Finite Group Databasebeta

← C2×#21461591 #30614132

Subgroups — C2×#21461591 #30614132

Order 15616.

1686 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519840C212yesmaximal
2C2×#16840721C211yesmaximal, characteristic
3C2×C4×C4⋊#6923C211yesmaximal, characteristic
4#21461591C218yesmaximal, direct product factor
5C2×#16840635C212yesmaximal
6C2×C4×Q8×D61C211yesmaximal, characteristic
7C22×D61⋊C8C2212yes—
8C22×C4⋊#6923C2212yes—
9C22×C4×#6923—21no—
10C2×#14519840C4116yescomplemented
11C2×#14519840C2218yes—
12#16840721—22no—
13#16840721C2214yes—
14C2×#14519832—21no—
15C2×#14519832—21no—
16C4×C4⋊#6923—22no—
17C4×C4⋊#6923C2214yes—
18C2×(C2×#6923)⋊C4—21no—
19#16840635C2218yes—
20C22×Q8×D61C2211yescharacteristic
21C2×Q8×Dic61C411yescharacteristic, complemented
22C2×C4×Dic122—21no—
23C2×C4×Dic122C411yescharacteristic, complemented
24C2×#14519742—21no—
25C2×#14519742C411yescharacteristic, complemented
26C4×Q8×D61—22no—
27C4×Q8×D61—22no—
28C4×Q8×D61C414yescomplemented
29C4×Q8×D61C2214yes—
30C2×C4⋊C4×D61—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C42×D61—21no—
33C2×C42×D61C2211yescharacteristic
34C2×C4×Q8×C61C411yescharacteristic, complemented
35C23×#6923—22no—
36C2×D61⋊C8—22no—
37C2×D61⋊C8—24no—
38C2×D61⋊C8C2×C418yes—
39C2×D61⋊C8C2314yes—
40C22×#92420—22no—
41C2×C4⋊#6923—22no—
42C2×C4⋊#6923—24no—
43C2×C4⋊#6923C2×C418yes—
44C2×C4⋊#6923C2314yes—
45C2×C4×#6923—24no—
46C2×C4×#6923—44no—
47#14519840C2×C4132yescomplemented
48#14519832—24no—
49#14519832—24no—
50(C2×#6923)⋊C4—24no—
51C22×Dic122—21no—
52C22×Dic122C2×C411yescharacteristic
53C2×Q8×D61—21no—
54C2×Q8×D61—21no—
55C2×Q8×D61—24no—
56C2×Q8×D61C2×C418yes—
57C2×Q8×D61C2×C412yes—
58C2×Q8×D61C2312yes—
59C22×C4×D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64Q8×Dic61—22no—
65Q8×Dic61C2×C414yescomplemented
66C4×Dic122—22no—
67C4×Dic122—24no—
68C4×Dic122—24no—
69C4×Dic122C2×C414yescomplemented
70#14519742—22no—
71#14519742—24no—
72#14519742—24no—
73#14519742C2×C414yescomplemented
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C4⋊C4×D61—24no—
80C4⋊C4×D61—24no—
81C4⋊C4×D61—21no—
82C4⋊C4×D61—21no—
83C4⋊C4×D61C2×C412yes—
84C4⋊C4×D61C2312yes—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61D411yescharacteristic
91C42×D61—24no—
92C42×D61—24no—
93C42×D61C2×C412yes—
94C42×D61D412yes—
95C42×D61D412yes—
96C42×D61C2312yes—
97C22×Q8×C61C2×C411yescharacteristic
98C4×Q8×C61—22no—
99C4×Q8×C61C2×C414yescomplemented
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C42×C61—21no—
103C2×C42×C61C2×C411yescharacteristic
104C23×D61C2×D411yescharacteristic
105C22×#6923—28no—
106C22×#6923—24no—
107C22×#6923—44no—
108C22×#6923—44no—
109C2×Q8×C61—21no—
110C2×Q8×C61—22no—
111C2×Q8×C61C4214yescomplemented
112C2×Q8×C61C22×C412yes—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61C22⋊C411yescharacteristic
116C22×C4×C61C22⋊C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C22×Dic61—21no—
119C22×Dic61—21no—
120C22×Dic61C22⋊C411yescharacteristic
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C2×D411yescharacteristic
123Q8×D61—24no—
124Q8×D61—28no—
125Q8×D61—28no—
126Q8×D61—24no—
127Q8×D61C4218yescomplemented
128Q8×D61C22×C418yes—
129C2×C4×D61—22no—
130C2×C4×D61—28no—
