Finite Group Databasebeta

← #11869715

Subgroups — #11869715

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595430C211yesmaximal, characteristic
2D3×#892C211yesmaximal, characteristic, complemented
3#10592503C211yesmaximal, characteristic, complemented
4C3×#4814C211yesmaximal, characteristic, complemented
5C3×#4811C211yesmaximal, characteristic, complemented
6#10591560C211yesmaximal, characteristic, complemented
7#10591558C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10590935C211yesmaximal, characteristic, complemented
10#10590714C211yesmaximal, characteristic, complemented
11#10590705C211yesmaximal, characteristic, complemented
12#10590679C211yesmaximal, characteristic, complemented
13#10590574C211yesmaximal, characteristic, complemented
14#10590424C211yesmaximal, characteristic, complemented
15#10590423C211yesmaximal, characteristic, complemented
16#81515—31nomaximal
17#81467—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C4×D32C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26#63923—21no—
27D3×(C2×D3)⋊C4—21no—
28#63909C2211yescharacteristic
29#63909C2211yescharacteristic
30#63897—21no—
31D3×C4⋊Dic3C2211yescharacteristic
32#63881—21no—
33#63881—21no—
34#63878—21no—
35C4×D3×Dic3—21no—
36#63849C2211yescharacteristic
37#63849C2211yescharacteristic
38#63841C2211yescharacteristic
39#63836—21no—
40C2×#3710C2211yescharacteristic
41C32×#103C2211yescharacteristic, complemented
42#63662C2211yescharacteristic, complemented
43#63648C2211yescharacteristic, complemented
44#63636C2211yescharacteristic, complemented
45C3×#835C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5627—31no—
62#5627—31no—
63D3×#117—31no—
64C2×#892—31no—
65C3×#485—31no—
66C3×#484—31no—
67#5045—31no—
68#5043—31no—
69#5003—31no—
70#4968—31no—
71#4885—31no—
72#4885—31no—
73#4882—31no—
74#4880—31no—
75#4880—31no—
76#4880—31no—
77#4863—31no—
78#4860—31no—
79#4814—31no—
80#4814D311yescharacteristic, complemented
81#4811D311yescharacteristic, complemented
82#4805—31no—
83#4804—31no—
84#4804—31no—
85#4804—31no—
86#4804—31no—
87#4804—61no—
88#4737—31no—
89#4736—31no—
90D3×C22⋊C8—31no—
91D3×C22⋊C8—31no—
92C22×D32D411yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#624D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3D411yescharacteristic
108C2×D3×Dic3D411yescharacteristic
109C4×D32—22no—
110C4×D32—22no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C8×C3⋊D3—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140#3710—22no—
141#3091—91noSylow
142C2×#239—31no—
143C2×#239—31no—
144C2×#239—61no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C3×C22⋊Q8—31no—
148C3×C22⋊Q8—31no—
149C3×#117—31no—
150C2×C3×C4⋊C4—31no—
151#946C2×D311yescharacteristic
152#946C2×D311yescharacteristic
153#930—31no—
154#930—31no—
155C2×(C2×D3)⋊C4—61no—
156#926—31no—
157C2×C4⋊Dic3—31no—
158C2×C4×Dic3—61no—
159C2×D3×C8—31no—
160C2×D3×C8—31no—
161C2×D3×C8—31no—
162C2×D3×C8—31no—
163C2×D3×C8—61no—
164#895—31no—
165#895—31no—
166#894—61no—
167#894—61no—
168#893—61no—
169#893—61no—
170#892—31no—
171#892—31no—
172#892—31no—
173#892—31no—
174#892—31no—
175#892—31no—
176#892—31no—
177#892—61no—
178#892—61no—
179#892—61no—
180#892C2×D311yescharacteristic
181D3×C4⋊C4—31no—
182D3×C4⋊C4C2×D311yescharacteristic
183#882—61no—
184#882—61no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187D3×C22⋊C4—61no—
188#877—61no—
189#872—61no—
190C42×D3—61no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#107—31no—
194C3×#106—31no—
195C3×#103—21no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103C2×D311yescharacteristic, complemented
199C3×#103C2×D311yescharacteristic, complemented
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202#835—31no—
203#835—31no—
204#835—61no—
205#835C2×D311yescharacteristic, complemented
206#835C2×D311yescharacteristic, complemented
207#830—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#818C2×D311yescharacteristic, complemented
220#818C2×D311yescharacteristic, complemented
221#817—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234#807C2×D311yescharacteristic, complemented
