Finite Group Databasebeta

← #28403181

Subgroups — #28403181

Order 14464.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#20299298C212yesmaximal, complemented
2#20299000C211yesmaximal, characteristic, complemented
3#20298920C212yesmaximal, complemented
4#20298910C212yesmaximal, complemented
5#20298898C212yesmaximal, complemented
6#20298848C212yesmaximal, complemented
7#20298677C211yesmaximal, characteristic, complemented
8#20298639C212yesmaximal, complemented
9C4×D8×C113C211yesmaximal, characteristic, complemented
10C2×#14268630C2212yes—
11#16813615—22no—
12#16813614C2212yes—
13#16813605—22no—
14#16813595—22no—
15#16813593C2212yes—
16#16813593C2212yes—
17C4×D452C2211yescharacteristic
18C4×C22⋊D113—22no—
19#16813580C2212yes—
20C4⋊C4×D113C2212yes—
21#16813556C2211yescharacteristic
22#16813556C2211yescharacteristic
23#16813555C2212yes—
24#16813554C2212yes—
25#16813553C2212yes—
26C4⋊#11744751C2211yescharacteristic
27#16813543C2212yes—
28#16813543C2212yes—
29#16813534C2212yes—
30C2×D8×C113C2211yescharacteristic
31C4×D4×C113C2212yes—
32#107×C113C2211yescharacteristic
33#102×C113C2212yes—
34C4×C8×C113C2211yescharacteristic
35C2×D452D411yescharacteristic
36C2×C22⋊D113—22no—
37C2×C22⋊D113—22no—
38C2×C4×D113—22no—
39C2×C4×D113C2312yes—
40#14268630—24no—
41C2×#11744751C2312yes—
42C4⋊Dic113D411yescharacteristic
43C4⋊Dic113C2312yes—
44C4⋊Dic113C2312yes—
45#14268626—22no—
46#14268626—22no—
47#14268626—22no—
48C22⋊Dic113—22no—
49C22⋊Dic113—22no—
50#14268624—22no—
51#14268624D412yes—
52C4×Dic113—22no—
53C2×D4×C113C2312yes—
54C22×C4×C113—22no—
55D8×C113—22no—
56C2×C8×C113C2311yescharacteristic
57C2×C8×C113C2311yescharacteristic
58C4⋊C4×C113C2312yes—
59C22⋊C4×C113—22no—
60C42×C113C2311yescharacteristic
61C23×C113—22no—
62C22×D113C2×D412yes—
63D4×C113—22no—
64D4×C113—22no—
65C2×C4×C113—22no—
66C2×C4×C113—82no—
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2×D411yescharacteristic
69C2×C4×C113C2411yescharacteristic
70C22⋊D113—44no—
71C22⋊D113—82no—
72C2×Dic113—22no—
73C2×Dic113—22no—
74C2×Dic113C2×D412yes—
75D452—41no—
76C4×D113—22no—
77C4×D113—22no—
78C4×D113—82no—
79C8×C113—21no—
80C8×C113#4112yes—
81#11744751—22no—
82C22×C113—42no—
83C22×C113—42no—
84C22×C113—42no—
85C22×C113C22×D411yescharacteristic
86C2×D113—22no—
87C2×D113—22no—
88C2×D113—22no—
89C4×C113—21no—
90C4×C113—21no—
91C4×C113—42no—
92C4×C113C2×#4111yescharacteristic
93C4×C1132−1+411yescharacteristic
94Dic113—22no—
95Dic113—42no—
96Dic113—42no—
97C2×C113—82no—
98C2×C113#54711yescharacteristic
99C2×C113#57511yescharacteristic
100C2×C113#57611yescharacteristic
101D113—42no—
102#3355—1131nomaximal, Sylow
103C113#335511yescharacteristic, complemented, Sylow
104#553—1132no—
105#499—1131no—
106#482—1132no—
107#480—1132no—
108#478—1132no—
109#469—1132no—
110C4×D8D11311yescharacteristic, complemented
111#436—1131no—
112#428—1132no—
113C2×D8C2×D11311yescharacteristic
114C2×M16—1132no—
115#126—2262no—
116#125—1132no—
117#123—2262no—
118#121—1132no—
119#121—1132no—
120#121—2262no—
121C4×D4—1131no—
122C4×D4—2262no—
123C4×D4C2×D11312yes—
124#117—1132no—
125C2×C4⋊C4—1132no—
126#107—1131no—
127#107—1131no—
128#107—1132no—
129#107C2×D11311yescharacteristic
130#106—1132no—
131#106—1132no—
132C4⋊C8—1131no—
133#102—1132no—
134#102—1132no—
135#102C2×D11312yes—
136C22⋊C8—1132no—
137C4×C8C2×D11311yescharacteristic
138C2×D4—1131no—
139C2×D4—2262no—
140C2×D4—2262no—
141C2×D4C22×D11312yes—
142C22×C4—22no—
143C22×C4—1132no—
144C22×C4—2262no—
145D8—22no—
146M16—2264no—
147C2×C8—1132no—
148C2×C8C22×D11311yescharacteristic
149C2×C8C22×D11311yescharacteristic
150C4⋊C4—1131no—
151C4⋊C4—1132no—
152C4⋊C4—1132no—
153C4⋊C4—2262no—
154C4⋊C4—2262no—
155C4⋊C4—2262no—
156C4⋊C4C22×D11312yes—
157C22⋊C4—22no—
158C22⋊C4—1132no—
159C22⋊C4—2262no—
160C22⋊C4—2262no—
161C22⋊C4—2262no—
162C42—2262no—
163C42C22×D11311yescharacteristic
164C23—22no—
165C23—1132no—
166D4—22no—
167D4—22no—
168D4—9042no—
169D4—4521no—
170D4—4524no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—1132no—
174C2×C4—9042no—
175C2×C4—2262no—
176C2×C4—2262no—
177C2×C4—2262no—
178C2×C4—2262no—
179C2×C4D4×D11311yescharacteristic
180C2×C4D4×D11311yescharacteristic
181C2×C4C23×D11311yescharacteristic
182C8—21no—
183C8—2262no—
184C8#1426864712yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—2262no—
189C22—2262no—
190C22—2262no—
191C22C2×D4×D11311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—4522no—
196C4—4522no—
197C4—2262no—
198C4C2×#1426864711yescharacteristic
199C4#1681366911yescharacteristic
200C2—82no—
201C2—4522no—
202C2#2029925311yescharacteristic
203C2#2029939511yescharacteristic
204C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×D8×C113C2
socleC22×C113C22×D4
hypercenterC4×D8D113
hypocenterC113#3355
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20299298C2semidirect
2. #20299000C2semidirect
3. #20298920C2semidirect
4. #20298910C2semidirect
5. #20298898C2semidirect
6. #20298848C2semidirect
7. #20298677C2semidirect
8. #20298639C2semidirect
9. C4×D8×C113C2semidirect
103. C113#3355semidirect
110. C4×D8D113semidirect

Maximal subgroups

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

subgroupindex
#202992982
#202990002
#202989202
#202989102
#202988982
#202988482
#202986772
#202986392
C4×D8×C1132
#3355113