Finite Group Databasebeta

← #10810697

Subgroups — #10810697

Order 768.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic
2C2×#5232C211yesmaximal, characteristic, complemented
3C22×#835C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#5011C211yesmaximal, characteristic, complemented
6#72135C211yesmaximal, characteristic, complemented
7#72132C211yesmaximal, characteristic, complemented
8#71726C211yesmaximal, characteristic, complemented
9#71721C211yesmaximal, characteristic, complemented
10#71697C211yesmaximal, characteristic, complemented
11#71692C211yesmaximal, characteristic, complemented
12#71681C211yesmaximal, characteristic, complemented
13#71677C211yesmaximal, characteristic, complemented
14#71631C211yesmaximal, characteristic, complemented
15#71626C211yesmaximal, characteristic, complemented
16#22421—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C3×#548—24no—
20C3×#548C418yescomplemented
21C2×C3×#124—21no—
22C2×C3×#124C2211yescharacteristic
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121—21no—
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4—21no—
29C2×C3×C4×D4C2211yescharacteristic
30C2×D4×Dic3—21no—
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×#208C2211yescharacteristic
34C23×C3⋊C8C2211yescharacteristic
35#5232—24no—
36C2×#835—24no—
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic
49#5212C2211yescharacteristic
50#5212C2211yescharacteristic
51C2×#830C2211yescharacteristic
52C2×#830C2211yescharacteristic
53#5011—24no—
54#4984—21no—
55#4950—21no—
56#4950—21no—
57#4935C2211yescharacteristic
58C4×C4⋊Dic3C2211yescharacteristic
59C2×C4⋊(C3⋊C8)C2211yescharacteristic
60C2×#803C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#548D311yescharacteristic
66C2×#435—31no—
67C2×#417—31no—
68C22×#103—31no—
69D4×C4⋊C4—31no—
70#1983—31no—
71#1959—31no—
72#1894—31no—
73#1893—31no—
74#1874—31no—
75#1872—31no—
76#1803—31no—
77#1788—31no—
78#1787—31no—
79#1763—31no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C2×C3×#41C2×C414yescomplemented
86C22×C3×Q8—21no—
87C22×C3×Q8—22no—
88C22×C3×Q8—22no—
89C22×C3×Q8—22no—
90C22×C3×Q8—41no—
91C22×C3×Q8—41no—
92C22×C3×Q8C2×C414yescomplemented
93C22×C3×Q8C2311yescharacteristic
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4D411yescharacteristic
98C22×C3×D4C2311yescharacteristic
99C23×C3×C4—21no—
100C23×C3×C4—21no—
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×Dic3—21no—
104C23×Dic3—21no—
105C3×#124—28no—
106C3×#124—22no—
107C3×#124C2×C414yescomplemented
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—28no—
110C3×C22⋊Q8C2×C414yescomplemented
111C3×#121—28no—
112C3×#121—22no—
113C3×#121C2×C414yescomplemented
114C3×C4×Q8—22no—
115C3×C4×Q8C2×C414yescomplemented
116C3×C4×D4—28no—
117C3×C4×D4C2×C414yes—
118C3×C4×D4D414yes—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4D411yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4D411yescharacteristic
128C2×C3×C22⋊C4D411yescharacteristic
129C2×C3×C42—21no—
130C2×C3×C42C2311yescharacteristic
131C2×#217—21no—
132C2×#217—21no—
133D4×Dic3—44no—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—21no—
137C2×C4⋊Dic3—21no—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3—41no—
141C2×C4⋊Dic3—41no—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4×Dic3—21no—
147C2×#208—22no—
148C2×#208—22no—
149C2×#208—41no—
150C22×C3⋊C8—22no—
151C22×C3⋊C8—22no—
152C22×C3⋊C8—41no—
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157#835—22no—
158#835—22no—
159#835—22no—
160#835—22no—
161#835—22no—
162#835—41no—
163#835—41no—
164#835D414yescomplemented
165#832—22no—
