Finite Group Databasebeta

← #28391382

Subgroups — #28391382

Order 14464.

336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16813611C211yesmaximal, characteristic
2C2×#16813546C211yesmaximal, characteristic, complemented
3C2×#16813544C211yesmaximal, characteristic
4C2×#16813542C211yesmaximal, characteristic
5C2×C8×Dic113C211yesmaximal, characteristic, complemented
6#20298463C211yesmaximal, characteristic, complemented
7C2×#103×C113C211yesmaximal, characteristic, complemented
8C22×D452C2211yescharacteristic
9C22×#11744751C2211yescharacteristic
10#16813611—22no—
11#16813611C414yescomplemented
12C2×C4⋊Dic113C2211yescharacteristic
13C2×#14268624—22no—
14C2×C4×Dic113C2211yescharacteristic
15#16813546—22no—
16#16813544—22no—
17#16813542—22no—
18C8×Dic113—22no—
19#16813529—22no—
20C22×Q8×C113C2211yescharacteristic
21C22×C8×C113C2211yescharacteristic
22C2×C4⋊C4×C113C2211yescharacteristic
23#103×C113—22no—
24C23×D113—21no—
25C2×D452—21no—
26C2×D452—21no—
27C2×D452—21no—
28C2×D452—21no—
29C2×D452—21no—
30C2×D452C2×C412yes—
31C22×Dic113—21no—
32C22×Dic113D412yes—
33C2×#11744751—21no—
34C2×#11744751—21no—
35C2×#11744751D412yes—
36C4⋊Dic113—21no—
37C4⋊Dic113—21no—
38#14268624—28no—
39C4×Dic113C2×C412yes—
40C4×Dic113D412yes—
41C2×Q8×C113—21no—
42C2×Q8×C113—21no—
43C2×Q8×C113—21no—
44C2×Q8×C113—21no—
45C2×Q8×C113—21no—
46C2×Q8×C113C2×C412yes—
47C22×C4×C113—21no—
48C22×C4×C113—21no—
49C22×C4×C113C2311yescharacteristic
50C2×C8×C113—21no—
51C2×C8×C113—21no—
52C2×C8×C113D412yes—
53C4⋊C4×C113—21no—
54C4⋊C4×C113—21no—
55C23×C113C2×D411yescharacteristic
56C22×D113—22no—
57C22×D113—41no—
58C22×D113—41no—
59C22×D113—42no—
60C22×D113—42no—
61Q8×C113—22no—
62Q8×C113—22no—
63Q8×C113—41no—
64Q8×C113—41no—
65C2×C4×C113—22no—
66C2×C4×C113—41no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113—42no—
70C2×C4×C113C22×C411yescharacteristic
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113#4111yescharacteristic
75C2×C4×C113#4111yescharacteristic
76C2×Dic113—22no—
77C2×Dic113—22no—
78C2×Dic113—41no—
79C2×Dic113—42no—
80C2×Dic113C22⋊C414yes—
81D452—22no—
82D452—22no—
83D452—41no—
84D452—41no—
85C8×C113—22no—
86#11744751—22no—
87C22×C113C2×C22⋊C411yescharacteristic
88C22×C113#12411yescharacteristic
89C22×C113#12711yescharacteristic
90C22×C113#13512yes—
91C22×C113#13512yes—
92C2×D113—42no—
93C2×D113—44no—
94C2×D113—82no—
95C2×D113—81no—
96C2×D113—81no—
97C4×C113—42no—
98C4×C113—81no—
99C4×C113C4×D411yescharacteristic
100C4×C113C4×D411yescharacteristic
101C4×C113#12111yescharacteristic
102C4×C113#12111yescharacteristic
103Dic113—24no—
104Dic113—81no—
105C2×C113#39011yescharacteristic
106C2×C113#41612yes—
107C2×C113#48812yes—
108C2×C113#49511yescharacteristic
109C2×C113#49511yescharacteristic
110D113—82no—
111#1958—1131nomaximal, Sylow
112C113#195811yescharacteristic, complemented, Sylow
113C2×#124—1131no—
114C2×#103—1131no—
115C2×#103D11311yescharacteristic, complemented
116C2×#102—1131no—
117C2×#102—1131no—
118C2×C4×C8—1131no—
119#382—1131no—
120C22×Q8C2×D11311yescharacteristic
121C22×D4—1131no—
122C22×C8—1131no—
123C22×C8C2×D11311yescharacteristic
124#124—1134no—
125#124—2262no—
126C2×C4⋊C4—1131no—
127C2×C4⋊C4C2×D11311yescharacteristic
128C2×C22⋊C4—2262no—
129C2×C42—1131no—
130#103—22no—
131#103—2262no—
132#102—2262no—
133#102—2262no—
134C4×C8—2262no—
135#95—2262no—
136C24—2261no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C4×D11312yes—
143C2×D4—1132no—
144C2×D4—2261no—
145C2×D4—2261no—
146C2×D4—2261no—
147C2×D4—2261no—
148C2×D4—2261no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—1132no—
152C22×C4—2261no—
153C22×C4C22×D11311yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—1132no—
157C2×C8—2261no—
158C2×C8—2261no—
159C2×C8C22⋊D11312yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—2261no—
163C4⋊C4—2261no—
164C22⋊C4—2268no—
165C42—1132no—
166C42—1132no—
167C23—4521no—
168C23—4521no—
169C23—4522no—
170C23—4522no—
171C23—2262no—
172C23D4×D11311yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—41no—
176Q8—41no—
177D4—4521no—
178D4—4521no—
179D4—2262no—
180D4—2262no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—1134no—
187C2×C4—4521no—
188C2×C4—4522no—
189C2×C4—2262no—
190C2×C4—2262no—
191C2×C4C2×C4×D11311yescharacteristic
192C2×C4D4×D11311yescharacteristic
193C2×C4D4×D11311yescharacteristic
194C2×C4C2×C22⋊D11311yescharacteristic
195C2×C4#1426864611yescharacteristic
196C2×C4#1426864711yescharacteristic
197C8—22no—
198C8—2262no—
199C22—9042no—
200C22—9041no—
201C22—9041no—
202C22—4522no—
203C22—4524no—
204C22C22⋊C4×D11311yescharacteristic
205C22#1681360811yescharacteristic
206C22#1681361811yescharacteristic
207C22#1681364312yes—
208C22#1681364512yes—
209C4—42no—
210C4—81no—
211C4—9041no—
212C4—2264no—
213C4#1681358211yescharacteristic
214C4C4×C22⋊D11311yescharacteristic
215C4#1681359411yescharacteristic
216C4#1681359511yescharacteristic
217C2—9042no—
218C2#2029849811yescharacteristic
219C2#2029859312yes—
220C2#2029895412yes—
221C2#2029897911yescharacteristic
222C2#2029898311yescharacteristic
subgroupG/H
centerC23D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#103×C113C2
socleC23×C113C2×D4
prime radicalC22×D452C22
cosocleC22×C4×C113C23
hypercenterC2×#103D113
hypocenterC113#1958
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#16813546C2semidirect
5. C2×C8×Dic113C2semidirect
6. #20298463C2semidirect
7. C2×#103×C113C2semidirect
11. #16813611C4semidirect
112. C113#1958semidirect
115. C2×#103D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136112
C2×#168135462
C2×#168135442
C2×#168135422
C2×C8×Dic1132
#202984632
C2×#103×C1132
#1958113