Finite Group Databasebeta

← #28399055

Subgroups — #28399055

Order 14464.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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×#16813669C211yesmaximal, characteristic
2#20299364C212yesmaximal, complemented
3#20298582C211yesmaximal, characteristic, complemented
4#20298579C214yesmaximal, complemented
5C2×#16813540C212yesmaximal, complemented
6#101×D113C214yesmaximal, complemented
7#413×C113C211yesmaximal, characteristic, complemented
8#16813669—24no—
9#16813669—24no—
10C2×#14268647C412yes—
11C2×#14268647C2211yescharacteristic
12C2×#14268646C414yes—
13C2×#14268646C2212yes—
14C22×Dic226C412yes—
15C22×Dic226C2211yescharacteristic
16C2×Q8×D113C2212yes—
17#16813630—24no—
18#16813628—24no—
19C2×#14268631C2212yes—
20M16×D113C2218yes—
21#16813541C2212yes—
22#16813540C2218yes—
23#16813539C2212yes—
24C2×#41×C113C2211yescharacteristic
25C2×M16×C113C2212yes—
26#101×C113C2212yes—
27#100×C113C2212yes—
28#14268647—24no—
29#14268647—24no—
30#14268647D414yes—
31#14268647D414yes—
32#14268646—216no—
33#14268646—28no—
34C2×Dic226—22no—
35C2×Dic226—22no—
36C2×Dic226—24no—
37C2×Dic226—24no—
38C2×Dic226C2×C414yes—
39C2×Dic226C2×C412yes—
40C2×Dic226C2×C411yescharacteristic
41C2×Dic226C2312yes—
42Q8×D113—28no—
43C2×D452C2×C411yescharacteristic
44C2×C22⋊D113C2×C414yes—
45C2×C22⋊D113C2×C412yes—
46C22×Dic113C2×C414yes—
47C22×Dic113C2×C412yes—
48C2×C4×D113C2×C414yes—
49C2×C4×D113C2312yes—
50#14268631—22no—
51#14268631C2314yes—
52#14268630—28no—
53C2×#11744751—22no—
54C8×D113—28no—
55#41×C113—22no—
56#41×C113—22no—
57C2×Q8×C113C2311yescharacteristic
58C2×D4×C113C2×C412yes—
59C2×D4×C113C2311yescharacteristic
60C22×C4×C113C2×C412yes—
61C22×C4×C113C2311yescharacteristic
62M16×C113—22no—
63M16×C113C2314yes—
64C2×C8×C113—22no—
65C23×C113C22×C412yes—
66C23×C113C22×C411yescharacteristic
67C22×D113C22×C412yes—
68Q8×C113—22no—
69D4×C113—24no—
70D4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113C22×C412yes—
74C2×C4×C113C22×C411yescharacteristic
75C2×C4×C113C2×D412yes—
76C2×C4×C113C2×D412yes—
77C2×C4×C113C2411yescharacteristic
78C22⋊D113—28no—
79C22⋊D113C22⋊C418yes—
80C2×Dic113—24no—
81C2×Dic113—28no—
82C2×Dic113C22×C414yes—
83C2×Dic113C22×C412yes—
84D452C22⋊C412yes—
85D452C22⋊C412yes—
86C4×D113—28no—
87C4×D113C2×D418yes—
88Dic226—22no—
89Dic226—22no—
90Dic226—24no—
91Dic226—28no—
92Dic226C22⋊C412yes—
93Dic226C22⋊C412yes—
94C8×C113—24no—
95#11744751—24no—
96C22×C113—22no—
97C22×C113—41no—
98C22×C113—42no—
99C22×C113C2×C22⋊C412yes—
100C22×C113C23×C411yescharacteristic
101C2×D113—42no—
102C2×D113C2×C22⋊C414yes—
103C4×C113—22no—
104C4×C113C2×C22⋊C411yescharacteristic
105C4×C113C2×C22⋊C411yescharacteristic
106C4×C113C22×D412yes—
107Dic113—24no—
108Dic113C2×C22⋊C414yes—
109C2×C113—21no—
110C2×C113—22no—
111C2×C113—42no—
112C2×C113C22×C22⋊C411yescharacteristic
