Finite Group Databasebeta

← #29700331

Subgroups — #29700331

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×#16839895C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C22×#14519697C211yesmaximal, characteristic, complemented
4C22⋊C4×D244C211yesmaximal, characteristic, complemented
5#21446694C211yesmaximal, characteristic, complemented
6#21446515C211yesmaximal, characteristic, complemented
7#21446446C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446079C211yesmaximal, characteristic, complemented
12#21446012C211yesmaximal, characteristic, complemented
13#21445647C211yesmaximal, characteristic, complemented
14#21445597C211yesmaximal, characteristic, complemented
15C61×#2361C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23#16839895C418yescomplemented
24#16839872—24no—
25C2×#14519708C2211yescharacteristic, complemented
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519698C2211yescharacteristic, complemented
28C2×#14519698C2211yescharacteristic, complemented
29C2×#14519697—24no—
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×#14519688C2211yescharacteristic, complemented
38C2×#14519688C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839640—21no—
42#16839640—21no—
43#16839622C2211yescharacteristic
44#16839617—21no—
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51C2×#121×C61C2211yescharacteristic
52C2×C4×D4×C61—21no—
53C2×C4×D4×C61C2211yescharacteristic, complemented
54C22×C4⋊C4×C61C2211yescharacteristic
55C61×#390C2211yescharacteristic, complemented
56C61×#389C2211yescharacteristic, complemented
57C61×#388—21no—
58C61×#386—21no—
59C61×#385—21no—
60C4×C4⋊C4×C61C2211yescharacteristic, complemented
61C4×C22⋊C4×C61C2211yescharacteristic
62C24×D61—21no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—21no—
66C22×D244—22no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244C2×C414yescomplemented
70C22×D244C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—41no—
77C2×#11758199—41no—
78C2×#11758199C2×C414yescomplemented
79C2×#11758199C2×C414yescomplemented
80C22×#92418—22no—
81C22×#92418—22no—
82C22×#92418—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C4×D244—22no—
88C4×D244—22no—
89C4×D244—41no—
90C4×D244—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C22⋊C4×D61—44no—
101#14519708—22no—
102#14519708—41no—
103#14519698—22no—
104#14519698—41no—
105#14519697—22no—
106#14519697—22no—
107#14519697—22no—
108#14519697C2×C414yescomplemented
109#14519697C2×C414yescomplemented
110#14519697D414yescomplemented
111C22⋊#92418C2×C414yescomplemented
112#14519688—22no—
113#14519688—41no—
114#14519684—21no—
115C22×D4×C61—21no—
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61—21no—
119C23×C4×C61C2311yescharacteristic
120#121×C61—22no—
121#121×C61C2×C414yescomplemented
122C4×D4×C61—22no—
123C4×D4×C61—41no—
124C4×D4×C61—44no—
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—41no—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140C2×C42×C61C2311yescharacteristic
141#95×C61—21no—
142#95×C61—21no—
143#95×C61D411yescharacteristic
144#95×C61D411yescharacteristic
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—24no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61—42no—
154C23×D61—81no—
155C23×D61—81no—
156C2×D4×C61—24no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61C22×C412yes—
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—42no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—81no—
177C22×C4×C61—81no—
178C22×C4×C61C22×C412yes—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61#4112yes—
185C22×C4×C61C2411yescharacteristic
186C22×Dic61—21no—
187C22×Dic61—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—28no—
196C2×D244—24no—
197C2×D244—21no—
198C2×D244—44no—
199C2×D244—44no—
200C2×D244—44no—
201C2×D244—42no—
202C2×D244—42no—
203C2×D244C22×C412yes—
204C2×D244C22×C412yes—
205C2×D244C2×D412yes—
206C2×D244#4112yes—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—81no—
212C2×C4×D61—81no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—42no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61C22×C412yes—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—24no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—81no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—42no—
232C22⋊Dic61—42no—
233#11758199—28no—
234#11758199—44no—
235#11758198—42no—
236#11758198—42no—
237#11758198—42no—
238#11758198—42no—
239#11758198—81no—
240#11758198—81no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—44no—
255C2×#92418C22×C412yes—
