Finite Group Databasebeta

← #29700335

Subgroups — #29700335

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×#16839898C211yesmaximal, characteristic
2C2×#16839875C211yesmaximal, characteristic, complemented
3C22×#14519699C211yesmaximal, characteristic, complemented
4#21448833C211yesmaximal, characteristic, complemented
5C22⋊C4×D244C211yesmaximal, characteristic, complemented
6#21446695C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446447C211yesmaximal, characteristic, complemented
9#21446247C211yesmaximal, characteristic, complemented
10#21446166C211yesmaximal, characteristic, complemented
11#21446166C211yesmaximal, characteristic, complemented
12#21446083C211yesmaximal, characteristic, complemented
13#21446014C211yesmaximal, characteristic, complemented
14#21445645C211yesmaximal, characteristic, complemented
15C61×#1752C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×D488C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic, complemented
23C2×#14519737—21no—
24C22×C4⋊Dic61C2211yescharacteristic
25C2×C22⋊C4×D61—21no—
26#16839898C418yescomplemented
27#16839875—24no—
28C2×#14519709C2211yescharacteristic, complemented
29C2×#14519709C2211yescharacteristic, complemented
30C2×#14519699—24no—
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839664C2211yescharacteristic, complemented
42#16839660C2211yescharacteristic, complemented
43#16839654—21no—
44#16839640—21no—
45#16839640—21no—
46#16839639—21no—
47#16839636—21no—
48#16839622C2211yescharacteristic
49#16839617—21no—
50C4×C4⋊Dic61C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55C23×C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic, complemented
58C2×#97×C61C2211yescharacteristic, complemented
59C4×C22⋊C4×C61C2211yescharacteristic
60C61×#336C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
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×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C23×Dic61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C2×D488—22no—
79C2×D488—22no—
80C2×D488—41no—
81C2×D488—41no—
82C2×D488C2×C414yescomplemented
83C2×D488C2×C414yescomplemented
84#14519751—22no—
85#14519751C2×C414yescomplemented
86C4×D244—22no—
87C4×D244—22no—
88C4×D244—22no—
89C4×D244—41no—
90C4×D244—41no—
91C4×D244—41no—
92#14519737—44no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—41no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C22⋊C4×D61—44no—
114C2×C4×Dic61—21no—
115#14519709—22no—
116#14519709—41no—
117#14519699—22no—
118#14519699—22no—
119#14519699—22no—
120#14519699—22no—
121#14519699—41no—
122#14519699C2×C414yescomplemented
123#14519699C2×C414yescomplemented
124#14519699D414yescomplemented
125#14519684—21no—
126#14519684—21no—
127#14519684—21no—
128C23×C4×C61C2311yescharacteristic
129C22×C8×C61—22no—
130C22×C8×C61—22no—
131C22×C8×C61—41no—
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C2×C42×C61C2311yescharacteristic
140C22⋊C8×C61C2×C414yescomplemented
141#97×C61—22no—
142#97×C61—41no—
143#95×C61D411yescharacteristic
144#95×C61D411yescharacteristic
145C24×C61C2×D411yescharacteristic
146C23×D61—21no—
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—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61C22×C412yes—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61#4112yes—
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—24no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—42no—
177C22×Dic61—42no—
178C22×Dic61—81no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—28no—
191C2×D244—24no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—44no—
195C2×D244—44no—
196C2×D244—44no—
197C2×D244—42no—
198C2×D244—42no—
199C2×D244C22×C412yes—
200C2×D244C22×C412yes—
201C2×D244C22×C412yes—
202C2×D244C2×D412yes—
203C2×D244#4112yes—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—81no—
211C2×C4×D61—81no—
212C2×C4×D61—81no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—44no—
223C2×C8×C61C22×C412yes—
224C2×C8×C61C22×C412yes—
225C2×C8×C61C2×D412yes—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C42×C61—21no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—21no—
232C22⋊Dic61—42no—
233#11758198—24no—
234#11758198—42no—
235#11758198—42no—
236#11758198—42no—
237#11758198—42no—
238#11758198—42no—
239#11758198—42no—
240#11758198—81no—
241#11758198—81no—
242#11758198—81no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—42no—
252C4⋊Dic61C22×C412yes—
253C4⋊Dic61C2×D412yes—
254#11758196—42no—
