Finite Group Databasebeta

← C2×#21448946 #29839708

Subgroups — C2×#21448946 #29839708

Order 15616.

2726 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
2#21448946C2116yesmaximal, direct product factor
3C2×#16839657C211yesmaximal, characteristic, complemented
4C2×#16839656C211yesmaximal, characteristic
5C2×#16839650C211yesmaximal, characteristic
6C2×#16839649C211yesmaximal, characteristic, complemented
7C2×#16839649C211yesmaximal, characteristic, complemented
8C2×#16839647C211yesmaximal, characteristic, complemented
9C2×#16839637C211yesmaximal, characteristic
10C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
11C2×C4×#11758196C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic61C211yesmaximal, characteristic
14C2×C22⋊C4×Dic61C211yesmaximal, characteristic
15C2×#16839607C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic
17C24×Dic61C2211yescharacteristic
18C2×#14519770C4116yescomplemented
19C2×#14519770C2218yes—
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839657C2218yescomplemented
38#16839656C2218yes—
39#16839650C2218yes—
40#16839649C2218yescomplemented
41#16839649C2218yescomplemented
42#16839647C2218yescomplemented
43#16839637C2218yes—
44C4⋊C4×Dic61C2218yescomplemented
45C4×#11758196C2218yescomplemented
46C4×C4⋊Dic61C2218yescomplemented
47C22⋊C4×Dic61C2218yes—
48C22⋊C4×Dic61C2218yes—
49#16839607C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C61×#388C2218yes—
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C23×Dic61—24no—
69C23×Dic61—24no—
70C23×Dic61—42no—
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2314yes—
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80#14519770C2×C4164yescomplemented
81C2×C4⋊Dic61—24no—
82C2×C4⋊Dic61—24no—
83C2×C4⋊Dic61C2×C418yescomplemented
84C2×C4⋊Dic61C2314yes—
85C2×C4⋊Dic61C2314yes—
86C2×C4⋊Dic61C2314yes—
87C2×#11758196—24no—
88C2×#11758196—42no—
89C2×#11758196C2×C418yescomplemented
90C2×#11758196C2×C418yescomplemented
91C2×#11758196C2314yes—
92C2×#11758196C2314yes—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×C22⋊Dic61—42no—
96C2×C22⋊Dic61C2×C418yes—
97C2×C22⋊Dic61C2×C418yes—
98C2×C22⋊Dic61C2314yes—
99C2×C22⋊Dic61C2314yes—
100C2×C22⋊Dic61C2314yes—
101C2×C4×Dic61—24no—
102C2×C4×Dic61—24no—
103C2×C4×Dic61—24no—
104C2×C4×Dic61—42no—
105C2×C4×Dic61—42no—
106C2×C4×Dic61—42no—
107C2×C4×Dic61C2×C418yescomplemented
108C2×C4×Dic61C2314yes—
109C2×C4×Dic61C2314yes—
110C2×C4×Dic61C2314yes—
111C2×C4×Dic61C2314yes—
112C2×C4×Dic61C2314yes—
113C2×C4×Dic61C2314yes—
114C2×C4×Dic61C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125C25×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—24no—
133C2×C4⋊C4×C61C2314yes—
134C2×C22⋊C4×C61—24no—
135C2×C22⋊C4×C61—24no—
136C2×C22⋊C4×C61C2×C418yes—
137C2×C22⋊C4×C61C2314yes—
138C2×C22⋊C4×C61C2314yes—
139C2×C22⋊C4×C61C2314yes—
140C2×C42×C61—24no—
141C2×C42×C61C2314yes—
142#95×C61C2314yes—
143#95×C61C2314yes—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61C22×C414yes—
151C24×C61C2412yes—
152C24×C61C2411yescharacteristic
153C22×C4×C61—22no—
154C22×C4×C61—22no—
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×C61C22×C414yes—
168C22×C4×C61C22×C414yes—
169C22×C4×C61#4114yes—
170C22×C4×C61#4114yes—
171C22×C4×C61C2412yes—
172C22×C4×C61C2412yes—
173C22×C4×C61C2412yes—
