Finite Group Databasebeta

← C2×#21448553 #29838836

Subgroups — C2×#21448553 #29838836

Order 15616.

2982 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic
2#21448553C2116yesmaximal, direct product factor
3C2×#16839667C211yesmaximal, characteristic, complemented
4C2×#16839666C211yesmaximal, characteristic, complemented
5C2×#16839657C211yesmaximal, characteristic, complemented
6C2×#16839649C211yesmaximal, characteristic, complemented
7C2×#16839648C211yesmaximal, characteristic, complemented
8C2×#16839646C211yesmaximal, characteristic, complemented
9C2×#16839643C211yesmaximal, characteristic, complemented
10C2×#16839633C211yesmaximal, characteristic
11C2×#16839633C211yesmaximal, characteristic
12C2×#16839619C211yesmaximal, characteristic
13C2×C4×#11758198C211yesmaximal, characteristic
14C2×#16839609C211yesmaximal, characteristic
15C2×#95×D61C211yesmaximal, characteristic
16C2×C61×#389C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519755C4116yescomplemented
22C2×#14519755C2218yes—
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839667C2218yescomplemented
36#16839666C2218yescomplemented
37#16839657C2218yescomplemented
38#16839649C2218yescomplemented
39#16839648C2218yescomplemented
40#16839646C2218yescomplemented
41#16839643C2218yescomplemented
42#16839633C2218yes—
43#16839633C2218yes—
44#16839619C2218yes—
45C4×#11758198C2218yes—
46#16839609C2218yes—
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59#95×D61C2218yes—
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C61×#389C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C24×D61C2311yescharacteristic
69C22×Dic122—42no—
70C22×Dic122—42no—
71C22×Dic122C2×C418yescomplemented
72C22×Dic122C2314yes—
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—24no—
81C22×C4×D61—42no—
82C22×C4×D61—42no—
83C22×C4×D61—42no—
84C22×C4×D61—42no—
85C22×C4×D61—42no—
86C22×C4×D61—42no—
87C22×C4×D61C2×C418yes—
88C22×C4×D61Q818yescomplemented
89C22×C4×D61C2314yes—
90C22×C4×D61C2314yes—
91C22×C4×D61C2314yes—
92#14519755C2×C4164yescomplemented
93C2×C4⋊Dic61—42no—
94C2×C4⋊Dic61C2314yes—
95C2×#11758196—42no—
96C2×#11758196—42no—
97C2×#11758196C2×C418yescomplemented
98C2×#11758196C2×C418yescomplemented
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758198—24no—
104C2×#11758198—24no—
105C2×#11758198C2×C418yes—
106C2×#11758198C2×C418yes—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×C4×Dic61—42no—
112C2×C4×Dic61—42no—
113C2×C4×Dic61—42no—
114C2×C4×Dic61C2314yes—
115C2×C4×Dic61C2314yes—
116C2×C4×Dic61C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61—42no—
137C2×C4⋊C4×C61—42no—
138C2×C4⋊C4×C61—42no—
139C2×C4⋊C4×C61C2×C418yescomplemented
140C2×C4⋊C4×C61C2314yes—
141C2×C4⋊C4×C61C2314yes—
142C2×C4⋊C4×C61C2314yes—
143C2×C4⋊C4×C61C2314yes—
144C2×C42×C61—42no—
145C2×C42×C61C2314yes—
146#95×C61C2314yes—
147#95×C61C2314yes—
148C24×C61C2411yescharacteristic
149C23×D61—22no—
150C23×D61—22no—
151C23×D61—22no—
152C23×D61—22no—
153C23×D61C22×C414yes—
154C23×D61C2×Q814yes—
155C23×D61#4114yes—
156C23×D61C2412yes—
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×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61C22×C414yes—
175C22×C4×C61C22×C414yes—
176C22×C4×C61C22×C414yes—
177C22×C4×C61C2×Q814yes—
178C22×C4×C61C2412yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
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×Dic61C22×C414yes—
203C22×Dic61C22×C414yes—
204C22×Dic61C22×C414yes—
205C22×Dic61C2×Q814yes—
206C22×Dic61C2412yes—
207C22×Dic61C2412yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C2×C4×D61—28no—
