Finite Group Databasebeta

← #11887282

Subgroups — #11887282

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595428C211yesmaximal, characteristic
2#10594584C211yesmaximal, characteristic, complemented
3#10592512C211yesmaximal, characteristic, complemented
4C3×#4804C211yesmaximal, characteristic, complemented
5C3×#4800C211yesmaximal, characteristic, complemented
6#10591599C211yesmaximal, characteristic, complemented
7#10591577C211yesmaximal, characteristic, complemented
8#10591553C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590825C211yesmaximal, characteristic, complemented
11#10590744C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590502C211yesmaximal, characteristic, complemented
15#10590467C211yesmaximal, characteristic, complemented
16#81652—31nomaximal
17#78845—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20#64155C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic
23#64106C2211yescharacteristic
24C3×#947C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#892C2211yescharacteristic, complemented
27C3×#890C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63908C2211yescharacteristic
31#63905—21no—
32C4×#626C2211yescharacteristic
33#63900C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63885—21no—
36#63869—21no—
37#63861—21no—
38#63857C2211yescharacteristic, complemented
39#63854—21no—
40#63844C2211yescharacteristic, complemented
41#63836—21no—
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5829—31no—
62#5694—31no—
63#5676—31no—
64#5529—31no—
65C3×#488—31no—
66C3×#416—31no—
67#5239—31no—
68#5114—31no—
69C8×#67—31no—
70#5066—31no—
71#5054—31no—
72#5003—31no—
73#4813—31no—
74#4813—31no—
75#4813—61no—
76#4808—31no—
77#4805—31no—
78#4805—31no—
79#4804D311yescharacteristic, complemented
80#4800D311yescharacteristic, complemented
81#4798—31no—
82#4779—31no—
83#4778—31no—
84#4776—31no—
85#4776—31no—
86D3×#102—31no—
87D3×#102—31no—
88#4763—31no—
89#4758—31no—
90C4×#204—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×#626D411yescharacteristic
104C2×#625—21no—
105C2×#625—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3756—41no—
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3716—22no—
143#3716—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C22×C3×C8—31no—
150C3×#125—31no—
151C3×#124—31no—
152C3×#117—31no—
153#947C2×D311yescharacteristic
154#946—31no—
155#946—31no—
156#946—61no—
157C2×#216—31no—
158C2×#216—31no—
159C2×#216—61no—
160#939—61no—
161#938—31no—
162#937—61no—
163D4×Dic3—31no—
164C2×#214—31no—
165C2×#214—31no—
166#930—31no—
167#929—61no—
168C4×#67—31no—
169C2×(C2×D3)⋊C4—61no—
170#924—31no—
171C2×#204—31no—
172C2×#204—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—61no—
176C2×D3×C8C2×D311yescharacteristic, complemented
177#898—61no—
178#897—31no—
179#897—31no—
180#897—31no—
181#897—61no—
182#894—61no—
183#892—61no—
184#892C2×D311yescharacteristic, complemented
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187#890—61no—
188#890C2×D311yescharacteristic, complemented
189#887—31no—
190#884—61no—
191#883—61no—
192#883—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196C4×D12—31no—
197C4×D12—31no—
198#872—61no—
199#870—61no—
200C4×Dic6—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103C2×D311yescharacteristic, complemented
205C3×#103C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×C4×C8—31no—
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#832—31no—
215#830—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#817—31no—
222#817—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809C2×D311yescharacteristic
231#809C2×D311yescharacteristic
232#808—31no—
233#808—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270#626—22no—
271#625—42no—
272#625—81no—
273#624—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—31no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—31no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312#239—22no—
313#239—41no—
314D3×D4—62no—
315D3×D4—62no—
316D3×D4—121no—
317D3×D4—121no—
318C2×D12—21no—
319C2×D12—31no—
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351#217—31no—
352#217—61no—
353#217—61no—
354#217—61no—
355#216—121no—
356#216—121no—
357#216—122no—
358#214—62no—
359#214—121no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
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—121no—
374(C2×D3)⋊C4—121no—
375C4⋊Dic3—21no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—121no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—121no—
396C4×Dic3—21no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405#204—62no—
406#204—121no—
407D3×C8—41no—
408D3×C8—121no—
409D3×C8—121no—
410D3×C8—122no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3#13512yes—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—91no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8—91no—
