Finite Group Databasebeta

← C2×#21448677 #29839237

Subgroups — C2×#21448677 #29839237

Order 15616.

3006 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519733C211yesmaximal, characteristic
2#21448677C2116yesmaximal, direct product factor
3C2×#16839649C211yesmaximal, characteristic, complemented
4C2×#16839649C211yesmaximal, characteristic, complemented
5C2×#16839643C211yesmaximal, characteristic, complemented
6C2×#16839643C211yesmaximal, characteristic, complemented
7C2×#16839637C211yesmaximal, characteristic
8C2×#16839629C211yesmaximal, characteristic, complemented
9C2×#16839627C211yesmaximal, characteristic, complemented
10C2×#16839623C211yesmaximal, characteristic
11C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic61C211yesmaximal, characteristic
13C2×C4×C22⋊Dic61C211yesmaximal, characteristic
14C2×#16839607C211yesmaximal, characteristic, complemented
15C22×#14519684C211yesmaximal, characteristic
16C2×C61×#385C211yesmaximal, characteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519733C4116yescomplemented
20C2×#14519733C2218yes—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839649C2218yescomplemented
34#16839649C2218yescomplemented
35#16839643C2218yescomplemented
36#16839643C2218yescomplemented
37#16839637C2218yes—
38#16839629C2218yescomplemented
39#16839627C2218yescomplemented
40#16839623C2218yes—
41C4⋊C4×Dic61C2218yescomplemented
42C22⋊C4×Dic61C2218yes—
43C4×C22⋊Dic61C2218yes—
44#16839607C2218yescomplemented
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2218yes—
60C24×C4×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C61×#385C2218yes—
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C23×Dic61—24no—
69C23×Dic61—24no—
70C23×Dic61—24no—
71C23×Dic61—24no—
72C23×Dic61—42no—
73C23×Dic61C2×C418yes—
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2314yes—
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2314yes—
83C23×Dic61C2311yescharacteristic
84#14519733C2×C4164yescomplemented
85C2×C4⋊Dic61—24no—
86C2×C4⋊Dic61—42no—
87C2×C4⋊Dic61C2314yes—
88C2×C4⋊Dic61C2314yes—
89C2×#11758196C2×C418yescomplemented
90C2×#11758196C2×C418yescomplemented
91C2×#11758196C2314yes—
92C2×#11758196C2314yes—
93C2×C22⋊Dic61—24no—
94C2×C22⋊Dic61C2×C418yes—
95C2×C22⋊Dic61C2314yes—
96C2×C22⋊Dic61C2314yes—
97C2×C4×Dic61—24no—
98C2×C4×Dic61—24no—
99C2×C4×Dic61—42no—
100C2×C4×Dic61—42no—
101C2×C4×Dic61C2×C418yescomplemented
102C2×C4×Dic61C2×C418yescomplemented
103C2×C4×Dic61C2314yes—
104C2×C4×Dic61C2314yes—
105C2×C4×Dic61C2314yes—
106C2×C4×Dic61C2314yes—
107C2×C4×Dic61C2314yes—
108C2×C4×Dic61C2314yes—
109#14519684C2314yes—
110#14519684C2314yes—
111#14519684C2314yes—
112#14519684C2314yes—
113#14519684C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123C25×C61C2311yescharacteristic
124C23×C4×C61—24no—
125C23×C4×C61—24no—
126C23×C4×C61—42no—
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2314yes—
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61—24no—
135C2×C4⋊C4×C61—42no—
136C2×C4⋊C4×C61C2314yes—
137C2×C4⋊C4×C61C2314yes—
138C2×C22⋊C4×C61—24no—
139C2×C22⋊C4×C61C2×C418yes—
140C2×C22⋊C4×C61C2314yes—
141C2×C22⋊C4×C61C2314yes—
142#95×C61C2314yes—
143#95×C61C2314yes—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61C22×C414yes—
149C24×C61#4114yes—
150C24×C61#4114yes—
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—28no—
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—28no—
170C22×C4×C61—44no—
171C22×C4×C61—416no—
