Finite Group Databasebeta

← #28392248

Subgroups — #28392248

Order 14464.

238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#20299169C211yesmaximal, characteristic
2#20298572C211yesmaximal, characteristic
3#20298392C214yesmaximal, complemented
4#410×C113C211yesmaximal, characteristic
5C22×Dic226C411yescharacteristic, complemented
6#16813620C412yescomplemented
7#16813609C2212yes—
8#16813603—21no—
9#16813603—21no—
10#16813601—21no—
11#16813601—21no—
12#16813581—21no—
13#16813581C411yescharacteristic, complemented
14#16813537—21no—
15#16813537C2212yes—
16C2×#41×C113C2211yescharacteristic
17#117×C113—21no—
18#99×C113—21no—
19#99×C113C2212yes—
20C2×Dic226—21no—
21C2×Dic226—41no—
22C2×Dic226—41no—
23C2×Dic226C2×C412yes—
24C22×Dic113—21no—
25C4⋊Dic113—21no—
26C4⋊Dic113—41no—
27#14268626—22no—
28#14268626—22no—
29C22⋊Dic113—21no—
30C22⋊Dic113—22no—
31C22⋊Dic113—22no—
32C22⋊Dic113—22no—
33C4×Dic113—41no—
34C4×Dic113C2×C412yes—
35#41×C113—41no—
36#41×C113—41no—
37C2×Q8×C113C2×C411yescharacteristic
38C2×D4×C113D411yescharacteristic
39C2×D4×C113D411yescharacteristic
40C2×D4×C113C2311yescharacteristic
41C22×C4×C113C2×C411yescharacteristic
42C22×C4×C113D411yescharacteristic
43C22×C4×C113D411yescharacteristic
44C4⋊C4×C113—41no—
45C22⋊C4×C113—22no—
46C42×C113—41no—
47C23×C113C22⋊C411yescharacteristic
48C23×C113C2×D411yescharacteristic
49C23×C113C2×D411yescharacteristic
50Q8×C113—41no—
51D4×C113—41no—
52D4×C113—41no—
53D4×C113—41no—
54C2×C4×C113—21no—
55C2×C4×C113—21no—
56C2×C4×C113—21no—
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—42no—
61C2×C4×C113C22⋊C411yescharacteristic
62C2×C4×C113C22⋊C411yescharacteristic
63C2×C4×C113C22⋊C411yescharacteristic
64C2×C4×C113C22×C411yescharacteristic
65C2×Dic113—22no—
66C2×Dic113—22no—
67C2×Dic113—42no—
68C2×Dic113—42no—
69Dic226—41no—
70Dic226—41no—
71Dic226—42no—
72C22×C113—21no—
73C22×C113—21no—
74C22×C113—21no—
75C22×C113—41no—
76C22×C113—41no—
77C22×C113—41no—
78C22×C113C2×C22⋊C411yescharacteristic
79C4×C113—21no—
80C4×C113—21no—
81C4×C113—21no—
82C4×C113—82no—
83C4×C113#9911yescharacteristic
84C4×C113#9911yescharacteristic
85Dic113—42no—
86Dic113—42no—
87Dic113—82no—
88C2×C113—21no—
89C2×C113—41no—
90C2×C113—41no—
91C2×C113—41no—
92C2×C113C2×#9911yescharacteristic
93#2129—1131nomaximal, Sylow
94C113#212911yescharacteristic, complemented, Sylow
95#536—1131no—
96#410—1131no—
97#410D11311yescharacteristic
98#354—1134no—
99C2×#41C2×D11311yescharacteristic
100C22×Q8—1131no—
101C4⋊Q8—1132no—
102#124—1132no—
103#123—2261no—
104#123—2261no—
105C22⋊Q8—2261no—
106C22⋊Q8—2261no—
107#117—21no—
108#117—1131no—
109#117—2261no—
110#99—21no—
111#99—1132no—
112#99—2261no—
113#99C2×D11312yes—
114#41—41no—
115#41—41no—
116C2×Q8—1132no—
117C2×Q8—4521no—
118C2×Q8—4521no—
119C2×Q8—2261no—
120C2×Q8C4×D11311yescharacteristic
121C2×D4D45211yescharacteristic
122C2×D4C22⋊D11311yescharacteristic
123C2×D4C22×D11311yescharacteristic
124C22×C4—2261no—
125C22×C4C4×D11311yescharacteristic
126C22×C4D45211yescharacteristic
127C22×C4C22⋊D11311yescharacteristic
128C4⋊C4—41no—
129C4⋊C4—4521no—
130C4⋊C4—2262no—
131C4⋊C4—2262no—
132C4⋊C4—2261no—
133C22⋊C4—22no—
134C22⋊C4—2262no—
135C22⋊C4—2261no—
136C22⋊C4—2262no—
137C22⋊C4—2262no—
138C42—41no—
139C42—1132no—
140C42—4521no—
141C23#1426862411yescharacteristic
142C23C2×C22⋊D11311yescharacteristic
143C23C2×D45211yescharacteristic
144Q8—41no—
145Q8—4522no—
146Q8—4521no—
147Q8—4521no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—4522no—
159C2×C4—4522no—
160C2×C4—2262no—
161C2×C4—2262no—
162C2×C4#1426862411yescharacteristic
163C2×C4#1426862411yescharacteristic
164C2×C4#1426862411yescharacteristic
165C2×C4C2×C4×D11311yescharacteristic
166C22—21no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22C2×#1426862411yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—9042no—
178C4—4522no—
179C4—4522no—
180C4#1681353611yescharacteristic
181C4#1681353611yescharacteristic
182C2—21no—
183C2—41no—
184C2—41no—
185C2—41no—
186C2C2×#1681353611yescharacteristic
subgroupG/H
centerC2C2×#16813536
commutatorC2×C4×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#410×C113C2
socleC2×C113C2×#99
prime radicalC2×#41×C113C22
cosocleC2×D4×C113C23
hypercenter#410D113
hypocenterC113#2129
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #20298392C2semidirect
5. C22×Dic226C4semidirect
6. #16813620C4semidirect
13. #16813581C4semidirect
94. C113#2129semidirect

Maximal subgroups

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

subgroupindex
#202991692
#202985722
#202983922
#410×C1132
#2129113