444#126—181no—
445#125—31no—
446#125—181no—
447#124—31no—
448#123—181no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459#117—31no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103D3211yescharacteristic, complemented
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479C4×C8—31no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3D3×D411yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×D4—32no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—122no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—62no—
524#67—122no—
525#67—122no—
526#67—241no—
527#67—241no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—241no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543D12—21no—
544D12—21no—
545D12—21no—
546D12—42no—
547D12—62no—
548D12#23512yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—121no—
557C4×D3—121no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—241no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—62no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C2×C32#54611yescharacteristic
578C2×C32C2×#13511yescharacteristic
579C2×C32#57711yescharacteristic
580C3⋊D3—22no—
581C3×D3—42no—
582C3×D3—41no—
583C3×D3—81no—
584C24—181no—
585#41—62no—
586#41—121no—
587C2×Q8—91no—
588C2×Q8C2×D3211yescharacteristic
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—182no—
595C2×D4—181no—
596C2×D4—361no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—91no—
600C22×C4—181no—
601C22×C4—181no—
602Q16—361no—
603SD16—182no—
604SD16—361no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—91no—
608C2×C8—121no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4C2×D3211yescharacteristic
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—31no—
634C42—61no—
635C42—181no—
636C22×C3—21no—
637C22×C3—62no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—22no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—32no—
653C2×D3—32no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—244no—
667C2×D3—244no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C2×#23511yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—61no—
691Dic3—61no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#329611yescharacteristic, complemented, Sylow
700C23—31no—
701C23—61no—
702C23—61no—
703C23—91no—
704C23—362no—
705C23—362no—
706C23—721no—
707Q8—21no—
708Q8—21no—
709Q8—181no—
710Q8—181no—
711D4—32no—
712D4—61no—
713D4—61no—
714D4—61no—
715D4—122no—
716D4—182no—
717D4—362no—
718D4—721no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—122no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—362no—
735C2×C4—721no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—122no—
745C2×C3—121no—
746C2×C3—241no—
747C2×C3#549011yescharacteristic
748C2×C3#567611yescharacteristic
749C2×C3D3×#13511yescharacteristic
750C2×C3D3×#13511yescharacteristic
751C2×C3#577011yescharacteristic
752C2×C3#577011yescharacteristic
753D3—41no—
754D3—42no—
755D3—62no—
756D3—62no—
757D3—81no—
758D3—122no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—62no—
763C22—92no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—181no—
770C22—181no—
771C22—724no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4#6431411yescharacteristic
785C3—21no—
786C3#7884511yescharacteristic, complemented
787C3#8165211yescharacteristic, complemented
788C2—121no—
789C2—122no—
790C2—182no—
791C2—241no—
792C2#1059428011yescharacteristic
793C2#1059475711yescharacteristic
794C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595428C2
hypercenter#103D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594584C2semidirect
3. #10592512C2semidirect
4. C3×#4804C2semidirect
5. C3×#4800C2semidirect
6. #10591599C2semidirect
7. #10591577C2semidirect
8. #10591553C2semidirect
9. #10590940C2semidirect
10. #10590825C2semidirect
11. #10590744C2semidirect
12. C8×#626C2semidirect
13. #10590597C2semidirect
14. #10590502C2semidirect
15. #10590467C2semidirect
21. C2×#3756C22semidirect
25. C2×C3×D3×C8C22semidirect
26. C3×#892C22semidirect
27. C3×#890C22semidirect
38. #63857C22semidirect
40. #63844C22semidirect
44. C32×#103C22semidirect
45. #63643C22semidirect
46. #63634C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×C8×Dic3C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #4804D3semidirect
80. #4800D3semidirect
176. C2×D3×C8C2×D3semidirect
184. #892C2×D3semidirect
188. #890C2×D3semidirect
204. C3×#103C2×D3semidirect
205. C3×#103C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
227. C8×Dic3C2×D3semidirect
470. #103D32semidirect
699. C32#3296semidirect
786. C3#78845semidirect
787. C3#81652semidirect

Maximal subgroups

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

subgroupindex
#105954282
#105945842
#105925122
C3×#48042
C3×#48002
#105915992
#105915772
#105915532
#105909402
#105908252
#105907442
C8×#6262
#105905972
#105905022
#105904672
#816523
#788453