Finite Group Databasebeta

← #46826114

Subgroups — #46826114

Order 34432.

328 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D269⋊(C22⋊C8)C212yesmaximal
2#31771451C212yesmaximal, complemented
3#31771450C212yesmaximal, complemented
4C2×C4⋊C4×D269C211yesmaximal, characteristic
5C2×D269⋊C8—22no—
6#22575510—22no—
7C22⋊#14524137C2214yes—
8C22×C4×D269C411yescharacteristic
9C22×C4×D269C411yescharacteristic
10C22×C4×D269C2211yescharacteristic
11C2×C4⋊Dic269C2211yescharacteristic
12C2×#16864381C411yescharacteristic
13C2×#16864381C2211yescharacteristic
14C4⋊C4×D269—22no—
15C4⋊C4×D269—22no—
16C2×C4⋊C4×C269C411yescharacteristic
17D269⋊C8—44no—
18C2×#14524137—24no—
19C23×D269C2×C411yescharacteristic
20C22×Dic269C2×C411yescharacteristic
21C22×Dic269C2×C411yescharacteristic
22C22×Dic269C2311yescharacteristic
23C2×C4×D269—21no—
24C2×C4×D269—21no—
25C2×C4×D269—22no—
26C2×C4×D269—21no—
27C2×C4×D269—21no—
28C2×C4×D269—42no—
29C2×C4×D269—42no—
30C2×C4×D269C814yescomplemented
31C2×C4×D269D412yes—
32C2×C4×D269D412yes—
33C4⋊Dic269—22no—
34#16864381—22no—
35#16864381—22no—
36C22×C4×C269C2×C411yescharacteristic
37C22×C4×C269C2×C411yescharacteristic
38C22×C4×C269C2×C411yescharacteristic
39C4⋊C4×C269—22no—
40#14524137—44no—
41C22×D269—22no—
42C22×D269—22no—
43C22×D269C22⋊C411yescharacteristic
44C22×D269C22⋊C411yescharacteristic
45C22×D269C2×C812yes—
46C22×D269M1612yes—
47C2×Dic269—21no—
48C2×Dic269—21no—
49C2×Dic269—21no—
50C2×Dic269—41no—
51C2×Dic269—41no—
52C2×Dic269C2×C812yescomplemented
53C2×Dic269C2×D412yes—
54C4×D269—24no—
55C4×D269—24no—
56C4×D269—24no—
57C4×D269—42no—
58C4×D269—42no—
59C4×D269—42no—
60C23×C269C22×C411yescharacteristic
61C2×C4×C269—21no—
62C2×C4×C269—21no—
63C2×C4×C269—21no—
64C2×C4×C269—41no—
65C2×C4×C269—41no—
66C2×C4×C269C22⋊C412yes—
67C2×C4×C269C2×C812yescomplemented
68C22×C269—21no—
69C22×C269—21no—
70C22×C269C2×C22⋊C411yescharacteristic
71C22×C269C22×C811yescharacteristic
72C22×C269C2×M1611yescharacteristic
73C2×D269—21no—
74C2×D269—21no—
75C2×D269—24no—
76C2×D269—24no—
77C2×D269C22⋊C812yes—
78C2×D269C22⋊C812yes—
79C2×D269#9912yes—
80C2×D269#10112yes—
81C4×C269—22no—
82C4×C269—22no—
83C4×C269—41no—
84Dic269—22no—
85Dic269—22no—
86Dic269—41no—
87C2×C269—21no—
88C2×C269—21no—
89C2×C269C2×C22⋊C811yescharacteristic
90C2×C269C2×#9911yescharacteristic
91C2×C269C2×#10111yescharacteristic
92D269—22no—
93D269#32414yescomplemented
94C269C2×#32411yescharacteristic, complemented, Sylow
95C2×#324—2691nomaximal, Sylow
96C22×C4⋊C4—2691no—
97C2×C22⋊C8—2692no—
98#324—2692no—
99#324—2692no—
100C23×C4—2691no—
101C23×C4—2691no—
102C23×C4—2691no—
103C22×C8—5382no—
104C2×C4⋊C4—2691no—
105C2×C4⋊C4—2691no—
106C2×C4⋊C4—2691no—
107C2×C4⋊C4—5382no—
108C2×C4⋊C4—5382no—
109C2×C4⋊C4#1176164011yescharacteristic
110C22⋊C8—2694no—
111C22⋊C8—5382no—
112C24—2691no—
113C22×C4—2691no—
114C22×C4—2691no—
115C22×C4—2692no—
116C22×C4—2694no—
117C22×C4—2692no—
118C22×C4—2691no—
119C22×C4—5381no—
120C22×C4—5381no—
121C22×C4—5382no—
122C22×C4—5381no—
123C22×C4—5381no—
124C22×C4—10762no—
125C22×C4—10762no—
126C22×C4C2×#1176164011yescharacteristic
127C22×C4C2×#1176164011yescharacteristic
128C22×C4C2×#1176164011yescharacteristic
129C2×C8—5384no—
130C2×C8—10764no—
131C4⋊C4—22no—
132C4⋊C4—5382no—
133C4⋊C4—5382no—
134C4⋊C4—5382no—
135C23—2691no—
136C23—2691no—
137C23—2692no—
138C23—2692no—
139C23—5382no—
140C23—5382no—
141C23C22×#1176164011yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—2692no—
148C2×C4—2692no—
149C2×C4—5384no—
150C2×C4—5384no—
151C2×C4—5384no—
152C2×C4—5381no—
153C2×C4—5381no—
154C2×C4—5381no—
155C2×C4—10762no—
156C2×C4—10762no—
157C2×C4—10762no—
158C2×C4—10761no—
159C2×C4—10761no—
160C2×C4C22⋊#1176164012yes—
161C2×C4D269⋊C812yescomplemented
162C8—10764no—
163C22—21no—
164C22—21no—
165C22—2692no—
166C22—2692no—
167C22—2692no—
168C22—2692no—
169C22—5384no—
170C22—5384no—
171C22—5381no—
172C22—5381no—
173C22C2×C22⋊#1176164011yescharacteristic
174C22C2×D269⋊C811yescharacteristic
175C22D269⋊M1611yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—5382no—
180C4—5382no—
181C4—10761no—
182C2—21no—
183C2—21no—
184C2—2694no—
185C2—5382no—
186C2D269⋊(C22⋊C8)11yescharacteristic
187C2D269⋊#9911yescharacteristic
188C2D269⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11761640
commutatorC22×C269C22×C8
FrattiniC23C22×#11761640
FittingC2×C4⋊C4×C269C4
socleC22×C269C2×C22⋊C4
prime radicalC23×D269C2×C4
cosocleC22×Dic269C23
hypercenterC2×C4⋊C4#11761640
hypocenterC269C2×#324
LCSG ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #31771451C2semidirect
3. #31771450C2semidirect
30. C2×C4×D269C8semidirect
52. C2×Dic269C2×C8semidirect
67. C2×C4×C269C2×C8semidirect
93. D269#324semidirect
94. C269C2×#324semidirect
161. C2×C4D269⋊C8semidirect

Maximal subgroups

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

subgroupindex
D269⋊(C22⋊C8)2
#317714512
#317714502
C2×C4⋊C4×D2692
C2×#324269