Finite Group Databasebeta

← C2×#21448449 #29838648

Subgroups — C2×#21448449 #29838648

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#21448449C2116yesmaximal, direct product factor
3C2×#16839655C211yesmaximal, characteristic, complemented
4C2×#16839646C211yesmaximal, characteristic, complemented
5C2×#16839644C211yesmaximal, characteristic, complemented
6C2×#16839638C211yesmaximal, characteristic
7C2×#16839638C211yesmaximal, characteristic
8C2×#16839636C211yesmaximal, characteristic, complemented
9C2×#16839633C211yesmaximal, characteristic, complemented
10C2×#16839629C211yesmaximal, characteristic, complemented
11C2×#16839627C211yesmaximal, characteristic, complemented
12C2×#16839623C211yesmaximal, characteristic, complemented
13C2×#16839620C211yesmaximal, characteristic, complemented
14C2×C4×#11758198C211yesmaximal, characteristic, complemented
15C2×#95×D61C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519737C4116yescomplemented
23C2×#14519737C2218yes—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839655C2218yescomplemented
36#16839646C2218yescomplemented
37#16839644C2218yescomplemented
38#16839638C2218yes—
39#16839638C2218yes—
40#16839636C2218yescomplemented
41#16839633C2218yescomplemented
42#16839629C2218yescomplemented
43#16839627C2218yescomplemented
44#16839623C2218yescomplemented
45#16839620C2218yescomplemented
46C4×#11758198C2218yescomplemented
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×D61C2218yescomplemented
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C61×#388C2218yescomplemented
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—42no—
74C23×Dic61—42no—
75C23×Dic61C2×C418yescomplemented
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2314yes—
84C22×C4×D61—24no—
85C22×C4×D61—24no—
86C22×C4×D61—42no—
87C22×C4×D61—42no—
88C22×C4×D61—42no—
89C22×C4×D61—42no—
90C22×C4×D61—42no—
91C22×C4×D61—42no—
92C22×C4×D61C2×C418yes—
93C22×C4×D61C2314yes—
94C22×C4×D61C2314yes—
95C22×C4×D61C2314yes—
96#14519737C2×C4164yescomplemented
97C2×C4⋊Dic61—42no—
98C2×C4⋊Dic61C2314yes—
99C2×#11758196—42no—
100C2×#11758196—42no—
101C2×#11758196C2×C418yescomplemented
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×C22⋊Dic61—42no—
106C2×C22⋊Dic61—42no—
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2314yes—
109C2×#11758198—24no—
110C2×#11758198—24no—
111C2×#11758198C2×C418yes—
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×C4×Dic61—42no—
116C2×C4×Dic61C2×C418yescomplemented
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131C25×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61—42no—
139C2×C4⋊C4×C61C2314yes—
140C2×C22⋊C4×C61—42no—
141C2×C22⋊C4×C61—42no—
142C2×C22⋊C4×C61C2×C418yescomplemented
143C2×C22⋊C4×C61C2314yes—
144C2×C22⋊C4×C61C2314yes—
145C2×C22⋊C4×C61C2314yes—
146C2×C42×C61—42no—
147C2×C42×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61C22×C414yes—
157C24×C61C2412yes—
158C24×C61C2411yescharacteristic
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61C22×C414yes—
164C23×D61#4114yes—
165C23×D61#4114yes—
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—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×C61C22×C414yes—
184C22×C4×C61C22×C414yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C2×C22⋊D61—232no—
192C2×C22⋊D61—28no—
193C2×C22⋊D61—28no—
194C2×C22⋊D61C22×C4116yes—
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×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—416no—
214C22×Dic61—44no—
215C22×Dic61—44no—
216C22×Dic61C22×C414yes—
217C22×Dic61C22×C414yes—
218C22×Dic61C22×C414yes—
219C22×Dic61C22×C4116yescomplemented
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C2×C4×D61—28no—
228C2×C4×D61—28no—
229C2×C4×D61—416no—
230C2×C4×D61—44no—
231C2×C4×D61—44no—
232C2×C4×D61—44no—
233C2×C4×D61—44no—
234C2×C4×D61—44no—
235C2×C4×D61—44no—
236C2×C4×D61—416no—
237C2×C4×D61—416no—
238C2×C4×D61C22×C4116yes—
239C4⋊C4×C61—44no—
240C22⋊C4×C61—44no—
241C22⋊C4×C61—44no—
