Finite Group Databasebeta

← C2×#21450490 #29849099

Subgroups — C2×#21450490 #29849099

Order 15616.

2466 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519770C211yesmaximal, characteristic
2C22×#14519767C211yesmaximal, characteristic, complemented
3#21450490C2116yesmaximal, direct product factor
4C2×#16839698C211yesmaximal, characteristic
5C2×#16839696C211yesmaximal, characteristic, complemented
6C2×#16839695C211yesmaximal, characteristic, complemented
7C2×#16839685C211yesmaximal, characteristic
8C2×#16839660C211yesmaximal, characteristic, complemented
9C2×#16839655C211yesmaximal, characteristic
10C2×#16839650C211yesmaximal, characteristic
11C2×#16839650C211yesmaximal, characteristic
12C2×#16839645C211yesmaximal, characteristic, complemented
13C2×#16839626C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
15C2×#16839613C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic
17C2×#14519770—28no—
18C2×#14519770C2218yes—
19C2×#14519767—28no—
20C2×#14519767C2218yescomplemented
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×C22⋊Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41#16839698C2218yes—
42#16839696C2218yescomplemented
43#16839695C2218yescomplemented
44#16839685C2218yes—
45#16839660C2218yescomplemented
46#16839655C2218yes—
47#16839650C2218yes—
48#16839650C2218yes—
49#16839645C2218yescomplemented
50#16839626C2218yescomplemented
51C4×C4⋊Dic61C2218yescomplemented
52#16839613C2218yescomplemented
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C42×C61C2211yescharacteristic
66C61×#388C2218yes—
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77#14519770—232no—
78#14519767—232no—
79C2×C4⋊Dic61—24no—
80C2×C4⋊Dic61—24no—
81C2×C4⋊Dic61—24no—
82C2×C4⋊Dic61D418yes—
83C2×C4⋊Dic61C2314yes—
84C2×C4⋊Dic61C2314yes—
85C2×C4⋊Dic61C2314yes—
86C2×C4⋊Dic61C2314yes—
87C2×#11758196—24no—
88C2×#11758196—24no—
89C2×#11758196—24no—
90C2×#11758196—24no—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196—24no—
94C2×#11758196—24no—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×#11758196C2314yes—
98C2×#11758196C2314yes—
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×C22⋊Dic61—24no—
104C2×C22⋊Dic61—24no—
105C2×C22⋊Dic61—24no—
106C2×C22⋊Dic61—24no—
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2314yes—
109C2×C22⋊Dic61C2314yes—
110C2×C22⋊Dic61C2314yes—
111C2×C4×Dic61—24no—
112C2×C4×Dic61—24no—
113C2×C4×Dic61—24no—
114C2×C4×Dic61—24no—
115C2×C4×Dic61C2314yes—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127C25×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61—24no—
135C2×C4⋊C4×C61C2314yes—
136C2×C22⋊C4×C61—24no—
137C2×C22⋊C4×C61—24no—
138C2×C22⋊C4×C61—24no—
139C2×C22⋊C4×C61C2314yes—
140C2×C22⋊C4×C61C2314yes—
141C2×C22⋊C4×C61C2314yes—
142C2×C42×C61—24no—
143C2×C42×C61C2314yes—
144#95×C61C2314yes—
145#95×C61C2314yes—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61C2412yes—
154C24×C61C2411yescharacteristic
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61C2×D414yes—
171C22×C4×C61#4114yes—
172C22×C4×C61#4114yes—
173C22×C4×C61C2412yes—
