Finite Group Databasebeta

← #11887323

Subgroups — #11887323

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#10595380C211yesmaximal, characteristic, complemented
2#10594633C211yesmaximal, characteristic
3#10592487C211yesmaximal, characteristic, complemented
4C3×#4813C211yesmaximal, characteristic, complemented
5C3×#4807C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591651C211yesmaximal, characteristic, complemented
8#10591612C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590868C211yesmaximal, characteristic, complemented
11C8×#625C211yesmaximal, characteristic, complemented
12#10590690C211yesmaximal, characteristic, complemented
13#10590446C211yesmaximal, characteristic, complemented
14#10590439C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#80775—31nomaximal
17#80671—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31#63922—21no—
32#63921—21no—
33#63916—21no—
34C4×#625C2211yescharacteristic
35#63891—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63878—21no—
38#63872C2211yescharacteristic, complemented
39#63863C2211yescharacteristic
40#63862—21no—
41#63854—21no—
42#63845—21no—
43#63841C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46C8×C3⋊Dic3C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5642—31no—
62#5639—31no—
63#5630—31no—
64#5612—31no—
65C3×#467—31no—
66C3×#465—31no—
67#5187—31no—
68#5185—31no—
69#5169—31no—
70#5166—31no—
71#5113—31no—
72C2×#821—31no—
73C8×#67—31no—
74C8×#67—31no—
75#5047—31no—
76#5046—31no—
77#5043—31no—
78#5035—31no—
79#4891—31no—
80#4885—31no—
81#4871—31no—
82#4862—31no—
83#4813D311yescharacteristic, complemented
84#4807D311yescharacteristic, complemented
85#4804—31no—
86#4800—31no—
87#4788—31no—
88#4788—31no—
89#4788—61no—
90D3×#102—31no—
91#4768—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#625D411yescharacteristic
104C2×#624—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3799—22no—
109#3799—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3755—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#216—41no—
120C3×#215—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133C3×D3×C8—41no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143Dic32—21no—
144#3296—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157#947—31no—
158#946C2×D311yescharacteristic
159#946C2×D311yescharacteristic, complemented
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—61no—
163C2×#216C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167C2×#215C2×D311yescharacteristic
168#938—61no—
169#937—61no—
170#936—31no—
171C4×#67—31no—
172C4×#67—31no—
173#926—31no—
174C2×C4⋊Dic3—31no—
175C2×D3×C8C2×D311yescharacteristic
176C2×D3×C8C2×D311yescharacteristic, complemented
177#898—61no—
178#897C2×D311yescharacteristic
179#895—61no—
180#895C2×D311yescharacteristic
181#894—61no—
182#893—31no—
183#893—31no—
184#893—61no—
185#892—31no—
186#892—61no—
187D3×C4⋊C4—31no—
188#890—31no—
189#890—31no—
190#890—61no—
191#889—61no—
192#886—61no—
193#883—61no—
194#883—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#879—61no—
199#877—61no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#103—21no—
203C3×#103—31no—
204C3×#103C2×D311yescharacteristic, complemented
205C3×#103C2×D311yescharacteristic, complemented
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#830—31no—
212#830—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—61no—
229#810—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#808—31no—
234#808—31no—
235#808—61no—
236#808C2×D311yescharacteristic, complemented
237#807C2×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—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
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—22no—
273#624—42no—
274D3×Dic3—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—91no—
283#482—91no—
284#478—91no—
285#467—31no—
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—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C2×#67—31no—
305C2×#67—31no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—61no—
309#239—62no—
310#239—121no—
311D3×D4—62no—
312D3×D4—121no—
313#235—62no—
314#235—121no—
315C2×D12—21no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—121no—
330C2×C4×D3C22×D311yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C3×SD16—121no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—121no—
339C2×C3×C8—121no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354#217—31no—
355#217—31no—
356#217—61no—
357#217—61no—
358#217—61no—
359#216—41no—
360#215—41no—
361#215—62no—
362#215—62no—
363#215—64no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—121no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
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—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
