Finite Group Databasebeta

← #10720134

Subgroups — #10720134

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#385C211yesmaximal, characteristic
2C2×C4×#217C211yesmaximal, characteristic
3C22×C3⋊#95C211yesmaximal, characteristic
4C2×#4980C211yesmaximal, characteristic, complemented
5C2×#4950C211yesmaximal, characteristic
6#71569C211yesmaximal, characteristic, complemented
7#71565C211yesmaximal, characteristic, complemented
8#71564C211yesmaximal, characteristic, complemented
9#71544C211yesmaximal, characteristic
10#71544C211yesmaximal, characteristic
11#71544C211yesmaximal, characteristic
12#69416C211yesmaximal, characteristic, complemented
13#69412C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14131—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C3×#385C418yescomplemented
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C4×#217—24no—
34C2×C3⋊#95—24no—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4980—24no—
56#4950—24no—
57C2×#387—31no—
58C2×#385—31no—
59C2×#385D311yescharacteristic
60C2×C4×C22⋊C4—31no—
61C22×#95—31no—
62#1445—31no—
63#1443—31no—
64#1442—31no—
65#1441—31no—
66#1436—31no—
67#1436—31no—
68#1434—31no—
69C22⋊#95—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C25×C3C2311yescharacteristic
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—41no—
78C23×C3×C4—41no—
79C23×C3×C4C2×C414yes—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×Dic3—22no—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—41no—
97C23×Dic3—41no—
98C23×Dic3—41no—
99C23×Dic3—41no—
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—41no—
111C2×C3×C4⋊C4—41no—
112C2×C3×C4⋊C4C2×C414yescomplemented
113C2×C3×C4⋊C4C2×C414yescomplemented
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4C2×C414yes—
119C2×C3×C22⋊C4C2×C414yes—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217D414yes—
125C2×#217Q814yes—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—22no—
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3—41no—
131C2×C4⋊Dic3—41no—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—22no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3—41no—
137C2×C4×Dic3—41no—
138C3×#95C2×C414yescomplemented
139C3×#95C2×C414yescomplemented
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—22no—
144C3⋊#95—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—41no—
154C3⋊#95—41no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C3⋊#95—41no—
159C3⋊#95D414yes—
160C24×C4—31no—
161C24×C4—31no—
162C24×C4C2×D311yescharacteristic
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4C2×D311yescharacteristic
166C22×C4⋊C4C2×D311yescharacteristic
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4C2×D311yescharacteristic
170C22×C22⋊C4C2×D311yescharacteristic
171C22×C42—31no—
172C22×C42—31no—
173#387—64no—
174#385—64no—
175#385Dic318yescomplemented
176C4×C22⋊C4—64no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—64no—
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3C22×C412yes—
209C24×C3C2×D412yes—
210C24×C3C2×Q812yes—
211C24×C3#4112yes—
212C24×C3#4112yes—
213C24×C3#4112yes—
214C24×C3#4112yes—
215C24×C3C2411yescharacteristic
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—28no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
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—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
