Finite Group Databasebeta

← #10800996

Subgroups — #10800996

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×C3×#520C211yesmaximal, characteristic, complemented
2C2×#5238C211yesmaximal, characteristic
3C2×C4×#215C211yesmaximal, characteristic, complemented
4C2×#5014C211yesmaximal, characteristic, complemented
5#82236C211yesmaximal, characteristic, complemented
6#72135C211yesmaximal, characteristic, complemented
7#71633C211yesmaximal, characteristic, complemented
8#71631C211yesmaximal, characteristic, complemented
9#71629C211yesmaximal, characteristic, complemented
10#71613C211yesmaximal, characteristic, complemented
11C4×#832C211yesmaximal, characteristic, complemented
12#71607C211yesmaximal, characteristic, complemented
13#71582C211yesmaximal, characteristic, complemented
14#71560C211yesmaximal, characteristic, complemented
15#71556C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C3×#520—24no—
19C3×#520—24no—
20C2×C3×C4×Q8C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×D4—21no—
23C2×C3×C4×D4—21no—
24C2×C3×C4×D4C2211yescharacteristic
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×#117—21no—
27C2×C3×#117C2211yescharacteristic
28C22×C3×C4⋊C4—21no—
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×#215C2211yescharacteristic
31C22×#213C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34#5238C418yescomplemented
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C4×#215—24no—
45#5014—24no—
46#4990—21no—
47#4989—21no—
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#808C2211yescharacteristic
52#4957—21no—
53#4956—21no—
54#4939C2211yescharacteristic
55C4×C4⋊Dic3C2211yescharacteristic
56#4928C2211yescharacteristic
57C2×#803C2211yescharacteristic
58C2×C4×C3⋊C8C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64#4524C2211yescharacteristic
65C2×#520D311yescharacteristic, complemented
66C2×#449—31no—
67C2×#442—31no—
68C2×C4×SD16—31no—
69#2324—31no—
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—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41C2×C414yescomplemented
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C22×#67—21no—
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C3×C4×Q8—22no—
98C3×C4×Q8—22no—
99C3×C4×Q8—22no—
100C3×C4×Q8D414yescomplemented
101C3×C4×D4—28no—
102C3×C4×D4—28no—
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C3×C4×D4D414yescomplemented
107C3×#117—28no—
108C3×#117—22no—
109C3×#117—22no—
110C2×C3×C4⋊C4—28no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4D411yescharacteristic
117C2×C3×C4⋊C4D411yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4D411yescharacteristic
123C2×C3×C22⋊C4D411yescharacteristic
124C2×C3×C42—21no—
125C2×C3×C42—21no—
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C2×#217—21no—
129C2×#215—22no—
130C2×#215—22no—
131C2×#215C2×C414yescomplemented
132C2×#213—22no—
133C2×#213—22no—
134C2×#213C2×C414yescomplemented
135#930—22no—
136#930C2×C414yescomplemented
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×Dic3⋊C4—21no—
145C2×C4×Dic3—21no—
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C4×D12—22no—
151C4×D12—22no—
152#835—22no—
153#835—22no—
154#835C2×C414yescomplemented
155#832—22no—
156#832—22no—
157#832C2×C414yescomplemented
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#830—22no—
162#830C2×C414yescomplemented
163#809—22no—
164#809—22no—
165#808—22no—
166#808—22no—
167#803—22no—
168C4×C3⋊C8—22no—
169C22×#41C2×D311yescharacteristic
170C22×SD16—31no—
171C22×D8—31no—
172C2×#121—31no—
173#520—24no—
174#520—24no—
175C2×C4×Q8C2×D311yescharacteristic
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4—21no—
179C2×C4×D4—31no—
180C2×C4×D4C2×D311yescharacteristic
181C2×C4×D4C2×D311yescharacteristic
182C2×#117—21no—
183C2×#117C2×D311yescharacteristic
184C22×C4⋊C4—21no—
185C22×C4⋊C4C2×D311yescharacteristic
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—31no—
204#390—61no—
205#389—31no—
206#388—61no—
207#386—61no—
208#385—61no—
209#380—31no—
210C4×C4⋊C4—31no—
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—