242C22⋊C4×C61C22×C4116yescomplemented
243C42×C61—44no—
244C22⋊Dic61—44no—
245C22⋊Dic61—44no—
246#11758198—28no—
247#11758198—28no—
248#11758198C22×C4116yes—
249C4⋊Dic61—44no—
250#11758196—44no—
251#11758196—44no—
252#11758196C22×C4116yescomplemented
253C4×Dic61—44no—
254C4×Dic61C22×C4116yescomplemented
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—28no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61C23×C414yes—
269C23×C61C23×C412yes—
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—28no—
281C22×D61—28no—
282C22×D61—28no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61#117116yes—
288C22×D61C23×C414yes—
289C22×D61C2×#4114yes—
290C22×D61C2×#4114yes—
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—44no—
310C2×C4×C61—44no—
311C2×C4×C61—44no—
312C2×C4×C61—44no—
313C2×C4×C61C23×C414yes—
314C2×C4×C61C23×C414yes—
315C22⋊D61—232no—
316C2×Dic61—28no—
317C2×Dic61—28no—
318C2×Dic61—28no—
319C2×Dic61—22no—
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—416no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61—44no—
342C2×Dic61C23×C414yes—
343C2×Dic61C23×C414yes—
344C2×Dic61C23×C414yes—
345C4×D61—416no—
346C4×D61—416no—
347C4×D61—416no—
348C2×#2318—611nomaximal, Sylow
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—24no—
352C22×C61—416no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
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—232no—
372C2×D61—24no—
373C2×D61—24no—
374C2×D61—24no—
375C2×D61—24no—
376C2×D61—24no—
377C2×D61—24no—
378C2×D61C2×#11718yes—
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×#388D6111yescharacteristic, complemented
396C2×#387—611no—
397C2×#387—611no—
398C2×#386—611no—
399C2×#386—611no—
400C2×#385—611no—
401C2×#385—611no—
402C2×#383—611no—
403C2×#382—611no—
404C2×#381—611no—
405C2×#380—611no—
406C2×C4×C22⋊C4—611no—
407C22×#95—611no—
408C2×C61—44no—
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—28no—
418C23×D4—611no—
419C24×C4—611no—
420C24×C4—611no—
421C24×C4—611no—
422C24×C4—611no—
423C2×C4×D4—6116no—
424C2×C4×D4—618no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
436C22×C22⋊C4C2×D6111yescharacteristic
437C22×C22⋊C4C2×D6111yescharacteristic
438C22×C42—611no—
439C22×C42—611no—
440C22×C42C2×D6111yescharacteristic
441#388—618no—
442#388C2×D6118yescomplemented
443#387—618no—
444#387—618no—
445#386—618no—
446#386—618no—
447#385—618no—
448#385—618no—
449#383—618no—
450#382—618no—
451#381—618no—
452#380—618no—
453C4×C22⋊C4—618no—
454C2×#95—611no—
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—618no—
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—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—618no—
480C23×C4—614no—
481C23×C4—618no—
482C23×C4—614no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—614no—
488C23×C4—614no—
489C23×C4—1224no—
490C23×C4—1224no—
491C23×C4—2442no—
492C23×C4—2442no—
493C23×C4—2442no—
494C23×C4—2442no—
495C23×C4—2442no—
496C23×C4—2442no—
497C23×C4—2442no—
498C23×C4—2442no—
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503C23×C4C22×D6111yescharacteristic
504C23×C4C22×D6111yescharacteristic
505C4×D4—6164no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—618no—
508C2×C4⋊C4—614no—
509C2×C4⋊C4—614no—
510C2×C4⋊C4—614no—
511C2×C4⋊C4—614no—
512C2×C4⋊C4—2442no—
513C2×C4⋊C4—2442no—
514C2×C4⋊C4—2442no—
515C2×C4⋊C4C22×D6114yes—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—618no—
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—1224no—
526C2×C22⋊C4—2442no—
527C2×C22⋊C4—2442no—
528C2×C22⋊C4C4×D6118yescomplemented
529C2×C22⋊C4C22×D6114yes—
530C2×C22⋊C4C22×D6114yes—
531C2×C22⋊C4C22×D6114yes—
532C2×C42—42no—
533C2×C42—618no—
534C2×C42—614no—
535C2×C42—614no—
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#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—22no—
557C24—22no—
558C24—614no—
559C24—614no—
560C24—614no—
561C24—612no—
562C24—1222no—
563C24—1222no—
564C24—1222no—
565C24—1222no—
566C24C2×C4×D6114yes—
567C24C23×D6112yes—
