Finite Group Databasebeta

← C2×#21448447 #29838646

Subgroups — C2×#21448447 #29838646

Order 15616.

3262 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2#21448447C2116yesmaximal, direct product factor
3C2×#16839654C211yesmaximal, characteristic, complemented
4C2×#16839652C211yesmaximal, characteristic, complemented
5C2×#16839649C211yesmaximal, characteristic, complemented
6C2×#16839643C211yesmaximal, characteristic, complemented
7C2×#16839641C211yesmaximal, characteristic
8C2×#16839639C211yesmaximal, characteristic
9C2×#16839637C211yesmaximal, characteristic, complemented
10C2×#16839629C211yesmaximal, characteristic, complemented
11C2×#16839627C211yesmaximal, characteristic, complemented
12C2×#16839624C211yesmaximal, characteristic, complemented
13C2×#16839619C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C22×#14519684C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519737C4116yescomplemented
22C2×#14519737C2218yes—
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839654C2218yescomplemented
36#16839652C2218yescomplemented
37#16839649C2218yescomplemented
38#16839643C2218yescomplemented
39#16839641C2218yes—
40#16839639C2218yes—
41#16839637C2218yescomplemented
42#16839629C2218yescomplemented
43#16839627C2218yescomplemented
44#16839624C2218yescomplemented
45#16839619C2218yescomplemented
46C22⋊C4×Dic61C2218yescomplemented
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2218yescomplemented
60C24×C4×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C61×#385C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C24×D61C2311yescharacteristic
69C22×C22⋊D61—24no—
70C22×C22⋊D61—24no—
71C22×C22⋊D61C2×C418yes—
72C22×C22⋊D61C2314yes—
73C23×Dic61—24no—
74C23×Dic61—42no—
75C23×Dic61—42no—
76C23×Dic61—42no—
77C23×Dic61—42no—
78C23×Dic61C2×C418yes—
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2314yes—
87C23×Dic61C2314yes—
88C22×C4×D61—42no—
89C22×C4×D61—42no—
90C22×C4×D61C2×C418yescomplemented
91C22×C4×D61C2314yes—
92#14519737C2×C4164yescomplemented
93C2×C4⋊Dic61—42no—
94C2×C4⋊Dic61—42no—
95C2×C4⋊Dic61C2314yes—
96C2×C4⋊Dic61C2314yes—
97C2×#11758196C2×C418yescomplemented
98C2×#11758196C2314yes—
99C2×C22⋊Dic61—24no—
100C2×C22⋊Dic61C2314yes—
101C2×#11758198—42no—
102C2×#11758198—42no—
103C2×#11758198—42no—
104C2×#11758198—42no—
105C2×#11758198C2×C418yescomplemented
106C2×#11758198C2314yes—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×C4×Dic61—42no—
112C2×C4×Dic61—42no—
113C2×C4×Dic61C2×C418yescomplemented
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—
129C25×C61C2311yescharacteristic
130C23×C4×C61—24no—
131C23×C4×C61—42no—
132C23×C4×C61—42no—
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2314yes—
140C2×C4⋊C4×C61—42no—
141C2×C4⋊C4×C61—42no—
142C2×C4⋊C4×C61C2314yes—
143C2×C4⋊C4×C61C2314yes—
144C2×C22⋊C4×C61—24no—
145C2×C22⋊C4×C61C2×C418yes—
146C2×C22⋊C4×C61C2314yes—
147C2×C22⋊C4×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61C22×C414yes—
155C24×C61#4114yes—
156C24×C61#4114yes—
157C24×C61C2412yes—
158C24×C61C2411yescharacteristic
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61C22×C414yes—
166C23×D61C2412yes—
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—28no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—44no—
185C22×C4×C61—44no—
186C22×C4×C61—416no—
187C22×C4×C61C22×C414yes—
188C22×C4×C61C22×C414yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C2×C22⋊D61—232no—
196C2×C22⋊D61—28no—
197C2×C22⋊D61—28no—
198C2×C22⋊D61C22×C4116yes—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—28no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—416no—