214C2×C4×D61—416no—
215C2×C4×D61—416no—
216C2×C4×D61—44no—
217C2×C4×D61—44no—
218C2×C4×D61—44no—
219C2×C4×D61—44no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C2×C4×D61—416no—
223C2×C4×D61C22×C4116yes—
224C2×C4×D61C2×Q8116yescomplemented
225C2×Dic122—416no—
226C2×Dic122—44no—
227C2×Dic122—44no—
228C2×Dic122C22×C4116yescomplemented
229C4⋊C4×C61—44no—
230C4⋊C4×C61—44no—
231C4⋊C4×C61—44no—
232C4⋊C4×C61C22×C4116yescomplemented
233C42×C61—44no—
234#11758198—28no—
235#11758198—28no—
236#11758198C22×C4116yes—
237#11758198C22×C4116yes—
238C4⋊Dic61—44no—
239#11758196—44no—
240#11758196—44no—
241#11758196C22×C4116yescomplemented
242#11758196C22×C4116yescomplemented
243C4×Dic61—44no—
244C4×Dic61—44no—
245C4×Dic61—44no—
246C23×C61C23×C412yes—
247C23×C61C22×Q812yes—
248C23×C61C2×#4112yes—
249C23×C61H(5,𝔽2)12yes—
250C23×C61H(5,𝔽2)12yes—
251C23×C61H(5,𝔽2)12yes—
252C23×C612−1+412yes—
253C23×C61C2511yescharacteristic
254C22×D61—28no—
255C22×D61—28no—
256C22×D61—28no—
257C22×D61—28no—
258C22×D61—28no—
259C22×D61—28no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61C4×Q8116yes—
265C22×D61C23×C414yes—
266C22×D61C22×Q814yes—
267C22×D61C2×#4114yes—
268C2×C4×C61—28no—
269C2×C4×C61—28no—
270C2×C4×C61—28no—
271C2×C4×C61—28no—
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—22no—
289C2×C4×C61—44no—
290C2×C4×C61—44no—
291C2×C4×C61—44no—
292C2×C4×C61C23×C414yes—
293C2×C4×C61C23×C414yes—
294C2×C4×C61C23×C414yes—
295C2×C4×C61C22×Q814yes—
296C2×Dic61—28no—
297C2×Dic61—28no—
298C2×Dic61—28no—
299C2×Dic61—28no—
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—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—44no—
318C2×Dic61—44no—
319C2×Dic61—44no—
320C2×Dic61C23×C414yes—
321C2×Dic61C23×C414yes—
322C2×Dic61C23×C414yes—
323C2×Dic61C22×Q814yes—
324C4×D61—416no—
325C4×D61—416no—
326C4×D61—416no—
327Dic122—416no—
328C2×#2329—611nomaximal, Sylow
329C22×C61C2×C4×Q814yes—
330C22×C61#51814yes—
331C22×C61#52014yes—
332C22×C61#53814yes—
333C22×C61#53914yes—
334C22×C61#54314yes—
335C22×C61#54414yes—
336C22×C61C24×C411yescharacteristic
337C22×C61C23×Q811yescharacteristic
338C22×C61C22×#4111yescharacteristic
339C22×C61C2×H(5,𝔽2)11yescharacteristic
340C22×C61C2×H(5,𝔽2)11yescharacteristic
341C22×C61C2×H(5,𝔽2)11yescharacteristic
342C22×C61C2×2−1+411yescharacteristic
343C2×D61—232no—
344C2×D61—24no—
345C2×D61—24no—
346C2×D61—24no—
347C2×D61—24no—
348C2×D61—24no—
349C2×D61—24no—
350C2×D61C2×C4×Q818yes—
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—24no—
354C4×C61—24no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—42no—
358Dic61—24no—
359Dic61—24no—
360Dic61—24no—
361Dic61—24no—
362Dic61—42no—
363Dic61—42no—
364Dic61—42no—
365C22×C22⋊Q8—611no—
366#2329—6116no—
367C2×#391—611no—
368C2×#391—611no—
369C2×#389—611no—
370C2×#389D6111yescharacteristic, complemented
371C2×#387—611no—
372C2×#387—611no—
373C2×#387—611no—
374C2×#387—611no—
375C2×#385—611no—
376C2×#385—611no—
377C2×#380—611no—
378C2×C4×C22⋊C4—611no—
379C2×C4×C22⋊C4—611no—
380C22×#95—611no—
381C2×C61#232918yescomplemented
382C2×C61C22×C4×Q811yescharacteristic
383C2×C61C2×#51811yescharacteristic
384C2×C61C2×#52011yescharacteristic
385C2×C61C2×#53811yescharacteristic
386C2×C61C2×#53911yescharacteristic
387C2×C61C2×#54311yescharacteristic
388C2×C61C2×#54411yescharacteristic
389D61—28no—
390C23×Q8—611no—
391C24×C4—611no—
392C24×C4—611no—
393C24×C4—611no—
394C2×C22⋊Q8—6116no—
395C2×C22⋊Q8—618no—
396C22×C4⋊C4—611no—
397C22×C4⋊C4—611no—
398C22×C4⋊C4—611no—
399C22×C4⋊C4—611no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4C2×D6111yescharacteristic