131C2×C4×D61—22no—
132C2×C4×D61—22no—
133C2×C4×D61—24no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—42no—
138C2×C4×D61—42no—
139C2×C4×D61C22⋊C412yes—
140C2×C4×D61C22⋊C412yes—
141C2×C4×D61C22×C411yescharacteristic
142C2×C4×D61C22×C414yes—
143C2×C4×D61C2×D412yes—
144C2×C4×D61C2×D412yes—
145C2×C4×D61C2×D411yescharacteristic
146C2×C4×D61C2×D411yescharacteristic
147C2×C4×D61#4114yes—
148C2×C4×D61C2411yescharacteristic
149C2×Dic122—21no—
150C2×Dic122—22no—
151C2×Dic122—22no—
152C2×Dic122—28no—
153C2×Dic122—22no—
154C2×Dic122C4214yescomplemented
155C2×Dic122C22×C412yes—
156C2×#92420—28no—
157C2×#92420—24no—
158C4⋊#6923—28no—
159C4⋊#6923—24no—
160C4⋊#6923C22×C418yes—
161C4×#6923—48no—
162D61⋊C8—28no—
163D61⋊C8—24no—
164D61⋊C8C22×C418yes—
165C4⋊C4×C61—24no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C412yes—
168C42×C61—24no—
169C42×C61C22⋊C412yes—
170C42×C61C22×C412yes—
171C4⋊Dic61—21no—
172C4⋊Dic61—24no—
173C4⋊Dic61C22×C412yes—
174#11758196—24no—
175#11758196—24no—
176#11758196—22no—
177#11758196—22no—
178C4×Dic61—24no—
179C4×Dic61—24no—
180C4×Dic61—24no—
181C4×Dic61C22⋊C412yes—
182C4×Dic61C22⋊C412yes—
183C4×Dic61C22⋊C412yes—
184C4×Dic61C22×C412yes—
185C4×Dic61C2×D412yes—
186C4×Dic61C2×D412yes—
187C23×C61C2×C22⋊C411yescharacteristic
188C22×D61C2×C22⋊C411yescharacteristic
189C22×D61C4×D414yes—
190C22×D61AGL(1,ℤ/8)12yes—
191C22×D61#13712yes—
192C22×D61#13714yes—
193C22×D61C22×D411yescharacteristic
194C2×#6923—28no—
195C2×#6923—44no—
196C2×#6923—44no—
197C2×#6923—416no—
198Q8×C61—22no—
199Q8×C61—24no—
200Q8×C61C2×C4214yescomplemented
201C2×C4×C61—22no—
202C2×C4×C61—24no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—42no—
207C2×C4×C61C2×C4212yes—
208C2×C4×C61C2×C22⋊C412yes—
209C2×C4×C61C2×C22⋊C412yes—
210C2×C4×C61C2×C22⋊C411yescharacteristic
211C2×C4×C61#11712yes—
212C2×C4×C61C23×C411yescharacteristic
213C2×Dic61—22no—
214C2×Dic61—24no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—42no—
219C2×Dic61C2×C22⋊C412yes—
220C2×Dic61C2×C22⋊C412yes—
221C2×Dic61C2×C22⋊C411yescharacteristic
222C2×Dic61C4×D414yes—
223C2×Dic61C22×D411yescharacteristic
224C4×D61—28no—
225C4×D61—22no—
226C4×D61—24no—
227C4×D61—22no—
228C4×D61—28no—
229C4×D61—24no—
230C4×D61—24no—
231C4×D61—42no—
232C4×D61—42no—
233C4×D61—44no—
234C4×D61C2×C4212yes—
235C4×D61#11712yes—
236C4×D61C4×D414yes—
237C4×D61C4×D414yes—
238C4×D61C23×C412yes—
239C4×D61C2×#4112yes—
240Dic122—22no—
241Dic122—24no—
242Dic122—28no—
243Dic122—28no—
244Dic122C2×C4214yescomplemented
245#92420—28no—
246C2×#1763—611nomaximal, Sylow
247C22×C61C4×C22⋊C412yes—
248C22×C61#41712yes—
249C22×C61#41912yes—
250C22×C61C22×C22⋊C411yescharacteristic
251C2×D61C4×C22⋊C412yes—
252C2×D61#41712yes—
253C2×D61#41912yes—
254C2×D61#44018yes—
255C2×D61#44118yes—
256C2×D61C2×C4×D412yes—
257C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
258C2×D61C2×#13712yes—
259C2×D61C2×#13711yescharacteristic
260#6923—48no—
261C4×C61—22no—
262C4×C61—22no—
263C4×C61—24no—
264C4×C61—42no—
265C4×C61C4×C22⋊C412yes—
266C4×C61C22×C4211yescharacteristic
267C4×C61C2×#11711yescharacteristic
268Dic61—22no—
269Dic61—22no—
270Dic61—24no—
271Dic61—42no—
272Dic61C4×C22⋊C412yes—
273Dic61C2×C4×D412yes—
274C22×C4×Q8—611no—
