Finite Group Databasebeta

← #11887293

Subgroups — #11887293

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594007C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×#4697C211yesmaximal, characteristic, complemented
5C3×C8×D12C211yesmaximal, characteristic, complemented
6#10590970C211yesmaximal, characteristic, complemented
7#10590946C211yesmaximal, characteristic, complemented
8D3×#821C211yesmaximal, characteristic, complemented
9#10590848C211yesmaximal, characteristic, complemented
10#10590837C211yesmaximal, characteristic, complemented
11#10590825C211yesmaximal, characteristic, complemented
12#10590690C211yesmaximal, characteristic, complemented
13#10590675C211yesmaximal, characteristic, complemented
14#10590378C211yesmaximal, characteristic, complemented
15#10590308C211yesmaximal, characteristic, complemented
16#81652—31nomaximal
17#79440—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#875C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×#870C2211yescharacteristic, complemented
28#63922—21no—
29#63921—21no—
30#63912—21no—
31#63908C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33#63884—21no—
34#63878—21no—
35#63862—21no—
36#63857C2211yescharacteristic
37#63857C2211yescharacteristic, complemented
38#63856C2211yescharacteristic
39#63854—21no—
40#63846—21no—
41#63841C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×C4×C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63644C2211yescharacteristic, complemented
47#63643C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5694—31no—
62#5676—31no—
63#5550—31no—
64#5541—31no—
65C3×#488—31no—
66C3×C8×D4—31no—
67#5116—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5066—31no—
72#5054—31no—
73#4847—31no—
74#4845—31no—
75#4813—31no—
76#4808—31no—
77#4805—31no—
78#4804—31no—
79#4779—31no—
80#4778—31no—
81#4776—31no—
82D3×#102—31no—
83#4737—31no—
84#4733—31no—
85#4731—31no—
86#4721—31no—
87#4697D311yescharacteristic, complemented
88C4×#204—31no—
89C4×#204—31no—
90C4×#204—61no—
91C8×D12D311yescharacteristic, complemented
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#625—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3799—22no—
109#3799—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C42C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118#3744—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131C3×D3×C8—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—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—
141Dic32—21no—
142#3719—41no—
143#3716—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C22×C3×C8—31no—
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×#124—31no—
153C3×C4×D4—31no—
154#946—31no—
155C2×#216—31no—
156#938—31no—
157#937—61no—
158#935—61no—
159C2×#214—31no—
160#930—31no—
161#926—31no—
162C2×C4⋊Dic3—31no—
163#924—31no—
164#924—31no—
165#924—31no—
166C2×Dic12—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—61no—
171C2×D3×C8C2×D311yescharacteristic
172C2×D3×C8C2×D311yescharacteristic, complemented
173#898—61no—
174#897—31no—
175#897—31no—
176#894—61no—
177#894—61no—
178#892—31no—
179#892—61no—
180D3×C4⋊C4—31no—
181#890—61no—
182#889—61no—
183#884—61no—
184#884—61no—
185#883—61no—
186#882—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189#879—61no—
190#877—61no—
191#875C2×D311yescharacteristic
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—61no—
195C4×D12C2×D311yescharacteristic
196#870C2×D311yescharacteristic, complemented
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—61no—
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×C4×C8—21no—
208C3×C4×C8C2×D311yescharacteristic, complemented
209C3×C4×C8C2×D311yescharacteristic, complemented
210#835—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#817—31no—
224#817—31no—
225#817—31no—
226#817—61no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—61no—
231#816C2×D311yescharacteristic, complemented
232#816C2×D311yescharacteristic, complemented
233#809—31no—
234#809—31no—
235#808—31no—
236#807—31no—
237C4⋊(C3⋊C8)C2×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)#4112yes—
253C4×C3⋊D3—81no—
254#634—21no—
255#634—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—22no—
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—42no—
271#626—42no—
272#625—81no—
273#624—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C32×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—31no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C22×Dic3—61no—
306#239—62no—
307#239—121no—
308D3×D4—62no—
309D3×D4—121no—
310#235—62no—
311#235—121no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—62no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—121no—
319C2×D12D1211yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—121no—
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—121no—
338C2×C3×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#216—121no—
361#214—121no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—61no—
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—121no—
372(C2×D3)⋊C4D1211yescharacteristic
373(C2×D3)⋊C4D1211yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3D1211yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
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—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—121no—
404#204—62no—
405#204—62no—
406#204—64no—
407#204—121no—
408D3×C8—41no—
409D3×C8—41no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—22no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
