Finite Group Databasebeta

← #11869712

Subgroups — #11869712

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594632C211yesmaximal, characteristic
2D3×#892C211yesmaximal, characteristic, complemented
3#10592559C211yesmaximal, characteristic, complemented
4C3×#4868C211yesmaximal, characteristic, complemented
5C3×#4863C211yesmaximal, characteristic, complemented
6#10590956C211yesmaximal, characteristic, complemented
7#10590935C211yesmaximal, characteristic, complemented
8#10590837C211yesmaximal, characteristic, complemented
9#10590675C211yesmaximal, characteristic, complemented
10#10590611C211yesmaximal, characteristic, complemented
11#10590574C211yesmaximal, characteristic, complemented
12#10590517C211yesmaximal, characteristic, complemented
13#10590502C211yesmaximal, characteristic, complemented
14#10590447C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#81515—31nomaximal
17#81324—31nomaximal
18C2×C4×D32C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21#64101C2211yescharacteristic
22#64101C2211yescharacteristic
23C3×#897C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27#63922—21no—
28D3×(C2×D3)⋊C4—21no—
29#63908C2211yescharacteristic
30#63902—21no—
31#63898—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33#63878—21no—
34C4×D3×Dic3—21no—
35#63856C2211yescharacteristic
36#63854—21no—
37#63849C2211yescharacteristic
38#63841C2211yescharacteristic
39#63836—21no—
40C2×#3710C2211yescharacteristic
41C32×#106C2211yescharacteristic, complemented
42#63644C2211yescharacteristic, complemented
43#63634C2211yescharacteristic, complemented
44#63634C2211yescharacteristic, complemented
45C3×#821C2211yescharacteristic, complemented
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#816C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5627—31no—
62#5606—31no—
63D3×#117—31no—
64C2×#892—31no—
65C3×#485—31no—
66C3×#481—31no—
67#5045—31no—
68#5033—31no—
69#5003—31no—
70#4970—31no—
71#4882—31no—
72#4880—31no—
73#4868—31no—
74#4868D311yescharacteristic, complemented
75#4863D311yescharacteristic, complemented
76#4860—31no—
77#4860—31no—
78#4860—31no—
79#4860—61no—
80#4811—31no—
81#4805—31no—
82#4804—31no—
83#4804—31no—
84#4779—31no—
85#4779—31no—
86#4772—31no—
87#4772—31no—
88#4737—31no—
89D3×C22⋊C8—31no—
90D3×C22⋊C8—31no—
91#4721—31no—
92C22×D32D411yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C3×D12—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#626—21no—
101C2×#625—21no—
102C2×#624D411yescharacteristic
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3D411yescharacteristic
106C2×D3×Dic3D411yescharacteristic
107C4×D32—22no—
108C4×D32—22no—
109#3796—22no—
110#3796—22no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C8×C3⋊D3—22no—
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×C4×Dic3—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140#3710—22no—
141#3091—91noSylow
142C2×#239—31no—
143C2×#237—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C3×C22⋊Q8—31no—
147C3×#121—31no—
148C3×#117—31no—
149C2×C3×C4⋊C4—31no—
150#946—31no—
151#938—31no—
152#937—61no—
153D4×Dic3—61no—
154#930—31no—
155C2×(C2×D3)⋊C4—61no—
156#926—31no—
157C2×C4⋊Dic3—31no—
158#924—31no—
159C2×C4×Dic3—61no—
160C2×D3×C8—31no—
161C2×D3×C8—31no—
162C2×D3×C8—31no—
163C2×D3×C8—31no—
164C2×D3×C8—61no—
165#897C2×D311yescharacteristic
166#895C2×D311yescharacteristic
167#894—61no—
168#893—61no—
169#892—31no—
170#892—31no—
171#892—31no—
172#892—31no—
173#892—31no—
174#892—31no—
175#892—31no—
176#892—61no—
177#892—61no—
178#892—61no—
179#892—61no—
180#892C2×D311yescharacteristic
181D3×C4⋊C4—31no—
182D3×C4⋊C4C2×D311yescharacteristic
183#883—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×#106—21no—
193C3×#106—31no—
194C3×#106C2×D311yescharacteristic, complemented
195C3×#106C2×D311yescharacteristic, complemented
196C3×#103—31no—
197C3×#103—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202#835—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#821—31no—
