Finite Group Databasebeta

← #28406735

Subgroups — #28406735

Order 14464.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D113⋊#108C211yesmaximal, characteristic, complemented
2#20299590C212yesmaximal, complemented
3D113⋊#100C212yesmaximal, complemented
4#20299561C211yesmaximal, characteristic, complemented
5C2×D8×D113C211yesmaximal, characteristic
6D113⋊M16C2212yes—
7D113⋊M16C2211yescharacteristic
8#16813701C2211yescharacteristic
9#16813693—21no—
10#16813692—21no—
11#16813684—24no—
12#16813682—24no—
13#16813676—21no—
14C8×#90673—21no—
15C2×D4×D113C2212yes—
16C2×D904C411yescharacteristic, complemented
17C2×#14268632C412yescomplemented
18D8×D113—21no—
19D8×D113—21no—
20D8×D113—21no—
21D8×D113—21no—
22C2×C8×D113C2211yescharacteristic
23C2×D8×C113C411yescharacteristic, complemented
24#14268657—21no—
25#14268657—22no—
26#14268656—22no—
27#14268656D412yes—
28#14268655—21no—
29#14268655—22no—
30C4⋊#90673D412yes—
31C22⋊#90673—21no—
32C4×#90673—21no—
33C23×D113—22no—
34C2×D452C2×C412yes—
35C2×C22⋊D113—22no—
36D4×D113—22no—
37D4×D113—22no—
38D4×D113—22no—
39D4×D113—22no—
40C2×C4×D113C2311yescharacteristic
41D904—21no—
42D904—21no—
43#14268632—22no—
44#14268632—22no—
45C2×#11744751C2×C411yescharacteristic
46C8×D113D411yescharacteristic
47C8×D113D411yescharacteristic
48C8×D113D411yescharacteristic
49C8×D113D411yescharacteristic
50C2×D4×C113C2×C412yes—
51D8×C113—21no—
52D8×C113—21no—
53C2×C8×C113C2×C411yescharacteristic
54C23×C113—22no—
55C22×D113—22no—
56C22×D113—42no—
57C22×D113—42no—
58C22×D113—84no—
59C22×D113#4111yescharacteristic
60C2×#90673—22no—
61D4×C113—22no—
62D4×C113—22no—
63C2×C4×C113C22×C411yescharacteristic
64C22⋊D113—42no—
65C22⋊D113—42no—
66C2×Dic113C2×D411yescharacteristic
67D452—22no—
68D452—22no—
69C4×D113C2×D411yescharacteristic
70C4×D113C2×D411yescharacteristic
71C4×D113C2×D411yescharacteristic
72C4×D113#4111yescharacteristic
73#11744753—22no—
74#11744753—42no—
75C8×C113C22⋊C411yescharacteristic
76C8×C113C22⋊C411yescharacteristic
77#11744751C22⋊C411yescharacteristic
78#11744751C22⋊C411yescharacteristic
79C22×C113—42no—
80C22×C113—82no—
81C22×C113C4×D411yescharacteristic
82C2×D113—22no—
83C2×D113—42no—
84C2×D113—84no—
85C2×D113—84no—
86C2×D113—82no—
87C2×D113#12111yescharacteristic
88C2×D113#12411yescharacteristic
89#90673—42no—
90C4×C113C2×C22⋊C411yescharacteristic
91C4×C113C4×D411yescharacteristic
92Dic113#12111yescharacteristic
93Dic113#12711yescharacteristic
94C2×C113—21no—
95C2×C113—82no—
96C2×C113#39011yescharacteristic
97D113—21no—
98D113—82no—
99D113#47212yes—
100#1978—1131nomaximal, Sylow
101C113#197811yescharacteristic, complemented, Sylow
102C22×D8—1131no—
103C2×#108—1131no—
104#418—1132no—
105C2×#100—1132no—
106#405—1131no—
107C22×D4—1132no—
108C2×D8—1132no—
109C2×D8—1131no—
110C2×D8—2261no—
111C2×D8—2261no—
112C2×D8—2261no—
113C2×D8—2261no—
114C2×D8#9067311yescharacteristic, complemented
115C2×M16—1131no—
116C2×M16—1132no—
117C22×C8—1131no—
118#117—1131no—
119#108—2261no—
120#108—2261no—
121#102—2264no—
122#100—2264no—
123#97—2261no—
124C4×C8—2261no—
125C24—2262no—
126C2×D4—1132no—
127C2×D4—2262no—
128C2×D4—2262no—
129C2×D4—2262no—
130C2×D4—2262no—
131C2×D4—2262no—
132C2×D4C2×#9067312yes—
133C22×C4—1131no—
134D8—21no—
135D8—21no—
136D8—2262no—
137D8—2262no—
138D8—2261no—
139D8—2261no—
140M16—1132no—
141M16—2262no—
142M16—2262no—
143M16—2261no—
144C2×C8—1131no—
145C2×C8—1131no—
146C2×C8—1131no—
147C2×C8—1131no—
148C2×C8—1131no—
149C2×C8—2262no—
150C2×C8—2261no—
151C2×C8C2×#9067311yescharacteristic
152C4⋊C4—1132no—
153C22⋊C4—2261no—
154C42—2261no—
155C23—22no—
156C23—1131no—
157C23—9044no—
158C23—4522no—
159C23—4522no—
160C23—2262no—
161D4—22no—
162D4—22no—
163D4—4522no—
164D4—4522no—
165D4—2262no—
166D4—2262no—
167C2×C4—1131no—
168C2×C4—1131no—
169C2×C4—1131no—
170C2×C4—1131no—
171C2×C4—1131no—
172C2×C4—2262no—
173C2×C4C22×#9067311yescharacteristic
174C8—1131no—
175C8—1131no—
176C8—4522no—
177C8—2262no—
178C8C22⋊#9067311yescharacteristic
179C8C22⋊#9067311yescharacteristic
180C22—42no—
181C22—82no—
182C22—1131no—
183C22—1131no—
184C22—9042no—
185C22—9044no—
186C22—9044no—
187C22—4522no—
188C22—2262no—
189C22D4×#9067311yescharacteristic
190C4—1131no—
191C4—1131no—
192C4—4522no—
193C4C2×C22⋊#9067311yescharacteristic
194C4D4×#9067311yescharacteristic
195C2—21no—
196C2—82no—
197C2—1132no—
198C2—9042no—
199C2—2261no—
200C2#2029955011yescharacteristic
subgroupG/H
centerC2#20299550
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×D8×C113C4
socleC2×C113#390
prime radicalC2×D8×D113C2
cosocleC2×C4×D113C23
hypercenterC2×D8#90673
hypocenterC113#1978
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D113⋊#108C2semidirect
2. #20299590C2semidirect
3. D113⋊#100C2semidirect
4. #20299561C2semidirect
16. C2×D904C4semidirect
17. C2×#14268632C4semidirect
23. C2×D8×C113C4semidirect
101. C113#1978semidirect
114. C2×D8#90673semidirect

Maximal subgroups

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

subgroupindex
D113⋊#1082
#202995902
D113⋊#1002
#202995612
C2×D8×D1132
#1978113