Finite Group Databasebeta

← #29700328

Subgroups — #29700328

Order 15616.

1386 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×#16839872C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic, complemented
4#21448834C211yesmaximal, characteristic, complemented
5D4×#11758198C211yesmaximal, characteristic, complemented
6#21446693C211yesmaximal, characteristic, complemented
7#21446515C211yesmaximal, characteristic, complemented
8#21446444C211yesmaximal, characteristic, complemented
9#21446246C211yesmaximal, characteristic, complemented
10#21446166C211yesmaximal, characteristic, complemented
11#21446165C211yesmaximal, characteristic, complemented
12#21446010C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#21445594C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×D488C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic, complemented
22C2×D4×Dic61C2211yescharacteristic
23C2×#14519739—21no—
24C2×C4⋊C4×D61C2211yescharacteristic
25C22×#11758198—21no—
26#16839897C418yescomplemented
27#16839872—24no—
28C2×#14519708C2211yescharacteristic, complemented
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic, complemented
35#102×D61—24no—
36C2×#14519689C2211yescharacteristic
37C2×#14519688C2211yescharacteristic, complemented
38C2×#14519687C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic
40#16839663C2211yescharacteristic
41#16839663C2211yescharacteristic, complemented
42#16839651—21no—
43#16839641—21no—
44#16839640—21no—
45#16839639—21no—
46#16839633—21no—
47#16839619C2211yescharacteristic
48#16839617—21no—
49C4⋊C4×Dic61C2211yescharacteristic, complemented
50C4×#11758198C2211yescharacteristic
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C2×C4×D4×C61C2211yescharacteristic
56C2×#106×C61C2211yescharacteristic, complemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#389C2211yescharacteristic, 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
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×D488—41no—
78C2×D488—41no—
79C2×D488C2×C414yescomplemented
80C2×#11758199—22no—
81C2×#11758199—22no—
82C2×#11758199C2×C414yescomplemented
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C2×C8×D61—22no—
86C2×C8×D61—22no—
87C2×C8×D61—41no—
88#14519752—22no—
89#14519752C2×C414yescomplemented
90C4×D244—22no—
91C4×D244—41no—
92D4×Dic61—22no—
93D4×Dic61—41no—
94#14519739—44no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61—41no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—44no—
111C2×#11758198D411yescharacteristic
112C2×#11758198D411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61C2311yescharacteristic
115#14519708—22no—
116#14519699—22no—
117#14519699—41no—
118#14519698D414yescomplemented
119#14519697—22no—
120#14519697—22no—
121#14519697C2×C414yescomplemented
122#14519689C2×C414yescomplemented
123#14519688—22no—
124#14519687—41no—
125#14519684—21no—
126#14519684—21no—
127#14519684D411yescharacteristic
128#14519684D411yescharacteristic
129C22×D4×C61C2311yescharacteristic
130C23×C4×C61—21no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C4×D4×C61—22no—
134C4×D4×C61—41no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C42×C61C2311yescharacteristic
141#106×C61—41no—
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×C61C22×C412yes—
160C2×D4×C61C2×D412yes—
161C2×D4×C61#4112yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61—81no—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2411yescharacteristic
171C2×C22⋊D61—24no—
172C2×C22⋊D61—42no—
173C2×C22⋊D61—42no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—42no—
177C22×Dic61—42no—
178C22×Dic61—81no—
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182D4×D61—28no—
183D4×D61—44no—
184D4×D61—44no—
185D4×D61—44no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—24no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—42no—
198C2×D244—42no—
199C2×D244C22×C412yes—
200C2×D244C22×C412yes—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
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×C61—21no—
224C4⋊C4×C61—42no—
225C4⋊C4×C61C22×C412yes—
226C22⋊C4×C61—42no—
227C42×C61—21no—
228C42×C61—21no—
229C22⋊Dic61—42no—
230#11758199—28no—
231#11758198—22no—
232#11758198—22no—
233#11758198—24no—
234#11758198—42no—
235#11758198—42no—
236#11758198—42no—
237#11758198—42no—
238#11758198—42no—
