Finite Group Databasebeta

← #11869713

Subgroups — #11869713

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594626C211yesmaximal, characteristic
2D3×#892C211yesmaximal, characteristic, complemented
3#10592567C211yesmaximal, characteristic, complemented
4C3×#4863C211yesmaximal, characteristic, complemented
5C3×#4860C211yesmaximal, characteristic, complemented
6#10590954C211yesmaximal, characteristic, complemented
7D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
8#10590674C211yesmaximal, characteristic, complemented
9#10590652C211yesmaximal, characteristic, complemented
10#10590608C211yesmaximal, characteristic, complemented
11#10590572C211yesmaximal, characteristic, complemented
12#10590512C211yesmaximal, characteristic, complemented
13#10590450C211yesmaximal, characteristic, complemented
14#10590438C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#81324—31nomaximal
17#79185—31nomaximal
18C2×C4×D32C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64106C2211yescharacteristic
21#64101C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×#895C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27#63922—21no—
28D3×(C2×D3)⋊C4—21no—
29#63916C2211yescharacteristic
30Dic3×D12—21no—
31#63891—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33#63880—21no—
34#63878—21no—
35C4×D3×Dic3—21no—
36#63857C2211yescharacteristic
37#63849C2211yescharacteristic
38#63841C2211yescharacteristic
39#63836—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#106C2211yescharacteristic, complemented
42#63647C2211yescharacteristic
43#63643C2211yescharacteristic, complemented
44#63637C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic, complemented
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#817C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5606—31no—
62#5524—31no—
63D3×#117—31no—
64C2×#892—31no—
65C3×#481—31no—
66C3×#427—31no—
67#5113—31no—
68C2×(C2×D3)⋊C8—31no—
69#5033—31no—
70#5002—31no—
71#4998—31no—
72#4970—31no—
73#4888—31no—
74#4885—31no—
75#4884—31no—
76#4882—31no—
77#4868—31no—
78#4868—31no—
79#4868—31no—
80#4868—61no—
81#4866—31no—
82#4863D311yescharacteristic, complemented
83#4862—31no—
84#4860—31no—
85#4860D311yescharacteristic, complemented
86#4779—31no—
87#4779—31no—
88#4772—31no—
89#4772—31no—
90D3×C22⋊C8—31no—
91#4721—31no—
92C22×D32D411yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
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#3795—22no—
110#3795—22no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—22no—
132Dic3⋊Dic3—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—
140D3×C3⋊C8—22no—
141#3091—91noSylow
142C2×#237—31no—
143C2×#235—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C3×C8—31no—
147C3×#121—31no—
148C3×#117—31no—
149C3×#117—31no—
150C2×C3×C4⋊C4—31no—
151#938—31no—
152#937—61no—
153D4×Dic3—61no—
154C2×(C2×D3)⋊C4—61no—
155#926—31no—
156C2×C4⋊Dic3—31no—
157#924—31no—
158C2×C4×Dic3—61no—
159C22×C3⋊C8—31no—
160C2×D3×C8—31no—
161C2×D3×C8C2×D311yescharacteristic
162#897—31no—
163#897—31no—
164#897—31no—
165#897—61no—
166#895—31no—
167#895C2×D311yescharacteristic
168#892—31no—
169#892—31no—
170#892—31no—
171#892—31no—
172#892—31no—
173#892—61no—
174#892—61no—
175#892—61no—
176#892C2×D311yescharacteristic
177#892C2×D311yescharacteristic
178D3×C4⋊C4—31no—
179D3×C4⋊C4C2×D311yescharacteristic
180#886—61no—
181#883—61no—
182#882—61no—
183#67⋊C4—61no—
184D3×C22⋊C4—61no—
185#877—61no—
186C4×D12—61no—
187C4×D12—61no—
188#872—61no—
189C42×D3—61no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#106—21no—
193C3×#106—31no—
194C3×#106—31no—
195C3×#106C2×D311yescharacteristic, complemented
196C3×#106C2×D311yescharacteristic, complemented
197C3×#102—31no—
198C3×#102—31no—
199C3×C22⋊C8—31no—
200#832—31no—
201#832—31no—
202#830—31no—
203#821—31no—
204#821C2×D311yescharacteristic, complemented
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—61no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212#817—31no—
213#817C2×D311yescharacteristic, complemented
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—61no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—61no—
224#809—31no—
225#809C2×D311yescharacteristic, complemented
226#808—31no—
227#808C2×D311yescharacteristic, complemented
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—61no—
233#807C2×D311yescharacteristic, complemented
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—21no—
249C4×C3⋊D3—21no—
250#634—21no—
251#634—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—42no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×C4×D3#4112yes—
264C3×C4×D3#4112yes—
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—91no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—31no—
285#480—91no—
286#427—31no—
287#427—91no—
288#416—91no—
289#416—91no—
290C2×C22⋊C8—91no—
291C23×D3—31no—
292C23×D3—31no—
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C2×#67—61no—
299C2×#67—61no—
300C2×#67—61no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305#237—62no—
306#237—62no—
307#235—62no—
308#235—62no—
309C2×D12—21no—
310C2×D12—61no—
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—62no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C3×C4⋊C4—21no—
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×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—61no—
351C3×C42—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
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—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—121no—
368(C2×D3)⋊C4—121no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383C4×Dic3—21no—
384C4×Dic3—21no—
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×C32C22×D411yescharacteristic
