Finite Group Databasebeta

← #28392268

Subgroups — #28392268

Order 14464.

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

normal subgroups only

This group has 230 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#20298582C211yesmaximal, characteristic
3#20298396C214yesmaximal, complemented
4#413×C113C211yesmaximal, characteristic
5C22×Dic226C411yescharacteristic
6C2×#14268631—21no—
7#16813620C2212yes—
8#16813609C412yes—
9#16813603—21no—
10#16813603—21no—
11#16813601—21no—
12#16813601—21no—
13#16813581C411yescharacteristic
14#16813541C2212yes—
15#16813539—21no—
16C2×#41×C113C2211yescharacteristic
17C2×M16×C113—21no—
18#101×C113C2212yes—
19#100×C113—21no—
20C2×Dic226—21no—
21C2×Dic226—41no—
22C2×Dic226—41no—
23C2×Dic226C2×C412yes—
24C22×Dic113—21no—
25#14268631—22no—
26#14268631—41no—
27C2×#11744751—41no—
28C4⋊Dic113—21no—
29#14268626—22no—
30#14268626—22no—
31C22⋊Dic113—21no—
32C22⋊Dic113—22no—
33C22⋊Dic113—22no—
34C4×Dic113C2×C412yes—
35#41×C113—41no—
36#41×C113—41no—
37C2×Q8×C113C2311yescharacteristic
38C2×D4×C113C2×C411yescharacteristic
39C2×D4×C113D411yescharacteristic
40C2×D4×C113D411yescharacteristic
41C22×C4×C113C2×C411yescharacteristic
42C22×C4×C113D411yescharacteristic
43C22×C4×C113D411yescharacteristic
44M16×C113—22no—
45M16×C113—41no—
46C2×C8×C113—41no—
47C23×C113C22⋊C411yescharacteristic
48C23×C113C22⋊C411yescharacteristic
49C23×C113C22⋊C411yescharacteristic
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×C113C22⋊C411yescharacteristic
61C2×C4×C113C22×C411yescharacteristic
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×D411yescharacteristic
64C2×Dic113—22no—
65C2×Dic113—22no—
66C2×Dic113—42no—
67Dic226—41no—
68Dic226—41no—
69Dic226—42no—
70C8×C113—42no—
71#11744751—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#9911yescharacteristic
83C4×C113#9911yescharacteristic
84Dic113—42no—
85Dic113—42no—
86C2×C113—21no—
87C2×C113—41no—
88C2×C113—41no—
89C2×C113—41no—
90C2×C113C2×#9911yescharacteristic
91#2135—1131nomaximal, Sylow
92C113#213511yescharacteristic, complemented, Sylow
93#536—1131no—
94#413—1131no—
95#413D11311yescharacteristic
96#356—1134no—
97C2×#41C2×D11311yescharacteristic
98C22×Q8—1131no—
99C2×M16—21no—
100C2×M16—2261no—
101C4⋊Q8—1132no—
102#124—1132no—
103#123—2261no—
104#123—2261no—
105C22⋊Q8—2261no—
106C22⋊Q8—2261no—
107#117—1131no—
108#101—1132no—
109#101C2×D11312yes—
110#100—21no—
111#100—2261no—
112#41—41no—
113#41—41no—
114C2×Q8—1132no—
115C2×Q8—4521no—
116C2×Q8—4521no—
117C2×Q8—2261no—
118C2×Q8C22×D11311yescharacteristic
119C2×D4C4×D11311yescharacteristic
120C2×D4D45211yescharacteristic
121C2×D4C22⋊D11311yescharacteristic
122C22×C4—2261no—
123C22×C4C4×D11311yescharacteristic
124C22×C4D45211yescharacteristic
125C22×C4C22⋊D11311yescharacteristic
126M16—22no—
127M16—41no—
128M16—4521no—
129M16—2262no—
130C2×C8—41no—
131C2×C8—4521no—
132C4⋊C4—2261no—
133C4⋊C4—2262no—
134C4⋊C4—2262no—
135C22⋊C4—2261no—
136C22⋊C4—2262no—
137C22⋊C4—2262no—
138C42—1132no—
139C23#1426862411yescharacteristic
140C23#1426862411yescharacteristic
141C23#1426862411yescharacteristic
142Q8—41no—
143Q8—4522no—
144Q8—4521no—
145Q8—4521no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—4522no—
156C2×C4—2262no—
157C2×C4—2262no—
158C2×C4#1426862411yescharacteristic
159C2×C4C2×C4×D11311yescharacteristic
160C2×C4C2×C22⋊D11311yescharacteristic
161C2×C4C2×D45211yescharacteristic
162C8—42no—
163C8—4522no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×#1426862411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—4522no—
175C4—4522no—
176C4#1681353611yescharacteristic
177C4#1681353611yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1681353611yescharacteristic
subgroupG/H
centerC2C2×#16813536
commutatorC2×C4×C113C22×C4
FrattiniC2×Q8C22×D113
Fitting#413×C113C2
socleC2×C113C2×#99
prime radicalC2×#41×C113C22
cosocleC2×Q8×C113C23
hypercenter#413D113
hypocenterC113#2135
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #20298396C2semidirect
92. C113#2135semidirect

Maximal subgroups

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

subgroupindex
#202991692
#202985822
#202983962
#413×C1132
#2135113