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#13512yes—
423D32—84no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—91no—
437C22×D4—91no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C22×C8—31no—
442C22×C8—31no—
443#126—181no—
444#125—31no—
445#125—181no—
446#124—31no—
447#123—181no—
448#123—181no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452#121—91no—
453#121—181no—
454#120—181no—
455C4×Q8—91no—
456C4×D4—31no—
457C4×D4—91no—
458#117—91no—
459#117—181no—
460C2×C4⋊C4—91no—
461C2×C22⋊C4—181no—
462#107—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—31no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—31no—
478C4×C8D3211yescharacteristic, complemented
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3C2×D1211yescharacteristic
493C22×D3C2×D1211yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×D4—62no—
497C3×D4—61no—
498C3×D4—61no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4C2×D1211yescharacteristic
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—122no—
518#67—122no—
519#67—241no—
520#67—241no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—122no—
534C2×Dic3C2×D1211yescharacteristic
535C2×Dic3C2×D1211yescharacteristic
536D12—22no—
537D12—21no—
538D12—21no—
539D12—32no—
540D12—32no—
541D12—62no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—122no—
546D12—122no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—242no—
557Dic6—21no—
558Dic6—21no—
559Dic6—62no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C2×C32#54611yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—42no—
579C3×D3—22no—
580C3×D3—41no—
581C3×D3—81no—
582C24—181no—
583#41—182no—
584#41—361no—
585C2×Q8—31no—
586C2×Q8—91no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—181no—
593C2×D4—181no—
594C2×D4—361no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600Q16—361no—
601SD16—182no—
602SD16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—121no—
606C2×C8—121no—
607C2×C8C2×D3211yescharacteristic
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C42—181no—
632C42—181no—
633C42C2×D3211yescharacteristic
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C22×D1211yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—122no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—241no—
662C2×D3—241no—
663C2×D3—244no—
664C2×D3—244no—
665C2×D3#90412yes—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4#100411yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4#100911yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—122no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697C32#329611yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23—61no—
701C23—181no—
702C23—362no—
703C23—362no—
704C23—721no—
705Q8—61no—
706Q8—61no—
707Q8—181no—
708Q8—181no—
709D4—62no—
710D4—61no—
711D4—61no—
712D4—92no—
713D4—181no—
714D4—362no—
715D4—362no—
716D4—721no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—362no—
730C2×C4—362no—
731C2×C4—721no—
732C2×C4D3×D1211yescharacteristic
733C2×C4D3×D1211yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—21no—
737C8—61no—
738C8—61no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—62no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3#555411yescharacteristic
746C2×C3#567611yescharacteristic
747C2×C3C2×#90411yescharacteristic
748C2×C3#575111yescharacteristic
749C2×C3D3×#13511yescharacteristic
750C2×C3#577011yescharacteristic
751D3—22no—
752D3—41no—
753D3—81no—
754D3—122no—
755D3—122no—
756D3—242no—
757C22—32no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—182no—
767C22—361no—
768C22—361no—
769C22—724no—
770C22C2×D3×D1211yescharacteristic
771C4—21no—
772C4—21no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—361no—
779C4—361no—
780C4—361no—
781C4#6430611yescharacteristic
782C4#6430711yescharacteristic
783C3—21no—
784C3#7944011yescharacteristic, complemented
785C3#8165211yescharacteristic, complemented
786C2—62no—
787C2—121no—
788C2—241no—
789C2—362no—
790C2#1059400511yescharacteristic
791C2D3×#90411yescharacteristic
792C2#1059467911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10594007C2
hypercenterC4×C8D32
hypocenterC32#3296
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. #10593920C2semidirect
3. C4×#3744C2semidirect
4. C3×#4697C2semidirect
5. C3×C8×D12C2semidirect
6. #10590970C2semidirect
7. #10590946C2semidirect
8. D3×#821C2semidirect
9. #10590848C2semidirect
10. #10590837C2semidirect
11. #10590825C2semidirect
12. #10590690C2semidirect
13. #10590675C2semidirect
14. #10590378C2semidirect
15. #10590308C2semidirect
22. C4×#634C22semidirect
24. C2×C3×D3×C8C22semidirect
27. C3×#870C22semidirect
37. #63857C22semidirect
41. #63841C22semidirect
42. C2×#3719C22semidirect
44. C32×C4×C8C22semidirect
46. #63644C22semidirect
47. #63643C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#816C22semidirect
53. C3×#816C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
87. #4697D3semidirect
91. C8×D12D3semidirect
172. C2×D3×C8C2×D3semidirect
196. #870C2×D3semidirect
208. C3×C4×C8C2×D3semidirect
209. C3×C4×C8C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
231. #816C2×D3semidirect
232. #816C2×D3semidirect
237. C4⋊(C3⋊C8)C2×D3semidirect
478. C4×C8D32semidirect
697. C32#3296semidirect
784. C3#79440semidirect
785. C3#81652semidirect

Maximal subgroups

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

subgroupindex
#105940072
#105939202
C4×#37442
C3×#46972
C3×C8×D122
#105909702
#105909462
D3×#8212
#105908482
#105908372
#105908252
#105906902
#105906752
#105903782
#105903082
#816523
#794403