174C22×C4×C61C2412yes—
175C22×C4×C61C2412yes—
176C22×C4×C61C2412yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2412yes—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61C2×D414yes—
200C22×Dic61C2×D414yes—
201C22×Dic61#4114yes—
202C22×Dic61#4114yes—
203C22×Dic61C2412yes—
204C22×Dic61C2412yes—
205C22×Dic61C2412yes—
206C22×Dic61C2412yes—
207C22×Dic61C2412yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C4⋊C4×C61—28no—
212C22⋊C4×C61—28no—
213C22⋊C4×C61—28no—
214C22⋊C4×C61—28no—
215C42×C61—28no—
216C22⋊Dic61—28no—
217C22⋊Dic61—28no—
218C22⋊Dic61—28no—
219C22⋊Dic61—28no—
220C4⋊Dic61—28no—
221C4⋊Dic61—28no—
222C4⋊Dic61—28no—
223C4⋊Dic61C2×D4116yes—
224#11758196—28no—
225#11758196—28no—
226#11758196—28no—
227#11758196—28no—
228#11758196—28no—
229#11758196—28no—
230#11758196—28no—
231#11758196—28no—
232C4×Dic61—28no—
233C4×Dic61—28no—
234C4×Dic61—28no—
235C4×Dic61—28no—
236C23×C61—22no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—44no—
244C23×C61—44no—
245C23×C61—44no—
246C23×C61—44no—
247C23×C61—44no—
248C23×C61—44no—
249C23×C61—44no—
250C23×C61C22×D412yes—
251C23×C61C2×#4112yes—
252C23×C61C2×#4112yes—
253C23×C61C2×#4112yes—
254C23×C61C2×#4112yes—
255C23×C612−1+412yes—
256C23×C612−1+412yes—
257C23×C61C2511yescharacteristic
258C2×C4×C61—28no—
259C2×C4×C61—28no—
260C2×C4×C61—28no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—44no—
277C2×C4×C61—44no—
278C2×C4×C61—44no—
279C2×C4×C61C22×D414yes—
280C2×C4×C61C2×#4114yes—
281C2×C4×C61C2×#4114yes—
282C2×Dic61—28no—
283C2×Dic61—28no—
284C2×Dic61—28no—
285C2×Dic61—28no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—44no—
307C2×Dic61—44no—
308C2×Dic61—44no—
309C2×Dic61—44no—
310C2×Dic61C22×D414yes—
311C2×Dic61C22×D414yes—
312C2×Dic61C2×#4114yes—
313C2×Dic61C2×#4114yes—
314C2×#2519—611nomaximal, Sylow
315C22×C61—42no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—88no—
323C22×C61#52914yes—
324C22×C61#53214yes—
325C22×C61#54114yes—
326C22×C61#54714yes—
327C22×C61#54814yes—
328C22×C61#55214yes—
329C22×C61#55214yes—
330C22×C61C23×D411yescharacteristic
331C22×C61C22×#4111yescharacteristic
332C22×C61C22×#4111yescharacteristic
333C22×C61C22×#4111yescharacteristic
334C22×C61C22×#4111yescharacteristic
335C22×C61C2×2−1+411yescharacteristic
336C22×C61C2×2−1+411yescharacteristic
337C4×C61—24no—
338C4×C61—24no—
339C4×C61—24no—
340C4×C61—42no—
341C4×C61—42no—
342C4×C61—42no—
343Dic61—24no—
344Dic61—24no—
345Dic61—24no—
346Dic61—24no—
347Dic61—42no—
348Dic61—42no—
349Dic61—42no—
350Dic61—42no—
351C22×#126—611no—
352C22×#125—611no—
353#2519—6116no—
354C2×#399—611no—
355C2×#398—611no—
356C2×#398—611no—
357C2×#396—611no—
358C2×#389—611no—
359C2×#388—611no—
360C2×#388—611no—
361C2×#388—611no—
362C2×#388D6111yescharacteristic
363C2×#387—611no—
364C2×#382—611no—
365C2×C4×C4⋊C4—611no—
366C2×C4×C4⋊C4—611no—
367C2×C61—82no—
368C2×C61#251918yescomplemented
369C2×C61C2×#52911yescharacteristic
370C2×C61C2×#53211yescharacteristic
371C2×C61C2×#54111yescharacteristic
372C2×C61C2×#54711yescharacteristic
373C2×C61C2×#54811yescharacteristic
374C2×C61C2×#55211yescharacteristic
