Finite Group Databasebeta

← C2×#21450899 #29850112

Subgroups — C2×#21450899 #29850112

Order 15616.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic
2#21450899C2116yesmaximal, direct product factor
3C2×#16839697C211yesmaximal, characteristic
4C2×#16839695C211yesmaximal, characteristic, complemented
5C2×#16839684C211yesmaximal, characteristic
6C2×#16839682C211yesmaximal, characteristic, complemented
7C2×#16839667C211yesmaximal, characteristic, complemented
8C2×#16839657C211yesmaximal, characteristic, complemented
9C2×#16839657C211yesmaximal, characteristic, complemented
10C2×#16839652C211yesmaximal, characteristic
11C2×#16839652C211yesmaximal, characteristic
12C2×#16839646C211yesmaximal, characteristic, complemented
13C2×#16839633C211yesmaximal, characteristic
14C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C2×C4×#11758198C211yesmaximal, characteristic
16C22×#125×C61C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519755—28no—
20C2×#14519755C2218yes—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839697C2218yes—
38#16839695C2218yescomplemented
39#16839684C2218yes—
40#16839682C2218yescomplemented
41#16839667C2218yescomplemented
42#16839657C2218yescomplemented
43#16839657C2218yescomplemented
44#16839652C2218yes—
45#16839652C2218yes—
46#16839646C2218yescomplemented
47#16839633C2218yes—
48C4⋊C4×Dic61C2218yescomplemented
49C4×#11758198C2218yes—
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#125×C61—28no—
61C2×#125×C61C2218yescomplemented
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C4⋊C4×C61C2211yescharacteristic
67C22×C4⋊C4×C61C2211yescharacteristic
68C22×C42×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C22×Dic122—24no—
71C22×Dic122—24no—
72C22×Dic122—42no—
73C22×Dic122C2314yes—
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C22×C4×D61—24no—
82C22×C4×D61—24no—
83C22×C4×D61—42no—
84C22×C4×D61C2314yes—
85#14519755—232no—
86C2×C4⋊Dic61—24no—
87C2×C4⋊Dic61C2314yes—
88C2×#11758196—24no—
89C2×#11758196—24no—
90C2×#11758196—24no—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196—42no—
94C2×#11758196C2314yes—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×#11758196C2314yes—
98C2×#11758196C2314yes—
99C2×#11758196C2314yes—
100C2×#11758198—24no—
101C2×#11758198—24no—
102C2×#11758198—24no—
103C2×#11758198—24no—
104C2×#11758198—42no—
105C2×#11758198Q818yescomplemented
106C2×#11758198C2314yes—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×C4×Dic61—24no—
113C2×C4×Dic61—42no—
114C2×C4×Dic61—42no—
115C2×C4×Dic61C2314yes—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135#125×C61—232no—
136C2×C4⋊C4×C61—24no—
137C2×C4⋊C4×C61—24no—
138C2×C4⋊C4×C61—24no—
139C2×C4⋊C4×C61—24no—
140C2×C4⋊C4×C61—24no—
141C2×C4⋊C4×C61D418yes—
142C2×C4⋊C4×C61C2314yes—
143C2×C4⋊C4×C61C2314yes—
144C2×C4⋊C4×C61C2314yes—
145C2×C4⋊C4×C61C2314yes—
146C2×C4⋊C4×C61C2314yes—
147C2×C4⋊C4×C61C2314yes—
148C2×C42×C61—24no—
149C2×C42×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×C61C2×D414yes—
177C22×C4×C61C2×D414yes—
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×Q814yes—
205C22×Dic61#4114yes—
206C22×Dic61#4114yes—
207C22×Dic61#4114yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C2×C4×D61—28no—
216C2×C4×D61—28no—
217C2×C4×D61—44no—
218C2×C4×D61—416no—
219C2×Dic122—28no—
220C2×Dic122—28no—
221C2×Dic122—44no—
222C2×Dic122—416no—
223C4⋊C4×C61—28no—
224C4⋊C4×C61—28no—
225C4⋊C4×C61—28no—
226C4⋊C4×C61—28no—
227C4⋊C4×C61—28no—
228C4⋊C4×C61C2×D4116yes—
229C42×C61—28no—
230#11758198—28no—
231#11758198—28no—
232#11758198—28no—
233#11758198—28no—
234#11758198—44no—
235#11758198C2×Q8116yescomplemented
236C4⋊Dic61—28no—
237#11758196—28no—
238#11758196—28no—
239#11758196—28no—
240#11758196—28no—
241#11758196—28no—
242#11758196—44no—
243C4×Dic61—28no—
244C4×Dic61—44no—
245C4×Dic61—44no—
246C23×C61C22×D412yes—
247C23×C61C22×Q812yes—
248C23×C61C2×#4112yes—
249C23×C61C2×#4112yes—
250C23×C61C2×#4112yes—
251C23×C61H(5,𝔽2)12yes—
252C23×C612−1+412yes—
253C23×C61C2511yescharacteristic
254C22×D61—28no—