239#11758198—81no—
240#11758198—81no—
241#11758198—81no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61C2×D412yes—
246#11758196—42no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—42no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418C22×C412yes—
255C2×#92418C2×D412yes—
256D488—44no—
257C8×D61—44no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
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—48no—
273C22×D61—41no—
274C22×D61—41no—
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×D61AGL(1,ℤ/8)12yes—
293C22×D61AGL(1,ℤ/8)12yes—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61C4×D414yescomplemented
298C2×C4×C61—22no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
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×C61—41no—
313C2×C4×C61—84no—
314C2×C4×C61C23×C411yescharacteristic
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C22⋊D61—48no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—22no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—84no—
336C2×Dic61C4×D412yes—
337D244—22no—
338D244—22no—
339D244—22no—
340D244—22no—
341D244—48no—
342D244—41no—
343D244—41no—
344D244—41no—
345D244—41no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—84no—
351C4×D61—84no—
352C8×C61—22no—
353C8×C61—41no—
354#92418—22no—
355#92418—22no—
356#22858—611nomaximal, Sylow
357C22×C61—24no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61C2×C4×D411yescharacteristic
365C22×C61D4211yescharacteristic
366C22×C61#54611yescharacteristic
367C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
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—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—816no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61#44214yescomplemented
393C4×C61—42no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—81no—
397C4×C61—81no—
398C4×C61C2×C4×D411yescharacteristic
399C4×C61#51811yescharacteristic
400C4×C61#54611yescharacteristic
401C4×C61#55111yescharacteristic
402Dic61—22no—
403Dic61—42no—
404Dic61—41no—
405Dic61—41no—
406Dic61—81no—
407C2×#447—611no—
408C2×#442—611no—
409C22×#102—611no—
410#2361—611no—
411D4×C22⋊C4—611no—
412#1972—611no—
413#1936—611no—
414#1926—611no—
415#1893—611no—
416#1879—611no—
417#1879—611no—
418#1864D6111yescharacteristic, complemented
419#1853—611no—
420#1762—611no—
421#1752—611no—
422C2×C61—44no—
423C2×C61#235811yescharacteristic
424C2×C61C2×#44211yescharacteristic
425C2×C61#294611yescharacteristic
426C2×C61#326411yescharacteristic
427C2×C61#326511yescharacteristic
428C2×C61#330611yescharacteristic
429C2×C61#331811yescharacteristic
430D61—24no—
431D61—82no—
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—1221no—
441C2×C4×D4C2×D6111yescharacteristic
442C22×C4⋊C4—611no—
443C22×C22⋊C4—1221no—
444#447—618no—
445#442—1224no—
446C2×#106—611no—
447C2×#106C2×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×#97—611no—
459C2×#97—611no—
460#390—611no—
461#390—611no—
462#390—611no—
463#389C2×D6111yescharacteristic, complemented
464#388—1221no—
465#386—1221no—
466#386—1221no—
467#386—1221no—
468#385—1221no—
469#380—611no—
470#379—1221no—
471C4×C4⋊C4—611no—
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#2285811yescharacteristic, 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—21no—
493C23×C4—611no—
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—22no—
513C4×D4—41no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—2441no—
517C4×D4—2441no—
518C4×D4—2444no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1222no—
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—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—1221no—
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—611no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545#106—41no—
546#106—1222no—
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—
556#97—1222no—
557#97—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—612no—
578C2×D4—612no—
579C2×D4—1224no—
580C2×D4—1224no—
581C2×D4—1228no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—2442no—
593C2×D4—2442no—
594C2×D4—2444no—
595C2×D4—2444no—
596C2×D4—2444no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4C2×C4×D6112yes—
600C2×D4D4×D6112yes—
601C2×D4#1175822612yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—611no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—4881no—
