Finite Group Databasebeta

← #28391723

Subgroups — #28391723

Order 14464.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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×#16813546C211yesmaximal, characteristic
3#20298505C211yesmaximal, characteristic
4#20298361C211yesmaximal, characteristic
5#20298360C211yesmaximal, characteristic
6#20298352C211yesmaximal, characteristic
7C2×#103×C113C211yesmaximal, characteristic
8C22×#11744751C2211yescharacteristic
9#16813613—22no—
10#16813613—22no—
11C2×C4⋊Dic113—21no—
12C2×C4⋊Dic113C2211yescharacteristic
13C2×C4⋊Dic113C2211yescharacteristic
14C2×#14268626—21no—
15C2×C4×Dic113C2211yescharacteristic
16#16813546—22no—
17#16813529—21no—
18#16813529—21no—
19C22×Q8×C113C2211yescharacteristic
20C22×C8×C113C2211yescharacteristic
21C2×C4⋊C4×C113C2211yescharacteristic
22#103×C113—22no—
23C22×Dic113—21no—
24C22×Dic113—21no—
25C22×Dic113D411yescharacteristic
26C22×Dic113D411yescharacteristic
27C2×#11744751—21no—
28C2×#11744751—21no—
29C2×#11744751—21no—
30C4⋊Dic113—24no—
31C4⋊Dic113—21no—
32C4⋊Dic113—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113D412yes—
35#14268626—24no—
36C4×Dic113—21no—
37C4×Dic113—21no—
38C2×Q8×C113—21no—
39C2×Q8×C113—21no—
40C2×Q8×C113—21no—
41C2×Q8×C113—21no—
42C2×Q8×C113—21no—
43C2×Q8×C113Q812yes—
44C22×C4×C113—21no—
45C22×C4×C113—21no—
46C22×C4×C113C2311yescharacteristic
47C2×C8×C113—21no—
48C2×C8×C113—21no—
49C2×C8×C113—21no—
50C4⋊C4×C113—21no—
51C4⋊C4×C113D412yes—
52C23×C113C2×D411yescharacteristic
53Q8×C113—22no—
54Q8×C113—22no—
55Q8×C113—41no—
56Q8×C113—41no—
57C2×C4×C113—22no—
58C2×C4×C113—22no—
59C2×C4×C113—41no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113C2×D411yescharacteristic
65C2×C4×C113C2×Q811yescharacteristic
66C2×C4×C113#4111yescharacteristic
67C2×C4×C113#4111yescharacteristic
68C2×C4×C113#4111yescharacteristic
69C2×Dic113—21no—
70C2×Dic113—21no—
71C2×Dic113—22no—
72C2×Dic113—21no—
73C2×Dic113—21no—
74C2×Dic113—21no—
75C2×Dic113—21no—
76C2×Dic113—41no—
77C2×Dic113—41no—
78C2×Dic113—41no—
79C2×Dic113—41no—
80C2×Dic113—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—42no—
92C4×C113C22⋊Q811yescharacteristic
93C4×C113C22⋊Q811yescharacteristic
94C4×C113#12411yescharacteristic
95C4×C113#12411yescharacteristic
96Dic113—41no—
97Dic113—41no—
98Dic113—42no—
99Dic113—81no—
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×#103D11311yescharacteristic
112#391—1131no—
113#340—1131no—
114#340—1131no—
115#336—1131no—
116C22×Q8C2×D11311yescharacteristic
117C22×C8—1131no—
118C22×C8C2×D11311yescharacteristic
119#125—2262no—
120#125—2262no—
121C2×C4⋊C4—1131no—
122C2×C4⋊C4—1131no—
123C2×C4⋊C4—2261no—
124C2×C4⋊C4—2261no—
125C2×C4⋊C4C2×D11311yescharacteristic
126C2×C42—1131no—
127#103—22no—
128#103—2262no—
129#95—2261no—
130#95—2261no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic22612yes—
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—1132no—
152C4⋊C4—2264no—
153C4⋊C4—2264no—
154C4⋊C4—2261no—
155C4⋊C4—2261no—
156C4⋊C4—2261no—
157C4⋊C4C22⋊D11312yes—
158C42—2261no—
159C42—2261no—
160C23D4×D11311yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
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—4521no—
176C2×C4—2261no—
177C2×C4—2261no—
178C2×C4—2262no—
179C2×C4—2261no—
180C2×C4—2261no—
181C2×C4—2261no—
182C2×C4—2261no—
183C2×C4D4×D11311yescharacteristic
184C2×C4C2×C22⋊D11311yescharacteristic
185C2×C4C2×Dic22611yescharacteristic
186C2×C4#1426864611yescharacteristic
187C2×C4#1426864611yescharacteristic
188C2×C4#1426864711yescharacteristic
189C8—41no—
190C8—4521no—
191C22#1681359011yescharacteristic
192C22#1681359911yescharacteristic
193C22#1681360811yescharacteristic
194C22#1681364311yescharacteristic
195C22#1681364511yescharacteristic
196C22#1681365111yescharacteristic
197C22#1681365411yescharacteristic
198C4—42no—
199C4—42no—
200C4—9041no—
201C4—4521no—
202C4—4522no—
203C4—4521no—
204C4#1681359911yescharacteristic
205C4#1681360111yescharacteristic
206C4#1681360811yescharacteristic
207C4#1681360911yescharacteristic
208C2#2029851011yescharacteristic
209C2#2029875711yescharacteristic
210C2#2029875911yescharacteristic
211C2#2029890311yescharacteristic
212C2#2029890711yescharacteristic
213C2#2029895411yescharacteristic
214C2#2029896511yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×#103×C113C2
socle, prime radicalC23×C113C2×D4
hypercenterC2×#103D113
hypocenterC113#2026
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
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×#168135462
#202985052
#202983612
#202983602
#202983522
C2×#103×C1132
#2026113