Finite Group Databasebeta

← #28406697

Subgroups — #28406697

Order 14464.

396 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×#16813689C211yesmaximal, characteristic, complemented
2C2×#16813679C212yesmaximal, complemented
3C2×C22⋊#11744753C212yesmaximal, complemented
4C2×C4×#11744753C211yesmaximal, characteristic, complemented
5C2×#16813582C211yesmaximal, characteristic
6C22×#11744753C2212yes—
7C22×#11744753C2212yes—
8#16813689—22no—
9#16813679—24no—
10C22⋊#11744753—24no—
11C4×#11744753—22no—
12C22×C22⋊D113C411yescharacteristic
13C23×Dic113C2211yescharacteristic
14C22×C4×D113C2211yescharacteristic
15#16813582—22no—
16#16813582—22no—
17C2×#14268626C411yescharacteristic
18C2×#14268624C411yescharacteristic
19C2×C4×Dic113C2211yescharacteristic
20C2×C22⋊C4×C113C411yescharacteristic
21C2×#11744753—22no—
22C2×#11744753—22no—
23C2×#11744753—22no—
24C2×#11744753—22no—
25C2×#11744753—22no—
26C2×#11744753D414yescomplemented
27C23×D113C2×C411yescharacteristic
28C2×C22⋊D113—22no—
29C2×C22⋊D113—22no—
30C2×C22⋊D113C814yescomplemented
31C22×Dic113—21no—
32C22×Dic113—21no—
33C22×Dic113—22no—
34C22×Dic113—22no—
35C22×Dic113C2×C411yescharacteristic
36C22×Dic113C2×C411yescharacteristic
37C22×Dic113C2311yescharacteristic
38C2×C4×D113—21no—
39C2×C4×D113—21no—
40C2×C4×D113—22no—
41C2×C4×D113—22no—
42#14268626—22no—
43#14268624—22no—
44C4×Dic113D412yes—
45C4×Dic113D412yes—
46C24×C113C2×C411yescharacteristic
47C22×C4×C113C2×C411yescharacteristic
48C22×C4×C113C2×C411yescharacteristic
49C22⋊C4×C113—22no—
50C23×C113—21no—
51C23×C113—22no—
52C23×C113—21no—
53C23×C113—22no—
54C23×C113C2×C812yes—
55C23×C113C22×C411yescharacteristic
56C22×D113—21no—
57C22×D113—22no—
58C22×D113—21no—
59C22×D113—22no—
60C22×D113C2×C812yes—
61C2×C4×C113—22no—
62C2×C4×C113—21no—
63C2×C4×C113—22no—
64C2×C4×C113C22⋊C412yes—
65C22⋊D113—28no—
66C2×Dic113—21no—
67C2×Dic113—22no—
68C2×Dic113—42no—
69C2×Dic113—41no—
70C2×Dic113—41no—
71C2×Dic113C22⋊C412yes—
72C2×Dic113C2×C812yes—
73C2×Dic113M1612yes—
74C2×Dic113C2×D411yescharacteristic
75C2×Dic113C2×D412yes—
76C2×Dic113C2×D411yescharacteristic
77C2×Dic113#4112yes—
78C4×D113—42no—
79C4×D113—41no—
80C4×D113—41no—
81#11744753—24no—
82#11744753—42no—
83C22×C113—22no—
84C22×C113—24no—
85C22×C113—41no—
86C22×C113—41no—
87C22×C113—42no—
88C22×C113C2×C22⋊C411yescharacteristic
89C22×C113C4×D412yes—
90C22×C113C22×C811yescharacteristic
91C22×C113C2×M1611yescharacteristic
92C22×C113#13112yes—
93C2×D113—22no—
94C2×D113—24no—
95C2×D113—41no—
96C2×D113—41no—
97C2×D113—42no—
98C4×C113—22no—
99C4×C113—41no—
100Dic113—41no—
101Dic113C22⋊C814yescomplemented
102Dic113#12112yes—
103Dic113#12411yescharacteristic
104Dic113#12711yescharacteristic
105C2×C113—42no—
106C2×C113#39011yescharacteristic
107C2×C113C2×C22⋊C811yescharacteristic
108C2×C113#40811yescharacteristic
109C2×C113C8×D412yes—
110C2×C113#43612yes—
