Finite Group Databasebeta

← #11887422

Subgroups — #11887422

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic, complemented
2#10594843C211yesmaximal, characteristic, complemented
3#10592747C211yesmaximal, characteristic, complemented
4C3×#5044C211yesmaximal, characteristic, complemented
5#10591614C211yesmaximal, characteristic, complemented
6#10591588C211yesmaximal, characteristic, complemented
7#10591568C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10591162C211yesmaximal, characteristic, complemented
10#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12#10590576C211yesmaximal, characteristic, complemented
13#10590542C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590446C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#81485—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3755C2211yescharacteristic, complemented
22#64139C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#947C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#895—21no—
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#893C2211yescharacteristic
31C3×#882—21no—
32C3×D3×C22⋊C4—21no—
33#63978—21no—
34#63952—21no—
35#63909C2211yescharacteristic, complemented
36#63894C2211yescharacteristic, complemented
37#63869C2211yescharacteristic, complemented
38#63854—21no—
39#63848—21no—
40#63841C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#830C2211yescharacteristic
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5630D311yescharacteristic, complemented
63#5565—31no—
64#5514—31no—
65C3×#484—31no—
66#5238—31no—
67#5233—31no—
68#5217—31no—
69C2×#832—31no—
70#5057—31no—
71#5056—31no—
72#5048—31no—
73#5048—31no—
74#5048—61no—
75#5044D311yescharacteristic, complemented
76#5038—31no—
77#5035—31no—
78C4×#213—31no—
79D4×C3⋊C8—31no—
80#5009—31no—
81C2×#809—31no—
82#4891—31no—
83#4885—31no—
84#4883—31no—
85#4872—31no—
86#4819—31no—
87#4810—31no—
88#4804—31no—
89#4800—31no—
90#4732—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C3×#67D411yescharacteristic
98C22×C3×Dic3—21no—
99C3×#239—22no—
100C3×#239—41no—
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×#626—21no—
112C2×#624—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116#3755—41no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)—41no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217D411yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3714—22no—
142#3714—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C3×#124—31no—
150C3×#123—61no—
151C3×C22⋊Q8—21no—
152C3×C22⋊Q8C2×D311yescharacteristic
153C3×C22⋊Q8C2×D311yescharacteristic
154C3×#121—31no—
155C3×#121—61no—
156C3×#120—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—61no—
161#947C2×D311yescharacteristic
162C2×#215—31no—
163C2×#215—31no—
164C2×#215—61no—
165#939—61no—
166C2×#213—31no—
167C2×#213—31no—
168#930—31no—
169#930—31no—
170#930—31no—
171#930—61no—
172#930—61no—
173C4×#67—61no—
174C4×#67C2×D311yescharacteristic
175#926—31no—
176C2×C4⋊Dic3C2×D311yescharacteristic
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180C22×C3⋊C8—61no—
181C2×D24—31no—
182C2×D24—31no—
183C2×D3×C8—31no—
184#898—61no—
185#898—61no—
186#895—21no—
187#895—31no—
188#895C2×D311yescharacteristic
189#894—21no—
190#894—61no—
191#893—31no—
192#893C2×D311yescharacteristic
193#892—31no—
194#890—31no—
195#883—61no—
196#882—21no—
197#67⋊C4—61no—
198D3×C22⋊C4—21no—
199C4×D12—31no—
200#870—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#835C2×D311yescharacteristic, complemented
210#835C2×D311yescharacteristic, complemented
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#830—31no—
218#830C2×D311yescharacteristic
219#821—31no—
220#821—31no—
221(C2×D3)⋊C8—31no—
222Dic3⋊C8—31no—
223C8×Dic3—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—61no—
231#808—31no—
232#808—31no—
233#808—61no—
234#807C2×D311yescharacteristic, complemented
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C3×#67—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12—42no—
270C3×D12—81no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275C3×C4×D3—81no—
276#626—81no—
277#624—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—31no—
284#488—91no—
285#484—31no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—121no—
323C2×#67#6711yescharacteristic
324C22×Dic3—21no—
325#239—22no—
326#239—41no—
327C2×D12—22no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—41no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3C22×D311yescharacteristic
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365#217—61no—
366#217#6711yescharacteristic
367#215—121no—
368#215—121no—
369#215—122no—
370#213—62no—
371#213—121no—
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—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—121no—
384(C2×D3)⋊C4#6711yescharacteristic
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4#6711yescharacteristic
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3C22×D311yescharacteristic
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⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—122no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—62no—
412D24—121no—
413D3×C8—121no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32#13512yes—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—91no—
448C22×C8—91no—
449#126—181no—
450#125—91no—
451#124—31no—
452#123—61no—
453#123—181no—
454C22⋊Q8D3211yescharacteristic
455#121—31no—
456#121—61no—
457#121—91no—
458#121—91no—
459#121—181no—
460#120—61no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—181no—
465#117—91no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—61no—
468#107—31no—
469#107—31no—
470#106—91no—
471C4⋊C8—91no—
472#103—31no—
473#103—31no—