172C22×C4×C61C22×C414yes—
173C22×C4×C61C22×C414yes—
174C22×C4×C61#4114yes—
175C22×C4×C61C2412yes—
176C22×C4×C61C2412yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2412yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×Dic61—232no—
182C22×Dic61—28no—
183C22×Dic61—28no—
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—28no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—28no—
205C22×Dic61—44no—
206C22×Dic61—416no—
207C22×Dic61C22×C414yes—
208C22×Dic61C22×C414yes—
209C22×Dic61C22×C4116yes—
210C22×Dic61C22×C414yes—
211C22×Dic61C22×C414yes—
212C22×Dic61#4114yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C22×Dic61C2412yes—
218C22×Dic61C2412yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C4⋊C4×C61—28no—
222C4⋊C4×C61—44no—
223C22⋊C4×C61—28no—
224C22⋊C4×C61C22×C4116yes—
225C22⋊Dic61—28no—
226C22⋊Dic61C22×C4116yes—
227C4⋊Dic61—28no—
228C4⋊Dic61—44no—
229#11758196C22×C4116yescomplemented
230#11758196C22×C4116yescomplemented
231C4×Dic61—28no—
232C4×Dic61—28no—
233C4×Dic61—44no—
234C4×Dic61—44no—
235C4×Dic61C22×C4116yescomplemented
236C4×Dic61C22×C4116yescomplemented
237C23×C61—28no—
238C23×C61—28no—
239C23×C61—28no—
240C23×C61—28no—
241C23×C61—28no—
242C23×C61—28no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61#117116yes—
248C23×C61C23×C414yes—
249C23×C61C23×C412yes—
250C23×C61C2×#4114yes—
251C23×C61C2×#4114yes—
252C23×C61C2×#4112yes—
253C23×C61C2×#4112yes—
254C23×C61C2×#4112yes—
255C23×C61C2×#4112yes—
256C23×C61H(5,𝔽2)12yes—
257C23×C612−1+412yes—
258C23×C61C2511yescharacteristic
259C2×C4×C61—28no—
260C2×C4×C61—28no—
261C2×C4×C61—28no—
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—22no—
277C2×C4×C61—416no—
278C2×C4×C61—44no—
279C2×C4×C61—44no—
280C2×C4×C61—44no—
281C2×C4×C61C23×C414yes—
282C2×C4×C61C23×C414yes—
283C2×C4×C61C2×#4114yes—
284C2×Dic61—232no—
285C2×Dic61—28no—
286C2×Dic61—28no—
287C2×Dic61—28no—
288C2×Dic61—28no—
289C2×Dic61—28no—
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—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—416no—
310C2×Dic61—44no—
311C2×Dic61—44no—
312C2×Dic61—44no—
313C2×Dic61C23×C414yes—
314C2×Dic61C23×C414yes—
315C2×Dic61C23×C414yes—
316C2×Dic61C23×C414yes—
317C2×Dic61C2×#4114yes—
318C2×#2343—611nomaximal, Sylow
319C22×C61—232no—
320C22×C61—24no—
321C22×C61—24no—
322C22×C61—24no—
323C22×C61—24no—
324C22×C61—24no—
325C22×C61—24no—
326C22×C61C2×#11718yes—
327C22×C61C2×#11714yes—
328C22×C61C4×#4114yes—
329C22×C61#52014yes—
330C22×C61#55114yes—
331C22×C61#55114yes—
332C22×C61#55214yes—
333C22×C61#55214yes—
334C22×C61C24×C411yescharacteristic
335C22×C61C22×#4111yescharacteristic
336C22×C61C22×#4111yescharacteristic
337C22×C61C22×#4111yescharacteristic
338C22×C61C22×#4111yescharacteristic
339C22×C61C2×H(5,𝔽2)11yescharacteristic
340C22×C61C2×2−1+411yescharacteristic
341C4×C61—24no—
342C4×C61—24no—
343C4×C61—24no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—42no—
347Dic61—24no—
348Dic61—24no—
349Dic61—24no—
350Dic61—24no—
351Dic61—24no—
352Dic61—42no—
353Dic61—42no—
354Dic61—42no—
355C22×#117—611no—
356#2343—6116no—
357C2×#387—611no—
358C2×#387—611no—
359C2×#387—611no—
360C2×#387—611no—
361C2×#385—611no—
362C2×#385D6111yescharacteristic
363C2×#383—611no—
364C2×#382—611no—
365C2×#381—611no—
366C2×C4×C4⋊C4—611no—
367C2×C4×C22⋊C4—611no—
368C2×C4×C22⋊C4—611no—
369C2×#376—611no—
370C22×#95—611no—
371C2×C61—28no—
372C2×C61#234318yescomplemented
373C2×C61C22×#11711yescharacteristic
