Finite Group Databasebeta

← C2×#21448627 #29838927

Subgroups — C2×#21448627 #29838927

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×#14519763C211yesmaximal, characteristic
2#21448627C2116yesmaximal, direct product factor
3C2×#16839668C211yesmaximal, characteristic, complemented
4C2×#16839666C211yesmaximal, characteristic, complemented
5C2×#16839656C211yesmaximal, characteristic, complemented
6C2×#16839655C211yesmaximal, characteristic, complemented
7C2×#16839653C211yesmaximal, characteristic, complemented
8C2×#16839651C211yesmaximal, characteristic, complemented
9C2×#16839641C211yesmaximal, characteristic
10C2×#16839638C211yesmaximal, characteristic
11C2×#16839636C211yesmaximal, characteristic, complemented
12C2×#16839635C211yesmaximal, characteristic, complemented
13C2×#16839629C211yesmaximal, characteristic, complemented
14C2×C4×#11758196C211yesmaximal, characteristic, complemented
15C2×C4×#11758198C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519763C4116yescomplemented
21C2×#14519763C2218yes—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839668C2218yescomplemented
38#16839666C2218yescomplemented
39#16839656C2218yescomplemented
40#16839655C2218yescomplemented
41#16839653C2218yescomplemented
42#16839651C2218yescomplemented
43#16839641C2218yes—
44#16839638C2218yes—
45#16839636C2218yescomplemented
46#16839635C2218yescomplemented
47#16839629C2218yescomplemented
48C4×#11758196C2218yescomplemented
49C4×#11758198C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C24×C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C4×C22⋊C4×C61C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C24×D61C2311yescharacteristic
69C22×Dic122—42no—
70C22×Dic122—42no—
71C22×Dic122C2×C418yescomplemented
72C22×Dic122C2314yes—
73C22×C22⋊D61—42no—
74C22×C22⋊D61—42no—
75C22×C22⋊D61C2×C418yes—
76C22×C22⋊D61C2314yes—
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C22×C4×D61—24no—
85C22×C4×D61—42no—
86C22×C4×D61—42no—
87C22×C4×D61C2314yes—
88#14519763C2×C4164yescomplemented
89C2×C4⋊Dic61—42no—
90C2×C4⋊Dic61C2314yes—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196—42no—
94C2×#11758196C2314yes—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×C22⋊Dic61—42no—
98C2×C22⋊Dic61—42no—
99C2×C22⋊Dic61C2×C418yescomplemented
100C2×C22⋊Dic61C2314yes—
101C2×C22⋊Dic61C2314yes—
102C2×C22⋊Dic61C2314yes—
103C2×#11758198—24no—
104C2×#11758198—42no—
105C2×#11758198—42no—
106C2×#11758198C2×C418yescomplemented
107C2×#11758198C2×C418yescomplemented
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×C4×Dic61—42no—
114C2×C4×Dic61—42no—
115C2×C4×Dic61C2×C418yescomplemented
116C2×C4×Dic61C2314yes—
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—
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×C22⋊C4×C61—24no—
141C2×C22⋊C4×C61C2×C418yescomplemented
142C2×C22⋊C4×C61C2314yes—
143C2×C22⋊C4×C61C2314yes—
144C2×C42×C61—42no—
145C2×C42×C61—42no—
146C2×C42×C61C2314yes—
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×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—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—28no—
182C22×C4×C61—44no—
183C22×C4×C61—44no—
184C22×C4×C61—416no—
185C22×C4×C61C22×C414yes—
186C22×C4×C61C22×C414yes—
187C22×C4×C61#4114yes—
188C22×C4×C61#4114yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C2×C22⋊D61—416no—
196C2×C22⋊D61—44no—
197C2×C22⋊D61—44no—
198C2×C22⋊D61C22×C4116yes—
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×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61C22×C414yes—
218C22×Dic61C22×C414yes—
219C22×Dic61C22×C414yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C2×C4×D61—28no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61—416no—
231C2×Dic122—416no—
232C2×Dic122—44no—
233C2×Dic122—44no—
234C2×Dic122C22×C4116yescomplemented
235C22⋊C4×C61—28no—
236C22⋊C4×C61C22×C4116yescomplemented
237C42×C61—44no—
238C42×C61—44no—
239C22⋊Dic61—44no—
240C22⋊Dic61—44no—
241C22⋊Dic61C22×C4116yescomplemented
242#11758198—28no—
243#11758198—44no—
244#11758198—44no—
245#11758198C22×C4116yescomplemented
246#11758198C22×C4116yescomplemented
247C4⋊Dic61—44no—
248#11758196—28no—
249#11758196—28no—
250#11758196—44no—
251C4×Dic61—44no—
252C4×Dic61—44no—
253C4×Dic61C22×C4116yescomplemented
254C23×C61—28no—
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61—44no—
