Finite Group Databasebeta

← #28391675

Subgroups — #28391675

Order 14464.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×Dic452C211yesmaximal, characteristic
2C22×#14268637C211yesmaximal, characteristic
3C2×#16813620C211yesmaximal, characteristic
4C2×#16813545C211yesmaximal, characteristic
5#20298503C211yesmaximal, characteristic
6#20298352C211yesmaximal, characteristic
7C2×#103×C113C211yesmaximal, characteristic
8C22×Dic226C2211yescharacteristic
9C22×Dic226C2211yescharacteristic
10C2×Dic452—22no—
11C2×Dic452—22no—
12C2×Dic452—22no—
13C2×#14268637—22no—
14C2×#14268637—22no—
15C2×#14268637—22no—
16C22×#11744751C2211yescharacteristic
17#16813620—22no—
18#16813620—22no—
19C2×#14268626—22no—
20C2×C4×Dic113C2211yescharacteristic
21#16813545—22no—
22#16813529—22no—
23C22×Q8×C113C2211yescharacteristic
24C22×C8×C113C2211yescharacteristic
25C2×C4⋊C4×C113C2211yescharacteristic
26#103×C113—22no—
27C2×Dic226—21no—
28C2×Dic226—21no—
29C2×Dic226—21no—
30C2×Dic226—21no—
31C2×Dic226—21no—
32C2×Dic226—21no—
33C2×Dic226—21no—
34C2×Dic226—21no—
35C2×Dic226—21no—
36C2×Dic226—21no—
37C2×Dic226D412yes—
38C2×Dic226D412yes—
39C22×Dic113—21no—
40C22×Dic113—21no—
41C22×Dic113D412yes—
42Dic452—28no—
43#14268637—28no—
44C2×#11744751—21no—
45C2×#11744751—21no—
46C2×#11744751D412yes—
47#14268626—28no—
48C4×Dic113—21no—
49C4×Dic113—21no—
50C2×Q8×C113—21no—
51C2×Q8×C113—21no—
52C2×Q8×C113—21no—
53C2×Q8×C113—21no—
54C2×Q8×C113—21no—
55C2×Q8×C113D412yes—
56C22×C4×C113—21no—
57C22×C4×C113—21no—
58C22×C4×C113C2311yescharacteristic
59C2×C8×C113—21no—
60C2×C8×C113—21no—
61C2×C8×C113D412yes—
62C4⋊C4×C113—21no—
63C4⋊C4×C113—21no—
64C23×C113C2×D411yescharacteristic
65Q8×C113—22no—
66Q8×C113—22no—
67Q8×C113—41no—
68Q8×C113—41no—
69C2×C4×C113—22no—
70C2×C4×C113—41no—
71C2×C4×C113—41no—
72C2×C4×C113—41no—
73C2×C4×C113—42no—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2×D411yescharacteristic
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113#4111yescharacteristic
80C2×Dic113—22no—
81C2×Dic113—22no—
82C2×Dic113—22no—
83C2×Dic113—22no—
84C2×Dic113—41no—
85C2×Dic113—41no—
86C2×Dic113—41no—
87C2×Dic113—41no—
88C2×Dic113Q1614yescomplemented
89Dic226—22no—
90Dic226—22no—
91Dic226—22no—
92Dic226—22no—
93Dic226—41no—
94Dic226—41no—
95Dic226—41no—
96Dic226—41no—
97C8×C113—22no—
98#11744751—22no—
99C22×C113#12011yescharacteristic
100C22×C113#12111yescharacteristic
101C22×C113#12711yescharacteristic
102C22×C113C2×Q1612yes—
103C22×C113#13712yes—
104C4×C113—42no—
105C4×C113—81no—
106C4×C113#12011yescharacteristic
107C4×C113#12011yescharacteristic
108C4×C113#12111yescharacteristic
109C4×C113#12111yescharacteristic
110Dic113—24no—
111Dic113—42no—
112Dic113—42no—
113C2×C113#39211yescharacteristic
114C2×C113#45112yes—
115C2×C113#46212yes—
116C2×C113#49411yescharacteristic
117C2×C113#49711yescharacteristic
