Finite Group Databasebeta

← #29700401

Subgroups — #29700401

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839907C211yesmaximal, characteristic
2C2×#16839860C211yesmaximal, characteristic, complemented
3C2×#16839763C211yesmaximal, characteristic, complemented
4#21448833C211yesmaximal, characteristic, complemented
5#21446684C211yesmaximal, characteristic, complemented
6#21446519C211yesmaximal, characteristic, complemented
7#21446436C211yesmaximal, characteristic, complemented
8#21446255C211yesmaximal, characteristic, complemented
9#21446174C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic, complemented
11#21446073C211yesmaximal, characteristic, complemented
12#21446006C211yesmaximal, characteristic, complemented
13C4×#14519701C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#2341C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×#14519737—21no—
22C22×C4⋊Dic61C2211yescharacteristic
23#16839907C418yescomplemented
24#16839860—24no—
25C2×#14519710C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27#16839763—24no—
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×#14519688C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839654—21no—
42#16839639—21no—
43#16839636—21no—
44C4×C4⋊Dic61C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C22×#41×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#390—21no—
55C61×#390—21no—
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#380—21no—
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758201C2×C414yescomplemented
69C2×#11758199—41no—
70C2×#11758199—41no—
71C2×#11758199C2×C414yescomplemented
72C2×#11758194—22no—
73C2×#11758194—22no—
74C2×#11758194—41no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519751—22no—
80#14519751C2×C414yes—
81C4×D244—22no—
82C4×D244—41no—
83#14519737—44no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96#14519710—22no—
97#14519710—41no—
98#14519701—22no—
99#14519701C2×C414yescomplemented
100#14519701D414yescomplemented
101#14519698—22no—
102#14519698—22no—
103#14519698C2×C414yescomplemented
104#14519697—22no—
105#14519697—41no—
106C22⋊#92418C2×C414yescomplemented
107#14519688—22no—
108C4×#92418—41no—
109#14519684—21no—
110#14519684—21no—
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—41no—
115C2×#41×C61—41no—
116C2×#41×C61C2×C414yescomplemented
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61—21no—
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C23×C4×C61C2311yescharacteristic
122C4×Q8×C61—22no—
123C4×Q8×C61—22no—
124C4×Q8×C61—41no—
125C4×Q8×C61—41no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140C2×C42×C61C2311yescharacteristic
141#95×C61—21no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C23×D61—21no—
147#41×C61—28no—
148#41×C61—44no—
149#41×C61—44no—
150#41×C61—44no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61C22×C412yes—
155C2×Q8×C61C2×D412yes—
156C2×Q8×C61#4112yes—
157C2×D4×C61—24no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61C22×C412yes—
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—21no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61#4112yes—
183C22×C4×C61C2411yescharacteristic
184C2×C22⋊D61—24no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—81no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244C22×C412yes—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—81no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—41no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—81no—
213C22⋊C4×C61—81no—
214C22⋊C4×C61—81no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—42no—
220C42×C61—42no—
221#11758201—28no—
222#11758199—44no—
223#11758198—24no—
224#11758198—42no—
225#11758198—42no—
226#11758198—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—42no—
232C4⋊Dic61C22×C412yes—
233C4⋊Dic61C2×D412yes—
234#11758196—42no—
235C4×Dic61—42no—
236#11758194—44no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418C22×C412yes—
247C2×#92418C22×C412yes—
248C2×#92418C2×D412yes—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—22no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61C4×D412yes—