219C22×Dic61—44no—
220C22×Dic61—44no—
221C22×Dic61—44no—
222C22×Dic61—44no—
223C22×Dic61—416no—
224C22×Dic61C22×C414yes—
225C22×Dic61C22×C414yes—
226C22×Dic61C22×C414yes—
227C22×Dic61C22×C4116yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×C4×D61—416no—
236C2×C4×D61—44no—
237C2×C4×D61—44no—
238C2×C4×D61C22×C4116yescomplemented
239C4⋊C4×C61—44no—
240C4⋊C4×C61—44no—
241C22⋊C4×C61—28no—
242C22⋊C4×C61C22×C4116yes—
243C22⋊Dic61—28no—
244#11758198—44no—
245#11758198—44no—
246#11758198—44no—
247#11758198—44no—
248#11758198C22×C4116yescomplemented
249C4⋊Dic61—44no—
250C4⋊Dic61—44no—
251#11758196C22×C4116yescomplemented
252C4×Dic61—44no—
253C4×Dic61—44no—
254C4×Dic61C22×C4116yescomplemented
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—28no—
258C23×C61—28no—
259C23×C61—28no—
260C23×C61—28no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61#117116yes—
266C23×C61C23×C414yes—
267C23×C61C23×C412yes—
268C23×C61C2×#4114yes—
269C23×C61C2×#4114yes—
270C23×C61C2×#4112yes—
271C23×C61C2×#4112yes—
272C23×C61H(5,𝔽2)12yes—
273C23×C61H(5,𝔽2)12yes—
274C23×C61H(5,𝔽2)12yes—
275C23×C612−1+412yes—
276C23×C61C2511yescharacteristic
277C22×D61—28no—
278C22×D61—28no—
279C22×D61—28no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61—44no—
290C22×D61C23×C414yes—
291C2×C4×C61—28no—
292C2×C4×C61—28no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—416no—
310C2×C4×C61—44no—
311C2×C4×C61—44no—
312C2×C4×C61—44no—
313C2×C4×C61—44no—
314C2×C4×C61C23×C414yes—
315C2×C4×C61C23×C414yes—
316C22⋊D61—232no—
317C2×Dic61—28no—
318C2×Dic61—28no—
319C2×Dic61—28no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—416no—
339C2×Dic61—416no—
340C2×Dic61—44no—
341C2×Dic61—44no—
342C2×Dic61—44no—
343C2×Dic61—44no—
344C2×Dic61C23×C414yes—
345C2×Dic61C23×C414yes—
346C2×Dic61C23×C414yes—
347C4×D61—416no—
348C2×#2318—611nomaximal, Sylow
349C22×C61—232no—
350C22×C61—24no—
351C22×C61—24no—
352C22×C61—24no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—24no—
356C22×C61C2×#11718yes—
357C22×C61C2×#11714yes—
358C22×C61#51814yes—
359C22×C61#52014yes—
360C22×C61#53814yes—
361C22×C61#53814yes—
362C22×C61#53914yes—
363C22×C61#53914yes—
364C22×C61C24×C411yescharacteristic
365C22×C61C22×#4111yescharacteristic
366C22×C61C22×#4111yescharacteristic
367C22×C61C2×H(5,𝔽2)11yescharacteristic
368C22×C61C2×H(5,𝔽2)11yescharacteristic
369C22×C61C2×H(5,𝔽2)11yescharacteristic
370C22×C61C2×2−1+411yescharacteristic
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—24no—
374C2×D61—416no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C4×C61—24no—
380C4×C61—24no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385Dic61—24no—
386Dic61—24no—
387Dic61—24no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392C22×C4×D4—611no—
393#2318—6116no—
394C2×#388—611no—
395C2×#388—611no—
396C2×#387—611no—
397C2×#387—611no—
398C2×#386—611no—
399C2×#386—611no—
400C2×#385—611no—
401C2×#385D6111yescharacteristic, complemented
402C2×#383—611no—
403C2×#382—611no—
404C2×#381—611no—
405C2×#380—611no—
406C2×C4×C22⋊C4—611no—
407C22×#95—611no—
408C2×C61—28no—
409C2×C61#231818yescomplemented
410C2×C61C22×#11711yescharacteristic
411C2×C61C2×#51811yescharacteristic
412C2×C61C2×#52011yescharacteristic
413C2×C61C2×#53811yescharacteristic
414C2×C61C2×#53811yescharacteristic
415C2×C61C2×#53911yescharacteristic
416C2×C61C2×#53911yescharacteristic
417D61—44no—
418C23×D4—611no—
419C24×C4—611no—
420C24×C4—611no—
421C24×C4—611no—
422C24×C4C2×D6111yescharacteristic
423C2×C4×D4—6116no—
424C2×C4×D4—618no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4C2×D6111yescharacteristic
