Finite Group Databasebeta

← #10722671

Subgroups — #10722671

Order 768.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4943C211yesmaximal, characteristic
2C2×#4942C211yesmaximal, characteristic
3C2×#4652C211yesmaximal, characteristic, complemented
4C3×#1437C211yesmaximal, characteristic
5#71547C211yesmaximal, characteristic
6#71547C211yesmaximal, characteristic
7#71545C211yesmaximal, characteristic
8#71544C211yesmaximal, characteristic
9#71536C211yesmaximal, characteristic, complemented
10#71534C211yesmaximal, characteristic, complemented
11#69421C211yesmaximal, characteristic, complemented
12#69418C211yesmaximal, characteristic, complemented
13#69414C211yesmaximal, characteristic, complemented
14#69409C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14372—31nomaximal, Sylow
17C24×Dic3C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
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#4943—24no—
53#4942C418yescomplemented
54#4652—24no—
55C2×#387—31no—
56C2×#381—31no—
57C2×#380—31no—
58#1445—31no—
59#1443—31no—
60#1442—31no—
61#1441—31no—
62#1439—31no—
63#1439—31no—
64#1437—31no—
65#1437D311yescharacteristic
66#1436—31no—
67#1436—31no—
68#1434—31no—
69C22⋊#95—31no—
70C25×C3C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×Dic3—22no—
78C23×Dic3—22no—
79C23×Dic3—22no—
80C23×Dic3—22no—
81C23×Dic3—41no—
82C23×Dic3—41no—
83C23×Dic3C2×C414yes—
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—41no—
97C2×C3×C22⋊C4—41no—
98C2×C3×C22⋊C4—41no—
99C2×C3×C22⋊C4—41no—
100C2×C3×C22⋊C4C2×C414yes—
101C2×C3×C42—22no—
102C2×C3×C42—41no—
103C2×C3×C42—41no—
104C2×#217—22no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—41no—
109C2×#217—41no—
110C2×#217—41no—
111C2×#217—41no—
112C2×#217C2×C414yes—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—41no—
118C2×Dic3⋊C4—41no—
119C2×Dic3⋊C4—41no—
120C2×Dic3⋊C4—41no—
121C2×Dic3⋊C4—41no—
122C2×Dic3⋊C4—41no—
123C2×Dic3⋊C4C2×C414yes—
124C2×Dic3⋊C4C2×C414yes—
125C2×C4×Dic3—22no—
126C2×C4×Dic3—41no—
127C2×C4×Dic3—41no—
128C3×#95—22no—
129C3×#95—41no—
130C3×#95—41no—
131C3⋊#95—22no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135C3⋊#95—22no—
136C3⋊#95—22no—
137C3⋊#95—22no—
138C3⋊#95—22no—
139C3⋊#95—41no—
140C3⋊#95—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95C2×C414yes—
148C3⋊#95C2×C414yes—
149C3⋊#95D414yes—
150C24×C4—31no—
151C22×C4⋊C4—31no—
152C22×C4⋊C4—31no—
153C22×C4⋊C4—31no—
154C22×C4⋊C4—31no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—31no—
158C22×C22⋊C4C2×D311yescharacteristic
159C22×C22⋊C4C2×D311yescharacteristic
160C22×C22⋊C4C2×D311yescharacteristic
161C22×C42—31no—
162C22×C42C2×D311yescharacteristic
163#387—64no—
164#381—64no—
165#380—38no—
166C2×#95—31no—
167C2×#95—31no—
168C2×#95—31no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95—31no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
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×#95C2×D311yescharacteristic
186C2×#95C2×D311yescharacteristic
187C2×#95C2×D311yescharacteristic
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3C22×C412yes—
201C24×C3#4112yes—
202C24×C3#4112yes—
203C24×C3C2411yescharacteristic
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×C4—21no—
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×C4C22×C412yes—
243C22×C3×C4C22×C412yes—
244C22×C3×C4C2×D412yes—
245C22×C3×C4#4112yes—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—28no—
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×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—28no—
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—44no—
297C22×Dic3—44no—
298C22×Dic3—44no—
299C22×Dic3—44no—
300C22×Dic3—44no—
301C22×Dic3C22×C412yes—
302C22×Dic3C22×C412yes—
303C22×Dic3C22×C412yes—
304C22×Dic3C22×C412yes—
305C22×Dic3C2×D412yes—
306C22×Dic3C2×D412yes—
307C22×Dic3#4112yes—
308C22×Dic3#4112yes—
309C3×C22⋊C4—44no—
310C3×C22⋊C4—44no—
311C3×C22⋊C4—44no—
312C3×C42—44no—
313#217—44no—
314#217—44no—
315#217—44no—
316Dic3⋊C4—28no—
317Dic3⋊C4—44no—
318Dic3⋊C4—44no—
319Dic3⋊C4—44no—
320C4×Dic3—44no—
321C25C22×D311yescharacteristic
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—34no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—62no—
