Finite Group Databasebeta

← #11887314

Subgroups — #11887314

Order 1152.

867 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594633C211yesmaximal, characteristic
2#10594551C211yesmaximal, characteristic, complemented
3#10592570C211yesmaximal, characteristic, complemented
4C3×#4864C211yesmaximal, characteristic, complemented
5C3×#4862C211yesmaximal, characteristic, complemented
6#10590942C211yesmaximal, characteristic, complemented
7#10590796C211yesmaximal, characteristic, complemented
8#10590717C211yesmaximal, characteristic, complemented
9#10590690C211yesmaximal, characteristic, complemented
10#10590616C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590539C211yesmaximal, characteristic, complemented
13#10590518C211yesmaximal, characteristic, complemented
14#10590483C211yesmaximal, characteristic, complemented
15#10590449C211yesmaximal, characteristic, complemented
16#81445—31nomaximal
17#80671—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64102C2211yescharacteristic
21#64099C2211yescharacteristic, complemented
22C2×C3×#204C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic, complemented
24C3×#897C2211yescharacteristic
25C3×#897C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28#63922—21no—
29#63921—21no—
30#63916—21no—
31#63905—21no—
32C4×#625C2211yescharacteristic
33#63863C2211yescharacteristic
34#63861—21no—
35#63856C2211yescharacteristic
36#63854—21no—
37#63847—21no—
38#63843C2211yescharacteristic, complemented
39#63841—21no—
40#63841C2211yescharacteristic, complemented
41C2×#3718C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#106C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63641C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63634C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5639—31no—
62#5630—31no—
63#5612—31no—
64#5513—31no—
65C3×#483—31no—
66C3×#465—31no—
67#5169—31no—
68#5166—31no—
69#5113—31no—
70C8×#67—31no—
71#5051—31no—
72#5047—31no—
73#5035—31no—
74C2×#809—31no—
75#4871—31no—
76#4871—31no—
77#4871—61no—
78#4866—31no—
79#4864D311yescharacteristic, complemented
80#4862D311yescharacteristic, complemented
81#4852—31no—
82#4813—31no—
83#4808—31no—
84#4804—31no—
85#4800—31no—
86#4798—31no—
87#4788—31no—
88D3×#102—31no—
89#4768—31no—
90#4731—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625D411yescharacteristic
105C2×#624—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3799—22no—
109#3799—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—41no—
129C3×D3×C8—41no—
130#3724—21no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140Dic32—21no—
141#3718—41no—
142#3717—22no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×SD16—31no—
150C22×C3×C8—31no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C2×C3×C4⋊C4—31no—
155#947—31no—
156#946—31no—
157Q8×Dic3—31no—
158C2×#216—31no—
159C2×#216—31no—
160C2×#215—31no—
161#938—61no—
162#937—61no—
163#936—31no—
164#929—61no—
165C4×#67—31no—
166C4×#67—31no—
167#926—31no—
168#926—61no—
169#924—31no—
170C22×C3⋊C8—31no—
171C2×#204—31no—
172C2×#204C2×D311yescharacteristic
173C2×D3×C8—31no—
174C2×D3×C8C2×D311yescharacteristic, complemented
175#898—61no—
176#897C2×D311yescharacteristic
177#897C2×D311yescharacteristic, complemented
178#895—61no—
179#895C2×D311yescharacteristic
180#894—61no—
181#893—31no—
182#893—31no—
183#893—61no—
184#892—31no—
185#892—61no—
186D3×C4⋊C4C2×D311yescharacteristic
187#890—31no—
188#890—31no—
189#890—61no—
190#889—61no—
191#889—61no—
192#887—31no—
193#883—61no—
194#883—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#879—61no—
199C3×#106—21no—
200C3×#106—31no—
201C3×#106C2×D311yescharacteristic, complemented
202C3×#106C2×D311yescharacteristic, complemented
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#816—31no—
220#816C2×D311yescharacteristic, complemented
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—61no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226#810C2×D311yescharacteristic, complemented
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807—61no—
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×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—42no—
273#625—22no—
274#624—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—31no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—31no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C2×#67—31no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307#239—62no—
308#239—121no—
309D3×D4—62no—
310D3×D4—121no—
311#235—62no—
312#235—121no—
313C2×D12—21no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—121no—
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—121no—
328C2×C4×D3C22×D311yescharacteristic
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C3×SD16—121no—
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—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#216—121no—
359#216—121no—
360#215—62no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
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—121no—
373C4⋊Dic3—21no—
374C4⋊Dic3—21no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—121no—
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—121no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405#204—41no—
406#204—62no—
407D3×C8—41no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—22no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3#13512yes—
422D32—84no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—91no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—91no—
440C22×C8—31no—
