Finite Group Databasebeta

← #11887387

Subgroups — #11887387

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595246C211yesmaximal, characteristic, complemented
2#10594562C211yesmaximal, characteristic, complemented
3#10592480C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4763C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591424C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590860C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590720C211yesmaximal, characteristic, complemented
12#10590652C211yesmaximal, characteristic, complemented
13#10590533C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#81187—31nomaximal
17#78760—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3744C2211yescharacteristic, complemented
22#64104C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#890C2211yescharacteristic, complemented
27#63978—21no—
28#63977—21no—
29#63962—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63916C2211yescharacteristic
32#63909—21no—
33#63909C2211yescharacteristic
34#63904—21no—
35C4×#626C2211yescharacteristic
36#63897—21no—
37#63894C2211yescharacteristic, complemented
38#63860C2211yescharacteristic
39#63857C2211yescharacteristic
40#63849C2211yescharacteristic, complemented
41#63848—21no—
42C2×#3714C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63647C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#817C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, 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
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5806—31no—
62#5695—31no—
63#5554—31no—
64#5514—31no—
65C3×#478—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5114—31no—
69C8×#67—31no—
70#5068—31no—
71C4×#213—31no—
72#4970—31no—
73#4884—31no—
74#4883—31no—
75#4866—31no—
76#4864—31no—
77#4844—31no—
78#4834—31no—
79#4787—31no—
80#4781—31no—
81#4781—31no—
82#4781—61no—
83#4779—31no—
84#4775—31no—
85#4773—31no—
86#4772—31no—
87#4772—31no—
88D3×#102D311yescharacteristic, complemented
89#4768—31no—
90#4763D311yescharacteristic, complemented
91#4756—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3—21no—
96#3830—22no—
97#3830—41no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626D411yescharacteristic
112C2×#624—21no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3753—22no—
116#3752—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3744—41no—
119C3×#217—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3714—41no—
143#3710—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×D3×D4C2×D311yescharacteristic
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×C4×D4—31no—
153C2×C3×C4⋊C4—31no—
154#953—61no—
155C2×#217—61no—
156#939—61no—
157#938—31no—
158#936—31no—
159#935—61no—
160D4×Dic3C2×D311yescharacteristic
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—61no—
165#930—31no—
166#930—61no—
167#930—61no—
168C4×#67—31no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171#924—31no—
172C2×D24—31no—
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—61no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8C2×D311yescharacteristic
179#898—61no—
180#898—61no—
181#897—31no—
182#895—31no—
183#895—31no—
184#895—31no—
185#895—31no—
186#895—61no—
187#895—61no—
188#894—61no—
189#894—61no—
190#893—31no—
191#893—61no—
192#892—31no—
193#892—31no—
194D3×C4⋊C4C2×D311yescharacteristic
195#890C2×D311yescharacteristic, complemented
196#886—61no—
197#882—61no—
198#875—31no—
199C4×D12—31no—
200C4×D12—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic
210C3×#102C2×D311yescharacteristic
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)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221#817C2×D311yescharacteristic, complemented
222#816—31no—
223#816—31no—
224Dic3⋊C8C2×D311yescharacteristic, complemented
225C8×Dic3—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—61no—
231#809—31no—
232#809—31no—
233#809C2×D311yescharacteristic
234#807—31no—
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—42no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—81no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259#634—21no—
260#634—21no—
261C3×#67—42no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—81no—
274#626—22no—
275#626—42no—
276#626—81no—
277#624—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—91no—
287#478—31no—
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—121no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—121no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320#237—62no—
321#237—62no—
322#237—122no—
323#237—121no—
324#237—121no—
325#237—122no—
326D3×D4—22no—
327D3×D4—41no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—121no—
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—61no—
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364C3×C42—31no—
365#217—21no—
366#217—31no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#213—62no—
372#213—62no—
373#213—122no—
374#213—121no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
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—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—121no—
391C4⋊Dic3—21no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—31no—
400Dic3⋊C4—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—121no—
410#204—121no—
411#204—121no—
412#204—122no—
413D3×C8—41no—
414D3×C8—121no—
415D3×C8—121no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—84no—
432C2×C3×D3#13512yes—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—21no—
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C2×#41—91no—
445C22×D4—31no—
446C2×SD16—91no—
447C2×D8—91no—
448C2×D8—91no—
449C22×C8—31no—
450C22×C8—91no—
451#126—181no—
452#125—31no—
453#124—91no—
454#123—181no—
455#123—181no—
456C22⋊Q8—91no—
457#121—91no—
458#121—91no—
459#121—91no—
460#121—181no—
461#121—181no—
462#120—181no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—181no—
467#117—91no—
468C2×C4⋊C4—31no—
469C2×C22⋊C4—181no—
470#107—31no—
471#107—91no—
472#106—31no—
473C4⋊C8—31no—
474#103—91no—
475#103—91no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102D3211yescharacteristic
