Finite Group Databasebeta

← C2×#20298936 #28400463

Subgroups — C2×#20298936 #28400463

Order 14464.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813581C211yesmaximal, characteristic
2#20298936C218yesmaximal, direct product factor
3C2×#16813555C211yesmaximal, characteristic, complemented
4C2×#16813553C211yesmaximal, characteristic, complemented
5C2×#16813546C211yesmaximal, characteristic, complemented
6C2×#16813546C211yesmaximal, characteristic, complemented
7C2×C22⋊#11744751C211yesmaximal, characteristic
8C2×C22⋊Q8×C113C211yesmaximal, characteristic
9C22×#11744751C2211yescharacteristic
10C22×#11744751C2211yescharacteristic
11#16813581—22no—
12#16813581C2214yes—
13C2×C4⋊Dic113C2211yescharacteristic
14C2×C4⋊Dic113C2211yescharacteristic
15C2×C22⋊Dic113—21no—
16C2×C4×Dic113—21no—
17#16813555C2214yescomplemented
18#16813553C2214yescomplemented
19#16813546C2214yescomplemented
20#16813546C2214yescomplemented
21C22⋊#11744751C2214yes—
22C22×Q8×C113C2211yescharacteristic
23C23×C4×C113C2211yescharacteristic
24C22⋊Q8×C113—22no—
25C22⋊Q8×C113C2214yes—
26C2×C4⋊C4×C113—21no—
27C2×C4⋊C4×C113C2211yescharacteristic
28C2×C22⋊C4×C113—21no—
29C22×Dic113—21no—
30C22×Dic113—21no—
31C2×#11744751—22no—
32C2×#11744751—22no—
33C2×#11744751C2312yes—
34C2×#11744751C2312yes—
35C4⋊Dic113—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113C2312yes—
38C4⋊Dic113C2312yes—
39C22⋊Dic113—24no—
40C4×Dic113—24no—
41C24×C113D411yescharacteristic
42C2×Q8×C113—21no—
43C2×Q8×C113—22no—
44C2×Q8×C113—22no—
45C2×Q8×C113C2312yes—
46C22×C4×C113—22no—
47C22×C4×C113—22no—
48C22×C4×C113—21no—
49C22×C4×C113—21no—
50C22×C4×C113D411yescharacteristic
51C22×C4×C113D412yes—
52C22×C4×C113C2312yes—
53C22×C4×C113C2311yescharacteristic
54C4⋊C4×C113—24no—
55C4⋊C4×C113—21no—
56C4⋊C4×C113C2312yes—
57C22⋊C4×C113—24no—
58C23×C113—22no—
59C23×C113—22no—
60C23×C113—22no—
61C23×C113C2×D412yes—
62C23×C113C2×D411yescharacteristic
63Q8×C113—22no—
64Q8×C113—22no—
65Q8×C113—42no—
66C2×C4×C113—22no—
67C2×C4×C113—24no—
68C2×C4×C113—22no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113—42no—
73C2×C4×C113—42no—
74C2×C4×C113C2×D412yes—
75C2×C4×C113C2×D411yescharacteristic
76C2×C4×C113#4112yes—
77C2×C4×C113#4112yes—
78C2×C4×C113C2411yescharacteristic
79C2×Dic113—22no—
80C2×Dic113—22no—
81C2×Dic113—42no—
82C2×Dic113—42no—
83#11744751—22no—
84#11744751—22no—
85C22×C113—22no—
86C22×C113—22no—
87C22×C113—22no—
88C22×C113—44no—
89C22×C113#12312yes—
90C22×C113#13512yes—
91C22×C113#13712yes—
92C22×C113C22×D411yescharacteristic
93C4×C113—22no—
94C4×C113—42no—
95C4×C113—42no—
96C4×C113#12312yes—
97C4×C113C2×#4111yescharacteristic
98C4×C113C2×#4111yescharacteristic
99Dic113—42no—
100Dic113—42no—
101C2×C113—42no—
102C2×C113#48514yescomplemented
103C2×C113C2×#12311yescharacteristic
104C2×C113C2×#13511yescharacteristic
105C2×C113C2×#13711yescharacteristic