441C22×C8—91no—
442#126—181no—
443#125—91no—
444#125—181no—
445#124—91no—
446#123—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—31no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×D4—91no—
456C4×D4—91no—
457#117—91no—
458#117—181no—
459C2×C4⋊C4—31no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—31no—
463#106D3211yescharacteristic, complemented
464C4⋊C8—91no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—91no—
469#102—31no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—31no—
476C22⋊C8—91no—
477C4×C8—91no—
478C23×C3—31no—
479C23×C3—31no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—122no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3D3×D411yescharacteristic
492C22×D3D3×D411yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—241no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—122no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—62no—
520#67—62no—
521#67—122no—
522#67—122no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—121no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537D12—21no—
538D12—21no—
539D12—32no—
540D12—32no—
541D12—62no—
542D12—61no—
543D12—61no—
544D12—81no—
545D12—121no—
546D12—122no—
547D12—122no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—42no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—242no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C2×C32#54611yescharacteristic
573C2×C32C2×#13511yescharacteristic
574C2×C32#57711yescharacteristic
575C3⋊D3—42no—
576C3×D3—22no—
577C3×D3—41no—
578C3×D3—81no—
579C24—181no—
580#41—182no—
581#41—361no—
582C2×Q8—31no—
583C2×Q8—31no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4—91no—
587C2×D4—91no—
588C2×D4—181no—
589C2×D4—182no—
590C2×D4—181no—
591C2×D4—361no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—181no—
596C22×C4—181no—
597Q16—361no—
598SD16—121no—
599SD16—182no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—91no—
603C2×C8—121no—
604C2×C8—361no—
605C2×C8C2×D3211yescharacteristic
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—91no—
629C42—181no—
630C42—181no—
631C22×C3—21no—
632C22×C3—32no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—122no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—241no—
659C2×D3—241no—
660C2×D3—244no—
661C2×D3—244no—
662C2×D3#91612yes—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—81no—
672C3×C4—81no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4#100411yescharacteristic
677C3×C4D3×#4111yescharacteristic
678C3×C4D3×#4111yescharacteristic
679C3×C4#100911yescharacteristic
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694C32#329611yescharacteristic, complemented, Sylow
695C23—31no—
696C23—31no—
697C23—61no—
698C23—181no—
699C23—362no—
700C23—362no—
701C23—721no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706D4—61no—
707D4—61no—
708D4—92no—
709D4—182no—
710D4—181no—
711D4—241no—
712D4—362no—
713D4—362no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—122no—
728C2×C4—181no—
729C2×C4—362no—
730C2×C4—721no—
731C2×C4C22×D3211yescharacteristic
732C8—21no—
733C8—61no—
734C8—61no—
735C8—181no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—62no—
740C2×C3—121no—
741C2×C3—241no—
742C2×C3#561011yescharacteristic
743C2×C3#565411yescharacteristic
744C2×C3C2×#91611yescharacteristic
745C2×C3#576211yescharacteristic
746C2×C3D3×#13511yescharacteristic
747C2×C3#577811yescharacteristic
748D3—22no—
749D3—41no—
750D3—81no—
751D3—122no—
752D3—122no—
753D3—242no—
754C22—32no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—182no—
764C22—361no—
765C22—361no—
766C22—724no—
767C22D32×D411yescharacteristic
768C4—41no—
769C4—41no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—181no—
776C4—181no—
777C4—361no—
778C4#6430711yescharacteristic
779C4#6431911yescharacteristic
780C3—21no—
781C3#8067111yescharacteristic, complemented
782C3#8144511yescharacteristic, complemented
783C2—62no—
784C2—121no—
785C2—241no—
786C2—362no—
787C2#1059461711yescharacteristic
788C2D3×#91611yescharacteristic
789C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594633C2
hypercenter#106D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594551C2semidirect
3. #10592570C2semidirect
4. C3×#4864C2semidirect
5. C3×#4862C2semidirect
6. #10590942C2semidirect
7. #10590796C2semidirect
8. #10590717C2semidirect
9. #10590690C2semidirect
10. #10590616C2semidirect
11. D3×#809C2semidirect
12. #10590539C2semidirect
13. #10590518C2semidirect
14. #10590483C2semidirect
15. #10590449C2semidirect
21. #64099C22semidirect
23. C2×C3×D3×C8C22semidirect
25. C3×#897C22semidirect
38. #63843C22semidirect
40. #63841C22semidirect
41. C2×#3718C22semidirect
44. C32×#106C22semidirect
46. #63641C22semidirect
48. #63634C22semidirect
50. C3×#816C22semidirect
51. C3×#810C22semidirect
52. C3×#810C22semidirect
54. C3×#808C22semidirect
55. #63566C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
79. #4864D3semidirect
80. #4862D3semidirect
174. C2×D3×C8C2×D3semidirect
177. #897C2×D3semidirect
201. C3×#106C2×D3semidirect
202. C3×#106C2×D3semidirect
220. #816C2×D3semidirect
226. #810C2×D3semidirect
227. #810C2×D3semidirect
234. #808C2×D3semidirect
463. #106D32semidirect
694. C32#3296semidirect
781. C3#80671semidirect
782. C3#81445semidirect

Maximal subgroups

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

subgroupindex
#105946332
#105945512
#105925702
C3×#48642
C3×#48622
#105909422
#105907962
#105907172
#105906902
#105906162
D3×#8092
#105905392
#105905182
#105904832
#105904492
#814453
#806713