Finite Group Databasebeta

← C2×#21448685 #29839246

Subgroups — C2×#21448685 #29839246

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519735C211yesmaximal, characteristic
2C22×#14519734C211yesmaximal, characteristic
3C22×C4⋊C4×D61C211yesmaximal, characteristic
4#21448685C2116yesmaximal, direct product factor
5C2×#16839659C211yesmaximal, characteristic, complemented
6C2×#16839657C211yesmaximal, characteristic, complemented
7C2×#16839648C211yesmaximal, characteristic, complemented
8C2×#16839647C211yesmaximal, characteristic, complemented
9C2×#16839645C211yesmaximal, characteristic, complemented
10C2×#16839624C211yesmaximal, characteristic
11C2×#16839624C211yesmaximal, characteristic
12C2×#16839621C211yesmaximal, characteristic
13C2×C4×#11758196C211yesmaximal, characteristic, complemented
14C2×#16839613C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic
16C2×C61×#387C211yesmaximal, characteristic, complemented
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519735—28no—
21C2×#14519735C2218yes—
22C2×#14519734—28no—
23C2×#14519734C2218yes—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C2×C4⋊C4×D61C4116yescomplemented
33C2×C4⋊C4×D61C2218yes—
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839659C2218yescomplemented
44#16839657C2218yescomplemented
45#16839648C2218yescomplemented
46#16839647C2218yescomplemented
47#16839645C2218yescomplemented
48#16839624C2218yes—
49#16839624C2218yes—
50#16839621C2218yes—
51C4×#11758196C2218yescomplemented
52#16839613C2218yescomplemented
53#16839609C2218yes—
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C61×#387C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C24×D61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C22×C4×D61—24no—
79C22×C4×D61—24no—
80C22×C4×D61—24no—
81C22×C4×D61—24no—
82C22×C4×D61—24no—
83C22×C4×D61—24no—
84C22×C4×D61C2×C418yes—
85C22×C4×D61C2×C418yes—
86C22×C4×D61C2×C418yes—
87C22×C4×D61C2314yes—
88C22×C4×D61C2314yes—
89C22×C4×D61C2314yes—
90#14519735—232no—
91#14519734—232no—
92C2×C4⋊Dic61—24no—
93C2×C4⋊Dic61C2×C418yes—
94C2×C4⋊Dic61C2314yes—
95C2×C4⋊Dic61C2314yes—
96C2×#11758196—24no—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196—24no—
100C2×#11758196C2×C418yes—
101C2×#11758196C2×C418yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C4⋊C4×D61C2×C4164yescomplemented
109C2×#11758198—24no—
110C2×#11758198—24no—
111C2×#11758198—24no—
112C2×#11758198D418yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×C4×Dic61—24no—
118C2×C4×Dic61—24no—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—24no—
122C2×C4×Dic61C2314yes—
123C2×C4×Dic61C2314yes—
124C2×C4×Dic61C2314yes—
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61—24no—
143C2×C4⋊C4×C61C2×C418yes—
144C2×C4⋊C4×C61C2314yes—
145C2×C4⋊C4×C61C2314yes—
146C2×C42×C61—24no—
147C2×C42×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150#95×C61C2314yes—
151#95×C61C2314yes—
152C24×C61C2411yescharacteristic
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61C22×C414yes—
158C23×D61C2×D414yes—
159C23×D61#4114yes—
160C23×D61C2412yes—
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×C61C22×C414yes—
179C22×C4×C61C22×C414yes—
180C22×C4×C61C22×C414yes—
181C22×C4×C61C2×D414yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
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×Dic61C22×C414yes—
205C22×Dic61C22×C414yes—
206C22×Dic61C22×C414yes—
207C22×Dic61C2×D414yes—
208C22×Dic61#4114yes—