375C2×C61C2×#55211yescharacteristic
376C2×#126—618no—
377C2×#126—1228no—
378C2×#125—618no—
379C2×#125—1228no—
380C22×C4⋊C4—611no—
381C22×C4⋊C4—611no—
382C22×C4⋊C4—611no—
383C22×C4⋊C4—611no—
384C22×C4⋊C4—611no—
385C22×C4⋊C4—611no—
386C22×C4⋊C4—611no—
387C22×C4⋊C4—611no—
388C22×C4⋊C4—611no—
389C22×C4⋊C4—611no—
390C22×C4⋊C4—611no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4C2×D6111yescharacteristic
393C22×C22⋊C4—611no—
394C22×C22⋊C4—611no—
395C22×C22⋊C4—611no—
396C22×C22⋊C4—611no—
397C22×C22⋊C4C2×D6111yescharacteristic
398C22×C22⋊C4C2×D6111yescharacteristic
399C22×C22⋊C4C2×D6111yescharacteristic
400C22×C42—611no—
401C22×C42—611no—
402C22×C42—611no—
403C22×C42—611no—
404C22×C42C2×D6111yescharacteristic
405#399—618no—
406#398—618no—
407#398—618no—
408#396—618no—
409#389—618no—
410#388—618no—
411#388—618no—
412#388—618no—
413#388C2×D6118yes—
414#387—618no—
415#382—618no—
416C4×C4⋊C4—618no—
417C4×C4⋊C4—618no—
418C2×#95—611no—
419C2×#95—611no—
420C2×#95—611no—
421C2×#95—611no—
422C2×#95—611no—
423C2×#95—611no—
424C2×#95—611no—
425C2×#95—611no—
426C2×#95C2×D6111yescharacteristic
427C2×#95C2×D6111yescharacteristic
428C61C2×#251911yescharacteristic, complemented, Sylow
429C25C22×D6111yescharacteristic
430C23×C4—611no—
431C23×C4—611no—
432C23×C4—611no—
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4C22×D6111yescharacteristic
439C23×C4C22×D6111yescharacteristic
440C23×C4C22×D6111yescharacteristic
441C23×C4C22×D6111yescharacteristic
442C23×C4C22×D6111yescharacteristic
443C23×C4C22×D6111yescharacteristic
444#126—12232no—
445#125—12232no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—618no—
448C2×C4⋊C4—614no—
449C2×C4⋊C4—614no—
450C2×C4⋊C4—614no—
451C2×C4⋊C4—614no—
452C2×C4⋊C4—614no—
453C2×C4⋊C4—614no—
454C2×C4⋊C4—614no—
455C2×C4⋊C4—614no—
456C2×C4⋊C4—614no—
457C2×C4⋊C4—614no—
458C2×C4⋊C4—614no—
459C2×C4⋊C4—614no—
460C2×C4⋊C4—1224no—
461C2×C4⋊C4—1224no—
462C2×C4⋊C4—1224no—
463C2×C4⋊C4—1224no—
464C2×C4⋊C4—1224no—
465C2×C4⋊C4—1224no—
466C2×C4⋊C4—1224no—
467C2×C4⋊C4—1224no—
468C2×C4⋊C4—1224no—
469C2×C4⋊C4—1224no—
470C2×C4⋊C4—1224no—
471C2×C4⋊C4C22×D6114yes—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—614no—
476C2×C22⋊C4—614no—
477C2×C22⋊C4—614no—
478C2×C22⋊C4—614no—
479C2×C22⋊C4—1224no—
480C2×C22⋊C4—1224no—
481C2×C22⋊C4—1224no—
482C2×C22⋊C4—1224no—
483C2×C22⋊C4C22×D6114yes—
484C2×C22⋊C4C22×D6114yes—
485C2×C22⋊C4C22×D6114yes—
486C2×C42—24no—
487C2×C42—614no—
488C2×C42—614no—
489C2×C42—614no—
490C2×C42—614no—
491C2×C42—1224no—
492C2×C42—1224no—
493C2×C42—1224no—
494C2×C42—1224no—
495C2×C42C22×D6114yes—
496#95—614no—
497#95—614no—
498#95—614no—
499#95—614no—
500#95—614no—
501#95—614no—
502#95—614no—
503#95—614no—
504#95C22×D6114yes—
505#95C22×D6114yes—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24C23×D6112yes—
514C24C23×D6111yescharacteristic
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—614no—
531C22×C4—614no—
532C22×C4—614no—
533C22×C4—614no—
534C22×C4—612no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4#1175822214yes—
563C22×C4D4×D6114yes—