174C22×C4×C61C2412yes—
175C22×C4×C61C2412yes—
176C22×C4×C61C2412yes—
177C22×Dic61—22no—
178C22×Dic61—22no—
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—28no—
196C22×Dic61—28no—
197C22×Dic61—44no—
198C22×Dic61—416no—
199C22×Dic61C22×C414yes—
200C22×Dic61C22×C414yes—
201C22×Dic61C22×C414yes—
202C22×Dic61C22×C414yes—
203C22×Dic61#4114yes—
204C22×Dic61#4114yes—
205C22×Dic61C2412yes—
206C22×Dic61C2412yes—
207C22×Dic61C2412yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C4⋊C4×C61—28no—
214C22⋊C4×C61—28no—
215C22⋊C4×C61—28no—
216C22⋊C4×C61C22×C4116yes—
217C42×C61—28no—
218C22⋊Dic61—44no—
219C22⋊Dic61C22×C4116yes—
220C22⋊Dic61C22×C4116yes—
221C4⋊Dic61—28no—
222C4⋊Dic61—28no—
223C4⋊Dic61C22×C4116yescomplemented
224#11758196—28no—
225#11758196—44no—
226#11758196C22×C4116yescomplemented
227#11758196C22×C4116yescomplemented
228C4×Dic61—28no—
229C4×Dic61—28no—
230C4×Dic61—28no—
231C4×Dic61—44no—
232C4×Dic61—44no—
233C4×Dic61—44no—
234C4×Dic61C22×C4116yescomplemented
235C23×C61—28no—
236C23×C61—28no—
237C23×C61—28no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—44no—
245C23×C61—44no—
246C23×C61—44no—
247C23×C61—44no—
248C23×C61C23×C414yes—
249C23×C61C23×C412yes—
250C23×C61C2×#4112yes—
251C23×C61C2×#4112yes—
252C23×C61C2×#4112yes—
253C23×C61C2×#4112yes—
254C23×C61H(5,𝔽2)12yes—
255C23×C612−1+412yes—
256C23×C61C2511yescharacteristic
257C2×C4×C61—28no—
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—44no—
276C2×C4×C61—44no—
277C2×C4×C61C23×C414yes—
278C2×C4×C61C23×C414yes—
279C2×C4×C61C2×#4114yes—
280C2×C4×C61C2×#4114yes—
281C2×Dic61—28no—
282C2×Dic61—28no—
283C2×Dic61—28no—
284C2×Dic61—28no—
285C2×Dic61—28no—
286C2×Dic61—28no—
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—416no—
306C2×Dic61—44no—
307C2×Dic61—44no—
308C2×Dic61C23×C414yes—
309C2×Dic61C23×C414yes—
310C2×Dic61C23×C414yes—
311C2×Dic61C23×C414yes—
312C2×Dic61C2×#4114yes—
313C2×Dic61C2×#4114yes—
314C2×#2373—611nomaximal, Sylow
315C22×C61—24no—
316C22×C61—24no—
317C22×C61—24no—
318C22×C61—416no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61C4×#4114yes—
324C22×C61C4×#4114yes—
325C22×C61#52014yes—
326C22×C61#55114yes—
327C22×C61#55214yes—
328C22×C61#55314yes—
329C22×C61#55614yes—
330C22×C61C24×C411yescharacteristic
331C22×C61C22×#4111yescharacteristic
332C22×C61C22×#4111yescharacteristic
333C22×C61C22×#4111yescharacteristic
334C22×C61C22×#4111yescharacteristic
335C22×C61C2×H(5,𝔽2)11yescharacteristic
336C22×C61C2×2−1+411yescharacteristic
337C4×C61—24no—
338C4×C61—24no—
339C4×C61—24no—
340C4×C61—24no—
341C4×C61—42no—
342C4×C61—42no—
343Dic61—24no—
344Dic61—24no—
345Dic61—24no—
346Dic61—24no—
347Dic61—24no—
348Dic61—24no—
349Dic61—42no—
350Dic61—42no—
351C22×#126—611no—
352#2373—6116no—
353C2×#389—611no—
354C2×#388—611no—
355C2×#388—611no—
356C2×#388D6111yescharacteristic
357C2×#387—611no—
358C2×#387—611no—
359C2×#387—611no—
360C2×#385—611no—
361C2×C4×C4⋊C4—611no—
362C2×C4×C4⋊C4—611no—
363C2×C4×C4⋊C4—611no—
364C2×C4×C22⋊C4—611no—
365C2×C4×C22⋊C4—611no—
366C2×#376—611no—
367C2×C61—44no—
368C2×C61#237318yescomplemented
369C2×C61C2×C4×#4111yescharacteristic
370C2×C61C2×C4×#4111yescharacteristic
371C2×C61C2×#52011yescharacteristic
372C2×C61C2×#55111yescharacteristic
373C2×C61C2×#55211yescharacteristic
374C2×C61C2×#55311yescharacteristic
