Finite Group Databasebeta

← #11869669

Subgroups — #11869669

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595301C211yesmaximal, characteristic
2D3×#892C211yesmaximal, characteristic, complemented
3#10592483C211yesmaximal, characteristic, complemented
4C3×#4774C211yesmaximal, characteristic, complemented
5C3×#4772C211yesmaximal, characteristic, complemented
6#10591425C211yesmaximal, characteristic, complemented
7#10591420C211yesmaximal, characteristic, complemented
8#10591415C211yesmaximal, characteristic, complemented
9D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
10#10590715C211yesmaximal, characteristic, complemented
11#10590707C211yesmaximal, characteristic, complemented
12#10590682C211yesmaximal, characteristic, complemented
13#10590571C211yesmaximal, characteristic, complemented
14#10590526C211yesmaximal, characteristic, complemented
15#10590516C211yesmaximal, characteristic, complemented
16#81281—31nomaximal
17#78842—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C4×D32C2211yescharacteristic
20#64147C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26#63983—21no—
27Dic3×#67—21no—
28#63969—21no—
29#63952—21no—
30D3×(C2×D3)⋊C4—21no—
31D3×C4⋊Dic3C2211yescharacteristic
32#63878—21no—
33C4×D3×Dic3—21no—
34#63871C2211yescharacteristic
35#63856C2211yescharacteristic
36#63849C2211yescharacteristic
37#63841C2211yescharacteristic
38#63841C2211yescharacteristic
39#63836—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#102C2211yescharacteristic, complemented
42#63659C2211yescharacteristic, complemented
43#63647C2211yescharacteristic
44#63645C2211yescharacteristic, complemented
45#63635C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5828—31no—
62#5606—31no—
63D3×#117—31no—
64C2×#892—31no—
65C3×#480—31no—
66C3×#416—31no—
67#5233—31no—
68C2×(C2×D3)⋊C8—31no—
69#5106—31no—
70#5034—31no—
71#4998—31no—
72#4971—31no—
73#4888—31no—
74#4888—31no—
75#4880—31no—
76#4880—31no—
77#4815—31no—
78#4814—31no—
79#4811—31no—
80#4805—31no—
81#4784—31no—
82#4784—31no—
83#4784—31no—
84#4784—61no—
85#4779—31no—
86#4777—31no—
87#4774D311yescharacteristic, complemented
88#4772—31no—
89#4772D311yescharacteristic, complemented
90D3×C22⋊C8—31no—
91#4722—31no—
92C22×D32D411yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—22no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
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#3757—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×D3×C8—22no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140D3×C3⋊C8—22no—
141#3091—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C3×C8—31no—
147C3×#121—31no—
148C3×#117—31no—
149C2×C3×C4⋊C4—31no—
150#946—31no—
151#946—31no—
152#938—31no—
153#938—31no—
154#938—61no—
155#938C2×D311yescharacteristic
156#937—61no—
157#937—61no—
158#935—61no—
159D4×Dic3—61no—
160C4×#67—61no—
161C4×#67—61no—
162C2×(C2×D3)⋊C4—61no—
163#926—31no—
164#926—31no—
165C2×C4⋊Dic3—31no—
166#924—31no—
167C2×C4×Dic3—61no—
168C22×C3⋊C8—31no—
169C2×D3×C8—31no—
170C2×D3×C8C2×D311yescharacteristic
171#897—31no—
172#892—31no—
173#892—31no—
174#892—31no—
175#892—31no—
176#892—31no—
177#892—31no—
178#892—61no—
179#892—61no—
180#892—61no—
181#892C2×D311yescharacteristic
182D3×C4⋊C4—31no—
183D3×C4⋊C4C2×D311yescharacteristic
184#883—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187#877—61no—
188#872—61no—
189C42×D3—61no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#102—21no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102C2×D311yescharacteristic, complemented
198C3×#102C2×D311yescharacteristic, complemented
199C3×C22⋊C8—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic, complemented
206#832C2×D311yescharacteristic, complemented
207#830—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—61no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#818—31no—
216#818—31no—
217#818—31no—
218#818—61no—
219#818C2×D311yescharacteristic, complemented
220#817—31no—
221#817—31no—
222#816—31no—
223#816C2×D311yescharacteristic, complemented
224#810—31no—
225#810C2×D311yescharacteristic, complemented
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807—31no—
234#807C2×D311yescharacteristic, complemented
235C23×C32—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—22no—
240C2×D32—22no—
241C2×D32—41no—
242C32×D4—21no—
243C32×D4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C3×#67—42no—
253C3×#67—42no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×C4×D3#4112yes—
265C3×C4×D3#4112yes—
266C3×Dic6—21no—
267C3×Dic6—21no—
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—91no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#480—31no—
286#427—91no—
287#427—91no—
288#416—31no—
289#416—91no—
290C2×C22⋊C8—91no—
291C23×D3—31no—
292C23×D3—31no—
293C3×#41—62no—
294C3×#41—62no—
295C2×C3×Q8—31no—
296C2×C3×D4—21no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—121no—
310C22×Dic3—21no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—61no—
314#237—22no—
315#237—22no—
316C2×C4×D3—21no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—62no—
327C2×C4×D3—62no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—62no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—61no—
348#217—21no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—121no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
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—121no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382C4×Dic3—21no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—62no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D3×C8—22no—
399D3×C8—62no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3#12312yes—
412C2×C3×D3#13512yes—
413D32—44no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3#12312yes—
