Finite Group Databasebeta

← C2×#21451651 #29847077

Subgroups — C2×#21451651 #29847077

Order 15616.

2614 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519767C211yesmaximal, characteristic, complemented
2C22×#14519735C211yesmaximal, characteristic
3#21451651C2116yesmaximal, direct product factor
4C2×#16839696C211yesmaximal, characteristic, complemented
5C2×#16839695C211yesmaximal, characteristic, complemented
6C2×#16839694C211yesmaximal, characteristic, complemented
7C2×#16839686C211yesmaximal, characteristic
8C2×#16839684C211yesmaximal, characteristic
9C2×#16839684C211yesmaximal, characteristic
10C2×#16839684C211yesmaximal, characteristic
11C2×#16839659C211yesmaximal, characteristic, complemented
12C2×#16839657C211yesmaximal, characteristic, complemented
13C2×#16839631C211yesmaximal, characteristic, complemented
14C2×#16839621C211yesmaximal, characteristic
15C2×#16839621C211yesmaximal, characteristic
16C2×C61×#398C211yesmaximal, characteristic, complemented
17C23×C4×D61C2211yescharacteristic
18C2×#14519767—28no—
19C2×#14519767C2218yescomplemented
20C2×#14519735—28no—
21C2×#14519735C2218yes—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44#16839696C2218yescomplemented
45#16839695C2218yescomplemented
46#16839694C2218yescomplemented
47#16839686C2218yes—
48#16839684C2218yes—
49#16839684C2218yes—
50#16839684C2218yes—
51#16839659C2218yescomplemented
52#16839657C2218yescomplemented
53#16839631C2218yescomplemented
54#16839621C2218yes—
55#16839621C2218yes—
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C61×#398C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C22×C4×D61—24no—
78C22×C4×D61—24no—
79C22×C4×D61Q818yes—
80C22×C4×D61C2314yes—
81#14519767—232no—
82#14519735—232no—
83C2×C4⋊Dic61—24no—
84C2×C4⋊Dic61—24no—
85C2×C4⋊Dic61—42no—
86C2×C4⋊Dic61—42no—
87C2×C4⋊Dic61C2314yes—
88C2×C4⋊Dic61C2314yes—
89C2×C4⋊Dic61C2314yes—
90C2×C4⋊Dic61C2314yes—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196—24no—
94C2×#11758196—24no—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196—42no—
98C2×#11758196—42no—
99C2×#11758196—42no—
100C2×#11758196—42no—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198—42no—
114C2×#11758198—42no—
115C2×#11758198—42no—
116C2×#11758198—42no—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×#11758198C2314yes—
120C2×#11758198C2314yes—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×C4×Dic61—24no—
124C2×C4×Dic61D418yes—
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61—24no—
140C2×C4⋊C4×C61—24no—
141C2×C4⋊C4×C61—42no—
142C2×C4⋊C4×C61—42no—
143C2×C4⋊C4×C61C2314yes—
144C2×C4⋊C4×C61C2314yes—
145C2×C4⋊C4×C61C2314yes—
146C2×C4⋊C4×C61C2314yes—
147#95×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150C24×C61C2411yescharacteristic
151C23×D61—22no—
152C23×D61—22no—
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61C2×Q814yes—
158C23×D61C2412yes—
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×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61C2×D414yes—
179C22×C4×C61C2×Q814yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
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×Dic61C2×D414yes—
205C22×Dic61C2×D414yes—
206C22×Dic61C2×Q814yes—
