Finite Group Databasebeta

← C4×#63661 #11783745

Subgroups — C4×#63661 #11783745

Order 1152.

1236 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C2×#63661C212yesmaximal
3C4×#3757C212yesmaximal, complemented
4#10589392C212yesmaximal, complemented
5C4×#834—34nomaximal
6C22×C32×D4C2211yescharacteristic
7C23×C32×C4C411yescharacteristic, complemented
8C23×C32×C4C2211yescharacteristic
9C32×C4×D4—22no—
10C32×C4×D4—22no—
11C2×C32×C4⋊C4C411yescharacteristic, complemented
12C2×C32×C22⋊C4C411yescharacteristic, complemented
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×C32×C42C411yescharacteristic, complemented
15C2×#3757C2214yes—
16C2×C4×C3⋊Dic3—22no—
17#63661C418yesdirect product factor
18#63658—22no—
19C2×C3×C4×D4D314yes—
20C2×#834—38no—
21C4×#217—38no—
22#4526—38no—
23C24×C32C2×C411yescharacteristic
24C24×C32C2311yescharacteristic
25C2×C32×D4—22no—
26C2×C32×D4—22no—
27C2×C32×D4C2×C414yes—
28C22×C32×C4—21no—
29C22×C32×C4—21no—
30C22×C32×C4—42no—
31C22×C32×C4—42no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D412yes—
38C22×C32×C4D412yes—
39C22×C3⋊Dic3—24no—
40C32×C4⋊C4—22no—
41C32×C22⋊C4—22no—
42C32×C22⋊C4—22no—
43C32×C42—21no—
44C32×C42—21no—
45#3757—24no—
46#3757C2×C418yescomplemented
47C4×C3⋊Dic3—44no—
48C4×#99—91noSylow
49C22×C3×D4C2×D314yes—
50C23×C3×C4Dic314yescomplemented
51C23×C3×C4C2×D314yes—
52C3×C4×D4—28no—
53C3×C4×D4—28no—
54C2×C3×C4⋊C4Dic314yescomplemented
55C2×C3×C22⋊C4Dic314yescomplemented
56C2×C3×C22⋊C4C2×D314yes—
57C2×C3×C42Dic314yescomplemented
58C2×#217—316no—
59C2×C4×Dic3—68no—
60#834—332no—
61C3⋊#95—68no—
62C23×C32—21no—
63C23×C32—21no—
64C23×C32—41no—
65C23×C32—41no—
66C23×C32—41no—
67C23×C32—41no—
68C23×C32C4212yescomplemented
69C23×C32C22×C412yes—
70C23×C32C22×C411yescharacteristic
71C23×C32C2×D412yes—
72C23×C32#4112yes—
73C32×D4—28no—
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4—24no—
77C2×C32×C4—22no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—41no—
81C2×C32×C4—42no—
82C2×C32×C4—42no—
83C2×C32×C4—42no—
84C2×C32×C4—41no—
85C2×C32×C4—41no—
86C2×C32×C4C4212yescomplemented
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C22⋊C412yes—
89C2×C32×C4C22⋊C411yescharacteristic
90C2×C3⋊Dic3—28no—
91C2×C3⋊Dic3—44no—
92C2×C3⋊Dic3—44no—
93C2×C4×D4C3⋊D311yescharacteristic
94C2×#99—92no—
95C4×C22⋊C4—92no—
96#342—92no—
97C24×C3C2×Dic314yes—
98C24×C3C22×D314yes—
99C2×C3×D4—28no—
100C2×C3×D4—28no—
101C2×C3×D4C4×D3116yes—
102C22×C3×C4—24no—
103C22×C3×C4—24no—
104C22×C3×C4—48no—
105C22×C3×C4—48no—
106C22×C3×C4C2×Dic314yes—
107C22×C3×C4C2×Dic314yes—
108C22×C3×C4C2×Dic314yes—
109C22×C3×C4C2×Dic314yes—
110C22×C3×C4C2×Dic314yes—
111C22×C3×C4#6718yes—
112C22×C3×C4#6718yes—
113C22×Dic3—616no—
114C3×C4⋊C4—28no—
115C3×C22⋊C4—28no—
116C3×C22⋊C4—28no—
117C3×C42—24no—
118C3×C42—24no—
119#217—332no—
120#217—616no—
121C4×Dic3—1216no—
122C22×C32—22no—
123C22×C32—21no—
124C22×C32—22no—
125C22×C32—21no—
126C22×C32—22no—
127C22×C32—42no—
128C22×C32—42no—
129C22×C32—42no—
130C22×C32—42no—
131C22×C32—41no—
132C22×C32—41no—
133C22×C32C2×C4211yescharacteristic
134C22×C32C2×C22⋊C411yescharacteristic
135C22×C32#11711yescharacteristic
136C22×C32C4×D414yes—
137C32×C4—22no—
138C32×C4—21no—
139C32×C4—22no—
140C32×C4—41no—
141C32×C4—41no—
142C32×C4#9912yescomplemented
143C3⋊Dic3—48no—
144C22×D4C2×C3⋊D311yescharacteristic
145C23×C4C3⋊Dic311yescharacteristic, complemented
146C23×C4C2×C3⋊D311yescharacteristic
147C4×D4—22no—
148C4×D4—22no—
149C2×C4⋊C4C3⋊Dic311yescharacteristic, complemented
150C2×C22⋊C4—94no—
151C2×C22⋊C4C3⋊Dic311yescharacteristic, complemented
152C2×C22⋊C4C2×C3⋊D311yescharacteristic
153C2×C42—182no—
154C2×C42C3⋊Dic311yescharacteristic, complemented
155#99—98no—
156#95—182no—
157C23×C3—24no—
158C23×C3—24no—
159C23×C3—44no—
160C23×C3—44no—
161C23×C3—44no—
162C23×C3—44no—
163C23×C3C4×Dic318yescomplemented
