Finite Group Databasebeta

← #10723734

Subgroups — #10723734

Order 768.

1190 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×#4975C211yesmaximal, characteristic
2C3×#1441C211yesmaximal, characteristic
3#71566C211yesmaximal, characteristic
4#71566C211yesmaximal, characteristic
5#71564C211yesmaximal, characteristic
6#69411C211yesmaximal, characteristic
7#69409C211yesmaximal, characteristic
8#69409C211yesmaximal, characteristic
9#69407C211yesmaximal, characteristic
10#69406C211yesmaximal, characteristic
11#69406C211yesmaximal, characteristic
12#69405C211yesmaximal, characteristic
13#69405C211yesmaximal, characteristic
14#69403C211yesmaximal, characteristic
15#69401C211yesmaximal, characteristic
16#14454—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic3C2211yescharacteristic
20C22×Dic3⋊C4C2211yescharacteristic
21C22×Dic3⋊C4C2211yescharacteristic
22C22×Dic3⋊C4C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
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#4975C418yescomplemented
53C2×#384—31no—
54#1441—31no—
55#1441—31no—
56#1441—31no—
57#1441—31no—
58#1441—31no—
59#1441D311yescharacteristic
60#1436—31no—
61#1436—31no—
62#1436—31no—
63#1436—31no—
64#1436—31no—
65#1436—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⋊C4—41no—
86C2×C3×C4⋊C4—41no—
87C2×C3×C4⋊C4—41no—
88C2×C3×C4⋊C4C2×C414yes—
89C2×C4⋊Dic3—41no—
90C2×C4⋊Dic3—41no—
91C2×C4⋊Dic3C2×C414yes—
92C2×Dic3⋊C4—41no—
93C2×Dic3⋊C4—41no—
94C2×Dic3⋊C4—41no—
95C2×Dic3⋊C4—41no—
96C2×Dic3⋊C4—41no—
97C2×Dic3⋊C4—41no—
98C2×Dic3⋊C4—41no—
99C2×Dic3⋊C4—41no—
100C2×Dic3⋊C4—41no—
101C2×Dic3⋊C4—41no—
102C2×Dic3⋊C4—41no—
103C2×Dic3⋊C4C2×C414yes—
104C2×Dic3⋊C4C2×C414yes—
105C2×Dic3⋊C4C2×C414yes—
106C2×Dic3⋊C4C2×C414yes—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—41no—
110C2×C4×Dic3—41no—
111C2×C4×Dic3—41no—
112C2×C4×Dic3—41no—
113C2×C4×Dic3—41no—
114C2×C4×Dic3—41no—
115C2×C4×Dic3C2×C414yes—
116C3×#95—22no—
117C3×#95—22no—
118C3×#95—41no—
119C3×#95—41no—
120C3×#95—41no—
121C3⋊#95—22no—
122C3⋊#95—22no—
123C3⋊#95—22no—
124C3⋊#95—22no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—22no—
128C3⋊#95—22no—
129C3⋊#95—41no—
130C3⋊#95—41no—
131C3⋊#95—41no—
132C3⋊#95—41no—
133C3⋊#95—41no—
134C3⋊#95—41no—
135C3⋊#95—41no—
136C3⋊#95—41no—
137C3⋊#95—41no—
138C3⋊#95Q814yes—
139C3⋊#95Q814yes—
140C22×C4⋊C4—31no—
141C22×C4⋊C4—31no—
142C22×C4⋊C4—31no—
143C22×C4⋊C4—31no—
144C22×C4⋊C4—31no—
145C22×C4⋊C4—31no—
146C22×C4⋊C4C2×D311yescharacteristic
147C22×C4⋊C4C2×D311yescharacteristic
148C22×C42—31no—
149C22×C42—31no—
150C22×C42—31no—
151#384—38no—
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×#95—31no—
168C2×#95—31no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95C2×D311yescharacteristic
172C2×#95C2×D311yescharacteristic
173C2×#95C2×D311yescharacteristic
174C2×#95C2×D311yescharacteristic
175C2×#95C2×D311yescharacteristic
176C24×C3C2411yescharacteristic
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×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4C22×C412yes—
221C22×C3×C4C22×C412yes—
222C22×C3×C4C22×C412yes—
223C22×C3×C4C2×Q812yes—
224C22×C3×C4C2×Q812yes—
225C22×C3×C4#4112yes—
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×Dic3C2×Q812yes—
276C22×Dic3C2×Q812yes—
277C22×Dic3C2×Q812yes—
278C22×Dic3C2×Q812yes—
279C22×Dic3#4112yes—
280C22×Dic3#4112yes—
281C22×Dic3#4112yes—
282C3×C4⋊C4—44no—
283C3×C4⋊C4—44no—
284C4⋊Dic3—44no—
285Dic3⋊C4—44no—
286Dic3⋊C4—44no—
287Dic3⋊C4—44no—
288Dic3⋊C4—44no—
289Dic3⋊C4—44no—
290C4×Dic3—28no—
291C4×Dic3—44no—
292C4×Dic3—44no—
293C23×C4—31no—
294C23×C4—31no—
295C23×C4—31no—
296C23×C4—31no—
297C23×C4—31no—
298C23×C4—31no—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4C22×D311yescharacteristic
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304C23×C4C22×D311yescharacteristic
305C23×C4C22×D311yescharacteristic
