Finite Group Databasebeta

← #10800992

Subgroups — #10800992

Order 768.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5523C211yesmaximal, characteristic, complemented
2C3×#2324C211yesmaximal, characteristic, complemented
3C2×#5037C211yesmaximal, characteristic
4C2×C4×#214C211yesmaximal, characteristic, complemented
5C2×#5014C211yesmaximal, characteristic, complemented
6#71677C211yesmaximal, characteristic, complemented
7#71582C211yesmaximal, characteristic, complemented
8#69660C211yesmaximal, characteristic, complemented
9#69657C211yesmaximal, characteristic, complemented
10#69632C211yesmaximal, characteristic, complemented
11#69626C211yesmaximal, characteristic, complemented
12#69522C211yesmaximal, characteristic, complemented
13#69505C211yesmaximal, characteristic, complemented
14#69475C211yesmaximal, characteristic, complemented
15C4×#809C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24#5523—24no—
25#5523—24no—
26C2×#892—21no—
27C2×D3×C4⋊C4—21no—
28C2×#67⋊C4—21no—
29C2×#67⋊C4—21no—
30C2×C4×D12C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×C4×Dic6C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#390—21no—
35C3×#390C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#388—21no—
38C3×#386—21no—
39C3×#385—21no—
40C3×#380C2211yescharacteristic
41C3×C4×C4⋊C4C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5037C418yescomplemented
47C4×#214—24no—
48#5014—24no—
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#808C2211yescharacteristic
56C2×#808C2211yescharacteristic
57C2×#803C2211yescharacteristic
58C2×C4×C3⋊C8C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64#4524C2211yescharacteristic
65C2×#520—31no—
66C2×#449—31no—
67C2×#442—31no—
68C2×C4×SD16—31no—
69#2324D311yescharacteristic, complemented
70#1880—31no—
71#1879—31no—
72#1874—31no—
73#1865—31no—
74#1864—31no—
75#1853—31no—
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750—31no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C23×Dic3—21no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235C2×C414yescomplemented
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×Dic6C2311yescharacteristic
97C3×#121—22no—
98C3×#121C2×C414yescomplemented
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×#117—22no—
102C3×#117—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4D411yescharacteristic
105C2×C3×C4⋊C4D411yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4D411yescharacteristic
115C2×C3×C22⋊C4D411yescharacteristic
116C2×C3×C42—21no—
117C2×C3×C42C2311yescharacteristic
118C2×C3×C42C2311yescharacteristic
119C2×#214—22no—
120C2×#214—22no—
121C2×#214C2×C414yescomplemented
122C2×#213—22no—
123C2×#213—22no—
124C2×#213C2×C414yescomplemented
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3—22no—
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3—21no—
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140#892—28no—
141D3×C4⋊C4—28no—
142#67⋊C4—28no—
143#67⋊C4—28no—
144C4×D12—22no—
145C4×D12—22no—
146C4×D12—22no—
147C4×D12D414yescomplemented
148C4×Dic6—22no—
149C4×Dic6—22no—
150C4×Dic6—22no—
151C4×Dic6D414yescomplemented
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155#832—22no—
156#832—22no—
157#830—22no—
158#830C2×C414yescomplemented
159#810—22no—
160#810—22no—
161#810C2×C414yescomplemented
162#809—22no—
163#809—22no—
164#809C2×C414yescomplemented
165#808—22no—
166#808—22no—
167#803—22no—
168C4×C3⋊C8—22no—
169C22×#41—31no—
170C22×SD16—31no—
171C22×D8—31no—
172C2×#121C2×D311yescharacteristic
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4—61no—
181C2×C4×D4C2×D311yescharacteristic
182C2×#117—61no—
183C2×#117C2×D311yescharacteristic
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#449—38no—
187#442—64no—
188C4×SD16—64no—
189C2×#106—31no—
190C2×#106—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×#97—31no—
202C2×C4×C8—31no—
203#390—21no—
204#390C2×D311yescharacteristic
205#389C2×D311yescharacteristic
206#388—21no—
207#386—21no—
208#385—21no—
209#380C2×D311yescharacteristic
210C4×C4⋊C4C2×D311yescharacteristic
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C2×C3×D4—24no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—81no—
227C2×C3×D4—81no—
228C2×C3×D4C22×C412yes—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—42no—
