Finite Group Databasebeta

← C2×#21449984 #29848461

Subgroups — C2×#21449984 #29848461

Order 15616.

2638 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519767C211yesmaximal, characteristic, complemented
2#21449984C2116yesmaximal, direct product factor
3C2×#16839700C211yesmaximal, characteristic, complemented
4C2×#16839693C211yesmaximal, characteristic, complemented
5C2×#16839687C211yesmaximal, characteristic
6C2×#16839685C211yesmaximal, characteristic
7C2×#16839660C211yesmaximal, characteristic, complemented
8C2×#16839656C211yesmaximal, characteristic
9C2×#16839650C211yesmaximal, characteristic
10C2×#16839648C211yesmaximal, characteristic, complemented
11C2×#16839646C211yesmaximal, characteristic, complemented
12C2×#16839646C211yesmaximal, characteristic, complemented
13C2×#16839635C211yesmaximal, characteristic
14C2×#16839635C211yesmaximal, characteristic
15C2×C4×#11758196C211yesmaximal, characteristic, complemented
16C22×#117×C61C211yesmaximal, characteristic
17C2×#14519767—28no—
18C2×#14519767C2218yescomplemented
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839700C2218yescomplemented
36#16839693C2218yescomplemented
37#16839687C2218yes—
38#16839685C2218yes—
39#16839660C2218yescomplemented
40#16839656C2218yes—
41#16839650C2218yes—
42#16839648C2218yescomplemented
43#16839646C2218yescomplemented
44#16839646C2218yescomplemented
45#16839635C2218yes—
46#16839635C2218yes—
47C4×#11758196C2218yescomplemented
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C24×C4×C61C2211yescharacteristic
61C2×#117×C61—28no—
62C2×#117×C61C2218yes—
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C42×C61C2211yescharacteristic
68C22×C42×C61C2211yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77#14519767—232no—
78C2×C4⋊Dic61—24no—
79C2×C4⋊Dic61—24no—
80C2×C4⋊Dic61C2314yes—
81C2×C4⋊Dic61C2314yes—
82C2×#11758196—24no—
83C2×#11758196—24no—
84C2×#11758196—24no—
85C2×#11758196—24no—
86C2×#11758196—24no—
87C2×#11758196—24no—
88C2×#11758196—24no—
89C2×#11758196—24no—
90C2×#11758196C2314yes—
91C2×#11758196C2314yes—
92C2×#11758196C2314yes—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×#11758196C2314yes—
98C2×C22⋊Dic61—24no—
99C2×C22⋊Dic61—24no—
100C2×C22⋊Dic61—24no—
101C2×C22⋊Dic61—24no—
102C2×C22⋊Dic61C2314yes—
103C2×C22⋊Dic61C2314yes—
104C2×C22⋊Dic61C2314yes—
105C2×C22⋊Dic61C2314yes—
106C2×C4×Dic61—24no—
107C2×C4×Dic61—24no—
108C2×C4×Dic61C2314yes—
109C2×C4×Dic61C2314yes—
110#14519684C2314yes—
111#14519684C2314yes—
112#14519684C2314yes—
113#14519684C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122C25×C61C2311yescharacteristic
123C23×C4×C61—24no—
124C23×C4×C61—24no—
125C23×C4×C61—24no—
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2314yes—
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133#117×C61—232no—
134C2×C4⋊C4×C61—24no—
135C2×C4⋊C4×C61D418yes—
136C2×C4⋊C4×C61C2314yes—
137C2×C4⋊C4×C61C2314yes—
138C2×C22⋊C4×C61—24no—
139C2×C22⋊C4×C61—24no—
140C2×C22⋊C4×C61C2314yes—
141C2×C22⋊C4×C61C2314yes—
142C2×C42×C61—24no—
143C2×C42×C61—24no—
144C2×C42×C61C2314yes—
145C2×C42×C61C2314yes—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61#4114yes—
153C24×C61C2412yes—
154C24×C61C2411yescharacteristic
155C22×C4×C61—232no—
156C22×C4×C61—22no—
157C22×C4×C61—28no—
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—28no—
166C22×C4×C61—28no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61C2×D414yes—
174C22×C4×C61C2×D414yes—
175C22×C4×C61C2×D414yes—
176C22×C4×C61#4114yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2412yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
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×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61#4114yes—
206C22×Dic61#4114yes—
207C22×Dic61C2412yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C4⋊C4×C61—28no—
216C4⋊C4×C61C2×D4116yes—
217C22⋊C4×C61—28no—
218C22⋊C4×C61—28no—
219C42×C61—28no—
220C42×C61—28no—
221C22⋊Dic61—28no—
222C22⋊Dic61—28no—
223C22⋊Dic61—28no—
224C22⋊Dic61—28no—
225C4⋊Dic61—28no—
226C4⋊Dic61—28no—
227#11758196—28no—
228#11758196—28no—
229#11758196—28no—
230#11758196—28no—
231#11758196—28no—
232#11758196—28no—
