Finite Group Databasebeta

← C2×#21461223 #30610934

Subgroups — C2×#21461223 #30610934

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840784C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
3#21461223C218yesmaximal, direct product factor
4C2×#16840616C212yesmaximal, complemented
5C2×#16840614C212yesmaximal
6C2×#16840299C211yesmaximal, characteristic
7C22×C4⋊#6923—21no—
8C22×C4×#6923—21no—
9#16840784—22no—
10#16840784C2214yescomplemented
11C2×C4⋊#92420—21no—
12C2×#14519834C2212yes—
13C2×#14519832—21no—
14C4×C4⋊#6923—22no—
15C4×C4⋊#6923C2214yescomplemented
16C2×(C2×#6923)⋊C4C2212yes—
17#16840616C2218yescomplemented
18#16840614C2218yes—
19#16840299—22no—
20#16840299—22no—
21#16840299C414yescomplemented
22#16840299C2214yes—
23C2×#14519772—21no—
24C2×#14519768C411yescharacteristic, complemented
25C2×#14519766C411yescharacteristic, complemented
26C2×#14519762—21no—
27C2×#14519753C2211yescharacteristic
28C2×#14519752C2211yescharacteristic
29C2×C4×D244—21no—
30C2×C4×D244C411yescharacteristic, complemented
31C2×#14519734—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×Q8×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C22×#92420—22no—
36C2×C4⋊#6923—28no—
37C2×C4⋊#6923—24no—
38C2×C4×#6923—24no—
39C2×C4×#6923—44no—
40C4⋊#92420—24no—
41#14519834—22no—
42#14519834C2314yes—
43#14519832—24no—
44(C2×#6923)⋊C4—22no—
45(C2×#6923)⋊C4C2314yes—
46C22×D244—21no—
47C22×D244C2×C411yescharacteristic
48C22×C4×D61—21no—
49C22×C4×D61D411yescharacteristic
50C22×C4×D61D411yescharacteristic
51C22×C4×D61C2311yescharacteristic
52#14519772—24no—
53#14519772—24no—
54#14519768—22no—
55#14519768C2×C414yescomplemented
56#14519766—22no—
57#14519766C2×C414yescomplemented
58#14519762—24no—
59#14519762—24no—
60#14519753—21no—
61#14519753—21no—
62#14519753C2×C412yes—
63#14519753C2312yes—
64#14519752—21no—
65#14519752—21no—
66#14519752C2×C412yes—
67#14519752C2312yes—
68C4×D244—24no—
69C4×D244—24no—
70C4×D244—22no—
71C4×D244C2×C414yescomplemented
72#14519734—24no—
73#14519734—24no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D411yescharacteristic
86C42×D61C2×C412yes—
87C42×D61D412yes—
88C42×D61D412yes—
89C42×D61C2312yes—
90C22×Q8×C61C2×C411yescharacteristic
91C4×Q8×C61—22no—
92C4×Q8×C61C2×C414yescomplemented
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C42×C61—21no—
96C2×C42×C61C2×C411yescharacteristic
97C23×D61—21no—
98C23×D61C2×D411yescharacteristic
99C22×#6923—28no—
100C22×#6923—24no—
101C22×#6923—44no—
102C22×#6923—44no—
103C2×Q8×C61—21no—
104C2×Q8×C61—42no—
105C2×Q8×C61C22×C412yes—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61C22⋊C411yescharacteristic
109C22×C4×C61C22⋊C411yescharacteristic
110C22×C4×C61C22×C411yescharacteristic
111C22×Dic61—21no—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C2×D411yescharacteristic
115C2×D244—22no—
116C2×D244—22no—
117C2×D244—21no—
118C2×D244—42no—
119C2×D244—42no—
120C2×D244—42no—
121C2×D244C22×C412yes—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—24no—
125C2×C4×D61—24no—
126C2×C4×D61—42no—
127C2×C4×D61—44no—
128C2×C4×D61C22⋊C412yes—
129C2×C4×D61C22⋊C412yes—
130C2×C4×D61C22×C411yescharacteristic
131C2×C4×D61C2×D412yes—
132C2×C4×D61C2×D412yes—
133C2×C4×D61C2×D411yescharacteristic
134C2×C4×D61C2×D411yescharacteristic
135C2×C4×D61C2411yescharacteristic
136C2×#92420—24no—
137C2×#92420—44no—
138C4⋊#6923—216no—
139C4×#6923—48no—
140C4⋊C4×C61—24no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61C22×C412yes—
143C42×C61—24no—
144C42×C61C22⋊C412yes—
145C42×C61C22×C412yes—
146#11758198—22no—
147#11758198—22no—
148#11758198—24no—
149#11758198—22no—
150#11758198—24no—
151#11758198—24no—
152#11758198—22no—
153C4⋊Dic61—21no—
154C4⋊Dic61—24no—
155C4⋊Dic61C22×C412yes—
156#11758196—22no—
