Finite Group Databasebeta

← #29700505

Subgroups — #29700505

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839897C211yesmaximal, characteristic
2C2×#16839844C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic, complemented
4#21448837C211yesmaximal, characteristic, complemented
5#21448640C211yesmaximal, characteristic, complemented
6#21446684C211yesmaximal, characteristic, complemented
7#21446504C211yesmaximal, characteristic, complemented
8#21446246C211yesmaximal, characteristic, complemented
9#21446166C211yesmaximal, characteristic, complemented
10#21446164C211yesmaximal, characteristic, complemented
11#21446067C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1925C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×D488C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×C4×D244—21no—
22C2×C4×D244C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×#14519739C2211yescharacteristic, complemented
25C2×C4⋊C4×D61C2211yescharacteristic
26C2×C22⋊C4×D61—21no—
27#16839897C418yescomplemented
28#16839844—24no—
29C2×#14519710C2211yescharacteristic, complemented
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic, complemented
36#102×D61—24no—
37C2×#14519689C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic, complemented
39C2×C8×Dic61C2211yescharacteristic, complemented
40#16839665C2211yescharacteristic
41#16839664C2211yescharacteristic, complemented
42#16839661C2211yescharacteristic, complemented
43#16839653—21no—
44#16839640—21no—
45#16839638—21no—
46#16839638—21no—
47#16839636—21no—
48#16839619C2211yescharacteristic
49#16839617—21no—
50C4×#11758198C2211yescharacteristic
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C2×#107×C61C2211yescharacteristic, complemented
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244—21no—
64C22×D244C2311yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—41no—
71C2×D4×D61—41no—
72C2×D4×D61C2×C414yescomplemented
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×D488—22no—
79C2×D488—22no—
80C2×D488C2×C414yescomplemented
81C2×#11758199—41no—
82C2×#11758199—41no—
83C2×#11758199C2×C414yescomplemented
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C2×C8×D61—22no—
87C2×C8×D61—22no—
88C2×C8×D61—41no—
89#14519752—22no—
90#14519752C2×C414yescomplemented
91C4×D244—22no—
92C4×D244—41no—
93C4×D244—44no—
94#14519739—22no—
95#14519739—22no—
96#14519739—41no—
97#14519739—41no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C4⋊C4×D61—22no—
103C4⋊C4×D61—41no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198D411yescharacteristic
114C2×#11758198D411yescharacteristic
115C22⋊C4×D61—44no—
116C2×C4×Dic61C2311yescharacteristic
117#14519710—41no—
118#14519699—22no—
119#14519699—41no—
120#14519698—22no—
121#14519697—22no—
122#14519697C2×C414yescomplemented
123#14519697D414yescomplemented
124#14519689C2×C414yescomplemented
125C4×#92418—41no—
126C8×Dic61—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684D411yescharacteristic
130#14519684D411yescharacteristic
131C22×D4×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61—21no—
140C2×C42×C61C2311yescharacteristic
141#107×C61—22no—
142#102×C61—22no—
143#102×C61C2×C414yescomplemented
144#95×C61—21no—
145C24×C61—21no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—24no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61—81no—
154C23×D61—81no—
155C23×D61C2×D411yescharacteristic
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61C22×C412yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—24no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176D4×D61—28no—
177D4×D61—44no—
178D4×D61—44no—
179D4×D61—44no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—24no—
188C2×D244—21no—
189C2×D244—42no—
190C2×D244—42no—
191C2×D244C22×C412yes—
192C2×D244C22×C412yes—
193C2×D244C2×D412yes—
194C2×D244#4112yes—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209C2×C4×D61—81no—
210C2×C4×D61—81no—
211C2×C4×D61C22×C412yes—
212C2×C4×D61#4112yes—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61C22×C412yes—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61C22×C412yes—
224C4⋊C4×C61C2×D412yes—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—81no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—42no—
230C22⋊Dic61—42no—
231C22⋊Dic61—81no—
232#11758199—44no—
233#11758198—22no—
234#11758198—24no—
235#11758198—42no—
236#11758198—42no—
237#11758198—42no—
238#11758198—42no—
239#11758198—42no—
240#11758198—81no—
241#11758198D814yescomplemented
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—42no—
247#11758196—42no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418C22×C412yes—
255C2×#92418C2×D412yes—
256D488—28no—
257C8×D61—44no—
258C23×C61—22no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61C22×D411yescharacteristic
