Finite Group Databasebeta

← #28391621

Subgroups — #28391621

Order 14464.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16813652C212yesmaximal, complemented
2C2×#16813549C212yesmaximal, complemented
3#20298503C211yesmaximal, characteristic, complemented
4#20298367C211yesmaximal, characteristic, complemented
5#537×C113C211yesmaximal, characteristic
6C22×Dic226C2211yescharacteristic
7#16813652—24no—
8#16813652—24no—
9C2×#14268637—22no—
10C2×#14268635—22no—
11C2×#14268631C2212yes—
12C2×C4×Dic113C2211yescharacteristic
13#16813549—24no—
14#16813529—22no—
15C2×#41×C113C2212yes—
16C22⋊Q8×C113—22no—
17#121×C113—22no—
18#121×C113—22no—
19C2×C4⋊C4×C113C2211yescharacteristic
20C2×Dic226—22no—
21C2×Dic226—22no—
22C2×Dic226—21no—
23C2×Dic226D412yescomplemented
24C22×Dic113—21no—
25C22×Dic113—21no—
26#14268637—28no—
27#14268635—28no—
28#14268631—22no—
29#14268631D414yescomplemented
30C2×#11744751—22no—
31C4×Dic113—22no—
32#41×C113—22no—
33#41×C113—22no—
34#41×C113—22no—
35#41×C113—22no—
36C2×Q8×C113D412yes—
37C2×D4×C113—22no—
38C2×D4×C113—22no—
39C2×D4×C113D412yes—
40C22×C4×C113—22no—
41C22×C4×C113D412yes—
42C22×C4×C113C2311yescharacteristic
43C4⋊C4×C113—22no—
44C4⋊C4×C113—22no—
45C22⋊C4×C113—24no—
46C23×C113—22no—
47C23×C113C2×D411yescharacteristic
48Q8×C113—22no—
49Q8×C113—22no—
50D4×C113—22no—
51D4×C113—22no—
52D4×C113—42no—
53D4×C113—42no—
54D4×C113—82no—
55C2×C4×C113—22no—
56C2×C4×C113—22no—
57C2×C4×C113—42no—
58C2×C4×C113—42no—
59C2×C4×C113—42no—
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×D412yes—
62C2×C4×C113C2×D412yes—
63C2×C4×C113#4111yescharacteristic
64C2×Dic113—22no—
65C2×Dic113—22no—
66C2×Dic113—41no—
67C2×Dic113—41no—
68C2×Dic113—41no—
69C2×Dic113—41no—
70Dic226—24no—
71Dic226—42no—
72#11744751—24no—
73C22×C113—21no—
74C22×C113—21no—
75C22×C113—42no—
76C22×C113—42no—
77C22×C113—42no—
78C22×C113#12011yescharacteristic
79C22×C113#12111yescharacteristic
80C22×C113#12711yescharacteristic
81C4×C113—42no—
82C4×C113—42no—
83C4×C113#12012yes—
84C4×C113#12112yes—
85Dic113—42no—
86Dic113—42no—
87C2×C113—21no—
88C2×C113—21no—
89C2×C113—82no—
90C2×C113#39211yescharacteristic
91C2×C113#45511yescharacteristic
92C2×C113#45611yescharacteristic
93#2007—1131nomaximal, Sylow
94C113#200711yescharacteristic, complemented, Sylow
95C2×#137—1132no—
96#537D11311yescharacteristic
97C2×#104—1132no—
98#391—1131no—
99#343—1131no—
100C2×#41C2×D11312yes—
101C22×Q8—1131no—
102#137—2264no—
103#137—2264no—
104C2×Q16—2262no—
105C2×SD16—2262no—
106C2×M16—1132no—
107C22⋊Q8—22no—
108#121—22no—
109#121—22no—
110C2×C4⋊C4C2×D11311yescharacteristic
111C2×C42—1131no—
112#104—2264no—
113#95—2262no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118C2×Q8—1132no—
119C2×Q8—2262no—
120C2×Q8—2262no—
121C2×Q8—2261no—
122C2×Q8C22⋊D11312yes—
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C22⋊D11312yes—
126C22×C4—22no—
127C22×C4—2261no—
128C22×C4—2261no—
129C22×C4C22⋊D11312yes—
130C22×C4C22×D11311yescharacteristic
131Q16—2268no—
132SD16—2268no—
133M16—1134no—
134M16—2262no—
135C2×C8—2262no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C22⋊C4—24no—
139C42—2262no—
140C23—22no—
141C23C2×C22⋊D11311yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—4522no—
145Q8—2264no—
146D4—22no—
147D4—22no—
148D4—42no—
149D4—42no—
150D4—82no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—4521no—
157C2×C4—4521no—
158C2×C4—4521no—
159C2×C4—4521no—
160C2×C4—2262no—
161C2×C4—2262no—
162C2×C4D4×D11311yescharacteristic
163C2×C4D4×D11312yes—
164C2×C4C2×C22⋊D11312yes—
165C2×C4#1426864611yescharacteristic
166C8—2264no—
167C22—21no—
168C22—21no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22#1681359111yescharacteristic
173C22#1681359311yescharacteristic
174C22#1681361811yescharacteristic
175C4—42no—
176C4—42no—
177C4—4522no—
178C4—4522no—
179C4#1681359012yes—
180C4#1681359412yes—
181C2—21no—
182C2—21no—
183C2—82no—
184C2#2029850611yescharacteristic
185C2#2029877611yescharacteristic
186C2#2029878111yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting, prime radical#537×C113C2
socleC22×C113#120
hypercenter#537D113
hypocenterC113#2007
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#16813652C2semidirect
2. C2×#16813549C2semidirect
3. #20298503C2semidirect
4. #20298367C2semidirect
23. C2×Dic226D4semidirect
29. #14268631D4semidirect
94. C113#2007semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
C2×#168135492
#202985032
#202983672
#537×C1132
#2007113