Finite Group Databasebeta

← #11889130

Subgroups — #11889130

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596052C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic
3C3×#5027C211yesmaximal, characteristic, complemented
4C3×#5026C211yesmaximal, characteristic, complemented
5#10591652C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591591C211yesmaximal, characteristic, complemented
8#10591590C211yesmaximal, characteristic, complemented
9#10590594C211yesmaximal, characteristic, complemented
10#10590593C211yesmaximal, characteristic, complemented
11#10590512C211yesmaximal, characteristic, complemented
12#10590510C211yesmaximal, characteristic, complemented
13#10590328C211yesmaximal, characteristic, complemented
14#10590275C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#80397—31nomaximal
17#79800—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C32×C4×Q8C2211yescharacteristic, complemented
22#64155C2211yescharacteristic, complemented
23#64155C2211yescharacteristic, complemented
24#64103—21no—
25#64101C2211yescharacteristic, complemented
26C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
27#64098—21no—
28#64085—21no—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30#64081—21no—
31#64079C2211yescharacteristic, complemented
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic, complemented
34C2×C3×#215C2211yescharacteristic, complemented
35C3×#874C2211yescharacteristic
36C3×C4×D12C2211yescharacteristic
37#63922—21no—
38#63922—21no—
39#63916C2211yescharacteristic
40#63916C2211yescharacteristic
41#63908—21no—
42C2×#3712C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
50C3×#803C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63557C2211yescharacteristic, complemented
61#5717—31no—
62#5581—31no—
63#5581—31no—
64#5581—61no—
65D4×D12—31no—
66C3×#460—31no—
67C3×#440—31no—
68#5174—31no—
69#5171—31no—
70#5169—31no—
71#5169—31no—
72#5169—31no—
73#5169—31no—
74#5071—31no—
75#5027D311yescharacteristic, complemented
76#5026D311yescharacteristic, complemented
77#5009—31no—
78#4885—31no—
79#4882—31no—
80#4847—31no—
81#4836—31no—
82#4812—31no—
83#4807—31no—
84#4779—31no—
85#4774—31no—
86#4770—31no—
87#4770—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4713—31no—
91#4706—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)D411yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#625—21no—
109#3802—22no—
110#3802—22no—
111#3802—41no—
112#3802—41no—
113D3×D12—44no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752D411yescharacteristic
122#3752D411yescharacteristic
123C4⋊(C3⋊Dic3)D411yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3750—21no—
128#3750—21no—
129#3750—21no—
130#3750—21no—
131C4×C3⋊Dic3—21no—
132C3×#215—22no—
133C3×#215—41no—
134C3×#215—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3712—41no—
144#3710—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C22×D12—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C3×#127—31no—
156C3×C4×Q8—21no—
157C3×C4×Q8C2×D311yescharacteristic, complemented
158C3×C4×Q8C2×D311yescharacteristic, complemented
159C3×C4×D4—31no—
160#946—31no—
161#946—31no—
162#946—31no—
163#946—31no—
164#946—61no—
165#946—61no—
166C2×#215C2×D311yescharacteristic
167C2×#215C2×D311yescharacteristic, complemented
168C2×#215C2×D311yescharacteristic, complemented
169#938—31no—
170#938—31no—
171#938—61no—
172#937—61no—
173#937—61no—
174#930—61no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179#895—31no—
180#895—31no—
181#894—61no—
182#894—61no—
183#894—62no—
184#892—31no—
185#892—31no—
186#892—61no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190#889—61no—
191#889—61no—
192#889—62no—
193#882—61no—
194#882—61no—
195#876—61no—
196#876—61no—
197#876—62no—
198#874C2×D311yescharacteristic
199C4×D12—31no—
200C4×D12—31no—
201C4×D12—61no—
202C4×D12C2×D311yescharacteristic
203#872—61no—
204#872—61no—
205#872—62no—
206#870—31no—
207#870—31no—
208#870—61no—
209C3×#107—31no—
210C3×C4⋊C8—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#97—31no—
216#835C2×D311yescharacteristic, complemented
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#832—31no—
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233#818—31no—
234#817—31no—
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic, complemented
237#809C2×D311yescharacteristic, complemented
238#808—31no—
239#807—31no—
240#807C2×D311yescharacteristic, complemented
241C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
242#803C2×D311yescharacteristic, complemented
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C2×D32—42no—
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—42no—
252C2×D32—81no—
253C2×D32—81no—
