Finite Group Databasebeta

← #367573

Subgroups — #367573

Order 512.

1218 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1940C211yesmaximal, characteristic
2C2×#1940C211yesmaximal, characteristic
3C2×#1940C211yesmaximal, characteristic
4C2×#1939C211yesmaximal, characteristic
5C2×#1842C211yesmaximal, characteristic
6C2×#1771C211yesmaximal, characteristic
7C4×#389C211yesmaximal, characteristic
8#11322C211yesmaximal, characteristic
9#11322C211yesmaximal, characteristic
10#11202C211yesmaximal, characteristic
11#11202C211yesmaximal, characteristic
12#10877C211yesmaximal, characteristic
13#10876C211yesmaximal, characteristic
14#10835C211yesmaximal, characteristic
15#10693C211yesmaximal, characteristic
16C22×C4⋊C8C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic
25C22×C4⋊C8C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×#97C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30C2×#389C411yescharacteristic
31C2×#389C411yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C43C2211yescharacteristic
37#1940—24no—
38#1940—24no—
39#1940—24no—
40#1939—24no—
41#1842—24no—
42#1771—24no—
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1436C411yescharacteristic
58#1436C411yescharacteristic
59#1436C411yescharacteristic
60#1436C411yescharacteristic
61C4⋊#95C411yescharacteristic
62C4⋊#95C411yescharacteristic
63C4×#95C2211yescharacteristic
64C4×#95C2211yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C22×C4⋊C4C2×C411yescharacteristic
74C22×C4⋊C4C2×C411yescharacteristic
75C22×C4⋊C4C2×C411yescharacteristic
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C4⋊C4C2×C411yescharacteristic
78C22×C4⋊C4C2×C411yescharacteristic
79C22×C4⋊C4C2×C411yescharacteristic
80C22×C4⋊C4C2×C411yescharacteristic
81C22×C42C2×C411yescharacteristic
82C22×C42C2×C411yescharacteristic
83C22×C42C2×C411yescharacteristic
84C22×C42C2×C411yescharacteristic
85C22×C42C2311yescharacteristic
86C22×C42C2311yescharacteristic
87C22×C42C2311yescharacteristic
88C22×C42C2311yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C2×C4⋊C8—22no—
93C2×C4⋊C8—22no—
94C2×C4⋊C8—22no—
95C2×C4⋊C8—22no—
96C2×C4⋊C8—22no—
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—41no—
114C2×C4⋊C8—41no—
115C2×C4⋊C8—41no—
116C2×C4⋊C8—41no—
117C2×C4⋊C8—41no—
118C2×C4⋊C8—41no—
119C2×C4⋊C8—41no—
120C2×C4⋊C8—41no—
121C2×C4⋊C8D414yes—
122C2×#97—22no—
123C2×#97—22no—
124C2×#97—22no—
125C2×#97—22no—
126C2×#97—22no—
127C2×#97—22no—
128C2×#97—22no—
129C2×#97—41no—
130C2×#97Q814yes—
131C2×C4×C8—22no—
132C2×C4×C8—22no—
133C2×C4×C8—41no—
134#389—24no—
135#389—24no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—22no—
141C4×C4⋊C4—22no—
142C4×C4⋊C4D414yes—
143C4×C4⋊C4Q814yes—
144C2×#95C2×C411yescharacteristic
145C2×#95C2×C411yescharacteristic
146C2×#95C2×C411yescharacteristic
147C2×#95C2×C411yescharacteristic
148C2×#95C2×C411yescharacteristic
149C2×#95C2×C411yescharacteristic
150C2×#95C2×C411yescharacteristic
151C2×#95C2×C411yescharacteristic
152C2×#95C2×C411yescharacteristic
153C2×#95C2×C411yescharacteristic
154C2×#95C2×C411yescharacteristic
155C2×#95C2×C411yescharacteristic
156C2×#95C2×C411yescharacteristic
157C2×#95C2×C411yescharacteristic
158C2×#95C2×C411yescharacteristic
159C2×#95C2×C411yescharacteristic
160C43—22no—
161C43—22no—
162#336—22no—
163#336—22no—
164#336—22no—
165#336—22no—
166#336—22no—
167#336—22no—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—41no—
173#336—41no—
174#336D414yes—
175#336Q814yes—
176C23×C4C22×C411yescharacteristic