374C2×C61C2×C4×#4111yescharacteristic
375C2×C61C2×#52011yescharacteristic
376C2×C61C2×#55111yescharacteristic
377C2×C61C2×#55111yescharacteristic
378C2×C61C2×#55211yescharacteristic
379C2×C61C2×#55211yescharacteristic
380C24×C4—611no—
381C24×C4—611no—
382C24×C4C2×D6111yescharacteristic
383C2×#117—6116no—
384C2×#117—618no—
385C22×C4⋊C4—611no—
386C22×C4⋊C4—611no—
387C22×C4⋊C4—611no—
388C22×C4⋊C4—611no—
389C22×C4⋊C4C2×D6111yescharacteristic
390C22×C4⋊C4C2×D6111yescharacteristic
391C22×C22⋊C4—611no—
392C22×C22⋊C4—611no—
393C22×C22⋊C4C2×D6111yescharacteristic
394C22×C22⋊C4C2×D6111yescharacteristic
395C22×C42—611no—
396C22×C42—611no—
397C22×C42—611no—
398C22×C42—611no—
399C22×C42—611no—
400C22×C42—611no—
401#387—618no—
402#387—618no—
403#387—618no—
404#387—618no—
405#385—618no—
406#385C2×D6118yes—
407#383—618no—
408#382—618no—
409#381—618no—
410C4×C4⋊C4—618no—
411C4×C22⋊C4—618no—
412C4×C22⋊C4—618no—
413#376—618no—
414C2×#95—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×#95—611no—
426C2×#95—611no—
427C2×#95—611no—
428C2×#95—611no—
429C2×#95C2×D6111yescharacteristic
430C2×#95C2×D6111yescharacteristic
431C61C2×#234311yescharacteristic, complemented, Sylow
432C25C22×D6111yescharacteristic
433C23×C4—24no—
434C23×C4—24no—
435C23×C4—42no—
436C23×C4—618no—
437C23×C4—614no—
438C23×C4—611no—
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—614no—
447C23×C4—1224no—
448C23×C4—1224no—
449C23×C4—1224no—
450C23×C4—1224no—
451C23×C4—2442no—
452C23×C4C22×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C23×C4C22×D6114yes—
456C23×C4C22×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458C23×C4C22×D6111yescharacteristic
459#117—6164no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—618no—
463C2×C4⋊C4—618no—
464C2×C4⋊C4—614no—
465C2×C4⋊C4—614no—
466C2×C4⋊C4—614no—
467C2×C4⋊C4—614no—
468C2×C4⋊C4—1224no—
469C2×C4⋊C4—2442no—
470C2×C4⋊C4C22×D6114yes—
471C2×C4⋊C4C22×D6114yes—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—618no—
474C2×C22⋊C4—614no—
475C2×C22⋊C4—614no—
476C2×C22⋊C4—1224no—
477C2×C22⋊C4C4×D6118yes—
478C2×C22⋊C4C22×D6114yes—
479C2×C22⋊C4C22×D6114yes—
480C2×C42—618no—
481C2×C42—618no—
482C2×C42—614no—
483C2×C42—614no—
484C2×C42—614no—
485C2×C42—614no—
486C2×C42—614no—
487C2×C42—614no—
488C2×C42—1224no—
489C2×C42—1224no—
490C2×C42—2442no—
491C2×C42—2442no—
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#95—614no—
503#95—614no—
504#95—614no—
505#95—614no—
506#95C22×D6114yes—
507#95C22×D6114yes—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24C2×C4×D6114yes—
513C24#1175822414yes—
514C24#1175822614yes—
515C24C23×D6112yes—
516C24C23×D6111yescharacteristic
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—28no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—28no—
534C22×C4—44no—
535C22×C4—416no—
536C22×C4—614no—
537C22×C4—614no—
538C22×C4—614no—
539C22×C4—614no—
540C22×C4—6116no—
541C22×C4—614no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—1228no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1228no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1228no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—12232no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1228no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—2444no—
575C22×C4—24416no—
576C22×C4C2×C4×D6114yes—
577C22×C4C2×C4×D6114yes—
578C22×C4#1175822414yes—
579C22×C4C23×D6112yes—
580C22×C4C23×D6112yes—
581C22×C4C23×D6112yes—
582C22×C4C23×D6112yes—
583C22×C4C23×D6112yes—