275C22×#103—612no—
276C22×#97—611no—
277C2×C4×C4⋊C4—611no—
278#1763—618no—
279C2×#340—612no—
280C2×C61#176314yescomplemented
281C2×C61C2×C4×C22⋊C411yescharacteristic
282C2×C61C2×#41911yescharacteristic
283C2×C61C2×#41711yescharacteristic
284D61#176314yescomplemented
285D61C2×#44012yes—
286D61C2×#44112yes—
287C23×Q8—611no—
288C23×C8—612no—
289C2×C4×Q8—611no—
290C2×C4×Q8—614no—
291C2×C4×Q8—614no—
292C2×C4×Q8—611no—
293C2×C4×Q8—611no—
294C2×C4×Q8—1221no—
295C2×C4×Q8—1221no—
296C2×C4×Q8—1222no—
297C2×C4×Q8—1222no—
298C2×C4×Q8#692311yescharacteristic, complemented
299C22×C4⋊C4—612no—
300C22×C4⋊C4—611no—
301C22×C4⋊C4—1221no—
302C22×C42—611no—
303C22×C42—1221no—
304C22×C42—1221no—
305C2×#103—6116no—
306C2×#103—618no—
307C2×#97—614no—
308C2×#97—1221no—
309C2×#97—1221no—
310C2×#97—1222no—
311C4×C4⋊C4—614no—
312C4×C4⋊C4—1222no—
313C2×#95—1221no—
314#340—618no—
315C61C2×#176311yescharacteristic, complemented, Sylow
316C22×Q8—618no—
317C22×Q8—612no—
318C22×Q8—612no—
319C22×Q8—611no—
320C22×Q8—1221no—
321C22×Q8—1221no—
322C22×Q8—1221no—
323C22×Q8—1224no—
324C22×Q8C2×#692311yescharacteristic
325C23×C4—611no—
326C23×C4—611no—
327C23×C4—611no—
328C23×C4—1221no—
329C23×C4—1221no—
330C23×C4—1222no—
331C22×C8—618no—
332C22×C8—614no—
333C22×C8—1222no—
334C22×C8—1224no—
335C22×C8—1222no—
336C4×Q8—22no—
337C4×Q8—614no—
338C4×Q8—614no—
339C4×Q8—614no—
340C4×Q8—1224no—
341C4×Q8—1224no—
342C4×Q8—1224no—
343C4×Q8—1224no—
344C4×Q8—1222no—
345C4×Q8—1222no—
346C4×Q8—1222no—
347C4×Q8C2×#692314yescomplemented
348C2×C4⋊C4—21no—
349C2×C4⋊C4—618no—
350C2×C4⋊C4—614no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—612no—
353C2×C4⋊C4—612no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1224no—
357C2×C4⋊C4—1224no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1221no—
360C2×C4⋊C4—1221no—
361C2×C4⋊C4—1224no—
362C2×C4⋊C4—1222no—
363C2×C4⋊C4—1221no—
364C2×C4⋊C4C2×#692311yescharacteristic
365C2×C42—21no—
366C2×C42—611no—
367C2×C42—611no—
368C2×C42—611no—
369C2×C42—612no—
370C2×C42—612no—
371C2×C42—612no—
372C2×C42—612no—
373C2×C42—1224no—
374C2×C42—1224no—
375C2×C42—1221no—
376C2×C42—1221no—
377C2×C42—1221no—
378C2×C42—1224no—
379C2×C42—2444no—
380C2×C42C2×#692311yescharacteristic
381#103—6132no—
382#97—1224no—
383#97—1224no—
384#95—1224no—
385C24—611no—
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—618no—
389C2×Q8—618no—
390C2×Q8—614no—
391C2×Q8—612no—
392C2×Q8—1222no—
393C2×Q8—1222no—
394C2×Q8—1228no—
395C2×Q8—1224no—
396C2×Q8—1224no—
397C2×Q8—1228no—
398C2×Q8—1228no—
399C2×Q8—1221no—
400C2×Q8—1222no—
401C2×Q8C4×#692314yescomplemented
402C2×Q8C22×#692312yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—611no—
406C22×C4—614no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—614no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—612no—
415C22×C4—612no—
416C22×C4—612no—
417C22×C4—612no—
418C22×C4—1222no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1222no—
422C22×C4—1224no—
423C22×C4—1228no—
424C22×C4—1222no—
425C22×C4—1222no—
426C22×C4—1221no—
427C22×C4—1224no—
428C22×C4—1228no—
429C22×C4—1221no—
430C22×C4—2442no—
431C22×C4—2442no—
432C22×C4—2444no—
433C22×C4—2444no—
434C22×C4C22⋊#692311yescharacteristic
435C22×C4C22⋊#692311yescharacteristic