209C22×Dic61#4114yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C2×C4×D61—232no—
218C2×C4×D61—232no—
219C2×C4×D61—28no—
220C2×C4×D61—28no—
221C2×C4×D61—28no—
222C2×C4×D61—28no—
223C2×C4×D61—232no—
224C2×C4×D61—28no—
225C2×C4×D61—28no—
226C2×C4×D61C22×C4116yes—
227C2×C4×D61C22×C4116yes—
228C2×C4×D61C22×C4116yes—
229C4⋊C4×C61—28no—
230C4⋊C4×C61C22×C4116yes—
231C42×C61—28no—
232#11758198—28no—
233#11758198—28no—
234#11758198—28no—
235#11758198C2×D4116yes—
236C4⋊Dic61—28no—
237C4⋊Dic61C22×C4116yes—
238#11758196—28no—
239#11758196—28no—
240#11758196—28no—
241#11758196—28no—
242#11758196C22×C4116yes—
243#11758196C22×C4116yes—
244C4×Dic61—28no—
245C4×Dic61—28no—
246C4×Dic61—28no—
247C4×Dic61—28no—
248C4×Dic61—28no—
249C23×C61C23×C412yes—
250C23×C61C22×D412yes—
251C23×C61C2×#4112yes—
252C23×C61C2×#4112yes—
253C23×C61C2×#4112yes—
254C23×C612−1+412yes—
255C23×C612−1+412yes—
256C23×C61C2511yescharacteristic
257C22×D61—28no—
258C22×D61—28no—
259C22×D61—28no—
260C22×D61—28no—
261C22×D61—28no—
262C22×D61—28no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61C4×D4116yes—
268C22×D61C23×C414yes—
269C22×D61C22×D414yes—
270C22×D61C2×#4114yes—
271C2×C4×C61—28no—
272C2×C4×C61—28no—
273C2×C4×C61—28no—
274C2×C4×C61—28no—
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—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—44no—
293C2×C4×C61—44no—
294C2×C4×C61—44no—
295C2×C4×C61C23×C414yes—
296C2×C4×C61C23×C414yes—
297C2×C4×C61C23×C414yes—
298C2×C4×C61C22×D414yes—
299C2×Dic61—28no—
300C2×Dic61—28no—
301C2×Dic61—28no—
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×Dic61#117116yescomplemented
321C2×Dic61C23×C414yes—
322C2×Dic61C23×C414yes—
323C2×Dic61C23×C414yes—
324C2×Dic61C22×D414yes—
325C2×Dic61C2×#4114yes—
326C2×Dic61C2×#4114yes—
327C4×D61—232no—
328C4×D61—232no—
329C4×D61—232no—
330C2×#2344—611nomaximal, Sylow
331C22×C61C2×#11714yes—
332C22×C61C2×C4×D414yes—
333C22×C61#51914yes—
334C22×C61#54714yes—
335C22×C61#54714yes—
336C22×C61#55214yes—
337C22×C61#55214yes—
338C22×C61C24×C411yescharacteristic
339C22×C61C23×D411yescharacteristic
340C22×C61C22×#4111yescharacteristic
341C22×C61C22×#4111yescharacteristic
342C22×C61C22×#4111yescharacteristic
343C22×C61C2×2−1+411yescharacteristic
344C22×C61C2×2−1+411yescharacteristic
345C2×D61—232no—
346C2×D61—24no—
347C2×D61—24no—
348C2×D61—24no—
349C2×D61—24no—
350C2×D61—24no—
351C2×D61—24no—
352C2×D61C2×C4×D418yes—
353C4×C61—24no—
354C4×C61—24no—
355C4×C61—24no—
356C4×C61—24no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61—42no—
360Dic61—24no—
361Dic61—24no—
362Dic61—24no—
363Dic61—42no—
364Dic61—42no—
365Dic61—42no—
366Dic61C2×#11718yescomplemented
367C22×#117—611no—
368C22×#117—611no—
369C23×C4⋊C4—611no—
370#2344—6116no—
371C2×#389—611no—
372C2×#389—611no—
373C2×#387—611no—
374C2×#387—611no—
375C2×#387—611no—
376C2×#387D6111yescharacteristic, complemented
377C2×#381—611no—
378C2×#381—611no—
379C2×#380—611no—
380C2×C4×C4⋊C4—611no—
381C2×C4×C4⋊C4—611no—
382C2×C4×C22⋊C4—611no—
383C2×C61#234418yescomplemented
384C2×C61C22×#11711yescharacteristic
385C2×C61C22×C4×D411yescharacteristic
386C2×C61C2×#51911yescharacteristic
387C2×C61C2×#54711yescharacteristic
388C2×C61C2×#54711yescharacteristic
389C2×C61C2×#55211yescharacteristic
390C2×C61C2×#55211yescharacteristic
391D61—28no—
392C24×C4—611no—
393C24×C4—611no—
394C24×C4—611no—
395C2×#117—618no—
396C2×#117—618no—
397C2×#117—1228no—
398C2×#117—1228no—