402C22×C4⋊C4C2×D6111yescharacteristic
403C22×C4⋊C4C2×D6111yescharacteristic
404C22×C4⋊C4C2×D6111yescharacteristic
405C22×C22⋊C4—611no—
406C22×C22⋊C4—611no—
407C22×C22⋊C4—611no—
408C22×C22⋊C4—611no—
409C22×C42—611no—
410C22×C42—611no—
411C22×C42—611no—
412C22×C42C2×D6111yescharacteristic
413#391—618no—
414#391—618no—
415#389—618no—
416#389C2×D6118yescomplemented
417#387—618no—
418#387—618no—
419#387—618no—
420#387—618no—
421#385—618no—
422#385—618no—
423#380—618no—
424C4×C22⋊C4—618no—
425C4×C22⋊C4—618no—
426C2×#95—611no—
427C2×#95—611no—
428C2×#95—611no—
429C2×#95—611no—
430C2×#95—611no—
431C2×#95—611no—
432C2×#95—611no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95—611no—
436C2×#95—611no—
437C2×#95—611no—
438C2×#95—618no—
439C2×#95C2×D6111yescharacteristic
440C2×#95C2×D6111yescharacteristic
441C61C2×#232911yescharacteristic, complemented, Sylow
442C25—611no—
443C22×Q8—618no—
444C22×Q8—614no—
445C22×Q8—2442no—
446C22×Q8—2442no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—618no—
452C23×C4—618no—
453C23×C4—614no—
454C23×C4—614no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—614no—
459C23×C4—1224no—
460C23×C4—2442no—
461C23×C4—2442no—
462C23×C4—2442no—
463C23×C4—2442no—
464C23×C4—2442no—
465C23×C4—2442no—
466C23×C4C22×D6111yescharacteristic
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C23×C4C22×D6111yescharacteristic
473C22⋊Q8—6164no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—618no—
478C2×C4⋊C4—618no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—614no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—2442no—
485C2×C4⋊C4—2442no—
486C2×C4⋊C4—2442no—
487C2×C4⋊C4C4×D6118yescomplemented
488C2×C4⋊C4C22×D6114yes—
489C2×C4⋊C4C22×D6114yes—
490C2×C4⋊C4C22×D6114yes—
491C2×C4⋊C4C22×D6114yes—
492C2×C22⋊C4—618no—
493C2×C22⋊C4—618no—
494C2×C22⋊C4—614no—
495C2×C22⋊C4—614no—
496C2×C22⋊C4—614no—
497C2×C22⋊C4—614no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—1224no—
500C2×C42—42no—
501C2×C42—614no—
502C2×C42—614no—
503C2×C42—614no—
504C2×C42—2442no—
505C2×C42—2442no—
506C2×C42—2442no—
507C2×C42C22×D6114yes—
508#95—614no—
509#95—614no—
510#95—614no—
511#95—614no—
512#95—614no—
513#95—614no—
514#95—614no—
515#95—614no—
516#95—614no—
517#95—614no—
518#95—614no—
519#95—614no—
520#95C22×D6114yes—
521#95C22×D6114yes—
522C24—614no—
523C24—614no—
524C24—614no—
525C24—612no—
526C24—1222no—
527C24—1222no—
528C24—1222no—
529C24—1222no—
530C24C23×D6111yescharacteristic
531C2×Q8—6116no—
532C2×Q8—24416no—
533C2×Q8—2444no—
534C2×Q8—2444no—
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—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—614no—
553C22×C4—614no—
554C22×C4—614no—
555C22×C4—614no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—6116no—
561C22×C4—6116no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—1228no—
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×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—24416no—
584C22×C4—2444no—
585C22×C4—2444no—
586C22×C4—2444no—
587C22×C4—2444no—
588C22×C4—24416no—
589C22×C4—2444no—
590C22×C4—2444no—
591C22×C4—24416no—
592C22×C4C2×C4×D6114yes—
593C22×C4C2×C4×D6114yes—
594C22×C4C2×C4×D6114yes—
595C22×C4Q8×D6114yes—
596C22×C4C23×D6112yes—
597C22×C4C23×D6112yes—
598C22×C4C23×D6112yes—
599C22×C4C23×D6112yes—
600C22×C4C23×D6112yes—
601C22×C4C23×D6112yes—
602C22×C4C23×D6112yes—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—6116no—
607C4⋊C4—6116no—
608C4⋊C4—2444no—
609C4⋊C4—2444no—
610C4⋊C4—2444no—
611C4⋊C4C2×C4×D61116yescomplemented
612C22⋊C4—6116no—
613C22⋊C4—6116no—