166#832—22no—
167#832—41no—
168#832—41no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#830—22no—
173#830—22no—
174C4⋊(C3⋊C8)—22no—
175#803—22no—
176C22×#41C2×D311yescharacteristic
177C23×Q8C2×D311yescharacteristic
178C22×M16—31no—
179C23×C8—31no—
180#548—24no—
181#548Dic318yescomplemented
182C2×#124—21no—
183C2×#124C2×D311yescharacteristic
184C2×C22⋊Q8—21no—
185C2×C22⋊Q8C2×D311yescharacteristic
186C2×#121—21no—
187C2×#121C2×D311yescharacteristic
188C2×C4×Q8C2×D311yescharacteristic
189C2×C4×D4—21no—
190C2×C4×D4—61no—
191C2×C4×D4C2×D311yescharacteristic
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194#435—64no—
195C2×C4⋊C8—31no—
196#417—64no—
197C2×#103—31no—
198C2×#103—31no—
199C2×#103—31no—
200C2×#103—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—64no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212C2×#97—31no—
213#389—61no—
214#385—61no—
215#385—61no—
216#384—31no—
217#380—31no—
218#380—31no—
219C4×C4⋊C4—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#340—31no—
224C24×C3—21no—
225C24×C3C2×D411yescharacteristic
226C24×C3C2×D411yescharacteristic
227C3×#41—28no—
228C3×#41—44no—
229C3×#41—44no—
230C3×#41—44no—
231C2×C3×Q8—24no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—28no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—42no—
242C2×C3×Q8—42no—
243C2×C3×Q8—44no—
244C2×C3×Q8—44no—
245C2×C3×Q8—44no—
246C2×C3×Q8C22×C412yes—
247C2×C3×Q8C22×C412yes—
248C2×C3×Q8C2×D412yes—
249C2×C3×Q8#4112yes—
250C2×C3×D4—22no—
251C2×C3×D4—22no—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4C22⋊C414yes—
264C2×C3×D4C22×C412yes—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—24no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—24no—
278C22×C3×C4—42no—
279C22×C3×C4—42no—
280C22×C3×C4—42no—
281C22×C3×C4—42no—
282C22×C3×C4C22×C412yes—
283C22×C3×C4C22×C412yes—
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2×D411yescharacteristic
286C22×C3×C4C2×D411yescharacteristic
287C22×C3×C4C2×D411yescharacteristic
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2411yescharacteristic
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—42no—
296C22×Dic3—42no—
297C22×Dic3—42no—
298C22×Dic3—42no—
299C22×Dic3—81no—
300C22×Dic3—81no—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—24no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4C22⋊C414yes—
305C3×C4⋊C4C22×C412yes—
306C3×C22⋊C4—24no—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—24no—
310C3×C22⋊C4C22⋊C414yes—
311C3×C22⋊C4C22⋊C414yes—
312C3×C42—24no—
313C3×C42C22×C412yes—
314C3×C42C2×D412yes—
315#217—42no—
316#217—42no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—42no—
325C4⋊Dic3—42no—
326C4⋊Dic3—42no—
327C4⋊Dic3—81no—
328C4⋊Dic3C2×D412yes—
329C4×Dic3—42no—
330#208—44no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—44no—
343C2×C3⋊C8C2×D412yes—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—41no—
348C2×#41—41no—
349C2×#41C2×Dic314yescomplemented
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—41no—
355C22×Q8—41no—
356C22×Q8C2×Dic314yescomplemented
357C22×Q8C22×D311yescharacteristic
358C22×Q8C22×D311yescharacteristic
359C22×D4—21no—
360C22×D4—21no—
361C22×D4#6711yescharacteristic
362C22×D4C22×D311yescharacteristic
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—61no—
366C23×C4—61no—
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C2×M16—62no—
370C2×M16—62no—
371C2×M16—121no—
372C22×C8—31no—
373C22×C8—31no—
374C22×C8—31no—
375C22×C8—31no—
376C22×C8—62no—
377C22×C8—62no—
378C22×C8—121no—
379#124—28no—
380#124—22no—
381#124C2×Dic314yescomplemented
382C22⋊Q8—22no—
383C22⋊Q8—28no—
