Finite Group Databasebeta

← #11887423

Subgroups — #11887423

Order 1152.

907 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#10594989C211yesmaximal, characteristic, complemented
2#10594889C211yesmaximal, characteristic, complemented
3#10592424C211yesmaximal, characteristic, complemented
4C3×#4732C211yesmaximal, characteristic, complemented
5C3×#4722C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590963C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10#10590868C211yesmaximal, characteristic, complemented
11#10590844C211yesmaximal, characteristic, complemented
12#10590780C211yesmaximal, characteristic, complemented
13#10590777C211yesmaximal, characteristic, complemented
14#10590751C211yesmaximal, characteristic, complemented
15#10590651C211yesmaximal, characteristic, complemented
16#81485—31nomaximal
17#80015—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C4×#638C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23C3×#930C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28#63978—21no—
29#63977—21no—
30Dic3×#67—21no—
31D3×#217—21no—
32#63916C2211yescharacteristic
33#63916C2211yescharacteristic, complemented
34#63898C2211yescharacteristic
35#63898C2211yescharacteristic, complemented
36#63890—21no—
37#63886—21no—
38#63884—21no—
39#63872C2211yescharacteristic, complemented
40#63863C2211yescharacteristic
41#63858—21no—
42#63849C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63647C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61#5806—31no—
62#5630—31no—
63#5618—31no—
64#5514—31no—
65C3×#484—31no—
66C3×#447—31no—
67C2×#832—31no—
68#5158—31no—
69#5157—31no—
70#5153—31no—
71Dic3×D8—31no—
72#5048—31no—
73#5041—31no—
74C2×#809—31no—
75#4891—31no—
76#4885—31no—
77#4883—31no—
78#4872—31no—
79#4819—31no—
80#4810—31no—
81#4804—31no—
82#4800—31no—
83#4784—31no—
84#4772—31no—
85#4768—31no—
86#4766—31no—
87#4732D311yescharacteristic, complemented
88#67⋊C8—31no—
89#67⋊C8—31no—
90#67⋊C8—61no—
91#4722D311yescharacteristic, complemented
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C2×C3×D12—22no—
99C2×C3×D12—21no—
100C2×C3×D12—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3796—22no—
112#3796—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3757D411yescharacteristic
116#3752D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)—41no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C8×C3⋊D3—41no—
123C3×#217—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×D24—22no—
132C3×D24—41no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3715—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×D8—31no—
150C2×C3×D8—31no—
151C3×C22⋊Q8—31no—
152C3×#121—31no—
153C2×C3×C4⋊C4—31no—
154#953—61no—
155C2×#217—61no—
156#947—31no—
157C2×#215—31no—
158#939—61no—
159#939—61no—
160#938—31no—
161#938—31no—
162#936—31no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167C2×#214—31no—
168#930—61no—
169#930C2×D311yescharacteristic
170C4×#67—31no—
171C4×#67—31no—
172C4×#67—61no—
173C4×#67—61no—
174C2×C4⋊Dic3C2×D311yescharacteristic
175#924C2×D311yescharacteristic
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—61no—
179C2×D24C2×D311yescharacteristic
180C2×D24C2×D311yescharacteristic
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183C2×D3×C8—61no—
184#898—61no—
185#895—31no—
186#895—31no—
187#895—61no—
188#894—61no—
189#894—61no—
190#893—31no—
191#893—31no—
192#892—31no—
193#892—31no—
194#890—31no—
195#890—31no—
196#886—61no—
197#882—61no—
198D3×C22⋊C4—61no—
199#879—61no—
200C3×#107—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8C2×D311yescharacteristic
208C3×C22⋊C8C2×D311yescharacteristic
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818C2×D311yescharacteristic, complemented
221#818C2×D311yescharacteristic, complemented
222#816C2×D311yescharacteristic, complemented
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#810—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#808—31no—
237#808—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—22no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12#4112yes—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273#626—81no—
274#626—81no—
275D3×Dic3—42no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3⋊(C3⋊C8)—21no—
281C3⋊(C3⋊C8)—21no—
282#553—91no—
283#546—91no—
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—31no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—121no—
307C22×C3×C4—21no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—21no—
312C2×#67—31no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322#239—62no—
323#239—121no—
324#237—62no—
325#237—121no—
326C2×D12—22no—
327C2×D12—21no—
328C2×D12—41no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12C22×D311yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×Dic6C22×D311yescharacteristic
342C3×D8—62no—
343C3×D8—121no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358#217—21no—
359#217—31no—
360#217—31no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#215—121no—
369#214—121no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
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—61no—
381(C2×D3)⋊C4—61no—
382C4⋊Dic3—21no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—122no—
409D24—22no—
410D24—41no—
411D3×C8—121no—
412D3×C8—121no—
413D3×C8—122no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32#13512yes—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
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×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—31no—
446C2×D8—31no—
447C22×C8—91no—
448C22×C8—91no—
449#126—181no—
450#125—91no—
451#124—91no—
452#123—181no—
453#123—181no—