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—21no—
250C22×C3×C4—21no—
251C22×C3×C4—28no—
252C22×C3×C4—44no—
253C22×C3×C4—44no—
254C22×C3×C4—44no—
255C22×C3×C4—44no—
256C22×C3×C4—44no—
257C22×C3×C4C22×C412yes—
258C22×C3×C4C22×C412yes—
259C22×C3×C4C22×C412yes—
260C22×C3×C4C22×C412yes—
261C22×C3×C4C22×C412yes—
262C22×C3×C4C22×C412yes—
263C22×C3×C4C2×D412yes—
264C22×C3×C4#4112yes—
265C22×Dic3—28no—
266C22×Dic3—28no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—44no—
316C22×Dic3—44no—
317C22×Dic3—44no—
318C22×Dic3—44no—
319C22×Dic3—44no—
320C22×Dic3—44no—
321C22×Dic3—44no—
322C22×Dic3—44no—
323C22×Dic3—44no—
324C22×Dic3—44no—
325C22×Dic3—44no—
326C22×Dic3—44no—
327C22×Dic3C2×D412yes—
328C22×Dic3C2×D412yes—
329C22×Dic3C2×D412yes—
330C22×Dic3C2×D412yes—
331C22×Dic3C2×Q812yes—
332C22×Dic3C2×Q812yes—
333C22×Dic3#4112yes—
334C22×Dic3#4112yes—
335C3×C4⋊C4—28no—
336C3×C4⋊C4—44no—
337C3×C22⋊C4—28no—
338C3×C22⋊C4—28no—
339#217—28no—
340#217—28no—
341C4⋊Dic3—44no—
342C4⋊Dic3—44no—
343C4×Dic3—44no—
344C4×Dic3—44no—
345C25C22×D311yescharacteristic
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—41no—
359C23×C4—41no—
360C23×C4—62no—
361C23×C4—62no—
362C23×C4—62no—
363C23×C4—62no—
364C23×C4—62no—
365C23×C4—62no—
366C23×C4—62no—
367C23×C4—62no—
368C23×C4—62no—
369C23×C4—62no—
370C23×C4—121no—
371C23×C4—121no—
372C23×C4—121no—
373C23×C4—121no—
374C23×C4C2×Dic314yes—
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—121no—
390C2×C4⋊C4—121no—
391C2×C4⋊C4C2×Dic314yescomplemented
392C2×C4⋊C4C2×Dic314yescomplemented
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4C2×Dic314yes—
404C2×C22⋊C4C2×Dic314yes—
405C2×C42—62no—
406C2×C42—62no—
407C2×C42—62no—
408C2×C42—62no—
409C2×C42—121no—
410C2×C42—121no—
411#95—34no—
412#95—62no—
413#95—62no—
414#95—62no—
415#95—62no—
416#95—62no—
417#95—62no—
418#95—62no—
419#95—62no—
420#95—62no—
421#95—62no—
422#95—62no—
423#95—62no—
424#95—62no—
425#95—121no—
426#95—121no—
427#95—121no—
428#95—121no—
429#95—121no—
430#95—121no—
431#95C2×Dic314yescomplemented
432#95C2×Dic314yescomplemented
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3#11714yes—
462C23×C3C4×D414yes—
463C23×C3C4×Q814yes—
464C23×C3C22⋊Q814yes—
465C23×C3#12314yes—
466C23×C3#12514yes—
467C23×C3#12614yes—
468C23×C3C23×C411yescharacteristic
469C23×C3C22×D411yescharacteristic
470C23×C3C22×D411yescharacteristic
471C23×C3C22×Q811yescharacteristic
472C23×C3C2×#4111yescharacteristic
473C23×C3C2×#4111yescharacteristic
474C23×C3C2×#4111yescharacteristic
475C23×C3C2×#4111yescharacteristic
476C23×C3C2×#4111yescharacteristic
477C23×C3C2×#4111yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C23×C3H(5,𝔽2)11yescharacteristic
480C23×C3H(5,𝔽2)11yescharacteristic
481C23×C3H(5,𝔽2)11yescharacteristic
482C23×C32−1+411yescharacteristic
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
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—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—416no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4C4×D414yes—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—416no—
551C2×Dic3—416no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24#23512yes—
593C24#23512yes—
594C24D3×D412yes—
595C24#23712yes—
596C24D3×Q812yes—
597C24#23912yes—
598C24C22×Dic312yes—
599C24C23×D311yescharacteristic