306C23×C4C22×D311yescharacteristic
307C23×C4C22×D311yescharacteristic
308C2×C4⋊C4—34no—
309C2×C4⋊C4—34no—
310C2×C4⋊C4—34no—
311C2×C4⋊C4—34no—
312C2×C4⋊C4—34no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—121no—
319C2×C4⋊C4—121no—
320C2×C4⋊C4—121no—
321C2×C4⋊C4—121no—
322C2×C4⋊C4—121no—
323C2×C4⋊C4—121no—
324C2×C4⋊C4—121no—
325C2×C4⋊C4—121no—
326C2×C4⋊C4—121no—
327C2×C4⋊C4—121no—
328C2×C4⋊C4—121no—
329C2×C4⋊C4—121no—
330C2×C4⋊C4—121no—
331C2×C4⋊C4C4×D314yes—
332C2×C42—34no—
333C2×C42—62no—
334C2×C42—62no—
335C2×C42—121no—
336C2×C42—121no—
337C2×C42—121no—
338C2×C42—121no—
339C2×C42—121no—
340C2×C42—121no—
341#95—22no—
342#95—22no—
343#95—34no—
344#95—34no—
345#95—41no—
346#95—41no—
347#95—41no—
348#95—62no—
349#95—62no—
350#95—62no—
351#95—62no—
352#95—62no—
353#95—62no—
354#95—62no—
355#95—62no—
356#95—121no—
357#95—121no—
358#95—121no—
359#95—121no—
360#95—121no—
361#95—121no—
362#95—121no—
363#95—121no—
364#95—121no—
365C23×C3C23×C411yescharacteristic
366C23×C3C22×Q811yescharacteristic
367C23×C3C22×Q811yescharacteristic
368C23×C3C2×#4111yescharacteristic
369C23×C3C2×#4111yescharacteristic
370C23×C3C2×#4111yescharacteristic
371C23×C3C2×#4111yescharacteristic
372C23×C3H(5,𝔽2)11yescharacteristic
373C23×C3H(5,𝔽2)11yescharacteristic
374C23×C3H(5,𝔽2)11yescharacteristic
375C23×C3H(5,𝔽2)11yescharacteristic
376C23×C3H(5,𝔽2)11yescharacteristic
377C23×C3H(5,𝔽2)11yescharacteristic
378C23×C32−1+411yescharacteristic
379C23×C32−1+411yescharacteristic
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—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
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×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4C4×Q814yes—
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—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
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—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3#11714yes—
484C2×Dic3C4×Q814yes—
485C24C23×D311yescharacteristic
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—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—32no—
532C22×C4—32no—
533C22×C4—32no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—32no—
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×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4C2×C4×D312yes—
586C22×C4C2×C4×D312yes—
587C22×C4C2×C4×D312yes—
588C22×C4#23712yes—
589C22×C4D3×Q812yes—
590C22×C4D3×Q812yes—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—124no—
594C4⋊C4—124no—
595C4⋊C4—124no—
596C4⋊C4—124no—
597C4⋊C4—124no—
598C4⋊C4—124no—
599C42—68no—
600C42—124no—
601C42—124no—
602C22×C3C2×#11711yescharacteristic
603C22×C3C2×C4×Q811yescharacteristic
604C22×C3C2×C4×Q811yescharacteristic
605C22×C3#51811yescharacteristic
606C22×C3#51811yescharacteristic
607C22×C3#51811yescharacteristic
608C22×C3#51911yescharacteristic
609C22×C3#53911yescharacteristic
610C22×C3#53911yescharacteristic
611C22×C3#53911yescharacteristic
612C22×C3#53911yescharacteristic
613C22×C3#54211yescharacteristic
614C22×C3#54211yescharacteristic
615C22×C3#54211yescharacteristic
616C22×C3#54211yescharacteristic
617C22×C3#54411yescharacteristic
618C22×C3#54411yescharacteristic
619C22×C3#54411yescharacteristic
620C22×C3#54411yescharacteristic
621C22×C3#55311yescharacteristic
622C22×C3#55311yescharacteristic
623C22×C3#55311yescharacteristic
624C22×C3#55311yescharacteristic
625C22×C3#55411yescharacteristic
626C22×C3#55411yescharacteristic
627C22×C3#55411yescharacteristic
628C22×C3#55411yescharacteristic
629C22×C3#55411yescharacteristic
630C22×C3#55411yescharacteristic
631C22×C3#55511yescharacteristic
632C22×C3Q8211yescharacteristic
633C22×C3#56011yescharacteristic
634C22×C3#56011yescharacteristic
635C22×C3#56011yescharacteristic
636C22×C3#56011yescharacteristic