263C23×C61C22×D411yescharacteristic
264C22×D61—22no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271Q8×C61—22no—
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61C4×D414yescomplemented
275D4×C61—22no—
276D4×C61—22no—
277D4×C61—48no—
278D4×C61—41no—
279D4×C61—41no—
280C2×C4×C61—22no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—48no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61C4×D412yes—
308C2×C4×C61AGL(1,ℤ/8)12yes—
309C2×C4×C61C23×C411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C22⋊D61—48no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—84no—
326D244—22no—
327D244—22no—
328D244—41no—
329D244—41no—
330C4×D61—84no—
331#92418—22no—
332#92418—22no—
333#92418—22no—
334#92418—41no—
335#22863—611nomaximal, Sylow
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61C2×C4×D411yescharacteristic
351C22×C61D4211yescharacteristic
352C22×C61#54611yescharacteristic
353C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C61#57511yescharacteristic
355C22×C61#57611yescharacteristic
356C22×C61#57811yescharacteristic
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C4×C61—22no—
365C4×C61—24no—
366C4×C61—22no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—81no—
371C4×C61—81no—
372C4×C61C2×C4×D411yescharacteristic
373C4×C61#51811yescharacteristic
374C4×C61#54611yescharacteristic
375C4×C61#55111yescharacteristic
376Dic61—42no—
377Dic61—42no—
378Dic61—81no—
379C2×#449—611no—
380C2×#440—611no—
381C2×#417—611no—
382#2361—611no—
383#2341D6111yescharacteristic, complemented
384#1970—611no—
385#1936—611no—
386#1925—611no—
387#1895—611no—
388#1880—611no—
389#1879—611no—
390#1863—611no—
391#1852—611no—
392C4×#103—611no—
393#1753—611no—
394C2×C61—42no—
395C2×C61—82no—
396C2×C61#235811yescharacteristic
397C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
398C2×C61#295111yescharacteristic
399C2×C61#327411yescharacteristic
400C2×C61#327711yescharacteristic
401C2×C61#330811yescharacteristic
402C2×C61#330911yescharacteristic
403D61—82no—
404C22×#41C2×D6111yescharacteristic
405C22×SD16—611no—
406C22×D8—611no—
407C22×M16—611no—
408C2×#121—611no—
409C2×C4×Q8C2×D6111yescharacteristic
410C2×C4×Q8C2×D6111yescharacteristic
411C2×C4×D4—611no—
412C2×C4×D4—1221no—
413C22×C4⋊C4—611no—
414#449—618no—
415#440—1224no—
416C2×#107—611no—
417C2×#107—611no—
418#417—1224no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×C22⋊C8—611no—
428C2×#97—611no—
429C2×C4×C8—611no—
430#390—21no—
431#390—21no—
432#390—611no—
433#390C2×D6111yescharacteristic
434#390C2×D6111yescharacteristic
435#389—611no—
436#388—1221no—
437#386—1221no—
438#385—1221no—
439#380—21no—
440#380C2×D6111yescharacteristic
441C4×C4⋊C4—611no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2×D6111yescharacteristic
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#336—611no—
449#336—611no—
450C61#2286311yescharacteristic, complemented, Sylow
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41C4×D6114yescomplemented
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4C22×D6111yescharacteristic
466C2×SD16—614no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×D8—614no—
470C2×D8—2441no—
471C2×D8—2441no—
472C2×M16—1222no—
473C2×M16—1222no—
474C2×M16—2441no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479#121—614no—
480#121—1222no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—41no—
484C4×Q8—41no—
485C4×D4—1222no—
486C4×D4—2441no—
487C4×D4—2444no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1222no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—2441no—
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4C22⋊D6111yescharacteristic
509C2×C22⋊C4C22⋊D6111yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—1221no—
513C2×C42C22×D6111yescharacteristic
514C2×C42C22×D6111yescharacteristic
515#107—1222no—
516#107—2441no—
517#103—614no—
518#103—614no—
519#103—1222no—
520#102—614no—
521#102—1222no—
522#102—1222no—
523#102—1222no—
524#102—2441no—
525C22⋊C8—614no—
526#97—1222no—
527C4×C8—2441no—
528#95—21no—
529#95—1221no—
530#95—1221no—