233#11758196—28no—
234#11758196—28no—
235C4×Dic61—28no—
236C4×Dic61—28no—
237C23×C61—28no—
238C23×C61—28no—
239C23×C61—28no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—44no—
247C23×C61—44no—
248C23×C61—44no—
249C23×C61—44no—
250C23×C61C22×D412yes—
251C23×C61C2×#4114yes—
252C23×C61C2×#4112yes—
253C23×C61C2×#4112yes—
254C23×C61C2×#4112yes—
255C23×C61C2×#4112yes—
256C23×C612−1+412yes—
257C23×C612−1+412yes—
258C23×C61C2511yescharacteristic
259C2×C4×C61—232no—
260C2×C4×C61—28no—
261C2×C4×C61—28no—
262C2×C4×C61—28no—
263C2×C4×C61—28no—
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—22no—
278C2×C4×C61—44no—
279C2×C4×C61—44no—
280C2×C4×C61C22×D414yes—
281C2×C4×C61C22×D414yes—
282C2×C4×C61C22×D414yes—
283C2×C4×C61C2×#4114yes—
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—22no—
307C2×Dic61—22no—
308C2×Dic61—44no—
309C2×Dic61—44no—
310C2×Dic61—44no—
311C2×Dic61—44no—
312C2×Dic61—44no—
313C2×Dic61—44no—
314C2×Dic61C2×#4114yes—
315C2×Dic61C2×#4114yes—
316C2×#2475—611nomaximal, Sylow
317C22×C61—24no—
318C22×C61—24no—
319C22×C61—24no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—416no—
325C22×C61#52514yes—
326C22×C61#52914yes—
327C22×C61#54114yes—
328C22×C61#54714yes—
329C22×C61#54814yes—
330C22×C61#55214yes—
331C22×C61#55214yes—
332C22×C61C23×D411yescharacteristic
333C22×C61C22×#4111yescharacteristic
334C22×C61C22×#4111yescharacteristic
335C22×C61C22×#4111yescharacteristic
336C22×C61C22×#4111yescharacteristic
337C22×C61C2×2−1+411yescharacteristic
338C22×C61C2×2−1+411yescharacteristic
339C4×C61—24no—
340C4×C61—24no—
341C4×C61—24no—
342C4×C61—24no—
343C4×C61—42no—
344C4×C61—42no—
345Dic61—24no—
346Dic61—24no—
347Dic61—42no—
348Dic61—42no—
349Dic61—42no—
350Dic61—42no—
351Dic61—42no—
352Dic61—42no—
353C22×#125—611no—
354C22×#117D6111yescharacteristic
355#2475—6116no—
356C2×#400—611no—
357C2×#398—611no—
358C2×#397—611no—
359C2×#396—611no—
360C2×#389—611no—
361C2×#388—611no—
362C2×#388—611no—
363C2×#387—611no—
364C2×#387—611no—
365C2×#387—611no—
366C2×#385—611no—
367C2×#385—611no—
368C2×C4×C4⋊C4—611no—
369C2×C61—44no—
370C2×C61#247518yescomplemented
371C2×C61C2×#52511yescharacteristic
372C2×C61C2×#52911yescharacteristic
373C2×C61C2×#54111yescharacteristic
374C2×C61C2×#54711yescharacteristic
375C2×C61C2×#54811yescharacteristic
376C2×C61C2×#55211yescharacteristic
377C2×C61C2×#55211yescharacteristic
378C24×C4C2×D6111yescharacteristic
379C2×#125—618no—
380C2×#125—1228no—
381C2×#117—28no—
382C2×#117C2×D6118yes—
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⋊C4—611no—
393C22×C4⋊C4C2×D6111yescharacteristic
394C22×C4⋊C4C2×D6111yescharacteristic
395C22×C22⋊C4—611no—
396C22×C22⋊C4—611no—
397C22×C22⋊C4—611no—
398C22×C22⋊C4—611no—
399C22×C22⋊C4C2×D6111yescharacteristic
400C22×C22⋊C4C2×D6111yescharacteristic
401C22×C42—611no—
402C22×C42—611no—
403C22×C42C2×D6111yescharacteristic
404C22×C42C2×D6111yescharacteristic
405#400—618no—
406#398—618no—
407#397—618no—
408#396—618no—
409#389—618no—
410#388—618no—
411#388—618no—
412#387—618no—
413#387—618no—
414#387—618no—
415#385—618no—
416#385—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×#95—611no—
427C2×#95—611no—
428C2×#95—611no—
429C2×#95—611no—
430C61C2×#247511yescharacteristic, complemented, Sylow
431C25C22×D6111yescharacteristic
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—24no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4C22×D6114yes—
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6111yescharacteristic
448C23×C4C22×D6111yescharacteristic
449C23×C4C22×D6111yescharacteristic
450#125—12232no—
451#117—232no—
452C2×C4⋊C4—24no—
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—614no—
461C2×C4⋊C4—614no—
462C2×C4⋊C4—614no—
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⋊C4—1224no—
472C2×C4⋊C4—1224no—
473C2×C4⋊C4C22⋊D6118yes—
474C2×C4⋊C4C22×D6114yes—
475C2×C4⋊C4C22×D6114yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—614no—
479C2×C22⋊C4—614no—
480C2×C22⋊C4—614no—
481C2×C22⋊C4—614no—
482C2×C22⋊C4—1224no—
483C2×C22⋊C4—1224no—
484C2×C22⋊C4—1224no—
485C2×C22⋊C4—1224no—
486C2×C22⋊C4C22×D6114yes—
487C2×C22⋊C4C22×D6114yes—
488C2×C42—24no—
489C2×C42—24no—