237C22×C3×C4—81no—
238C22×C3×C4—81no—
239C22×C3×C4C22×C412yes—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4#4112yes—
246C22×C3×C4C2411yescharacteristic
247C2×#67—24no—
248C2×#67—24no—
249C2×#67—24no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—24no—
254C22×Dic3—81no—
255C22×Dic3—81no—
256#235—28no—
257#235—28no—
258#235—28no—
259#235—28no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12C22×C412yes—
264C2×D12C2×D412yes—
265C2×D12#4112yes—
266C2×C4×D3—24no—
267C2×C4×D3—24no—
268C2×C4×D3—24no—
269C2×C4×D3—24no—
270C2×C4×D3—24no—
271C2×C4×D3—81no—
272C2×C4×D3—81no—
273C2×C4×D3—81no—
274C2×C4×D3—81no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6C22×C412yes—
279C2×Dic6C2×D412yes—
280C2×Dic6#4112yes—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—81no—
289C3×C4⋊C4C22×C412yes—
290C3×C22⋊C4—24no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—42no—
294C3×C22⋊C4—81no—
295C3×C22⋊C4—81no—
296C3×C22⋊C4—81no—
297C3×C42—21no—
298C3×C42—21no—
299C3×C42—81no—
300C3×C42C2×D412yes—
301C3×C42C2×D412yes—
302#214—28no—
303#213—28no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—24no—
306C4⋊Dic3—24no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3C2×D412yes—
310C4⋊Dic3C2×D412yes—
311Dic3⋊C4—24no—
312Dic3⋊C4—24no—
313C4×Dic3—24no—
314C4×Dic3—24no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8C22×C412yes—
326C2×C3⋊C8C22×C412yes—
327C2×#41—34no—
328C2×#41—62no—
329C2×#41—62no—
330C2×#41—62no—
331C2×#41—62no—
332C2×#41—62no—
333C22×Q8—31no—
334C22×D4—21no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4C22×D311yescharacteristic
338C23×C4—21no—
339C23×C4—61no—
340C23×C4—61no—
341C23×C4—61no—
342C23×C4—61no—
343C23×C4C22×D311yescharacteristic
344C2×SD16—34no—
345C2×SD16—62no—
346C2×SD16—62no—
347C2×D8—34no—
348C2×D8—62no—
349C2×D8—62no—
350C22×C8—31no—
351C22×C8—31no—
352C22×C8—31no—
353C22×C8—31no—
354#121—22no—
355#121C4×D314yescomplemented
356C4×Q8—34no—
357C4×Q8—62no—
358C4×Q8—62no—
359C4×Q8—62no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—34no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—68no—
366C4×D4—68no—
367C4×D4—62no—
368#117—22no—
369#117—22no—
370#117—68no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—68no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4#6711yescharacteristic
381C2×C4⋊C4#6711yescharacteristic
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4#6711yescharacteristic
393C2×C22⋊C4#6711yescharacteristic
394C2×C42—21no—
395C2×C42—61no—
396C2×C42—61no—
397C2×C42C22×D311yescharacteristic
398C2×C42C22×D311yescharacteristic
399#106—62no—
400#106—62no—
401#103—34no—
402#103—62no—
403#103—62no—
404#102—34no—
405#102—62no—
406#102—62no—
407#102—62no—
408#102—62no—
409C22⋊C8—34no—
410C22⋊C8—62no—
411#97—62no—
412C4×C8—62no—
413#95—21no—
414#95—21no—
415#95—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—22no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3C4×D412yes—
430C23×C3C22×D411yescharacteristic
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—84no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—84no—
469C2×C3×C4C4×D412yes—
470C2×C3×C4#12012yes—
471C2×C3×C4#12012yes—
472C2×C3×C4C23×C411yescharacteristic
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478#67—216no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—84no—
489D12—22no—
490D12—22no—
491D12—22no—
492D12C4×D414yes—
493C4×D3—216no—
494C4×D3—84no—
495C4×D3—84no—
496Dic6—22no—
497Dic6—22no—
498Dic6—22no—
499Dic6C4×D414yes—
500C3⋊C8—22no—
501C3⋊C8—22no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C24—21no—
505C24—61no—
506C24C2×#6711yescharacteristic
507#41—68no—
508#41—68no—
509#41—68no—
510#41—68no—
511C2×Q8—32no—
512C2×Q8—32no—
513C2×Q8—32no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—24no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—32no—
524C2×D4—32no—
525C2×D4—32no—
526C2×D4—64no—
527C2×D4—64no—
528C2×D4—64no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4C2×C4×D312yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—61no—
547C22×C4—64no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—64no—
551C22×C4—64no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4—241no—
560C22×C4C2×C4×D312yes—
561C22×C4#23512yes—
562C22×C4C2×#6711yescharacteristic
563C22×C4C2×#6711yescharacteristic