375C2×C61C2×#55611yescharacteristic
376C24×C4—611no—
377C2×#126—6116no—
378C2×#126—618no—
379C22×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
387C22×C22⋊C4—611no—
388C22×C22⋊C4—611no—
389C22×C22⋊C4—611no—
390C22×C22⋊C4C2×D6111yescharacteristic
391C22×C22⋊C4C2×D6111yescharacteristic
392C22×C22⋊C4C2×D6111yescharacteristic
393C22×C42—611no—
394C22×C42—611no—
395C22×C42—611no—
396C22×C42—611no—
397C22×C42—611no—
398C22×C42—611no—
399C22×C42—611no—
400C22×C42C2×D6111yescharacteristic
401#389—618no—
402#388—618no—
403#388—618no—
404#388C2×D6118yes—
405#387—618no—
406#387—618no—
407#387—618no—
408#385—618no—
409C4×C4⋊C4—618no—
410C4×C4⋊C4—618no—
411C4×C4⋊C4—618no—
412C4×C22⋊C4—618no—
413C4×C22⋊C4—618no—
414#376—618no—
415C2×#95—611no—
416C2×#95—611no—
417C2×#95—611no—
418C2×#95—611no—
419C2×#95—611no—
420C2×#95—611no—
421C2×#95—611no—
422C2×#95—611no—
423C2×#95—611no—
424C2×#95—611no—
425C2×#95C2×D6111yescharacteristic
426C2×#95C2×D6111yescharacteristic
427C61C2×#237311yescharacteristic, complemented, Sylow
428C25C22×D6111yescharacteristic
429C23×C4—611no—
430C23×C4—611no—
431C23×C4—611no—
432C23×C4—611no—
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—614no—
438C23×C4—1224no—
439C23×C4—1224no—
440C23×C4—2442no—
441C23×C4C22×D6111yescharacteristic
442C23×C4C22×D6111yescharacteristic
443C23×C4C22×D6111yescharacteristic
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447#126—6164no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—618no—
450C2×C4⋊C4—618no—
451C2×C4⋊C4—618no—
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—1224no—
460C2×C4⋊C4—1224no—
461C2×C4⋊C4—1224no—
462C2×C4⋊C4—2442no—
463C2×C4⋊C4C22×D6114yes—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—618no—
467C2×C22⋊C4—618no—
468C2×C22⋊C4—614no—
469C2×C22⋊C4—614no—
470C2×C22⋊C4—614no—
471C2×C22⋊C4—2442no—
472C2×C22⋊C4C4×D6118yes—
473C2×C22⋊C4C22×D6114yes—
474C2×C22⋊C4C22×D6114yes—
475C2×C22⋊C4C22×D6114yes—
476C2×C42—24no—
477C2×C42—618no—
478C2×C42—614no—
479C2×C42—614no—
480C2×C42—614no—
481C2×C42—614no—
482C2×C42—614no—
483C2×C42—614no—
484C2×C42—614no—
485C2×C42—1224no—
486C2×C42—1224no—
487C2×C42—1224no—
488C2×C42—2442no—
489C2×C42—2442no—
490C2×C42—2442no—
491C2×C42C22×D6114yes—
492#95—614no—
493#95—614no—
494#95—614no—
495#95—614no—
496#95—614no—
497#95—614no—
498#95—614no—
499#95—614no—
500#95—614no—
501#95—614no—
502#95C22×D6114yes—
503#95C22×D6114yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C2×C4×D6114yes—
511C24C23×D6112yes—
512C24C23×D6111yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
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—614no—
528C22×C4—614no—
529C22×C4—614no—
530C22×C4—614no—
531C22×C4—614no—
532C22×C4—614no—
533C22×C4—612no—
534C22×C4—612no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—1228no—
542C22×C4—1228no—
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—2444no—
562C22×C4—24416no—
563C22×C4C2×C4×D6114yes—
564C22×C4C2×C4×D6114yes—
565C22×C4#1175822414yes—
566C22×C4#1175822414yes—
567C22×C4C23×D6112yes—
568C22×C4C23×D6112yes—
569C22×C4C23×D6112yes—
570C22×C4C23×D6112yes—
571C22×C4C23×D6112yes—
572C22×C4C23×D6112yes—
573C4⋊C4—28no—
574C4⋊C4—6116no—
575C4⋊C4—6116no—
576C4⋊C4—6116no—
577C4⋊C4—1228no—
578C4⋊C4—1228no—
579C4⋊C4—1228no—