620C22×C4—4881no—
621C22×C4—4881no—
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—21no—
651C4⋊C4—42no—
652C4⋊C4—612no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—2442no—
657C4⋊C4C2×C4×D6112yes—
658C22⋊C4—42no—
659C22⋊C4—1224no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—4881no—
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—1221no—
674C42—1221no—
675C42—2442no—
676C23—22no—
677C23—22no—
678C23—22no—
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—4884no—
693C23—4884no—
694C23—4884no—
695C23—4884no—
696C23—4884no—
697C23—2448no—
698C23—2448no—
699C23—2441no—
700C23—2441no—
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—22no—
715D4—1222no—
716D4—1222no—
717D4—1222no—
718D4—1222no—
719D4—2448no—
720D4—2448no—
721D4—2441no—
722D4—2441no—
723D4—2441no—
724D4—2441no—
725D4#1451973914yescomplemented
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
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—41no—
741C2×C4—84no—
742C2×C4—612no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1222no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—4884no—
757C2×C4—4884no—
758C2×C4—4884no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6111yescharacteristic
767C2×C4C2×#1175822611yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982311yescharacteristic
770C8—22no—
771C8—41no—
772C8—1222no—
773C8—1222no—
774C22—24no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—614no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—1222no—
787C22—1222no—
788C22—48816no—
789C22—4881no—
790C22—4881no—
791C22—4881no—
792C22—4881no—
793C22—4881no—
794C22—4881no—
795C22—4881no—
796C22—4881no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22C4×D4×D6111yescharacteristic
804C22#1684039411yescharacteristic
805C22#1684040311yescharacteristic
806C22AGL(1,ℤ/8)×D6111yescharacteristic
807C22AGL(1,ℤ/8)×D6111yescharacteristic
808C22#1684056411yescharacteristic
809C22#1684056811yescharacteristic
810C4—42no—
811C4—41no—
812C4—41no—
813C4—81no—
814C4—81no—
815C4—1222no—
816C4—4881no—
817C4—2441no—
818C4—2441no—
819C4—2442no—
820C4C2×#1451973911yescharacteristic
821C4#1684023411yescharacteristic
822C4#1684040411yescharacteristic
823C4#1684043911yescharacteristic
824C2—44no—
825C2—1224no—
826C2—4882no—
827C2—4882no—
828C2#2144879511yescharacteristic
829C2#442×D6111yescharacteristic
830C2#2145464611yescharacteristic
831C2#2145730211yescharacteristic
832C2#2145731211yescharacteristic
833C2#2145777711yescharacteristic
834C2#2145795711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1864C2
socleC23×C61C22×D4
prime radicalC2×#16839897C2
cosocleC22×C4×C61C24
hypercenter#1864D61
hypocenterC61#22858
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C2×#102×D61C2semidirect
4. #21448834C2semidirect
5. D4×#11758198C2semidirect
6. #21446693C2semidirect
7. #21446515C2semidirect
8. #21446444C2semidirect
9. #21446246C2semidirect
10. #21446166C2semidirect
11. #21446165C2semidirect
12. #21446010C2semidirect
13. #21445646C2semidirect
14. #21445594C2semidirect
15. C61×#1864C2semidirect
21. C2×C4×D244C22semidirect
26. #16839897C4semidirect
28. C2×#14519708C22semidirect
30. C2×#14519699C22semidirect
34. C2×#14519697C22semidirect
37. C2×#14519688C22semidirect
38. C2×#14519687C22semidirect
41. #16839663C22semidirect
49. C4⋊C4×Dic61C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839516C22semidirect
56. C2×#106×C61C22semidirect
59. C61×#389C22semidirect
60. C61×#340C22semidirect
61. C61×#336C22semidirect
72. C2×D4×D61C2×C4semidirect
79. C2×D488C2×C4semidirect
82. C2×#11758199C2×C4semidirect
89. #14519752C2×C4semidirect
118. #14519698D4semidirect
121. #14519697C2×C4semidirect
122. #14519689C2×C4semidirect
143. #102×C61C2×C4semidirect
297. D4×C61C4×D4semidirect
392. C2×D61#442semidirect
418. #1864D61semidirect
447. C2×#106C2×D61semidirect
463. #389C2×D61semidirect
476. #340C2×D61semidirect
478. #336C2×D61semidirect
479. C61#22858semidirect
554. #102C4×D61semidirect
725. D4#14519739semidirect

Maximal subgroups

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

subgroupindex
C2×#168398972
C2×#168398722
C2×#102×D612
#214488342
D4×#117581982
#214466932
#214465152
#214464442
#214462462
#214461662
#214461652
#214460102
#214456462
#214455942
C61×#18642
#2285861