Finite Group Databasebeta

← #28391724

Subgroups — #28391724

Order 14464.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16813613C211yesmaximal, characteristic
2C2×#16813547C211yesmaximal, characteristic
3C2×#16813545C211yesmaximal, characteristic
4#20298503C211yesmaximal, characteristic
5#20298360C211yesmaximal, characteristic
6#20298352C211yesmaximal, characteristic
7#340×C113C211yesmaximal, characteristic
8C22×Dic226C2211yescharacteristic
9C22×#11744751C2211yescharacteristic
10#16813613—22no—
11#16813613—22no—
12C2×C4⋊Dic113—21no—
13C2×C4⋊Dic113C2211yescharacteristic
14C2×#14268626—21no—
15C2×C4×Dic113C2211yescharacteristic
16#16813547—22no—
17#16813545—22no—
18#16813529—21no—
19#16813529—21no—
20C22×C8×C113C2211yescharacteristic
21C2×C4⋊C4×C113C2211yescharacteristic
22C2×C4⋊C4×C113C2211yescharacteristic
23C2×Dic226—21no—
24C2×Dic226—21no—
25C2×Dic226—21no—
26C2×Dic226—21no—
27C2×Dic226—21no—
28C2×Dic226Q812yes—
29C22×Dic113—21no—
30C22×Dic113—21no—
31C22×Dic113D411yescharacteristic
32C22×Dic113D411yescharacteristic
33C2×#11744751—21no—
34C2×#11744751—21no—
35C2×#11744751—21no—
36C4⋊Dic113—24no—
37C4⋊Dic113—21no—
38C4⋊Dic113D412yes—
39#14268626—24no—
40C4×Dic113—21no—
41C4×Dic113—21no—
42C22×C4×C113—21no—
43C22×C4×C113—21no—
44C22×C4×C113C2311yescharacteristic
45C2×C8×C113—21no—
46C2×C8×C113—21no—
47C2×C8×C113—21no—
48C4⋊C4×C113—21no—
49C4⋊C4×C113—21no—
50C4⋊C4×C113—21no—
51C4⋊C4×C113D412yes—
52C23×C113C2×D411yescharacteristic
53C2×C4×C113—22no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×Q811yescharacteristic
62C2×C4×C113#4111yescharacteristic
63C2×C4×C113#4111yescharacteristic
64C2×C4×C113#4111yescharacteristic
65C2×Dic113—21no—
66C2×Dic113—21no—
67C2×Dic113—22no—
68C2×Dic113—22no—
69C2×Dic113—21no—
70C2×Dic113—21no—
71C2×Dic113—21no—
72C2×Dic113—21no—
73C2×Dic113—41no—
74C2×Dic113—41no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77Dic226—22no—
78Dic226—22no—
79Dic226—41no—
80Dic226—41no—
81C8×C113—41no—
82#11744751—41no—
83C22×C113#12011yescharacteristic
84C22×C113C22⋊Q811yescharacteristic
85C22×C113#12411yescharacteristic
86C22×C113#13511yescharacteristic
87C22×C113#13511yescharacteristic
88C22×C113#13711yescharacteristic
89C22×C113#13711yescharacteristic
90C4×C113—42no—
91C4×C113—81no—
92C4×C113C22⋊Q811yescharacteristic
93C4×C113C22⋊Q811yescharacteristic
94C4×C113#12411yescharacteristic
95C4×C113#12411yescharacteristic
96Dic113—42no—
97Dic113—41no—
98Dic113—41no—
99Dic113—42no—
100C2×C113#39311yescharacteristic
101C2×C113#45211yescharacteristic
102C2×C113#45211yescharacteristic
103C2×C113#47911yescharacteristic
104C2×C113#47911yescharacteristic
105C2×C113#48811yescharacteristic
106C2×C113#49111yescharacteristic
107#2026—1131nomaximal, Sylow
108C113#202611yescharacteristic, complemented, Sylow
109C2×#125—1131no—
110C2×#103—1131no—
111C2×#103—1131no—
112#391—1131no—
113#340—1131no—
114#340D11311yescharacteristic
115#336—1131no—
116C22×Q8—1131no—
117C22×C8—1131no—
118C22×C8C2×D11311yescharacteristic
119#125—2262no—
120#125—2262no—
121C2×C4⋊C4—1131no—
122C2×C4⋊C4—2261no—
123C2×C4⋊C4—2261no—
124C2×C4⋊C4C2×D11311yescharacteristic
125C2×C4⋊C4C2×D11311yescharacteristic
126C2×C42—1131no—
127#103—2262no—
128#103—2262no—
129#95—2261no—
130#95—2261no—
131C2×Q8—1132no—
132C2×Q8—2261no—
133C2×Q8—2261no—
134C2×Q8—2261no—
135C2×Q8—2261no—
136C2×Q8—2261no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—1131no—
140C22×C4—1131no—
141C22×C4—2261no—
142C22×C4—2261no—
143C22×C4C22×D11311yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—2261no—
148C2×C8—2261no—
149C2×C8—2261no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—1132no—
154C4⋊C4—2264no—
155C4⋊C4—2264no—
156C4⋊C4—2261no—
157C4⋊C4D45212yes—
158C42—2261no—
159C42—2261no—
160C23D4×D11311yescharacteristic
161Q8—4521no—
162Q8—4521no—
163Q8—2262no—
164Q8—2262no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—4521no—
172C2×C4—4521no—
173C2×C4—4521no—
174C2×C4—4521no—
175C2×C4—2261no—
176C2×C4—2261no—
177C2×C4—2262no—
178C2×C4—2262no—
179C2×C4—2261no—
180C2×C4—2261no—
181C2×C4—2261no—
182C2×C4—2261no—
183C2×C4D4×D11311yescharacteristic
184C2×C4C2×D45211yescharacteristic
185C2×C4Q8×D11311yescharacteristic
186C2×C4#1426864611yescharacteristic
187C2×C4#1426864711yescharacteristic
188C2×C4#1426864711yescharacteristic
189C8—41no—
190C8—4521no—
191C22#1681359211yescharacteristic
192C22#1681360011yescharacteristic
193C22#1681360811yescharacteristic
194C22#1681364111yescharacteristic
195C22#1681364311yescharacteristic
196C22#1681365111yescharacteristic
197C22#1681365411yescharacteristic
198C4—42no—
199C4—81no—
200C4—4521no—
201C4—4522no—
202C4—4521no—
203C4—4522no—
204C4#1681360011yescharacteristic
205C4#1681360211yescharacteristic
206C4#1681360811yescharacteristic
207C4#1681361011yescharacteristic
208C2#2029851111yescharacteristic
209C2#2029876111yescharacteristic
210C2#2029876311yescharacteristic
211C2#2029890411yescharacteristic
212C2#2029890811yescharacteristic
213C2#2029895111yescharacteristic
214C2#2029896511yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#340×C113C2
socle, prime radicalC23×C113C2×D4
hypercenter#340D113
hypocenterC113#2026
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
108. C113#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#168136132
C2×#168135472
C2×#168135452
#202985032
#202983602
#202983522
#340×C1132
#2026113