426C2×#41—31no—
427C23×C4—91no—
428C22×C8—31no—
429C22×C8—91no—
430#123—181no—
431C22⋊Q8—91no—
432C22⋊Q8—91no—
433#121—31no—
434#121—91no—
435#120—181no—
436C4×D4—181no—
437C4×D4—181no—
438#117—31no—
439#117—91no—
440#117—91no—
441#117—91no—
442#117—91no—
443#117—181no—
444#117—181no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—91no—
447C2×C22⋊C4—181no—
448C2×C42—181no—
449#107—31no—
450#107—31no—
451#107—91no—
452#107—91no—
453#106—91no—
454#106—91no—
455#106—91no—
456#106—91no—
457#103—31no—
458#103—31no—
459#103—91no—
460#103—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102D3211yescharacteristic, complemented
465C22⋊C8—31no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—31no—
473C23×C3—41no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—61no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—121no—
482C22×D3—121no—
483C22×D3D3×D411yescharacteristic
484C22×D3D3×D411yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—122no—
494C3×D4—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—31no—
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—122no—
510C2×C3×C4—122no—
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—42no—
514#67—42no—
515#67—122no—
516#67—122no—
517#67—242no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—42no—
525C2×Dic3—61no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—122no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—42no—
540C4×D3—62no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—61no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—62no—
548C4×D3—121no—
549C4×D3—121no—
550C4×D3—122no—
551C4×D3#23512yes—
552C4×D3#23712yes—
553Dic6—21no—
554Dic6—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C2×C32—81no—
566C2×C32C2×#12311yescharacteristic
567C2×C32C2×#13511yescharacteristic
568C2×C32#57511yescharacteristic
569C3⋊D3—41no—
570C3×D3—22no—
571C3×D3—22no—
572C24—91no—
573#41—62no—
574#41—62no—
575C2×Q8—31no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—181no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—91no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—91no—
588C22×C4—182no—
589C22×C4—182no—
590C22×C4—181no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—62no—
594C2×C8—91no—
595C2×C8—182no—
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4C2×D3211yescharacteristic
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—61no—
617C42—181no—
618C42—181no—
619C42—181no—
620C42—181no—
621C22×C3—21no—
622C22×C3—32no—
623C22×C3—32no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—124no—
653C2×D3—124no—
654C2×D3#88312yes—
655C2×D3#91212yes—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—32no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—81no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×#23711yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—61no—
677Dic3—61no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—241no—
684Dic3—241no—
685Dic3#88312yes—
686C32#309111yescharacteristic, complemented, Sylow
687C23—21no—
688C23—31no—
689C23—31no—
690C23—91no—
691C23—182no—
692C23—182no—
693C23—361no—
694Q8—61no—
695Q8—61no—
696D4—21no—
697D4—21no—
698D4—122no—
699D4—122no—
700D4—362no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—91no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—182no—
716C2×C4—182no—
717C2×C4—182no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—362no—
723C2×C4C22×D3211yescharacteristic
724C8—21no—
725C8—61no—
726C8—61no—
727C8—181no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—62no—
732C2×C3—62no—
733C2×C3—81no—
734C2×C3—81no—
735C2×C3—161no—
736C2×C3C2×#88311yescharacteristic
737C2×C3D3×#12311yescharacteristic
738C2×C3C2×#91211yescharacteristic
739C2×C3D3×#13511yescharacteristic
740C2×C3#576811yescharacteristic
741C2×C3#577711yescharacteristic
742D3—22no—
743D3—22no—
744D3—121no—
745D3—121no—
746D3—241no—
747C22—32no—
748C22—32no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—181no—
757C22—181no—
758C22—181no—
759C22—364no—
760C22D32×D411yescharacteristic
761C4—32no—
762C4—41no—
763C4—61no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—181no—
769C4—361no—
770C4—361no—
771C4D3×#23511yescharacteristic
772C4D3×#23711yescharacteristic
773C3—21no—
774C3#7884211yescharacteristic, complemented
775C3#8128111yescharacteristic, complemented
776C2—62no—
777C2—62no—
778C2—81no—
779C2—361no—
780C2D3×#88311yescharacteristic
781C2D3×#91211yescharacteristic
782C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595301C2
hypercenter#102D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. D3×#892C2semidirect
3. #10592483C2semidirect
4. C3×#4774C2semidirect
5. C3×#4772C2semidirect
6. #10591425C2semidirect
7. #10591420C2semidirect
8. #10591415C2semidirect
9. D3×(C2×D3)⋊C8C2semidirect
10. #10590715C2semidirect
11. #10590707C2semidirect
12. #10590682C2semidirect
13. #10590571C2semidirect
14. #10590526C2semidirect
15. #10590516C2semidirect
41. C32×#102C22semidirect
42. #63659C22semidirect
44. #63645C22semidirect
45. #63635C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×#810C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
87. #4774D3semidirect
89. #4772D3semidirect
197. C3×#102C2×D3semidirect
198. C3×#102C2×D3semidirect
205. #832C2×D3semidirect
206. #832C2×D3semidirect
219. #818C2×D3semidirect
223. #816C2×D3semidirect
225. #810C2×D3semidirect
234. #807C2×D3semidirect
464. #102D32semidirect
686. C32#3091semidirect
774. C3#78842semidirect
775. C3#81281semidirect

Maximal subgroups

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

subgroupindex
#105953012
D3×#8922
#105924832
C3×#47742
C3×#47722
#105914252
#105914202
#105914152
D3×(C2×D3)⋊C82
#105907152
#105907072
#105906822
#105905712
#105905262
#105905162
#812813
#788423