Finite Group Databasebeta

← #11887461

Subgroups — #11887461

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
1#10595228C211yesmaximal, characteristic, complemented
2#10594559C211yesmaximal, characteristic, complemented
3#10592486C211yesmaximal, characteristic, complemented
4C3×#4779C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591449C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic, complemented
8#10591403C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590782C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13#10590608C211yesmaximal, characteristic, complemented
14#10590459C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#81382—31nomaximal
17#78760—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64145C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C2×#3744C2211yescharacteristic, complemented
23#64102C2211yescharacteristic, complemented
24C3×#938C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#892C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic
28#63976—21no—
29#63970—21no—
30#63969—21no—
31D3×#217—21no—
32#63909C2211yescharacteristic
33#63909C2211yescharacteristic, complemented
34#63906—21no—
35C4×#626—21no—
36C4×#625C2211yescharacteristic
37#63898C2211yescharacteristic
38#63872C2211yescharacteristic, complemented
39#63868—21no—
40#63857C2211yescharacteristic
41#63853—21no—
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63641C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5806—31no—
62#5612—31no—
63#5530—31no—
64#5514—31no—
65C3×#482—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5114—31no—
69C8×#67—31no—
70#5038—31no—
71#5002—31no—
72#4970—31no—
73#4884—31no—
74#4872—31no—
75#4871—31no—
76#4864—31no—
77#4787—31no—
78#4787—31no—
79#4787—61no—
80#4781—31no—
81#4779D311yescharacteristic, complemented
82#4775—31no—
83#4773—31no—
84#4772—31no—
85D3×#102D311yescharacteristic, complemented
86#4768—31no—
87#4768—31no—
88#4763—31no—
89#4756—31no—
90#4734—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×D3×D4—22no—
100C3×D3×D4—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#625D411yescharacteristic
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795—41no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116#3757—21no—
117#3753—41no—
118#3752—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3744—41no—
122C3×#217—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3714—22no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235—31no—
149C22×C3×C8—31no—
150C3×#121—31no—
151C3×#117—31no—
152C2×C3×C4⋊C4—31no—
153#953—61no—
154C2×#217—61no—
155#939—61no—
156#938—61no—
157#938C2×D311yescharacteristic
158#937—61no—
159#936—31no—
160#936—31no—
161#936—61no—
162#935—61no—
163D4×Dic3—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—61no—
168#930—31no—
169#930—31no—
170#930—61no—
171C4×#67—31no—
172C4×#67—31no—
173C4×#67—61no—
174#924—31no—
175C22×C3⋊C8—31no—
176C2×D24—31no—
177C2×#204—31no—
178C2×#204—31no—
179C2×#204—61no—
180C2×D3×C8—31no—
181C2×D3×C8C2×D311yescharacteristic
182#898—61no—
183#897—31no—
184#895—31no—
185#895—31no—
186#894—61no—
187#893—31no—
188#893—31no—
189#893—31no—
190#893—61no—
191#892C2×D311yescharacteristic, complemented
192D3×C4⋊C4C2×D311yescharacteristic
193#890—31no—
194#890—31no—
195#884—61no—
196#883—61no—
197#883—61no—
198D3×C22⋊C4—61no—
199#876—61no—
200C4×D12—61no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×C22⋊C8—31no—
211#832—31no—
212#832C2×D311yescharacteristic
213#832C2×D311yescharacteristic
214#830—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic, complemented
219#817C2×D311yescharacteristic, complemented
220#816—31no—
221#816—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—61no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#809—31no—
233#809—31no—
234#809C2×D311yescharacteristic
235#807—31no—
236#807—31no—
237#807C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4×C3⋊D3—81no—
256#634—21no—
257#634—21no—
258C3×#67—42no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272#626—42no—
273#626—81no—
274#625—22no—
275#625—42no—
276D3×Dic3—42no—
277D3×Dic3—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—31no—
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—31no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—121no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C2×#67—31no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320#237—62no—
321#237—121no—
322D3×D4—22no—
323D3×D4—41no—
324#235—62no—
325#235—121no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×C4×D3C22×D311yescharacteristic
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—61no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—61no—
359#217—21no—
360#217—31no—
361#217—31no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#217—121no—
370#213—62no—
371#213—121no—
372#213—121no—
373#213—122no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
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—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—121no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—21no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409#204—121no—
410#204—121no—
411#204—122no—
412D3×C8—41no—
413D3×C8—121no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—84no—
430C2×C3×D3#13512yes—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—31no—
448C22×C8—91no—
449#126—181no—
450#125—91no—
451#124—91no—
452#123—181no—
453#123—181no—
454C22⋊Q8—91no—
455#121—31no—
456#121—91no—
457#121—91no—
458#121—181no—
459#121—181no—
460#120—181no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—181no—