220C3×#41—28no—
221C3×#41—28no—
222C3×#41—28no—
223C3×#41—28no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C22×C412yes—
228C2×C3×Q8C2×D412yes—
229C2×C3×Q8#4112yes—
230C2×C3×D4—24no—
231C2×C3×D4—24no—
232C2×C3×D4—24no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4C22×C412yes—
237C2×C3×D4C2×D412yes—
238C2×C3×D4#4112yes—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—21no—
242C22×C3×C4—24no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—24no—
250C22×C3×C4—24no—
251C22×C3×C4—24no—
252C22×C3×C4—81no—
253C22×C3×C4—81no—
254C22×C3×C4—81no—
255C22×C3×C4—81no—
256C22×C3×C4—81no—
257C22×C3×C4—81no—
258C22×C3×C4C22×C412yes—
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4#4112yes—
265C22×C3×C4C2411yescharacteristic
266C2×#67—24no—
267C2×#67—81no—
268C2×#67—81no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12C22×C412yes—
278C2×C4×D3—42no—
279C2×C4×D3—81no—
280C2×C4×D3—81no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—24no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4C2×D412yes—
289C3×C4⋊C4C2×D412yes—
290C3×C22⋊C4—24no—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—22no—
294C3×C42—24no—
295C3×C42—24no—
296C3×C42—21no—
297C3×C42—21no—
298C3×C42C2×D412yes—
299C3×C42C2×D412yes—
300#217—81no—
301#215—28no—
302#213—28no—
303(C2×D3)⋊C4—24no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—81no—
306(C2×D3)⋊C4—81no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3C22×C412yes—
313Dic3⋊C4—81no—
314C4×Dic3—81no—
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—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41C4×D314yescomplemented
333C22×Q8C22×D311yescharacteristic
334C22×D4—21no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4C22×D311yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
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—34no—
355#121—62no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8#6714yescomplemented
360C4×D4—28no—
361C4×D4—28no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—62no—
366C4×D4—62no—
367C4×D4#6714yescomplemented
368#117—28no—
369#117—22no—
370#117—22no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4#6711yescharacteristic
382C2×C4⋊C4#6711yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4#6711yescharacteristic
393C2×C22⋊C4#6711yescharacteristic
394C2×C42—21no—
395C2×C42—21no—
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—61no—
414#95—61no—
415#95—61no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—21no—
420C23×C3—22no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3C4×D412yes—
430C23×C3C22×D411yescharacteristic
431C22×D3—22no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8C4×D414yes—
442C3×D4—216no—
443C3×D4—22no—
444C3×D4—22no—
445C3×D4—22no—
446C3×D4C4×D414yes—
447C2×C3×C4—216no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—84no—
474C2×C3×C4—84no—
475C2×C3×C4—84no—
476C2×C3×C4C4×D412yes—
477C2×C3×C4#12012yes—
478C2×C3×C4#12012yes—
479C2×C3×C4C23×C411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485#67—84no—
486C2×Dic3—22no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495D12—22no—
496D12—22no—
497D12—41no—
498D12—41no—
499C4×D3—84no—
500C3⋊C8—22no—
501C3⋊C8—22no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C24—21no—
505C24—61no—
506C24C2×#6711yescharacteristic
507#41—28no—
508#41—28no—
509#41—28no—
510#41—28no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8C2×C4×D312yes—
515C2×Q8#23512yes—
516C2×Q8C2×#6712yes—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—32no—
524C2×D4—64no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—241no—
531C2×D4—241no—
532C2×D4C2×C4×D312yes—
533C2×D4#23512yes—
534C2×D4C2×#6712yes—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—122no—
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—24no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—32no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—241no—
596C4⋊C4C2×#6712yes—
597C4⋊C4C2×#6712yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—64no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C22⋊C4—241no—