255C4×Dic61—42no—
256D488—28no—
257D488—44no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61C4×D412yes—
263C23×C61AGL(1,ℤ/8)12yes—
264C23×C61AGL(1,ℤ/8)12yes—
265C23×C61C22×D411yescharacteristic
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—48no—
272C22×D61—41no—
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—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—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61C4×D412yes—
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—22no—
321C2×Dic61—22no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—84no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—22no—
340D244—22no—
341D244—22no—
342D244—22no—
343D244—48no—
344D244—41no—
345D244—41no—
346D244—41no—
347D244—41no—
348D244C4×D414yescomplemented
349C4×D61—84no—
350C4×D61—84no—
351C4×D61—84no—
352C8×C61—22no—
353C8×C61—22no—
354C8×C61—22no—
355C8×C61—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#44214yescomplemented
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—24no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—816no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C4×C61—22no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—41no—
397C4×C61—41no—
398C4×C61C2×C4×D411yescharacteristic
399C4×C61#51811yescharacteristic
400C4×C61#54611yescharacteristic
401C4×C61#55111yescharacteristic
402Dic61—42no—
403Dic61—42no—
404Dic61—81no—
405Dic61—81no—
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#1864—611no—
419#1853—611no—
420#1762—611no—
421#1752D6111yescharacteristic, complemented
422C2×C61—24no—
423C2×C61#235811yescharacteristic
424C2×C61C2×#44211yescharacteristic
425C2×C61#294611yescharacteristic
426C2×C61#326411yescharacteristic
427C2×C61#326511yescharacteristic
428C2×C61#330611yescharacteristic
429C2×C61#331811yescharacteristic
430D61—44no—
431D61—82no—
432D61—82no—
433C23×D4—611no—
434C22×D8—611no—
435C22×D8—611no—
436C23×C8C2×D6111yescharacteristic
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—
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⋊C8C2×D6111yescharacteristic
458C2×#97C2×D6111yescharacteristic, complemented
459C2×#97C2×D6111yescharacteristic, complemented
460#390—611no—
461#390—611no—
462#390—611no—
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⋊C4—611no—
472C4×C22⋊C4C2×D6111yescharacteristic
473#340—611no—
474#340—611no—
475#340—611no—
476#340—611no—
477#336C2×D6111yescharacteristic, complemented
478#336C2×D6111yescharacteristic, complemented
479C61#2285811yescharacteristic, complemented, Sylow
480C25—1221no—
481C22×D4—614no—
482C22×D4—611no—
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—1222no—
486C22×D4—1222no—
487C22×D4—1221no—
488C22×D4—1221no—
489C22×D4—1222no—
490C22×D4—2441no—
491C22×D4—2441no—
492C23×C4—1221no—
493C23×C4—1221no—
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—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8C22×D6111yescharacteristic
507C22×C8C22×D6111yescharacteristic
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—2441no—
517C4×D4—2441no—
518C4×D4—2444no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1222no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—2441no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
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—2444no—
540C2×C22⋊C4D24411yescharacteristic
541C2×C22⋊C4D24411yescharacteristic
542C2×C42—1221no—
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⋊C8C4×D6114yescomplemented
556#97—22no—
557#97—41no—
558#95—1221no—
559#95—1221no—
560#95—1221no—
561#95D24411yescharacteristic
562#95D24411yescharacteristic
563C24—1221no—
564C24—1224no—
565C24—1221no—
566C24—1221no—
567C24—4881no—
568C24—4881no—
569C24—2442no—
570C24—2442no—
571C24—2442no—
572C24—2442no—
573C24C2×D24411yescharacteristic
574C2×D4—612no—
575C2×D4—612no—
576C2×D4—612no—
577C2×D4—612no—
578C2×D4—612no—
579C2×D4—1228no—
580C2×D4—1224no—
581C2×D4—1221no—
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—1221no—
593C2×D4—1221no—
594C2×D4—1224no—
595C2×D4—2444no—
596C2×D4—2444no—
597C2×D4—2444no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2442no—
601C2×D4—2442no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—4881no—
612C22×C4—4881no—
613C22×C4—4881no—
614C22×C4—4881no—
615C22×C4—2442no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4C2×C4×D6112yes—
624C22×C4C2×D24411yescharacteristic
625C22×C4C2×D24411yescharacteristic
