Finite Group Databasebeta

← #28401316

Subgroups — #28401316

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#20299152C212yesmaximal
2#20298995C211yesmaximal, characteristic, complemented
3#20298976C211yesmaximal, characteristic, complemented
4#20298947C212yesmaximal, complemented
5#20298857C211yesmaximal, characteristic
6#20298855C212yesmaximal
7#20298853C211yesmaximal, characteristic
8#20298706C211yesmaximal, characteristic, complemented
9#20298703C212yesmaximal, complemented
10#20298550C211yesmaximal, characteristic
11#441×C113C211yesmaximal, characteristic, complemented
12C2×Dic452C2211yescharacteristic
13C2×#14268637C2212yes—
14C2×#14268630C2211yescharacteristic
15C2×#14268630C2211yescharacteristic
16#16813621C2212yes—
17#16813620C2212yes—
18#16813612—22no—
19#16813602C2212yes—
20#16813600—22no—
21#16813598C2212yes—
22C4×Dic226—22no—
23C4×Dic226C2212yes—
24#16813579—22no—
25C42×D113C2211yescharacteristic
26#16813554C2211yescharacteristic
27#16813553C2212yes—
28#16813547C2212yes—
29#16813546C2212yes—
30#16813545C2212yes—
31#16813533C2211yescharacteristic
32C8×Dic113C2211yescharacteristic
33C8×Dic113C2211yescharacteristic
34C2×Q16×C113C2211yescharacteristic
35C4×Q8×C113C2212yes—
36#106×C113C2211yescharacteristic
37#103×C113C2212yes—
38#97×C113C2211yescharacteristic
39C2×Dic226—22no—
40C2×Dic226C2312yes—
41C2×C4×D113D412yes—
42C2×C4×D113C2311yescharacteristic
43Dic452—22no—
44#14268637—24no—
45#14268630—22no—
46#14268630—22no—
47C2×#11744751C2311yescharacteristic
48C2×#11744751C2311yescharacteristic
49C4⋊Dic113—22no—
50C4⋊Dic113C2312yes—
51#14268626—22no—
52#14268626—22no—
53#14268626—22no—
54#14268626—22no—
55#14268626—22no—
56#14268624—22no—
57#14268624—22no—
58C4×Dic113—22no—
59C4×Dic113D412yes—
60C4×Dic113C2311yescharacteristic
61C2×Q8×C113C2312yes—
62Q16×C113—22no—
63C2×C8×C113C2311yescharacteristic
64C2×C8×C113C2311yescharacteristic
65C4⋊C4×C113—22no—
66C4⋊C4×C113C2312yes—
67C42×C113—22no—
68C42×C113C2311yescharacteristic
69C22×D113C2×D411yescharacteristic
70Q8×C113—22no—
71Q8×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—22no—
74C2×C4×C113C2×D412yes—
75C2×C4×C113C2411yescharacteristic
76C2×Dic113—22no—
77C2×Dic113—22no—
78C2×Dic113C2×D411yescharacteristic
79C2×Dic113C2×D412yes—
80C4×D113—21no—
81C4×D113—21no—
82C4×D113—24no—
83Dic226—22no—
84Dic226—22no—
85Dic226—44no—
86C8×C113—21no—
87C8×C113#4112yes—
88#11744751—21no—
89#11744751#4112yes—
90C22×C113C22×D411yescharacteristic
91C2×D113—21no—
92C2×D113—22no—
93C4×C113—22no—
94C4×C113—42no—
95C4×C113—42no—
96C4×C113C2×#4111yescharacteristic
97C4×C113C2×#4111yescharacteristic
98Dic113—21no—
99Dic113—42no—
100Dic113—42no—
101Dic113#13714yes—
102C2×C113#53211yescharacteristic
103C2×C113C2×#13712yes—
104D113—41no—
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—1131no—
113#470—1132no—
114#441—1132no—
115#441—1131no—
116#441D11311yescharacteristic, complemented
117C4×M16—1131no—
118C2×Q16—1132no—
119C2×Q16—1131no—
120C2×Q16C2×D11311yescharacteristic
121C2×M16—1131no—
122C2×M16—1131no—
123C4⋊Q8—1132no—
124C4⋊Q8—1132no—
125#125—2262no—
126C22⋊Q8—1132no—
127C22⋊Q8—1132no—
128C22⋊Q8—2262no—
129C4×Q8—1132no—
130C4×Q8—2262no—
131C4×Q8C2×D11312yes—
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#97C2×D11311yescharacteristic
143C4×C8—1131no—
144C4×C8—1131no—
145C2×Q8—1132no—
146C2×Q8—2262no—
147C2×Q8C22×D11312yes—
148C22×C4—1132no—
149C22×C4—1131no—
150Q16—22no—
151Q16—2264no—
152Q16—2262no—
153M16—2262no—
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—2262no—
169C22⋊C4—2262no—
170C42—22no—
171C42—1132no—
172C42—1131no—
173C42—2262no—
174C42C22×D11311yescharacteristic
175C23—1131no—
176Q8—22no—
177Q8—22no—
178Q8—4524no—
179Q8—2262no—
180Q8—2262no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—1132no—
184C2×C4—1131no—
185C2×C4—2264no—
186C2×C4—2262no—
187C2×C4—2262no—
188C2×C4—2261no—
189C2×C4—2261no—
190C2×C4D4×D11312yes—
191C2×C4C23×D11311yescharacteristic
192C8—21no—
193C8—1132no—
194C8—2261no—
195C8#1426864712yes—
196C22—2262no—
197C22—2261no—
198C22C2×D4×D11311yescharacteristic
199C4—22no—
200C4—42no—
201C4—42no—
202C4—1134no—
203C4—4522no—
204C4—4522no—
205C4—2261no—
206C4#41×D11311yescharacteristic
207C4C2×#1426864711yescharacteristic
208C2—4521no—
209C2#2029914511yescharacteristic
210C2#137×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#441×C113C2
socleC22×C113C22×D4
prime radicalC22×D113C2×D4
hypercenter#441D113
hypocenterC113#3185
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #20298995C2semidirect
3. #20298976C2semidirect
4. #20298947C2semidirect
8. #20298706C2semidirect
9. #20298703C2semidirect
11. #441×C113C2semidirect
106. C113#3185semidirect
116. #441D113semidirect

Maximal subgroups

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

subgroupindex
#202991522
#202989952
#202989762
#202989472
#202988572
#202988552
#202988532
#202987062
#202987032
#202985502
#441×C1132
#3185113