Finite Group Databasebeta

← #29708180

Subgroups — #29708180

Order 15616.

1272 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758201C211yesmaximal, characteristic, complemented
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3C4×#14519751C211yesmaximal, characteristic, complemented
4#21447154C211yesmaximal, characteristic, complemented
5#21447055C211yesmaximal, characteristic, complemented
6#21447019C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446962C211yesmaximal, characteristic, complemented
9#21446896C211yesmaximal, characteristic, complemented
10#21446820C211yesmaximal, characteristic, complemented
11#21446815C211yesmaximal, characteristic
12C4×#14519701C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14C4×C22⋊#92418C211yesmaximal, characteristic, complemented
15C2×C61×#529C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×C22⋊D61—21no—
21C4×#11758201—24no—
22C4×#11758199—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37#16839664C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839653—21no—
40#16839641—21no—
41#16839622C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×#11758198—21no—
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#529—24no—
51C61×#529—24no—
52C2×#126×C61—21no—
53C2×#125×C61C2211yescharacteristic
54C2×#124×C61C2211yescharacteristic
55C2×#123×C61—21no—
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×D4×C61—21no—
60C2×C4×D4×C61C2211yescharacteristic
61C2×#117×C61—21no—
62C22×C42×C61C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C4×D61—21no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758201—22no—
69C2×#11758199—22no—
70C2×#11758199—22no—
71C2×#11758199—22no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519751—22no—
77#14519751—22no—
78C4×D244—22no—
79C4×D244—22no—
80C4×C22⋊D61—44no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×C4×Dic61—21no—
91#14519710—22no—
92#14519708—22no—
93#14519701—22no—
94#14519701—22no—
95#14519701—22no—
96#14519698—22no—
97#14519698—22no—
98#14519698—22no—
99#14519697—22no—
100#14519697—22no—
101C22⋊#92418—22no—
102C22⋊#92418—22no—
103C4×#92418—22no—
104C4×#92418—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108C22×Q8×C61C2311yescharacteristic
109C22×D4×C61—21no—
110C22×D4×C61C2311yescharacteristic
111C23×C4×C61—21no—
112C23×C4×C61D411yescharacteristic
113C23×C4×C61D411yescharacteristic
114C23×C4×C61C2311yescharacteristic
115#126×C61—28no—
116#125×C61—22no—
117#125×C61—22no—
118#124×C61—22no—
119#124×C61—22no—
120#123×C61—28no—
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123#121×C61—22no—
124#121×C61—22no—
125C4×Q8×C61—22no—
126C4×Q8×C61D414yescomplemented
127C4×D4×C61—28no—
128C4×D4×C61—22no—
129C4×D4×C61D414yescomplemented
130#117×C61—28no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C42×C61—21no—
143C2×C42×C61—22no—
144C2×C42×C61—22no—
145C2×C42×C61D411yescharacteristic
146C2×C42×C61D411yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C24×C61—21no—
150C24×C61C2×D411yescharacteristic
151C23×D61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61C2×D412yes—
158C2×D4×C61—24no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61C2×D412yes—
167C22×C4×C61—22no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—24no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—41no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—24no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244#4112yes—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C4⋊C4×C61—24no—
207C4⋊C4×C61—24no—
208C4⋊C4×C61—24no—
209C4⋊C4×C61—24no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61C2×D412yes—
213C4⋊C4×C61C2×D412yes—
214C22⋊C4×C61—24no—
215C22⋊C4×C61—24no—
216C22⋊C4×C61—24no—
217C22⋊C4×C61—24no—
218C22⋊C4×C61—24no—
219C42×C61—22no—
220C42×C61—22no—
221C42×C61—24no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61C2×D412yes—
225C42×C61C2×D412yes—
226C22⋊Dic61—42no—
227#11758201—28no—
228#11758199—28no—
229#11758198—24no—
230#11758198—42no—
231#11758198—42no—
232#11758198—42no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61#4112yes—
