Finite Group Databasebeta

← #11887325

Subgroups — #11887325

Order 1152.

878 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595379C211yesmaximal, characteristic, complemented
2#10594629C211yesmaximal, characteristic
3#10592506C211yesmaximal, characteristic, complemented
4C3×#4813C211yesmaximal, characteristic, complemented
5C3×#4788C211yesmaximal, characteristic, complemented
6#10591656C211yesmaximal, characteristic, complemented
7#10591651C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10D3×#821C211yesmaximal, characteristic, complemented
11#10590872C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590542C211yesmaximal, characteristic, complemented
14#10590451C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#80775—31nomaximal
17#79677—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64155C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23#64104C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic
31#63923—21no—
32D3×(C2×D3)⋊C4—21no—
33#63909—21no—
34C4×#626C2211yescharacteristic
35#63890—21no—
36#63890—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63877—21no—
39#63869C2211yescharacteristic, complemented
40#63868—21no—
41#63864C2211yescharacteristic
42#63849C2211yescharacteristic, complemented
43#63846—21no—
44C32×#103C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#816C2211yescharacteristic, complemented
49C3×C8×Dic3C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5642—31no—
62#5630—31no—
63#5581—31no—
64#5554—31no—
65C3×#467—31no—
66C3×C4×SD16—31no—
67#5187—31no—
68#5185—31no—
69#5173—31no—
70#5169—31no—
71C2×#821—31no—
72C8×#67—31no—
73#5046—31no—
74#5043—31no—
75#5028—31no—
76#5009—31no—
77#4891—31no—
78#4885—31no—
79#4866—31no—
80#4862—31no—
81#4813D311yescharacteristic, complemented
82#4807—31no—
83#4807—31no—
84#4807—61no—
85#4804—31no—
86#4800—31no—
87#4788D311yescharacteristic, complemented
88#4772—31no—
89D3×#102—31no—
90#4697—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#626D411yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3796—22no—
109#3796—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3755—41no—
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C8×C3⋊D3—41no—
119C3×#216—41no—
120C3×#215—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—41no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722—21no—
139#3722—21no—
140#3722—21no—
141#3722D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143Dic32—21no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156#947—31no—
157#946—31no—
158#946—31no—
159#946—61no—
160#946C2×D311yescharacteristic
161Q8×Dic3C2×D311yescharacteristic, complemented
162C2×#216C2×D311yescharacteristic, complemented
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—61no—
166C2×#215C2×D311yescharacteristic
167#930—61no—
168C4×#67—31no—
169C2×(C2×D3)⋊C4—61no—
170C2×C4⋊Dic3—31no—
171C2×D3×C8—31no—
172C2×D3×C8—31no—
173C2×D3×C8—61no—
174C2×D3×C8C2×D311yescharacteristic
175#898—61no—
176#897C2×D311yescharacteristic
177#895—31no—
178#895—31no—
179#895—61no—
180#895—61no—
181#894—61no—
182#894—61no—
183#893C2×D311yescharacteristic
184#892—31no—
185#892—31no—
186D3×C4⋊C4—31no—
187#890—31no—
188#890—61no—
189#889—61no—
190#886—61no—
191#886—61no—
192#882—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#877—61no—
196#876—61no—
197#875—31no—
198C4×D12—31no—
199#872—61no—
200#870—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103C2×D311yescharacteristic, complemented
206C3×#103C2×D311yescharacteristic, complemented
207C3×#102—31no—
208C3×C4×C8—31no—
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#830—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#816—31no—
225#816C2×D311yescharacteristic, complemented
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808C2×D311yescharacteristic, complemented
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—81no—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—22no—
271#626—42no—
272#626—42no—
273D3×Dic3—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—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—31no—
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—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C2×#67—31no—
304C2×#67—61no—
305C2×#67—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308#239—62no—
309#239—121no—
310#237—62no—
311#237—121no—
312D3×D4—62no—
313D3×D4—121no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—62no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—121no—
324C2×D12—121no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6C22×D311yescharacteristic
334C3×Q16—121no—
335C3×SD16—62no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
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×C42—31no—
354C3×C42—61no—
355#217—31no—
356#216—41no—
357#215—22no—
358#215—121no—
359#215—121no—
360#215—122no—
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—31no—
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—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—21no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
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—21no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3#13512yes—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—91no—
439C2×Q16—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8—91no—
444#126—181no—
445#125—91no—
