Finite Group Databasebeta

← #28391706

Subgroups — #28391706

Order 14464.

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

normal subgroups only

This group has 430 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
1#20299160C211yesmaximal, characteristic
2C2×#16813606C212yesmaximal, complemented
3C2×#16813536C212yesmaximal, complemented
4#20298459C211yesmaximal, characteristic, complemented
5#342×C113C211yesmaximal, characteristic, complemented
6C22×C22⋊D113C2212yes—
7C23×Dic113C2211yescharacteristic
8#16813606—22no—
9#16813606—24no—
10#16813606—24no—
11#16813596—22no—
12#16813592—22no—
13C2×C4⋊Dic113—22no—
14C2×C22⋊Dic113C2211yescharacteristic
15C2×#14268624—22no—
16#16813536—24no—
17#16813529—22no—
18C2×C22⋊C4×C113C2211yescharacteristic
19C2×C22⋊C4×C113C2212yes—
20C23×D113D412yes—
21C2×D452—22no—
22C2×C22⋊D113—22no—
23C2×C22⋊D113—22no—
24C2×C22⋊D113—22no—
25C2×C22⋊D113—22no—
26C2×C22⋊D113—22no—
27C2×C22⋊D113—22no—
28C22×Dic113—22no—
29C22×Dic113—22no—
30C22×Dic113—21no—
31C22×Dic113—21no—
32C22×Dic113—21no—
33C22×Dic113D412yes—
34C22×Dic113D412yescomplemented
35C4⋊Dic113—28no—
36C4⋊Dic113—22no—
37C22⋊Dic113—22no—
38#14268624—28no—
39#14268624—24no—
40C24×C113C2311yescharacteristic
41C22×C4×C113—22no—
42C22×C4×C113D412yes—
43C22⋊C4×C113—22no—
44C22⋊C4×C113—22no—
45C22⋊C4×C113D414yescomplemented
46C23×C113—42no—
47C23×C113C2×D412yes—
48C23×C113C2×D411yescharacteristic
49C23×C113C2×D411yescharacteristic
50C23×C113C2×D412yes—
51C23×C113#4111yescharacteristic
52C22×D113—22no—
53C22×D113—22no—
54C22×D113—22no—
55C22×D113—44no—
56C2×C4×C113—22no—
57C2×C4×C113—24no—
58C2×C4×C113—44no—
59C2×C4×C113—42no—
60C22⋊D113—42no—
61C22⋊D113—42no—
62C22⋊D113—42no—
63C22⋊D113—42no—
64C2×Dic113—24no—
65C2×Dic113—22no—
66C2×Dic113—22no—
67C2×Dic113—22no—
68C2×Dic113—22no—
69C2×Dic113—41no—
70C2×Dic113—42no—
71C2×Dic113—41no—
72C2×Dic113—42no—
73C2×Dic113—41no—
74D452—82no—
75C22×C113—22no—
76C22×C113—24no—
77C22×C113—41no—
78C22×C113—42no—
79C22×C113—41no—
80C22×C113#12012yes—
81C22×C113#12011yescharacteristic
82C22×C113#12111yescharacteristic
83C22×C113#12112yes—
84C22×C113#12711yescharacteristic
85C2×D113—44no—
86C2×D113—42no—
87C2×D113—44no—
88C2×D113—82no—
89C4×C113—44no—
90C4×C113—42no—
91Dic113—42no—
92Dic113—42no—
93Dic113—81no—
94C2×C113—21no—
95C2×C113—22no—
96C2×C113—22no—
97C2×C113—21no—
98C2×C113#39211yescharacteristic
99C2×C113#45812yes—
100D113—82no—
101#2022—1131nomaximal, Sylow
102C113#202211yescharacteristic, complemented, Sylow
103#534—1131no—
104C2×#123—1132no—
105C2×#99—1132no—
106#381—1131no—
107#342D11311yescharacteristic, complemented
108C22×D4—1132no—
109C23×C4—1131no—
110#123—2264no—
111#123—2262no—
112#123—2264no—
113#121—2262no—
114#120—2262no—
115C2×C4⋊C4—2262no—
116C2×C22⋊C4—1131no—
117C2×C22⋊C4—2262no—
118C2×C22⋊C4C2×D11311yescharacteristic
119C2×C22⋊C4C2×D11312yes—
120#99—2264no—
121#95—2262no—
122C24—1132no—
123C24C22×D11311yescharacteristic
124C2×D4—2262no—
125C2×D4—2262no—
126C2×D4—2262no—
127C2×D4—2262no—
128C2×D4—2262no—
129C2×D4—2262no—
130C2×D4—2262no—
131C22×C4—22no—
132C22×C4—1132no—
133C22×C4—1132no—
134C22×C4—2261no—
135C22×C4—2262no—
136C22×C4—2261no—
137C22×C4—2262no—
138C22×C4—2261no—
139C22×C4D45212yes—
140C4⋊C4—2268no—
141C4⋊C4—2262no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—2268no—
145C22⋊C4—2264no—
146C22⋊C4—2262no—
147C22⋊C4D45214yescomplemented
148C23—42no—
149C23—4524no—
150C23—2262no—
151C23—2262no—
152C23—2262no—
153C23D4×D11312yes—
154C23D4×D11311yescharacteristic
155C23C2×D45211yescharacteristic
156C23C2×D45212yes—
157C23#1426864811yescharacteristic
158D4—9042no—
159D4—4522no—
160D4—4522no—
161D4—4522no—
162D4—4522no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—4522no—
168C2×C4—4521no—
169C2×C4—4521no—
170C2×C4—4522no—
171C2×C4—4521no—
172C2×C4—2264no—
173C2×C4—2262no—
174C2×C4—2262no—
175C2×C4—2262no—
176C2×C4—2262no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—9042no—
183C22—4524no—
184C22—4522no—
185C22—4524no—
186C22#1681359212yes—
187C22#1681359211yescharacteristic
188C22#1681359712yes—
189C22#1681359711yescharacteristic
190C22#1681361911yescharacteristic
191C4—44no—
192C4—42no—
193C4—9041no—
194C4—4522no—
195C4—4522no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—9042no—
201C2#2029850811yescharacteristic
202C2#2029878912yes—
subgroupG/H
centerC22#16813592
commutator, cosocleC24×C113C23
FrattiniC24C22×D113
Fitting#342×C113C2
socleC22×C113#120
prime radical#20299160C2
hypercenter#342D113
hypocenterC113#2022
LCSG ▷ C24×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#16813606C2semidirect
3. C2×#16813536C2semidirect
4. #20298459C2semidirect
5. #342×C113C2semidirect
34. C22×Dic113D4semidirect
45. C22⋊C4×C113D4semidirect
102. C113#2022semidirect
107. #342D113semidirect
147. C22⋊C4D452semidirect

Maximal subgroups

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

subgroupindex
#202991602
C2×#168136062
C2×#168135362
#202984592
#342×C1132
#2022113