Finite Group Databasebeta

← #28400105

Subgroups — #28400105

Order 14464.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813655C211yesmaximal, characteristic
2C22×Dic452C211yesmaximal, characteristic, complemented
3#20299174C211yesmaximal, characteristic
4#20299075C211yesmaximal, characteristic, complemented
5#20298821C214yesmaximal, complemented
6#20298809C214yesmaximal, complemented
7#20298608C211yesmaximal, characteristic, complemented
8#20298595C211yesmaximal, characteristic
9#424×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C22×Dic226C2211yescharacteristic
12C22×Dic226C2211yescharacteristic
13#16813655—24no—
14C2×Dic452—24no—
15C2×Dic452C2212yes—
16C2×Dic452C2214yes—
17C2×#14268636C2212yes—
18#16813622C2212yes—
19#16813610C2212yes—
20#16813606—22no—
21#16813602—22no—
22C4×Dic226C2214yes—
23#16813587—22no—
24#16813581C2211yescharacteristic
25#16813578—22no—
26#16813547C2212yes—
27#16813547C2214yes—
28#16813544C2212yes—
29C2×M16×C113C2211yescharacteristic
30C22×C8×C113C2211yescharacteristic
31#117×C113C2211yescharacteristic
32C4⋊C8×C113C2214yes—
33#14268647—22no—
34#14268647—22no—
35C2×Dic226—21no—
36C2×Dic226—22no—
37C2×Dic226—22no—
38C2×Dic226—22no—
39C2×Dic226—21no—
40C2×Dic226D414yes—
41C2×Dic226C2312yes—
42C2×Dic226C2311yescharacteristic
43C2×Dic226C2312yes—
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—21no—
46C22×Dic113—21no—
47C22×Dic113—21no—
48C2×C4×D113—21no—
49Dic452—28no—
50Dic452—24no—
51#14268636—24no—
52C4⋊Dic113—24no—
53C4⋊Dic113C2312yes—
54#14268626—24no—
55C22⋊Dic113—21no—
56#14268624—24no—
57C4×Dic113—24no—
58C4×Dic113—21no—
59C22×C4×C113C2311yescharacteristic
60M16×C113—22no—
61C2×C8×C113—22no—
62C2×C8×C113C2312yes—
63C2×C8×C113C2312yes—
64C4⋊C4×C113D412yes—
65C22⋊C4×C113D412yes—
66C42×C113C2312yes—
67C23×C113C2×D411yescharacteristic
68C22×D113—21no—
69C2×C4×C113C2×D412yes—
70C2×C4×C113C2×D414yes—
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113#4112yes—
73C2×C4×C113C2411yescharacteristic
74C22⋊D113—42no—
75C2×Dic113—24no—
76C2×Dic113—22no—
77C2×Dic113—22no—
78C2×Dic113—22no—
79C2×Dic113—21no—
80C2×Dic113—42no—
81D452—21no—
82D452—21no—
83C4×D113—42no—
84Dic226—24no—
85Dic226—22no—
86Dic226—22no—
87Dic226—21no—
88Dic226—22no—
89Dic226—21no—
90Dic226—42no—
91Dic226C2×D414yes—
92C8×C113—22no—
93C8×C113—22no—
94C22×C113—22no—
95C22×C113#12112yes—
96C22×C113C22×D411yescharacteristic
97C2×D113—41no—
98C2×D113—42no—
99C4×C113—24no—
100C4×C113#12112yes—
101C4×C113C22×D411yescharacteristic
102C4×C113C2×#4111yescharacteristic
103Dic113—24no—
104Dic113—42no—
105Dic113—41no—
106Dic113—42no—
107C2×C113—22no—
108C2×C113C2×#12111yescharacteristic
109C2×C113#57812yes—
110D113—81no—
111#3044—1131nomaximal, Sylow
112C113#304411yescharacteristic, complemented, Sylow
113C2×#137—1131no—
114C22×Q16—1131no—
115#536—1131no—
116#519—1131no—
117#464—1134no—
118#462—1134no—
119#424D11311yescharacteristic, complemented
120#419—1131no—
121#416—1131no—
122C2×#41—1131no—
123C22×Q8—1131no—
124C22×Q8—1131no—
125#137—2264no—
126C2×Q16—1134no—
127C2×Q16—1132no—
128C2×Q16—2264no—
129C2×SD16—1132no—
130C2×M16C2×D11311yescharacteristic
131C22×C8C2×D11311yescharacteristic
132C4⋊Q8—1132no—
133#124—1132no—
134#123—2262no—
135C22⋊Q8—2262no—
136C4×Q8—1134no—
137C4×Q8—2262no—
138#117—1131no—
139#117—2262no—
140#117C2×D11311yescharacteristic
141C4⋊C8C2×D11314yes—
142#103—1132no—
143#103—1134no—
144#102—1132no—
145#41—2262no—
146#41—2262no—
147C2×Q8—1134no—
148C2×Q8—1132no—
149C2×Q8—1132no—
150C2×Q8—1131no—
151C2×Q8—2262no—
152C2×Q8—2262no—
153C2×Q8—2261no—
154C2×Q8—2261no—
155C2×Q8—2262no—
156C2×D4—1131no—
157C2×D4—2261no—
158C22×C4—2261no—
159C22×C4—2261no—
160C22×C4—2261no—
161C22×C4C22×D11311yescharacteristic
162Q16—2268no—
163Q16—2264no—
164SD16—2264no—
165M16—22no—
166C2×C8—22no—
167C2×C8C22×D11312yes—
168C2×C8C22×D11312yes—
169C4⋊C4—1132no—
170C4⋊C4—2264no—
171C4⋊C4—2264no—
172C4⋊C4D45212yes—
173C22⋊C4—2261no—
174C22⋊C4—2264no—
175C22⋊C4D45212yes—
176C42—2261no—
177C42—2264no—
178C42C22×D11312yes—
179C23—2261no—
180C23C2×D45211yescharacteristic
181Q8—1134no—
182Q8—4522no—
183Q8—2262no—
184Q8—2261no—
185Q8—2262no—
186Q8—2261no—
187Q8—2264no—
188Q8—2262no—
189D4—4522no—
190D4—2261no—
191D4—2261no—
192C2×C4—4522no—
193C2×C4—4522no—
194C2×C4—2262no—
195C2×C4—2262no—
196C2×C4—2261no—
197C2×C4—2264no—
198C2×C4—2262no—
199C2×C4D4×D11312yes—
200C2×C4C2×D45214yes—
201C2×C4C2×D45211yescharacteristic
202C2×C4#1426864812yes—
203C2×C4C23×D11311yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—4521no—
208C22—4522no—
209C22#1681359712yes—
210C22C22×D45211yescharacteristic
211C4—24no—
212C4—4521no—
213C4—4522no—
214C4—4522no—
215C4—2264no—
216C4#1681359712yes—
217C4C2×D4×D11311yescharacteristic
218C4C2×#1426864811yescharacteristic
219C2—22no—
220C2—9041no—
221C2C2×#1681359711yescharacteristic
222C2#2029941512yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#424×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#424D113
hypocenterC113#3044
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic452C2semidirect
4. #20299075C2semidirect
5. #20298821C2semidirect
6. #20298809C2semidirect
7. #20298608C2semidirect
9. #424×C113C2semidirect
112. C113#3044semidirect
119. #424D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
C22×Dic4522
#202991742
#202990752
#202988212
#202988092
#202986082
#202985952
#424×C1132
#3044113