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—28no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—28no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—68no—
650C22×C4—68no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—124no—
700C22×C4—124no—
701C22×C4—124no—
702C22×C4—124no—
703C22×C4—124no—
704C22×C4—124no—
705C22×C4—124no—
706C22×C4—124no—
707C22×C4—124no—
708C22×C4—124no—
709C22×C4—124no—
710C22×C4—124no—
711C22×C4D3×D412yes—
712C22×C4#23712yes—
713C22×C4C22×Dic312yes—
714C22×C4C22×Dic312yes—
715C22×C4C22×Dic312yes—
716C22×C4C22×Dic312yes—
717C22×C4C22×Dic312yes—
718C22×C4C22×Dic312yes—
719C4⋊C4—28no—
720C4⋊C4—44no—
721C4⋊C4—124no—
722C4⋊C4—124no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—68no—
726C22⋊C4—68no—
727C42—124no—
728C42—124no—
729C22×C3—24no—
730C22×C3—24no—
731C22×C3—24no—
732C22×C3—24no—
733C22×C3—24no—
734C22×C3—24no—
735C22×C3—24no—
736C22×C3—24no—
737C22×C3—24no—
738C22×C3—24no—
739C22×C3—24no—
740C22×C3—24no—
741C22×C3—24no—
742C22×C3—24no—
743C22×C3#38718yescomplemented
744C22×C3C2×#11711yescharacteristic
745C22×C3C2×C4×D411yescharacteristic
746C22×C3C2×C4×D411yescharacteristic
747C22×C3C2×C4×Q811yescharacteristic
748C22×C3C4×#4111yescharacteristic
749C22×C3#51811yescharacteristic
750C22×C3#52011yescharacteristic
751C22×C3C2×C22⋊Q811yescharacteristic
752C22×C3C2×#12311yescharacteristic
753C22×C3#52511yescharacteristic
754C22×C3#52511yescharacteristic
755C22×C3C2×#12511yescharacteristic
756C22×C3C2×#12611yescharacteristic
757C22×C3#52911yescharacteristic
758C22×C3#52911yescharacteristic
759C22×C3#53811yescharacteristic
760C22×C3#53811yescharacteristic
761C22×C3#53911yescharacteristic
762C22×C3#53911yescharacteristic
763C22×C3D4211yescharacteristic
764C22×C3#54611yescharacteristic
765C22×C3#54611yescharacteristic
766C22×C3#54611yescharacteristic
767C22×C3#54611yescharacteristic
768C22×C3#54711yescharacteristic
769C22×C3D4×Q811yescharacteristic
770C22×C3#55111yescharacteristic
771C22×C3#55111yescharacteristic
772C22×C3#55111yescharacteristic
773C22×C3#55111yescharacteristic
774C22×C3#55211yescharacteristic
775C22×C3#55211yescharacteristic
776C22×C3#55411yescharacteristic
777C22×C3#55411yescharacteristic
778C22×C3#55411yescharacteristic
779C3×C4—24no—
780C3×C4—42no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—42no—
784C3×C4—42no—
785Dic3—42no—
786Dic3—42no—
787Dic3—42no—
788Dic3—42no—
789Dic3—42no—
790Dic3—42no—
791Dic3—42no—
792Dic3—42no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23#88914yes—
822C23#89414yes—
823C23#89614yes—
824C23#89814yes—
825C23#92614yes—
826C23D4×Dic314yes—
827C23Q8×Dic314yes—
828C23C2×#23511yescharacteristic
829C23C2×#23511yescharacteristic
830C23C2×D3×D411yescharacteristic
831C23C2×D3×D411yescharacteristic
832C23C2×#23711yescharacteristic
833C23C2×#23711yescharacteristic
834C23#100411yescharacteristic
835C23#100411yescharacteristic
836C23C2×D3×Q811yescharacteristic
837C23C2×#23911yescharacteristic
838C23D3×#4111yescharacteristic
839C23D3×#4111yescharacteristic
840C23#100911yescharacteristic
841C23#101011yescharacteristic
842C23C23×Dic311yescharacteristic
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—416no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—62no—
909C2×C4—1216no—
910C2×C4—1216no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4D4×Dic314yes—