454C22⋊Q8—31no—
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—91no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—31no—
470#106—91no—
471C4⋊C8—91no—
472#103—31no—
473#103—31no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—91no—
483C22⋊C8D3211yescharacteristic
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—122no—
490C23×C3—122no—
491C23×C3—241no—
492C23×C3D3×D411yescharacteristic
493C23×C3D3×D411yescharacteristic
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—61no—
502C22×D3—81no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—32no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—122no—
512C3×D4—122no—
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—41no—
520C2×C3×C4—41no—
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×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—42no—
532#67—64no—
533#67—62no—
534#67—62no—
535#67—122no—
536#67—241no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—81no—
553C2×Dic3—122no—
554C2×Dic3—241no—
555C2×Dic3—241no—
556D12—21no—
557D12—21no—
558D12—21no—
559D12—21no—
560D12—21no—
561D12—42no—
562D12—122no—
563D12—241no—
564D12—241no—
565D12#23712yes—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—61no—
569C4×D3—61no—
570C4×D3—121no—
571C4×D3—121no—
572C4×D3—122no—
573C4×D3—241no—
574C4×D3—241no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—41no—
582C3×C8—41no—
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—41no—
594C3×D3—42no—
595C3×D3—81no—
596C3×D3—81no—
597C24—61no—
598#41—182no—
599#41—361no—
600C2×Q8—31no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—62no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—91no—
608C2×D4—121no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—181no—
612C22×C4—61no—
613C22×C4—91no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618SD16—361no—
619D8—62no—
620D8—121no—
621C2×C8—91no—
622C2×C8—91no—
623C2×C8—361no—
624C2×C8—361no—
625C2×C8C2×D3211yescharacteristic
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
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—91no—
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—62no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3#91212yes—
668C22×C3#91912yes—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C2×D3—22no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—84no—
688C2×D3—121no—
689C2×D3—121no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×#23711yescharacteristic
701C3×C4#100411yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4#100911yescharacteristic
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—62no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—61no—
716Dic3—121no—
717Dic3—121no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—61no—
720C23—61no—
721C23—61no—
722C23—91no—
723C23—122no—
724C23—122no—
725C23—241no—
726C23#380211yescharacteristic
727Q8—61no—
728Q8—61no—
729D4—32no—
730D4—61no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—122no—
736D4—122no—
737D4—182no—
738D4—362no—
739D4—721no—
740D4—721no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—91no—
749C2×C4—91no—
750C2×C4—91no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—241no—
754C2×C4—362no—
755C2×C4—721no—
756C2×C4—721no—
757C2×C4#380211yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—21no—
760C8—21no—
761C8—181no—
762C8—181no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—122no—
770C2×C3—241no—
771C2×C3—241no—
772C2×C3#559111yescharacteristic
773C2×C3#565411yescharacteristic
774C2×C3C2×#91211yescharacteristic
775C2×C3C2×#91911yescharacteristic
776C2×C3#577411yescharacteristic
777C2×C3#577411yescharacteristic
778D3—42no—
779D3—81no—
780D3—81no—
781D3—122no—
782D3—121no—
783D3—121no—
784C22—21no—
785C22—21no—
786C22—62no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—181no—
796C22—181no—
797C22—181no—
798C22—244no—
799C22#6381012yes—
800C22C2×#380211yescharacteristic
801C4—21no—
802C4—121no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—181no—
808C4—181no—
809C4—181no—
810C4D3×#23711yescharacteristic
811C4#6431411yescharacteristic
812C3—21no—
813C3#8001511yescharacteristic, complemented
814C3#8148511yescharacteristic, complemented
815C2—22no—
816C2—122no—
817C2—241no—
818C2—241no—
819C2—361no—
820C2#1059429411yescharacteristic
821C2C2×#6381011yescharacteristic
822C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594989C2semidirect
2. #10594889C2semidirect
3. #10592424C2semidirect
4. C3×#4732C2semidirect
5. C3×#4722C2semidirect
6. #10591179C2semidirect
7. C2×#63562C2semidirect
8. #10590963C2semidirect
9. #10590956C2semidirect
10. #10590868C2semidirect
11. #10590844C2semidirect
12. #10590780C2semidirect
13. #10590777C2semidirect
14. #10590751C2semidirect
15. #10590651C2semidirect
22. C2×C8×C3⋊D3C22semidirect
33. #63916C22semidirect
35. #63898C22semidirect
39. #63872C22semidirect
42. #63849C22semidirect
43. C2×#3715C22semidirect
45. #63647C22semidirect
46. #63641C22semidirect
47. C8×C3⋊Dic3C22semidirect
50. C3×#818C22semidirect
51. C3×#818C22semidirect
52. C3×#816C22semidirect
53. C3×#816C22semidirect
54. #63574C22semidirect
55. #63565C22semidirect
60. #63562C22semidirect
87. #4732D3semidirect
91. #4722D3semidirect
220. #818C2×D3semidirect
221. #818C2×D3semidirect
222. #816C2×D3semidirect
223. #816C2×D3semidirect
718. C32#3297semidirect
813. C3#80015semidirect
814. C3#81485semidirect

Maximal subgroups

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

subgroupindex
#105949892
#105948892
#105924242
C3×#47322
C3×#47222
#105911792
C2×#635622
#105909632
#105909562
#105908682
#105908442
#105907802
#105907772
#105907512
#105906512
#814853
#800153