239#11758196—42no—
240C4×Dic61—42no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418#4112yes—
252C2×#92418#4112yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—22no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61#13512yes—
267C23×C61C22×D411yescharacteristic
268C22×D61—22no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—41no—
278Q8×C61—41no—
279D4×C61—22no—
280D4×C61—22no—
281D4×C61—48no—
282D4×C61—41no—
283D4×C61—41no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
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—44no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
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×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—44no—
310C2×C4×C61—48no—
311C2×C4×C61#12012yes—
312C2×C4×C61#12012yes—
313C2×C4×C61#13512yes—
314C2×C4×C61AGL(1,ℤ/8)12yes—
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C22⋊D61—48no—
322C2×Dic61—22no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331D244—22no—
332D244—22no—
333D244—41no—
334D244—41no—
335C4×D61—84no—
336#92418—22no—
337#92418—22no—
338#92418—41no—
339#92418—41no—
340#23569—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61C2×#12011yescharacteristic
356C22×C61#52511yescharacteristic
357C22×C61#53211yescharacteristic
358C22×C61C2×#13511yescharacteristic
359C22×C61C2×#13511yescharacteristic
360C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C61#57511yescharacteristic
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—42no—
372C4×C61—41no—
373C4×C61—42no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61#44914yes—
377C4×C61#52511yescharacteristic
378C4×C61#52511yescharacteristic
379C4×C61#53211yescharacteristic
380C4×C61#53211yescharacteristic
381Dic61—42no—
382Dic61—81no—
383Dic61—81no—
384C2×#529D6111yescharacteristic, complemented
385C2×C4×SD16—611no—
386C2×C4×D8—611no—
387C4×#121—611no—
388#2059—611no—
389#2042—611no—
390#2036—611no—
391#2034—611no—
392#2025—611no—
393#2012—611no—
394#2000—611no—
395#1999—611no—
396C4×#103—611no—
397C4×#102—611no—
398C4×C22⋊C8—611no—
399C2×C61—42no—
400C2×C61—82no—
401C2×C61#238811yescharacteristic
402C2×C61C2×#44911yescharacteristic
403C2×C61#300211yescharacteristic
404C2×C61#310211yescharacteristic
405C2×C61#310511yescharacteristic
406C2×C61#316811yescharacteristic
407C2×C61#317111yescharacteristic
408D61—82no—
409C22×SD16—611no—
410C22×D8—611no—
411#529—24no—
412#529—24no—
413C2×#126—21no—
414C2×#125C2×D6111yescharacteristic
415C2×#124C2×D6111yescharacteristic
416C2×#123—21no—
417C2×C22⋊Q8C2×D6111yescharacteristic
418C2×#121—611no—
419C2×#121C2×D6111yescharacteristic
420C2×C4×Q8C2×D6111yescharacteristic
421C2×C4×D4—21no—
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C2×C4×D4C2×D6111yescharacteristic
425C2×#117—21no—
426C22×C42C2×D6111yescharacteristic
427C4×SD16—1224no—
428C4×D8—1224no—
429C2×#107—611no—
430C2×#106—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C4×C8—611no—
442C2×C4×C8—611no—
443#390—611no—
444#389—611no—
445#388—1221no—
446#386—1221no—
447#380—611no—
448C4×C4⋊C4—611no—
449C4×C22⋊C4—1221no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2356911yescharacteristic, complemented, Sylow
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—1221no—
464C23×C4C22⋊D6111yescharacteristic
465C23×C4C22⋊D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×SD16—1222no—
470C2×D8—1222no—
471C2×D8—1222no—
472C2×D8—1222no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—611no—
477#126—28no—
478#125—22no—
479#125—22no—
480#124—22no—
481#124—22no—
482#123—28no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485#121—22no—
486#121—22no—
487#121—1222no—
488#121—1222no—
489C4×Q8—22no—
490C4×Q8C22⋊D6114yescomplemented
491C4×D4—28no—
492C4×D4—22no—
493C4×D4—1222no—
494C4×D4—1222no—
495C4×D4—2444no—
496C4×D4C22⋊D6114yescomplemented
497#117—28no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C42—21no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—1221no—
522C2×C42C22⋊D6111yescharacteristic
