Finite Group Databasebeta

← C2×#21448631 #29838931

Subgroups — C2×#21448631 #29838931

Order 15616.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519766C211yesmaximal, characteristic
2#21448631C2116yesmaximal, direct product factor
3C2×#16839669C211yesmaximal, characteristic, complemented
4C2×#16839654C211yesmaximal, characteristic, complemented
5C2×#16839653C211yesmaximal, characteristic, complemented
6C2×#16839652C211yesmaximal, characteristic, complemented
7C2×#16839651C211yesmaximal, characteristic, complemented
8C2×#16839640C211yesmaximal, characteristic
9C2×#16839640C211yesmaximal, characteristic
10C2×#16839636C211yesmaximal, characteristic, complemented
11C2×#16839633C211yesmaximal, characteristic, complemented
12C2×#16839629C211yesmaximal, characteristic, complemented
13C2×#16839613C211yesmaximal, characteristic, complemented
14C2×C4×#11758198C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#391C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519766C4116yescomplemented
21C2×#14519766C2218yes—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839669C2218yescomplemented
40#16839654C2218yescomplemented
41#16839653C2218yescomplemented
42#16839652C2218yescomplemented
43#16839651C2218yescomplemented
44#16839640C2218yes—
45#16839640C2218yes—
46#16839636C2218yescomplemented
47#16839633C2218yescomplemented
48#16839629C2218yescomplemented
49#16839613C2218yescomplemented
50C4×#11758198C2218yescomplemented
51#16839609C2218yescomplemented
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C23×Q8×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C42×C61C2211yescharacteristic
63C61×#391C2218yescomplemented
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C24×D61C2311yescharacteristic
69C24×D61C2311yescharacteristic
70C22×D244—42no—
71C22×D244—42no—
72C22×D244C2×C418yes—
73C22×D244C2314yes—
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—24no—
81C22×C4×D61—24no—
82C22×C4×D61—42no—
83C22×C4×D61—42no—
84C22×C4×D61—42no—
85C22×C4×D61—42no—
86C22×C4×D61C2314yes—
87C22×C4×D61C2314yes—
88#14519766C2×C4164yescomplemented
89C2×C4⋊Dic61—42no—
90C2×C4⋊Dic61C2314yes—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×#11758198—24no—
96C2×#11758198—24no—
97C2×#11758198—42no—
98C2×#11758198—42no—
99C2×#11758198—42no—
100C2×#11758198—42no—
101C2×#11758198C2×C418yescomplemented
102C2×#11758198C2×C418yescomplemented
103C2×#11758198C2×C418yescomplemented
104C2×#11758198C2×C418yescomplemented
105C2×#11758198C2314yes—
106C2×#11758198C2314yes—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×C4×Dic61—42no—
116C2×C4×Dic61—42no—
117C2×C4×Dic61—42no—
118C2×C4×Dic61C2×C418yescomplemented
119C2×C4×Dic61C2314yes—
120C2×C4×Dic61C2314yes—
121C2×C4×Dic61C2314yes—
122C2×C4×Dic61C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131C22×Q8×C61—42no—
132C22×Q8×C61—42no—
133C22×Q8×C61C2×C418yescomplemented
134C22×Q8×C61C2314yes—
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—42no—
143C2×C4⋊C4×C61C2314yes—
144C2×C42×C61—42no—
145C2×C42×C61C2314yes—
146#95×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×D61—22no—
158C23×D61—22no—
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61C22×C414yes—
164C23×D61C22×C414yes—
165C23×D61C2412yes—
166C23×D61C2412yes—
167C2×Q8×C61—416no—
168C2×Q8×C61—44no—
169C2×Q8×C61—44no—
170C2×Q8×C61C22×C4116yescomplemented
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×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—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61C22×C414yes—
189C22×C4×C61C22×C414yes—
190C22×C4×C61C22×C414yes—
191C22×C4×C61#4114yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
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×Dic61C22×C414yes—
215C22×Dic61C22×C414yes—