164C23×C3C2×C4×D318yes—
165C23×C3#23518yes—
166C23×C3C22×Dic314yes—
167C23×C3C2×#6718yes—
168C3×D4—232no—
169C2×C3×C4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—216no—
172C2×C3×C4—28no—
173C2×C3×C4—24no—
174C2×C3×C4—24no—
175C2×C3×C4—44no—
176C2×C3×C4—48no—
177C2×C3×C4—48no—
178C2×C3×C4—48no—
179C2×C3×C4—44no—
180C2×C3×C4—44no—
181C2×C3×C4C4×Dic318yescomplemented
182C2×C3×C4#21714yes—
183C2×C3×C4#21718yes—
184C2×C3×C4#21714yes—
185C2×Dic3—632no—
186C2×Dic3—1216no—
187C2×Dic3—1216no—
188C2×C32—24no—
189C2×C32—21no—
190C2×C32—21no—
191C2×C32—42no—
192C2×C32C4×C22⋊C411yescharacteristic
193C2×C32C2×#9911yescharacteristic
194C2×C32#41011yescharacteristic
195C24C2×C3⋊Dic311yescharacteristic
196C24C22×C3⋊D311yescharacteristic
197C2×D4—22no—
198C2×D4—22no—
199C2×D4C4×C3⋊D314yes—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—184no—
205C22×C4C2×C3⋊Dic311yescharacteristic
206C22×C4C2×C3⋊Dic311yescharacteristic
207C22×C4C2×C3⋊Dic311yescharacteristic
208C22×C4C2×C3⋊Dic311yescharacteristic
209C22×C4C2×C3⋊Dic311yescharacteristic
210C22×C4#63812yes—
211C22×C4#63812yes—
212C4⋊C4—22no—
213C22⋊C4—22no—
214C22⋊C4—22no—
215C22⋊C4—98no—
216C22⋊C4—184no—
217C42—21no—
218C42—21no—
219C42—364no—
220C22×C3—28no—
221C22×C3—24no—
222C22×C3—28no—
223C22×C3—24no—
224C22×C3—28no—
225C22×C3—48no—
226C22×C3—48no—
227C22×C3—48no—
228C22×C3—48no—
229C22×C3—44no—
230C22×C3—44no—
231C22×C3C2×C4×Dic314yes—
232C22×C3#92614yes—
233C22×C3C4×#67116yes—
234C22×C3C2×#21714yes—
235C3×C4—28no—
236C3×C4—24no—
237C3×C4—28no—
238C3×C4—44no—
239C3×C4—44no—
240C3×C4#83418yescomplemented
241Dic3—1232no—
242C32C4×#9911yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23C4×C3⋊Dic312yescomplemented
250C23C2×C4×C3⋊D312yes—
251C23#382812yes—
252C23C22×C3⋊Dic311yescharacteristic
253C23C2×#63812yes—
254D4—28no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—24no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—188no—
268C2×C4—364no—
269C2×C4—364no—
270C2×C4C4×C3⋊Dic312yescomplemented
271C2×C4#375711yescharacteristic
272C2×C4#375712yes—
273C2×C4#375711yescharacteristic
274C2×C3—216no—
275C2×C3—24no—
276C2×C3—24no—
277C2×C3—48no—
278C2×C3C4×#21714yes—
279C2×C3C2×#83414yes—
280C2×C3#524014yes—
281C22—21no—
282C22—22no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22C2×C4×C3⋊Dic311yescharacteristic
293C22#6413511yescharacteristic
294C22C4×#63814yes—
295C22C2×#375711yescharacteristic
296C4—22no—
297C4—21no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—368no—
302C4#6366112yesdirect product factor
303C3C4×#83414yescomplemented
304C2—24no—
305C2—21no—
306C2—21no—
307C2—42no—
308C2C4×#375711yescharacteristic
309C2C2×#6366111yescharacteristic
310C2#1059293911yescharacteristic
subgroupG/H
centerC2×C4#3757
commutatorC22×C32C2×C42
FrattiniC24C22×C3⋊D3
FittingC2×C32×C4×D4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C22
cosocleC24×C32C23
hypercenterC2×C4×D4C3⋊D3
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. C4×#3757C2semidirect
4. #10589392C2semidirect
7. C23×C32×C4C4semidirect
11. C2×C32×C4⋊C4C4semidirect
12. C2×C32×C22⋊C4C4semidirect
14. C2×C32×C42C4semidirect
17. #63661C4direct (N × H)
46. #3757C2×C4semidirect
50. C23×C3×C4Dic3semidirect
54. C2×C3×C4⋊C4Dic3semidirect
55. C2×C3×C22⋊C4Dic3semidirect
57. C2×C3×C42Dic3semidirect
68. C23×C32C42semidirect
86. C2×C32×C4C42semidirect
142. C32×C4#99semidirect
145. C23×C4C3⋊Dic3semidirect
149. C2×C4⋊C4C3⋊Dic3semidirect
151. C2×C22⋊C4C3⋊Dic3semidirect
154. C2×C42C3⋊Dic3semidirect
163. C23×C3C4×Dic3semidirect
181. C2×C3×C4C4×Dic3semidirect
240. C3×C4#834semidirect
242. C32C4×#99semidirect
249. C23C4×C3⋊Dic3semidirect
270. C2×C4C4×C3⋊Dic3semidirect
302. C4#63661direct (N × H)
303. C3C4×#834semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×#636612
C4×#37572
#105893922
C4×#8343