Finite Group Databasebeta

← #29700360

Subgroups — #29700360

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839907C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3#21448857C211yesmaximal, characteristic, complemented
4#21448649C211yesmaximal, characteristic, complemented
5#21446697C211yesmaximal, characteristic, complemented
6#21446506C211yesmaximal, characteristic, complemented
7#21446456C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic, complemented
9#21446165C211yesmaximal, characteristic, complemented
10#21446150C211yesmaximal, characteristic, complemented
11#21446064C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#21445595C211yesmaximal, characteristic, complemented
15C2×C61×#416C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22#16839907C418yescomplemented
23#16839871—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33#16839669C2211yescharacteristic
34#16839669C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839662—21no—
37#16839658C2211yescharacteristic
38#16839653—21no—
39#16839642—21no—
40#16839642—21no—
41#16839638—21no—
42#16839625—21no—
43#16839622C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4×#11758198—21no—
46C4×C22⋊Dic61C2211yescharacteristic
47C2×#14519684—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C61×#416—24no—
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C23×Dic61—21no—
66C22×C4×D61—21no—
67C2×#11758201—41no—
68C2×#11758201—41no—
69C2×#11758201C2×C414yescomplemented
70C2×#11758199—22no—
71C2×#11758199—22no—
72C2×#11758199C2×C414yes—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519751—22no—
76#14519751C2×C414yescomplemented
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—41no—
80D4×Dic61—41no—
81#14519739—22no—
82#14519739—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61D411yescharacteristic
91C2×C22⋊Dic61D411yescharacteristic
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99#14519710—41no—
100#14519708—22no—
101#14519701C2×C414yescomplemented
102#14519699—22no—
103#14519699—41no—
104#14519698C2×C414yescomplemented
105C22⋊#92418C2×C414yescomplemented
106#14519687—22no—
107#14519687—41no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—41no—
121C2×#41×C61—41no—
122C2×#41×C61C2×C414yescomplemented
123C22×Q8×C61C2311yescharacteristic
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—22no—
129C22×C8×C61—22no—
130C22×C8×C61—41no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133#117×C61—22no—
134#117×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139#103×C61—22no—
140#103×C61—22no—
141#102×C61—22no—
142#102×C61D414yescomplemented
143C24×C61—21no—
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146#41×C61—28no—
147#41×C61—44no—
148#41×C61—44no—
149#41×C61—44no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61C22×C412yes—
156C2×D4×C61—24no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61C22×C412yes—
163C2×D4×C61C2×D412yes—
164C2×D4×C61#4112yes—
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—24no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61C22×C412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61#4112yes—
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—24no—
180C2×C22⋊D61—81no—
181C2×C22⋊D61—81no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61—81no—
190C22×Dic61—81no—
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244C22×C412yes—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—81no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—44no—
210C2×C8×C61C2×D412yes—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61C2×D412yes—
215C22⋊C4×C61—42no—
216C42×C61—42no—
217C22⋊Dic61—41no—
218C22⋊Dic61—41no—
219C22⋊Dic61—42no—
220C22⋊Dic61—42no—
221C22⋊Dic61—81no—
222#11758201—44no—
223#11758199—28no—
224#11758198—24no—
225#11758198—42no—
226#11758198—42no—
227#11758198—81no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61C22×C412yes—
234#11758196—81no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—81no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418C22×C412yes—
