Finite Group Databasebeta

← #28391620

Subgroups — #28391620

Order 14464.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#16813653C212yesmaximal, complemented
2#20299179C211yesmaximal, characteristic
3C2×#16813550C212yesmaximal, complemented
4#20298367C211yesmaximal, characteristic, complemented
5#391×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2212yes—
7#16813653—24no—
8#16813653—24no—
9C2×#14268637—22no—
10C2×#14268634—22no—
11C2×#14268631C2212yes—
12#16813602—22no—
13#16813597—22no—
14#16813596—22no—
15#16813550—24no—
16C22×Q8×C113C2211yescharacteristic
17C2×C4⋊C4×C113C2211yescharacteristic
18C2×C42×C113C2211yescharacteristic
19#95×C113—22no—
20#14268647—22no—
21#14268647—22no—
22#14268647—22no—
23#14268647—22no—
24C2×Dic226D412yes—
25C2×D452—22no—
26C2×D452D412yes—
27C2×C22⋊D113—22no—
28C2×C4×D113—22no—
29#14268637—28no—
30#14268634—28no—
31#14268631—22no—
32#14268631D414yescomplemented
33C2×#11744751—22no—
34C4⋊Dic113—22no—
35#14268624—24no—
36C2×Q8×C113—21no—
37C2×Q8×C113—22no—
38C2×Q8×C113—22no—
39C2×Q8×C113D412yescomplemented
40C22×C4×C113—21no—
41C22×C4×C113—21no—
42C22×C4×C113D412yes—
43C22×C4×C113C2311yescharacteristic
44C4⋊C4×C113—22no—
45C42×C113—22no—
46C23×C113C2×D411yescharacteristic
47C22×D113—22no—
48Q8×C113—24no—
49Q8×C113—42no—
50C2×C4×C113—22no—
51C2×C4×C113—22no—
52C2×C4×C113—22no—
53C2×C4×C113—41no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113—42no—
58C2×C4×C113C2×D412yes—
59C2×C4×C113C2×D412yes—
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113#4111yescharacteristic
62C22⋊D113—42no—
63C22⋊D113—42no—
64C2×Dic113—22no—
65D452—22no—
66D452—22no—
67D452—82no—
68C4×D113—42no—
69C4×D113—42no—
70Dic226—22no—
71Dic226—22no—
72#11744751—24no—
73C22×C113—21no—
74C22×C113—21no—
75C22×C113#12011yescharacteristic
76C22×C113#12111yescharacteristic
77C22×C113#12711yescharacteristic
78C2×D113—42no—
79C2×D113—42no—
80C2×D113—42no—
81C4×C113—42no—
82C4×C113—42no—
83C4×C113—42no—
84C4×C113#12012yes—
85C4×C113#12112yes—
86Dic113—42no—
87C2×C113—21no—
88C2×C113—21no—
89C2×C113#39211yescharacteristic
90C2×C113#45511yescharacteristic
91C2×C113#45611yescharacteristic
92D113—82no—
93#2007—1131nomaximal, Sylow
94C113#200711yescharacteristic, complemented, Sylow
95C2×#137—1132no—
96#537—1131no—
97C2×#104—1132no—
98#391D11311yescharacteristic, complemented
99#343—1131no—
100C2×#41—1132no—
101C22×Q8C2×D11311yescharacteristic
102#137—2264no—
103#137—2264no—
104C2×Q16—2262no—
105C2×SD16—2262no—
106C2×M16—1132no—
107C22⋊Q8—2262no—
108#121—2262no—
109#121—2262no—
110C2×C4⋊C4C2×D11311yescharacteristic
111C2×C42C2×D11311yescharacteristic
112#104—2264no—
113#95—22no—
114#41—2262no—
115#41—2262no—
116#41—2262no—
117#41—2262no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—1132no—
122C2×Q8D45212yescomplemented
123C2×D4—1132no—
124C2×D4—2262no—
125C2×D4—2262no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—2262no—
129C22×C4C22⋊D11312yes—
130C22×C4C22×D11311yescharacteristic
131Q16—2268no—
132SD16—2268no—
133M16—1134no—
134M16—2262no—
135C2×C8—2262no—
136C4⋊C4—22no—
137C4⋊C4—2262no—
138C22⋊C4—2264no—
139C42—22no—
140C23—2262no—
141C23C2×C22⋊D11311yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—2262no—
145Q8—2262no—
146D4—9042no—
147D4—4522no—
148D4—4522no—
149D4—2262no—
150D4—2262no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—4522no—
160C2×C4—4522no—
161C2×C4—2262no—
162C2×C4D4×D11312yes—
163C2×C4D4×D11312yes—
164C2×C4C2×D45211yescharacteristic
165C2×C4#1426864711yescharacteristic
166C8—2264no—
167C22—21no—
168C22—21no—
169C22—4522no—
170C22—4522no—
171C22—4522no—
172C22#1681359011yescharacteristic
173C22#1681359611yescharacteristic
174C22#1681361811yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—4522no—
179C4#1681359212yes—
180C4#1681359512yes—
181C2—21no—
182C2—21no—
183C2—9042no—
184C2#2029850711yescharacteristic
185C2#2029877511yescharacteristic
186C2#2029878011yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#391×C113C2
socleC22×C113#120
prime radical#20299179C2
hypercenter#391D113
hypocenterC113#2007
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
3. C2×#16813550C2semidirect
4. #20298367C2semidirect
5. #391×C113C2semidirect
32. #14268631D4semidirect
39. C2×Q8×C113D4semidirect
94. C113#2007semidirect
98. #391D113semidirect
122. C2×Q8D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
#202991792
C2×#168135502
#202983672
#391×C1132
#2007113