235C22×C3⋊D3—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—22no—
240C2×D32—22no—
241C2×D32—41no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—42no—
252C4×C3⋊D3—42no—
253C4×C3⋊D3#4112yes—
254C4×C3⋊D3#4112yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266#626—42no—
267#626—42no—
268#624—22no—
269D3×Dic3—22no—
270D3×Dic3—22no—
271D3×Dic3—42no—
272C32×C8—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—91no—
277C2×#117—91no—
278#485—31no—
279#485—91no—
280#484—31no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—91no—
289#416—91no—
290C2×C22⋊C8—91no—
291C23×D3—31no—
292C23×D3—31no—
293C2×C3×Q8—21no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C2×#67—61no—
300C2×#67—61no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—61no—
304#239—62no—
305#239—62no—
306#239—62no—
307#239—62no—
308#239—64no—
309#239—122no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—121no—
318C2×C4×D3—21no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—62no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—62no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—61no—
355#217—61no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
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—121no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383C4×Dic3—21no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—121no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D3×C8—62no—
399D3×C8—62no—
400D3×C8—62no—
401D3×C8—62no—
402D3×C8—122no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3#12312yes—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3#13512yes—
416D32—44no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—41no—
422C3⋊Dic3#12312yes—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—91no—
430C23×C4—91no—
431C22×C8—91no—
432C22×C8—91no—
433#123—181no—
434C22⋊Q8—31no—
435C22⋊Q8—31no—
436#121—91no—
437#121—91no—
438#120—181no—
439C4×D4—181no—
440C4×D4—181no—
441#117—31no—
442#117—91no—
443#117—91no—
444#117—91no—
445#117—91no—
446#117—181no—
447#117—181no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—91no—
450C2×C22⋊C4—181no—
451C2×C42—181no—
452#107—31no—
453#107—31no—
454#107—31no—
455#107—91no—
456#106—31no—
457#106—91no—
458#106—91no—
459#106—91no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103D3211yescharacteristic, complemented
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468C22⋊C8—31no—
469C22⋊C8—31no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472C23×C3—31no—
473C23×C3—31no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—61no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—121no—
484C22×D3—121no—
485C22×D3—121no—
486C22×D3D3×D411yescharacteristic
487C22×D3D3×D411yescharacteristic
488C3×Q8—22no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—41no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
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×C4—122no—
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—122no—
515#67—122no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—122no—
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531D12—62no—
532D12—61no—
533D12—61no—
534D12—61no—
535D12—61no—
536D12—121no—
537D12—122no—
538D12—122no—
539D12—124no—
540D12—122no—
541D12—122no—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—32no—
547C4×D3—32no—
548C4×D3—32no—
549C4×D3—32no—
550C4×D3—42no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—62no—
554C4×D3—62no—
555C4×D3—62no—
556C4×D3—62no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—124no—
560C4×D3—122no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C2×C32C2×#12311yescharacteristic
572C2×C32C2×#13511yescharacteristic
573C2×C32#57511yescharacteristic
574C3⋊D3—22no—
575C3⋊D3—81no—
576C3×D3—22no—
577C3×D3—41no—
578C24—91no—
579#41—182no—
580#41—182no—
581C2×Q8C2×D3211yescharacteristic
582C2×D4—91no—
583C2×D4—181no—
584C2×D4—181no—
585C2×D4—181no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—61no—
589C22×C4—91no—
590C22×C4—91no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—181no—
594C22×C4—182no—
595C22×C4—182no—