267C23×C61C23×C414yes—
268C23×C61C23×C412yes—
269C23×C61C2×#4112yes—
270C23×C61C2×#4112yes—
271C23×C61H(5,𝔽2)12yes—
272C23×C61H(5,𝔽2)12yes—
273C23×C61H(5,𝔽2)12yes—
274C23×C612−1+412yes—
275C23×C61C2511yescharacteristic
276C22×D61—28no—
277C22×D61—28no—
278C22×D61—28no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—44no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61C23×C414yes—
290C2×C4×C61—28no—
291C2×C4×C61—28no—
292C2×C4×C61—28no—
293C2×C4×C61—28no—
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—416no—
309C2×C4×C61—44no—
310C2×C4×C61—44no—
311C2×C4×C61C23×C414yes—
312C2×C4×C61C23×C414yes—
313C2×C4×C61C2×#4114yes—
314C2×C4×C61C2×#4114yes—
315C22⋊D61—416no—
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—44no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61C23×C414yes—
342C2×Dic61C23×C414yes—
343C2×Dic61C23×C414yes—
344C4×D61—416no—
345Dic122—416no—
346C2×#2337—611nomaximal, Sylow
347C22×C61—24no—
348C22×C61—24no—
349C22×C61—24no—
350C22×C61—416no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61C4×#4114yes—
356C22×C61#51814yes—
357C22×C61#52014yes—
358C22×C61#53814yes—
359C22×C61#53814yes—
360C22×C61#54214yes—
361C22×C61#54214yes—
362C22×C61C24×C411yescharacteristic
363C22×C61C22×#4111yescharacteristic
364C22×C61C22×#4111yescharacteristic
365C22×C61C2×H(5,𝔽2)11yescharacteristic
366C22×C61C2×H(5,𝔽2)11yescharacteristic
367C22×C61C2×H(5,𝔽2)11yescharacteristic
368C22×C61C2×2−1+411yescharacteristic
369C2×D61—24no—
370C2×D61—24no—
371C2×D61—24no—
372C2×D61—416no—
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—
383Dic61—24no—
384Dic61—24no—
385Dic61—24no—
386Dic61—42no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390C22×#124—611no—
391#2337—6116no—
392C2×#391—611no—
393C2×#391—611no—
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⋊C4D6111yescharacteristic, complemented
406C2×C61—44no—
407C2×C61#233718yescomplemented
408C2×C61C2×C4×#4111yescharacteristic
409C2×C61C2×#51811yescharacteristic
410C2×C61C2×#52011yescharacteristic
411C2×C61C2×#53811yescharacteristic
412C2×C61C2×#53811yescharacteristic
413C2×C61C2×#54211yescharacteristic
414C2×C61C2×#54211yescharacteristic
415D61—44no—
416C23×Q8—611no—
417C23×D4—611no—
418C24×C4—611no—
419C24×C4C2×D6111yescharacteristic
420C2×#124—6116no—
421C2×#124—618no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
435C22×C22⋊C4C2×D6111yescharacteristic
436C22×C42—611no—
437C22×C42—611no—
438C22×C42—611no—
439C22×C42C2×D6111yescharacteristic
440C22×C42C2×D6111yescharacteristic
441#391—618no—
442#391—618no—
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⋊C4C2×D6118yescomplemented
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×#95C2×D6111yescharacteristic
466C2×#95C2×D6111yescharacteristic
467C61C2×#233711yescharacteristic, complemented, Sylow
468C25—611no—
469C25C22×D6111yescharacteristic
470C22×Q8—618no—
471C22×Q8—614no—
472C22×Q8—2442no—
473C22×Q8—2442no—
474C22×D4—618no—
475C22×D4—614no—
476C22×D4—2442no—
477C22×D4—2442no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—614no—
489C23×C4—1224no—
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×D6114yes—
499#124—6164no—
500C2×C4⋊C4—614no—
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⋊C4—2442no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—618no—
510C2×C22⋊C4—614no—
511C2×C22⋊C4—618no—
512C2×C22⋊C4—618no—
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—1224no—
521C2×C22⋊C4—2442no—
522C2×C22⋊C4—2442no—
523C2×C22⋊C4—2442no—
524C2×C22⋊C4—2442no—
525C2×C22⋊C4C4×D6118yescomplemented
526C2×C22⋊C4C22×D6114yes—
527C2×C22⋊C4C22×D6114yes—
528C2×C42—42no—
529C2×C42—42no—
530C2×C42—618no—
531C2×C42—614no—
532C2×C42—614no—
533C2×C42—614no—
534C2×C42—2442no—
535C2×C42—2442no—
536C2×C42C22×D6114yes—
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#95C22×D6114yes—
549#95C22×D6114yes—
550C24—22no—
551C24—22no—
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—
565C24C23×D6112yes—
566C24C23×D6111yescharacteristic
567C2×Q8—6116no—
568C2×Q8—24416no—
569C2×Q8—2444no—
570C2×Q8—2444no—
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—28no—
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—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
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—1228no—
