Finite Group Databasebeta

← #11870534

Subgroups — #11870534

Order 1152.

950 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#893C211yesmaximal, characteristic
2#10594385C211yesmaximal, characteristic, complemented
3#10592569C211yesmaximal, characteristic, complemented
4C3×#4862C211yesmaximal, characteristic, complemented
5C3×#4852C211yesmaximal, characteristic, complemented
6#10590942C211yesmaximal, characteristic
7#10590792C211yesmaximal, characteristic, complemented
8#10590748C211yesmaximal, characteristic, complemented
9#10590655C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic
11#10590565C211yesmaximal, characteristic, complemented
12#10590516C211yesmaximal, characteristic, complemented
13#10590475C211yesmaximal, characteristic, complemented
14#10590472C211yesmaximal, characteristic, complemented
15#10590458C211yesmaximal, characteristic, complemented
16#81412—31nomaximal
17#79651—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20#64102C2211yescharacteristic
21#64097C2211yescharacteristic, complemented
22C2×C3×#204C2211yescharacteristic
23C3×#897C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#887C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28#63904—21no—
29#63898C2211yescharacteristic
30#63896—21no—
31#63894C2211yescharacteristic
32#63881—21no—
33#63877—21no—
34C4×D3×Dic3C2211yescharacteristic
35#63873C2211yescharacteristic, complemented
36#63856C2211yescharacteristic
37#63847—21no—
38#63844—21no—
39Dic3×Dic6C2211yescharacteristic, complemented
40C2×#3717C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C32×#106C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5622—31no—
62#5578—31no—
63C4×D3×D4—31no—
64C2×#893—31no—
65C3×#483—31no—
66C3×C4×SD16—31no—
67#5169—31no—
68#5162—31no—
69#5046—31no—
70C4×#215—31no—
71C4×#214—31no—
72#4971—31no—
73#4870—31no—
74#4870—31no—
75#4870—31no—
76#4870—61no—
77#4862D311yescharacteristic, complemented
78#4852—31no—
79#4852D311yescharacteristic, complemented
80#4818—31no—
81#4818—31no—
82#4818—31no—
83#4805—31no—
84#4788—31no—
85#4788—31no—
86#4776—31no—
87#4761—31no—
88#4731—31no—
89#4718—31no—
90C4×#204—31no—
91#4685—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3D411yescharacteristic
106C2×D3×Dic3D411yescharacteristic
107D3×D12—22no—
108D3×D12—22no—
109C4×D32—44no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—22no—
129#3724—21no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32D411yescharacteristic
138Dic32D411yescharacteristic
139#3717—22no—
140#3717—22no—
141#3715—22no—
142#3101—91noSylow
143C2×D3×D4—31no—
144C22×D12—31no—
145C22×C4×D3—61no—
146C22×C4×D3—61no—
147C2×C3×SD16—31no—
148C3×C22⋊Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×D4—31no—
151C2×C3×C4⋊C4—31no—
152#946—31no—
153Q8×Dic3—31no—
154#944—31no—
155#944—31no—
156C2×#215—31no—
157C2×#215—31no—
158C2×#215—31no—
159D4×Dic3—31no—
160C2×#214—31no—
161C4×#67—61no—
162C2×(C2×D3)⋊C4—61no—
163#924—31no—
164C2×C4×Dic3—31no—
165C2×#204—31no—
166C2×#204—31no—
167C2×#204C2×D311yescharacteristic
168#897C2×D311yescharacteristic
169#896—61no—
170#893—31no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—61no—
175#893—61no—
176#893—61no—
177#893C2×D311yescharacteristic
178D3×C4⋊C4C2×D311yescharacteristic
179#889—61no—
180#889—61no—
181#888—31no—
182#888—31no—
183#888—61no—
184#887—61no—
185#887C2×D311yescharacteristic, complemented
186#67⋊C4—61no—
187D3×C22⋊C4—61no—
188#878—61no—
189#877—61no—
190C4×D12—31no—
191#872—61no—
192C42×D3—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C3×#106—21no—
196C3×#106—31no—
197C3×#106C2×D311yescharacteristic, complemented
198C3×#106C2×D311yescharacteristic, complemented
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204C3×C4×C8—31no—
205#835—31no—
206#832—31no—
207#830—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—61no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8C2×D311yescharacteristic
214#817—31no—
215#816C2×D311yescharacteristic, complemented
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221C8×Dic3—31no—
222C8×Dic3C2×D311yescharacteristic, complemented
223#810—31no—
224#810C2×D311yescharacteristic, complemented
225#810C2×D311yescharacteristic, complemented
226#809—31no—