523C2×C42C22⋊D6111yescharacteristic
524C2×C42C22×D6111yescharacteristic
525C2×C42C22×D6111yescharacteristic
526#107—1222no—
527#106—1222no—
528#103—1222no—
529#103—1222no—
530#103—1222no—
531#102—1222no—
532#102—1222no—
533#102—1222no—
534#102—1222no—
535#102—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C4×C8—1222no—
539C4×C8—1222no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543C24—21no—
544C24—1221no—
545C24C2×C22⋊D6111yescharacteristic
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8C2×C22⋊D6112yes—
552C2×D4—24no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—612no—
561C2×D4—1224no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—2442no—
568C2×D4—2442no—
569C2×D4C2×C22⋊D6112yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C23×D6111yescharacteristic
600SD16—1228no—
601D8—1228no—
602C2×C8—612no—
603C2×C8—612no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—24no—
620C4⋊C4—612no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—2442no—
627C4⋊C4C2×C22⋊D6112yes—
628C4⋊C4C2×C22⋊D6112yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—1224no—
635C22⋊C4—2442no—
636C22⋊C4—2442no—
637C22⋊C4—2442no—
638C22⋊C4—2442no—
639C42—21no—
640C42—21no—
641C42—22no—
642C42—22no—
643C42—24no—
644C42—2442no—
645C42C2×C22⋊D6112yes—
646C42C2×C22⋊D6112yes—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—1222no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23#1451979712yes—
668C23C22×C22⋊D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673D4—22no—
674D4—22no—
675D4—48no—
676D4—41no—
677D4—41no—
678D4—1222no—
679D4—1222no—
680D4—2448no—
681D4—2441no—
682D4—2441no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—44no—
709C2×C4—48no—
710C2×C4—1222no—
711C2×C4—4884no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4#1451974612yes—
721C2×C4#1451974612yes—
722C2×C4#1451979712yes—
723C2×C4#1451980212yes—
724C2×C4C22×C22⋊D6111yescharacteristic
725C2×C4C22×C22⋊D6111yescharacteristic
726C2×C4#41×D6111yescharacteristic
727C2×C4#41×D6111yescharacteristic
728C2×C4#41×D6111yescharacteristic
729C2×C4#41×D6111yescharacteristic
730C8—1222no—
731C8—1222no—
732C8—2441no—
733C8—2441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—4881no—
749C22—4881no—
750C22—4881no—
751C22—4881no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22C2×#1451974611yescharacteristic
756C22#1684026911yescharacteristic
757C22#1684030811yescharacteristic
758C22C2×#1451979711yescharacteristic
759C22C2×#1451979711yescharacteristic
760C22C2×#1451980211yescharacteristic
761C22#1684056011yescharacteristic
762C4—22no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—4881no—
770C4—4881no—
771C4—2442no—
772C4#1683990714yes—
773C4#1684026911yescharacteristic
774C4#1684026911yescharacteristic
775C4#1684030811yescharacteristic
776C4#1684030811yescharacteristic
777C2—42no—
778C2—82no—
779C2—4882no—
780C2#2144903211yescharacteristic
781C2C2×#1683990711yescharacteristic
782C2#2145503711yescharacteristic
783C2#2145583111yescharacteristic
784C2#2145586211yescharacteristic
785C2#2145638311yescharacteristic
786C2#2145641511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#529C2
socleC23×C61C22×D4
prime radical#21446815C2
hypercenterC2×#529D61
hypocenterC61#23569
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758201C2semidirect
2. C2×C4×#11758199C2semidirect
3. C4×#14519751C2semidirect
4. #21447154C2semidirect
5. #21447055C2semidirect
6. #21447019C2semidirect
7. #21447005C2semidirect
8. #21446962C2semidirect
9. #21446896C2semidirect
10. #21446820C2semidirect
12. C4×#14519701C2semidirect
13. C4×#14519698C2semidirect
14. C4×C22⋊#92418C2semidirect
15. C2×C61×#529C2semidirect
126. C4×Q8×C61D4semidirect
129. C4×D4×C61D4semidirect
384. C2×#529D61semidirect
456. C61#23569semidirect
490. C4×Q8C22⋊D61semidirect
496. C4×D4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582012
C2×C4×#117581992
C4×#145197512
#214471542
#214470552
#214470192
#214470052
#214469622
#214468962
#214468202
#214468152
C4×#145197012
C4×#145196982
C4×C22⋊#924182
C2×C61×#5292
#2356961