484C22⋊C8—91no—
485C22⋊C8—91no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—61no—
492C23×C3—122no—
493C23×C3—122no—
494C23×C3—241no—
495C22×D3—21no—
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—42no—
499C22×D3—42no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—81no—
504C22×D3—121no—
505C22×D3D3×D411yescharacteristic
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—22no—
509C3×D4—41no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—122no—
513C3×D4#23512yes—
514C3×D4#23912yes—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—241no—
528C2×C3×C4—241no—
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—42no—
532#67—62no—
533#67—122no—
534#67—122no—
535#67—122no—
536#67—124no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—81no—
547C2×Dic3—121no—
548C2×Dic3—122no—
549C2×Dic3—122no—
550C2×Dic3—124no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554D12—21no—
555D12—21no—
556D12—62no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—121no—
562D12—121no—
563D12—122no—
564D12—241no—
565D12—241no—
566D12—242no—
567D12—241no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—61no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—81no—
575C4×D3—121no—
576C4×D3—121no—
577C4×D3—241no—
578C4×D3—241no—
579Dic6—62no—
580Dic6—61no—
581Dic6—61no—
582Dic6—61no—
583Dic6—61no—
584Dic6—121no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—41no—
588C3×C8—61no—
589C3×C8—61no—
590C3⋊C8—21no—
591C3⋊C8—21no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—121no—
595C2×C32—42no—
596C2×C32#54611yescharacteristic
597C2×C32C2×#13511yescharacteristic
598C2×C32#57611yescharacteristic
599C3⋊D3—41no—
600C3⋊D3—81no—
601C3×D3—22no—
602C3×D3—81no—
603C24—61no—
604#41—182no—
605#41—361no—
606C2×Q8—91no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—62no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—121no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4C2×D3211yescharacteristic
618C22×C4—31no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—91no—
622C22×C4—181no—
623C22×C4—181no—
624SD16—361no—
625D8—182no—
626D8—361no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—91no—
630C2×C8—121no—
631C2×C8—361no—
632C2×C8C2×D3211yescharacteristic
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—91no—
640C4⋊C4—181no—
641C4⋊C4C2×D3211yescharacteristic
642C22⋊C4—61no—
643C22⋊C4—91no—
644C22⋊C4—91no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—31no—
654C42—181no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—244no—
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C2×D3×D411yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—84no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—241no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3#91612yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23511yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4C2×#23911yescharacteristic
713C3×C4#100911yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—21no—
717Dic3—41no—
718Dic3—41no—
719Dic3—41no—
720Dic3—61no—
721Dic3—61no—
722Dic3—121no—
723Dic3—122no—
724Dic3—121no—
725Dic3—121no—
726C32#329711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—31no—
729C23—61no—
730C23—91no—
731C23—122no—
732C23—122no—
733C23—181no—
734C23—241no—
735Q8—181no—
736Q8—181no—
737D4—21no—
738D4—61no—
739D4—61no—
740D4—122no—
741D4—182no—
742D4—181no—
743D4—181no—
744D4—362no—
745D4—362no—
746D4—721no—
747D4—721no—
748D4#379912yes—
749C2×C4—21no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—91no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—241no—
763C2×C4—241no—
764C2×C4—362no—
765C2×C4—721no—
766C2×C4C22×D3211yescharacteristic
767C8—21no—
768C8—61no—
769C8—61no—
770C8—181no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—42no—
775C2×C3—42no—
776C2×C3—62no—
777C2×C3—82no—
778C2×C3—241no—
779C2×C3#549011yescharacteristic
780C2×C3#563011yescharacteristic
781C2×C3#575711yescharacteristic
782C2×C3C2×#91611yescharacteristic
783C2×C3D3×#13511yescharacteristic
784C2×C3#577411yescharacteristic
785D3—22no—
786D3—81no—
787D3—121no—
788D3—121no—
789D3—241no—
790D3—241no—
791D3—241no—
792D3—481no—
793C22—22no—
794C22—32no—
795C22—41no—
796C22—41no—
797C22—61no—
798C22—61no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—181no—
803C22—181no—
804C22—181no—
805C22—244no—
806C22—361no—
807C22—361no—
808C22—361no—
809C22D32×D411yescharacteristic
810C4—41no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—121no—
815C4—121no—
816C4—121no—
817C4—181no—
818C4—361no—
819C4C2×#379911yescharacteristic
820C4#6431411yescharacteristic
821C3—21no—
822C3#7876011yescharacteristic, complemented
823C3#8118711yescharacteristic, complemented
824C2—42no—
825C2—62no—
826C2—241no—
827C2—361no—
828C2—721no—
829C2#1059418711yescharacteristic
830C2#1059473211yescharacteristic
831C2D3×#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. #10595246C2semidirect
2. #10594562C2semidirect
3. #10592480C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4763C2semidirect
6. #10591448C2semidirect
7. #10591424C2semidirect
8. #10591400C2semidirect
9. #10590860C2semidirect
10. #10590830C2semidirect
11. #10590720C2semidirect
12. #10590652C2semidirect
13. #10590533C2semidirect
14. #10590509C2semidirect
15. #10590427C2semidirect
21. C2×#3744C22semidirect
22. #64104C22semidirect
26. C3×#890C22semidirect
37. #63894C22semidirect
40. #63849C22semidirect
43. C2×#3710C22semidirect
45. #63647C22semidirect
46. #63637C22semidirect
50. C3×#817C22semidirect
51. C3×Dic3⋊C8C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63564C22semidirect
60. Dic3×C3⋊C8C22semidirect
88. D3×#102D3semidirect
90. #4763D3semidirect
195. #890C2×D3semidirect
221. #817C2×D3semidirect
224. Dic3⋊C8C2×D3semidirect
236. #807C2×D3semidirect
726. C32#3297semidirect
822. C3#78760semidirect
823. C3#81187semidirect

Maximal subgroups

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

subgroupindex
#105952462
#105945622
#105924802
C3×D3×#1022
C3×#47632
#105914482
#105914242
#105914002
#105908602
#105908302
#105907202
#105906522
#105905332
#105905092
#105904272
#811873
#787603