944C2×C3—28no—
945C2×C3C2×#38711yescharacteristic
946C2×C3#229011yescharacteristic
947C2×C3#231811yescharacteristic
948C2×C3#235811yescharacteristic
949C2×C3#235911yescharacteristic
950C2×C3#236011yescharacteristic
951C2×C3#236811yescharacteristic
952C2×C3#241811yescharacteristic
953C2×C3#241911yescharacteristic
954C2×C3#244911yescharacteristic
955C2×C3#245011yescharacteristic
956C2×C3#247311yescharacteristic
957C2×C3#248011yescharacteristic
958C2×C3#249311yescharacteristic
959C2×C3#250511yescharacteristic
960C22—24no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22#498018yescomplemented
975C22C2×#88911yescharacteristic
976C22C2×#89411yescharacteristic
977C22C2×#89611yescharacteristic
978C22C2×#89811yescharacteristic
979C22#553811yescharacteristic
980C22#553811yescharacteristic
981C22#554711yescharacteristic
982C22#554711yescharacteristic
983C22#556011yescharacteristic
984C22#556011yescharacteristic
985C22#556411yescharacteristic
986C22#556411yescharacteristic
987C22#558711yescharacteristic
988C22#559011yescharacteristic
989C22#559111yescharacteristic
990C22#559111yescharacteristic
991C22#563011yescharacteristic
992C22#563211yescharacteristic
993C22#563511yescharacteristic
994C22#563611yescharacteristic
995C22#563611yescharacteristic
996C22#563711yescharacteristic
997C22#563711yescharacteristic
998C22#564211yescharacteristic
999C22#565011yescharacteristic
1000C22#565411yescharacteristic
1001C22#565511yescharacteristic
1002C22#565811yescharacteristic
1003C22C2×#92611yescharacteristic
1004C22C2×D4×Dic311yescharacteristic
1005C22C2×D4×Dic311yescharacteristic
1006C22#579811yescharacteristic
1007C22C2×Q8×Dic311yescharacteristic
1008C22Dic3×#4111yescharacteristic
1009C22#582711yescharacteristic
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—122no—
1017C4—122no—
1018C4—122no—
1019C4—122no—
1020C4—122no—
1021C4—122no—
1022C4—122no—
1023C4—122no—
1024C3#1413111yescharacteristic, complemented, Sylow
1025C2—28no—
1026C2#7440811yescharacteristic
1027C2#7442111yescharacteristic
1028C2#7442311yescharacteristic
1029C2#7444011yescharacteristic
1030C2#7445211yescharacteristic
1031C2#7445811yescharacteristic
1032C2#7446211yescharacteristic
1033C2#7460311yescharacteristic
1034C2C2×#498011yescharacteristic
1035C2#8231811yescharacteristic
1036C2#8232411yescharacteristic
1037C2#8257911yescharacteristic
1038C2#8274711yescharacteristic
1039C2#8274911yescharacteristic
1040C2#8283811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#385C2
socle, cosocleC24×C3C24
prime radicalC25×C3C23
hypercenterC2×#385D3
hypocenterC3#14131
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#4980C2semidirect
6. #71569C2semidirect
7. #71565C2semidirect
8. #71564C2semidirect
12. #69416C2semidirect
13. #69412C2semidirect
14. #69407C2semidirect
15. #69401C2semidirect
30. C3×#385C4semidirect
112. C2×C3×C4⋊C4C2×C4semidirect
113. C2×C3×C4⋊C4C2×C4semidirect
138. C3×#95C2×C4semidirect
139. C3×#95C2×C4semidirect
175. #385Dic3semidirect
391. C2×C4⋊C4C2×Dic3semidirect
392. C2×C4⋊C4C2×Dic3semidirect
431. #95C2×Dic3semidirect
432. #95C2×Dic3semidirect
743. C22×C3#387semidirect
974. C22#4980semidirect
1024. C3#14131semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3852
C2×C4×#2172
C22×C3⋊#952
C2×#49802
C2×#49502
#715692
#715652
#715642
#715442
#694162
#694122
#694072
#694012
#141313