446#125—181no—
447#124—91no—
448#123—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—91no—
459#117—91no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—31no—
464#106—31no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103D3211yescharacteristic, complemented
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479C4×C8—31no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—61no—
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×D3D3×D411yescharacteristic
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—32no—
505C3×D4—61no—
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—61no—
521C2×C3×C4—241no—
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
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—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3D3×D411yescharacteristic
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541D12—21no—
542D12—62no—
543D12—61no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—121no—
548D12—121no—
549D12—122no—
550D12—122no—
551D12—241no—
552D12—241no—
553D12—242no—
554D12#23512yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—81no—
562C4×D3—121no—
563C4×D3—121no—
564C4×D3—122no—
565C4×D3—122no—
566Dic6—21no—
567Dic6—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—62no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C2×C32#54611yescharacteristic
579C2×C32C2×#13511yescharacteristic
580C2×C32#57711yescharacteristic
581C3⋊D3—41no—
582C3⋊D3—81no—
583C3×D3—22no—
584C3×D3—42no—
585C24—181no—
586#41—182no—
587#41—361no—
588C2×Q8—31no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—181no—
595C2×D4—182no—
596C2×D4—181no—
597C2×D4—361no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—91no—
601C22×C4—181no—
602C22×C4—181no—
603Q16—121no—
604SD16—62no—
605SD16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—121no—
610C2×C8—361no—
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—61no—
636C42—181no—
637C22×C3—21no—
638C22×C3—32no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—62no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—22no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—62no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—241no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3#91912yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23511yescharacteristic
687C3×C4#100411yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4#100911yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—241no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—91no—
706C23—181no—
707C23—362no—
708C23—362no—
709C23—721no—
710Q8—21no—
711Q8—21no—
712Q8—61no—
713Q8—61no—
714D4—32no—
715D4—61no—
716D4—182no—
717D4—181no—
718D4—181no—
719D4—362no—
720D4—362no—
721D4—721no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—91no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—241no—
737C2×C4—362no—
738C2×C4—362no—
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—61no—
742C8—61no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—62no—
748C2×C3—122no—
749C2×C3#555011yescharacteristic
750C2×C3#561011yescharacteristic
751C2×C3#576211yescharacteristic
752C2×C3C2×#91911yescharacteristic
753C2×C3D3×#13511yescharacteristic
754C2×C3#577011yescharacteristic
755D3—22no—
756D3—42no—
757D3—122no—
758D3—121no—
759D3—121no—
760D3—241no—
761D3—241no—
762D3—481no—
763C22—32no—
764C22—61no—
765C22—61no—
766C22—62no—
767C22—121no—
768C22—121no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—361no—
773C22—361no—
774C22—361no—
775C22—724no—
776C22D32×D411yescharacteristic
777C4—41no—
778C4—41no—
779C4—61no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—181no—
786C4—361no—
787C4D3×#23511yescharacteristic
788C4#6431411yescharacteristic
789C3—21no—
790C3#7967711yescharacteristic, complemented
791C3#8077511yescharacteristic, complemented
792C2—62no—
793C2—122no—
794C2—361no—
795C2—721no—
796C2#1059428311yescharacteristic
797C2#1059475311yescharacteristic
798C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594629C2
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. #10595379C2semidirect
3. #10592506C2semidirect
4. C3×#4813C2semidirect
5. C3×#4788C2semidirect
6. #10591656C2semidirect
7. #10591651C2semidirect
8. #10591607C2semidirect
9. #10590956C2semidirect
10. D3×#821C2semidirect
11. #10590872C2semidirect
12. C8×#626C2semidirect
13. #10590542C2semidirect
14. #10590451C2semidirect
15. #10590439C2semidirect
20. #64155C22semidirect
22. C2×C8×C3⋊D3C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
39. #63869C22semidirect
42. #63849C22semidirect
44. C32×#103C22semidirect
46. #63635C22semidirect
48. C3×#816C22semidirect
49. C3×C8×Dic3C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
59. #63557C22semidirect
81. #4813D3semidirect
87. #4788D3semidirect
161. Q8×Dic3C2×D3semidirect
162. C2×#216C2×D3semidirect
205. C3×#103C2×D3semidirect
206. C3×#103C2×D3semidirect
225. #816C2×D3semidirect
227. C8×Dic3C2×D3semidirect
235. #808C2×D3semidirect
236. #807C2×D3semidirect
470. #103D32semidirect
702. C32#3296semidirect
790. C3#79677semidirect
791. C3#80775semidirect

Maximal subgroups

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

subgroupindex
#105953792
#105946292
#105925062
C3×#48132
C3×#47882
#105916562
#105916512
#105916072
#105909562
D3×#8212
#105908722
C8×#6262
#105905422
#105904512
#105904392
#807753
#796773