Finite Group Databasebeta

← #11889744

Subgroups — #11889744

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594003C211yesmaximal, characteristic
2#10593956C211yesmaximal, characteristic, complemented
3#10592544C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4836C211yesmaximal, characteristic, complemented
6#10590969C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8D3×#821C211yesmaximal, characteristic, complemented
9#10590852C211yesmaximal, characteristic, complemented
10#10590838C211yesmaximal, characteristic, complemented
11#10590684C211yesmaximal, characteristic, complemented
12#10590679C211yesmaximal, characteristic, complemented
13#10590670C211yesmaximal, characteristic, complemented
14#10590360C211yesmaximal, characteristic, complemented
15#10590294C211yesmaximal, characteristic, complemented
16#80982—31nomaximal
17#79503—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3746C2211yescharacteristic, complemented
21C2×#3744C2211yescharacteristic
22#64084C2211yescharacteristic
23C4×#634C2211yescharacteristic, complemented
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×#869C2211yescharacteristic, complemented
29#63922—21no—
30D3×(C2×D3)⋊C4—21no—
31#63909C2211yescharacteristic
32#63906—21no—
33#63898—21no—
34#63890—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37#63887—21no—
38#63887—21no—
39#63872—21no—
40#63857C2211yescharacteristic
41#63857C2211yescharacteristic
42#63857C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5730—31no—
62#5554—31no—
63#5550—31no—
64#5543—31no—
65C3×#474—31no—
66C3×#435—31no—
67#5134—31no—
68#5133—31no—
69#5116—31no—
70C2×#821—31no—
71#5089—31no—
72#5018—31no—
73#4887—31no—
74#4886—31no—
75#4884—31no—
76#4882—31no—
77#4846D311yescharacteristic, complemented
78#4845—31no—
79#4845—31no—
80#4845—61no—
81#4836D311yescharacteristic, complemented
82#4783—31no—
83#4776—31no—
84#4771—31no—
85D3×#102—31no—
86#4736—31no—
87#4733—31no—
88#4731—31no—
89#4722—31no—
90#4714—31no—
91#4710—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C42C2311yescharacteristic
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120#3746—41no—
121#3744—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—41no—
133C3×D3×C8—41no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3716—22no—
144#3314—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×M16—31no—
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154#946—61no—
155#946—61no—
156#937—61no—
157D4×Dic3—61no—
158C2×#214—31no—
159#930—31no—
160#930—61no—
161C2×(C2×D3)⋊C4—61no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164#924—31no—
165#924—31no—
166#924—31no—
167C2×Dic12—31no—
168C2×Dic12—31no—
169C2×Dic12—61no—
170C2×#204—31no—
171C2×#204—31no—
172C2×#204—31no—
173C2×#204—61no—
174C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
175C2×D3×C8C2×D311yescharacteristic
176#897—31no—
177#897—31no—
178#897—31no—
179#895—31no—
180#894—61no—
181#893—61no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184#890—61no—
185#890—61no—
186#886—61no—
187#884—61no—
188#882—61no—
189D3×C22⋊C4—61no—
190#878—61no—
191#878—61no—
192#875—31no—
193#875—31no—
194#875—61no—
195C4×D12C2×D311yescharacteristic
196C4×D12C2×D311yescharacteristic
197#869C2×D311yescharacteristic, complemented
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C3×#107—31no—
202C3×#107—31no—
203C3×C4⋊C8—21no—
204C3×C4⋊C8C2×D311yescharacteristic, complemented
205C3×C4⋊C8C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×#97—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222#818—31no—
223#818C2×D311yescharacteristic, complemented
224#818C2×D311yescharacteristic, complemented
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—61no—
231#810—31no—
232#810—31no—
233#810—31no—
234#809—31no—
235#809—31no—
236#807—31no—
237#803C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253#634—21no—
254#634—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×Dic6—81no—
271#626—42no—
272#626—81no—
273#625—42no—
274D3×Dic3—42no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C32×C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—31no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—31no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—61no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311#237—62no—
312#237—121no—
313D3×D4—62no—
314D3×D4—121no—
315#235—62no—
316#235—121no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—62no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—121no—
324C2×D12D1211yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—21no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C3×M16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#217—61no—
361#217—61no—
362#217—61no—
363#214—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4—121no—
376(C2×D3)⋊C4D1211yescharacteristic
377(C2×D3)⋊C4D1211yescharacteristic
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3D1211yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—121no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—121no—
405Dic12—121no—
406Dic12—122no—
407#204—62no—
408#204—121no—
409#204—121no—
410#204—122no—
411ΓL(1,𝔽25)—41no—
412D3×C8—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13712yes—
426D32—84no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—31no—
445C22×C8—31no—
446C4⋊Q8—31no—
447#125—181no—