429C22×C4⋊C4C2×D6111yescharacteristic
430C22×C22⋊C4—611no—
431C22×C22⋊C4—611no—
432C22×C22⋊C4—611no—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—611no—
436C22×C22⋊C4C2×D6111yescharacteristic
437C22×C22⋊C4C2×D6111yescharacteristic
438C22×C42—611no—
439C22×C42—611no—
440C22×C42—611no—
441#388—618no—
442#388—618no—
443#387—618no—
444#387—618no—
445#386—618no—
446#386—618no—
447#385—618no—
448#385C2×D6118yescomplemented
449#383—618no—
450#382—618no—
451#381—618no—
452#380—618no—
453C4×C22⋊C4—618no—
454C2×#95—618no—
455C2×#95—611no—
456C2×#95—611no—
457C2×#95—611no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95—611no—
466C2×#95—611no—
467C2×#95C2×D6111yescharacteristic
468C2×#95C2×D6111yescharacteristic
469C61C2×#231811yescharacteristic, complemented, Sylow
470C25—611no—
471C25C22×D6111yescharacteristic
472C22×D4—618no—
473C22×D4—614no—
474C22×D4—1224no—
475C22×D4—1224no—
476C23×C4—24no—
477C23×C4—42no—
478C23×C4—42no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—618no—
483C23×C4—614no—
484C23×C4—618no—
485C23×C4—614no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—614no—
491C23×C4—1224no—
492C23×C4—2442no—
493C23×C4—2442no—
494C23×C4—2442no—
495C23×C4—2442no—
496C23×C4—2442no—
497C23×C4—2442no—
498C23×C4C22×D6111yescharacteristic
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503C23×C4C22×D6111yescharacteristic
504C23×C4C22×D6114yes—
505C4×D4—6164no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—618no—
509C2×C4⋊C4—614no—
510C2×C4⋊C4—614no—
511C2×C4⋊C4—614no—
512C2×C4⋊C4—2442no—
513C2×C4⋊C4—2442no—
514C2×C4⋊C4C22×D6114yes—
515C2×C4⋊C4C22×D6114yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—618no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—614no—
522C2×C22⋊C4—614no—
523C2×C22⋊C4—614no—
524C2×C22⋊C4—1224no—
525C2×C22⋊C4—2442no—
526C2×C22⋊C4—2442no—
527C2×C22⋊C4—2442no—
528C2×C22⋊C4—2442no—
529C2×C22⋊C4C4×D6118yes—
530C2×C22⋊C4C22×D6114yes—
531C2×C22⋊C4C22×D6114yes—
532C2×C42—618no—
533C2×C42—614no—
534C2×C42—614no—
535C2×C42—614no—
536C2×C42—2442no—
537C2×C42—2442no—
538#95—614no—
539#95—614no—
540#95—614no—
541#95—614no—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95—614no—
549#95—614no—
550#95C22×D6114yes—
551#95C22×D6114yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—614no—
557C24—612no—
558C24—1222no—
559C24—1222no—
560C24—1222no—
561C24—1222no—
562C24—1222no—
563C24—1222no—
564C24C2×C4×D6114yes—
565C24#1175822414yes—
566C24#1175822614yes—
567C24C23×D6112yes—
568C24C23×D6111yescharacteristic
569C2×D4—6116no—
570C2×D4—1228no—
571C2×D4—1228no—
572C2×D4—12232no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—416no—
593C22×C4—614no—
594C22×C4—614no—
595C22×C4—614no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—6116no—
600C22×C4—6116no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1228no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—24416no—
625C22×C4—2444no—
626C22×C4—2444no—
627C22×C4—24416no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4—24416no—
633C22×C4C2×C4×D6114yes—
634C22×C4C2×C4×D6114yes—
635C22×C4C23×D6112yes—
636C22×C4C23×D6112yes—
637C22×C4C23×D6112yes—
638C22×C4C23×D6112yes—
639C22×C4C23×D6112yes—
640C22×C4C23×D6112yes—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—6116no—
644C4⋊C4—2444no—
645C4⋊C4—2444no—
646C22⋊C4—28no—
647C22⋊C4—6116no—
648C22⋊C4—1228no—
649C22⋊C4—2444no—
650C22⋊C4—2444no—
651C22⋊C4—2444no—
652C22⋊C4—2444no—
653C22⋊C4C2×C4×D61116yes—
654C42—6116no—
655C42—2444no—
656C42—2444no—
657C23—28no—
