Finite Group Databasebeta

← #29727473

Subgroups — #29727473

Order 15616.

1106 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839964C211yesmaximal, characteristic, complemented
2C2×#16839922C211yesmaximal, characteristic
3C2×#16839922C211yesmaximal, characteristic
4C2×C4×#11758201C211yesmaximal, characteristic, complemented
5#21448650C211yesmaximal, characteristic
6#21447197C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21447012C211yesmaximal, characteristic, complemented
9#21446919C211yesmaximal, characteristic, complemented
10#21446679C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446160C211yesmaximal, characteristic, complemented
13#21446156C211yesmaximal, characteristic, complemented
14#21446065C211yesmaximal, characteristic, complemented
15C61×#2429C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23#16839964—24no—
24#16839922—24no—
25#16839922—24no—
26C4×#11758201—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839668C2211yescharacteristic
43#16839638—21no—
44#16839638—21no—
45#16839624—21no—
46#16839622C2211yescharacteristic
47#95×D61—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C61×#398—21no—
57C61×#396—21no—
58C61×#391C2211yescharacteristic
59C61×#389—21no—
60C61×#389C2211yescharacteristic
61C61×#388—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C22×Dic122C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758202—22no—
76C2×#11758202—22no—
77C2×#11758202—22no—
78C2×#11758202—22no—
79C2×#11758202—41no—
80C2×#11758202—41no—
81C2×#11758201—22no—
82C2×#11758201—22no—
83C2×#11758201—22no—
84C2×#11758201—22no—
85C2×#11758201—22no—
86C2×#11758201D414yes—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—41no—
94C4×D244—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100#14519710—41no—
101#14519708—22no—
102C4⋊#92418—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701—22no—
106#14519701—41no—
107#14519700—22no—
108#14519700—22no—
109#14519697—22no—
110#14519697D414yes—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C4×#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×Q8×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C4⋊Q8×C61—22no—
123C4⋊Q8×C61—41no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127C22⋊Q8×C61—41no—
128C4×Q8×C61—22no—
129C4×Q8×C61—41no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61D411yescharacteristic
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C42×C61—21no—
143C2×C42×C61C2311yescharacteristic
144C2×C42×C61C2311yescharacteristic
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61C2×D411yescharacteristic
151C23×D61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61C2×D412yes—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—24no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186#11758222—44no—
187#11758222—44no—
188#11758222—44no—
189#11758222—44no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244C2×D412yes—
194C2×D244C2×D412yes—
195C2×D244#4112yes—
196C2×C4×D61—24no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—81no—
204C2×C4×D61—81no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122#4112yes—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61—42no—
217C4⋊C4×C61—42no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—42no—
230C22⋊Dic61—81no—
231#11758202—44no—
232#11758202—44no—
233#11758201—28no—
234#11758201—44no—
235#11758198—42no—
236#11758198—42no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418C2×D412yes—
252C2×#92418C2×D412yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61C22×D411yescharacteristic
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—41no—
271Q8×C61—41no—
272Q8×C61—41no—
273Q8×C61—41no—
274Q8×C61—41no—
275Q8×C61—41no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61#13512yes—
306C2×C4×C61#13712yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C22⋊D61—48no—
314C2×Dic61—22no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323D244—22no—
324D244—22no—
325D244—22no—
326D244#12114yes—
327C4×D61—48no—
328C4×D61—84no—
329C4×D61—84no—
330Dic122—22no—
331Dic122—22no—
332Dic122—41no—
333Dic122—41no—
334#92418—22no—
335#92418—22no—
336#92418—41no—
337#92418—41no—
338#25154—611nomaximal, Sylow
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61#52511yescharacteristic
347C22×C61D4211yescharacteristic
348C22×C61D4211yescharacteristic
349C22×C61C2×#13511yescharacteristic
350C22×C61C2×#13711yescharacteristic
351C22×C61#57711yescharacteristic
352C22×C61#57811yescharacteristic
353C2×D61—24no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—42no—
367C4×C61—81no—
368C4×C61—81no—
369C4×C61C2×#12111yescharacteristic
370C4×C61#53811yescharacteristic
371C4×C61#54611yescharacteristic
372C4×C61#54611yescharacteristic
373Dic61—42no—
374Dic61—81no—
375Dic61—81no—
376C2×#461—611no—
377C2×#452—611no—
378C2×#452—611no—
379C2×C4×SD16—611no—
380#2429D6111yescharacteristic, complemented
381#2339—611no—
382#2066—611no—
383#2036—611no—
384#2035—611no—
385#2016—611no—
386#1969—611no—
387#1923—611no—
388#1878—611no—
389#1877—611no—
390#1862—611no—
391C2×C61—81no—
392C2×C61#242411yescharacteristic
393C2×C61#310711yescharacteristic
394C2×C61#312011yescharacteristic
395C2×C61#326611yescharacteristic
396C2×C61#327611yescharacteristic
397C2×C61#328211yescharacteristic
398C2×C61#328311yescharacteristic
399D61—44no—
400C22×#41—611no—
401C22×Q16—611no—
402C22×Q16—611no—
403C22×SD16—611no—
404C22×SD16—611no—
405C2×C4⋊Q8C2×D6111yescharacteristic
406C2×C22⋊Q8C2×D6111yescharacteristic
407C2×C22⋊Q8C2×D6111yescharacteristic
408C2×C4×Q8C2×D6111yescharacteristic
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411#461—1224no—