568C24C23×D6111yescharacteristic
569C2×D4—6116no—
570C2×D4—12232no—
571C2×D4—1228no—
572C2×D4—1228no—
573C22×C4—22no—
574C22×C4—22no—
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—614no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—6116no—
596C22×C4—6116no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—1228no—
602C22×C4—1228no—
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—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—24416no—
622C22×C4—2444no—
623C22×C4—2444no—
624C22×C4—2444no—
625C22×C4—2444no—
626C22×C4—2444no—
627C22×C4—2444no—
628C22×C4—24416no—
629C22×C4—24416no—
630C22×C4—24416no—
631C22×C4—2444no—
632C22×C4—2444no—
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—6116no—
643C4⋊C4—2444no—
644C4⋊C4—2444no—
645C4⋊C4—2444no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—6116no—
649C22⋊C4—1228no—
650C22⋊C4—1228no—
651C22⋊C4—2444no—
652C22⋊C4—2444no—
653C22⋊C4C2×C4×D61116yescomplemented
654C42—44no—
655C42—6116no—
656C42—2444no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—6116no—
671C23—614no—
672C23—614no—
673C23—614no—
674C23—1228no—
675C23—1228no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23—1228no—
681C23—1228no—
682C23—1228no—
683C23—1228no—
684C23C22×C4×D6114yes—
685C23C22×C4×D6112yes—
686C23#41×D6112yes—
687C23#41×D6112yes—
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—44no—
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—1228no—
722C2×C4—1222no—
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—24416no—
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—416no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—618no—
759C22—12232no—
760C22—1224no—
761C22—1224no—
762C22—1224no—
763C22—1224no—
764C22—1224no—
765C22—1224no—
766C22#117×D6114yes—
767C22#1684023414yes—
768C22#1684024114yes—
769C22#1684034414yes—
770C22#1684034614yes—
771C22#1684035314yes—
772C22#1684035514yes—
773C22C23×C4×D6111yescharacteristic
774C22C2×#41×D6111yescharacteristic
775C22C2×#41×D6111yescharacteristic
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—44no—
794C2—1228no—
795C2#2144844918yesdirect product factor
796C2C2×#117×D6111yescharacteristic
797C2C2×#1684023411yescharacteristic
798C2C2×#1684024111yescharacteristic
799C2C2×#1684034411yescharacteristic
800C2C2×#1684034611yescharacteristic
801C2C2×#1684035311yescharacteristic
802C2C2×#1684035511yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2318
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #21448449C2direct (N × H)
3. C2×#16839655C2semidirect
4. C2×#16839646C2semidirect
5. C2×#16839644C2semidirect
8. C2×#16839636C2semidirect
9. C2×#16839633C2semidirect
10. C2×#16839629C2semidirect
11. C2×#16839627C2semidirect
12. C2×#16839623C2semidirect
13. C2×#16839620C2semidirect
14. C2×C4×#11758198C2semidirect
15. C2×#95×D61C2semidirect
16. C2×C61×#388C2semidirect
22. C2×#14519737C4semidirect
35. #16839655C22semidirect
36. #16839646C22semidirect
37. #16839644C22semidirect
40. #16839636C22semidirect
41. #16839633C22semidirect
42. #16839629C22semidirect
43. #16839627C22semidirect
44. #16839623C22semidirect
45. #16839620C22semidirect
46. C4×#11758198C22semidirect
59. #95×D61C22semidirect
65. C61×#388C22semidirect
75. C23×Dic61C2×C4semidirect
96. #14519737C2×C4semidirect
101. C2×#11758196C2×C4semidirect
116. C2×C4×Dic61C2×C4semidirect
142. C2×C22⋊C4×C61C2×C4semidirect
219. C22×Dic61C22×C4semidirect
242. C22⋊C4×C61C22×C4semidirect
252. #11758196C22×C4semidirect
254. C4×Dic61C22×C4semidirect
395. C2×#388D61semidirect
409. C2×C61#2318semidirect
442. #388C2×D61semidirect
469. C61C2×#2318semidirect
528. C2×C22⋊C4C4×D61semidirect
653. C22⋊C4C2×C4×D61semidirect
795. C2#21448449direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197372
#214484492
C2×#168396552
C2×#168396462
C2×#168396442
C2×#168396382
C2×#168396362
C2×#168396332
C2×#168396292
C2×#168396272
C2×#168396232
C2×#168396202
C2×C4×#117581982
C2×#95×D612
C2×C61×#3882
C2×#231861