531#95C22⋊D6111yescharacteristic
532#95C22⋊D6111yescharacteristic
533C24—21no—
534C24—1221no—
535C24C2×C22⋊D6111yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C4×D6112yes—
544C2×Q8D4×D6112yes—
545C2×Q8#1175822412yes—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—612no—
555C2×D4—1224no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—1221no—
561C2×D4—2442no—
562C2×D4—2442no—
563C2×D4C2×C4×D6112yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—4881no—
578C22×C4—4881no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4C2×C4×D6112yes—
584C22×C4#1175822212yes—
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C2×C22⋊D6111yescharacteristic
590C22×C4C23×D6111yescharacteristic
591SD16—1228no—
592D8—2444no—
593M16—2444no—
594C2×C8—612no—
595C2×C8—612no—
596C2×C8—612no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—612no—
613C4⋊C4—612no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—2442no—
619C4⋊C4—2442no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—1224no—
628C22⋊C4—4881no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—42no—
637C42—2442no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—1222no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23C4×C22⋊D6112yes—
659C23C22×C22⋊D6111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8#1451973714yescomplemented
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—1222no—
670D4—1222no—
671D4—2448no—
672D4—2441no—
673D4—2441no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—4884no—
704C2×C4—4884no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4C4×C22⋊D6112yes—
713C2×C4#1451980212yes—
714C2×C4C22×C4×D6111yescharacteristic
715C2×C4C2×D4×D6111yescharacteristic
716C2×C4C2×#1175822411yescharacteristic
717C2×C4C2×#1175822211yescharacteristic
718C2×C4#1451982211yescharacteristic
719C2×C4#1451982211yescharacteristic
720C8—1222no—
721C8—1222no—
722C8—1222no—
723C8—2441no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—4881no—
739C22—4881no—
740C22—4881no—
741C22—4881no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22C2×C4×C22⋊D6111yescharacteristic
746C22D4×C22⋊D6111yescharacteristic
747C22#1684040611yescharacteristic
748C22C2×#1451980211yescharacteristic
749C22#1684056011yescharacteristic
750C22#1684056511yescharacteristic
751C22#1684057711yescharacteristic
752C4—22no—
753C4—24no—
754C4—22no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—4881no—
761C4—2442no—
762C4—2442no—
763C4C2×#1451973711yescharacteristic
764C4#1684023511yescharacteristic
765C4#1684040211yescharacteristic
766C4#1684043811yescharacteristic
767C2—42no—
768C2—82no—
769C2—4882no—
770C2#2144879811yescharacteristic
771C2C4×#1451980211yescharacteristic
772C2#2145469211yescharacteristic
773C2#2145743911yescharacteristic
774C2#2145747211yescharacteristic
775C2#2145781011yescharacteristic
776C2#2145782511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2341C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
cosocleC22×C4×C61C24
hypercenter#2341D61
hypocenterC61#22863
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#16839860C2semidirect
3. C2×#16839763C2semidirect
4. #21448833C2semidirect
5. #21446684C2semidirect
6. #21446519C2semidirect
7. #21446436C2semidirect
8. #21446255C2semidirect
9. #21446174C2semidirect
10. #21446170C2semidirect
11. #21446073C2semidirect
12. #21446006C2semidirect
13. C4×#14519701C2semidirect
14. #21445603C2semidirect
15. C61×#2341C2semidirect
23. #16839907C4semidirect
68. C2×#11758201C2×C4semidirect
71. C2×#11758199C2×C4semidirect
99. #14519701C2×C4semidirect
100. #14519701D4semidirect
103. #14519698C2×C4semidirect
106. C22⋊#92418C2×C4semidirect
116. C2×#41×C61C2×C4semidirect
274. Q8×C61C4×D4semidirect
383. #2341D61semidirect
450. C61#22863semidirect
456. C2×#41C4×D61semidirect
663. Q8#14519737semidirect

Maximal subgroups

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

subgroupindex
C2×#168399072
C2×#168398602
C2×#168397632
#214488332
#214466842
#214465192
#214464362
#214462552
#214461742
#214461702
#214460732
#214460062
C4×#145197012
#214456032
C61×#23412
#2286361