255C22×D61—28no—
256C22×D61—28no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—44no—
264C22×D61—44no—
265C22×D61—44no—
266C22×D61—44no—
267C22×D61C22×Q814yes—
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×C61C22×D414yes—
293C2×C4×C61C22×D414yes—
294C2×C4×C61C22×D414yes—
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×Dic61C22×Q814yes—
321C2×Dic61C2×#4114yes—
322C2×Dic61C2×#4114yes—
323C2×Dic61C2×#4114yes—
324C4×D61—416no—
325Dic122—416no—
326C2×#2556—611nomaximal, Sylow
327C22×C61#53214yes—
328C22×C61#53314yes—
329C22×C61#53914yes—
330C22×C61#54614yes—
331C22×C61D4×Q814yes—
332C22×C61#55214yes—
333C22×C61#55414yes—
334C22×C61C23×D411yescharacteristic
335C22×C61C23×Q811yescharacteristic
336C22×C61C22×#4111yescharacteristic
337C22×C61C22×#4111yescharacteristic
338C22×C61C22×#4111yescharacteristic
339C22×C61C2×H(5,𝔽2)11yescharacteristic
340C22×C61C2×2−1+411yescharacteristic
341C2×D61—24no—
342C2×D61—24no—
343C2×D61—24no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—416no—
349C4×C61—24no—
350C4×C61—24no—
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61—42no—
356Dic61—24no—
357Dic61—24no—
358Dic61—24no—
359Dic61—24no—
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
363C22×#125D6111yescharacteristic, complemented
364C22×C22⋊Q8—611no—
365#2556—6116no—
366C2×#399—611no—
367C2×#398—611no—
368C2×#396—611no—
369C2×#395—611no—
370C2×#391—611no—
371C2×#389—611no—
372C2×#389—611no—
373C2×#388—611no—
374C2×#388—611no—
375C2×#387—611no—
376C2×#385—611no—
377C2×C4×C4⋊C4—611no—
378C2×C4×C22⋊C4—611no—
379C2×C61#255618yescomplemented
380C2×C61C2×#53211yescharacteristic
381C2×C61C2×#53311yescharacteristic
382C2×C61C2×#53911yescharacteristic
383C2×C61C2×#54611yescharacteristic
384C2×C61C2×D4×Q811yescharacteristic
385C2×C61C2×#55211yescharacteristic
386C2×C61C2×#55411yescharacteristic
387D61—44no—
388C23×Q8—611no—
389C24×C4—611no—
390C2×#125—28no—
391C2×#125C2×D6118yescomplemented
392C2×C22⋊Q8—618no—
393C2×C22⋊Q8—1228no—
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⋊C4C2×D6111yescharacteristic
402C22×C4⋊C4C2×D6111yescharacteristic
403C22×C4⋊C4C2×D6111yescharacteristic
404C22×C4⋊C4C2×D6111yescharacteristic
405C22×C4⋊C4C2×D6111yescharacteristic
406C22×C4⋊C4C2×D6111yescharacteristic
407C22×C22⋊C4—611no—
408C22×C22⋊C4—611no—
409C22×C22⋊C4—611no—
410C22×C22⋊C4—611no—
411C22×C22⋊C4—611no—
412C22×C22⋊C4—611no—
413C22×C42—611no—
414C22×C42—611no—
415C22×C42—611no—
416C22×C42C2×D6111yescharacteristic
417#399—618no—
418#398—618no—
419#396—618no—
420#395—618no—
421#391—618no—
422#389—618no—
423#389—618no—
424#388—618no—
425#388—618no—
426#387—618no—
427#385—618no—
428C4×C4⋊C4—618no—
429C4×C22⋊C4—618no—
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—611no—
439C2×#95—611no—
440C61C2×#255611yescharacteristic, complemented, Sylow
441C25—611no—
442C22×Q8—614no—
443C22×Q8—1224no—
444C22×Q8—1224no—
445C22×Q8—2442no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—614no—
454C23×C4—1224no—
455C23×C4—1224no—
456C23×C4—2442no—
457C23×C4C22×D6111yescharacteristic
458C23×C4C22×D6111yescharacteristic
459C23×C4C22×D6111yescharacteristic
460C23×C4C22×D6111yescharacteristic
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464#125—232no—
465C22⋊Q8—12232no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
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—2442no—
485C2×C4⋊C4C22⋊D6118yes—
486C2×C4⋊C4C22×D6114yes—
487C2×C4⋊C4C22×D6114yes—
488C2×C4⋊C4C22×D6114yes—
489C2×C4⋊C4C22×D6114yes—
490C2×C4⋊C4C22×D6114yes—
491C2×C4⋊C4C22×D6114yes—
492C2×C22⋊C4—618no—
493C2×C22⋊C4—614no—
494C2×C22⋊C4—614no—
495C2×C22⋊C4—614no—
496C2×C22⋊C4—614no—
497C2×C22⋊C4—614no—
498C2×C22⋊C4—614no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—2442no—
504C2×C42—24no—
505C2×C42—614no—
506C2×C42—614no—
507C2×C42—614no—
508C2×C42—1224no—
509C2×C42—2442no—
510C2×C42—2442no—
511C2×C42C22×D6114yes—
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#95—614no—
521#95—614no—
522C24—614no—
523C24—612no—
524C24—1222no—
525C24—1222no—