254C32×Q8—21no—
255C32×Q8—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4⋊(C3⋊D3)—22no—
266C4×C3⋊D3—21no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—42no—
271C2×C3×Dic3—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—42no—
278C3×D12—81no—
279C3×D12#4112yes—
280C3×C4×D3—42no—
281#626—42no—
282#626—42no—
283#625—42no—
284#625—42no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289#552—91no—
290D42—91no—
291#490—91no—
292#482—91no—
293#480—91no—
294#478—91no—
295#468—91no—
296#465—91no—
297#460—31no—
298#450—91no—
299#450—91no—
300#440—31no—
301#435—91no—
302#418—91no—
303C2×#102—91no—
304C23×D3—61no—
305C23×D3—61no—
306C23×D3—61no—
307C23×D3—61no—
308C2×C3×Q8—21no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C22×C3×C4—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323D3×D4—62no—
324D3×D4—62no—
325D3×D4—62no—
326D3×D4—62no—
327D3×D4—124no—
328D3×D4—121no—
329D3×D4—121no—
330D3×D4—121no—
331D3×D4—121no—
332C2×D12—21no—
333C2×D12—21no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—124no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—21no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—62no—
353C3×SD16—62no—
354C3×SD16—121no—
355C3×SD16—121no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C3×C4⋊C4—22no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C22⋊C4—61no—
368C3×C42—22no—
369C3×C42—21no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42C22×D311yescharacteristic
373C3×C42C22×D311yescharacteristic
374#217—61no—
375#217—61no—
376#215—22no—
377#215—41no—
378#215—41no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—31no—
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—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3C22×D311yescharacteristic
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—62no—
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429ΓL(1,𝔽25)—121no—
430ΓL(1,𝔽25)—121no—
431D3×C8—121no—
432D3×C8—121no—
433C22×C32C22×D411yescharacteristic
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3AGL(1,ℤ/8)12yes—
440C2×C3×D3—22no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449D32—84no—
450D32—84no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—41no—
454C32×C4—41no—
455C32×C4C2×#4111yescharacteristic
456C32×C4H(5,𝔽2)11yescharacteristic
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—41no—
460C3⋊Dic3—41no—
461C3×Dic3—41no—
462C22×D4—91no—
463C22×D4—91no—
464C22×D4—181no—
465C2×SD16—31no—
466C2×SD16—31no—
467C2×SD16—31no—
468C2×M16—91no—
469C22×C8—91no—
470#127—31no—
471#126—181no—
472#125—91no—
473#125—181no—
474#123—181no—
475C22⋊Q8—91no—
476C22⋊Q8—91no—
477#121—91no—
478#121—91no—
479#121—181no—
480#120—181no—
481#120—181no—
482C4×Q8D3211yescharacteristic, complemented
483C4×D4—31no—
484C4×D4—91no—
485#117—91no—
486#117—181no—
487C2×C4⋊C4—91no—
488#107—31no—
489#107—91no—
490#106—91no—
491C4⋊C8—31no—
492#103—31no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—91no—
497#102—91no—
498#102—91no—
499#102—91no—
500#102—91no—
501#102—91no—
502C22⋊C8—91no—
503C22⋊C8—91no—
504#97—31no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—31no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3—241no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—41no—
534C3×Q8—41no—
535C3×D4—32no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—122no—
542C3×D4—241no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—61no—
553C2×C3×C4—122no—
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4D3×D411yescharacteristic
556C2×C3×C4D3×D411yescharacteristic
557C2×C3×C4D3×D411yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566C2×Dic3—21no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—62no—
574C2×Dic3—62no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579D12—21no—
580D12—21no—
581D12—21no—
582D12—21no—
583D12—21no—
584D12—42no—
585D12—62no—
586D12—62no—
587D12—81no—
588D12—122no—
589D12—122no—
590D12—122no—
591D12#23512yes—
592C4×D3—42no—
593C4×D3—61no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—61no—
600C4×D3—61no—
601C4×D3—121no—
602C4×D3—121no—
603C4×D3—121no—
604C4×D3—121no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—124no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C2×C32#54611yescharacteristic
617C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
618C2×C32#57711yescharacteristic
619C3⋊D3—22no—
620C3⋊D3—41no—
621C3×D3—42no—
622C3×D3—81no—
623C3×D3—81no—
624C24—181no—
625C24—181no—
626C2×Q8C2×D3211yescharacteristic
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—91no—
633C2×D4—181no—
634C2×D4—181no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—182no—
638C2×D4—182no—
639C2×D4—364no—
