Finite Group Databasebeta

← #29647290

Subgroups — #29647290

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C2×#16839726C211yesmaximal, characteristic, complemented
3#21444360C214yesmaximal, complemented
4#21444351C212yesmaximal, complemented
5#21444347C212yesmaximal, complemented
6#21444308C214yesmaximal, complemented
7C61×#2280C211yesmaximal, characteristic, complemented
8C22×#11758222C411yescharacteristic, complemented
9C22×#11758194—21no—
10#16840273—21no—
11#16840273—21no—
12#16840273—21no—
13#16840273—21no—
14#16840273C412yescomplemented
15#16840273C412yescomplemented
16#16840273C2212yes—
17#16840273C2212yes—
18C2×#14519760—21no—
19C2×#14519756C411yescharacteristic, complemented
20C2×#14519756C2211yescharacteristic
21C2×#14519751C411yescharacteristic, complemented
22C2×#14519751C2211yescharacteristic
23C2×#14519746—21no—
24C2×C4×C22⋊D61—21no—
25C2×C4×C22⋊D61—21no—
26C2×#14519736C411yescharacteristic, complemented
27#16839726—21no—
28#16839726—21no—
29#16839726C2212yes—
30#16839726C2212yescomplemented
31C2×C22⋊#92418—21no—
32C2×C22⋊#92418C2212yescomplemented
33#16839498C2218yescomplemented
34#16839495C2218yescomplemented
35C24×C4×C61C2211yescharacteristic
36C2×#117×C61—21no—
37C61×#381C2212yes—
38C61×#380—21no—
39C61×#380C2212yescomplemented
40C61×#379—21no—
41C4×C22⋊C4×C61—21no—
42C4×C22⋊C4×C61C2212yescomplemented
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—44no—
46C2×#11758222C2×C412yes—
47C2×#11758222C2×C412yes—
48C22×Dic122C2×C411yescharacteristic
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61—21no—
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C22×C4×D61—21no—
54C2×#11758194—22no—
55C2×#11758194—22no—
56C2×#11758194—44no—
57C22×#92418—22no—
58#14519760—22no—
59#14519760—22no—
60#14519760—22no—
61#14519760—22no—
62#14519756—21no—
63#14519756—21no—
64#14519756—21no—
65#14519756—21no—
66#14519756C2×C412yes—
67#14519756C2×C412yes—
68#14519756C2×C412yes—
69#14519756C2312yes—
70#14519751—21no—
71#14519751—21no—
72#14519751—21no—
73#14519751—21no—
74#14519751C2×C412yes—
75#14519751C2×C412yes—
76#14519751C2×C412yes—
77#14519751C2312yes—
78#14519746—22no—
79#14519746—22no—
80#14519746—22no—
81#14519746—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90#14519736—21no—
91#14519736—21no—
92#14519736C2×C412yes—
93#14519736C2×C412yes—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104C22⋊#92418—22no—
105C22⋊#92418—22no—
106C22⋊#92418—22no—
107C22⋊#92418C2314yes—
108C25×C61D411yescharacteristic
109C23×C4×C61—44no—
110C23×C4×C61C2×C411yescharacteristic
111C23×C4×C61C2×C411yescharacteristic
112C23×C4×C61C2×C411yescharacteristic
113C23×C4×C61C2×C411yescharacteristic
114C23×C4×C61D411yescharacteristic
115C23×C4×C61D411yescharacteristic
116C23×C4×C61D411yescharacteristic
117C23×C4×C61D411yescharacteristic
118C23×C4×C61D411yescharacteristic
119C23×C4×C61D411yescharacteristic
120C23×C4×C61D411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124#117×C61—44no—
125C2×C4⋊C4×C61—22no—
126C2×C22⋊C4×C61—22no—
127C2×C22⋊C4×C61—22no—
128C2×C22⋊C4×C61—22no—
129C2×C42×C61—22no—
130#95×C61—22no—
131#95×C61C2314yes—
132C24×C61—42no—
133C24×C61—42no—
134C24×C61—42no—
135C24×C61C22⋊C411yescharacteristic
136C24×C61C22⋊C411yescharacteristic
137C24×C61C22⋊C411yescharacteristic
138C24×C61C22⋊C411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C22×C4×C61—24no—
144C22×C4×C61—24no—
145C22×C4×C61—24no—
146C22×C4×C61—24no—
147C22×C4×C61—42no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C22⋊C411yescharacteristic
159C22×C4×C61C22⋊C411yescharacteristic
160C22×C4×C61C22⋊C411yescharacteristic
161C22×C4×C61C22⋊C411yescharacteristic
162C22×C4×C61C22⋊C411yescharacteristic
163C22×C4×C61C22⋊C411yescharacteristic
164C22×C4×C61C22⋊C411yescharacteristic
165C22×C4×C61C22⋊C411yescharacteristic
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—44no—
193C2×C22⋊D61—44no—
194C2×C22⋊D61—44no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198#11758222—44no—
199#11758222—44no—
200#11758222—44no—
201#11758222—44no—
202C2×D244—21no—
203C2×D244—42no—
204C2×D244C22×C412yes—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—44no—
208C2×Dic122—21no—
209C2×Dic122—42no—
210C2×Dic122C22×C412yes—
211C4⋊C4×C61—44no—
212C22⋊C4×C61—44no—
213C22⋊C4×C61—44no—
214C22⋊C4×C61—44no—