113D113—24no—
114#2889—1131nomaximal, Sylow
115C113#288911yescharacteristic, complemented, Sylow
116C2×2−1+4—1131no—
117#568—1132no—
118#413—1131no—
119#413—1134no—
120#413D11311yescharacteristic, complemented
121C2×#101—1132no—
122C2×#101—1134no—
1232−1+4—2264no—
1242−1+4—2264no—
125C2×#41—1134no—
126C2×#41—1132no—
127C2×#41—1132no—
128C2×#41—1131no—
129C2×#41C2×D11311yescharacteristic
130C22×Q8—1132no—
131C22×Q8—1132no—
132C22×Q8—1131no—
133#131—2264no—
134#131—2264no—
135C2×M16—1132no—
136C2×M16—1138no—
137C2×M16C2×D11312yes—
138#101—1132no—
139#101—1138no—
140#101C2×D11312yes—
141#100—1132no—
142#100C2×D11312yes—
143#41—22no—
144#41—22no—
145#41—1134no—
146#41—1134no—
147#41—2264no—
148#41—2264no—
149#41—2268no—
150#41—22616no—
151C2×Q8—1131no—
152C2×Q8—1134no—
153C2×Q8—1132no—
154C2×Q8—1132no—
155C2×Q8—2264no—
156C2×Q8—2264no—
157C2×Q8—2268no—
158C2×Q8—2262no—
159C2×Q8—2262no—
160C2×Q8C22×D11311yescharacteristic
161C2×D4—1132no—
162C2×D4—1134no—
163C2×D4—1131no—
164C2×D4C4×D11312yes—
165C2×D4C22×D11311yescharacteristic
166C22×C4—1132no—
167C22×C4—1134no—
168C22×C4—1132no—
169C22×C4—1134no—
170C22×C4C4×D11312yes—
171C22×C4C22×D11311yescharacteristic
172M16—22no—
173M16—1134no—
174M16—2268no—
175M16—2262no—
176M16C22×D11314yes—
177C2×C8—22no—
178C2×C8—2268no—
179C2×C8—2262no—
180C23—1132no—
181C23C2×C4×D11312yes—
182C23C2×C4×D11311yescharacteristic
183Q8—22no—
184Q8—1132no—
185Q8—1132no—
186Q8—2268no—
187Q8—2262no—
188Q8—2262no—
189Q8—2264no—
190D4—24no—
191D4—22no—
192D4—1138no—
193D4—1132no—
194D4—1132no—
195D4—2268no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—1132no—
199C2×C4—1138no—
200C2×C4—1134no—
201C2×C4—2268no—
202C2×C4—2268no—
203C2×C4—2264no—
204C2×C4C2×C4×D11312yes—
205C2×C4C2×C4×D11311yescharacteristic
206C2×C4D4×D11312yes—
207C2×C4D4×D11312yes—
208C2×C4C23×D11311yescharacteristic
209C8—24no—
210C8—2264no—
211C22—22no—
212C22—41no—
213C22—42no—
214C22—1134no—
215C22—4522no—
216C22C22⋊C4×D11312yes—
217C22C22×C4×D11311yescharacteristic
218C4—22no—
219C4—1134no—
220C4—2264no—
221C4C22⋊C4×D11311yescharacteristic
222C4C22⋊C4×D11311yescharacteristic
223C4C2×D4×D11312yes—
224C2—21no—
225C2—22no—
226C2—42no—
227C2—2264no—
228C2C2×C22⋊C4×D11311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D113
commutatorC22×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#413×C113C2
socleC2×C113C22×C22⋊C4
prime radicalC2×#16813669C2
cosocleC2×C4×C113C24
hypercenter#413D113
hypocenterC113#2889
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #20299364C2semidirect
3. #20298582C2semidirect
4. #20298579C2semidirect
5. C2×#16813540C2semidirect
6. #101×D113C2semidirect
7. #413×C113C2semidirect
115. C113#2889semidirect
120. #413D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136692
#202993642
#202985822
#202985792
C2×#168135402
#101×D1132
#413×C1132
#2889113