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—48no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—48no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61—84no—
291C22×D61C4×D412yes—
292C22×D61C2×D812yes—
293C22×D61#13512yes—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—41no—
297D4×C61—41no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61C2×D812yes—
313C2×C4×C61C23×C411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C22⋊D61—48no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61C4×D412yes—
334C2×Dic61C2×D812yes—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—22no—
340D244—48no—
341D244—41no—
342D244—41no—
343D244C4×D414yescomplemented
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—84no—
349C4×D61—84no—
350C4×D61—84no—
351C4×D61—84no—
352C8×C61—22no—
353C8×C61—41no—
354#92418—22no—
355#92418—22no—
356#22870—611nomaximal, Sylow
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61C2×C4×D411yescharacteristic
365C22×C61D4211yescharacteristic
366C22×C61#54611yescharacteristic
367C22×C61C22×D811yescharacteristic
368C22×C61C2×#13511yescharacteristic
369C22×C61#57611yescharacteristic
370C22×C61#57711yescharacteristic
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—24no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—816no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61C4×D814yescomplemented
393C4×C61—22no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61—41no—
397C4×C61—81no—
398C4×C61C2×C4×D411yescharacteristic
399C4×C61#51811yescharacteristic
400C4×C61#54611yescharacteristic
401C4×C61#55111yescharacteristic
402Dic61—22no—
403Dic61—22no—
404Dic61—41no—
405Dic61—81no—
406Dic61—81no—
407C2×#447—611no—
408C2×C4×D8—611no—
409C22×#102—611no—
410#2361—611no—
411D4×C22⋊C4—611no—
412#1970—611no—
413#1934—611no—
414#1925D6111yescharacteristic, complemented
415#1893—611no—
416#1879—611no—
417#1879—611no—
418#1862—611no—
419#1852—611no—
420C4×#102—611no—
421C8×C22⋊C4—611no—
422C2×C61—82no—
423C2×C61#235811yescharacteristic
424C2×C61C2×C4×D811yescharacteristic
425C2×C61#294611yescharacteristic
426C2×C61D4×D811yescharacteristic
427C2×C61#328211yescharacteristic
428C2×C61#329411yescharacteristic
429C2×C61#329711yescharacteristic
430D61—24no—
431D61—44no—
432D61—82no—
433C23×D4—611no—
434C22×D8—611no—
435C22×D8—611no—
436C23×C8—611no—
437C2×#121—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×C4×D4—1221no—
442C22×C4⋊C4—611no—
443C22×C22⋊C4—1221no—
444#447—618no—
445C4×D8—1224no—
446C2×#107—611no—
447C2×#107C2×D6111yescharacteristic, complemented
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—1224no—
455C2×#102C2×D6111yescharacteristic
456C2×#102C2×D6111yescharacteristic
457C2×C22⋊C8—611no—
458C2×C4×C8—611no—
459C2×C4×C8—611no—
460#390—611no—
461#390—611no—
462#390C2×D6111yescharacteristic
463#389—611no—
464#388—1221no—
465#386—1221no—
466#386—1221no—
467#386—1221no—
468#385—1221no—
469#380—611no—
470#379—1221no—
471C4×C4⋊C4C2×D6111yescharacteristic, complemented
472C4×C22⋊C4—611no—
473#340—611no—
474#340—611no—
475#340—611no—
476#340C2×D6111yescharacteristic, complemented
477#336—611no—
478#336C2×D6111yescharacteristic, complemented
479C61#2287011yescharacteristic, complemented, Sylow
480C25—1221no—
481C22×D4—614no—
482C22×D4—611no—
483C22×D4—611no—
484C22×D4—1221no—
485C22×D4—1222no—
486C22×D4—1221no—
487C22×D4—1222no—
488C22×D4—1222no—
489C22×D4—2441no—
490C22×D4—2441no—
491C22×D4C22×D6111yescharacteristic
492C23×C4—611no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4—1221no—
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1222no—
500C2×D8—1222no—
501C2×D8—2441no—
502C2×D8—2441no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—1222no—
506C22×C8—1222no—
507C22×C8—2441no—
508C22×C8C22×D6111yescharacteristic
509C22×C8C22×D6111yescharacteristic
510#121—614no—
511#121—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—2441no—
516C4×D4—2444no—
517C4×D4—2441no—
518C4×D4—2441no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—1222no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—2441no—
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—2444no—
542C2×C42—21no—
543C2×C42—611no—
544C2×C42C22×D6111yescharacteristic
545#107—22no—
546#107—2441no—
547#102—22no—
548#102—614no—
549#102—614no—
550#102—1222no—
551#102—1222no—
552#102—1222no—
553#102—2441no—
554#102C4×D6114yescomplemented
555C22⋊C8—614no—
556C4×C8—1222no—
557C4×C8—2441no—
558#95—21no—
559#95—611no—
560#95—611no—
561#95—1221no—
562#95—1221no—
563C24—21no—
564C24—611no—
565C24—1224no—
566C24—1221no—
567C24—1221no—
568C24—4881no—
569C24—4881no—
570C24—2442no—
571C24—2442no—
572C24—2442no—
573C24—2442no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—612no—
580C2×D4—612no—
581C2×D4—612no—
582C2×D4—612no—
583C2×D4—1224no—