245C2×#92418C22×C412yes—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—21no—
249C23×C61—22no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61C4×D412yes—
260C23×C61C22×D411yescharacteristic
261C22×D61—22no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—41no—
271Q8×C61—41no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—48no—
276D4×C61C4×D414yes—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—48no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61C4×D412yes—
294C2×C4×C61C23×C411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C22⋊D61—84no—
301C2×Dic61—22no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—84no—
323C2×Dic61—84no—
324D244—22no—
325D244—22no—
326D244—41no—
327D244—41no—
328C4×D61—84no—
329C8×C61—22no—
330C8×C61—41no—
331#92418—22no—
332#92418—22no—
333#22860—611nomaximal, Sylow
334C22×C61—22no—
335C22×C61—24no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—41no—
348C22×C61C2×C4×D411yescharacteristic
349C22×C61D4211yescharacteristic
350C22×C61#54611yescharacteristic
351C22×C61#57511yescharacteristic
352C22×C61#57511yescharacteristic
353C22×C61#57611yescharacteristic
354C22×C61#57711yescharacteristic
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—81no—
366C4×C61C2×C4×D411yescharacteristic
367C4×C61#51811yescharacteristic
368C4×C61#54611yescharacteristic
369C4×C61#55111yescharacteristic
370Dic61—42no—
371Dic61—41no—
372Dic61—41no—
373Dic61—41no—
374Dic61—41no—
375Dic61—81no—
376Dic61—81no—
377C2×#449—611no—
378C2×#442—611no—
379C2×#416D6111yescharacteristic, complemented
380#2363—611no—
381#2339—611no—
382#1973—611no—
383#1935—611no—
384#1927—611no—
385#1893—611no—
386#1879—611no—
387#1877—611no—
388#1862—611no—
389#1854—611no—
390#1762—611no—
391#1752—611no—
392C2×C61—42no—
393C2×C61—44no—
394C2×C61#235811yescharacteristic
395C2×C61#294311yescharacteristic
396C2×C61#294611yescharacteristic
397C2×C61#326711yescharacteristic
398C2×C61#326811yescharacteristic
399C2×C61#330711yescharacteristic
400C2×C61#331911yescharacteristic
401D61—82no—
402C22×#41C2×D6111yescharacteristic
403C22×SD16—611no—
404C22×D8—611no—
405C23×C8C2×D6111yescharacteristic
406C2×#121—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×#117C2×D6111yescharacteristic
411#449—618no—
412#442—1224no—
413C2×#107—611no—
414C2×#106—611no—
415#416—24no—
416C2×#103—611no—
417C2×#103C2×D6111yescharacteristic
418C2×#103C2×D6111yescharacteristic
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102C2×D6111yescharacteristic
423C2×#102C2×D6111yescharacteristic
424C2×C22⋊C8—611no—
425C2×#97—611no—
426C2×#97—611no—
427#391—611no—
428#391—611no—
429#390—611no—
430#390—1221no—
431#389—611no—
432#388—1221no—
433#386—1221no—
434#386—1221no—
435#386—1221no—
436#381—1221no—
437#380—611no—
438C4×C4⋊C4—611no—
439C4×C22⋊C4—611no—
440C4×C22⋊C4—1221no—
441C2×#95—1221no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#336—611no—
447#336—611no—
448C61#2286011yescharacteristic, complemented, Sylow
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—41no—
453C2×#41—41no—
454C2×#41C4×D6114yescomplemented
455C22×Q8C22×D6111yescharacteristic
456C22×D4—21no—
457C22×D4—611no—
458C22×D4—1221no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C2×SD16—614no—
466C2×SD16—2441no—
467C2×SD16—2441no—
468C2×D8—614no—
469C2×D8—1222no—
470C2×D8—1222no—
471C22×C8—22no—
472C22×C8—22no—
473C22×C8—41no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478#121—614no—
479#121—1222no—
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1222no—
483C4×D4—2441no—
484C4×D4—2441no—
485C4×D4—2441no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—21no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—1221no—
508#107—2441no—
509#106—1222no—
510#103—22no—
511#103—22no—
512#103—614no—
513#102—22no—
514#102—614no—
515#102—1222no—
516#102—2441no—
517#102C22⋊D6114yescomplemented
518C22⋊C8—614no—
519#97—1222no—
520#97—2441no—
521#95—611no—
522#95—611no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—21no—