256C2×#92418C22×C412yes—
257C2×#92418C2×D412yes—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—22no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61C4×D412yes—
270C23×C61AGL(1,ℤ/8)12yes—
271C23×C61AGL(1,ℤ/8)12yes—
272C23×C61C22×D411yescharacteristic
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—48no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—48no—
289C22×D61—84no—
290C22×D61—84no—
291C22×D61—84no—
292C22×D61—84no—
293C22×D61—84no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—48no—
297D4×C61—41no—
298D4×C61—41no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—84no—
327C2×C4×C61—84no—
328C2×C4×C61C4×D412yes—
329C2×C4×C61C23×C411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—22no—
345D244—22no—
346D244—48no—
347D244—41no—
348D244—41no—
349D244C4×D414yescomplemented
350C4×D61—84no—
351C4×D61—84no—
352#92418—22no—
353#92418—22no—
354#92418—22no—
355#92418—41no—
356#22858—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61#44214yescomplemented
371C22×C61C2×C4×D411yescharacteristic
372C22×C61D4211yescharacteristic
373C22×C61#54611yescharacteristic
374C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C61#57611yescharacteristic
377C22×C61#57711yescharacteristic
378C2×D61—24no—
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—42no—
388C2×D61—816no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C4×C61—22no—
394C4×C61—42no—
395C4×C61—41no—
396C4×C61—42no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61—81no—
401C4×C61C2×C4×D411yescharacteristic
402C4×C61#51811yescharacteristic
403C4×C61#54611yescharacteristic
404C4×C61#55111yescharacteristic
405Dic61—81no—
406Dic61—81no—
407C2×#447—611no—
408C2×#442—611no—
409C22×#102—611no—
410#2361D6111yescharacteristic, complemented
411D4×C22⋊C4—611no—
412#1972—611no—
413#1936—611no—
414#1926—611no—
415#1893—611no—
416#1879—611no—
417#1879—611no—
418#1864—611no—
419#1853—611no—
420#1762—611no—
421#1752—611no—
422C2×C61—24no—
423C2×C61—82no—
424C2×C61#235811yescharacteristic
425C2×C61C2×#44211yescharacteristic
426C2×C61#294611yescharacteristic
427C2×C61#326411yescharacteristic
428C2×C61#326511yescharacteristic
429C2×C61#330611yescharacteristic
430C2×C61#331811yescharacteristic
431D61—44no—
432D61—82no—
433C23×D4—611no—
434C22×D8—611no—
435C22×D8—611no—
436C23×C8—611no—
437C2×#121C2×D6111yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×C4×D4C2×D6111yescharacteristic, complemented
442C22×C4⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4—1221no—
444#447—618no—
445#442—1224no—
446C2×#106—611no—
447C2×#106—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—1224no—
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×#97—611no—
460#390—611no—
461#390—611no—
462#390C2×D6111yescharacteristic, complemented
463#389C2×D6111yescharacteristic, complemented
464#388—21no—
465#386—21no—
466#386—1221no—
467#386—1221no—
468#385—21no—
469#380—611no—
470#379—1221no—
471C4×C4⋊C4C2×D6111yescharacteristic, complemented
472C4×C22⋊C4C2×D6111yescharacteristic
473#340—611no—
474#340—611no—
475#340—611no—
476#340—611no—
477#336—611no—
478#336—611no—
479C61#2285811yescharacteristic, complemented, Sylow
480C25—1221no—
481C22×D4—21no—
482C22×D4—614no—
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—1222no—
486C22×D4—1222no—
487C22×D4—1222no—
488C22×D4—1221no—
489C22×D4—2441no—
490C22×D4—2441no—
491C22×D4C22×D6111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
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—611no—
506C22×C8—611no—
507C22×C8—1222no—
508C22×C8—1222no—
509C22×C8—2441no—
510#121—22no—
511#121C4×D6114yescomplemented
512C4×D4—22no—
513C4×D4—41no—
514C4×D4—44no—
515C4×D4—1222no—
516C4×D4—1222no—
517C4×D4—2441no—
518C4×D4—2441no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
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—2444no—
540C2×C22⋊C4C22⋊D6111yescharacteristic
541C2×C22⋊C4C22⋊D6111yescharacteristic
542C2×C42—21no—
543C2×C42C22×D6111yescharacteristic
544C2×C42C22×D6111yescharacteristic
545#106—1222no—
546#106—2441no—
547#102—614no—
548#102—614no—
549#102—614no—
550#102—1222no—
551#102—1222no—
552#102—1222no—
553#102—1222no—
554#102—2441no—
555C22⋊C8—614no—
556#97—1222no—
557#97—2441no—
558#95—21no—
559#95—21no—
560#95—1221no—
561#95C22⋊D6111yescharacteristic
562#95C22⋊D6111yescharacteristic
563C24—21no—
564C24—1221no—
565C24—1224no—
566C24—1221no—
567C24—4881no—
568C24—4881no—
569C24—2442no—
570C24—2442no—
571C24—2442no—
572C24—2442no—
573C24C2×C22⋊D6111yescharacteristic
