Finite Group Databasebeta

← #11870533

Subgroups — #11870533

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#893C211yesmaximal, characteristic
2#10594387C211yesmaximal, characteristic, complemented
3#10592551C211yesmaximal, characteristic, complemented
4C3×#4870C211yesmaximal, characteristic, complemented
5C3×#4862C211yesmaximal, characteristic, complemented
6#10590946C211yesmaximal, characteristic
7#10590760C211yesmaximal, characteristic, complemented
8#10590742C211yesmaximal, characteristic, complemented
9#10590656C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic
11#10590559C211yesmaximal, characteristic, complemented
12#10590483C211yesmaximal, characteristic, complemented
13#10590466C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#81412—31nomaximal
17#81044—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3744C2211yescharacteristic
21#64102C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C3×#897C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28#63904—21no—
29#63898C2211yescharacteristic
30#63894C2211yescharacteristic
31#63887—21no—
32#63881—21no—
33#63878—21no—
34C4×D3×Dic3C2211yescharacteristic
35#63866C2211yescharacteristic, complemented
36#63857C2211yescharacteristic
37#63846—21no—
38#63843—21no—
39#63843C2211yescharacteristic, complemented
40C2×#3717C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C32×#106C2211yescharacteristic, complemented
44C8×C3⋊Dic3C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5728—31no—
62#5622—31no—
63C4×D3×D4—31no—
64C2×#893—31no—
65C3×#483—31no—
66C3×#476—31no—
67#5084—31no—
68#5046—31no—
69#5019—31no—
70#4971—31no—
71#4870—31no—
72#4870D311yescharacteristic, complemented
73#4862—31no—
74#4862D311yescharacteristic, complemented
75#4852—31no—
76#4852—31no—
77#4852—31no—
78#4852—31no—
79#4852—61no—
80#4841—31no—
81#4833—31no—
82#4818—31no—
83#4818—31no—
84#4788—31no—
85#4788—31no—
86#4776—31no—
87#4776—31no—
88#4758—31no—
89#4758—31no—
90#4731—31no—
91#4718—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
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—
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3744—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—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#3716—22no—
141#3715—22no—
142#3101—91noSylow
143C2×D3×D4—31no—
144C22×D12—31no—
145C22×C4×D3—61no—
146C22×C4×D3—61no—
147C3×C4⋊Q8—31no—
148C3×C22⋊Q8—31no—
149C3×C4×D4—31no—
150C2×C3×C4⋊C4—31no—
151#946—61no—
152Q8×Dic3—31no—
153Q8×Dic3—61no—
154#944—31no—
155C2×#215—31no—
156C2×#215—31no—
157D4×Dic3—31no—
158C2×#214—31no—
159C2×#214—31no—
160C4×#67—61no—
161C2×(C2×D3)⋊C4—61no—
162#924—31no—
163C2×C4×Dic3—31no—
164C2×#204—31no—
165C2×#204—31no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—61no—
169#897—31no—
170#897C2×D311yescharacteristic
171#893—31no—
172#893—31no—
173#893—31no—
174#893—31no—
175#893—61no—
176#893—61no—
177#893—61no—
178#893C2×D311yescharacteristic
179#892—61no—
180D3×C4⋊C4C2×D311yescharacteristic
181#890—61no—
182#889—61no—
183#888C2×D311yescharacteristic, complemented
184#887—31no—
185#887—31no—
186#887—31no—
187#887—61no—
188#887—61no—
189#67⋊C4—61no—
190D3×C22⋊C4—61no—
191#878—61no—
192#877—61no—
193C4×D12—31no—
194C42×D3—31no—
195#869—31no—
196C3×#106—21no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#106C2×D311yescharacteristic, complemented
200C3×#106C2×D311yescharacteristic, complemented
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207#830—31no—
208#821—31no—
209#821C2×D311yescharacteristic
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212#816—31no—
213#816C2×D311yescharacteristic, complemented
214Dic3⋊C8—31no—
215Dic3⋊C8C2×D311yescharacteristic, complemented
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—61no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#810C2×D311yescharacteristic, complemented
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808C2×D311yescharacteristic, complemented
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—21no—
252#634—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12#4112yes—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
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—31no—
282#476—91no—
283#461—91no—
284#461—91no—
285#450—91no—
286#450—91no—
287C4×SD16—91no—
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—61no—
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—21no—
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C22×D311yescharacteristic
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
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—
350#217—61no—
351#217—61no—
352#215—62no—
353#215—62no—
354#214—62no—
355#214—62no—
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—121no—
365C4⋊Dic3—21no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3C22×D311yescharacteristic
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—121no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—121no—
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399#204—62no—
400#204—62no—
401#204—64no—
402#204—62no—
403#204—62no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—22no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3C2×SD1612yes—
414D32—48no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—21no—