436C22×C4C22×#692311yescharacteristic
437C2×C8—618no—
438C2×C8—1224no—
439C2×C8—1224no—
440C2×C8—1228no—
441C2×C8—1228no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—618no—
445C4⋊C4—612no—
446C4⋊C4—1222no—
447C4⋊C4—1222no—
448C4⋊C4—1224no—
449C4⋊C4—1224no—
450C4⋊C4—1224no—
451C4⋊C4—1228no—
452C4⋊C4—1221no—
453C4⋊C4—1224no—
454C4⋊C4C22×#692312yes—
455C42—24no—
456C42—612no—
457C42—612no—
458C42—612no—
459C42—612no—
460C42—612no—
461C42—612no—
462C42—1224no—
463C42—1224no—
464C42—1224no—
465C42—2448no—
466C42C22⋊#692312yes—
467C42C22×#692312yes—
468C23—612no—
469C23—612no—
470C23—614no—
471C23—611no—
472C23—611no—
473C23—614no—
474C23C2×C22⋊#692311yescharacteristic
475Q8—22no—
476Q8—24no—
477Q8—614no—
478Q8—1228no—
479Q8—1228no—
480Q8—1222no—
481Q8—1224no—
482Q8C2×C4×#692314yescomplemented
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—42no—
489C2×C4—611no—
490C2×C4—611no—
491C2×C4—614no—
492C2×C4—612no—
493C2×C4—612no—
494C2×C4—612no—
495C2×C4—612no—
496C2×C4—614no—
497C2×C4—614no—
498C2×C4—612no—
499C2×C4—612no—
500C2×C4—1222no—
501C2×C4—1224no—
502C2×C4—1224no—
503C2×C4—1222no—
504C2×C4—1224no—
505C2×C4—1228no—
506C2×C4—1228no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1224no—
511C2×C4—1228no—
512C2×C4—1222no—
513C2×C4—2442no—
514C2×C4—2442no—
515C2×C4—2444no—
516C2×C4—2444no—
517C2×C4—24416no—
518C2×C4—2444no—
519C2×C4—2442no—
520C2×C4C2×C4×#692312yes—
521C2×C4C2×C22⋊#692312yes—
522C2×C4C2×C22⋊#692312yes—
523C2×C4C2×C22⋊#692311yescharacteristic
524C2×C4#1451985612yes—
525C2×C4C23×#692311yescharacteristic
526C8—1228no—
527C22—618no—
528C22—618no—
529C22—612no—
530C22—612no—
531C22—611no—
532C22—611no—
533C22—612no—
534C22—612no—
535C22—612no—
536C22C4×C22⋊#692312yes—
537C22#1684075312yes—
538C22#1684075512yes—
539C22C22×C22⋊#692311yescharacteristic
540C4—22no—
541C4—22no—
542C4—24no—
543C4—42no—
544C4—612no—
545C4—612no—
546C4—1222no—
547C4—1222no—
548C4—1224no—
549C4—2448no—
550C4—2442no—
551C4C4×C22⋊#692312yes—
552C4C22×C4×#692311yescharacteristic
553C4C2×#1451985611yescharacteristic
554C2—612no—
555C2—612no—
556C2—614no—
557C2#2146159114yesdirect product factor
558C2C2×C4×C22⋊#692311yescharacteristic
559C2C2×#1684075511yescharacteristic
560C2C2×#1684075311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×#1763
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
4. #21461591C2direct (N × H)
10. C2×#14519840C4semidirect
21. C2×Q8×Dic61C4semidirect
23. C2×C4×Dic122C4semidirect
25. C2×#14519742C4semidirect
28. C4×Q8×D61C4semidirect
34. C2×C4×Q8×C61C4semidirect
47. #14519840C2×C4semidirect
65. Q8×Dic61C2×C4semidirect
69. C4×Dic122C2×C4semidirect
73. #14519742C2×C4semidirect
99. C4×Q8×C61C2×C4semidirect
111. C2×Q8×C61C42semidirect
127. Q8×D61C42semidirect
154. C2×Dic122C42semidirect
200. Q8×C61C2×C42semidirect
244. Dic122C2×C42semidirect
280. C2×C61#1763semidirect
284. D61#1763semidirect
298. C2×C4×Q8#6923semidirect
315. C61C2×#1763semidirect
347. C4×Q8C2×#6923semidirect
401. C2×Q8C4×#6923semidirect
482. Q8C2×C4×#6923semidirect
557. C2#21461591direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198402
C2×#168407212
C2×C4×C4⋊#69232
#214615912
C2×#168406352
C2×C4×Q8×D612
C2×#176361