622C22×C4—2444no—
623C22×C4—2444no—
624C22×C4—24416no—
625C22×C4C2×C4×D6114yes—
626C22×C4C2×C4×D6114yes—
627C22×C4#1175822214yes—
628C22×C4#1175822214yes—
629C22×C4C23×D6112yes—
630C22×C4C23×D6112yes—
631C22×C4C23×D6112yes—
632C22×C4C23×D6112yes—
633C22×C4C23×D6112yes—
634C22×C4C23×D6112yes—
635C4⋊C4—1228no—
636C4⋊C4—1228no—
637C4⋊C4—2444no—
638C4⋊C4—2444no—
639C22⋊C4—28no—
640C22⋊C4—6116no—
641C22⋊C4—6116no—
642C22⋊C4—6116no—
643C22⋊C4—1228no—
644C22⋊C4—2444no—
645C22⋊C4—2444no—
646C22⋊C4—2444no—
647C22⋊C4—2444no—
648C22⋊C4C2×C4×D61116yescomplemented
649C42—44no—
650C42—44no—
651C42—6116no—
652C42—2444no—
653C42—2444no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
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—
681C23C22×C4×D6114yes—
682C23C22×C4×D6112yes—
683C23C2×#1175822212yes—
684C23C2×#1175822212yes—
685C23#1451982212yes—
686C23#1451982212yes—
687C23#1451982312yes—
688C23#1451982412yes—
689C23C24×D6111yescharacteristic
690Q8—24416no—
691D4—24416no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—614no—
714C2×C4—614no—
715C2×C4—614no—
716C2×C4—1228no—
717C2×C4—1228no—
718C2×C4—1228no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
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—24416no—
738C2×C4—2444no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4—2444no—
742C2×C4C22×C4×D6114yes—
743C2×C4C22×C4×D6114yes—
744C2×C4C2×#1175822214yes—
745C2×C4C2×#1175822214yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—1224no—
755C22—1224no—
756C22—1224no—
757C22—24416no—
758C22—2442no—
759C22—2442no—
760C22—2442no—
761C22—2442no—
762C22C4×#1175822214yes—
763C22#1684023414yes—
764C22#1684024114yes—
765C22#1684034514yes—
766C22#1684035014yes—
767C22#1684037714yes—
768C22#1684038314yes—
769C22C23×C4×D6111yescharacteristic
770C22C22×#1175822211yescharacteristic
771C22C22×#1175822211yescharacteristic
772C22C2×#1451982211yescharacteristic
773C22C2×#1451982211yescharacteristic
774C22C2×#1451982311yescharacteristic
775C22C2×#1451982411yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—1224no—
783C4—1224no—
784C4—1224no—
785C4—2442no—
786C4—2442no—
787C4—2442no—
788C4—2442no—
789C2—44no—
790C2—2444no—
791C2#2144862718yesdirect product factor
792C2C2×C4×#1175822211yescharacteristic
793C2C2×#1684023411yescharacteristic
794C2C2×#1684024111yescharacteristic
795C2C2×#1684034511yescharacteristic
796C2C2×#1684035011yescharacteristic
797C2C2×#1684037711yescharacteristic
798C2C2×#1684038311yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C4×C22⋊C4×C61C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×#2337
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21448627C2direct (N × H)
3. C2×#16839668C2semidirect
4. C2×#16839666C2semidirect
5. C2×#16839656C2semidirect
6. C2×#16839655C2semidirect
7. C2×#16839653C2semidirect
8. C2×#16839651C2semidirect
11. C2×#16839636C2semidirect
12. C2×#16839635C2semidirect
13. C2×#16839629C2semidirect
14. C2×C4×#11758196C2semidirect
15. C2×C4×#11758198C2semidirect
16. C2×C4×C22⋊C4×C61C2semidirect
20. C2×#14519763C4semidirect
37. #16839668C22semidirect
38. #16839666C22semidirect
39. #16839656C22semidirect
40. #16839655C22semidirect
41. #16839653C22semidirect
42. #16839651C22semidirect
45. #16839636C22semidirect
46. #16839635C22semidirect
47. #16839629C22semidirect
48. C4×#11758196C22semidirect
49. C4×#11758198C22semidirect
65. C4×C22⋊C4×C61C22semidirect
71. C22×Dic122C2×C4semidirect
88. #14519763C2×C4semidirect
99. C2×C22⋊Dic61C2×C4semidirect
106. C2×#11758198C2×C4semidirect
107. C2×#11758198C2×C4semidirect
115. C2×C4×Dic61C2×C4semidirect
141. C2×C22⋊C4×C61C2×C4semidirect
234. C2×Dic122C22×C4semidirect
236. C22⋊C4×C61C22×C4semidirect
241. C22⋊Dic61C22×C4semidirect
245. #11758198C22×C4semidirect
246. #11758198C22×C4semidirect
253. C4×Dic61C22×C4semidirect
405. C2×C4×C22⋊C4D61semidirect
407. C2×C61#2337semidirect
454. C4×C22⋊C4C2×D61semidirect
467. C61C2×#2337semidirect
525. C2×C22⋊C4C4×D61semidirect
648. C22⋊C4C2×C4×D61semidirect
791. C2#21448627direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
#214486272
C2×#168396682
C2×#168396662
C2×#168396562
C2×#168396552
C2×#168396532
C2×#168396512
C2×#168396412
C2×#168396382
C2×#168396362
C2×#168396352
C2×#168396292
C2×C4×#117581962
C2×C4×#117581982
C2×C4×C22⋊C4×C612
C2×#233761