580C4⋊C4—2444no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—6116no—
584C22⋊C4—6116no—
585C22⋊C4—2444no—
586C22⋊C4C2×C4×D61116yes—
587C42—28no—
588C42—6116no—
589C42—1228no—
590C42—1228no—
591C42—1228no—
592C42—2444no—
593C42—2444no—
594C42—2444no—
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C22×C4×D6114yes—
609C23C22×C4×D6112yes—
610C23#41×D6112yes—
611C23#41×D6112yes—
612C23C2×#1175822412yes—
613C23C2×#1175822412yes—
614C23#1451982312yes—
615C23#1451982412yes—
616C23C24×D6111yescharacteristic
617C2×C4—28no—
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—44no—
636C2×C4—44no—
637C2×C4—614no—
638C2×C4—614no—
639C2×C4—614no—
640C2×C4—614no—
641C2×C4—614no—
642C2×C4—614no—
643C2×C4—1228no—
644C2×C4—1228no—
645C2×C4—1228no—
646C2×C4—1228no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1228no—
660C2×C4—1228no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—24416no—
668C2×C4—2444no—
669C2×C4—2444no—
670C2×C4C22×C4×D6114yes—
671C2×C4C22×C4×D6114yes—
672C2×C4C2×#1175822414yes—
673C2×C4C2×#1175822414yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—416no—
682C22C4×#1175822414yes—
683C22C4×#1175822414yes—
684C22#1684024214yes—
685C22#1684043714yes—
686C22#1684044914yes—
687C22#1684046414yes—
688C22#1684048114yes—
689C22C23×C4×D6111yescharacteristic
690C22C2×#41×D6111yescharacteristic
691C22C2×#41×D6111yescharacteristic
692C22C22×#1175822411yescharacteristic
693C22C22×#1175822411yescharacteristic
694C22C2×#1451982311yescharacteristic
695C22C2×#1451982411yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—1224no—
703C4—1224no—
704C4—1224no—
705C4—1224no—
706C4—1224no—
707C4—1224no—
708C4—2442no—
709C4—2442no—
710C2—44no—
711C2#2144894618yesdirect product factor
712C2C2×C4×#1175822411yescharacteristic
713C2C2×C4×#1175822411yescharacteristic
714C2C2×#1684024211yescharacteristic
715C2C2×#1684043711yescharacteristic
716C2C2×#1684044911yescharacteristic
717C2C2×#1684046411yescharacteristic
718C2C2×#1684048111yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC25×C61C23
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2373
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #21448946C2direct (N × H)
3. C2×#16839657C2semidirect
6. C2×#16839649C2semidirect
7. C2×#16839649C2semidirect
8. C2×#16839647C2semidirect
10. C2×C4⋊C4×Dic61C2semidirect
11. C2×C4×#11758196C2semidirect
12. C2×C4×C4⋊Dic61C2semidirect
15. C2×#16839607C2semidirect
18. C2×#14519770C4semidirect
37. #16839657C22semidirect
40. #16839649C22semidirect
41. #16839649C22semidirect
42. #16839647C22semidirect
44. C4⋊C4×Dic61C22semidirect
45. C4×#11758196C22semidirect
46. C4×C4⋊Dic61C22semidirect
49. #16839607C22semidirect
80. #14519770C2×C4semidirect
83. C2×C4⋊Dic61C2×C4semidirect
89. C2×#11758196C2×C4semidirect
90. C2×#11758196C2×C4semidirect
107. C2×C4×Dic61C2×C4semidirect
223. C4⋊Dic61C22×C4semidirect
226. #11758196C22×C4semidirect
227. #11758196C22×C4semidirect
234. C4×Dic61C22×C4semidirect
368. C2×C61#2373semidirect
427. C61C2×#2373semidirect
711. C2#21448946direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197702
#214489462
C2×#168396572
C2×#168396562
C2×#168396502
C2×#168396492
C2×#168396472
C2×#168396372
C2×C4⋊C4×Dic612
C2×C4×#117581962
C2×C4×C4⋊Dic612
C2×C22⋊C4×Dic612
C2×#168396072
C2×C61×#3882
C2×#237361