209#821C2×D311yescharacteristic, complemented
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8C2×D311yescharacteristic
213(C2×D3)⋊C8C2×D311yescharacteristic
214#818—31no—
215#817—31no—
216#817—31no—
217#817—31no—
218#817—61no—
219#816—31no—
220#816C2×D311yescharacteristic, complemented
221#810—31no—
222#810C2×D311yescharacteristic, complemented
223#809—31no—
224#809C2×D311yescharacteristic, complemented
225#808—31no—
226#808C2×D311yescharacteristic, complemented
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—61no—
233#807—61no—
234#807C2×D311yescharacteristic, complemented
235C22×C3⋊D3C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—22no—
240C2×D32—22no—
241C2×D32—41no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3#4112yes—
249C4×C3⋊D3#4112yes—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—42no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265#626—42no—
266#625—42no—
267#624—22no—
268D3×Dic3—22no—
269D3×Dic3—22no—
270D3×Dic3—42no—
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—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—31no—
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—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C2×#67—61no—
300C2×#67—61no—
301C2×#67—61no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306#239—62no—
307#239—62no—
308#237—62no—
309#237—62no—
310C2×D12—21no—
311C2×D12—61no—
312C2×D12C22×D311yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—61no—
321C2×C4×D3—62no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×C3×C8—21no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—61no—
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—121no—
365(C2×D3)⋊C4—121no—
366C4⋊Dic3—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380C4×Dic3—21no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—121no—
390C4×Dic3—121no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396D3×C8—62no—
397D3×C8—62no—
398D3×C8—62no—
399D3×C8—62no—
400D3×C8—64no—
401C22×C32C22×D411yescharacteristic
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3#12312yes—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3#13512yes—
414D32—44no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3⋊Dic3#12312yes—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C2×#41—91no—
428C23×C4—91no—
429C22×C8—91no—
430C22×C8—91no—
431#123—181no—
432C22⋊Q8—31no—
433C22⋊Q8—91no—
434#121—31no—
435#121—91no—
436#120—181no—
437C4×D4—181no—
438C4×D4—181no—
439#117—31no—
440#117—91no—
441#117—91no—
442#117—91no—
443#117—91no—
444#117—181no—
445#117—181no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—91no—
448C2×C22⋊C4—181no—
449C2×C42—181no—
450#107—31no—
451#107—91no—
452#107—91no—
453#107—91no—
454#106—31no—
455#106—91no—
456#106—91no—
457#106D3211yescharacteristic, complemented
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466C22⋊C8—31no—
467C22⋊C8—31no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—61no—
473C22×D3—21no—
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—61no—
488C3×D4—61no—
489C3×D4—122no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—122no—
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—122no—
510#67—122no—
511#67—122no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3—122no—
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530D12—21no—
531D12—21no—
532D12—42no—
533D12—122no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—32no—
539C4×D3—32no—
540C4×D3—32no—
541C4×D3—32no—
542C4×D3—42no—
543C4×D3—62no—
544C4×D3—62no—
545C4×D3—62no—
546C4×D3—62no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—122no—
550C4×D3—122no—
551Dic6—21no—
552Dic6—21no—
553C3×C8—22no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—62no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C2×C32C2×#12311yescharacteristic
564C2×C32C2×#13511yescharacteristic
565C2×C32#57511yescharacteristic
566C3⋊D3—22no—
567C3×D3—22no—
568C3×D3—41no—
569C3×D3—81no—
570C24—91no—
571#41—182no—