637C3×C4—24no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—81no—
642C3×C4—81no—
643C3×C4—81no—
644Dic3—24no—
645Dic3—24no—
646Dic3—42no—
647Dic3—42no—
648Dic3—42no—
649Dic3—42no—
650Dic3—42no—
651Dic3—81no—
652C23C22×C4×D311yescharacteristic
653C23C2×#23711yescharacteristic
654C23#100411yescharacteristic
655C23#100411yescharacteristic
656C23#100411yescharacteristic
657C23#100411yescharacteristic
658C23C2×D3×Q811yescharacteristic
659C23C2×D3×Q811yescharacteristic
660C23#100711yescharacteristic
661C23D3×#4111yescharacteristic
662C23D3×#4111yescharacteristic
663C23D3×#4111yescharacteristic
664C23#100911yescharacteristic
665C23#100911yescharacteristic
666C23#101011yescharacteristic
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—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—34no—
683C2×C4—34no—
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—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
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×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
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#88714yes—
772C2×C3#231311yescharacteristic
773C2×C3#233111yescharacteristic
774C2×C3#233111yescharacteristic
775C2×C3#234511yescharacteristic
776C2×C3#234511yescharacteristic
777C2×C3#236911yescharacteristic
778C2×C3#238011yescharacteristic
779C2×C3#279011yescharacteristic
780C2×C3#279011yescharacteristic
781C2×C3#279011yescharacteristic
782C2×C3#279011yescharacteristic
783C2×C3#279211yescharacteristic
784C2×C3#279211yescharacteristic
785C2×C3#279511yescharacteristic
786C2×C3#279511yescharacteristic
787C22#548611yescharacteristic
788C22C2×#88711yescharacteristic
789C22D3×#11711yescharacteristic
790C22#554511yescharacteristic
791C22#554511yescharacteristic
792C22C4×D3×Q811yescharacteristic
793C22#557211yescharacteristic
794C22#559511yescharacteristic
795C22#560111yescharacteristic
796C22#560111yescharacteristic
797C22#560311yescharacteristic
798C22#561611yescharacteristic
799C22#562011yescharacteristic
800C22#562011yescharacteristic
801C22#562311yescharacteristic
802C22#563511yescharacteristic
803C22#563611yescharacteristic
804C22#563611yescharacteristic
805C22#563611yescharacteristic
806C22#563811yescharacteristic
807C22#564011yescharacteristic
808C22#564311yescharacteristic
809C22#566011yescharacteristic
810C22#566111yescharacteristic
811C22#566611yescharacteristic
812C22#566911yescharacteristic
813C22#568911yescharacteristic
814C22#569011yescharacteristic
815C22#569011yescharacteristic
816C22#569211yescharacteristic
817C22#570711yescharacteristic
818C22#570911yescharacteristic
819C22#572211yescharacteristic
820C22#572911yescharacteristic
821C22#572911yescharacteristic
822C4—24no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—64no—
827C4—64no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4—122no—
832C4—122no—
833C4—122no—
834C4—122no—
835C4—122no—
836C4—241no—
837C3#1445411yescharacteristic, complemented, Sylow
838C2#7388011yescharacteristic
839C2#7468511yescharacteristic
840C2#7496211yescharacteristic
841C2#7529611yescharacteristic
842C2#7597411yescharacteristic
843C2#7598711yescharacteristic
844C2#7648611yescharacteristic
845C2#7707311yescharacteristic
846C2#7723611yescharacteristic
847C2#7739511yescharacteristic
848C2#7739811yescharacteristic
849C2#7790511yescharacteristic
850C2#7790611yescharacteristic
851C2#7791311yescharacteristic
852C2#7829711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1441C2
socle, prime radical, cosocleC24×C3C24
hypercenter#1441D3
hypocenterC3#14454
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
52. #4975C4semidirect
837. C3#14454semidirect

Maximal subgroups

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

subgroupindex
C2×#49752
C3×#14412
#715662
#715642
#694112
#694092
#694072
#694062
#694052
#694032
#694012
#144543