216C22×Dic61#4114yes—
217C22×Dic61C2412yes—
218C22×Dic61C2412yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C2×D244—416no—
224C2×D244—44no—
225C2×D244—44no—
226C2×D244C22×C4116yes—
227C2×C4×D61—28no—
228C2×C4×D61—28no—
229C2×C4×D61—44no—
230C2×C4×D61—44no—
231C2×C4×D61—44no—
232C2×C4×D61—44no—
233C2×C4×D61—416no—
234C2×C4×D61—416no—
235C4⋊C4×C61—44no—
236C42×C61—44no—
237#11758198—28no—
238#11758198—28no—
239#11758198—44no—
240#11758198—44no—
241#11758198—44no—
242#11758198—44no—
243#11758198C22×C4116yescomplemented
244#11758198C22×C4116yescomplemented
245#11758198C22×C4116yescomplemented
246#11758198C22×C4116yescomplemented
247C4⋊Dic61—44no—
248#11758196—28no—
249#11758196—28no—
250C4×Dic61—44no—
251C4×Dic61—44no—
252C4×Dic61—44no—
253C4×Dic61C22×C4116yescomplemented
254C23×C61C23×C412yes—
255C23×C61C2×#4112yes—
256C23×C61C2×#4112yes—
257C23×C61H(5,𝔽2)12yes—
258C23×C61H(5,𝔽2)12yes—
259C23×C61H(5,𝔽2)12yes—
260C23×C612−1+412yes—
261C23×C61C2511yescharacteristic
262C22×D61—28no—
263C22×D61—28no—
264C22×D61—28no—
265C22×D61—28no—
266C22×D61—28no—
267C22×D61—28no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—44no—
281C22×D61—44no—
282C22×D61—44no—
283C22×D61—44no—
284C22×D61—44no—
285C22×D61—44no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61C23×C414yes—
289C22×D61C23×C414yes—
290Q8×C61—416no—
291C2×C4×C61—28no—
292C2×C4×C61—28no—
293C2×C4×C61—28no—
294C2×C4×C61—28no—
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—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—44no—
313C2×C4×C61—44no—
314C2×C4×C61—44no—
315C2×C4×C61C23×C414yes—
316C2×C4×C61C23×C414yes—
317C2×C4×C61C23×C414yes—
318C2×C4×C61C2×#4114yes—
319C2×Dic61—28no—
320C2×Dic61—28no—
321C2×Dic61—28no—
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—44no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61C23×C414yes—
341C2×Dic61C23×C414yes—
342C2×Dic61C2×#4114yes—
343D244—416no—
344C4×D61—416no—
345C4×D61—416no—
346C2×#2337—611nomaximal, Sylow
347C22×C61C4×#4114yes—
348C22×C61#51814yes—
349C22×C61#52014yes—
350C22×C61#53814yes—
351C22×C61#53814yes—
352C22×C61#54214yes—
353C22×C61#54214yes—
354C22×C61C24×C411yescharacteristic
355C22×C61C22×#4111yescharacteristic
356C22×C61C22×#4111yescharacteristic
357C22×C61C2×H(5,𝔽2)11yescharacteristic
358C22×C61C2×H(5,𝔽2)11yescharacteristic
359C22×C61C2×H(5,𝔽2)11yescharacteristic
360C22×C61C2×2−1+411yescharacteristic
361C2×D61—24no—
362C2×D61—24no—
363C2×D61—24no—
364C2×D61—24no—
365C2×D61—24no—
366C2×D61—24no—
367C2×D61—416no—
368C2×D61—416no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C4×C61—24no—
378C4×C61—24no—
379C4×C61—24no—
380C4×C61—24no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61—42no—
384Dic61—24no—
385Dic61—24no—
386Dic61—24no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390C22×#124—611no—
391#2337—6116no—
392C2×#391—611no—
393C2×#391D6111yescharacteristic, complemented
394C2×#388—611no—
395C2×#388—611no—
396C2×#388—611no—
397C2×#388—611no—
398C2×#386—611no—
399C2×#386—611no—
400C2×#385—611no—
401C2×#385—611no—
402C2×#383—611no—
403C2×C4×C4⋊C4—611no—
404C2×C4×C22⋊C4—611no—
405C2×C4×C22⋊C4—611no—
406C2×C61#233718yescomplemented
407C2×C61C2×C4×#4111yescharacteristic
408C2×C61C2×#51811yescharacteristic
409C2×C61C2×#52011yescharacteristic
410C2×C61C2×#53811yescharacteristic
411C2×C61C2×#53811yescharacteristic
412C2×C61C2×#54211yescharacteristic
413C2×C61C2×#54211yescharacteristic
414D61—44no—
415D61—44no—
416C23×Q8C2×D6111yescharacteristic
417C23×D4—611no—
418C24×C4—611no—
419C24×C4—611no—
420C2×#124—6116no—
421C2×#124—618no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4C2×D6111yescharacteristic
426C22×C22⋊C4—611no—
427C22×C22⋊C4—611no—
428C22×C22⋊C4—611no—
429C22×C22⋊C4—611no—