384C22⋊Q8C2×Dic314yescomplemented
385#121—28no—
386#121—22no—
387#121C2×Dic314yescomplemented
388C4×Q8—22no—
389C4×Q8C2×Dic314yescomplemented
390C4×D4—28no—
391C4×D4—124no—
392C4×D4C2×Dic314yes—
393C4×D4#6714yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4—121no—
407C2×C4⋊C4—121no—
408C2×C4⋊C4#6711yescharacteristic
409C2×C4⋊C4C22×D311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4#6711yescharacteristic
417C2×C22⋊C4#6711yescharacteristic
418C2×C42—21no—
419C2×C42—61no—
420C2×C42C22×D311yescharacteristic
421C4⋊C8—62no—
422#103—34no—
423#103—62no—
424#103—62no—
425#103—62no—
426#103—62no—
427#103—62no—
428#103—121no—
429#103—121no—
430#102—62no—
431#102—62no—
432#102—121no—
433#102—121no—
434C22⋊C8—62no—
435C22⋊C8—62no—
436#97—62no—
437#95—61no—
438#95—61no—
439#95—61no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—22no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3C2×C22⋊C412yes—
458C23×C3C2×C22⋊C412yes—
459C23×C3AGL(1,ℤ/8)12yes—
460C23×C3#13712yes—
461C23×C3C22×D411yescharacteristic
462C3×Q8—22no—
463C3×Q8—22no—
464C3×Q8—22no—
465C3×Q8—22no—
466C3×Q8—22no—
467C3×Q8—48no—
468C3×Q8—41no—
469C3×Q8—41no—
470C3×Q8C4×D414yescomplemented
471C3×D4—28no—
472C3×D4—22no—
473C3×D4—22no—
474C3×D4—48no—
475C3×D4—48no—
476C3×D4—41no—
477C3×D4—41no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—48no—
500C2×C3×C4—48no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4C2×C22⋊C412yes—
506C2×C3×C4C2×C22⋊C412yes—
507C2×C3×C4C2×C22⋊C412yes—
508C2×C3×C4C2×C22⋊C412yes—
509C2×C3×C4C23×C411yescharacteristic
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C2×#4111yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514C2×C3×C4H(5,𝔽2)11yescharacteristic
515C2×Dic3—22no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—84no—
528C2×Dic3—84no—
529C3⋊C8—22no—
530C3⋊C8—41no—
531C3⋊C8—41no—
532C3⋊C8—41no—
533C24—21no—
534C24C2×#6711yescharacteristic
535C24C2×#6711yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—24no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—28no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×Q8—42no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8D3×D412yes—
556C2×Q8#23712yes—
557C2×Q8C22×Dic312yes—
558C2×Q8C22×Dic312yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4#21714yes—
573C2×D4C22×Dic312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—122no—
596C22×C4—122no—
597C22×C4—122no—
598C22×C4—122no—
599C22×C4—241no—
600C22×C4—241no—
601C22×C4C22×Dic312yes—
602C22×C4C22×Dic312yes—
603C22×C4C2×#6711yescharacteristic
604C22×C4C2×#6711yescharacteristic
605C22×C4C2×#6711yescharacteristic
606C22×C4C2×#6711yescharacteristic
607C22×C4C2×#6712yes—
608C22×C4C2×#6712yes—
609C22×C4C23×D311yescharacteristic
610M16—124no—
611C2×C8—32no—
612C2×C8—61no—
613C2×C8—61no—
614C2×C8—61no—
615C2×C8—61no—
616C2×C8—61no—
617C2×C8—61no—
618C2×C8—61no—
619C2×C8—61no—
620C2×C8—61no—
621C2×C8—61no—
622C2×C8—61no—
623C2×C8—124no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—32no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—122no—
636C4⋊C4—122no—
637C4⋊C4—122no—
638C4⋊C4—241no—
639C4⋊C4#21714yes—
640C4⋊C4C22×Dic312yes—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—122no—
646C22⋊C4—122no—
647C22⋊C4#21714yes—
648C22⋊C4#21714yes—
649C42—24no—
650C42—122no—
651C42C22×Dic312yes—
652C42C2×#6712yes—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3#41714yescomplemented
674C22×C3C22×C22⋊C411yescharacteristic
675C22×C3D4211yescharacteristic
676C22×C3#54611yescharacteristic
677C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
