Finite Group Databasebeta

← #28401314

Subgroups — #28401314

Order 14464.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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#20299150C212yesmaximal
2#20298995C211yesmaximal, characteristic, complemented
3#20298976C211yesmaximal, characteristic, complemented
4#20298947C212yesmaximal, complemented
5#20298856C211yesmaximal, characteristic
6#20298854C212yesmaximal
7#20298705C211yesmaximal, characteristic, complemented
8#20298704C211yesmaximal, characteristic, complemented
9#20298702C212yesmaximal, complemented
10M16×Dic113C211yesmaximal, characteristic
11#470×C113C211yesmaximal, characteristic
12C2×Dic452C2211yescharacteristic
13C2×#14268637C2212yes—
14C2×#14268631C2211yescharacteristic
15#16813621C2212yes—
16#16813620C2212yes—
17#16813612—22no—
18#16813601C2212yes—
19#16813599—22no—
20Q8×Dic113C2212yes—
21#16813587—22no—
22#16813587C2212yes—
23#16813578—22no—
24C2×C4×Dic113C2211yescharacteristic
25#16813554C2211yescharacteristic
26#16813553C2212yes—
27#16813547C2212yes—
28#16813546C2212yes—
29#16813545C2212yes—
30#16813532C2211yescharacteristic
31#16813532C2211yescharacteristic
32C8×Dic113C2211yescharacteristic
33C8×Dic113C2211yescharacteristic
34C2×Q16×C113C2211yescharacteristic
35C2×M16×C113C2211yescharacteristic
36C22⋊Q8×C113C2212yes—
37#106×C113C2211yescharacteristic
38#103×C113C2212yes—
39C2×Dic226—22no—
40C2×Dic226C2312yes—
41C22×Dic113D412yes—
42Dic452—22no—
43#14268637—24no—
44#14268631—22no—
45C2×#11744751C2311yescharacteristic
46C2×#11744751C2311yescharacteristic
47C4⋊Dic113—22no—
48C4⋊Dic113C2312yes—
49#14268626—22no—
50#14268626—22no—
51#14268626—22no—
52#14268626—22no—
53#14268626—22no—
54C22⋊Dic113—22no—
55C4×Dic113—22no—
56C4×Dic113—22no—
57C4×Dic113D412yes—
58C4×Dic113C2311yescharacteristic
59C4×Dic113C2311yescharacteristic
60C2×Q8×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62Q16×C113—22no—
63M16×C113—22no—
64C2×C8×C113C2311yescharacteristic
65C2×C8×C113C2311yescharacteristic
66C4⋊C4×C113—22no—
67C4⋊C4×C113C2312yes—
68C22⋊C4×C113—22no—
69C23×C113C2×D411yescharacteristic
70Q8×C113—22no—
71Q8×C113—22no—
72C2×C4×C113—21no—
73C2×C4×C113—21no—
74C2×C4×C113—22no—
75C2×C4×C113—22no—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2411yescharacteristic
78C2×Dic113—24no—
79C2×Dic113—22no—
80C2×Dic113—22no—
81C2×Dic113C2×D412yes—
82C2×Dic113C2×D412yes—
83Dic226—22no—
84Dic226—22no—
85Dic226—44no—
86C8×C113—21no—
87C8×C113#4112yes—
88#11744751—21no—
89#11744751#4112yes—
90C22×C113—21no—
91C22×C113—22no—
92C22×C113C22×D411yescharacteristic
93C4×C113—21no—
94C4×C113—42no—
95C4×C113—42no—
96C4×C113C2×#4111yescharacteristic
97C4×C113C2×#4111yescharacteristic
98Dic113—22no—
99Dic113—42no—
100Dic113—42no—
101Dic113#13714yes—
102C2×C113—41no—
103C2×C113#53211yescharacteristic
104C2×C113C2×#13712yes—
105#3185—1131nomaximal, Sylow
106C113#318511yescharacteristic, complemented, Sylow
107#533—1132no—
108#498—1131no—
109#494—1131no—
110#487—1132no—
111#470—1131no—
112#470—1132no—
113#470D11311yescharacteristic
114#441—1131no—
115#441—1131no—
116#441—1132no—
117C4×M16—1131no—
118C2×Q16—1132no—
119C2×Q16—1131no—
120C2×Q16C2×D11311yescharacteristic
121C2×M16—1131no—
122C2×M16C2×D11311yescharacteristic
123C4⋊Q8—1132no—
124C4⋊Q8—1132no—
125#125—2262no—
126C22⋊Q8—1132no—
127C22⋊Q8—2262no—
128C22⋊Q8C2×D11312yes—
129C4×Q8—1132no—
130C4×Q8—1132no—
131C4×Q8—2262no—
132#117—2262no—
133C2×C42—1131no—
134#106—1131no—
135#106—1132no—
136#106C2×D11311yescharacteristic
137#103—1132no—
138#103—1132no—
139#103—1132no—
140#103C2×D11312yes—
141#97—1131no—
142#97—1131no—
143C4×C8—1131no—
144C4×C8—1131no—
145C2×Q8—1132no—
146C2×Q8—2262no—
147C2×Q8C22×D11312yes—
148C22×C4—1132no—
149C22×C4C22×D11311yescharacteristic
150Q16—22no—
151Q16—2264no—
152Q16—2262no—
153M16—22no—
154M16—2262no—
155C2×C8—1131no—
156C2×C8—1131no—
157C2×C8C22×D11311yescharacteristic
158C2×C8C22×D11311yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—1132no—
161C4⋊C4—2262no—
162C4⋊C4—2262no—
163C4⋊C4—2262no—
164C4⋊C4—2262no—
165C4⋊C4—2262no—
166C4⋊C4—2262no—
167C4⋊C4C22×D11312yes—
168C22⋊C4—22no—
169C22⋊C4—2262no—
170C42—1132no—
171C42—1131no—
172C42—1131no—
173C42—2262no—
174C42—2262no—
175C23D4×D11311yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—4524no—
179Q8—2262no—
180Q8—2262no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—1132no—
186C2×C4—1132no—
187C2×C4—2264no—
188C2×C4—2262no—
189C2×C4—2262no—
190C2×C4D4×D11311yescharacteristic
191C2×C4C23×D11311yescharacteristic
192C8—21no—
193C8—1132no—
194C8—2261no—
195C8#1426864612yes—
196C22—22no—
197C22—21no—
198C22C2×D4×D11311yescharacteristic
199C4—21no—
200C4—42no—
201C4—42no—
202C4—1134no—
203C4—4522no—
204C4—4522no—
205C4—2262no—
206C4#41×D11311yescharacteristic
207C4C2×#1426864611yescharacteristic
208C2—41no—
209C2#2029914311yescharacteristic
210C2#137×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
prime radicalC23×C113C2×D4
hypercenter#470D113
hypocenterC113#3185
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #20298995C2semidirect
3. #20298976C2semidirect
4. #20298947C2semidirect
7. #20298705C2semidirect
8. #20298704C2semidirect
9. #20298702C2semidirect
106. C113#3185semidirect

Maximal subgroups

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

subgroupindex
#202991502
#202989952
#202989762
#202989472
#202988562
#202988542
#202987052
#202987042
#202987022
M16×Dic1132
#470×C1132
#3185113