215C42×C61—44no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220C22⋊Dic61—22no—
221C22⋊Dic61—22no—
222#11758198—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198—22no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61C22×C412yes—
229C4⋊Dic61C22×C412yes—
230#11758196—22no—
231#11758196—22no—
232#11758196—22no—
233#11758196—22no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236#11758194—44no—
237#11758194—44no—
238C2×#92418—24no—
239C2×#92418—44no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—416no—
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61C2×C22⋊C411yescharacteristic
267C23×C61C2×C22⋊C411yescharacteristic
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—42no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—44no—
301C2×C4×C61—44no—
302C2×C4×C61—44no—
303C2×C4×C61#9914yes—
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C22⋊D61—44no—
313C22⋊D61—44no—
314C22⋊D61—44no—
315C22⋊D61—44no—
316C22⋊D61—44no—
317C22⋊D61—44no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324D244—42no—
325D244—42no—
326C4×D61—44no—
327C4×D61—44no—
328Dic122—42no—
329Dic122—42no—
330#92418—44no—
331#17559—611nomaximal, Sylow
332C22×C61—21no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—44no—
351C22×C61—44no—
352C22×C61—44no—
353C22×C61—44no—
354C22×C61—44no—
355C22×C61—44no—
356C22×C61—44no—
357C22×C61C2×#9912yes—
358C22×C61#42112yes—
359C22×C61C22×C22⋊C411yescharacteristic
360C22×C61#57512yes—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—84no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—84no—
372C4×C61C2×#9912yes—
373C4×C61C2×#9912yes—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377C2×#525—611no—
378C2×#407—611no—
379#2280D6111yescharacteristic, complemented
380#1513—614no—
381#1511—612no—
382#1510—612no—
383#1501—614no—
384C2×C61—22no—
385C2×C61—22no—
386C2×C61—22no—
387C2×C61—41no—
388C2×C61—41no—
389C2×C61—41no—
390C2×C61—41no—
391C2×C61C22×#9911yescharacteristic
392C2×C61#289611yescharacteristic
393C2×C61C2×#42111yescharacteristic
394D61—82no—
395C22×#41—611no—
396C24×C4C2×D6111yescharacteristic
397C22×M16—1221no—
398#525—612no—
399#525—612no—
400#525—612no—
401#525—612no—
402#525—1221no—
403#525—1221no—
404#525—1221no—
405#525—1221no—
406C2×#123—1221no—
407C2×C22⋊Q8—611no—
408C2×C22⋊Q8—611no—
409C2×#121—611no—
410C2×#121—611no—
411C2×#120—1221no—
412C2×C4×D4—1221no—
413C2×C4×D4—1221no—
414C2×#117—21no—
415C2×#117—611no—
416#407—612no—
417#407—612no—
418#407—1221no—
419#407—1221no—
420C2×C22⋊C8—612no—
421C2×C22⋊C8—1221no—
422#381C2×D6112yes—
423#380—21no—
424#380C2×D6112yescomplemented
425#379—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4C2×D6112yescomplemented
428#328—618no—
429#327—618no—
430C61#1755911yescharacteristic, complemented, Sylow
431C25C22⋊D6111yescharacteristic
432C2×#41—612no—
433C2×#41—612no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—2444no—
437C22×Q8—611no—
438C22×D4—611no—
439C22×D4—1221no—
440C22×D4—1221no—
441C22×D4—1221no—
442C23×C4—44no—
443C23×C4—1221no—
444C23×C4C4×D6111yescharacteristic
445C23×C4C4×D6111yescharacteristic
446C23×C4C4×D6111yescharacteristic
447C23×C4C4×D6111yescharacteristic
448C23×C4D24411yescharacteristic
449C23×C4D24411yescharacteristic
450C23×C4D24411yescharacteristic
451C23×C4D24411yescharacteristic
452C23×C4C22⋊D6111yescharacteristic
453C23×C4C22⋊D6111yescharacteristic
454C23×C4C22⋊D6111yescharacteristic
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—2444no—
461C22×C8—1222no—
462#123—1222no—
463#123—1222no—
464#123—1222no—
465#123—1222no—
466C22⋊Q8—612no—
467C22⋊Q8—612no—
468C22⋊Q8—612no—
469C22⋊Q8—612no—
470C22⋊Q8—1221no—
471C22⋊Q8—1221no—
472C22⋊Q8—1221no—
473C22⋊Q8—1221no—
474#121—612no—
475#121—612no—
476#121—612no—
477#121—612no—
478#121—1221no—
479#121—1221no—
480#121—1221no—
481#121—1221no—
482#120—1222no—
483#120—1222no—
484#120—1222no—
485#120—1222no—
486C4×D4—1222no—
487C4×D4—1222no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494#117—44no—
495#117—612no—
496#117—612no—
497#117—1221no—
498#117—1221no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C42—22no—
513C2×C42—1221no—
514C22⋊C8—614no—
515C22⋊C8—1222no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518#95—22no—
519#95C22×D6114yes—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—1221no—