678C22×C3C2×#13711yescharacteristic
679C22×C3#57711yescharacteristic
680C22×C3#57811yescharacteristic
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—24no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4C2×C4×D411yescharacteristic
689C3×C4#51811yescharacteristic
690C3×C4D4211yescharacteristic
691C3×C4#54611yescharacteristic
692Dic3—42no—
693Dic3—81no—
694Dic3—81no—
695Dic3—81no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23#94912yes—
714C23#95112yes—
715C23C2×#21712yes—
716C23C2×#21712yes—
717C23C22×#6711yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8D4×Dic314yescomplemented
727D4—28no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—48no—
732D4—41no—
733D4—41no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—62no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—244no—
774C2×C4—244no—
775C2×C4C2×#21712yes—
776C2×C4C2×#21712yes—
777C2×C4C2×#21712yes—
778C2×C4C2×#21712yes—
779C2×C4C2×D3×D411yescharacteristic
780C2×C4C2×#23711yescharacteristic
781C2×C4#100411yescharacteristic
782C2×C4#100411yescharacteristic
783C2×C4C23×Dic311yescharacteristic
784C2×C4C22×#6711yescharacteristic
785C8—62no—
786C8—121no—
787C8—121no—
788C8—121no—
789C2×C3—24no—
790C2×C3—42no—
791C2×C3—82no—
792C2×C3D4×C22⋊C411yescharacteristic
793C2×C3C2×#41711yescharacteristic
794C2×C3#289811yescharacteristic
795C2×C3#326511yescharacteristic
796C2×C3#327011yescharacteristic
797C2×C3#330811yescharacteristic
798C2×C3#331611yescharacteristic
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22#523214yescomplemented
820C22D4×#6711yescharacteristic
821C22#580611yescharacteristic
822C22C2×#94911yescharacteristic
823C22C2×#95111yescharacteristic
824C22#583711yescharacteristic
825C22#583811yescharacteristic
826C22C22×#21711yescharacteristic
827C4—22no—
828C4—22no—
829C4—24no—
830C4—22no—
831C4—22no—
832C4—42no—
833C4—42no—
834C4—122no—
835C4—241no—
836C4—241no—
837C4—241no—
838C4C2×D4×Dic311yescharacteristic
839C4#579811yescharacteristic
840C4D4×#6711yescharacteristic
841C4#580611yescharacteristic
842C3#2242111yescharacteristic, complemented, Sylow
843C2—24no—
844C2—42no—
845C2—82no—
846C2#8353611yescharacteristic
847C2#8353811yescharacteristic
848C2#8354211yescharacteristic
849C2#8354611yescharacteristic
850C2D4×#21711yescharacteristic
851C2C2×#523211yescharacteristic
852C2#8411111yescharacteristic
subgroupG/H
centerC23C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#548C2
socleC23×C3C22×D4
cosocleC22×C3×C4C24
hypercenterC2×#548D3
hypocenterC3#22421
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
2. C2×#5232C2semidirect
3. C22×#835C2semidirect
4. D4×C4⋊Dic3C2semidirect
5. C2×#5011C2semidirect
6. #72135C2semidirect
7. #72132C2semidirect
8. #71726C2semidirect
9. #71721C2semidirect
10. #71697C2semidirect
11. #71692C2semidirect
12. #71681C2semidirect
13. #71677C2semidirect
14. #71631C2semidirect
15. #71626C2semidirect
20. C3×#548C4semidirect
85. C2×C3×#41C2×C4semidirect
92. C22×C3×Q8C2×C4semidirect
107. C3×#124C2×C4semidirect
110. C3×C22⋊Q8C2×C4semidirect
113. C3×#121C2×C4semidirect
115. C3×C4×Q8C2×C4semidirect
164. #835D4semidirect
181. #548Dic3semidirect
349. C2×#41C2×Dic3semidirect
356. C22×Q8C2×Dic3semidirect
381. #124C2×Dic3semidirect
384. C22⋊Q8C2×Dic3semidirect
387. #121C2×Dic3semidirect
389. C4×Q8C2×Dic3semidirect
470. C3×Q8C4×D4semidirect
673. C22×C3#417semidirect
726. Q8D4×Dic3semidirect
819. C22#5232semidirect
842. C3#22421semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C2×#52322
C22×#8352
D4×C4⋊Dic32
C2×#50112
#721352
#721322
#717262
#717212
#716972
#716922
#716812
#716772
#716312
#716262
#224213