399C22×C4⋊C4—611no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—6116no—
403C22×C4⋊C4—618no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4—611no—
409C22×C4⋊C4C2×D6111yescharacteristic
410C22×C4⋊C4C2×D6111yescharacteristic
411C22×C22⋊C4—611no—
412C22×C22⋊C4—611no—
413C22×C22⋊C4—611no—
414C22×C22⋊C4—611no—
415C22×C42—611no—
416C22×C42—611no—
417C22×C42—611no—
418C22×C42—611no—
419C22×C42—611no—
420C22×C42C2×D6111yescharacteristic
421#389—618no—
422#389—618no—
423#387—618no—
424#387—618no—
425#387—618no—
426#387C2×D6118yescomplemented
427#381—618no—
428#381—618no—
429#380—618no—
430C4×C4⋊C4—618no—
431C4×C4⋊C4—618no—
432C4×C22⋊C4—618no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95—611no—
436C2×#95—611no—
437C2×#95—611no—
438C2×#95—611no—
439C2×#95—611no—
440C2×#95—611no—
441C2×#95C2×D6111yescharacteristic
442C2×#95C2×D6111yescharacteristic
443C2×#95C2×D6111yescharacteristic
444C2×#95C2×D6111yescharacteristic
445C61C2×#234411yescharacteristic, complemented, Sylow
446C25—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—618no—
452C23×C4—618no—
453C23×C4—618no—
454C23×C4—614no—
455C23×C4—614no—
456C23×C4—614no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—1224no—
461C23×C4—1224no—
462C23×C4—1224no—
463C23×C4—1224no—
464C23×C4—1224no—
465C23×C4—1224no—
466C23×C4C22×D6111yescharacteristic
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C23×C4C22×D6111yescharacteristic
473#117—12232no—
474#117—12232no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—618no—
477C2×C4⋊C4—618no—
478C2×C4⋊C4—618no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—6164no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4—614no—
486C2×C4⋊C4—614no—
487C2×C4⋊C4—614no—
488C2×C4⋊C4—1224no—
489C2×C4⋊C4—1224no—
490C2×C4⋊C4—1224no—
491C2×C4⋊C4—1224no—
492C2×C4⋊C4—1224no—
493C2×C4⋊C4C4×D6118yes—
494C2×C4⋊C4C22×D6114yes—
495C2×C4⋊C4C22×D6114yes—
496C2×C22⋊C4—618no—
497C2×C22⋊C4—614no—
498C2×C22⋊C4—614no—
499C2×C22⋊C4—614no—
500C2×C22⋊C4—614no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1224no—
504C2×C42—24no—
505C2×C42—614no—
506C2×C42—614no—
507C2×C42—614no—
508C2×C42—614no—
509C2×C42—614no—
510C2×C42—1224no—
511C2×C42—1224no—
512C2×C42—1224no—
513C2×C42—1224no—
514C2×C42—1224no—
515C2×C42C22×D6114yes—
516#95—614no—
517#95—614no—
518#95—614no—
519#95—614no—
520#95—614no—
521#95—614no—
522#95—614no—
523#95—614no—
524#95C22×D6114yes—
525#95C22×D6114yes—
526#95C22×D6114yes—
527#95C22×D6114yes—
528C24—614no—
529C24—614no—
530C24—614no—
531C24—612no—
532C24—1222no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24C23×D6111yescharacteristic
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—22no—
553C22×C4—22no—
554C22×C4—614no—
555C22×C4—614no—
556C22×C4—614no—
557C22×C4—612no—
558C22×C4—614no—
559C22×C4—614no—
560C22×C4—614no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—6116no—
565C22×C4—6116no—
566C22×C4—6116no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—12232no—
571C22×C4—1228no—
572C22×C4—1228no—
573C22×C4—1228no—
574C22×C4—1228no—
575C22×C4—12232no—
576C22×C4—12232no—
577C22×C4—1228no—
578C22×C4—1228no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4C2×C4×D6114yes—
595C22×C4C2×C4×D6114yes—
596C22×C4C2×C4×D6114yes—
597C22×C4D4×D6114yes—
598C22×C4C23×D6112yes—
599C22×C4C23×D6112yes—
600C22×C4C23×D6112yes—
601C22×C4C23×D6112yes—
602C22×C4C23×D6112yes—
603C22×C4C23×D6112yes—
604C22×C4C23×D6112yes—
605C4⋊C4—28no—
606C4⋊C4—6116no—
607C4⋊C4—6116no—
608C4⋊C4—6116no—