111D113—42no—
112#1954—1131nomaximal, Sylow
113C113#195411yescharacteristic, complemented, Sylow
114C2×C4×D4—1131no—
115C2×C4⋊C8—1131no—
116C2×C22⋊C8—1132no—
117C2×C22⋊C8—1132no—
118C2×C4×C8—1131no—
119C22×D4—1131no—
120C23×C4—1131no—
121C23×C4—1131no—
122C22×C8—1132no—
123C22×C8—1132no—
124C4×D4—2262no—
125C4×D4—2262no—
126C2×C4⋊C4—1131no—
127C2×C22⋊C4—1131no—
128C2×C22⋊C4#9067311yescharacteristic
129C2×C42—1131no—
130C4⋊C8—2262no—
131C22⋊C8—2264no—
132C22⋊C8—2264no—
133C4×C8—2262no—
134C24—1131no—
135C24C2×#9067311yescharacteristic
136C2×D4—1134no—
137C2×D4—2262no—
138C2×D4—2262no—
139C22×C4—1131no—
140C22×C4—1131no—
141C22×C4—1131no—
142C22×C4—2262no—
143C22×C4—2261no—
144C22×C4—2261no—
145C22×C4—2262no—
146C22×C4—2262no—
147C22×C4—2261no—
148C22×C4—2261no—
149C22×C4—2262no—
150C22×C4C2×#9067311yescharacteristic
151C22×C4C2×#9067311yescharacteristic
152C2×C8—1134no—
153C2×C8—2262no—
154C2×C8—2262no—
155C2×C8—2262no—
156C2×C8—2262no—
157C2×C8—2262no—
158C4⋊C4—2262no—
159C22⋊C4—22no—
160C22⋊C4—2262no—
161C42—1132no—
162C42—1132no—
163C23—21no—
164C23—22no—
165C23—21no—
166C23—22no—
167C23—1132no—
168C23—2261no—
169C23—2262no—
170C23—2261no—
171C23—2262no—
172C23#1426865512yes—
173C23C22×#9067311yescharacteristic
174D4—2268no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—1132no—
179C2×C4—1131no—
180C2×C4—1131no—
181C2×C4—1132no—
182C2×C4—1132no—
183C2×C4—1132no—
184C2×C4—1132no—
185C2×C4—4521no—
186C2×C4—4522no—
187C2×C4—4521no—
188C2×C4—4521no—
189C2×C4—4522no—
190C2×C4—4521no—
191C2×C4—2261no—
192C2×C4—2262no—
193C2×C4C22⋊#9067312yes—
194C8—4522no—
195C8—2264no—
196C22—22no—
197C22—24no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—4521no—
202C22—4521no—
203C22—4522no—
204C22—2262no—
205C22—2264no—
206C22C2×C22⋊#9067311yescharacteristic
207C22D4×#9067312yes—
208C22C2×#1426865511yescharacteristic
209C22D113⋊M1611yescharacteristic
210C22#1681370912yes—
211C4—22no—
212C4—41no—
213C4—1131no—
214C4—1132no—
215C4—1131no—
216C4—1134no—
217C4—4521no—
218C2—42no—
219C2—4522no—
220C2#2029955011yescharacteristic
221C2#2029956611yescharacteristic
222C2#2029957111yescharacteristic
223C2#2029962512yes—
224C2#2029963112yes—
subgroupG/H
center, FrattiniC23C22×#90673
commutatorC22×C113C22×C8
FittingC2×C22⋊C4×C113C4
socleC23×C113C22×C4
prime radicalC22×C22⋊D113C4
cosocleC22×Dic113C23
hypercenterC2×C22⋊C4#90673
hypocenterC113#1954
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16813689C2semidirect
2. C2×#16813679C2semidirect
3. C2×C22⋊#11744753C2semidirect
4. C2×C4×#11744753C2semidirect
26. C2×#11744753D4semidirect
30. C2×C22⋊D113C8semidirect
101. Dic113C22⋊C8semidirect
113. C113#1954semidirect

Maximal subgroups

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

subgroupindex
C2×#168136892
C2×#168136792
C2×C22⋊#117447532
C2×C4×#117447532
C2×#168135822
#1954113