572#41—182no—
573C2×Q8—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—181no—
577C2×D4—181no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—61no—
581C22×C4—91no—
582C22×C4—91no—
583C22×C4—91no—
584C22×C4—91no—
585C22×C4—182no—
586C22×C4—182no—
587C22×C4—181no—
588C22×C4—181no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—182no—
593C2×C8—182no—
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4C2×D3211yescharacteristic
604C4⋊C4C2×D3211yescharacteristic
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—61no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42—181no—
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C2×D3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—32no—
637C2×D3—32no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—62no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—124no—
649C2×D3—124no—
650C2×D3#91612yes—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—32no—
671Dic3—32no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—62no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682C32#309111yescharacteristic, complemented, Sylow
683C23—31no—
684C23—31no—
685C23—61no—
686C23—91no—
687C23—182no—
688C23—182no—
689C23—361no—
690Q8—61no—
691Q8—61no—
692D4—61no—
693D4—61no—
694D4—122no—
695D4—362no—
696D4—362no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—91no—
709C2×C4—92no—
710C2×C4—92no—
711C2×C4—122no—
712C2×C4—182no—
713C2×C4—182no—
714C2×C4—182no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—362no—
718C2×C4—362no—
719C2×C4C22×D3211yescharacteristic
720C8—21no—
721C8—61no—
722C8—61no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—62no—
728C2×C3—121no—
729C2×C3—241no—
730C2×C3D3×#12311yescharacteristic
731C2×C3D3×#12311yescharacteristic
732C2×C3C2×#91611yescharacteristic
733C2×C3D3×#13511yescharacteristic
734C2×C3#577311yescharacteristic
735C2×C3#577711yescharacteristic
736D3—22no—
737D3—41no—
738D3—62no—
739D3—62no—
740D3—81no—
741D3—122no—
742C22—32no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—92no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—181no—
753C22—181no—
754C22—364no—
755C22D32×D411yescharacteristic
756C4—41no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—92no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—361no—
765C4—361no—
766C4#6430611yescharacteristic
767C4#6431911yescharacteristic
768C3—21no—
769C3#8132411yescharacteristic, complemented
770C3#8151511yescharacteristic, complemented
771C2—62no—
772C2—121no—
773C2—182no—
774C2—241no—
775C2#1059460811yescharacteristic
776C2D3×#91611yescharacteristic
777C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594632C2
hypercenter#106D32
hypocenterC32#3091
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. D3×#892C2semidirect
3. #10592559C2semidirect
4. C3×#4868C2semidirect
5. C3×#4863C2semidirect
6. #10590956C2semidirect
7. #10590935C2semidirect
8. #10590837C2semidirect
9. #10590675C2semidirect
10. #10590611C2semidirect
11. #10590574C2semidirect
12. #10590517C2semidirect
13. #10590502C2semidirect
14. #10590447C2semidirect
15. #10590438C2semidirect
41. C32×#106C22semidirect
42. #63644C22semidirect
43. #63634C22semidirect
44. #63634C22semidirect
45. C3×#821C22semidirect
48. C3×#816C22semidirect
49. C3×#810C22semidirect
50. C3×#809C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
74. #4868D3semidirect
75. #4863D3semidirect
194. C3×#106C2×D3semidirect
195. C3×#106C2×D3semidirect
209. #821C2×D3semidirect
220. #816C2×D3semidirect
222. #810C2×D3semidirect
224. #809C2×D3semidirect
226. #808C2×D3semidirect
234. #807C2×D3semidirect
457. #106D32semidirect
682. C32#3091semidirect
769. C3#81324semidirect
770. C3#81515semidirect

Maximal subgroups

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

subgroupindex
#105946322
D3×#8922
#105925592
C3×#48682
C3×#48632
#105909562
#105909352
#105908372
#105906752
#105906112
#105905742
#105905172
#105905022
#105904472
#105904382
#815153
#813243