227#809—31no—
228#809—61no—
229#809C2×D311yescharacteristic
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#808C2×D311yescharacteristic, complemented
235C4×C3⋊C8—31no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—42no—
241C2×D32—42no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)#4112yes—
250C4×C3⋊D3—42no—
251#634—42no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#626—24no—
269#624—42no—
270D3×Dic3—41no—
271D3×Dic3—42no—
272D3×Dic3SD1614yescomplemented
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#533—91no—
278C2×C4×D4—91no—
279#483—31no—
280#483—91no—
281#476—91no—
282#476—91no—
283#461—91no—
284#461—91no—
285#450—91no—
286#450—91no—
287C4×SD16—31no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C23×D3—61no—
293C23×D3—61no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×D4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—61no—
304D3×D4—62no—
305D3×D4—62no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—61no—
309C2×D12—62no—
310C2×D12—61no—
311C2×D12—62no—
312C2×D12C22×D311yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—121no—
323C2×C4×D3—124no—
324C2×C4×D3—124no—
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—121no—
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×SD16—62no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
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×C42—31no—
350C3×C42—61no—
351#217—61no—
352#217—61no—
353#215—62no—
354#215—62no—
355#215—62no—
356#214—62no—
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—121no—
366C4⋊Dic3—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3C22×D311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—121no—
384C4×Dic3—21no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400#204—22no—
401#204—62no—
402#204—62no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3C2×SD1612yes—
413D32—48no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3C2×SD1612yes—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3C2×SD1612yes—
427C22×D4—91no—
428C23×C4—181no—
429C2×SD16—31no—
430C2×SD16—91no—
431C2×SD16—91no—
432C2×SD16—91no—
433C4⋊Q8—91no—
434C4⋊Q8—91no—
435#125—181no—
436C22⋊Q8—31no—
437C22⋊Q8—91no—
438C22⋊Q8—181no—
439C4×Q8—31no—
440C4×Q8—91no—
441C4×Q8—181no—
442C4×D4—31no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—181no—
447C4×D4—181no—
448#117—181no—
449C2×C4⋊C4—31no—
450C2×C22⋊C4—181no—
451C2×C42—91no—
452#106—31no—
453#106—91no—
454#106—91no—
455#106D3211yescharacteristic, complemented
456C4⋊C8—91no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—91no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466C22⋊C8—31no—
467C22⋊C8—91no—
468C4×C8—31no—
469C4×C8—91no—
470C23×C3—31no—
471C23×C3—61no—
472C22×D3—21no—
473C22×D3—64no—
474C22×D3—64no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—121no—
478C22×D3—122no—
479C22×D3—122no—
480C22×D3—122no—
481C22×D3—122no—
482C22×D3D3×D411yescharacteristic
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—32no—
488C3×D4—61no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
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—122no—
505C2×C3×C4—122no—
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—64no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—34no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—122no—
524C2×Dic3D3×D411yescharacteristic
525C2×Dic3D3×D411yescharacteristic
526C2×Dic3D3×D411yescharacteristic
527D12—21no—
528D12—32no—
529D12—32no—
530D12—62no—
531D12—64no—
532D12—61no—
533D12—61no—
534D12—121no—
535D12#23512yes—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—34no—
539C4×D3—42no—
540C4×D3—42no—
541C4×D3—122no—
542C4×D3—122no—
543C4×D3—122no—
544C4×D3—122no—
545C4×D3—121no—
546C4×D3—122no—
547C4×D3—242no—
548Dic6—21no—
549Dic6—21no—
550Dic6—21no—
551Dic6—21no—
552Dic6—122no—
553Dic6—122no—
554Dic6—242no—
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#52511yescharacteristic
566C2×C32C22×SD1611yescharacteristic
567C2×C32#57511yescharacteristic
568C3⋊D3—42no—
569C3×D3—22no—
570C3×D3—42no—
571C24—181no—
572C2×Q8—31no—
573C2×Q8—31no—
574C2×Q8—181no—
575C2×D4—31no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—182no—