490C2×C42—614no—
491C2×C42—614no—
492C2×C42—1224no—
493C2×C42—1224no—
494C2×C42C22×D6114yes—
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#95—614no—
505#95—614no—
506#95—614no—
507#95—614no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24#1175822214yes—
515C24C23×D6112yes—
516C24C23×D6111yescharacteristic
517C22×C4—232no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—614no—
536C22×C4—614no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—612no—
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—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4#1175822214yes—
568C22×C4C2×C22⋊D6114yes—
569C22×C4C2×C22⋊D6114yes—
570C22×C4C2×C22⋊D6114yes—
571C22×C4C23×D6112yes—
572C22×C4C23×D6112yes—
573C22×C4C23×D6112yes—
574C22×C4C23×D6112yes—
575C22×C4C23×D6112yes—
576C22×C4C23×D6112yes—
577C4⋊C4—28no—
578C4⋊C4—1228no—
579C4⋊C4—1228no—
580C4⋊C4—1228no—
581C4⋊C4—1228no—
582C4⋊C4—1228no—
583C4⋊C4—1228no—
584C4⋊C4—1228no—
585C4⋊C4—1228no—
586C4⋊C4—1228no—
587C4⋊C4—1228no—
588C4⋊C4C2×C22⋊D61116yes—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—1228no—
592C22⋊C4—1228no—
593C22⋊C4—1228no—
594C22⋊C4—1228no—
595C42—28no—
596C42—28no—
597C42—1228no—
598C42—1228no—
599C23—28no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—28no—
607C23—28no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23C22×C22⋊D6112yes—
613C23#41×D6112yes—
614C23#41×D6112yes—
615C23C2×#1175822214yes—
616C23C2×#1175822212yes—
617C23C2×#1175822212yes—
618C23#1451982412yes—
619C23#1451982412yes—
620C23C24×D6111yescharacteristic
621C2×C4—232no—
622C2×C4—28no—
623C2×C4—28no—
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—28no—
633C2×C4—28no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—614no—
643C2×C4—614no—
644C2×C4—1228no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1228no—
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—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—2444no—
669C2×C4—2444no—
670C2×C4—2444no—
671C2×C4—2444no—
672C2×C4—2444no—
673C2×C4—2444no—
674C2×C4C22×C22⋊D6114yes—
675C2×C4C22×C22⋊D6114yes—
676C2×C4C22×C22⋊D6114yes—
677C2×C4C2×#1175822214yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—416no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22#1684027314yes—
687C22#1684029014yes—
688C22#1684037414yes—
689C22#1684041114yes—
690C22#1684041914yes—
691C22#1684044514yes—
692C22#1684044514yes—
693C22C23×C22⋊D6111yescharacteristic
694C22C2×#41×D6111yescharacteristic
695C22C2×#41×D6111yescharacteristic
696C22C22×#1175822211yescharacteristic
697C22C22×#1175822211yescharacteristic
698C22C2×#1451982411yescharacteristic
699C22C2×#1451982411yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—42no—
705C4—42no—
706C4—1224no—
707C4—1224no—
708C4—2442no—
709C4—2442no—
710C4—2442no—
711C4—2442no—
712C4—2442no—
713C4—2442no—
714C2—44no—
715C2#2144998418yesdirect product factor
716C2C2×#1684027311yescharacteristic
717C2C2×#1684029011yescharacteristic
718C2C2×#1684037411yescharacteristic
719C2C2×#1684041111yescharacteristic
720C2C2×#1684041911yescharacteristic
721C2C2×#1684044511yescharacteristic
722C2C2×#1684044511yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×#117×C61C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC22×#117D61
hypocenterC61C2×#2475
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#14519767C2semidirect
2. #21449984C2direct (N × H)
3. C2×#16839700C2semidirect
4. C2×#16839693C2semidirect
7. C2×#16839660C2semidirect
10. C2×#16839648C2semidirect
11. C2×#16839646C2semidirect
12. C2×#16839646C2semidirect
15. C2×C4×#11758196C2semidirect
18. C2×#14519767C22semidirect
35. #16839700C22semidirect
36. #16839693C22semidirect
39. #16839660C22semidirect
42. #16839648C22semidirect
43. #16839646C22semidirect
44. #16839646C22semidirect
47. C4×#11758196C22semidirect
370. C2×C61#2475semidirect
430. C61C2×#2475semidirect
715. C2#21449984direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197672
#214499842
C2×#168397002
C2×#168396932
C2×#168396872
C2×#168396852
C2×#168396602
C2×#168396562
C2×#168396502
C2×#168396482
C2×#168396462
C2×#168396352
C2×C4×#117581962
C22×#117×C612
C2×#247561