118#2016—1131nomaximal, Sylow
119C113#201611yescharacteristic, complemented, Sylow
120C22×Q16—1131no—
121C22×Q16—1131no—
122C2×C4⋊Q8—1131no—
123C2×#103—1131no—
124C2×#103D11311yescharacteristic
125#391—1131no—
126#336—1131no—
127C22×Q8—1131no—
128C22×Q8—1131no—
129C22×Q8C2×D11311yescharacteristic
130C2×Q16—2262no—
131C2×Q16—2262no—
132C2×Q16—2262no—
133C2×Q16—2262no—
134C2×Q16—2262no—
135C2×Q16—2262no—
136C22×C8—1131no—
137C22×C8C2×D11311yescharacteristic
138C4⋊Q8—2262no—
139C4⋊Q8—2262no—
140C2×C4⋊C4—2262no—
141C2×C4⋊C4C2×D11311yescharacteristic
142C2×C42—1131no—
143#103—22no—
144#103—2262no—
145#95—2262no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—1132no—
152C2×Q8—1132no—
153C2×Q8—2261no—
154C2×Q8—2261no—
155C2×Q8—2261no—
156C2×Q8—2261no—
157C2×Q8—2261no—
158C2×Q8—2261no—
159C2×Q8—2261no—
160C2×Q8—2261no—
161C2×Q8—2261no—
162C2×Q8—2261no—
163C2×Q8D45212yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—1132no—
167C22×C4—2261no—
168C22×C4—2261no—
169C22×C4C22×D11311yescharacteristic
170Q16—2268no—
171Q16—2268no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—1132no—
175C2×C8—2261no—
176C2×C8—2261no—
177C2×C8C22⋊D11312yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—2268no—
181C42—2261no—
182C42—2261no—
183C23D4×D11311yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—4521no—
189Q8—4521no—
190Q8—4521no—
191Q8—4521no—
192Q8—2262no—
193Q8—2262no—
194Q8—2262no—
195Q8—2262no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—1134no—
202C2×C4—4521no—
203C2×C4—4521no—
204C2×C4—4521no—
205C2×C4—4521no—
206C2×C4—2262no—
207C2×C4—2262no—
208C2×C4—2262no—
209C2×C4—2262no—
210C2×C4D4×D11311yescharacteristic
211C2×C4D4×D11311yescharacteristic
212C2×C4D4×D11311yescharacteristic
213C2×C4C2×C22⋊D11311yescharacteristic
214C2×C4C2×D45211yescharacteristic
215C2×C4#1426864711yescharacteristic
216C8—22no—
217C8—2262no—
218C22#1681359211yescharacteristic
219C22#1681359511yescharacteristic
220C22#1681361811yescharacteristic
221C22Q16×D11312yes—
222C22#1681365112yes—
223C4—42no—
224C4—81no—
225C4—4522no—
226C4—4522no—
227C4—2264no—
228C4#1681359011yescharacteristic
229C4#1681359211yescharacteristic
230C4#1681359511yescharacteristic
231C4#1681359611yescharacteristic
232C2#2029850711yescharacteristic
233C2#2029875512yes—
234C2#2029880712yes—
235C2#2029897611yescharacteristic
236C2#2029898911yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×#103×C113C2
socle, prime radicalC23×C113C2×D4
hypercenterC2×#103D113
hypocenterC113#2016
LCSG ▷ C22×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
88. C2×Dic113Q16semidirect
119. C113#2016semidirect

Maximal subgroups

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

subgroupindex
C22×Dic4522
C22×#142686372
C2×#168136202
C2×#168135452
#202985032
#202983522
C2×#103×C1132
#2016113