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—31no—
439C2×SD16—31no—
440C2×SD16—91no—
441C22×C8—31no—
442C22×C8—31no—
443#126—181no—
444#125—91no—
445#125—181no—
446#124—91no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452#121—31no—
453#121—181no—
454#120—181no—
455C4×Q8—91no—
456C4×D4—91no—
457C4×D4—91no—
458#117—91no—
459#117—181no—
460C2×C4⋊C4—91no—
461C2×C22⋊C4—181no—
462#107—31no—
463#106—31no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103D3211yescharacteristic, complemented
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478C4×C8—91no—
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×D3D3×D411yescharacteristic
493C22×D3D3×D411yescharacteristic
494C3×Q8—22no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—241no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—62no—
524#67—62no—
525#67—122no—
526#67—122no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—122no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—21no—
543D12—21no—
544D12—32no—
545D12—32no—
546D12—62no—
547D12—61no—
548D12—61no—
549D12—81no—
550D12—121no—
551D12—122no—
552D12—122no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—242no—
563Dic6—21no—
564Dic6—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—62no—
573C3⋊C8—61no—
574C3⋊C8—61no—
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×Q8C2×D3211yescharacteristic
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—91no—
591C2×D4—181no—
592C2×D4—182no—
593C2×D4—181no—
594C2×D4—361no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600Q16—121no—
601SD16—121no—
602SD16—182no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—121no—
607C2×C8—121no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
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⋊C4C2×D3211yescharacteristic
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—91no—
626C22⋊C4—91no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C42—91no—
632C42—181no—
633C42—181no—
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×C3C2×D3×D411yescharacteristic
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#91912yes—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—42no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4#100411yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—62no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#329611yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23—61no—
701C23—181no—
702C23—362no—
703C23—362no—
704C23—721no—
705Q8—21no—
706Q8—21no—
707Q8—61no—
708Q8—61no—
709D4—61no—
710D4—61no—
711D4—92no—
712D4—182no—
713D4—181no—
714D4—241no—
715D4—362no—
716D4—362no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—181no—
731C2×C4—362no—
732C2×C4—362no—
733C2×C4—721no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—62no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3#561011yescharacteristic
746C2×C3#561011yescharacteristic
747C2×C3#576211yescharacteristic
748C2×C3C2×#91911yescharacteristic
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—
770C22D32×D411yescharacteristic
771C4—41no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—181no—
779C4—181no—
780C4—361no—
781C4#6430611yescharacteristic
782C4#6431311yescharacteristic
783C3—21no—
784C3#8067111yescharacteristic, complemented
785C3#8077511yescharacteristic, complemented
786C2—62no—
787C2—121no—
788C2—241no—
789C2—362no—
790C2#1059427611yescharacteristic
791C2#1059475311yescharacteristic
792C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594633C2
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
1. #10595380C2semidirect
3. #10592487C2semidirect
4. C3×#4813C2semidirect
5. C3×#4807C2semidirect
6. #10591657C2semidirect
7. #10591651C2semidirect
8. #10591612C2semidirect
9. D3×#821C2semidirect
10. #10590868C2semidirect
11. C8×#625C2semidirect
12. #10590690C2semidirect
13. #10590446C2semidirect
14. #10590439C2semidirect
15. #10590435C2semidirect
20. Q8×C3⋊Dic3C22semidirect
24. C3×#946C22semidirect
25. C2×C3×#216C22semidirect
28. C2×C3×D3×C8C22semidirect
38. #63872C22semidirect
43. #63841C22semidirect
44. C32×#103C22semidirect
46. C8×C3⋊Dic3C22semidirect
47. #63635C22semidirect
49. C3×#816C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #4813D3semidirect
84. #4807D3semidirect
159. #946C2×D3semidirect
163. C2×#216C2×D3semidirect
176. C2×D3×C8C2×D3semidirect
204. C3×#103C2×D3semidirect
205. C3×#103C2×D3semidirect
223. #816C2×D3semidirect
236. #808C2×D3semidirect
237. #807C2×D3semidirect
469. #103D32semidirect
697. C32#3296semidirect
784. C3#80671semidirect
785. C3#80775semidirect

Maximal subgroups

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

subgroupindex
#105953802
#105946332
#105924872
C3×#48132
C3×#48072
#105916572
#105916512
#105916122
D3×#8212
#105908682
C8×#6252
#105906902
#105904462
#105904392
#105904352
#807753
#806713