579C2×D4—182no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—91no—
584C22×C4—91no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—364no—
589SD16—62no—
590SD16—182no—
591SD16—182no—
592SD16—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4C2×D3211yescharacteristic
608C4⋊C4C2×D3211yescharacteristic
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—61no—
617C42—91no—
618C42—91no—
619C42—91no—
620C42—181no—
621C22×C3—21no—
622C22×C3—32no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—62no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3C2×D3×D411yescharacteristic
629C22×C3C2×D3×D411yescharacteristic
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—22no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—122no—
638C2×D3—128no—
639C2×D3—128no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—241no—
645C2×D3—241no—
646C2×D3D3×SD1612yes—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—32no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4C2×#23511yescharacteristic
662C3×C4D3×#4111yescharacteristic
663C3×C4D3×#4111yescharacteristic
664C3×C4D3×#4111yescharacteristic
665Dic3—21no—
666Dic3—21no—
667Dic3—32no—
668Dic3—32no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—62no—
673Dic3—61no—
674Dic3—61no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679Dic3D3×SD1612yes—
680C32#310111yescharacteristic, complemented, Sylow
681C23—31no—
682C23—61no—
683C23—184no—
684C23—181no—
685C23—362no—
686C23—362no—
687Q8—61no—
688Q8—61no—
689Q8—61no—
690Q8—61no—
691Q8—362no—
692D4—32no—
693D4—61no—
694D4—92no—
695D4—184no—
696D4—181no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—94no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—181no—
713C2×C4—362no—
714C2×C4—362no—
715C2×C4—361no—
716C2×C4—362no—
717C2×C4C22×D3211yescharacteristic
718C8—21no—
719C8—61no—
720C8—61no—
721C8—181no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—62no—
726C2×C3—122no—
727C2×C3#554711yescharacteristic
728C2×C3#565611yescharacteristic
729C2×C3C2×D3×SD1611yescharacteristic
730C2×C3C2×D3×SD1611yescharacteristic
731C2×C3#576811yescharacteristic
732C2×C3#577711yescharacteristic
733D3—22no—
734D3—42no—
735D3—122no—
736D3—122no—
737D3—242no—
738C22—32no—
739C22—61no—
740C22—61no—
741C22—62no—
742C22—121no—
743C22—121no—
744C22—182no—
745C22—368no—
746C22—361no—
747C22—361no—
748C22D32×D411yescharacteristic
749C4—32no—
750C4—41no—
751C4—41no—
752C4—61no—
753C4—61no—
754C4—92no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—181no—
759C4—361no—
760C4D3×#23511yescharacteristic
761C4#6431911yescharacteristic
762C3—21no—
763C3#7965111yescharacteristic, complemented
764C3#8141211yescharacteristic, complemented
765C2—62no—
766C2—122no—
767C2—362no—
768C2#1059461411yescharacteristic
769C2D32×SD1611yescharacteristic
770C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#106D32
hypocenterC32#3101
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. #10594385C2semidirect
3. #10592569C2semidirect
4. C3×#4862C2semidirect
5. C3×#4852C2semidirect
7. #10590792C2semidirect
8. #10590748C2semidirect
9. #10590655C2semidirect
11. #10590565C2semidirect
12. #10590516C2semidirect
13. #10590475C2semidirect
14. #10590472C2semidirect
15. #10590458C2semidirect
21. #64097C22semidirect
26. C3×#887C22semidirect
35. #63873C22semidirect
39. Dic3×Dic6C22semidirect
43. C32×#106C22semidirect
45. #63641C22semidirect
47. #63635C22semidirect
49. C3×#816C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#810C22semidirect
52. C3×#810C22semidirect
54. C3×#808C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
77. #4862D3semidirect
79. #4852D3semidirect
185. #887C2×D3semidirect
197. C3×#106C2×D3semidirect
198. C3×#106C2×D3semidirect
215. #816C2×D3semidirect
222. C8×Dic3C2×D3semidirect
224. #810C2×D3semidirect
225. #810C2×D3semidirect
234. #808C2×D3semidirect
272. D3×Dic3SD16semidirect
455. #106D32semidirect
680. C32#3101semidirect
763. C3#79651semidirect
764. C3#81412semidirect

Maximal subgroups

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

subgroupindex
D3×#8932
#105943852
#105925692
C3×#48622
C3×#48522
#105909422
#105907922
#105907482
#105906552
#105905962
#105905652
#105905162
#105904752
#105904722
#105904582
#814123
#796513