524C24#1175819811yescharacteristic
525C24#1175819811yescharacteristic
526C24#1175819811yescharacteristic
527C24#1175819811yescharacteristic
528C24C2×C22⋊D6111yescharacteristic
529C24C2×C22⋊D6111yescharacteristic
530C24C2×C22⋊D6111yescharacteristic
531#41—2444no—
532#41—2444no—
533#41—2444no—
534#41—2444no—
535C2×Q8—612no—
536C2×Q8—1221no—
537C2×Q8—2442no—
538C2×D4—612no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—1221no—
546C2×D4—2442no—
547C2×D4—2444no—
548C2×D4—2444no—
549C2×D4—2444no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—2444no—
571C22×C4#1175819811yescharacteristic
572C22×C4#1175819811yescharacteristic
573C22×C4#1175819811yescharacteristic
574C22×C4#1175819811yescharacteristic
575C22×C4#1175819811yescharacteristic
576C22×C4#1175819811yescharacteristic
577C22×C4#1175819811yescharacteristic
578C22×C4#1175819811yescharacteristic
579C22×C4#1175819811yescharacteristic
580C22×C4#1175819811yescharacteristic
581C22×C4#1175819811yescharacteristic
582C22×C4#1175819811yescharacteristic
583C22×C4C2×C4×D6111yescharacteristic
584C22×C4C2×C4×D6111yescharacteristic
585C22×C4C2×C4×D6111yescharacteristic
586C22×C4C2×C4×D6111yescharacteristic
587C22×C4C2×C4×D6111yescharacteristic
588C22×C4C2×C4×D6111yescharacteristic
589C22×C4C2×D24411yescharacteristic
590C22×C4C2×D24411yescharacteristic
591C22×C4C2×D24411yescharacteristic
592C22×C4C2×D24411yescharacteristic
593C22×C4C2×D24411yescharacteristic
594C22×C4C2×D24411yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C23×D6111yescharacteristic
599M16—2444no—
600M16—2444no—
601C2×C8—1224no—
602C2×C8—2444no—
603C4⋊C4—44no—
604C4⋊C4—612no—
605C4⋊C4—612no—
606C4⋊C4—1222no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1222no—
610C4⋊C4—1222no—
611C4⋊C4—1222no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C42—44no—
626C42—1222no—
627C42—1222no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—1222no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23C2×#1175819811yescharacteristic
655C23C2×#1175819811yescharacteristic
656C23C2×#1175819811yescharacteristic
657C23C2×#1175819811yescharacteristic
658C23C2×#1175819811yescharacteristic
659C23C2×#1175819811yescharacteristic
660C23C22×C22⋊D6111yescharacteristic
661Q8—2442no—
662Q8—2442no—
663D4—2442no—
664D4—2442no—
665D4—2444no—
666D4—2444no—
667D4—2444no—
668D4—2444no—
669D4—2444no—
670D4—2444no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2444no—
708C2×C4—2444no—
709C2×C4#1451969114yes—
710C2×C4C2×#1175819811yescharacteristic
711C2×C4C2×#1175819811yescharacteristic
712C2×C4C2×#1175819811yescharacteristic
713C2×C4C2×#1175819811yescharacteristic
714C2×C4C2×#1175819811yescharacteristic
715C2×C4C2×#1175819811yescharacteristic
716C2×C4C22×C4×D6111yescharacteristic
717C2×C4C22×D24411yescharacteristic
718C8—2444no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—4884no—
745C22—2442no—
746C22—2442no—
747C22—2442no—
748C22C2×#1451969112yes—
749C22#1683978012yes—
750C22C22×#1175819811yescharacteristic
751C22#1684056012yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—84no—
759C4—2442no—
760C4—2442no—
761C4—2442no—
762C4C2×#1451969112yes—
763C4C2×#1451969112yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—4882no—
772C2C22×#1451969111yescharacteristic
773C2#2145433611yescharacteristic
774C2C2×#1683978011yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2280C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840273C2
cosocleC22×C4×C61C24
hypercenter#2280D61
hypocenterC61#17559
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#16839726C2semidirect
3. #21444360C2semidirect
4. #21444351C2semidirect
5. #21444347C2semidirect
6. #21444308C2semidirect
7. C61×#2280C2semidirect
8. C22×#11758222C4semidirect
14. #16840273C4semidirect
15. #16840273C4semidirect
19. C2×#14519756C4semidirect
21. C2×#14519751C4semidirect
26. C2×#14519736C4semidirect
30. #16839726C22semidirect
32. C2×C22⋊#92418C22semidirect
33. #16839498C22semidirect
34. #16839495C22semidirect
39. C61×#380C22semidirect
42. C4×C22⋊C4×C61C22semidirect
379. #2280D61semidirect
424. #380C2×D61semidirect
427. C4×C22⋊C4C2×D61semidirect
430. C61#17559semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C2×#168397262
#214443602
#214443512
#214443472
#214443082
C61×#22802
#1755961