177C23×C4C22×C411yescharacteristic
178C23×C4C22×C411yescharacteristic
179C23×C4C22×C411yescharacteristic
180C23×C4C22×C411yescharacteristic
181C23×C4C22×C411yescharacteristic
182C23×C4C22×C411yescharacteristic
183C23×C4C22×C411yescharacteristic
184C23×C4C22×C411yescharacteristic
185C23×C4C22×C411yescharacteristic
186C23×C4C22×C411yescharacteristic
187C23×C4C22×C411yescharacteristic
188C23×C4C22×C411yescharacteristic
189C23×C4C22×C411yescharacteristic
190C23×C4C2411yescharacteristic
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8C2×D412yes—
240C22×C8C2×D412yes—
241C22×C8C2×D412yes—
242C22×C8C2×D412yes—
243C22×C8C2×Q812yes—
244C22×C8C2×Q812yes—
245C22×C8C2×Q812yes—
246C22×C8C2×Q812yes—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—41no—
263C2×C4⋊C4—41no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4—41no—
266C2×C4⋊C4—41no—
267C2×C4⋊C4—41no—
268C2×C4⋊C4C4⋊C414yes—
269C2×C4⋊C4C4⋊C414yes—
270C2×C4⋊C4M1614yes—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—41no—
308C2×C42—41no—
309C2×C42—41no—
310C2×C42—41no—
311C2×C42C2×D412yes—
312C2×C42C2×D412yes—
313C2×C42C2×D412yes—
314C2×C42C2×D412yes—
315C2×C42C2×D412yes—
316C2×C42C2×Q812yes—
317C2×C42C2×Q812yes—
318C2×C42C2×Q812yes—
319C2×C42C2×Q812yes—
320C2×C42C2×Q812yes—
321C2×C42#4112yes—
322C2×C42#4112yes—
323C2×C42#4112yes—
324C2×C42#4112yes—
325C4⋊C8—28no—
326C4⋊C8—44no—
327C4⋊C8—44no—
328C4⋊C8—44no—
329C4⋊C8—44no—
330C4⋊C8—44no—
331C4⋊C8—44no—
332C4⋊C8—44no—
333C4⋊C8—44no—
334C4⋊C8—44no—
335#97—28no—
336#97—44no—
337#97—44no—
338C4×C8—44no—
339#95—22no—
340#95—22no—
341#95—22no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—41no—
351#95—41no—
352#95C4⋊C414yes—
353#95C4⋊C414yes—
354#95M1614yes—
355C24C23×C411yescharacteristic
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4C2×C4⋊C412yes—
433C22×C4C2×C4⋊C412yes—
434C22×C4C2×C4⋊C412yes—
435C22×C4C2×C4⋊C412yes—
436C22×C4C2×C4⋊C412yes—
437C22×C4C2×C4⋊C412yes—
438C22×C4C4×D412yes—
439C22×C4C4×D412yes—
440C22×C4C4×D412yes—
441C22×C4C4×D412yes—
442C22×C4C4×Q812yes—
443C22×C4C4×Q812yes—
444C22×C4C4×Q812yes—
445C22×C4C4×Q812yes—
446C22×C4C2×M1612yes—
447C22×C4C2×M1612yes—
448C22×C4C2×M1612yes—
449C22×C4C2×M1612yes—
450C22×C4C2×M1612yes—
451C22×C4C2×M1612yes—
452C22×C4#13112yes—
453C22×C4#13112yes—
454C22×C4C22×D411yescharacteristic
455C22×C4C22×D411yescharacteristic
456C22×C4C22×D411yescharacteristic
457C22×C4C22×Q811yescharacteristic
458C22×C4C22×Q811yescharacteristic
459C22×C4C22×Q811yescharacteristic
460C22×C4C2×#4111yescharacteristic
461C22×C4C2×#4111yescharacteristic
462C22×C4C2×#4111yescharacteristic
463C22×C4C2×#4111yescharacteristic
464C22×C4H(5,𝔽2)11yescharacteristic
465C22×C4H(5,𝔽2)11yescharacteristic
466C22×C42−1+411yescharacteristic
467C22×C42−1+411yescharacteristic
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8C4⋊Q814yes—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—44no—
527C4⋊C4—44no—
528C4⋊C4—44no—
529C4⋊C4—44no—
530C4⋊C4—44no—
531C4⋊C4—44no—
532C42—28no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—44no—
550C42—44no—
551C42—44no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42#12114yes—
561C42C22⋊Q814yes—
562C42#12514yes—
563C42C4⋊Q814yes—
564C23C22×C4⋊C411yescharacteristic
565C23C2×C4×D411yescharacteristic
566C23C2×C4×D411yescharacteristic
567C23C2×C4×Q811yescharacteristic
568C23C2×C4×Q811yescharacteristic
569C23#52011yescharacteristic
570C23#52011yescharacteristic
571C23C22×M1611yescharacteristic