157#11758196—24no—
158#11758196—22no—
159C4×Dic61C22⋊C412yes—
160C4×Dic61C22⋊C412yes—
161C4×Dic61C22⋊C412yes—
162C4×Dic61C22×C412yes—
163C4×Dic61C2×D412yes—
164C4×Dic61C2×D412yes—
165C23×C61C2×C22⋊C411yescharacteristic
166C22×D61—22no—
167C22×D61—22no—
168C22×D61—22no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—42no—
172C22×D61C2×C22⋊C411yescharacteristic
173C22×D61AGL(1,ℤ/8)12yes—
174C22×D61#13712yes—
175C22×D61C22×D411yescharacteristic
176C2×#6923—28no—
177C2×#6923—44no—
178C2×#6923—416no—
179C2×#6923—44no—
180Q8×C61—42no—
181Q8×C61—42no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61#10414yes—
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C2×C22⋊C412yes—
191C2×C4×C61C2×C22⋊C412yes—
192C2×C4×C61C23×C411yescharacteristic
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61—42no—
198C2×Dic61C2×C22⋊C411yescharacteristic
199C2×Dic61C2×C22⋊C412yes—
200C2×Dic61C2×C22⋊C412yes—
201C2×Dic61C22×D411yescharacteristic
202D244—42no—
203D244—42no—
204D244—42no—
205D244—42no—
206D244—44no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—24no—
210C4×D61—24no—
211C4×D61—24no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215C4×D61—41no—
216C4×D61—48no—
217#92420—44no—
218C2×#1509—611nomaximal, Sylow
219C22×C61#41012yes—
220C22×C61#41712yes—
221C22×C61C2×#10412yes—
222C22×C61C22×C22⋊C411yescharacteristic
223C2×D61—21no—
224C2×D61—21no—
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—24no—
228C2×D61—24no—
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—84no—
233C2×D61#41712yes—
234C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
235C2×D61C2×#13711yescharacteristic
236#6923—48no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—22no—
240C4×C61—42no—
241C4×C61—42no—
242C4×C61C2×#10414yes—
243Dic61—21no—
244Dic61—21no—
245Dic61—22no—
246Dic61—22no—
247Dic61—42no—
248C2×#529—611no—
249C2×#432—611no—
250C2×C4×C4⋊C4—611no—
251#1509—618no—
252C2×#328—612no—
253C2×#327—612no—
254C2×C61#150914yescomplemented
255C2×C61C2×#41011yescharacteristic
256C2×C61C2×#41711yescharacteristic
257C2×C61C22×#10411yescharacteristic
258D61—21no—
259D61—21no—
260D61—22no—
261D61—82no—
262#529—614no—
263#529—614no—
264#529—1222no—
265#529—1222no—
266C2×#126—1221no—
267C2×#125—611no—
268C2×#124—611no—
269C2×#123—1221no—
270C2×C22⋊Q8—611no—
271C2×#121—611no—
272C2×C4×Q8#692311yescharacteristic, complemented
273C2×C4×D4—611no—
274C2×C4×D4—1221no—
275C2×#117—1221no—
276C22×C4⋊C4—1221no—
277C22×C42—611no—
278C22×C42—1221no—
279#432—614no—
280#432—1222no—
281C2×C4⋊C8—1221no—
282C2×C22⋊C8—612no—
283C2×#97—1221no—
284C4×C4⋊C4—614no—
285C4×C4⋊C4—1222no—
286C2×#95—612no—
287#328—618no—
288#327—618no—
289C61C2×#150911yescharacteristic, complemented, Sylow
290C22×Q8C2×#692311yescharacteristic
291C22×D4—611no—
292C22×D4—1221no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4—1222no—
297C23×C4—1221no—
298C22×C8—1222no—
299#126—1224no—
300#126—1224no—
301#125—614no—
302#125—1222no—
303#124—614no—
304#124—1222no—
305#123—1224no—
306#123—1224no—
307C22⋊Q8—612no—
308C22⋊Q8—612no—
309C22⋊Q8—1221no—
310C22⋊Q8—1221no—
311#121—612no—
312#121—612no—
313#121—1221no—
314#121—1221no—
315C4×Q8—22no—
316C4×Q8C2×#692314yescomplemented
317C4×D4—614no—
318C4×D4—1224no—
319C4×D4—1224no—
320C4×D4—1222no—
321#117—1224no—
322#117—1224no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—611no—
325C2×C4⋊C4—1221no—
326C2×C4⋊C4—1221no—
327C2×C4⋊C4—1221no—
328C2×C4⋊C4—1224no—
329C2×C4⋊C4—1228no—
330C2×C4⋊C4C2×#692311yescharacteristic
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—1221no—
336C2×C42—21no—
337C2×C42—611no—
338C2×C42—611no—
339C2×C42—611no—
340C2×C42—612no—
341C2×C42—612no—
342C2×C42—612no—
343C2×C42—612no—
344C2×C42—1224no—
345C2×C42—2444no—