412#452—1224no—
413#452—1224no—
414C4×SD16—1224no—
415C2×#107—611no—
416C2×#106—611no—
417C2×C4⋊C8—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×C22⋊C8—611no—
427C2×C22⋊C8—611no—
428C2×C4×C8—611no—
429#398—21no—
430#396—21no—
431#391—611no—
432#391—611no—
433#391C2×D6111yescharacteristic
434#389—21no—
435#389C2×D6111yescharacteristic
436#388—21no—
437#386—1221no—
438#386—1221no—
439#381—1221no—
440#380—611no—
441C4×C22⋊C4C2×D6111yescharacteristic
442C2×#95—1221no—
443#340—611no—
444#340—611no—
445#336—611no—
446#336—611no—
447C61#2515411yescharacteristic, complemented, Sylow
448C2×#41—1222no—
449C2×#41—1222no—
450C2×#41—1222no—
451C2×#41—1222no—
452C2×#41—2441no—
453C2×#41—2441no—
454C22×Q8—611no—
455C22×Q8C22×D6111yescharacteristic
456C22×Q8C22×D6111yescharacteristic
457C22×D4—611no—
458C22×D4—1221no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4C22×D6111yescharacteristic
463C2×Q16—1222no—
464C2×Q16—1222no—
465C2×Q16—1222no—
466C2×Q16—1222no—
467C2×Q16—2441no—
468C2×Q16—2441no—
469C2×SD16—614no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—1222no—
473C2×SD16—1222no—
474C2×SD16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C4⋊Q8—22no—
480C4⋊Q8—41no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—41no—
484C22⋊Q8—41no—
485C4×Q8—22no—
486C4×Q8—41no—
487C4×D4—1222no—
488C4×D4—1222no—
489C4×D4—2441no—
490C4×D4—2441no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4C22⋊D6111yescharacteristic
507C2×C22⋊C4C22⋊D6111yescharacteristic
508C2×C42—21no—
509C2×C42C22×D6111yescharacteristic
510C2×C42C22×D6111yescharacteristic
511#107—2441no—
512#106—1222no—
513C4⋊C8—1222no—
514#103—1222no—
515#103—1222no—
516#103—1222no—
517#103—1222no—
518#103—1222no—
519#103—2441no—
520#102—614no—
521#102—1222no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524C4×C8—1222no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—1221no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95C22⋊D6111yescharacteristic
534#95C22⋊D6111yescharacteristic
535C24—1221no—
536C24C2×C22⋊D6111yescharacteristic
537#41—2444no—
538#41—2444no—
539#41—2444no—
540#41—2444no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—612no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8D4×D6112yes—
559C2×D4—612no—
560C2×D4—612no—
561C2×D4—612no—
562C2×D4—1224no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—2442no—
567C2×D4—2442no—
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—1224no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—4881no—
583C22×C4—4881no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4C2×C22⋊D6111yescharacteristic
591C22×C4C2×C22⋊D6111yescharacteristic
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C23×D6111yescharacteristic
596Q16—2444no—
597Q16—2444no—
598SD16—1228no—
599SD16—2444no—
600C2×C8—612no—
601C2×C8—612no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4D4×D6112yes—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—4881no—
631C22⋊C4—2442no—
632C22⋊C4—2442no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—42no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—1222no—
646C23—1222no—
647C23—1222no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23C22×C22⋊D6111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—1222no—
662Q8—1222no—
663Q8—2441no—
664Q8—2441no—
665D4—614no—
666D4—1222no—
667D4—1222no—
668D4—1222no—
669D4—2448no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
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—1222no—
700C2×C4—4884no—
701C2×C4—4884no—
702C2×C4—2448no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4#1451979712yes—
712C2×C4#1451980812yes—
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4#41×D6111yescharacteristic
716C2×C4#41×D6111yescharacteristic
717C2×C4#1451982211yescharacteristic
718C2×C4#1451982211yescharacteristic
719C8—1222no—
720C8—1222no—
721C8—2441no—
722C8—2441no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—1224no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22#1684026911yescharacteristic
738C22D4×C22⋊D6111yescharacteristic
739C22D4×C22⋊D6111yescharacteristic
740C22C2×#1451979711yescharacteristic
741C22C2×#1451980811yescharacteristic
742C22#1684057011yescharacteristic
743C22#1684057711yescharacteristic
744C4—22no—
745C4—22no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—81no—
752C4—81no—
753C4—4881no—
754C4—4881no—
755C4—2442no—
756C4#121×D6111yescharacteristic
757C4#1684034411yescharacteristic
758C4#1684040111yescharacteristic
759C4#1684040911yescharacteristic
760C2—81no—
761C2—2444no—
762C2#2144935211yescharacteristic
763C2#2145588411yescharacteristic
764C2#2145602711yescharacteristic
765C2#2145733011yescharacteristic
766C2#2145746511yescharacteristic
767C2#2145752711yescharacteristic
768C2#2145753711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2429C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenter#2429D61
hypocenterC61#25154
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×#16839964C2semidirect
4. C2×C4×#11758201C2semidirect
6. #21447197C2semidirect
7. #21447019C2semidirect
8. #21447012C2semidirect
9. #21446919C2semidirect
10. #21446679C2semidirect
11. #21446427C2semidirect
12. #21446160C2semidirect
13. #21446156C2semidirect
14. #21446065C2semidirect
15. C61×#2429C2semidirect
380. #2429D61semidirect
447. C61#25154semidirect

Maximal subgroups

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

subgroupindex
C2×#168399642
C2×#168399222
C2×C4×#117582012
#214486502
#214471972
#214470192
#214470122
#214469192
#214466792
#214464272
#214461602
#214461562
#214460652
C61×#24292
#2515461