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3#12312yes—
412C2×C3×D3#13512yes—
413D32—44no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3#12312yes—
426C2×#41—91no—
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—31no—
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—31no—
454#106—31no—
455#106—91no—
456#106D3211yescharacteristic, complemented
457#103—91no—
458#103—91no—
459#103—91no—
460#103—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C23×C3—31no—
470C23×C3—31no—
471C23×C3—61no—
472C22×D3—21no—
473C22×D3—31no—
474C22×D3—31no—
475C22×D3—61no—
476C22×D3—62no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—121no—
481C22×D3—121no—
482C22×D3D3×D411yescharacteristic
483C22×D3D3×D411yescharacteristic
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—122no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—122no—
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—122no—
507#67—122no—
508#67—122no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—61no—
515C2×Dic3—62no—
516C2×Dic3—62no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—122no—
524C2×Dic3—122no—
525C2×Dic3D3×D411yescharacteristic
526C2×Dic3D3×D411yescharacteristic
527D12—21no—
528D12—21no—
529D12—42no—
530D12—122no—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—42no—
534C4×D3—62no—
535C4×D3—62no—
536C4×D3—62no—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—62no—
542C4×D3—121no—
543C4×D3—121no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3#23512yes—
547C4×D3#23912yes—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—121no—
553Dic6—121no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—121no—
564C2×C32C2×#12311yescharacteristic
565C2×C32C2×#13511yescharacteristic
566C2×C32#57511yescharacteristic
567C3⋊D3—41no—
568C3×D3—22no—
569C3×D3—22no—
570C3×D3—81no—
571C24—91no—
572#41—182no—
573#41—182no—
574C2×Q8—91no—
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—181no—
578C2×D4—181no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—91no—
583C22×C4—91no—
584C22×C4—91no—
585C22×C4—91no—
586C22×C4—182no—
587C22×C4—182no—
588C22×C4—181no—
589C22×C4—181no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—62no—
593C2×C8—91no—
594C2×C8—182no—
595C2×C8C2×D3211yescharacteristic
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4C2×D3211yescharacteristic
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—61no—
616C42—61no—
617C42—181no—
618C42—181no—
619C42—181no—
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—32no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—124no—
649C2×D3—124no—
650C2×D3#89412yes—
651C2×D3#91612yes—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—32no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23511yescharacteristic
666C3×C4C2×#23911yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—61no—
674Dic3—61no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682Dic3#89412yes—
683C32#309111yescharacteristic, complemented, Sylow
684C23—31no—
685C23—31no—
686C23—61no—
687C23—91no—
688C23—182no—
689C23—182no—
690C23—361no—
691Q8—181no—
692Q8—181no—
693D4—61no—
694D4—61no—
695D4—122no—
696D4—362no—
697D4—362no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—91no—
710C2×C4—122no—
711C2×C4—182no—
712C2×C4—182no—
713C2×C4—182no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—362no—
719C2×C4—362no—
720C2×C4C22×D3211yescharacteristic
721C8—21no—
722C8—61no—
723C8—61no—
724C8—181no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—62no—
729C2×C3—62no—
730C2×C3—241no—
731C2×C3C2×#89411yescharacteristic
732C2×C3D3×#12311yescharacteristic
733C2×C3C2×#91611yescharacteristic
734C2×C3D3×#13511yescharacteristic
735C2×C3#576811yescharacteristic
736C2×C3#577311yescharacteristic
737D3—22no—
738D3—22no—
739D3—81no—
740D3—121no—
741D3—121no—
742D3—241no—
743C22—32no—
744C22—32no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—181no—
753C22—181no—
754C22—181no—
755C22—364no—
756C22D32×D411yescharacteristic
757C4—32no—
758C4—41no—
759C4—41no—
760C4—61no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—181no—
765C4—361no—
766C4—361no—
767C4D3×#23511yescharacteristic
768C4D3×#23911yescharacteristic
769C3—21no—
770C3#7918511yescharacteristic, complemented
771C3#8132411yescharacteristic, complemented
772C2—62no—
773C2—62no—
774C2—241no—
775C2—361no—
776C2D3×#89411yescharacteristic
777C2D3×#91611yescharacteristic
778C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594626C2
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. #10592567C2semidirect
4. C3×#4863C2semidirect
5. C3×#4860C2semidirect
6. #10590954C2semidirect
7. D3×(C2×D3)⋊C8C2semidirect
8. #10590674C2semidirect
9. #10590652C2semidirect
10. #10590608C2semidirect
11. #10590572C2semidirect
12. #10590512C2semidirect
13. #10590450C2semidirect
14. #10590438C2semidirect
15. #10590427C2semidirect
41. C32×#106C22semidirect
43. #63643C22semidirect
44. #63637C22semidirect
45. #63634C22semidirect
46. C3×#821C22semidirect
48. C3×#817C22semidirect
49. C3×#809C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
82. #4863D3semidirect
85. #4860D3semidirect
195. C3×#106C2×D3semidirect
196. C3×#106C2×D3semidirect
204. #821C2×D3semidirect
213. #817C2×D3semidirect
225. #809C2×D3semidirect
227. #808C2×D3semidirect
233. #807C2×D3semidirect
234. #807C2×D3semidirect
456. #106D32semidirect
683. C32#3091semidirect
770. C3#79185semidirect
771. C3#81324semidirect

Maximal subgroups

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

subgroupindex
#105946262
D3×#8922
#105925672
C3×#48632
C3×#48602
#105909542
D3×(C2×D3)⋊C82
#105906742
#105906522
#105906082
#105905722
#105905122
#105904502
#105904382
#105904272
#813243
#791853