Finite Group Databasebeta

← #28390608

Subgroups — #28390608

Order 14464.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C22×#14268630C211yesmaximal, characteristic
2C2×#16813554C211yesmaximal, characteristic, complemented
3#20298455C212yesmaximal
4#20298360C212yesmaximal, complemented
5C2×#107×C113C211yesmaximal, characteristic, complemented
6C22×C4×D113C2211yescharacteristic
7C2×#14268630—22no—
8C2×#14268630—22no—
9C2×#14268630C414yescomplemented
10C22×#11744751C2211yescharacteristic
11C2×C4⋊Dic113C2212yes—
12C2×#14268624—22no—
13#16813554—22no—
14#16813529—22no—
15C22×C8×C113C2211yescharacteristic
16C2×C4⋊C4×C113C2212yes—
17#107×C113—22no—
18C23×D113D411yescharacteristic
19C22×Dic113—22no—
20C22×Dic113D411yescharacteristic
21C2×C4×D113—21no—
22C2×C4×D113—21no—
23C2×C4×D113—21no—
24C2×C4×D113—21no—
25C2×C4×D113C2×C412yes—
26C2×C4×D113Q812yes—
27#14268630—28no—
28C2×#11744751—21no—
29C2×#11744751—21no—
30C2×#11744751C2×C412yes—
31C4⋊Dic113—22no—
32C4⋊Dic113—22no—
33#14268624—44no—
34C22×C4×C113—22no—
35C22×C4×C113C2311yescharacteristic
36C2×C8×C113C2×C412yes—
37C2×C8×C113D412yes—
38C2×C8×C113D412yes—
39C4⋊C4×C113—22no—
40C4⋊C4×C113—22no—
41C23×C113C2×D411yescharacteristic
42C22×D113—21no—
43C22×D113—21no—
44C22×D113—22no—
45C22×D113—22no—
46C22×D113C4⋊C412yes—
47C2×C4×C113—42no—
48C2×C4×C113—42no—
49C2×C4×C113—42no—
50C2×C4×C113C22×C411yescharacteristic
51C2×C4×C113C2×D411yescharacteristic
52C2×C4×C113C2×D411yescharacteristic
53C2×C4×C113C2×Q811yescharacteristic
54C2×C4×C113#4111yescharacteristic
55C2×C4×C113#4111yescharacteristic
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—42no—
59C2×Dic113—42no—
60C2×Dic113—42no—
61C2×Dic113C4⋊C412yes—
62C4×D113—22no—
63C4×D113—22no—
64C4×D113—22no—
65C4×D113—22no—
66C8×C113C22⋊C414yescomplemented
67#11744751—22no—
68C22×C113C2×C4⋊C411yescharacteristic
69C22×C113#12111yescharacteristic
70C22×C113#12111yescharacteristic
71C22×C113AGL(1,ℤ/8)12yes—
72C22×C113#13712yes—
73C2×D113—22no—
74C2×D113—24no—
75C2×D113—42no—
76C2×D113—41no—
77C2×D113—41no—
78C4×C113—82no—
79C4×C113C2×C22⋊C411yescharacteristic
80C4×C113#11711yescharacteristic
81C4×C113C22⋊Q811yescharacteristic
82C4×C113C22⋊Q811yescharacteristic
83Dic113—22no—
84Dic113—82no—
85C2×C113#38011yescharacteristic
86C2×C113#42812yes—
87C2×C113#46812yes—
88C2×C113#46911yescharacteristic
89C2×C113#47011yescharacteristic
90D113—42no—
91#1809—1131nomaximal, Sylow
92C113#180911yescharacteristic, complemented, Sylow
93C22×M16—1131no—
94C2×#107D11311yescharacteristic, complemented
95C2×#106—1131no—
96#380—1132no—
97#340—1132no—
98C23×C4—1131no—
99C2×M16—1134no—
100C2×M16—2262no—
101C2×M16—2262no—
102C22×C8—1131no—
103C22×C8C2×D11311yescharacteristic
104C2×C4⋊C4—1132no—
105C2×C4⋊C4C2×D11312yes—
106C2×C22⋊C4—2262no—
107#107—22no—
108#106—2262no—
109#95—2262no—
110C24—1131no—
111C22×C4—22no—
112C22×C4—1131no—
113C22×C4—1132no—
114C22×C4—1132no—
115C22×C4—2262no—
116C22×C4—2261no—
117C22×C4—2261no—
118C22×C4—2261no—
119C22×C4—2261no—
120C22×C4C22×D11311yescharacteristic
121M16—2268no—
122C2×C8—1132no—
123C2×C8—2261no—
124C2×C8—2261no—
125C2×C8C4×D11312yes—
126C2×C8D45212yes—
127C2×C8C22⋊D11312yes—
128C4⋊C4—22no—
129C4⋊C4—22no—
130C4⋊C4—2262no—
131C4⋊C4—2262no—
132C22⋊C4—4524no—
133C23—1132no—
134C23—2261no—
135C23—2261no—
136C23—2262no—
137C23—2262no—
138C23D4×D11311yescharacteristic
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—1132no—
143C2×C4—4522no—
144C2×C4—4522no—
145C2×C4—4522no—
146C2×C4—2261no—
147C2×C4—2261no—
148C2×C4—2262no—
149C2×C4—2262no—
150C2×C4—2262no—
151C2×C4—2262no—
152C2×C4C2×C4×D11311yescharacteristic
153C2×C4C2×C22⋊D11311yescharacteristic
154C2×C4C2×D45211yescharacteristic
155C2×C4Q8×D11311yescharacteristic
156C2×C4#1426864611yescharacteristic
157C2×C4#1426864811yescharacteristic
158C8—2262no—
159C8#1426862414yescomplemented
160C22—4522no—
161C22—4521no—
162C22—4521no—
163C22—2264no—
164C22—2262no—
165C22C4⋊C4×D11311yescharacteristic
166C22#1681359311yescharacteristic
167C22#1681359711yescharacteristic
168C22#1681364612yes—
169C22#1681365412yes—
170C4—82no—
171C4—9042no—
172C4—2262no—
173C4C2×#1426862411yescharacteristic
174C4#1681358011yescharacteristic
175C4#1681359811yescharacteristic
176C4#1681360211yescharacteristic
177C2—4522no—
178C2#2029845511yescharacteristic
179C2#2029863912yes—
180C2#2029884512yes—
181C2#2029884811yescharacteristic
182C2#2029885311yescharacteristic
subgroupG/H
centerC23D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#107×C113C2
socleC23×C113C2×D4
prime radicalC23×D113D4
cosocleC22×C4×C113C23
hypercenterC2×#107D113
hypocenterC113#1809
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#16813554C2semidirect
4. #20298360C2semidirect
5. C2×#107×C113C2semidirect
9. C2×#14268630C4semidirect
66. C8×C113C22⋊C4semidirect
92. C113#1809semidirect
94. C2×#107D113semidirect
159. C8#14268624semidirect

Maximal subgroups

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

subgroupindex
C22×#142686302
C2×#168135542
#202984552
#202983602
C2×#107×C1132
#1809113