609C4⋊C4—1228no—
610C4⋊C4—1228no—
611C4⋊C4—1228no—
612C4⋊C4—1228no—
613C4⋊C4—1228no—
614C4⋊C4C2×C4×D61116yes—
615C22⋊C4—6116no—
616C22⋊C4—1228no—
617C22⋊C4—1228no—
618C22⋊C4—1228no—
619C42—28no—
620C42—1228no—
621C42—1228no—
622C42—1228no—
623C42—1228no—
624C42—1228no—
625C23—6116no—
626C23—614no—
627C23—614no—
628C23—614no—
629C23—1228no—
630C23—1228no—
631C23—1228no—
632C23—1222no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—1228no—
637C23—1228no—
638C23—1228no—
639C23C22×C4×D6112yes—
640C23C2×D4×D6112yes—
641C23#41×D6112yes—
642C23#41×D6112yes—
643C23#41×D6112yes—
644C23#1451982412yes—
645C23#1451982512yes—
646C23C24×D6111yescharacteristic
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
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—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—6116no—
672C2×C4—614no—
673C2×C4—614no—
674C2×C4—614no—
675C2×C4—614no—
676C2×C4—614no—
677C2×C4—614no—
678C2×C4—12232no—
679C2×C4—12232no—
680C2×C4—12232no—
681C2×C4—1228no—
682C2×C4—1228no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1228no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—2444no—
700C2×C4—2444no—
701C2×C4—2444no—
702C2×C4C22×C4×D6114yes—
703C2×C4C22×C4×D6114yes—
704C2×C4C22×C4×D6114yes—
705C2×C4C2×D4×D6114yes—
706C22—618no—
707C22—1224no—
708C22—1224no—
709C22—1224no—
710C22—1224no—
711C22—1224no—
712C22—1224no—
713C22—12232no—
714C22#117×D6114yes—
715C22C4×D4×D6114yes—
716C22#1684023814yes—
717C22#1684041014yes—
718C22#1684041414yes—
719C22#1684044414yes—
720C22#1684044814yes—
721C22C23×C4×D6111yescharacteristic
722C22C22×D4×D6111yescharacteristic
723C22C2×#41×D6111yescharacteristic
724C22C2×#41×D6111yescharacteristic
725C22C2×#41×D6111yescharacteristic
726C22C2×#1451982411yescharacteristic
727C22C2×#1451982511yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—618no—
736C4—1224no—
737C4—1224no—
738C4—1224no—
739C4—2442no—
740C4—2442no—
741C4—2442no—
742C2—1228no—
743C2#2144868518yesdirect product factor
744C2C2×#117×D6111yescharacteristic
745C2C2×C4×D4×D6111yescharacteristic
746C2C2×#1684023811yescharacteristic
747C2C2×#1684041011yescharacteristic
748C2C2×#1684041411yescharacteristic
749C2C2×#1684044411yescharacteristic
750C2C2×#1684044811yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#387C2
socleC24×C61C24
prime radicalC24×D61C23
cosocleC23×C61C25
hypercenterC2×#387D61
hypocenterC61C2×#2344
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
4. #21448685C2direct (N × H)
5. C2×#16839659C2semidirect
6. C2×#16839657C2semidirect
7. C2×#16839648C2semidirect
8. C2×#16839647C2semidirect
9. C2×#16839645C2semidirect
13. C2×C4×#11758196C2semidirect
14. C2×#16839613C2semidirect
16. C2×C61×#387C2semidirect
32. C2×C4⋊C4×D61C4semidirect
43. #16839659C22semidirect
44. #16839657C22semidirect
45. #16839648C22semidirect
46. #16839647C22semidirect
47. #16839645C22semidirect
51. C4×#11758196C22semidirect
52. #16839613C22semidirect
65. C61×#387C22semidirect
108. C4⋊C4×D61C2×C4semidirect
320. C2×Dic61#117semidirect
366. Dic61C2×#117semidirect
376. C2×#387D61semidirect
383. C2×C61#2344semidirect
426. #387C2×D61semidirect
445. C61C2×#2344semidirect
743. C2#21448685direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197352
C22×#145197342
C22×C4⋊C4×D612
#214486852
C2×#168396592
C2×#168396572
C2×#168396482
C2×#168396472
C2×#168396452
C2×#168396242
C2×#168396212
C2×C4×#117581962
C2×#168396132
C2×#168396092
C2×C61×#3872
C2×#234461