Finite Group Databasebeta

← #28402020

Subgroups — #28402020

Order 14464.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299210C211yesmaximal, characteristic, complemented
2#20298902C212yesmaximal, complemented
3#20298898C212yesmaximal, complemented
4#20298842C212yesmaximal, complemented
5#20298825C212yesmaximal, complemented
6#20298803C212yesmaximal, complemented
7#20298795C212yesmaximal, complemented
8#20298625C211yesmaximal, characteristic, complemented
9#540×C113C211yesmaximal, characteristic
10C2×#14268635C2212yes—
11C2×#14268635C2212yes—
12C2×#14268631C2211yescharacteristic
13C22×#11744751C2211yescharacteristic
14#16813622C2211yescharacteristic
15#16813615—22no—
16#16813614C2211yescharacteristic
17#16813612—22no—
18#16813601C2212yes—
19C4×Dic226C2212yes—
20#16813555C2212yes—
21#16813553C2212yes—
22C4⋊#11744751C2212yes—
23C4⋊#11744751C2212yes—
24#16813545C2212yes—
25#16813545C2212yes—
26#16813543C2212yes—
27#16813543C2212yes—
28#127×C113C2211yescharacteristic
29#125×C113C2211yescharacteristic
30#123×C113—22no—
31#121×C113—22no—
32#121×C113C2212yes—
33C4×D4×C113C2212yes—
34#117×C113C2211yescharacteristic
35C2×Dic226C2312yes—
36#14268635—42no—
37#14268635—42no—
38#14268631—41no—
39C2×#11744751—41no—
40C2×#11744751C2312yes—
41C2×#11744751C2312yes—
42C4⋊Dic113—22no—
43C4⋊Dic113C2312yes—
44#14268626—22no—
45#14268626—22no—
46#14268626—22no—
47C22⋊Dic113—22no—
48C4×Dic113—22no—
49C2×D4×C113—22no—
50C2×D4×C113—22no—
51C2×D4×C113C2312yes—
52C22×C4×C113—22no—
53C22×C4×C113C2311yescharacteristic
54C4⋊C4×C113—22no—
55C4⋊C4×C113D412yes—
56C4⋊C4×C113C2312yes—
57C22⋊C4×C113—22no—
58C22⋊C4×C113—22no—
59C22⋊C4×C113D412yes—
60C42×C113C2311yescharacteristic
61C42×C113C2311yescharacteristic
62C23×C113—22no—
63C23×C113C2×D411yescharacteristic
64D4×C113—22no—
65D4×C113—22no—
66D4×C113—82no—
67D4×C113—82no—
68C2×C4×C113—21no—
69C2×C4×C113—21no—
70C2×C4×C113—22no—
71C2×C4×C113—82no—
72C2×C4×C113C2×D412yes—
73C2×C4×C113C2×D412yes—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2411yescharacteristic
76C2×Dic113—22no—
77C2×Dic113—22no—
78Dic226—22no—
79Dic226—22no—
80#11744751—22no—
81#11744751—22no—
82C22×C113—21no—
83C22×C113—22no—
84C22×C113—42no—
85C22×C113—42no—
86C22×C113—42no—
87C22×C113C22×D411yescharacteristic
88C4×C113—21no—
89C4×C113—22no—
90C4×C113—22no—
91C4×C113—42no—
92C4×C113H(5,𝔽2)11yescharacteristic
93C4×C1132−1+411yescharacteristic
94Dic113—42no—
95Dic113—42no—
96C2×C113—41no—
97C2×C113—82no—
98C2×C113#53711yescharacteristic
99C2×C113#57712yes—
100#3260—1131nomaximal, Sylow
101C113#326011yescharacteristic, complemented, Sylow
102#541—1131no—
103#540D11311yescharacteristic
104#479—1132no—
105#478—1132no—
106#468—1132no—
107#465—1132no—
108#461—1132no—
109#460—1132no—
110#424—1131no—
111C2×SD16—1132no—
112C2×SD16—1132no—
113C2×M16—1131no—
114C22×C8—1131no—
115C4⋊Q8—1131no—
116#127C2×D11311yescharacteristic
117#126—2262no—
118#125—1131no—
119#125—2262no—
120#125C2×D11311yescharacteristic
121#123—22no—
122C22⋊Q8—1132no—
123#121—22no—
124#121C2×D11312yes—
125C4×Q8—1132no—
126C4×D4C2×D11312yes—
127#117C2×D11311yescharacteristic
128#107—1132no—
129#106—1132no—
130C4⋊C8—1132no—
131C4⋊C8—1132no—
132#103—1132no—
133#103—1132no—
134#102—1132no—
135#102—1132no—
136C2×Q8—1132no—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4C22×D11312yes—
140C22×C4—22no—
141C22×C4C22×D11311yescharacteristic
142SD16—4522no—
143SD16—4522no—
144M16—4521no—
145C2×C8—1132no—
146C2×C8—1132no—
147C2×C8—4521no—
148C4⋊C4—22no—
149C4⋊C4—1132no—
150C4⋊C4—2262no—
151C4⋊C4—2262no—
152C4⋊C4—2262no—
153C4⋊C4—2262no—
154C4⋊C4C22⋊D11312yes—
155C4⋊C4C22×D11312yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—2262no—
159C22⋊C4C22⋊D11312yes—
160C42—2262no—
161C42C22×D11311yescharacteristic
162C42C22×D11311yescharacteristic
163C23—22no—
164C23C2×C22⋊D11311yescharacteristic
165Q8—2262no—
166Q8—2262no—
167D4—22no—
168D4—22no—
169D4—82no—
170D4—82no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—82no—
175C2×C4—2262no—
176C2×C4—2262no—
177C2×C4C2×C22⋊D11312yes—
178C2×C4C2×C22⋊D11312yes—
179C2×C4C2×C22⋊D11311yescharacteristic
180C2×C4C23×D11311yescharacteristic
181C8—2262no—
182C8—2262no—
183C22—22no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22C22×C22⋊D11311yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—42no—
193C4—4522no—
194C4—4522no—
195C4#1681366811yescharacteristic
196C4#1681366911yescharacteristic
197C2—41no—
198C2—82no—
199C2#2029917611yescharacteristic
200C2#2029940912yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#540×C113C2
socleC22×C113C22×D4
hypercenter#540D113
hypocenterC113#3260
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20299210C2semidirect
2. #20298902C2semidirect
3. #20298898C2semidirect
4. #20298842C2semidirect
5. #20298825C2semidirect
6. #20298803C2semidirect
7. #20298795C2semidirect
8. #20298625C2semidirect
101. C113#3260semidirect

Maximal subgroups

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

subgroupindex
#202992102
#202989022
#202988982
#202988422
#202988252
#202988032
#202987952
#202986252
#540×C1132
#3260113