564C22×C4C2×#6711yescharacteristic
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C22×C4C23×D311yescharacteristic
568SD16—68no—
569D8—68no—
570C2×C8—32no—
571C2×C8—32no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—32no—
590C4⋊C4—32no—
591C4⋊C4—64no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—81no—
597C4⋊C4C2×C4×D312yes—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—42no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C42—21no—
608C42—21no—
609C42—64no—
610C42—64no—
611C42—81no—
612C42D3×D412yes—
613C42D3×D412yes—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3C2×C4×D411yescharacteristic
629C22×C3C2×#12011yescharacteristic
630C22×C3#52511yescharacteristic
631C22×C3#57611yescharacteristic
632C22×C3#57711yescharacteristic
633C22×C3#57711yescharacteristic
634C22×C3#57711yescharacteristic
635C2×D3—24no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—42no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4C2×C4×D411yescharacteristic
651C3×C4C2×C4×D411yescharacteristic
652C3×C4#52511yescharacteristic
653C3×C4#52511yescharacteristic
654Dic3—24no—
655Dic3—42no—
656Dic3—42no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—62no—
671C23—62no—
672C23—62no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23C4×#6712yes—
678C23C22×#6711yescharacteristic
679Q8—34no—
680Q8—62no—
681Q8—62no—
682Q8—62no—
683D4—22no—
684D4—22no—
685D4—34no—
686D4—41no—
687D4—41no—
688D4—616no—
689D4—62no—
690D4—62no—
691D4—62no—
692D4—84no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—616no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—84no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—244no—
730C2×C4—244no—
731C2×C4—244no—
732C2×C4C4×#6712yes—
733C2×C4#93712yes—
734C2×C4#93712yes—
735C2×C4C22×C4×D311yescharacteristic
736C2×C4C2×#23511yescharacteristic
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4D3×#4111yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C8—62no—
742C8—62no—
743C8—121no—
744C8—121no—
745C2×C3—42no—
746C2×C3—82no—
747C2×C3C4×#12011yescharacteristic
748C2×C3#294611yescharacteristic
749C2×C3#295211yescharacteristic
750C2×C3#301011yescharacteristic
751C2×C3#301211yescharacteristic
752C2×C3#311911yescharacteristic
753C2×C3#312511yescharacteristic
754D3—44no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—64no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22C2×C4×#6711yescharacteristic
777C22C2×#93711yescharacteristic
778C22#582811yescharacteristic
779C22#583511yescharacteristic
780C22#583611yescharacteristic
781C22#583611yescharacteristic
782C22#583711yescharacteristic
783C4—22no—
784C4—22no—
785C4—22no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—64no—
790C4—81no—
791C4—81no—
792C4—122no—
793C4—122no—
794C4C4×D3×D411yescharacteristic
795C4C4×D3×D411yescharacteristic
796C4#554711yescharacteristic
797C4#554711yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—42no—
800C2—82no—
801C2—124no—
802C2C4×#93711yescharacteristic
803C2#8253711yescharacteristic
804C2#8255811yescharacteristic
805C2#8339011yescharacteristic
806C2#8342411yescharacteristic
807C2#8343411yescharacteristic
808C2#8346211yescharacteristic
subgroupG/H
centerC23C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#2324C2
socleC23×C3C22×D4
prime radicalC2×#5037C2
cosocleC22×C3×C4C24
hypercenter#2324D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#5523C2semidirect
2. C3×#2324C2semidirect
4. C2×C4×#214C2semidirect
5. C2×#5014C2semidirect
6. #71677C2semidirect
7. #71582C2semidirect
8. #69660C2semidirect
9. #69657C2semidirect
10. #69632C2semidirect
11. #69626C2semidirect
12. #69522C2semidirect
13. #69505C2semidirect
14. #69475C2semidirect
15. C4×#809C2semidirect
46. #5037C4semidirect
69. #2324D3semidirect
91. C2×#235C2×C4semidirect
98. C3×#121C2×C4semidirect
121. C2×#214C2×C4semidirect
124. C2×#213C2×C4semidirect
147. C4×D12D4semidirect
151. C4×Dic6D4semidirect
158. #830C2×C4semidirect
161. #810C2×C4semidirect
164. #809C2×C4semidirect
355. #121C4×D3semidirect
798. C3#21464semidirect

Maximal subgroups

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

subgroupindex
C2×#55232
C3×#23242
C2×#50372
C2×C4×#2142
C2×#50142
#716772
#715822
#696602
#696572
#696322
#696262
#695222
#695052
#694752
C4×#8092
#214643