346C2×C42C2×#692311yescharacteristic
347C4⋊C8—1224no—
348C22⋊C8—614no—
349C22⋊C8—1222no—
350#97—1224no—
351#95—614no—
352#95—1222no—
353C24—611no—
354C24—1221no—
355C2×Q8—21no—
356C2×Q8—42no—
357C2×Q8C22×#692312yes—
358C2×D4—612no—
359C2×D4—1222no—
360C2×D4—1222no—
361C2×D4—1221no—
362C2×D4—2442no—
363C2×D4—2442no—
364C2×D4—2442no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—612no—
371C22×C4—612no—
372C22×C4—612no—
373C22×C4—612no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—1222no—
379C22×C4—1222no—
380C22×C4—1224no—
381C22×C4—1224no—
382C22×C4—1228no—
383C22×C4—1221no—
384C22×C4—1224no—
385C22×C4—2442no—
386C22×C4—2444no—
387C22×C4—2444no—
388C22×C4—2444no—
389C22×C4C22⋊#692311yescharacteristic
390C22×C4C22⋊#692311yescharacteristic
391C22×C4C22×#692311yescharacteristic
392C2×C8—1224no—
393C2×C8—2444no—
394C4⋊C4—24no—
395C4⋊C4—21no—
396C4⋊C4—612no—
397C4⋊C4—1222no—
398C4⋊C4—1222no—
399C4⋊C4—1224no—
400C4⋊C4—1224no—
401C4⋊C4—12216no—
402C4⋊C4—1221no—
403C4⋊C4C22×#692312yes—
404C22⋊C4—1222no—
405C22⋊C4—1222no—
406C22⋊C4—1224no—
407C22⋊C4—1224no—
408C22⋊C4—1222no—
409C22⋊C4—1222no—
410C22⋊C4—1224no—
411C42—24no—
412C42—612no—
413C42—612no—
414C42—612no—
415C42—612no—
416C42—612no—
417C42—612no—
418C42—2448no—
419C42C22⋊#692312yes—
420C42C22×#692312yes—
421C23—612no—
422C23—612no—
423C23—611no—
424C23—611no—
425C23—1222no—
426C23—1222no—
427C23—1222no—
428C23—2442no—
429C23—2442no—
430C23—2442no—
431C23C2×C22⋊#692311yescharacteristic
432Q8—42no—
433Q8—42no—
434D4—2442no—
435D4—2442no—
436D4—2442no—
437D4—2442no—
438D4—2444no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—611no—
446C2×C4—612no—
447C2×C4—612no—
448C2×C4—611no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—1224no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1224no—
456C2×C4—1224no—
457C2×C4—1228no—
458C2×C4—1222no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2444no—
464C2×C4—2444no—
465C2×C4—24416no—
466C2×C4—2442no—
467C2×C4—2448no—
468C2×C4#1451984214yes—
469C2×C4C2×C22⋊#692311yescharacteristic
470C2×C4C2×C22⋊#692312yes—
471C2×C4C2×C22⋊#692312yes—
472C2×C4C23×#692311yescharacteristic
473C8—2444no—
474C22—611no—
475C22—611no—
476C22—612no—
477C22—1221no—
478C22—1221no—
479C22—1221no—
480C22—1221no—
481C22—1224no—
482C22—1224no—
483C22—4884no—
484C22—2442no—
485C22—2442no—
486C22—2442no—
487C22#1684074112yes—
488C22#1684075312yes—
489C22C2×#1451984212yes—
490C22C22×C22⋊#692311yescharacteristic
491C4—21no—
492C4—21no—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—1221no—
497C4—1221no—
498C4—1222no—
499C4—1222no—
500C4—2448no—
501C4—2442no—
502C4C2×#1451984214yes—
503C2—1221no—
504C2—1221no—
505C2—1222no—
506C2—4882no—
507C2#2146122314yesdirect product factor
508C2C2×#1684074111yescharacteristic
509C2C2×#1684075311yescharacteristic
510C2C22×#1451984211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C22
cosocleC2×C4×D61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×#1509
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840784C2semidirect
2. C2×C4×C4⋊#6923C2semidirect
3. #21461223C2direct (N × H)
4. C2×#16840616C2semidirect
10. #16840784C22semidirect
15. C4×C4⋊#6923C22semidirect
17. #16840616C22semidirect
21. #16840299C4semidirect
24. C2×#14519768C4semidirect
25. C2×#14519766C4semidirect
30. C2×C4×D244C4semidirect
33. C2×C4×Q8×C61C4semidirect
55. #14519768C2×C4semidirect
57. #14519766C2×C4semidirect
71. C4×D244C2×C4semidirect
92. C4×Q8×C61C2×C4semidirect
254. C2×C61#1509semidirect
272. C2×C4×Q8#6923semidirect
289. C61C2×#1509semidirect
316. C4×Q8C2×#6923semidirect
507. C2#21461223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407842
C2×C4×C4⋊#69232
#214612232
C2×#168406162
C2×#168406142
C2×#168402992
C2×#150961