Finite Group Databasebeta

← C2×#20298882 #28400338

Subgroups — C2×#20298882 #28400338

Order 14464.

416 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#16813621C211yesmaximal, characteristic
2C2×#16813587C211yesmaximal, characteristic
3#20298882C218yesmaximal, direct product factor
4C2×#16813553C211yesmaximal, characteristic
5C2×#16813551C211yesmaximal, characteristic
6C2×#16813547C211yesmaximal, characteristic
7C2×#16813545C211yesmaximal, characteristic
8C2×#106×C113C211yesmaximal, characteristic
9C22×Dic226—21no—
10C22×Dic226C2211yescharacteristic
11C22×#11744751C2211yescharacteristic
12#16813621—22no—
13#16813621C2214yes—
14#16813587—22no—
15#16813587C2214yes—
16C2×C4⋊Dic113C2211yescharacteristic
17C2×#14268626—21no—
18C2×#14268626—21no—
19C2×C4×Dic113—21no—
20C2×C4×Dic113C2211yescharacteristic
21#16813553C2214yes—
22#16813551C2214yes—
23#16813547C2214yes—
24#16813545C2214yes—
25C22×C8×C113C2211yescharacteristic
26C2×C4⋊C4×C113C2211yescharacteristic
27C2×C4⋊C4×C113C2211yescharacteristic
28#106×C113C2214yes—
29C2×Dic226—21no—
30C2×Dic226—22no—
31C2×Dic226—24no—
32C2×Dic226—44no—
33C2×Dic226Q814yescomplemented
34C2×Dic226C2312yes—
35C22×Dic113—21no—
36C22×Dic113—21no—
37C22×Dic113D411yescharacteristic
38C22×Dic113D411yescharacteristic
39C2×#11744751—22no—
40C2×#11744751C2312yes—
41C4⋊Dic113—21no—
42C4⋊Dic113C2312yes—
43#14268626—24no—
44#14268626—24no—
45C4×Dic113—24no—
46C4×Dic113D412yes—
47C4×Dic113C2312yes—
48C22×C4×C113—21no—
49C22×C4×C113—21no—
50C22×C4×C113C2311yescharacteristic
51C2×C8×C113—22no—
52C2×C8×C113C2312yes—
53C4⋊C4×C113—21no—
54C4⋊C4×C113—21no—
55C4⋊C4×C113C2312yes—
56C4⋊C4×C113C2312yes—
57C23×C113C2×D411yescharacteristic
58C2×C4×C113—22no—
59C2×C4×C113—22no—
60C2×C4×C113—42no—
61C2×C4×C113—42no—
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×Q812yes—
64C2×C4×C113#4112yes—
65C2×C4×C113C2411yescharacteristic
66C2×Dic113—24no—
67C2×Dic113—22no—
68C2×Dic113—22no—
69C2×Dic113—22no—
70C2×Dic113—42no—
71C2×Dic113SD1614yes—
72C2×Dic113C2×D412yes—
73C2×Dic113C2×D412yes—
74Dic226—24no—
75Dic226—22no—
76Dic226—48no—
77Dic226C2×Q814yescomplemented
78C8×C113—22no—
79#11744751—22no—
80C22×C113C22⋊Q812yes—
81C22×C113C2×SD1612yes—
82C22×C113#13712yes—
83C22×C113C22×D411yescharacteristic
84C4×C113—42no—
85C4×C113—42no—
86C4×C113C22⋊Q812yes—
87C4×C113C22×Q811yescharacteristic
88C4×C113C2×#4111yescharacteristic
89Dic113—24no—
90Dic113—22no—
91Dic113—42no—
92Dic113C2×SD1614yes—
93C2×C113#47514yescomplemented
94C2×C113C2×C22⋊Q811yescharacteristic
95C2×C113C22×SD1611yescharacteristic
96C2×C113C2×#13711yescharacteristic
97C2×#475—1131nomaximal, Sylow
98C113C2×#47511yescharacteristic, complemented, Sylow
99C2×C4⋊Q8—1131no—
100C2×C4×Q8—1131no—
101#475—1138no—
102C2×#106—1131no—
103C2×#106D11311yescharacteristic
104C2×C4⋊C8—1131no—
105C2×#103—1131no—
106C2×#103—1131no—
107C22×Q8—1131no—
108C22×Q8—2261no—
109C22×C8—1131no—
110C22×C8C2×D11311yescharacteristic
111C4⋊Q8—1134no—
112C4⋊Q8—2262no—
113C4×Q8—1134no—
114C4×Q8—2262no—
115C2×C4⋊C4—1131no—
116C2×C4⋊C4—2261no—
117C2×C4⋊C4—2261no—
118C2×C4⋊C4C2×D11311yescharacteristic
119C2×C4⋊C4C2×D11311yescharacteristic
120C2×C42—1131no—
121C2×C42—2261no—
122#106—1134no—
123#106C2×D11314yes—
124C4⋊C8—1134no—
125#103—1134no—
126#103—1134no—
127C2×Q8—1134no—
128C2×Q8—1132no—
129C2×Q8—4524no—
130C2×Q8—2264no—
131C2×Q8—2261no—
132C2×Q8—2262no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—1131no—
136C22×C4—1131no—
137C22×C4—2261no—
138C22×C4—2261no—
139C22×C4C22×D11311yescharacteristic
140C2×C8—22no—
141C2×C8—1132no—
142C2×C8—2262no—
143C2×C8C22×D11312yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1132no—
147C4⋊C4—2264no—
148C4⋊C4—2264no—
149C4⋊C4—2261no—
150C4⋊C4C22×D11312yes—
151C4⋊C4C22×D11312yes—
152C42—1132no—
153C42—1132no—
154C42—2264no—
155C23D4×D11311yescharacteristic
156Q8—1134no—
157Q8—4528no—
158Q8—2264no—
159Q8—2262no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—1134no—
165C2×C4—1132no—
166C2×C4—1132no—
167C2×C4—4522no—
168C2×C4—2262no—
169C2×C4—2264no—
170C2×C4—2262no—
171C2×C4—2262no—
172C2×C4D4×D11311yescharacteristic
173C2×C4Q8×D11312yes—
174C2×C4#1426864712yes—
175C2×C4C23×D11311yescharacteristic
176C8—22no—
177C8—2262no—
178C22#1681360012yes—
179C22SD16×D11312yes—
180C22#1681365112yes—
181C22C2×D4×D11311yescharacteristic
182C4—42no—
183C4—42no—
184C4—1134no—
185C4—4522no—
186C4—2264no—
187C4—2262no—
188C4#1681360012yes—
189C4C2×Q8×D11311yescharacteristic
190C4C2×#1426864711yescharacteristic
191C2#2029888214yesdirect product factor
192C2C2×#1681360011yescharacteristic
193C2C2×SD16×D11311yescharacteristic
194C2C2×#1681365111yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#106×C113C2
socle, prime radicalC23×C113C2×D4
hypercenterC2×#106D113
hypocenterC113C2×#475
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #20298882C2direct (N × H)
33. C2×Dic226Q8semidirect
77. Dic226C2×Q8semidirect
93. C2×C113#475semidirect
98. C113C2×#475semidirect
191. C2#20298882direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168136212
C2×#168135872
#202988822
C2×#168135532
C2×#168135512
C2×#168135472
C2×#168135452
C2×#106×C1132
C2×#475113