626C22×C4C2×D24411yescharacteristic
627C22×C4C2×D24411yescharacteristic
628C22×C4C2×D24411yescharacteristic
629C22×C4#1175822212yes—
630C22×C4C23×D6111yescharacteristic
631D8—1228no—
632D8—2444no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—44no—
643C2×C8C2×C4×D6112yes—
644C2×C8C2×C4×D6112yes—
645C2×C8D4×D6112yes—
646C4⋊C4—612no—
647C4⋊C4—612no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—2442no—
657C4⋊C4—2442no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—1224no—
661C22⋊C4—4881no—
662C22⋊C4—4881no—
663C22⋊C4—4881no—
664C22⋊C4—2442no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—2442no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—4884no—
686C23—4884no—
687C23—4884no—
688C23—4884no—
689C23—4884no—
690C23—2448no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2448no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23C4×D24412yes—
709C23#1451980512yes—
710C23#1451980512yes—
711C23C22×D24411yescharacteristic
712D4—614no—
713D4—1222no—
714D4—1222no—
715D4—1222no—
716D4—1222no—
717D4—1222no—
718D4—1222no—
719D4—1222no—
720D4—2448no—
721D4—2448no—
722D4—2441no—
723D4—2441no—
724D4—2441no—
725D4—2441no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
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—21no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—4884no—
749C2×C4—4884no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4C4×D24412yes—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6111yescharacteristic
767C2×C4C2×#1175822211yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982311yescharacteristic
770C8—22no—
771C8—22no—
772C8—22no—
773C8—41no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—1224no—
781C22—48816no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—4881no—
786C22—4881no—
787C22—4881no—
788C22—4881no—
789C22—4881no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22#1683987514yescomplemented
803C22C2×C4×D24411yescharacteristic
804C22D4×D24411yescharacteristic
805C22#1684040711yescharacteristic
806C22C2×#1451980511yescharacteristic
807C22C2×#1451980511yescharacteristic
808C22#1684056711yescharacteristic
809C22#1684057411yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—4881no—
816C4—4881no—
817C4—4881no—
818C4—2442no—
819C4—2442no—
820C4C4×D4×D6111yescharacteristic
821C4#1684023411yescharacteristic
822C4#1684040211yescharacteristic
823C4#1684043611yescharacteristic
824C2—24no—
825C2—4882no—
826C2—4882no—
827C2—2444no—
828C2#2144880111yescharacteristic
829C2C2×#1683987511yescharacteristic
830C2#2145465311yescharacteristic
831C2#2145730411yescharacteristic
832C2#2145731911yescharacteristic
833C2#2145778211yescharacteristic
834C2#2145796211yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1752C2
socleC23×C61C22×D4
prime radicalC2×#16839898C2
cosocleC22×C4×C61C24
hypercenter#1752D61
hypocenterC61#22858
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C2×#16839875C2semidirect
3. C22×#14519699C2semidirect
4. #21448833C2semidirect
5. C22⋊C4×D244C2semidirect
6. #21446695C2semidirect
7. #21446516C2semidirect
8. #21446447C2semidirect
9. #21446247C2semidirect
10. #21446166C2semidirect
11. #21446166C2semidirect
12. #21446083C2semidirect
13. #21446014C2semidirect
14. #21445645C2semidirect
15. C61×#1752C2semidirect
22. C2×C4×D244C22semidirect
26. #16839898C4semidirect
28. C2×#14519709C22semidirect
29. C2×#14519709C22semidirect
37. C2×#14519699C22semidirect
38. C2×#14519699C22semidirect
41. #16839664C22semidirect
42. #16839660C22semidirect
50. C4×C4⋊Dic61C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
57. C2×#97×C61C22semidirect
58. C2×#97×C61C22semidirect
60. C61×#336C22semidirect
61. C61×#336C22semidirect
69. C22×D244C2×C4semidirect
82. C2×D488C2×C4semidirect
83. C2×D488C2×C4semidirect
85. #14519751C2×C4semidirect
122. #14519699C2×C4semidirect
123. #14519699C2×C4semidirect
124. #14519699D4semidirect
140. C22⋊C8×C61C2×C4semidirect
348. D244C4×D4semidirect
363. C22×C61#442semidirect
421. #1752D61semidirect
458. C2×#97C2×D61semidirect
459. C2×#97C2×D61semidirect
477. #336C2×D61semidirect
478. #336C2×D61semidirect
479. C61#22858semidirect
555. C22⋊C8C4×D61semidirect
802. C22#16839875semidirect

Maximal subgroups

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

subgroupindex
C2×#168398982
C2×#168398752
C22×#145196992
#214488332
C22⋊C4×D2442
#214466952
#214465162
#214464472
#214462472
#214461662
#214460832
#214460142
#214456452
C61×#17522
#2285861