474#103—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—91no—
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—122no—
490C23×C3—122no—
491C23×C3—241no—
492C23×C3D3×D411yescharacteristic
493C23×C3C2×#6711yescharacteristic
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—81no—
501C22×D3—121no—
502C22×D3C2×#6711yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×D4—32no—
510C3×D4—62no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—122no—
515C3×D4—122no—
516C3×D4—241no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—122no—
539C2×C3×C4—241no—
540C2×C3×C4—241no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—22no—
546#67—122no—
547#67—122no—
548#67—242no—
549#67—241no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—81no—
555C2×Dic3—121no—
556C2×Dic3C2×#6711yescharacteristic
557C2×Dic3C2×#6711yescharacteristic
558C2×Dic3C2×#6711yescharacteristic
559D12—21no—
560D12—21no—
561D12—21no—
562D12—42no—
563D12—42no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—61no—
568D12—81no—
569D12—121no—
570D12—121no—
571D12—241no—
572D12#23712yes—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—42no—
576C4×D3—81no—
577C4×D3—241no—
578C4×D3—241no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—62no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—121no—
589C2×C32—22no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13511yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—81no—
594C3×D3—41no—
595C3×D3—42no—
596C3×D3—81no—
597C24—61no—
598#41—62no—
599#41—121no—
600C2×Q8C2×D3211yescharacteristic
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—62no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—91no—
609C2×D4—121no—
610C2×D4—181no—
611C2×D4—181no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618SD16—361no—
619D8—182no—
620D8—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—91no—
624C2×C8—91no—
625C2×C8—361no—
626C2×C8—361no—
627C4⋊C4—21no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—91no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4C2×D3211yescharacteristic
636C22⋊C4—21no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—31no—
648C42—181no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—22no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—61no—
658C22×C3—62no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3#91912yes—
668C22×C3#95012yes—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C22×#6711yescharacteristic
671C2×D3—21no—
672C2×D3—22no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—84no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—241no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—81no—
703C3×C4—81no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4C2×#23711yescharacteristic
707C3×C4#100411yescharacteristic
708C3×C4D3×#4111yescharacteristic
709C3×C4#100911yescharacteristic
710Dic3—21no—
711Dic3—21no—
712Dic3—21no—
713Dic3—41no—
714Dic3—41no—
715Dic3—121no—
716Dic3—121no—
717Dic3—241no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—31no—
720C23—61no—
721C23—61no—
722C23—122no—
723C23—122no—
724C23—181no—
725C23—241no—
726C23D3×#6711yescharacteristic
727Q8—21no—
728Q8—21no—
729D4—32no—
730D4—62no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—122no—
735D4—122no—
736D4—181no—
737D4—181no—
738D4—241no—
739D4—362no—
740D4—721no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—122no—
753C2×C4—181no—
754C2×C4—241no—
755C2×C4—241no—
756C2×C4—721no—
757C2×C4D3×#6711yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—61no—
760C8—61no—
761C8—181no—
762C8—181no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—121no—
770C2×C3—122no—
771C2×C3—241no—
772C2×C3#565411yescharacteristic
773C2×C3C2×#91911yescharacteristic
774C2×C3#577411yescharacteristic
775C2×C3#580611yescharacteristic
776C2×C3C2×#95011yescharacteristic
777C2×C3#583511yescharacteristic
778D3—41no—
779D3—42no—
780D3—81no—
781D3—241no—
782D3—241no—
783D3—481no—
784C22—21no—
785C22—21no—
786C22—61no—
787C22—61no—
788C22—62no—
789C22—61no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—244no—
796C22—361no—
797C22—361no—
798C22—361no—
799C22#6394912yes—
800C22C2×D3×#6711yescharacteristic
801C4—21no—
802C4—41no—
803C4—41no—
804C4—61no—
805C4—61no—
806C4—61no—
807C4—121no—
808C4—121no—
809C4—361no—
810C4D3×#23711yescharacteristic
811C4#6431411yescharacteristic
812C3—21no—
813C3#8148511yescharacteristic, complemented
814C3#8349511yescharacteristic, complemented
815C2—22no—
816C2—121no—
817C2—122no—
818C2—241no—
819C2—721no—
820C2#1059514811yescharacteristic
821C2C2×#6394911yescharacteristic
822C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3297
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
1. C3×#5630C2semidirect
2. #10594843C2semidirect
3. #10592747C2semidirect
4. C3×#5044C2semidirect
5. #10591614C2semidirect
6. #10591588C2semidirect
7. #10591568C2semidirect
8. #10591556C2semidirect
9. #10591162C2semidirect
10. #67⋊(C3⋊C8)C2semidirect
11. C2×#63562C2semidirect
12. #10590576C2semidirect
13. #10590542C2semidirect
14. #10590456C2semidirect
15. #10590446C2semidirect
21. C2×#3755C22semidirect
35. #63909C22semidirect
36. #63894C22semidirect
37. #63869C22semidirect
40. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63636C22semidirect
46. #63635C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5630D3semidirect
75. #5044D3semidirect
209. #835C2×D3semidirect
210. #835C2×D3semidirect
234. #807C2×D3semidirect
235. #807C2×D3semidirect
718. C32#3297semidirect
813. C3#81485semidirect
814. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
#105948432
#105927472
C3×#50442
#105916142
#105915882
#105915682
#105915562
#105911622
#67⋊(C3⋊C8)2
C2×#635622
#105905762
#105905422
#105904562
#105904462
#834953
#814853