658C23—28no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—614no—
668C23—1228no—
669C23—1228no—
670C23—1228no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—2444no—
678C23—2444no—
679C23—2444no—
680C23—2444no—
681C23#14519735116yes—
682C23C22×C4×D6114yes—
683C23C22×C4×D6112yes—
684C23C2×#1175822414yes—
685C23C2×#1175822412yes—
686C23C2×#1175822614yes—
687C23C2×#1175822612yes—
688C23#1451982212yes—
689C23#1451982212yes—
690C23#1451982312yes—
691C23#1451982412yes—
692C23C24×D6111yescharacteristic
693D4—12232no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—416no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—614no—
718C2×C4—614no—
719C2×C4—614no—
720C2×C4—1228no—
721C2×C4—1228no—
722C2×C4—1228no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—24416no—
742C2×C4—24416no—
743C2×C4—24416no—
744C2×C4—2444no—
745C2×C4—2444no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4C22×C4×D6114yes—
749C2×C4C22×C4×D6114yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—232no—
757C22—1224no—
758C22—1224no—
759C22—1224no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22—2442no—
764C22—24416no—
765C22C2×#1451973518yes—
766C22C2×#1451973514yes—
767C22#1684023414yes—
768C22#1684024114yes—
769C22#1684034714yes—
770C22#1684035214yes—
771C22#1684035614yes—
772C22#1684036114yes—
773C22C23×C4×D6111yescharacteristic
774C22C22×#1175822411yescharacteristic
775C22C22×#1175822611yescharacteristic
776C22C2×#1451982211yescharacteristic
777C22C2×#1451982211yescharacteristic
778C22C2×#1451982311yescharacteristic
779C22C2×#1451982411yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—1224no—
787C4—1224no—
788C4—1224no—
789C4—2442no—
790C4—2442no—
791C4—2442no—
792C4—2442no—
793C2—28no—
794C2—2444no—
795C2#2144844718yesdirect product factor
796C2C22×#1451973511yescharacteristic
797C2C2×#1684023411yescharacteristic
798C2C2×#1684024111yescharacteristic
799C2C2×#1684034711yescharacteristic
800C2C2×#1684035211yescharacteristic
801C2C2×#1684035611yescharacteristic
802C2C2×#1684036111yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#385D61
hypocenterC61C2×#2318
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #21448447C2direct (N × H)
3. C2×#16839654C2semidirect
4. C2×#16839652C2semidirect
5. C2×#16839649C2semidirect
6. C2×#16839643C2semidirect
9. C2×#16839637C2semidirect
10. C2×#16839629C2semidirect
11. C2×#16839627C2semidirect
12. C2×#16839624C2semidirect
13. C2×#16839619C2semidirect
14. C2×C22⋊C4×Dic61C2semidirect
15. C22×#14519684C2semidirect
16. C2×C61×#385C2semidirect
21. C2×#14519737C4semidirect
35. #16839654C22semidirect
36. #16839652C22semidirect
37. #16839649C22semidirect
38. #16839643C22semidirect
41. #16839637C22semidirect
42. #16839629C22semidirect
43. #16839627C22semidirect
44. #16839624C22semidirect
45. #16839619C22semidirect
46. C22⋊C4×Dic61C22semidirect
59. C2×#14519684C22semidirect
65. C61×#385C22semidirect
90. C22×C4×D61C2×C4semidirect
92. #14519737C2×C4semidirect
97. C2×#11758196C2×C4semidirect
105. C2×#11758198C2×C4semidirect
113. C2×C4×Dic61C2×C4semidirect
238. C2×C4×D61C22×C4semidirect
248. #11758198C22×C4semidirect
251. #11758196C22×C4semidirect
254. C4×Dic61C22×C4semidirect
401. C2×#385D61semidirect
409. C2×C61#2318semidirect
448. #385C2×D61semidirect
469. C61C2×#2318semidirect
795. C2#21448447direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197372
#214484472
C2×#168396542
C2×#168396522
C2×#168396492
C2×#168396432
C2×#168396412
C2×#168396392
C2×#168396372
C2×#168396292
C2×#168396272
C2×#168396242
C2×#168396192
C2×C22⋊C4×Dic612
C22×#145196842
C2×C61×#3852
C2×#231861