564C22×C4#1175822414yes—
565C22×C4C23×D6112yes—
566C22×C4C23×D6112yes—
567C22×C4C23×D6112yes—
568C22×C4C23×D6112yes—
569C22×C4C23×D6112yes—
570C22×C4C23×D6112yes—
571C4⋊C4—28no—
572C4⋊C4—6116no—
573C4⋊C4—1228no—
574C4⋊C4—1228no—
575C4⋊C4—1228no—
576C4⋊C4—1228no—
577C4⋊C4—1228no—
578C4⋊C4—1228no—
579C4⋊C4—1228no—
580C4⋊C4—1228no—
581C4⋊C4—1228no—
582C4⋊C4—1228no—
583C4⋊C4—1228no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—1228no—
588C22⋊C4—1228no—
589C22⋊C4—1228no—
590C22⋊C4—1228no—
591C42—28no—
592C42—1228no—
593C42—1228no—
594C42—1228no—
595C42—1228no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23C2×D4×D6112yes—
611C23#41×D6112yes—
612C23#41×D6112yes—
613C23C2×#1175822412yes—
614C23C2×#1175822212yes—
615C23#1451982412yes—
616C23#1451982412yes—
617C23C24×D6111yescharacteristic
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—614no—
640C2×C4—614no—
641C2×C4—614no—
642C2×C4—614no—
643C2×C4—1228no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1228no—
653C2×C4—1228no—
654C2×C4—1228no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—2444no—
668C2×C4—2444no—
669C2×C4—2444no—
670C2×C4—2444no—
671C2×C4C2×D4×D6114yes—
672C2×C4C2×#1175822414yes—
673C2×C4C2×#1175822214yes—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—88no—
682C22#1684029014yes—
683C22#1684030714yes—
684C22#1684036914yes—
685C22#1684041714yes—
686C22#1684042014yes—
687C22#1684044914yes—
688C22#1684045214yes—
689C22C22×D4×D6111yescharacteristic
690C22C2×#41×D6111yescharacteristic
691C22C2×#41×D6111yescharacteristic
692C22C22×#1175822411yescharacteristic
693C22C22×#1175822211yescharacteristic
694C22C2×#1451982411yescharacteristic
695C22C2×#1451982411yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—1224no—
703C4—1224no—
704C4—1224no—
705C4—1224no—
706C4—2442no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C2—82no—
711C2#2145049018yesdirect product factor
712C2C2×#1684029011yescharacteristic
713C2C2×#1684030711yescharacteristic
714C2C2×#1684036911yescharacteristic
715C2C2×#1684041711yescharacteristic
716C2C2×#1684042011yescharacteristic
717C2C2×#1684044911yescharacteristic
718C2C2×#1684045211yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61C2×#2519
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14519767C2semidirect
3. #21450490C2direct (N × H)
5. C2×#16839696C2semidirect
6. C2×#16839695C2semidirect
8. C2×#16839660C2semidirect
12. C2×#16839645C2semidirect
13. C2×#16839626C2semidirect
14. C2×C4×C4⋊Dic61C2semidirect
15. C2×#16839613C2semidirect
20. C2×#14519767C22semidirect
42. #16839696C22semidirect
43. #16839695C22semidirect
45. #16839660C22semidirect
49. #16839645C22semidirect
50. #16839626C22semidirect
51. C4×C4⋊Dic61C22semidirect
52. #16839613C22semidirect
368. C2×C61#2519semidirect
428. C61C2×#2519semidirect
711. C2#21450490direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197702
C22×#145197672
#214504902
C2×#168396982
C2×#168396962
C2×#168396952
C2×#168396852
C2×#168396602
C2×#168396552
C2×#168396502
C2×#168396452
C2×#168396262
C2×C4×C4⋊Dic612
C2×#168396132
C2×C61×#3882
C2×#251961