614C22⋊C4—1228no—
615C22⋊C4—1228no—
616C42—44no—
617C42—2444no—
618C42—2444no—
619C42—2444no—
620C23—6116no—
621C23—614no—
622C23—614no—
623C23—614no—
624C23—1228no—
625C23—1228no—
626C23—1222no—
627C23—1222no—
628C23—1222no—
629C23—1222no—
630C23—1228no—
631C23—1228no—
632C23—1228no—
633C23—1228no—
634C23C22×C4×D6112yes—
635C23C2×Q8×D6112yes—
636C23#41×D6112yes—
637C23#1451982212yes—
638C23#1451982212yes—
639C23#1451982312yes—
640C23#1451982512yes—
641C23C24×D6111yescharacteristic
642Q8—24416no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
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—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—614no—
668C2×C4—614no—
669C2×C4—614no—
670C2×C4—614no—
671C2×C4—1228no—
672C2×C4—1228no—
673C2×C4—1228no—
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—1228no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—24416no—
693C2×C4—24416no—
694C2×C4—24416no—
695C2×C4—2444no—
696C2×C4—2444no—
697C2×C4—2444no—
698C2×C4C22×C4×D6114yes—
699C2×C4C22×C4×D6114yes—
700C2×C4C22×C4×D6114yes—
701C2×C4C2×Q8×D6114yes—
702C22—618no—
703C22—1224no—
704C22—1224no—
705C22—1224no—
706C22—1224no—
707C22—12232no—
708C22—1224no—
709C22—1224no—
710C22C4×Q8×D6114yes—
711C22#1684023414yes—
712C22#1684024314yes—
713C22#1684034414yes—
714C22#1684036014yes—
715C22#1684038714yes—
716C22#1684038914yes—
717C22C23×C4×D6111yescharacteristic
718C22C22×Q8×D6111yescharacteristic
719C22C2×#41×D6111yescharacteristic
720C22C2×#1451982211yescharacteristic
721C22C2×#1451982211yescharacteristic
722C22C2×#1451982311yescharacteristic
723C22C2×#1451982511yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—1224no—
732C4—1224no—
733C4—1224no—
734C4—1224no—
735C4—2442no—
736C4—2442no—
737C4—2442no—
738C2—1228no—
739C2#2144855318yesdirect product factor
740C2C2×C4×Q8×D6111yescharacteristic
741C2C2×#1684023411yescharacteristic
742C2C2×#1684024311yescharacteristic
743C2C2×#1684034411yescharacteristic
744C2C2×#1684036011yescharacteristic
745C2C2×#1684038711yescharacteristic
746C2C2×#1684038911yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#389C2
socleC24×C61C24
prime radicalC24×D61C23
cosocleC23×C61C25
hypercenterC2×#389D61
hypocenterC61C2×#2329
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. #21448553C2direct (N × H)
3. C2×#16839667C2semidirect
4. C2×#16839666C2semidirect
5. C2×#16839657C2semidirect
6. C2×#16839649C2semidirect
7. C2×#16839648C2semidirect
8. C2×#16839646C2semidirect
9. C2×#16839643C2semidirect
16. C2×C61×#389C2semidirect
21. C2×#14519755C4semidirect
35. #16839667C22semidirect
36. #16839666C22semidirect
37. #16839657C22semidirect
38. #16839649C22semidirect
39. #16839648C22semidirect
40. #16839646C22semidirect
41. #16839643C22semidirect
65. C61×#389C22semidirect
71. C22×Dic122C2×C4semidirect
88. C22×C4×D61Q8semidirect
92. #14519755C2×C4semidirect
97. C2×#11758196C2×C4semidirect
98. C2×#11758196C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
224. C2×C4×D61C2×Q8semidirect
228. C2×Dic122C22×C4semidirect
232. C4⋊C4×C61C22×C4semidirect
241. #11758196C22×C4semidirect
242. #11758196C22×C4semidirect
370. C2×#389D61semidirect
381. C2×C61#2329semidirect
416. #389C2×D61semidirect
441. C61C2×#2329semidirect
487. C2×C4⋊C4C4×D61semidirect
611. C4⋊C4C2×C4×D61semidirect
739. C2#21448553direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197552
#214485532
C2×#168396672
C2×#168396662
C2×#168396572
C2×#168396492
C2×#168396482
C2×#168396462
C2×#168396432
C2×#168396332
C2×#168396192
C2×C4×#117581982
C2×#168396092
C2×#95×D612
C2×C61×#3892
C2×#232961