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×C42—611no—
437C22×C42—611no—
438C22×C42—611no—
439C22×C42—611no—
440C22×C42C2×D6111yescharacteristic
441#391—618no—
442#391C2×D6118yescomplemented
443#388—618no—
444#388—618no—
445#388—618no—
446#388—618no—
447#386—618no—
448#386—618no—
449#385—618no—
450#385—618no—
451#383—618no—
452C4×C4⋊C4—618no—
453C4×C22⋊C4—618no—
454C4×C22⋊C4—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×#95C2×D6111yescharacteristic
464C2×#95C2×D6111yescharacteristic
465C2×#95C2×D6111yescharacteristic
466C2×#95C2×D6111yescharacteristic
467C61C2×#233711yescharacteristic, complemented, Sylow
468C25—611no—
469C25—611no—
470C22×Q8—42no—
471C22×Q8—42no—
472C22×Q8C4×D6118yescomplemented
473C22×Q8C22×D6114yes—
474C22×D4—618no—
475C22×D4—614no—
476C22×D4—2442no—
477C22×D4—2442no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—614no—
485C23×C4—614no—
486C23×C4—1224no—
487C23×C4—1224no—
488C23×C4—2442no—
489C23×C4—2442no—
490C23×C4—2442no—
491C23×C4—2442no—
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496C23×C4C22×D6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499#124—6164no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—614no—
504C2×C4⋊C4—1224no—
505C2×C4⋊C4—1224no—
506C2×C4⋊C4—2442no—
507C2×C4⋊C4C22×D6114yes—
508C2×C22⋊C4—618no—
509C2×C22⋊C4—618no—
510C2×C22⋊C4—618no—
511C2×C22⋊C4—618no—
512C2×C22⋊C4—614no—
513C2×C22⋊C4—614no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—614no—
516C2×C22⋊C4—614no—
517C2×C22⋊C4—614no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—614no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—1224no—
524C2×C22⋊C4—2442no—
525C2×C22⋊C4—2442no—
526C2×C22⋊C4—2442no—
527C2×C22⋊C4—2442no—
528C2×C42—42no—
529C2×C42—618no—
530C2×C42—614no—
531C2×C42—614no—
532C2×C42—614no—
533C2×C42—614no—
534C2×C42—2442no—
535C2×C42—2442no—
536C2×C42—2442no—
537C2×C42C22×D6114yes—
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#95C22×D6114yes—
547#95C22×D6114yes—
548#95C22×D6114yes—
549#95C22×D6114yes—
550C24—614no—
551C24—614no—
552C24—612no—
553C24—612no—
554C24—1222no—
555C24—1222no—
556C24—1222no—
557C24—1222no—
558C24—1222no—
559C24—1222no—
560C24—1222no—
561C24—1222no—
562C24—1222no—
563C24—1222no—
564C24—1222no—
565C24—1222no—
566C24C23×D6111yescharacteristic
567C2×Q8—416no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8C2×C4×D61116yescomplemented
571C2×D4—6116no—
572C2×D4—24416no—
573C2×D4—2444no—
574C2×D4—2444no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
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—22no—
591C22×C4—22no—
592C22×C4—614no—
593C22×C4—614no—
594C22×C4—614no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—1228no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
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—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1228no—
618C22×C4—2444no—
619C22×C4—2444no—
620C22×C4—2444no—
621C22×C4—2444no—
622C22×C4—24416no—
623C22×C4—24416no—
624C22×C4C2×C4×D6114yes—
625C22×C4C2×C4×D6114yes—
626C22×C4C2×C4×D6114yes—
627C22×C4#1175822614yes—
628C22×C4C23×D6112yes—
629C22×C4C23×D6112yes—
630C22×C4C23×D6112yes—
631C22×C4C23×D6112yes—
632C22×C4C23×D6112yes—
633C22×C4C23×D6112yes—
634C22×C4C23×D6112yes—
635C4⋊C4—44no—
636C4⋊C4—1228no—
637C4⋊C4—1228no—
638C4⋊C4—2444no—
639C22⋊C4—6116no—
640C22⋊C4—6116no—
641C22⋊C4—6116no—
642C22⋊C4—6116no—
643C22⋊C4—1228no—
644C22⋊C4—1228no—
645C22⋊C4—2444no—
646C22⋊C4—2444no—
647C22⋊C4—2444no—
648C22⋊C4—2444no—
649C42—44no—
650C42—6116no—
651C42—2444no—
652C42—2444no—
653C42—2444no—
654C23—614no—
655C23—614no—
656C23—1228no—
657C23—1228no—
658C23—1228no—
659C23—1228no—
660C23—1228no—
661C23—1228no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—2444no—
675C23—2444no—
676C23—2444no—