207C22×Dic61#4114yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C2×C4×D61—232no—
216C2×C4×D61—28no—
217C2×C4×D61—28no—
218C2×C4×D61C2×Q8116yes—
219C4⋊C4×C61—28no—
220C4⋊C4×C61—28no—
221C4⋊C4×C61—44no—
222C4⋊C4×C61—44no—
223#11758198—28no—
224#11758198—28no—
225#11758198—44no—
226#11758198—44no—
227#11758198—44no—
228#11758198—44no—
229C4⋊Dic61—28no—
230C4⋊Dic61—28no—
231C4⋊Dic61—44no—
232C4⋊Dic61—44no—
233#11758196—28no—
234#11758196—28no—
235#11758196—28no—
236#11758196—28no—
237#11758196—28no—
238#11758196—28no—
239#11758196—44no—
240#11758196—44no—
241#11758196—44no—
242#11758196—44no—
243C4×Dic61—28no—
244C4×Dic61C2×D4116yes—
245C23×C61C22×D412yes—
246C23×C61C22×Q812yes—
247C23×C61C2×#4112yes—
248C23×C61H(5,𝔽2)12yes—
249C23×C61H(5,𝔽2)12yes—
250C23×C612−1+412yes—
251C23×C612−1+412yes—
252C23×C61C2511yescharacteristic
253C22×D61—28no—
254C22×D61—28no—
255C22×D61—28no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—44no—
263C22×D61—44no—
264C22×D61—44no—
265C22×D61—44no—
266C22×D61C22×Q814yes—
267C2×C4×C61—28no—
268C2×C4×C61—28no—
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—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—44no—
289C2×C4×C61—44no—
290C2×C4×C61—44no—
291C2×C4×C61—44no—
292C2×C4×C61—44no—
293C2×C4×C61C22×D414yes—
294C2×C4×C61C22×Q814yes—
295C2×Dic61—28no—
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—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—44no—
314C2×Dic61—44no—
315C2×Dic61—44no—
316C2×Dic61—44no—
317C2×Dic61—44no—
318C2×Dic61C22⋊Q8116yes—
319C2×Dic61C22×D414yes—
320C2×Dic61C22×D414yes—
321C2×Dic61C22×Q814yes—
322C2×Dic61C2×#4114yes—
323C4×D61—232no—
324C2×#2629—611nomaximal, Sylow
325C22×C61C2×C22⋊Q814yes—
326C22×C61#53714yes—
327C22×C61#53714yes—
328C22×C61#54014yes—
329C22×C61#54114yes—
330C22×C61#54414yes—
331C22×C61#54414yes—
332C22×C61C23×D411yescharacteristic
333C22×C61C23×Q811yescharacteristic
334C22×C61C22×#4111yescharacteristic
335C22×C61C2×H(5,𝔽2)11yescharacteristic
336C22×C61C2×H(5,𝔽2)11yescharacteristic
337C22×C61C2×2−1+411yescharacteristic
338C22×C61C2×2−1+411yescharacteristic
339C2×D61—24no—
340C2×D61—24no—
341C2×D61—24no—
342C2×D61—416no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C4×C61—24no—
348C4×C61—24no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—42no—
354Dic61—24no—
355Dic61—42no—
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61C2×C22⋊Q818yes—
361C22×#125—611no—
362C22×#117—611no—
363#2629—6116no—
364C2×#398—611no—
365C2×#398—611no—
366C2×#398—611no—
367C2×#398D6111yescharacteristic, complemented
368C2×#396—611no—
369C2×#396—611no—
370C2×#396—611no—
371C2×#396—611no—
372C2×#389—611no—
373C2×#389—611no—
374C2×#384—611no—
375C2×#380—611no—
376C2×#380—611no—
377C2×C61#262918yescomplemented
378C2×C61C22×C22⋊Q811yescharacteristic
379C2×C61C2×#53711yescharacteristic
380C2×C61C2×#53711yescharacteristic
381C2×C61C2×#54011yescharacteristic
382C2×C61C2×#54111yescharacteristic
383C2×C61C2×#54411yescharacteristic
384C2×C61C2×#54411yescharacteristic
385D61—44no—
386C24×C4—611no—
387C2×#125—618no—
388C2×#125—1228no—
389C2×#117—618no—
390C2×#117—1228no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4—611no—
394C22×C4⋊C4—611no—