584C2×D4—1224no—
585C2×D4—1228no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—2442no—
595C2×D4—2442no—
596C2×D4—2444no—
597C2×D4—2444no—
598C2×D4—2444no—
599C2×D4—2442no—
600C2×D4—2442no—
601C2×D4C2×C4×D6112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—611no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—4881no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4D4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4C23×D6111yescharacteristic
631D8—1228no—
632D8—2444no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—612no—
639C2×C8—612no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—2444no—
645C2×C8C2×C4×D6112yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—2442no—
655C4⋊C4—2442no—
656C4⋊C4C2×C4×D6112yes—
657C4⋊C4D4×D6112yes—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C22⋊C4—614no—
661C22⋊C4—1224no—
662C22⋊C4—1222no—
663C22⋊C4—4881no—
664C22⋊C4—4881no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C42—21no—
672C42—21no—
673C42—42no—
674C42—1221no—
675C42—1221no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—612no—
684C23—612no—
685C23—612no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—4884no—
695C23—4884no—
696C23—4884no—
697C23—4884no—
698C23—4884no—
699C23—2448no—
700C23—2448no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23C2×D4×D6111yescharacteristic
712D4—22no—
713D4—22no—
714D4—41no—
715D4—41no—
716D4—614no—
717D4—1222no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—1222no—
722D4—2448no—
723D4—2448no—
724D4—2441no—
725D4—2441no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—4884no—
754C2×C4—4884no—
755C2×C4—4884no—
756C2×C4—4884no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4D8×D6112yes—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6111yescharacteristic
767C2×C4#41×D6111yescharacteristic
768C2×C4#1451982311yescharacteristic
769C2×C4#1451982311yescharacteristic
770C8—22no—
771C8—41no—
772C8—1222no—
773C8—1222no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—614no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—1222no—
787C22—1222no—
788C22—1224no—
789C22—48816no—
790C22—4881no—
791C22—4881no—
792C22—4881no—
793C22—4881no—
794C22—2442no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22C4×D4×D6111yescharacteristic
804C22#1684039611yescharacteristic
805C22#1684040411yescharacteristic
806C22C2×D8×D6111yescharacteristic
807C22#135×D6111yescharacteristic
808C22#1684056611yescharacteristic
809C22#1684057111yescharacteristic
810C4—22no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—81no—
815C4—1222no—
816C4—1222no—
817C4—4881no—
818C4—4881no—
819C4—2441no—
820C4C4×D4×D6111yescharacteristic
821C4#1684023611yescharacteristic
822C4#1684040511yescharacteristic
823C4#1684043711yescharacteristic
824C2—82no—
825C2—1224no—
826C2—4882no—
827C2—2444no—
828C2#2144879711yescharacteristic
829C2C4×D8×D6111yescharacteristic
830C2#2145465011yescharacteristic
831C2#2145749111yescharacteristic
832C2#2145752111yescharacteristic
833C2#2145763011yescharacteristic
834C2#2145767211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1925C2
socleC23×C61C22×D4
prime radicalC2×#16839897C2
cosocleC22×C4×C61C24
hypercenter#1925D61
hypocenterC61#22870
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. C2×#16839844C2semidirect
3. C2×#102×D61C2semidirect
4. #21448837C2semidirect
5. #21448640C2semidirect
6. #21446684C2semidirect
7. #21446504C2semidirect
8. #21446246C2semidirect
9. #21446166C2semidirect
10. #21446164C2semidirect
11. #21446067C2semidirect
12. #21446005C2semidirect
13. C4×#14519697C2semidirect
14. #21445589C2semidirect
15. C61×#1925C2semidirect
24. C2×#14519739C22semidirect
27. #16839897C4semidirect
29. C2×#14519710C22semidirect
31. C2×#14519699C22semidirect
35. C2×#14519697C22semidirect
38. C2×C4×#92418C22semidirect
39. C2×C8×Dic61C22semidirect
41. #16839664C22semidirect
42. #16839661C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839516C22semidirect
55. C2×#107×C61C22semidirect
59. C4×C4⋊C4×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#336C22semidirect
72. C2×D4×D61C2×C4semidirect
80. C2×D488C2×C4semidirect
83. C2×#11758199C2×C4semidirect
90. #14519752C2×C4semidirect
122. #14519697C2×C4semidirect
123. #14519697D4semidirect
124. #14519689C2×C4semidirect
143. #102×C61C2×C4semidirect
241. #11758198D8semidirect
343. D244C4×D4semidirect
392. C2×D61C4×D8semidirect
414. #1925D61semidirect
447. C2×#107C2×D61semidirect
471. C4×C4⋊C4C2×D61semidirect
476. #340C2×D61semidirect
478. #336C2×D61semidirect
479. C61#22870semidirect
554. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398972
C2×#168398442
C2×#102×D612
#214488372
#214486402
#214466842
#214465042
#214462462
#214461662
#214461642
#214460672
#214460052
C4×#145196972
#214455892
C61×#19252
#2287061