Finite Group Databasebeta

← #28406433

Subgroups — #28406433

Order 14464.

312 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 92 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×C4⋊#11744753C211yesmaximal, characteristic, complemented
3C2×#16813679C212yesmaximal
4#20299464C212yesmaximal, complemented
5C2×#16813580C211yesmaximal, characteristic
6C22×#11744753C2212yes—
7C22×#11744753C2212yes—
8#16813689—22no—
9C4⋊#11744753—22no—
10#16813679—24no—
11C22×C4×D113C2211yescharacteristic
12#16813580—22no—
13#16813580—22no—
14C2×C4⋊Dic113C411yescharacteristic
15C2×#14268624C411yescharacteristic
16C2×#14268624C411yescharacteristic
17C2×C4×Dic113C2211yescharacteristic
18C2×C4×Dic113C2211yescharacteristic
19C2×C4⋊C4×C113C411yescharacteristic
20C2×#11744753—22no—
21C2×#11744753—22no—
22C2×#11744753—22no—
23C2×#11744753—22no—
24C2×#11744753—22no—
25C2×#11744753—22no—
26C23×D113C2×C411yescharacteristic
27C22×Dic113C2×C411yescharacteristic
28C22×Dic113C2×C411yescharacteristic
29C22×Dic113C2311yescharacteristic
30C2×C4×D113—21no—
31C2×C4×D113—21no—
32C2×C4×D113—21no—
33C2×C4×D113—21no—
34C2×C4×D113D412yes—
35C2×C4×D113Q812yes—
36C4⋊Dic113—22no—
37#14268624—22no—
38#14268624—22no—
39C4×Dic113—21no—
40C4×Dic113—21no—
41C4×Dic113D412yes—
42C4×Dic113D412yes—
43C22×C4×C113C2×C411yescharacteristic
44C22×C4×C113C2×C411yescharacteristic
45C22×C4×C113C2×C411yescharacteristic
46C4⋊C4×C113—22no—
47C23×C113C22×C411yescharacteristic
48C22×D113—21no—
49C22×D113—21no—
50C22×D113—22no—
51C22×D113—22no—
52C22×D113C4⋊C412yes—
53C2×C4×C113—21no—
54C2×C4×C113—21no—
55C2×C4×C113—22no—
56C2×C4×C113—21no—
57C2×C4×C113—22no—
58C2×C4×C113C22⋊C412yes—
59C2×C4×C113C4⋊C412yes—
60C2×Dic113—22no—
61C2×Dic113—21no—
62C2×Dic113—22no—
63C2×Dic113C22⋊C412yes—
64C2×Dic113C2×D411yescharacteristic
65C2×Dic113C2×D411yescharacteristic
66C2×Dic113C2×D411yescharacteristic
67C2×Dic113C2×Q811yescharacteristic
68C2×Dic113#4111yescharacteristic
69C2×Dic113#4111yescharacteristic
70C4×D113—22no—
71C4×D113—22no—
72C4×D113—22no—
73C4×D113—22no—
74#11744753—42no—
75#11744753—42no—
76C22×C113C2×C22⋊C411yescharacteristic
77C22×C113C2×C4⋊C411yescharacteristic
78C22×C113#11711yescharacteristic
79C22×C113#13112yes—
80C22×C113#13112yes—
81C2×D113—22no—
82C2×D113—24no—
83C2×D113—41no—
84C2×D113—41no—
85C2×D113—42no—
86C4×C113—22no—
87C4×C113—22no—
88C4×C113—41no—
89Dic113—22no—
90Dic113—41no—
91Dic113#12111yescharacteristic
92Dic113#12111yescharacteristic
93Dic113C22⋊Q811yescharacteristic
94Dic113C22⋊Q811yescharacteristic
95C2×C113#38011yescharacteristic
96C2×C113#40811yescharacteristic
97C2×C113#40811yescharacteristic
98C2×C113#42412yes—
99C2×C113#43312yes—
100D113—42no—
101#1798—1131nomaximal, Sylow
102C113#179811yescharacteristic, complemented, Sylow
103C2×#117—1131no—
104C2×C4⋊C8—1131no—
105C2×C4⋊C8—1131no—
106C2×C22⋊C8—1132no—
107#336—1132no—
108C23×C4—1131no—
109C22×C8—1132no—
110C22×C8—1132no—
111#117—2262no—
112#117—2262no—
113C2×C4⋊C4—1131no—
114C2×C4⋊C4#9067311yescharacteristic
115C2×C22⋊C4—1131no—
116C2×C22⋊C4—1131no—
117C2×C42—1131no—
118C2×C42—1131no—
119C4⋊C8—2262no—
120C4⋊C8—2262no—
121C22⋊C8—2264no—
122C24—1131no—
123C22×C4—1131no—
124C22×C4—1131no—
125C22×C4—1132no—
126C22×C4—1132no—
127C22×C4—1131no—
128C22×C4—2261no—
129C22×C4—2261no—
130C22×C4—2261no—
131C22×C4—2261no—
132C22×C4C2×#9067311yescharacteristic
133C22×C4C2×#9067311yescharacteristic
134C22×C4C2×#9067311yescharacteristic
135C2×C8—2262no—
136C2×C8—2262no—
137C2×C8—2262no—
138C2×C8—2262no—
139C2×C8—2262no—
140C2×C8—2262no—
141C4⋊C4—22no—
142C4⋊C4—2262no—
143C22⋊C4—2262no—
144C22⋊C4—2262no—
145C42—1132no—
146C42—1132no—
147C42—2261no—
148C42—2261no—
149C23—1132no—
150C23—2261no—
151C23—2261no—
152C23—2262no—
153C23—2262no—
154C23C22×#9067311yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—1131no—
161C2×C4—1131no—
162C2×C4—1131no—
163C2×C4—1131no—
164C2×C4—1131no—
165C2×C4—1131no—
166C2×C4—1132no—
167C2×C4—2262no—
168C2×C4—2262no—
169C2×C4—2262no—
170C2×C4—2262no—
171C2×C4—2261no—
172C2×C4—2262no—
173C2×C4—2262no—
174C2×C4C22⋊#9067312yes—
175C2×C4C4⋊#9067312yes—
176C8—4522no—
177C8—4522no—
178C22—4521no—
179C22—4521no—
180C22—4522no—
181C22—2262no—
182C22—2264no—
183C22C2×C22⋊#9067311yescharacteristic
184C22C2×C4⋊#9067311yescharacteristic
185C22#1681370111yescharacteristic
186C22#1681370912yes—
187C22#1681371012yes—
188C4—22no—
189C4—22no—
190C4—41no—
191C4—1131no—
192C4—1131no—
193C4—1131no—
194C4—1131no—
195C4—4521no—
196C4—2262no—
197C2—4522no—
198C2#2029954011yescharacteristic
199C2#2029957111yescharacteristic
200C2#2029957311yescharacteristic
201C2#2029960512yes—
202C2#2029962312yes—
subgroupG/H
center, FrattiniC23C22×#90673
commutator, socleC23×C113C22×C4
FittingC2×C4⋊C4×C113C4
prime radicalC23×D113C2×C4
cosocleC22×Dic113C23
hypercenterC2×C4⋊C4#90673
hypocenterC113#1798
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16813689C2semidirect
2. C2×C4⋊#11744753C2semidirect
4. #20299464C2semidirect
102. C113#1798semidirect

Maximal subgroups

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

subgroupindex
C2×#168136892
C2×C4⋊#117447532
C2×#168136792
#202994642
C2×#168135802
#1798113