395C22×C4⋊C4—611no—
396C22×C4⋊C4—611no—
397C22×C4⋊C4—611no—
398C22×C4⋊C4—611no—
399C22×C4⋊C4—611no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—611no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4C2×D6111yescharacteristic
406C22×C4⋊C4C2×D6111yescharacteristic
407C22×C4⋊C4C2×D6111yescharacteristic
408C22×C4⋊C4C2×D6111yescharacteristic
409C22×C22⋊C4—611no—
410C22×C22⋊C4—611no—
411C22×C22⋊C4—611no—
412C22×C22⋊C4—611no—
413C22×C22⋊C4—611no—
414C22×C22⋊C4—611no—
415C22×C42—611no—
416C22×C42—611no—
417#398—618no—
418#398—618no—
419#398—618no—
420#398C2×D6118yescomplemented
421#396—618no—
422#396—618no—
423#396—618no—
424#396—618no—
425#389—618no—
426#389—618no—
427#384—618no—
428#380—618no—
429#380—618no—
430C2×#95—611no—
431C2×#95—611no—
432C2×#95—611no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95C2×D6111yescharacteristic
436C2×#95C2×D6111yescharacteristic
437C2×#95C2×D6111yescharacteristic
438C61C2×#262911yescharacteristic, complemented, Sylow
439C25—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—618no—
443C23×C4—614no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—1224no—
450C23×C4—1224no—
451C23×C4C22×D6111yescharacteristic
452C23×C4C22×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458#125—12232no—
459#117—12232no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—614no—
465C2×C4⋊C4—614no—
466C2×C4⋊C4—614no—
467C2×C4⋊C4—614no—
468C2×C4⋊C4—614no—
469C2×C4⋊C4—614no—
470C2×C4⋊C4—614no—
471C2×C4⋊C4—614no—
472C2×C4⋊C4—614no—
473C2×C4⋊C4—614no—
474C2×C4⋊C4—614no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—1224no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—1224no—
481C2×C4⋊C4—1224no—
482C2×C4⋊C4—1224no—
483C2×C4⋊C4—1224no—
484C2×C4⋊C4—1224no—
485C2×C4⋊C4—1224no—
486C2×C4⋊C4—2442no—
487C2×C4⋊C4—2442no—
488C2×C4⋊C4—2442no—
489C2×C4⋊C4—2442no—
490C2×C4⋊C4—2442no—
491C2×C4⋊C4—2442no—
492C2×C4⋊C4C22×D6114yes—
493C2×C4⋊C4C22×D6114yes—
494C2×C4⋊C4C22×D6114yes—
495C2×C4⋊C4C22×D6114yes—
496C2×C22⋊C4—614no—
497C2×C22⋊C4—614no—
498C2×C22⋊C4—614no—
499C2×C22⋊C4—614no—
500C2×C22⋊C4—614no—
501C2×C22⋊C4—614no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1224no—
504C2×C22⋊C4—2442no—
505C2×C22⋊C4—2442no—
506C2×C22⋊C4—2442no—
507C2×C22⋊C4—2442no—
508C2×C42—618no—
509C2×C42—614no—
510C2×C42—614no—
511C2×C42—1224no—
512#95—614no—
513#95—614no—
514#95—614no—
515#95—614no—
516#95—614no—
517#95C22×D6114yes—
518#95C22×D6114yes—
519#95C22×D6114yes—
520C24—614no—
521C24—612no—
522C24—1222no—
523C24—1222no—
524C24—1222no—
525C24—1222no—
526C24—1222no—
527C24—1222no—
528C24C23×D6111yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—614no—
549C22×C4—614no—
550C22×C4—614no—
551C22×C4—612no—
552C22×C4—614no—
553C22×C4—612no—
554C22×C4—6116no—
555C22×C4—612no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—1228no—
561C22×C4—12232no—
562C22×C4—1228no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4D4×D6114yes—
581C22×C4Q8×D6114yes—
582C22×C4C23×D6112yes—
583C22×C4C23×D6112yes—
584C22×C4C23×D6112yes—
585C22×C4C23×D6112yes—
586C22×C4C23×D6112yes—
587C22×C4C23×D6112yes—
588C22×C4C23×D6112yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—1228no—
594C4⋊C4—1228no—