465#117—31no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—91no—
470#106—31no—
471C4⋊C8—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102D3211yescharacteristic
482C22⋊C8—31no—
483C22⋊C8—91no—
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C23×C3—122no—
492C23×C3—122no—
493C23×C3—241no—
494C22×D3—21no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—81no—
500C22×D3—121no—
501C22×D3D3×D411yescharacteristic
502C22×D3D3×D411yescharacteristic
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—61no—
511C3×D4—122no—
512C3×D4—241no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—241no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—42no—
530#67—62no—
531#67—62no—
532#67—81no—
533#67—122no—
534#67—122no—
535#67—122no—
536#67—241no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3—241no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—21no—
554D12—62no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—121no—
560D12—122no—
561D12—241no—
562D12#23512yes—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—81no—
568C4×D3—122no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—242no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—61no—
577Dic6—121no—
578Dic6—121no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—41no—
582C3×C8—61no—
583C3×C8—61no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—121no—
589C2×C32—81no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13511yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—81no—
594C3×D3—22no—
595C3×D3—41no—
596C3×D3—42no—
597C24—61no—
598#41—182no—
599#41—361no—
600C2×Q8—91no—
601C2×D4—31no—
602C2×D4—61no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4—91no—
606C2×D4—91no—
607C2×D4—121no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618SD16—361no—
619D8—182no—
620D8—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—91no—
624C2×C8—121no—
625C2×C8—361no—
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4C2×D3211yescharacteristic
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—61no—
648C42—91no—
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—62no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—244no—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—22no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—84no—
680C2×D3—122no—
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#91612yes—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×#23511yescharacteristic
701C3×C4#100411yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4#100911yescharacteristic
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—61no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—241no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—31no—
722C23—61no—
723C23—122no—
724C23—122no—
725C23—181no—
726C23—241no—
727Q8—181no—
728Q8—181no—
729D4—21no—
730D4—21no—
731D4—32no—
732D4—61no—
733D4—122no—
734D4—182no—
735D4—181no—
736D4—181no—
737D4—241no—
738D4—362no—
739D4—362no—
740D4—721no—
741C2×C4—21no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—91no—
752C2×C4—91no—
753C2×C4—181no—
754C2×C4—241no—
755C2×C4—362no—
756C2×C4—721no—
757C2×C4—721no—
758C2×C4C22×D3211yescharacteristic
759C8—21no—
760C8—61no—
761C8—61no—
762C8—181no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—62no—
767C2×C3—81no—
768C2×C3—81no—
769C2×C3—121no—
770C2×C3—122no—
771C2×C3—161no—
772C2×C3#549011yescharacteristic
773C2×C3#565411yescharacteristic
774C2×C3#575711yescharacteristic
775C2×C3C2×#91611yescharacteristic
776C2×C3D3×#13511yescharacteristic
777C2×C3#577411yescharacteristic
778D3—22no—
779D3—42no—
780D3—41no—
781D3—242no—
782D3—241no—
783D3—241no—
784C22—32no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—62no—
794C22—121no—
795C22—121no—
796C22—244no—
797C22—361no—
798C22—361no—
799C22—361no—
800C22D32×D411yescharacteristic
801C4—41no—
802C4—61no—
803C4—61no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—181no—
808C4—181no—
809C4—361no—
810C4D3×#23511yescharacteristic
811C4#6431411yescharacteristic
812C3—21no—
813C3#7876011yescharacteristic, complemented
814C3#8138211yescharacteristic, complemented
815C2—62no—
816C2—81no—
817C2—121no—
818C2—122no—
819C2—721no—
820C2#1059427211yescharacteristic
821C2#1059473211yescharacteristic
822C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595228C2semidirect
2. #10594559C2semidirect
3. #10592486C2semidirect
4. C3×#4779C2semidirect
5. C3×D3×#102C2semidirect
6. #10591449C2semidirect
7. #10591448C2semidirect
8. #10591403C2semidirect
9. #10590968C2semidirect
10. #10590830C2semidirect
11. #10590782C2semidirect
12. #10590717C2semidirect
13. #10590608C2semidirect
14. #10590459C2semidirect
15. #10590427C2semidirect
22. C2×#3744C22semidirect
23. #64102C22semidirect
26. C3×#892C22semidirect
33. #63909C22semidirect
38. #63872C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63641C22semidirect
46. #63637C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#817C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63564C22semidirect
60. #63553C22semidirect
81. #4779D3semidirect
85. D3×#102D3semidirect
191. #892C2×D3semidirect
218. (C2×D3)⋊C8C2×D3semidirect
219. #817C2×D3semidirect
237. #807C2×D3semidirect
718. C32#3297semidirect
813. C3#78760semidirect
814. C3#81382semidirect

Maximal subgroups

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

subgroupindex
#105952282
#105945592
#105924862
C3×#47792
C3×D3×#1022
#105914492
#105914482
#105914032
#105909682
#105908302
#105907822
#105907172
#105906082
#105904592
#105904272
#813823
#787603