607C42—24no—
608C42—24no—
609C42—21no—
610C42—21no—
611C42—241no—
612C42C2×#6712yes—
613C42C2×#6712yes—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—24no—
618C22×C3—41no—
619C22×C3—42no—
620C22×C3—41no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—42no—
628C22×C3C2×C4×D411yescharacteristic
629C22×C3C2×#12011yescharacteristic
630C22×C3#52511yescharacteristic
631C22×C3#57611yescharacteristic
632C22×C3#57711yescharacteristic
633C22×C3#57711yescharacteristic
634C22×C3#57711yescharacteristic
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—24no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4C2×C4×D411yescharacteristic
651C3×C4C2×C4×D411yescharacteristic
652C3×C4#52511yescharacteristic
653C3×C4#52511yescharacteristic
654Dic3—42no—
655Dic3—81no—
656Dic3—81no—
657C23—22no—
658C23—21no—
659C23—22no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—62no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23C4×#6712yes—
678C23C22×#6711yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8C4×#6714yes—
683D4—216no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—62no—
688D4—62no—
689D4—121no—
690D4—121no—
691D4—244no—
692D4C4×#6714yes—
693C2×C4—216no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—62no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—244no—
732C2×C4C4×#6712yes—
733C2×C4#95312yes—
734C2×C4#95312yes—
735C2×C4C22×C4×D311yescharacteristic
736C2×C4C2×#23511yescharacteristic
737C2×C4C2×#23511yescharacteristic
738C2×C4C2×#23511yescharacteristic
739C2×C4C22×#6711yescharacteristic
740C2×C4C22×#6711yescharacteristic
741C8—62no—
742C8—62no—
743C8—121no—
744C8—121no—
745C2×C3—42no—
746C2×C3—44no—
747C2×C3C4×#12011yescharacteristic
748C2×C3#294611yescharacteristic
749C2×C3#295211yescharacteristic
750C2×C3#301011yescharacteristic
751C2×C3#301211yescharacteristic
752C2×C3#311911yescharacteristic
753C2×C3#312511yescharacteristic
754D3—82no—
755C22—22no—
756C22—24no—
757C22—22no—
758C22—22no—
759C22—42no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—241no—
773C22—241no—
774C22—241no—
775C22—241no—
776C22C2×C4×#6711yescharacteristic
777C22#579111yescharacteristic
778C22#583511yescharacteristic
779C22#583611yescharacteristic
780C22#583711yescharacteristic
781C22#583711yescharacteristic
782C22C2×#95311yescharacteristic
783C4—22no—
784C4—24no—
785C4—22no—
786C4—22no—
787C4—41no—
788C4—42no—
789C4—42no—
790C4—41no—
791C4—122no—
792C4—241no—
793C4—241no—
794C4C2×C4×#6711yescharacteristic
795C4C2×C4×#6711yescharacteristic
796C4#579111yescharacteristic
797C4#579111yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—42no—
800C2—44no—
801C2—242no—
802C2#8255811yescharacteristic
803C2#8256411yescharacteristic
804C2#8256811yescharacteristic
805C2#8257611yescharacteristic
806C2C4×#95311yescharacteristic
807C2#8410211yescharacteristic
808C2#8411311yescharacteristic
subgroupG/H
centerC23C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#520C2
socleC23×C3C22×D4
prime radicalC2×#5238C2
cosocleC22×C3×C4C24
hypercenterC2×#520D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×C3×#520C2semidirect
3. C2×C4×#215C2semidirect
4. C2×#5014C2semidirect
5. #82236C2semidirect
6. #72135C2semidirect
7. #71633C2semidirect
8. #71631C2semidirect
9. #71629C2semidirect
10. #71613C2semidirect
11. C4×#832C2semidirect
12. #71607C2semidirect
13. #71582C2semidirect
14. #71560C2semidirect
15. #71556C2semidirect
34. #5238C4semidirect
65. C2×#520D3semidirect
85. C2×C3×#41C2×C4semidirect
100. C3×C4×Q8D4semidirect
106. C3×C4×D4D4semidirect
131. C2×#215C2×C4semidirect
134. C2×#213C2×C4semidirect
136. #930C2×C4semidirect
154. #835C2×C4semidirect
157. #832C2×C4semidirect
162. #830C2×C4semidirect
332. C2×#41C4×D3semidirect
359. C4×Q8#67semidirect
367. C4×D4#67semidirect
798. C3#21464semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5202
C2×#52382
C2×C4×#2152
C2×#50142
#822362
#721352
#716332
#716312
#716292
#716132
C4×#8322
#716072
#715822
#715602
#715562
#214643