106C2×#485—1131nomaximal, Sylow
107C113C2×#48511yescharacteristic, complemented, Sylow
108C2×C22⋊Q8D11311yescharacteristic
109C2×#117—1131no—
110#485—1138no—
111C2×#107—1131no—
112C2×#106—1131no—
113C2×#103—1131no—
114C2×#103—1131no—
115C2×C22⋊C8—1131no—
116C22×Q8C2×D11311yescharacteristic
117C23×C4C2×D11311yescharacteristic
118C22×C8—1131no—
119C22×C8—1131no—
120C22⋊Q8—22no—
121C22⋊Q8C2×D11314yes—
122#117—1134no—
123#117—2262no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—1131no—
126C2×C4⋊C4—1131no—
127C2×C4⋊C4C2×D11311yescharacteristic
128C2×C22⋊C4—21no—
129C2×C22⋊C4—2261no—
130C2×C42—2261no—
131#107—1134no—
132#106—1134no—
133#103—1134no—
134#103—1134no—
135C22⋊C8—1134no—
136C24C22⋊D11311yescharacteristic
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8C22×D11312yes—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2261no—
146C22×C4—2261no—
147C22×C4C22⋊D11312yes—
148C22×C4C22⋊D11311yescharacteristic
149C22×C4C22×D11312yes—
150C22×C4C22×D11311yescharacteristic
151C2×C8—1132no—
152C2×C8—1132no—
153C2×C8—2262no—
154C2×C8—2262no—
155C4⋊C4—24no—
156C4⋊C4—21no—
157C4⋊C4—1132no—
158C4⋊C4—1132no—
159C4⋊C4—2261no—
160C4⋊C4—2261no—
161C4⋊C4C22×D11312yes—
162C22⋊C4—24no—
163C22⋊C4—2264no—
164C42—2264no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23C2×C22⋊D11312yes—
169C23C2×C22⋊D11311yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—42no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—4522no—
182C2×C4—4522no—
183C2×C4—2262no—
184C2×C4—2262no—
185C2×C4C2×C22⋊D11312yes—
186C2×C4C2×C22⋊D11311yescharacteristic
187C2×C4#1426864612yes—
188C2×C4#1426864612yes—
189C2×C4C23×D11311yescharacteristic
190C8—2262no—
191C8—2262no—
192C22—22no—
193C22—22no—
194C22—22no—
195C22—44no—
196C22#1681360312yes—
197C22#1681364212yes—
198C22#1681365312yes—
199C22C22×C22⋊D11311yescharacteristic
200C4—22no—
201C4—42no—
202C4—42no—
203C4—4522no—
204C4—4522no—
205C4#1681360312yes—
206C4C2×#1426864611yescharacteristic
207C4C2×#1426864611yescharacteristic
208C2—42no—
209C2#2029893614yesdirect product factor
210C2C2×#1681360311yescharacteristic
211C2C2×#1681364211yescharacteristic
212C2C2×#1681365311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C22⋊Q8×C113C2
socleC23×C113C2×D4
prime radicalC24×C113D4
hypercenterC2×C22⋊Q8D113
hypocenterC113C2×#485
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #20298936C2direct (N × H)
3. C2×#16813555C2semidirect
4. C2×#16813553C2semidirect
5. C2×#16813546C2semidirect
6. C2×#16813546C2semidirect
17. #16813555C22semidirect
18. #16813553C22semidirect
19. #16813546C22semidirect
20. #16813546C22semidirect
102. C2×C113#485semidirect
107. C113C2×#485semidirect
209. C2#20298936direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168135812
#202989362
C2×#168135552
C2×#168135532
C2×#168135462
C2×C22⋊#117447512
C2×C22⋊Q8×C1132
C2×#485113