572C23C22×M1611yescharacteristic
573C23C2×#13111yescharacteristic
574C23C2×#13111yescharacteristic
575C23#56811yescharacteristic
576C23#56811yescharacteristic
577C23#56811yescharacteristic
578C23#56811yescharacteristic
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4#38914yes—
673C2×C4#38914yes—
674C2×C4#42314yes—
675C2×C4#43514yes—
676C2×C4#44614yes—
677C2×C4C2×#12111yescharacteristic
678C2×C4C2×C22⋊Q811yescharacteristic
679C2×C4C2×#12511yescharacteristic
680C2×C4C2×C4⋊Q811yescharacteristic
681C2×C4C2×C4⋊Q811yescharacteristic
682C2×C4#53211yescharacteristic
683C2×C4#53311yescharacteristic
684C2×C4#53311yescharacteristic
685C2×C4#54011yescharacteristic
686C2×C4#54111yescharacteristic
687C2×C4#54411yescharacteristic
688C2×C4#54411yescharacteristic
689C2×C4D4211yescharacteristic
690C2×C4D4211yescharacteristic
691C2×C4#54611yescharacteristic
692C2×C4#54711yescharacteristic
693C2×C4#54711yescharacteristic
694C2×C4#54811yescharacteristic
695C2×C4D4×Q811yescharacteristic
696C2×C4D4×Q811yescharacteristic
697C2×C4D4×Q811yescharacteristic
698C2×C4#55011yescharacteristic
699C2×C4#55211yescharacteristic
700C2×C4#55311yescharacteristic
701C2×C4#55411yescharacteristic
702C2×C4#55411yescharacteristic
703C2×C4#55711yescharacteristic
704C2×C4Q8211yescharacteristic
705C8—24no—
706C8—42no—
707C8—42no—
708C8—42no—
709C8—42no—
710C8—42no—
711C8—81no—
712C8—81no—
713C22C2×#38911yescharacteristic
714C22C4×C4⋊Q811yescharacteristic
715C22#233011yescharacteristic
716C22D4×C4⋊C411yescharacteristic
717C22Q8×C4⋊C411yescharacteristic
718C22#236011yescharacteristic
719C22#236111yescharacteristic
720C22C2×#42311yescharacteristic
721C22#290511yescharacteristic
722C22#290611yescharacteristic
723C22#290611yescharacteristic
724C22C2×#43511yescharacteristic
725C22#292911yescharacteristic
726C22#293011yescharacteristic
727C22#293211yescharacteristic
728C22D4×M1611yescharacteristic
729C22D4×M1611yescharacteristic
730C22D4×M1611yescharacteristic
731C22#293511yescharacteristic
732C22C2×#44611yescharacteristic
733C22#296111yescharacteristic
734C22#296211yescharacteristic
735C22#296211yescharacteristic
736C22#296211yescharacteristic
737C22Q8×M1611yescharacteristic
738C22Q8×M1611yescharacteristic
739C22Q8×M1611yescharacteristic
740C22#298911yescharacteristic
741C22#298911yescharacteristic
742C22#299011yescharacteristic
743C22#299011yescharacteristic
744C22#299211yescharacteristic
745C22#299211yescharacteristic
746C22#299511yescharacteristic
747C22#299511yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—81no—
761C4—81no—
762C4#242811yescharacteristic
763C4#242911yescharacteristic
764C4#244011yescharacteristic
765C4#244111yescharacteristic
766C4#250611yescharacteristic
767C4#250711yescharacteristic
768C4#255011yescharacteristic
769C4#255111yescharacteristic
770C2#1400511yescharacteristic
771C2#2114611yescharacteristic
772C2#2114711yescharacteristic
773C2#2171311yescharacteristic
774C2#2171411yescharacteristic
775C2#2230511yescharacteristic
776C2#2230511yescharacteristic
777C2#2264811yescharacteristic
778C2#2265211yescharacteristic
779C2#2272211yescharacteristic
780C2#2272311yescharacteristic
781C2#2295411yescharacteristic
782C2#2295511yescharacteristic
783C2#2298711yescharacteristic
784C2#2298811yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socle, prime radicalC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#19402
C2×#19392
C2×#18422
C2×#17712
C4×#3892
#113222
#112022
#108772
#108762
#108352
#106932