531C24—1221no—
532C24D4×D6111yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C2×C4×D6112yes—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—612no—
550C2×D4—1224no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—4881no—
557C2×D4—4881no—
558C2×D4C2×C4×D6112yes—
559C2×D4#1175822212yes—
560C2×D4C2×C22⋊D6112yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—4881no—
579C22×C4—4881no—
580C22×C4—4881no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4C2×C4×D6112yes—
588C22×C4D4×D6111yescharacteristic
589C22×C4#1175822412yes—
590C22×C4C23×D6111yescharacteristic
591SD16—2444no—
592D8—1228no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8—612no—
600C2×C8—612no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8C2×C22⋊D6112yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—612no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—4881no—
616C4⋊C4C2×C22⋊D6112yes—
617C22⋊C4—42no—
618C22⋊C4—1224no—
619C22⋊C4—4881no—
620C22⋊C4—4881no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C22⋊C4—2441no—
624C22⋊C4—2441no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C42—42no—
628C42—1221no—
629C42—1221no—
630C42—1221no—
631C42—1221no—
632C42—4881no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—1222no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23#1451973712yes—
654C23C2×D4×D6111yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—1222no—
664D4—1222no—
665D4—4884no—
666D4—2441no—
667D4—2441no—
668D4C4×C22⋊D6114yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—1222no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—4884no—
699C2×C4—4884no—
700C2×C4—4884no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4#1451973712yes—
710C2×C4C22×C4×D6111yescharacteristic
711C2×C4C22×C22⋊D6111yescharacteristic
712C2×C4C2×#1175822411yescharacteristic
713C2×C4C2×#1175822211yescharacteristic
714C2×C4#1451982211yescharacteristic
715C2×C4#1451982211yescharacteristic
716C8—22no—
717C8—41no—
718C8—1222no—
719C8—1222no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—4881no—
735C22—4881no—
736C22—4881no—
737C22—4881no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22C2×#1451973711yescharacteristic
742C22D4×C22⋊D6111yescharacteristic
743C22#1684040211yescharacteristic
744C22#1684055911yescharacteristic
745C22#1684055911yescharacteristic
746C22#1684056411yescharacteristic
747C22#1684056911yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—81no—
752C4—4881no—
753C4—4881no—
754C4—2441no—
755C4—2442no—
756C4—2441no—
757C4—2441no—
758C4—2441no—
759C4C2×C4×C22⋊D6111yescharacteristic
760C4#1684023511yescharacteristic
761C4#1684040611yescharacteristic
762C4#1684043811yescharacteristic
763C2—42no—
764C2—44no—
765C2—4882no—
766C2#2144879811yescharacteristic
767C2#2145461511yescharacteristic
768C2#2145465411yescharacteristic
769C2#2145734411yescharacteristic
770C2#2145735911yescharacteristic
771C2#2145779111yescharacteristic
772C2#2145797111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
cosocleC22×C4×C61C24
hypercenterC2×#416D61
hypocenterC61#22860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. #21448857C2semidirect
4. #21448649C2semidirect
5. #21446697C2semidirect
6. #21446506C2semidirect
7. #21446456C2semidirect
8. #21446247C2semidirect
9. #21446165C2semidirect
10. #21446150C2semidirect
11. #21446064C2semidirect
12. #21446018C2semidirect
13. #21445646C2semidirect
14. #21445595C2semidirect
15. C2×C61×#416C2semidirect
22. #16839907C4semidirect
69. C2×#11758201C2×C4semidirect
76. #14519751C2×C4semidirect
101. #14519701C2×C4semidirect
104. #14519698C2×C4semidirect
105. C22⋊#92418C2×C4semidirect
122. C2×#41×C61C2×C4semidirect
142. #102×C61D4semidirect
379. C2×#416D61semidirect
448. C61#22860semidirect
454. C2×#41C4×D61semidirect
517. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399072
C2×#168398712
#214488572
#214486492
#214466972
#214465062
#214464562
#214462472
#214461652
#214461502
#214460642
#214460182
#214456462
#214455952
C2×C61×#4162
#2286061