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—612no—
583C2×D4—612no—
584C2×D4—612no—
585C2×D4—612no—
586C2×D4—1228no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1224no—
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—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4C2×C4×D6112yes—
624C22×C4#1175822212yes—
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C2×C22⋊D6111yescharacteristic
629C22×C4C2×C22⋊D6111yescharacteristic
630C22×C4C23×D6111yescharacteristic
631D8—1228no—
632D8—2444no—
633C2×C8—612no—
634C2×C8—612no—
635C2×C8—612no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—2444no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4C2×C4×D6112yes—
657C4⋊C4D4×D6112yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—4881no—
665C22⋊C4—4881no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—4884no—
692C23—4884no—
693C23—4884no—
694C23—4884no—
695C23—4884no—
696C23—2448no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2448no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23C4×C22⋊D6112yes—
709C23#1451980212yes—
710C23#1451980312yes—
711C23C22×C22⋊D6111yescharacteristic
712D4—22no—
713D4—22no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—614no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—1222no—
722D4—1222no—
723D4—2448no—
724D4—2441no—
725D4—2441no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—84no—
754C2×C4—84no—
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×C4C4×C22⋊D6112yes—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6111yescharacteristic
767C2×C4C2×#1175822211yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982311yescharacteristic
770C8—1222no—
771C8—1222no—
772C8—1222no—
773C8—2441no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—1224no—
788C22—48816no—
789C22—4881no—
790C22—4881no—
791C22—4881no—
792C22—4881no—
793C22—2442no—
794C22—2442no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22#1683987214yescomplemented
803C22C2×C4×C22⋊D6111yescharacteristic
804C22D4×C22⋊D6111yescharacteristic
805C22#1684040011yescharacteristic
806C22C2×#1451980211yescharacteristic
807C22C2×#1451980311yescharacteristic
808C22#1684056511yescharacteristic
809C22#1684057011yescharacteristic
810C4—22no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—42no—
816C4—41no—
817C4—81no—
818C4—4881no—
819C4—4881no—
820C4C4×D4×D6111yescharacteristic
821C4#1684023411yescharacteristic
822C4#1684040811yescharacteristic
823C4#1684044111yescharacteristic
824C2—24no—
825C2—82no—
826C2—4882no—
827C2—2444no—
828C2#2144879611yescharacteristic
829C2C2×#1683987211yescharacteristic
830C2#2145464711yescharacteristic
831C2#2145729511yescharacteristic
832C2#2145731511yescharacteristic
833C2#2145777411yescharacteristic
834C2#2145795411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2361C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
cosocleC22×C4×C61C24
hypercenter#2361D61
hypocenterC61#22858
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C22×#14519697C2semidirect
4. C22⋊C4×D244C2semidirect
5. #21446694C2semidirect
6. #21446515C2semidirect
7. #21446446C2semidirect
8. #21446248C2semidirect
9. #21446170C2semidirect
10. #21446167C2semidirect
11. #21446079C2semidirect
12. #21446012C2semidirect
13. #21445647C2semidirect
14. #21445597C2semidirect
15. C61×#2361C2semidirect
23. #16839895C4semidirect
25. C2×#14519708C22semidirect
26. C2×#14519708C22semidirect
27. C2×#14519698C22semidirect
28. C2×#14519698C22semidirect
37. C2×#14519688C22semidirect
38. C2×#14519688C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839517C22semidirect
50. #16839517C22semidirect
53. C2×C4×D4×C61C22semidirect
55. C61×#390C22semidirect
56. C61×#389C22semidirect
60. C4×C4⋊C4×C61C22semidirect
69. C22×D244C2×C4semidirect
78. C2×#11758199C2×C4semidirect
79. C2×#11758199C2×C4semidirect
108. #14519697C2×C4semidirect
109. #14519697C2×C4semidirect
110. #14519697D4semidirect
111. C22⋊#92418C2×C4semidirect
121. #121×C61C2×C4semidirect
349. D244C4×D4semidirect
370. C22×C61#442semidirect
410. #2361D61semidirect
441. C2×C4×D4C2×D61semidirect
462. #390C2×D61semidirect
463. #389C2×D61semidirect
471. C4×C4⋊C4C2×D61semidirect
479. C61#22858semidirect
511. #121C4×D61semidirect
802. C22#16839872semidirect

Maximal subgroups

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

subgroupindex
C2×#168398952
C2×#168398722
C22×#145196972
C22⋊C4×D2442
#214466942
#214465152
#214464462
#214462482
#214461702
#214461672
#214460792
#214460122
#214456472
#214455972
C61×#23612
#2285861