596C22×C4—181no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8—182no—
601C2×C8—182no—
602C2×C8C2×D3211yescharacteristic
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4C2×D3211yescharacteristic
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—61no—
623C42—181no—
624C42—181no—
625C42—181no—
626C42—181no—
627C22×C3—21no—
628C22×C3—32no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C2×D3×D411yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—32no—
642C2×D3—32no—
643C2×D3—62no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—124no—
651C2×D3—124no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—241no—
660C2×D3—241no—
661C2×D3#91912yes—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—42no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—81no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4D3×#4111yescharacteristic
677C3×C4D3×#4111yescharacteristic
678C3×C4D3×#4111yescharacteristic
679C3×C4D3×#4111yescharacteristic
680Dic3—21no—
681Dic3—21no—
682Dic3—32no—
683Dic3—32no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—62no—
689Dic3—121no—
690Dic3—121no—
691Dic3—241no—
692C32#309111yescharacteristic, complemented, Sylow
693C23—31no—
694C23—31no—
695C23—91no—
696C23—182no—
697C23—182no—
698C23—181no—
699C23—361no—
700Q8—21no—
701Q8—21no—
702D4—181no—
703D4—181no—
704D4—362no—
705D4—362no—
706D4—362no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—91no—
720C2×C4—92no—
721C2×C4—92no—
722C2×C4—122no—
723C2×C4—182no—
724C2×C4—182no—
725C2×C4—182no—
726C2×C4—181no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4C22×D3211yescharacteristic
730C8—21no—
731C8—61no—
732C8—61no—
733C8—181no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—62no—
738C2×C3—121no—
739C2×C3D3×#12311yescharacteristic
740C2×C3D3×#12311yescharacteristic
741C2×C3C2×#91911yescharacteristic
742C2×C3D3×#13511yescharacteristic
743C2×C3#577311yescharacteristic
744C2×C3#577711yescharacteristic
745D3—22no—
746D3—41no—
747D3—62no—
748D3—62no—
749D3—122no—
750D3—242no—
751D3—241no—
752D3—241no—
753C22—32no—
754C22—61no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—92no—
760C22—181no—
761C22—181no—
762C22—364no—
763C22—361no—
764C22—361no—
765C22—361no—
766C22D32×D411yescharacteristic
767C4—41no—
768C4—41no—
769C4—61no—
770C4—61no—
771C4—92no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—361no—
777C4#6430611yescharacteristic
778C4#6431211yescharacteristic
779C3—21no—
780C3#8146711yescharacteristic, complemented
781C3#8151511yescharacteristic, complemented
782C2—62no—
783C2—121no—
784C2—182no—
785C2—721no—
786C2#1059426011yescharacteristic
787C2#1059474411yescharacteristic
788C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595430C2
hypercenter#103D32
hypocenterC32#3091
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. D3×#892C2semidirect
3. #10592503C2semidirect
4. C3×#4814C2semidirect
5. C3×#4811C2semidirect
6. #10591560C2semidirect
7. #10591558C2semidirect
8. #10591549C2semidirect
9. #10590935C2semidirect
10. #10590714C2semidirect
11. #10590705C2semidirect
12. #10590679C2semidirect
13. #10590574C2semidirect
14. #10590424C2semidirect
15. #10590423C2semidirect
41. C32×#103C22semidirect
42. #63662C22semidirect
43. #63648C22semidirect
44. #63636C22semidirect
45. C3×#835C22semidirect
46. C3×#835C22semidirect
49. C3×#818C22semidirect
50. C3×#818C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63574C22semidirect
56. #63573C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
80. #4814D3semidirect
81. #4811D3semidirect
198. C3×#103C2×D3semidirect
199. C3×#103C2×D3semidirect
205. #835C2×D3semidirect
206. #835C2×D3semidirect
219. #818C2×D3semidirect
220. #818C2×D3semidirect
232. #808C2×D3semidirect
234. #807C2×D3semidirect
463. #103D32semidirect
692. C32#3091semidirect
780. C3#81467semidirect
781. C3#81515semidirect

Maximal subgroups

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

subgroupindex
#105954302
D3×#8922
#105925032
C3×#48142
C3×#48112
#105915602
#105915582
#105915492
#105909352
#105907142
#105907052
#105906792
#105905742
#105904242
#105904232
#815153
#814673