640C2×D4—361no—
641C2×D4—361no—
642C22×C4—61no—
643C22×C4—91no—
644C22×C4—91no—
645C22×C4—181no—
646SD16—62no—
647SD16—121no—
648SD16—121no—
649M16—361no—
650C2×C8—31no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—361no—
655C4⋊C4—21no—
656C4⋊C4—31no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—91no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C4⋊C4—181no—
665C4⋊C4C2×D3211yescharacteristic
666C22⋊C4—61no—
667C22⋊C4—91no—
668C22⋊C4—91no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C42—21no—
675C42—181no—
676C42C2×D3211yescharacteristic
677C22×C3—21no—
678C22×C3—62no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3C2×D3×D411yescharacteristic
688C22×C3C2×D3×D411yescharacteristic
689C2×D3—22no—
690C2×D3—32no—
691C2×D3—32no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—62no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—244no—
717C2×D3—244no—
718C2×D3—244no—
719C2×D3—244no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—121no—
735C3×C4C2×#23511yescharacteristic
736C3×C4#100411yescharacteristic
737C3×C4D3×#4111yescharacteristic
738C3×C4#100911yescharacteristic
739Dic3—41no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—121no—
745Dic3—121no—
746Dic3—122no—
747Dic3—122no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752C32#331011yescharacteristic, complemented, Sylow
753C23—61no—
754C23—61no—
755C23—61no—
756C23—91no—
757C23—91no—
758C23—362no—
759C23—362no—
760C23—362no—
761C23—362no—
762C23—721no—
763C23—721no—
764Q8—21no—
765Q8—21no—
766D4—32no—
767D4—61no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—122no—
773D4—182no—
774D4—241no—
775D4—362no—
776D4—362no—
777D4—362no—
778D4—362no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—61no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—122no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—362no—
792C2×C4#381111yescharacteristic
793C2×C4#381111yescharacteristic
794C2×C4C22×D3211yescharacteristic
795C8—61no—
796C8—61no—
797C8—61no—
798C8—61no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—122no—
803C2×C3—241no—
804C2×C3—241no—
805C2×C3#555011yescharacteristic
806C2×C3#561211yescharacteristic
807C2×C3#576211yescharacteristic
808C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
809C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
810C2×C3#577811yescharacteristic
811D3—42no—
812D3—62no—
813D3—62no—
814D3—81no—
815D3—81no—
816D3—122no—
817D3—121no—
818D3—121no—
819D3—241no—
820C22—62no—
821C22—92no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22—724no—
836C22—724no—
837C22C2×#381111yescharacteristic
838C4—21no—
839C4—21no—
840C4—41no—
841C4—41no—
842C4—121no—
843C4—181no—
844C4—181no—
845C4—361no—
846C4—361no—
847C4D3×#23511yescharacteristic
848C4#6430711yescharacteristic
849C3—21no—
850C3#7980011yescharacteristic, complemented
851C3#8039711yescharacteristic, complemented
852C2—122no—
853C2—182no—
854C2—241no—
855C2—241no—
856C2—361no—
857C2#1059507811yescharacteristic
858C2#1059532411yescharacteristic
859C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4×Q8D32
hypocenterC32#3310
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. #10596052C2semidirect
3. C3×#5027C2semidirect
4. C3×#5026C2semidirect
5. #10591652C2semidirect
6. #10591652C2semidirect
7. #10591591C2semidirect
8. #10591590C2semidirect
9. #10590594C2semidirect
10. #10590593C2semidirect
11. #10590512C2semidirect
12. #10590510C2semidirect
13. #10590328C2semidirect
14. #10590275C2semidirect
15. #10590271C2semidirect
21. C32×C4×Q8C22semidirect
22. #64155C22semidirect
23. #64155C22semidirect
25. #64101C22semidirect
26. C4⋊C4×C3⋊D3C22semidirect
31. #64079C22semidirect
33. C2×C3×#215C22semidirect
34. C2×C3×#215C22semidirect
42. C2×#3712C22semidirect
43. C2×#3710C22semidirect
44. C3×#835C22semidirect
46. C3×#809C22semidirect
47. C3×#809C22semidirect
48. C3×#807C22semidirect
49. C3×C4⋊(C3⋊C8)C22semidirect
50. C3×#803C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63557C22semidirect
75. #5027D3semidirect
76. #5026D3semidirect
157. C3×C4×Q8C2×D3semidirect
158. C3×C4×Q8C2×D3semidirect
167. C2×#215C2×D3semidirect
168. C2×#215C2×D3semidirect
216. #835C2×D3semidirect
236. #809C2×D3semidirect
237. #809C2×D3semidirect
240. #807C2×D3semidirect
241. C4⋊(C3⋊C8)C2×D3semidirect
242. #803C2×D3semidirect
482. C4×Q8D32semidirect
752. C32#3310semidirect
850. C3#79800semidirect
851. C3#80397semidirect

Maximal subgroups

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

subgroupindex
#105960522
#105940042
C3×#50272
C3×#50262
#105916522
#105915912
#105915902
#105905942
#105905932
#105905122
#105905102
#105903282
#105902752
#105902712
#803973
#798003