332C23×C4—62no—
333C23×C4—62no—
334C23×C4—62no—
335C23×C4—121no—
336C23×C4—121no—
337C23×C4C22×D311yescharacteristic
338C23×C4C22×D311yescharacteristic
339C23×C4C22×D311yescharacteristic
340C23×C4C22×D311yescharacteristic
341C23×C4C22×D311yescharacteristic
342C23×C4C22×D311yescharacteristic
343C2×C4⋊C4—34no—
344C2×C4⋊C4—34no—
345C2×C4⋊C4—62no—
346C2×C4⋊C4—62no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—62no—
349C2×C4⋊C4—121no—
350C2×C4⋊C4—121no—
351C2×C4⋊C4—121no—
352C2×C4⋊C4—121no—
353C2×C4⋊C4—121no—
354C2×C4⋊C4—121no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—34no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—62no—
365C2×C22⋊C4—62no—
366C2×C22⋊C4—62no—
367C2×C22⋊C4—62no—
368C2×C22⋊C4—121no—
369C2×C22⋊C4—121no—
370C2×C22⋊C4—121no—
371C2×C22⋊C4—121no—
372C2×C22⋊C4C4×D314yes—
373C2×C42—22no—
374C2×C42—41no—
375C2×C42—41no—
376C2×C42—62no—
377C2×C42—121no—
378C2×C42—121no—
379#95—22no—
380#95—34no—
381#95—34no—
382#95—34no—
383#95—41no—
384#95—41no—
385#95—62no—
386#95—62no—
387#95—62no—
388#95—62no—
389#95—62no—
390#95—62no—
391#95—62no—
392#95—62no—
393#95—121no—
394#95—121no—
395#95—121no—
396#95—121no—
397#95—121no—
398#95—121no—
399#95—121no—
400#95—121no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3#11714yes—
436C23×C3C23×C411yescharacteristic
437C23×C3C22×D411yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3C2×#4111yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3C2×#4111yescharacteristic
442C23×C3C2×#4111yescharacteristic
443C23×C3H(5,𝔽2)11yescharacteristic
444C23×C3H(5,𝔽2)11yescharacteristic
445C23×C3H(5,𝔽2)11yescharacteristic
446C23×C3H(5,𝔽2)11yescharacteristic
447C23×C3H(5,𝔽2)11yescharacteristic
448C23×C32−1+411yescharacteristic
449C23×C32−1+411yescharacteristic
450C23×C32−1+411yescharacteristic
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—416no—
515C2×Dic3—41no—
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—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3C4×D414yes—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24—21no—
562C24C2×C4×D312yes—
563C24#23512yes—
564C24#23512yes—
565C24C23×D311yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
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—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—32no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—32no—
608C22×C4—32no—
609C22×C4—32no—
610C22×C4—32no—
611C22×C4—32no—
612C22×C4—68no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—68no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
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—124no—
663C22×C4—124no—
664C22×C4—124no—
665C22×C4—124no—
666C22×C4—124no—
667C22×C4C2×C4×D312yes—
668C22×C4C2×C4×D312yes—
669C22×C4D3×D412yes—
670C22×C4#23712yes—
671C4⋊C4—68no—
672C4⋊C4—124no—
673C4⋊C4—124no—
674C4⋊C4—124no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—124no—
679C22⋊C4—124no—
680C22⋊C4—124no—
681C42—44no—
682C42—124no—
683C22×C3—24no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3C2×#11711yescharacteristic
699C22×C3C2×C4×D411yescharacteristic
700C22×C3C4×#4111yescharacteristic
701C22×C3#51811yescharacteristic
702C22×C3#51811yescharacteristic
703C22×C3#51911yescharacteristic
704C22×C3#52011yescharacteristic
705C22×C3#53511yescharacteristic
706C22×C3#53711yescharacteristic
707C22×C3#53811yescharacteristic
708C22×C3#53811yescharacteristic
709C22×C3#53911yescharacteristic
710C22×C3#53911yescharacteristic
711C22×C3#53911yescharacteristic
712C22×C3#53911yescharacteristic
713C22×C3#54011yescharacteristic
714C22×C3#54011yescharacteristic
715C22×C3#54011yescharacteristic
716C22×C3#54211yescharacteristic
717C22×C3#54611yescharacteristic
718C22×C3#54611yescharacteristic
719C22×C3#54711yescharacteristic
720C22×C3#54811yescharacteristic
721C22×C3#55111yescharacteristic
722C22×C3#55111yescharacteristic
723C22×C3#55111yescharacteristic
724C22×C3#55111yescharacteristic
725C22×C3#55211yescharacteristic
726C22×C3#55211yescharacteristic
727C22×C3#55211yescharacteristic
728C22×C3#55611yescharacteristic
729C22×C3#56211yescharacteristic
730C22×C3#56211yescharacteristic
