3—42no—
754D3—242no—
755D3—241no—
756D3—241no—
757C22—61no—
758C22—61no—
759C22—62no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—121no—
765C22—121no—
766C22—361no—
767C22—361no—
768C22—361no—
769C22C2×D3×#6711yescharacteristic
770C4—21no—
771C4—21no—
772C4—41no—
773C4—41no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—361no—
780C4D3×#23711yescharacteristic
781C4#6431411yescharacteristic
782C3—21no—
783C3#8174811yescharacteristic, complemented
784C3#8351211yescharacteristic, complemented
785C2—121no—
786C2—121no—
787C2—122no—
788C2—721no—
789C2#1059522911yescharacteristic
790C2#1059531711yescharacteristic
791C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3307
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×#5726C2semidirect
2. #10593925C2semidirect
3. #10592782C2semidirect
4. C3×#5082C2semidirect
5. #10591589C2semidirect
6. #10591588C2semidirect
7. #10591588C2semidirect
8. #10591585C2semidirect
9. #10591559C2semidirect
10. #10591556C2semidirect
11. #10591550C2semidirect
12. #10591549C2semidirect
13. #10590346C2semidirect
14. #10590326C2semidirect
15. #10590270C2semidirect
62. #5726D3semidirect
73. #5082D3semidirect
697. C32#3307semidirect
783. C3#81748semidirect
784. C3#83512semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
#105939252
#105927822
C3×#50822
#105915892
#105915882
#105915852
#105915592
#105915562
#105915502
#105915492
#105903462
#105903262
#105902702
#835123
#817483