448#124—91no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—31no—
467#107—91no—
468C4⋊C8D3211yescharacteristic, complemented
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—31no—
481#97—31no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3C2×D1211yescharacteristic
496C22×D3C2×D1211yescharacteristic
497C3×Q8—241no—
498C3×D4—32no—
499C3×D4—62no—
500C3×D4—61no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—241no—
514C2×C3×C4C2×D1211yescharacteristic
515C2×C3×C4C2×D1211yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—122no—
521#67—122no—
522#67—122no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3C2×D1211yescharacteristic
540C2×Dic3C2×D1211yescharacteristic
541D12—22no—
542D12—21no—
543D12—61no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—121no—
548D12—121no—
549D12—122no—
550D12—241no—
551D12#23912yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—81no—
557C4×D3—122no—
558C4×D3—241no—
559C4×D3—241no—
560Dic6—62no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—81no—
570Dic6—121no—
571Dic6—121no—
572Dic6—121no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—41no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C2×C32#54611yescharacteristic
584C2×C32C2×#13711yescharacteristic
585C2×C32#57611yescharacteristic
586C3⋊D3—81no—
587C3×D3—22no—
588C3×D3—42no—
589C3×D3—41no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—61no—
594C2×Q8—91no—
595C2×Q8—91no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—91no—
599C2×D4—181no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—361no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—361no—
611SD16—182no—
612SD16—361no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—121no—
617C2×C8C2×D3211yescharacteristic
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—181no—
641C42C2×D3211yescharacteristic
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—62no—
649C22×C3—61no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3C22×D1211yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—22no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—244no—
672C2×D3—244no—
673C2×D3#90912yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4#100411yescharacteristic
688C3×C4C2×#23911yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4#100911yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—122no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—31no—
708C23—61no—
709C23—181no—
710C23—362no—
711C23—362no—
712C23—721no—
713Q8—181no—
714Q8—181no—
715Q8—181no—
716Q8—181no—
717Q8—241no—
718D4—32no—
719D4—62no—
720D4—61no—
721D4—181no—
722D4—181no—
723D4—362no—
724D4—362no—
725D4—721no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—362no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4D3×D1211yescharacteristic
743C2×C4D3×D1211yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—21no—
747C8—61no—
748C8—61no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—62no—
753C2×C3—121no—
754C2×C3—122no—
755C2×C3#555411yescharacteristic
756C2×C3#563011yescharacteristic
757C2×C3C2×#90911yescharacteristic
758C2×C3#575211yescharacteristic
759C2×C3#575711yescharacteristic
760C2×C3D3×#13711yescharacteristic
761D3—22no—
762D3—42no—
763D3—41no—
764D3—241no—
765D3—241no—
766D3—481no—
767C22—32no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—62no—
772C22—61no—
773C22—61no—
774C22—121no—
775C22—121no—
776C22—361no—
777C22—361no—
778C22—361no—
779C22—724no—
780C22C2×D3×D1211yescharacteristic
781C4—21no—
782C4—21no—
783C4—61no—
784C4—61no—
785C4—121no—
786C4—121no—
787C4—121no—
788C4—361no—
789C4—361no—
790C4—361no—
791C4#6431411yescharacteristic
792C4D3×#23911yescharacteristic
793C3—21no—
794C3#7950311yescharacteristic, complemented
795C3#8098211yescharacteristic, complemented
796C2—62no—
797C2—121no—
798C2—122no—
799C2—721no—
800C2#1059462911yescharacteristic
801C2#1059467811yescharacteristic
802C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594003C2
hypercenterC4⋊C8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593956C2semidirect
3. #10592544C2semidirect
4. C3×#4846C2semidirect
5. C3×#4836C2semidirect
6. #10590969C2semidirect
7. #10590946C2semidirect
8. D3×#821C2semidirect
9. #10590852C2semidirect
10. #10590838C2semidirect
11. #10590684C2semidirect
12. #10590679C2semidirect
13. #10590670C2semidirect
14. #10590360C2semidirect
15. #10590294C2semidirect
20. C2×#3746C22semidirect
23. C4×#634C22semidirect
24. C2×C3×ΓL(1,𝔽25)C22semidirect
28. C3×#869C22semidirect
36. D3×C4⋊Dic3C22semidirect
42. #63857C22semidirect
44. C32×C4⋊C8C22semidirect
46. #63643C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
52. C3×#818C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
77. #4846D3semidirect
81. #4836D3semidirect
174. C2×ΓL(1,𝔽25)C2×D3semidirect
197. #869C2×D3semidirect
204. C3×C4⋊C8C2×D3semidirect
205. C3×C4⋊C8C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
223. #818C2×D3semidirect
224. #818C2×D3semidirect
237. #803C2×D3semidirect
468. C4⋊C8D32semidirect
705. C32#3314semidirect
794. C3#79503semidirect
795. C3#80982semidirect

Maximal subgroups

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

subgroupindex
#105940032
#105939562
#105925442
C3×#48462
C3×#48362
#105909692
#105909462
D3×#8212
#105908522
#105908382
#105906842
#105906792
#105906702
#105903602
#105902942
#809823
#795033