526C24—1222no—
527C24—1222no—
528C24—1222no—
529C24—1222no—
530C24C23×D6111yescharacteristic
531C2×Q8—1228no—
532C2×Q8—1228no—
533C2×Q8—2444no—
534C2×Q8—24416no—
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—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—1228no—
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×C4—1222no—
581C22×C4—1228no—
582C22×C4—2444no—
583C22×C4—24416no—
584C22×C4Q8×D6114yes—
585C22×C4C2×C22⋊D6114yes—
586C22×C4C2×C22⋊D6114yes—
587C22×C4C2×C22⋊D6114yes—
588C22×C4C23×D6112yes—
589C22×C4C23×D6112yes—
590C22×C4C23×D6112yes—
591C22×C4C23×D6112yes—
592C22×C4C23×D6112yes—
593C22×C4C23×D6112yes—
594C22×C4C23×D6112yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—1228no—
601C4⋊C4—1228no—
602C4⋊C4—1228no—
603C4⋊C4—1228no—
604C4⋊C4—1228no—
605C4⋊C4—1228no—
606C4⋊C4—2444no—
607C4⋊C4C2×C22⋊D61116yes—
608C22⋊C4—6116no—
609C22⋊C4—1228no—
610C22⋊C4—1228no—
611C22⋊C4—1228no—
612C22⋊C4—1228no—
613C22⋊C4—2444no—
614C42—28no—
615C42—1228no—
616C42—2444no—
617C42—2444no—
618C23—614no—
619C23—1228no—
620C23—1228no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—1222no—
625C23—1222no—
626C23—1222no—
627C23—1228no—
628C23—2444no—
629C23—2444no—
630C23—2444no—
631C23—2444no—
632C23C22×C22⋊D6112yes—
633C23C2×Q8×D6112yes—
634C23#41×D6112yes—
635C23#41×D6112yes—
636C23#41×D6112yes—
637C23#1451982312yes—
638C23#1451982512yes—
639C23C24×D6111yescharacteristic
640Q8—24416no—
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—28no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—614no—
666C2×C4—614no—
667C2×C4—614no—
668C2×C4—614no—
669C2×C4—1228no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1228no—
679C2×C4—1228no—
680C2×C4—1228no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—24416no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2444no—
694C2×C4C22×C22⋊D6114yes—
695C2×C4C22×C22⋊D6114yes—
696C2×C4C22×C22⋊D6114yes—
697C2×C4C2×Q8×D6114yes—
698C22—1224no—
699C22—1224no—
700C22—1224no—
701C22—2442no—
702C22—2442no—
703C22—24416no—
704C22—2442no—
705C22—2442no—
706C22#1684030814yes—
707C22#1684031814yes—
708C22#1684036014yes—
709C22#1684040014yes—
710C22Q8×C22⋊D6114yes—
711C22#1684044414yes—
712C22#1684046814yes—
713C22C23×C22⋊D6111yescharacteristic
714C22C22×Q8×D6111yescharacteristic
715C22C2×#41×D6111yescharacteristic
716C22C2×#41×D6111yescharacteristic
717C22C2×#41×D6111yescharacteristic
718C22C2×#1451982311yescharacteristic
719C22C2×#1451982511yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1224no—
728C4—1224no—
729C4—1224no—
730C4—1224no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C2—2444no—
735C2#2145089918yesdirect product factor
736C2C2×#1684030811yescharacteristic
737C2C2×#1684031811yescharacteristic
738C2C2×#1684036011yescharacteristic
739C2C2×#1684040011yescharacteristic
740C2C2×Q8×C22⋊D6111yescharacteristic
741C2C2×#1684044411yescharacteristic
742C2C2×#1684046811yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×#125×C61C2
socleC24×C61C24
prime radicalC24×D61C23
hypercenterC22×#125D61
hypocenterC61C2×#2556
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #21450899C2direct (N × H)
4. C2×#16839695C2semidirect
6. C2×#16839682C2semidirect
7. C2×#16839667C2semidirect
8. C2×#16839657C2semidirect
9. C2×#16839657C2semidirect
12. C2×#16839646C2semidirect
14. C2×C4⋊C4×Dic61C2semidirect
16. C22×#125×C61C2semidirect
38. #16839695C22semidirect
40. #16839682C22semidirect
41. #16839667C22semidirect
42. #16839657C22semidirect
43. #16839657C22semidirect
46. #16839646C22semidirect
48. C4⋊C4×Dic61C22semidirect
61. C2×#125×C61C22semidirect
105. C2×#11758198Q8semidirect
235. #11758198C2×Q8semidirect
363. C22×#125D61semidirect
379. C2×C61#2556semidirect
391. C2×#125C2×D61semidirect
440. C61C2×#2556semidirect
735. C2#21450899direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197552
#214508992
C2×#168396972
C2×#168396952
C2×#168396842
C2×#168396822
C2×#168396672
C2×#168396572
C2×#168396522
C2×#168396462
C2×#168396332
C2×C4⋊C4×Dic612
C2×C4×#117581982
C22×#125×C612
C2×#255661