677C23—2444no—
678C23—2444no—
679C23—2444no—
680C23—2444no—
681C23—2444no—
682C23C22×C4×D6112yes—
683C23#41×D6112yes—
684C23C2×#1175822612yes—
685C23#1451982212yes—
686C23#1451982212yes—
687C23#1451982312yes—
688C23#1451982512yes—
689C23C24×D6111yescharacteristic
690Q8—416no—
691D4—24416no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—28no—
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—22no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—614no—
717C2×C4—614no—
718C2×C4—614no—
719C2×C4—1228no—
720C2×C4—1228no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1228no—
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—24416no—
738C2×C4—24416no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4—2444no—
742C2×C4C22×C4×D6114yes—
743C2×C4C22×C4×D6114yes—
744C2×C4C22×C4×D6114yes—
745C2×C4C2×#1175822614yes—
746C22—1224no—
747C22—1224no—
748C22—1224no—
749C22—1224no—
750C22—1224no—
751C22—1224no—
752C22—2442no—
753C22—2442no—
754C22—24416no—
755C22—24416no—
756C22—2442no—
757C22—2442no—
758C22—2442no—
759C22—2442no—
760C22—2442no—
761C22—2442no—
762C22C4×#1175822614yes—
763C22#1684023514yes—
764C22#1684024414yes—
765C22#1684034614yes—
766C22#1684035214yes—
767C22#1684038214yes—
768C22#1684038614yes—
769C22C23×C4×D6111yescharacteristic
770C22C2×#41×D6111yescharacteristic
771C22C22×#1175822611yescharacteristic
772C22C2×#1451982211yescharacteristic
773C22C2×#1451982211yescharacteristic
774C22C2×#1451982311yescharacteristic
775C22C2×#1451982511yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—1224no—
784C4—1224no—
785C4—1224no—
786C4—2442no—
787C4—2442no—
788C4—2442no—
789C2—2444no—
790C2—2444no—
791C2#2144863118yesdirect product factor
792C2C2×C4×#1175822611yescharacteristic
793C2C2×#1684023511yescharacteristic
794C2C2×#1684024411yescharacteristic
795C2C2×#1684034611yescharacteristic
796C2C2×#1684035211yescharacteristic
797C2C2×#1684038211yescharacteristic
798C2C2×#1684038611yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#391C2
socleC24×C61C24
prime radicalC23×D244C22
cosocleC23×C61C25
hypercenterC2×#391D61
hypocenterC61C2×#2337
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. #21448631C2direct (N × H)
3. C2×#16839669C2semidirect
4. C2×#16839654C2semidirect
5. C2×#16839653C2semidirect
6. C2×#16839652C2semidirect
7. C2×#16839651C2semidirect
10. C2×#16839636C2semidirect
11. C2×#16839633C2semidirect
12. C2×#16839629C2semidirect
13. C2×#16839613C2semidirect
14. C2×C4×#11758198C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#391C2semidirect
20. C2×#14519766C4semidirect
39. #16839669C22semidirect
40. #16839654C22semidirect
41. #16839653C22semidirect
42. #16839652C22semidirect
43. #16839651C22semidirect
46. #16839636C22semidirect
47. #16839633C22semidirect
48. #16839629C22semidirect
49. #16839613C22semidirect
50. C4×#11758198C22semidirect
51. #16839609C22semidirect
63. C61×#391C22semidirect
88. #14519766C2×C4semidirect
101. C2×#11758198C2×C4semidirect
102. C2×#11758198C2×C4semidirect
103. C2×#11758198C2×C4semidirect
104. C2×#11758198C2×C4semidirect
118. C2×C4×Dic61C2×C4semidirect
133. C22×Q8×C61C2×C4semidirect
170. C2×Q8×C61C22×C4semidirect
243. #11758198C22×C4semidirect
244. #11758198C22×C4semidirect
245. #11758198C22×C4semidirect
246. #11758198C22×C4semidirect
253. C4×Dic61C22×C4semidirect
393. C2×#391D61semidirect
406. C2×C61#2337semidirect
442. #391C2×D61semidirect
467. C61C2×#2337semidirect
472. C22×Q8C4×D61semidirect
570. C2×Q8C2×C4×D61semidirect
791. C2#21448631direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197662
#214486312
C2×#168396692
C2×#168396542
C2×#168396532
C2×#168396522
C2×#168396512
C2×#168396402
C2×#168396362
C2×#168396332
C2×#168396292
C2×#168396132
C2×C4×#117581982
C2×#168396092
C2×C61×#3912
C2×#233761