420C3⋊Dic3—41no—
421C3⋊Dic3C2×SD1612yes—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×SD1612yes—
428C22×D4—91no—
429C23×C4—181no—
430C2×SD16—91no—
431C2×SD16—91no—
432C2×SD16—91no—
433C2×SD16—91no—
434C4⋊Q8—31no—
435C4⋊Q8—91no—
436#125—181no—
437C22⋊Q8—31no—
438C22⋊Q8—91no—
439C22⋊Q8—181no—
440C4×Q8—91no—
441C4×Q8—91no—
442C4×Q8—181no—
443C4×D4—31no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—181no—
448C4×D4—181no—
449#117—181no—
450C2×C4⋊C4—31no—
451C2×C22⋊C4—181no—
452C2×C42—91no—
453#106—31no—
454#106—31no—
455#106—91no—
456#106D3211yescharacteristic, complemented
457C4⋊C8—31no—
458C4⋊C8—91no—
459#103—31no—
460#103—31no—
461#103—91no—
462#103—91no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467C22⋊C8—31no—
468C22⋊C8—91no—
469C4×C8—91no—
470C4×C8—91no—
471C23×C3—31no—
472C23×C3—61no—
473C22×D3—21no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3—122no—
480C22×D3—122no—
481C22×D3—122no—
482C22×D3—122no—
483C22×D3D3×D411yescharacteristic
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—122no—
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#23912yes—
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—42no—
551Dic6—62no—
552Dic6—61no—
553Dic6—61no—
554Dic6—61no—
555Dic6—61no—
556Dic6—121no—
557C3×C8—22no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—121no—
567C2×C32#52511yescharacteristic
568C2×C32C22×SD1611yescharacteristic
569C2×C32#57511yescharacteristic
570C3⋊D3—42no—
571C3×D3—22no—
572C3×D3—42no—
573C24—181no—
574C2×Q8—31no—
575C2×Q8—61no—
576C2×Q8—91no—
577C2×D4—31no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4—182no—
581C2×D4—182no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—364no—
591SD16—182no—
592SD16—182no—
593SD16—182no—
594SD16—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—91no—
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4C2×D3211yescharacteristic
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—91no—
619C42—91no—
620C42—91no—
621C42—181no—
622C42—181no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—62no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—122no—
640C2×D3—128no—
641C2×D3—128no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—241no—
647C2×D3—241no—
648C2×D3D3×SD1612yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23911yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—32no—
670Dic3—32no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—62no—
675Dic3—61no—
676Dic3—61no—
677Dic3—121no—
678Dic3—122no—
679Dic3—121no—
680Dic3—121no—
681Dic3D3×SD1612yes—
682C32#310111yescharacteristic, complemented, Sylow
683C23—31no—
684C23—61no—
685C23—184no—
686C23—181no—
687C23—362no—
688C23—362no—
689Q8—61no—
690Q8—61no—
691Q8—122no—
692Q8—181no—
693Q8—181no—
694D4—32no—
695D4—61no—
696D4—92no—
697D4—184no—
698D4—181no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—94no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—181no—
715C2×C4—362no—
716C2×C4—362no—
717C2×C4—361no—
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—122no—
729C2×C3#562711yescharacteristic
730C2×C3#565611yescharacteristic
731C2×C3C2×D3×SD1611yescharacteristic
732C2×C3C2×D3×SD1611yescharacteristic
733C2×C3#577311yescharacteristic
734C2×C3#577711yescharacteristic
735D3—22no—
736D3—42no—
737D3—122no—
738D3—122no—
739D3—242no—
740C22—32no—
741C22—61no—
742C22—61no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—182no—
747C22—368no—
748C22—361no—
749C22—361no—
750C22D32×D411yescharacteristic
751C4—32no—
752C4—41no—
753C4—41no—
754C4—61no—
755C4—61no—
756C4—92no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—181no—
761C4—361no—
762C4#6430611yescharacteristic
763C4D3×#23911yescharacteristic
764C3—21no—
765C3#8104411yescharacteristic, complemented
766C3#8141211yescharacteristic, complemented
767C2—62no—
768C2—122no—
769C2—362no—
770C2#1059461511yescharacteristic
771C2D32×SD1611yescharacteristic
772C2#1059474411yescharacteristic
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. #10594387C2semidirect
3. #10592551C2semidirect
4. C3×#4870C2semidirect
5. C3×#4862C2semidirect
7. #10590760C2semidirect
8. #10590742C2semidirect
9. #10590656C2semidirect
11. #10590559C2semidirect
12. #10590483C2semidirect
13. #10590466C2semidirect
14. #10590460C2semidirect
15. #10590426C2semidirect
22. #64096C22semidirect
26. C3×#888C22semidirect
35. #63866C22semidirect
39. #63843C22semidirect
43. C32×#106C22semidirect
44. C8×C3⋊Dic3C22semidirect
45. #63637C22semidirect
49. C3×#816C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
53. C3×#808C22semidirect
54. C3×#808C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
60. #63553C22semidirect
72. #4870D3semidirect
74. #4862D3semidirect
183. #888C2×D3semidirect
199. C3×#106C2×D3semidirect
200. C3×#106C2×D3semidirect
213. #816C2×D3semidirect
215. Dic3⋊C8C2×D3semidirect
225. #810C2×D3semidirect
233. #808C2×D3semidirect
234. #808C2×D3semidirect
272. D3×Dic3SD16semidirect
456. #106D32semidirect
682. C32#3101semidirect
765. C3#81044semidirect
766. C3#81412semidirect

Maximal subgroups

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

subgroupindex
D3×#8932
#105943872
#105925512
C3×#48702
C3×#48622
#105909462
#105907602
#105907422
#105906562
#105905962
#105905592
#105904832
#105904662
#105904602
#105904262
#814123
#810443