Finite Group Databasebeta

← #10723741

Subgroups — #10723741

Order 768.

1146 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4977C211yesmaximal, characteristic
2C3×#1436C211yesmaximal, characteristic
3#71565C211yesmaximal, characteristic
4#71536C211yesmaximal, characteristic
5#71534C211yesmaximal, characteristic
6#69420C211yesmaximal, characteristic
7#69417C211yesmaximal, characteristic
8#69414C211yesmaximal, characteristic
9#69414C211yesmaximal, characteristic
10#69411C211yesmaximal, characteristic
11#69407C211yesmaximal, characteristic
12#69407C211yesmaximal, characteristic
13#69406C211yesmaximal, characteristic
14Dic3⋊#95C211yesmaximal, characteristic
15#69401C211yesmaximal, characteristic
16#14455—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
19C22×C4⋊Dic3C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×Dic3⋊C4C2211yescharacteristic
22C22×Dic3⋊C4C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×C4×Dic3C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2211yescharacteristic
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
52#4977C418yescomplemented
53C2×#382—31no—
54#1444—31no—
55#1443—31no—
56#1442—31no—
57#1442—31no—
58#1441—31no—
59#1441—31no—
60#1436—31no—
61#1436—31no—
62#1436—31no—
63#1436—31no—
64#1436D311yescharacteristic
65C4⋊#95—31no—
66#1434—31no—
67#1434—31no—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C2×C3×C4⋊C4—41no—
84C2×C3×C4⋊C4—41no—
85C2×C3×C4⋊C4C2×C414yes—
86C2×C3×C42—22no—
87C2×C3×C42—41no—
88C2×C3×C42—41no—
89C2×C4⋊Dic3—22no—
90C2×C4⋊Dic3—41no—
91C2×C4⋊Dic3—41no—
92C2×C4⋊Dic3—41no—
93C2×C4⋊Dic3—41no—
94C2×C4⋊Dic3C2×C414yes—
95C2×Dic3⋊C4—22no—
96C2×Dic3⋊C4—22no—
97C2×Dic3⋊C4—22no—
98C2×Dic3⋊C4—22no—
99C2×Dic3⋊C4—41no—
100C2×Dic3⋊C4—41no—
101C2×Dic3⋊C4—41no—
102C2×Dic3⋊C4—41no—
103C2×Dic3⋊C4—41no—
104C2×C4×Dic3—22no—
105C2×C4×Dic3—22no—
106C2×C4×Dic3—41no—
107C2×C4×Dic3—41no—
108C2×C4×Dic3—41no—
109C2×C4×Dic3C2×C414yes—
110C3×#95—22no—
111C3×#95—22no—
112C3×#95—41no—
113C3×#95—41no—
114C3×#95Q814yes—
115C3⋊#95—22no—
116C3⋊#95—22no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—22no—
120C3⋊#95—41no—
121C3⋊#95—41no—
122C3⋊#95—41no—
123C3⋊#95—41no—
124C3⋊#95—41no—
125C3⋊#95—41no—
126C3⋊#95—41no—
127C3⋊#95—41no—
128C3⋊#95—41no—
129C3⋊#95—41no—
130C3⋊#95—41no—
131C3⋊#95—41no—
132C3⋊#95C2×C414yes—
133C3⋊#95C2×C414yes—
134C3⋊#95C2×C414yes—
135C3⋊#95C2×C414yes—
136C22×C4⋊C4—31no—
137C22×C4⋊C4—31no—
138C22×C4⋊C4—31no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4—31no—
141C22×C4⋊C4C2×D311yescharacteristic
142C22×C42—31no—
143C22×C42—31no—
144C22×C42C2×D311yescharacteristic
145#382—38no—
146C2×#95—31no—
147C2×#95—31no—
148C2×#95—31no—
149C2×#95—31no—
150C2×#95—31no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95—31no—
154C2×#95—31no—
155C2×#95—31no—
156C2×#95—31no—
157C2×#95—31no—
158C2×#95—31no—
159C2×#95—31no—
160C2×#95—31no—
161C2×#95—31no—
162C2×#95—31no—
163C2×#95—31no—
164C2×#95—31no—
165C2×#95—31no—
166C2×#95—31no—
167C2×#95C2×D311yescharacteristic
168C2×#95C2×D311yescharacteristic
169C2×#95C2×D311yescharacteristic
170C2×#95C2×D311yescharacteristic
171C2×#95C2×D311yescharacteristic
172C24×C3C2411yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4C22×C412yes—
215C22×C3×C4C22×C412yes—
216C22×C3×C4C22×C412yes—
217C22×C3×C4C2×Q812yes—
218C22×C3×C4C2×Q812yes—
219C22×C3×C4C2×Q812yes—
220C22×C3×C4#4112yes—
221C22×C3×C4#4112yes—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3C22×C412yes—
272C22×Dic3C22×C412yes—
273C22×Dic3C22×C412yes—
274C22×Dic3C22×C412yes—
275C22×Dic3#4112yes—
276C22×Dic3#4112yes—
277C22×Dic3#4112yes—
278C3×C4⋊C4—44no—
279C3×C42—44no—
280C4⋊Dic3—44no—
281C4⋊Dic3—44no—