731C22×C3#56311yescharacteristic
732C22×C3#56311yescharacteristic
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—42no—
736C3×C4—42no—
737C3×C4—81no—
738C3×C4—81no—
739Dic3—24no—
740Dic3—42no—
741Dic3—42no—
742Dic3—42no—
743Dic3—42no—
744Dic3—42no—
745Dic3—81no—
746Dic3—81no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#87214yes—
782C23C22×C4×D311yescharacteristic
783C23C2×#23511yescharacteristic
784C23C2×#23511yescharacteristic
785C23C2×D3×D411yescharacteristic
786C23C2×#23711yescharacteristic
787C23#100411yescharacteristic
788C23#100411yescharacteristic
789C23#100411yescharacteristic
790C23#100411yescharacteristic
791C23D3×#4111yescharacteristic
792C23D3×#4111yescharacteristic
793C23#100911yescharacteristic
794C23#101011yescharacteristic
795C23#101011yescharacteristic
796C23#101011yescharacteristic
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—34no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—1216no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—121no—
876C2×C4—121no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4—121no—
892C2×C4—121no—
893C2×C4—121no—
894C2×C4—121no—
895C2×C4—121no—
896C2×C3—44no—
897C2×C3#231311yescharacteristic
898C2×C3#232411yescharacteristic
899C2×C3#233311yescharacteristic
900C2×C3#234211yescharacteristic
901C2×C3#234311yescharacteristic
902C2×C3#236211yescharacteristic
903C2×C3#237811yescharacteristic
904C2×C3#269511yescharacteristic
905C2×C3#269611yescharacteristic
906C2×C3#270611yescharacteristic
907C2×C3#270711yescharacteristic
908C2×C3#273811yescharacteristic
909C2×C3#274011yescharacteristic
910C2×C3#274311yescharacteristic
911C2×C3#274511yescharacteristic
912C22—24no—
913C22—24no—
914C22—24no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22C2×#87211yescharacteristic
928C22#548611yescharacteristic
929C22#549011yescharacteristic
930C22#549511yescharacteristic
931C22#551611yescharacteristic
932C22#552711yescharacteristic
933C22#553111yescharacteristic
934C22C4×#23711yescharacteristic
935C22#554111yescharacteristic
936C22C4×D3×D411yescharacteristic
937C22#554511yescharacteristic
938C22#554611yescharacteristic
939C22#555011yescharacteristic
940C22#555611yescharacteristic
941C22#555611yescharacteristic
942C22#556411yescharacteristic
943C22#556411yescharacteristic
944C22#556411yescharacteristic
945C22#556411yescharacteristic
946C22#559311yescharacteristic
947C22#559711yescharacteristic
948C22#561111yescharacteristic
949C22#561311yescharacteristic
950C22#561511yescharacteristic
951C22#561911yescharacteristic
952C22#562111yescharacteristic
953C22#565011yescharacteristic
954C22#565111yescharacteristic
955C22#566311yescharacteristic
956C22#566911yescharacteristic
957C22#567711yescharacteristic
958C22#568411yescharacteristic
959C22#570211yescharacteristic
960C22#571211yescharacteristic
961C22#571511yescharacteristic
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—64no—
967C4—81no—
968C4—81no—
969C4—122no—
970C4—122no—
971C4—122no—
972C4—122no—
973C4—122no—
974C4—241no—
975C4—241no—
976C3#1437211yescharacteristic, complemented, Sylow
977C2—44no—
978C2#7344511yescharacteristic
979C2#7345511yescharacteristic
980C2#7357411yescharacteristic
981C2#7466811yescharacteristic
982C2#7480611yescharacteristic
983C2#7483511yescharacteristic
984C2#7547811yescharacteristic
985C2#7549211yescharacteristic
986C2#7568911yescharacteristic
987C2#7571411yescharacteristic
988C2#7571811yescharacteristic
989C2#7572711yescharacteristic
990C2#7629611yescharacteristic
991C2#7638411yescharacteristic
992C2#7639011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC25×C3C23
hypercenter#1437D3
hypocenterC3#14372
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#4652C2semidirect
9. #71536C2semidirect
10. #71534C2semidirect
11. #69421C2semidirect
12. #69418C2semidirect
13. #69414C2semidirect
14. #69409C2semidirect
15. #69406C2semidirect
53. #4942C4semidirect
976. C3#14372semidirect

Maximal subgroups

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

subgroupindex
C2×#49432
C2×#49422
C2×#46522
C3×#14372
#715472
#715452
#715442
#715362
#715342
#694212
#694182
#694142
#694092
#694062
#143723