584C22×C4C23×D6112yes—
585C4⋊C4—28no—
586C4⋊C4—44no—
587C4⋊C4—6116no—
588C4⋊C4—6116no—
589C4⋊C4—1228no—
590C4⋊C4—2444no—
591C22⋊C4—28no—
592C22⋊C4—6116no—
593C22⋊C4—1228no—
594C22⋊C4C2×C4×D61116yes—
595C42—6116no—
596C42—6116no—
597C42—1228no—
598C42—1228no—
599C42—2444no—
600C42—2444no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—28no—
610C23—28no—
611C23#14519735116yes—
612C23C22×C4×D6114yes—
613C23C22×C4×D6112yes—
614C23#41×D6112yes—
615C23C2×#1175822414yes—
616C23C2×#1175822412yes—
617C23C2×#1175822412yes—
618C23C2×#1175822614yes—
619C23C2×#1175822612yes—
620C23#1451982212yes—
621C23#1451982412yes—
622C23C24×D6111yescharacteristic
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—28no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—416no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—614no—
646C2×C4—614no—
647C2×C4—614no—
648C2×C4—614no—
649C2×C4—614no—
650C2×C4—12232no—
651C2×C4—1228no—
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—1228no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—24416no—
676C2×C4—2444no—
677C2×C4—2444no—
678C2×C4—2444no—
679C2×C4C22×C4×D6114yes—
680C2×C4C22×C4×D6114yes—
681C2×C4C2×#1175822414yes—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—232no—
689C22C2×#1451973518yes—
690C22C2×#1451973514yes—
691C22C4×#1175822414yes—
692C22#1684024114yes—
693C22#1684043914yes—
694C22#1684044314yes—
695C22#1684044914yes—
696C22#1684045414yes—
697C22C23×C4×D6111yescharacteristic
698C22C2×#41×D6111yescharacteristic
699C22C22×#1175822411yescharacteristic
700C22C22×#1175822411yescharacteristic
701C22C22×#1175822611yescharacteristic
702C22C2×#1451982211yescharacteristic
703C22C2×#1451982411yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—1224no—
711C4—1224no—
712C4—1224no—
713C4—1224no—
714C4—1224no—
715C4—2442no—
716C4—2442no—
717C4—2442no—
718C2—28no—
719C2#2144867718yesdirect product factor
720C2C22×#1451973511yescharacteristic
721C2C2×C4×#1175822411yescharacteristic
722C2C2×#1684024111yescharacteristic
723C2C2×#1684043911yescharacteristic
724C2C2×#1684044311yescharacteristic
725C2C2×#1684044911yescharacteristic
726C2C2×#1684045411yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC25×C61C23
cosocleC23×C61C25
hypercenterC2×#385D61
hypocenterC61C2×#2343
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #21448677C2direct (N × H)
3. C2×#16839649C2semidirect
4. C2×#16839649C2semidirect
5. C2×#16839643C2semidirect
6. C2×#16839643C2semidirect
8. C2×#16839629C2semidirect
9. C2×#16839627C2semidirect
11. C2×C4⋊C4×Dic61C2semidirect
14. C2×#16839607C2semidirect
19. C2×#14519733C4semidirect
33. #16839649C22semidirect
34. #16839649C22semidirect
35. #16839643C22semidirect
36. #16839643C22semidirect
38. #16839629C22semidirect
39. #16839627C22semidirect
41. C4⋊C4×Dic61C22semidirect
44. #16839607C22semidirect
84. #14519733C2×C4semidirect
89. C2×#11758196C2×C4semidirect
90. C2×#11758196C2×C4semidirect
101. C2×C4×Dic61C2×C4semidirect
102. C2×C4×Dic61C2×C4semidirect
229. #11758196C22×C4semidirect
230. #11758196C22×C4semidirect
235. C4×Dic61C22×C4semidirect
236. C4×Dic61C22×C4semidirect
372. C2×C61#2343semidirect
431. C61C2×#2343semidirect
719. C2#21448677direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197332
#214486772
C2×#168396492
C2×#168396432
C2×#168396372
C2×#168396292
C2×#168396272
C2×#168396232
C2×C4⋊C4×Dic612
C2×C22⋊C4×Dic612
C2×C4×C22⋊Dic612
C2×#168396072
C22×#145196842
C2×C61×#3852
C2×#234361