282Dic3⋊C4—44no—
283Dic3⋊C4—44no—
284Dic3⋊C4—44no—
285C4×Dic3—28no—
286C4×Dic3—44no—
287C23×C4—31no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—31no—
292C23×C4—31no—
293C23×C4—31no—
294C23×C4—31no—
295C23×C4C22×D311yescharacteristic
296C23×C4C22×D311yescharacteristic
297C23×C4C22×D311yescharacteristic
298C23×C4C22×D311yescharacteristic
299C23×C4C22×D311yescharacteristic
300C23×C4C22×D311yescharacteristic
301C23×C4C22×D311yescharacteristic
302C2×C4⋊C4—34no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—62no—
306C2×C4⋊C4—62no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—62no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—121no—
311C2×C4⋊C4—121no—
312C2×C4⋊C4—121no—
313C2×C4⋊C4—121no—
314C2×C4⋊C4—121no—
315C2×C4⋊C4—121no—
316C2×C4⋊C4—121no—
317C2×C4⋊C4—121no—
318C2×C4⋊C4—121no—
319C2×C4⋊C4C4×D314yes—
320C2×C42—22no—
321C2×C42—34no—
322C2×C42—41no—
323C2×C42—41no—
324C2×C42—62no—
325C2×C42—62no—
326C2×C42—121no—
327C2×C42—121no—
328C2×C42—121no—
329#95—22no—
330#95—22no—
331#95—34no—
332#95—34no—
333#95—34no—
334#95—34no—
335#95—41no—
336#95—41no—
337#95—62no—
338#95—62no—
339#95—62no—
340#95—62no—
341#95—62no—
342#95—121no—
343#95—121no—
344#95—121no—
345#95—121no—
346#95—121no—
347#95—121no—
348#95—121no—
349#95—121no—
350#95—121no—
351#95—121no—
352#95—121no—
353#95—121no—
354#95Dic614yes—
355C23×C3C23×C411yescharacteristic
356C23×C3C22×Q811yescharacteristic
357C23×C3C2×#4111yescharacteristic
358C23×C3C2×#4111yescharacteristic
359C23×C3C2×#4111yescharacteristic
360C23×C3C2×#4111yescharacteristic
361C23×C3C2×#4111yescharacteristic
362C23×C3H(5,𝔽2)11yescharacteristic
363C23×C3H(5,𝔽2)11yescharacteristic
364C23×C3H(5,𝔽2)11yescharacteristic
365C23×C3H(5,𝔽2)11yescharacteristic
366C23×C3H(5,𝔽2)11yescharacteristic
367C23×C32−1+411yescharacteristic
368C23×C32−1+411yescharacteristic
369C23×C32−1+411yescharacteristic
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4C4×Q814yes—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3#11714yes—
475C24C23×D311yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—32no—
522C22×C4—32no—
523C22×C4—32no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4C2×Dic612yes—
574C22×C4C2×Dic612yes—
575C22×C4C2×Dic612yes—
576C22×C4C2×C4×D312yes—
577C22×C4C2×C4×D312yes—
578C22×C4C2×C4×D312yes—
579C22×C4#23512yes—
580C22×C4#23712yes—
581C4⋊C4—44no—
582C4⋊C4—124no—
583C4⋊C4—124no—
584C4⋊C4—124no—
585C4⋊C4—124no—
586C4⋊C4—124no—
587C42—44no—
588C42—68no—
589C42—124no—
590C22×C3C2×#11711yescharacteristic
591C22×C3C2×C4×Q811yescharacteristic
592C22×C3C4×#4111yescharacteristic
593C22×C3#51811yescharacteristic
594C22×C3#52011yescharacteristic
595C22×C3#52011yescharacteristic
596C22×C3#52011yescharacteristic
597C22×C3#53811yescharacteristic
598C22×C3#53811yescharacteristic
599C22×C3#54011yescharacteristic
600C22×C3#54011yescharacteristic
601C22×C3#54111yescharacteristic
602C22×C3#54111yescharacteristic
603C22×C3#54211yescharacteristic
604C22×C3#54211yescharacteristic
605C22×C3#54211yescharacteristic
606C22×C3#54211yescharacteristic
607C22×C3#54411yescharacteristic
608C22×C3#54411yescharacteristic
609C22×C3#55111yescharacteristic
610C22×C3#55111yescharacteristic
611C22×C3#55211yescharacteristic
612C22×C3#55211yescharacteristic
613C22×C3#55211yescharacteristic
614C22×C3#55311yescharacteristic
615C22×C3#55311yescharacteristic
616C22×C3#55311yescharacteristic
617C22×C3#55411yescharacteristic
618C22×C3#55411yescharacteristic
619C22×C3#55411yescharacteristic
620C22×C3#55711yescharacteristic
621C22×C3H(3,𝔽4)11yescharacteristic
622C22×C3#56211yescharacteristic
623C22×C3#56211yescharacteristic
624C22×C3#56311yescharacteristic
