Finite Group Databasebeta

← C2×#10622803 #13079055

Subgroups — C2×#10622803 #13079055

Order 1408.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×Q16C211yesmaximal, characteristic, complemented
2C2×#67000C211yesmaximal, characteristic
3C2×#66997C211yesmaximal, characteristic, complemented
4C22×#4326C211yesmaximal, characteristic, complemented
5C22×#4325C211yesmaximal, characteristic
6C22×#4314C211yesmaximal, characteristic
7#10622803C218yesmaximal, direct product factor
8C2×#66879C211yesmaximal, characteristic, complemented
9C22×Q8×C11C2211yescharacteristic
10C22×Q8×C11C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×Q16—24no—
14C2×C11×Q16C2214yescomplemented
15C22×C8×C11C2211yescharacteristic
16#67000—22no—
17#67000C2214yes—
18#66997—22no—
19#66997C2214yescomplemented
20C2×#4326—24no—
21C2×#4326C2214yescomplemented
22C2×#4325—24no—
23C2×#4325C2214yes—
24C2×(C2×D11)⋊C4—22no—
25C2×Dic11⋊C4—22no—
26C2×C4×Dic11C2211yescharacteristic
27C22×C11⋊C8C2211yescharacteristic
28C2×#4314—24no—
29C2×#4314C2214yes—
30#66879C2214yescomplemented
31C23×D11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11—21no—
34C2×Q8×C11—22no—
35C2×Q8×C11—22no—
36C2×Q8×C11—22no—
37C2×Q8×C11—22no—
38C2×Q8×C11C2312yes—
39C2×Q8×C11C2312yes—
40C22×C4×C11—21no—
41C22×C4×C11—21no—
42C22×C4×C11C2311yescharacteristic
43C22×Dic11—21no—
44C22×Dic11D412yes—
45C2×D44—21no—
46C2×D44—22no—
47C2×D44—22no—
48C2×D44C2312yes—
49C2×Dic22—22no—
50C2×Dic22—22no—
51C2×Dic22—21no—
52C2×Dic22C2312yes—
53C11×Q16—28no—
54C2×C8×C11D414yes—
55C2×C8×C11C2312yes—
56#4326—28no—
57#4325—28no—
58(C2×D11)⋊C4—28no—
59Dic11⋊C4—28no—
60C4×Dic11D412yes—
61C4×Dic11C2312yes—
62C2×C11⋊C8D414yes—
63C2×C11⋊C8C2312yes—
64#4314—28no—
65C2×#497—111nomaximal, Sylow
66C23×C11C2×D411yescharacteristic
67C22×D11—22no—
68C22×D11—42no—
69C22×D11—44no—
70Q8×C11—22no—
71Q8×C11—22no—
72Q8×C11—22no—
73Q8×C11—22no—
74Q8×C11—42no—
75Q8×C11—42no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D412yes—
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2411yescharacteristic
84C2×Dic11—24no—
85C2×Dic11—22no—
86C2×Dic11—42no—
87C2×Dic11C2×D414yes—
88D44—22no—
89D44—22no—
90D44—42no—
91Dic22—22no—
92Dic22—22no—
93Dic22—42no—
94C8×C11C2×D414yes—
95C11⋊C8C2×D414yes—
96C22×Q16—111no—
97C22×Q16D1111yescharacteristic, complemented
98C22×SD16—111no—
99C22×SD16—111no—
100C2×C4⋊Q8—111no—
101C2×#124—111no—
102#497—118no—
103C2×#97—111no—
104C22×C11#12712yes—
105C22×C11#13714yes—
106C22×C11C22×D411yescharacteristic
107C2×D11—42no—
108C2×D11—44no—
109C2×D11—84no—
110C4×C11—42no—
111C4×C11—42no—
112C4×C11#12712yes—
113C4×C11C22×D411yescharacteristic
114C4×C11C22×D411yescharacteristic
115Dic11—24no—
116Dic11—42no—
117C22×Q8—111no—
118C22×Q8C2×D1111yescharacteristic
119C22×Q8C2×D1111yescharacteristic
120C22×D4—111no—
121C2×Q16—24no—
122C2×Q16—114no—
123C2×Q16—224no—
124C2×Q16C2×D1114yescomplemented
125C2×SD16—114no—
126C2×SD16—114no—
127C2×SD16—224no—
128C2×SD16—224no—
129C22×C8—111no—
130C22×C8C2×D1111yescharacteristic
131C4⋊Q8—114no—
132C4⋊Q8—222no—
133#124—114no—
134#124—222no—
135C2×C4⋊C4—222no—
136C2×C22⋊C4—222no—
137C2×C42—111no—
138#97—114no—
139C2×C11#49714yescomplemented
140C2×C11C2×#12711yescharacteristic
141C2×C11C2×#13712yes—
142D11—82no—
143C24—221no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—112no—
151C2×Q8—221no—
152C2×Q8—222no—
153C2×Q8—222no—
154C2×Q8C22×D1112yes—
155C2×Q8C22×D1112yes—
156C2×D4—112no—
157C2×D4—222no—
158C2×D4—221no—
159C2×D4—222no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—112no—
163C22×C4—221no—
164C22×C4C22×D1111yescharacteristic
165Q16—28no—
166Q16—228no—
167SD16—228no—
168SD16—228no—
169C2×C8—114no—
170C2×C8—112no—
171C2×C8C22⋊D1114yes—
172C2×C8C22×D1112yes—
173C4⋊C4—228no—
174C22⋊C4—228no—
175C42—112no—
176C42—112no—
177C11C2×#49711yescharacteristic, complemented, Sylow
178C23—222no—
179C23—444no—
180C23—442no—
181C23D4×D1111yescharacteristic
182Q8—22no—
183Q8—22no—
184Q8—22no—
185Q8—22no—
186Q8—42no—
187Q8—42no—
188Q8—222no—
189Q8—222no—
190Q8—442no—
191D4—222no—
192D4—222no—
193D4—442no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—114no—
199C2×C4—224no—
200C2×C4—222no—
201C2×C4—442no—
202C2×C4D4×D1111yescharacteristic
203C2×C4D4×D1112yes—
204C2×C4C2×C22⋊D1112yes—
205C2×C4C23×D1111yescharacteristic
206C8—114no—
207C8C2×C22⋊D1114yes—
208C22—444no—
209C22—442no—
210C22—884no—
211C22#6697114yes—
212C22#6699312yes—
213C22C2×D4×D1111yescharacteristic
214C4—42no—
215C4—42no—
216C4—224no—
217C4—442no—
218C4#6699312yes—
219C4C2×D4×D1111yescharacteristic
220C4C22×C22⋊D1111yescharacteristic
221C2—882no—
222C2#1062280314yesdirect product factor
223C2C2×#6697112yes—
224C2C2×#6699311yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC22×C11×Q16C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenterC22×Q16D11
hypocenterC11C2×#497
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C22×C11×Q16C2semidirect
3. C2×#66997C2semidirect
4. C22×#4326C2semidirect
7. #10622803C2direct (N × H)
8. C2×#66879C2semidirect
14. C2×C11×Q16C22semidirect
19. #66997C22semidirect
21. C2×#4326C22semidirect
30. #66879C22semidirect
97. C22×Q16D11semidirect
124. C2×Q16C2×D11semidirect
139. C2×C11#497semidirect
177. C11C2×#497semidirect
222. C2#10622803direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×Q162
C2×#670002
C2×#669972
C22×#43262
C22×#43252
C22×#43142
#106228032
C2×#668792
C2×#49711