595C4⋊C4—1228no—
596C4⋊C4—1228no—
597C4⋊C4—1228no—
598C4⋊C4—1228no—
599C4⋊C4—1228no—
600C4⋊C4—1228no—
601C4⋊C4—2444no—
602C4⋊C4—2444no—
603C4⋊C4—2444no—
604C4⋊C4—2444no—
605C4⋊C4—2444no—
606C4⋊C4—2444no—
607C22⋊C4—1228no—
608C22⋊C4—1228no—
609C22⋊C4—2444no—
610C22⋊C4—2444no—
611C22⋊C4—2444no—
612C22⋊C4—2444no—
613C42—6116no—
614C42—1228no—
615C23—614no—
616C23—1228no—
617C23—1222no—
618C23—1222no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—1222no—
623C23—1228no—
624C23—1228no—
625C23—2444no—
626C23—2444no—
627C23—2444no—
628C23—2444no—
629C23C2×D4×D6112yes—
630C23C2×Q8×D6112yes—
631C23#41×D6112yes—
632C23#1451982212yes—
633C23#1451982312yes—
634C23#1451982412yes—
635C23#1451982512yes—
636C23C24×D6111yescharacteristic
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—28no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—6116no—
664C2×C4—614no—
665C2×C4—614no—
666C2×C4—614no—
667C2×C4—614no—
668C2×C4—12232no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1228no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—2444no—
688C2×C4—2444no—
689C2×C4—2444no—
690C2×C4—2444no—
691C2×C4—2444no—
692C2×C4C2×D4×D6114yes—
693C2×C4C2×Q8×D6114yes—
694C22—1224no—
695C22—1224no—
696C22—1224no—
697C22—24416no—
698C22—2442no—
699C22—2442no—
700C22—2442no—
701C22—2442no—
702C22C22⋊Q8×D6114yes—
703C22#1684033914yes—
704C22#1684034214yes—
705C22#1684036414yes—
706C22#1684037114yes—
707C22#1684038914yes—
708C22#1684039214yes—
709C22C22×D4×D6111yescharacteristic
710C22C22×Q8×D6111yescharacteristic
711C22C2×#41×D6111yescharacteristic
712C22C2×#1451982211yescharacteristic
713C22C2×#1451982311yescharacteristic
714C22C2×#1451982411yescharacteristic
715C22C2×#1451982511yescharacteristic
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—618no—
724C4—1224no—
725C4—2442no—
726C4—2442no—
727C4—2442no—
728C4—2442no—
729C4—2442no—
730C2—2444no—
731C2#2145165118yesdirect product factor
732C2C2×C22⋊Q8×D6111yescharacteristic
733C2C2×#1684033911yescharacteristic
734C2C2×#1684034211yescharacteristic
735C2C2×#1684036411yescharacteristic
736C2C2×#1684037111yescharacteristic
737C2C2×#1684038911yescharacteristic
738C2C2×#1684039211yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#398C2
socleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×#398D61
hypocenterC61C2×#2629
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#14519767C2semidirect
3. #21451651C2direct (N × H)
4. C2×#16839696C2semidirect
5. C2×#16839695C2semidirect
6. C2×#16839694C2semidirect
11. C2×#16839659C2semidirect
12. C2×#16839657C2semidirect
13. C2×#16839631C2semidirect
16. C2×C61×#398C2semidirect
19. C2×#14519767C22semidirect
44. #16839696C22semidirect
45. #16839695C22semidirect
46. #16839694C22semidirect
51. #16839659C22semidirect
52. #16839657C22semidirect
53. #16839631C22semidirect
65. C61×#398C22semidirect
367. C2×#398D61semidirect
377. C2×C61#2629semidirect
420. #398C2×D61semidirect
438. C61C2×#2629semidirect
731. C2#21451651direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197672
C22×#145197352
#214516512
C2×#168396962
C2×#168396952
C2×#168396942
C2×#168396862
C2×#168396842
C2×#168396592
C2×#168396572
C2×#168396312
C2×#168396212
C2×C61×#3982
C2×#262961