625C3×C4—24no—
626C3×C4—42no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4—42no—
631C3×C4—81no—
632Dic3—24no—
633Dic3—42no—
634Dic3—42no—
635Dic3—42no—
636Dic3—42no—
637Dic3—81no—
638Dic3—81no—
639Dic3—81no—
640C23C22×Dic611yescharacteristic
641C23C22×C4×D311yescharacteristic
642C23C2×#23511yescharacteristic
643C23C2×#23711yescharacteristic
644C23#100411yescharacteristic
645C23#100411yescharacteristic
646C23#100411yescharacteristic
647C23#100711yescharacteristic
648C23#100711yescharacteristic
649C23D3×#4111yescharacteristic
650C23D3×#4111yescharacteristic
651C23D3×#4111yescharacteristic
652C23#100911yescharacteristic
653C23#100911yescharacteristic
654C23#101011yescharacteristic
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—34no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—121no—
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—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4C4×Dic614yes—
760C2×C3#231411yescharacteristic
761C2×C3#233011yescharacteristic
762C2×C3#233711yescharacteristic
763C2×C3#234311yescharacteristic
764C2×C3#234511yescharacteristic
765C2×C3#237011yescharacteristic
766C2×C3#237911yescharacteristic
767C2×C3#275311yescharacteristic
768C2×C3#275511yescharacteristic
769C2×C3#276111yescharacteristic
770C2×C3#276311yescharacteristic
771C2×C3#276611yescharacteristic
772C2×C3#276811yescharacteristic
773C2×C3#277211yescharacteristic
774C2×C3#277411yescharacteristic
775C22C2×C4×Dic611yescharacteristic
776C22#548611yescharacteristic
777C22#550011yescharacteristic
778C22#551311yescharacteristic
779C22#551911yescharacteristic
780C22D3×#11711yescharacteristic
781C22#553011yescharacteristic
782C22C4×#23711yescharacteristic
783C22#553911yescharacteristic
784C22#553911yescharacteristic
785C22#554011yescharacteristic
786C22#554011yescharacteristic
787C22#554311yescharacteristic
788C22#554611yescharacteristic
789C22#556211yescharacteristic
790C22#556911yescharacteristic
791C22#557411yescharacteristic
792C22#557411yescharacteristic
793C22#558311yescharacteristic
794C22#559311yescharacteristic
795C22#560311yescharacteristic
796C22#561311yescharacteristic
797C22#563911yescharacteristic
798C22#564011yescharacteristic
799C22#564711yescharacteristic
800C22#564711yescharacteristic
801C22#565811yescharacteristic
802C22#566211yescharacteristic
803C22#566311yescharacteristic
804C22#568311yescharacteristic
805C22#569311yescharacteristic
806C22#569611yescharacteristic
807C22#570511yescharacteristic
808C22#571011yescharacteristic
809C22#573511yescharacteristic
810C4—24no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—64no—
817C4—81no—
818C4—122no—
819C4—122no—
820C4—122no—
821C4—122no—
822C4—241no—
823C4—241no—
824C4—241no—
825C3#1445511yescharacteristic, complemented, Sylow
826C2#7345811yescharacteristic
827C2#7362611yescharacteristic
828C2#7366111yescharacteristic
829C2#7455211yescharacteristic
830C2#7455911yescharacteristic
831C2#7467111yescharacteristic
832C2#7494411yescharacteristic
833C2#7518711yescharacteristic
834C2#7521811yescharacteristic
835C2#7530311yescharacteristic
836C2#7573411yescharacteristic
837C2#7574811yescharacteristic
838C2#7614111yescharacteristic
839C2#7615311yescharacteristic
840C2#7649611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, prime radical, cosocleC24×C3C24
hypercenter#1436D3
hypocenterC3#14455
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
52. #4977C4semidirect
825. C3#14455semidirect

Maximal subgroups

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

subgroupindex
C2×#49772
C3×#14362
#715652
#715362
#715342
#694202
#694172
#694142
#694112
#694072
#694062
Dic3⋊#952
#694012
#144553