Finite Group Databasebeta

← #28402290

Subgroups — #28402290

Order 14464.

484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16813641C211yesmaximal, characteristic, complemented
2#20299247C212yesmaximal, complemented
3#20298976C211yesmaximal, characteristic, complemented
4#20298839C211yesmaximal, characteristic, complemented
5#20298836C211yesmaximal, characteristic, complemented
6#20298801C212yesmaximal, complemented
7#20298760C212yesmaximal, complemented
8#20298757C212yesmaximal, complemented
9D8×Dic113C211yesmaximal, characteristic, complemented
10C8×C22⋊D113C211yesmaximal, characteristic, complemented
11C2×#135×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2212yes—
13#16813641—24no—
14C2×Dic452C2211yescharacteristic
15C2×#14268637C2212yes—
16C2×#14268635C2212yes—
17C2×C8×D113C2211yescharacteristic
18#16813620C2212yes—
19#16813605—22no—
20#16813603—22no—
21#16813601C2212yes—
22#16813598C2212yes—
23#16813594—22no—
24D4×Dic113C2212yes—
25C4×C22⋊D113C2211yescharacteristic
26C2×#14268626—22no—
27#16813556C2211yescharacteristic
28#16813551C2211yescharacteristic
29#16813547C2212yes—
30#16813546C2212yes—
31#16813543C2212yes—
32C22⋊#11744751C2211yescharacteristic
33#16813534C2211yescharacteristic
34C8×Dic113C2211yescharacteristic
35C2×#41×C113C2212yes—
36#135×C113—24no—
37C2×Q16×C113C2211yescharacteristic
38C2×SD16×C113C2212yes—
39C2×D8×C113C2211yescharacteristic
40C22×C8×C113C2211yescharacteristic
41#14268646—24no—
42#14268646—42no—
43C2×Dic226C2312yes—
44C2×C22⋊D113—22no—
45C2×C22⋊D113D411yescharacteristic
46C22×Dic113—22no—
47C22×Dic113—22no—
48C2×C4×D113C2311yescharacteristic
49Dic452—22no—
50#14268637—42no—
51#14268635—24no—
52C2×#11744751C2311yescharacteristic
53C2×#11744751C2311yescharacteristic
54C8×D113—22no—
55C4⋊Dic113C2312yes—
56#14268626—22no—
57#14268626—22no—
58#14268626—22no—
59#14268626—22no—
60#14268626D411yescharacteristic
61C22⋊Dic113—22no—
62C22⋊Dic113—22no—
63C22⋊Dic113D411yescharacteristic
64#14268624—22no—
65#14268624D411yescharacteristic
66C4×Dic113C2311yescharacteristic
67#41×C113—24no—
68#41×C113—42no—
69C2×Q8×C113C2312yes—
70C2×D4×C113—22no—
71C2×D4×C113C2312yes—
72C22×C4×C113—22no—
73C22×C4×C113C2311yescharacteristic
74Q16×C113—22no—
75SD16×C113—24no—
76D8×C113D414yescomplemented
77C2×C8×C113—22no—
78C2×C8×C113C2311yescharacteristic
79C2×C8×C113C2311yescharacteristic
80C23×C113—22no—
81C23×C113C2×D411yescharacteristic
82C22×D113C2×D411yescharacteristic
83Q8×C113—22no—
84Q8×C113—22no—
85D4×C113—22no—
86D4×C113—44no—
87D4×C113C2×D414yes—
88C2×C4×C113—21no—
89C2×C4×C113—21no—
90C2×C4×C113—22no—
91C2×C4×C113—44no—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2411yescharacteristic
94C22⋊D113—22no—
95C22⋊D113—44no—
96C2×Dic113—22no—
97C2×Dic113—22no—
98C2×Dic113—44no—
99C2×Dic113—44no—
100C2×Dic113C2×D411yescharacteristic
101C2×Dic113C2×D411yescharacteristic
102C2×Dic113C2×D411yescharacteristic
103C4×D113—21no—
104C4×D113—21no—
105Dic226—22no—
106Dic226—22no—
107C8×C113—21no—
108C8×C113C2×D412yes—
109#11744751—21no—
110#11744751—21no—
111C22×C113—24no—
112C22×C113—21no—
113C22×C113—21no—
114C22×C113—21no—
115C22×C113—42no—
116C22×C113—42no—
117C22×C113C22×D411yescharacteristic
118C2×D113—21no—
119C2×D113—21no—
120C2×D113—21no—
121C4×C113—21no—
122C4×C113—42no—
123C4×C113C22×D411yescharacteristic
124C4×C113H(5,𝔽2)11yescharacteristic
125Dic113—21no—
126Dic113—21no—
127Dic113—42no—
128Dic113—42no—
129Dic113#13512yescomplemented
130C2×C113—41no—
131C2×C113—44no—
132C2×C113D4211yescharacteristic
133C2×C113C2×#13511yescharacteristic
134C2×C113#57811yescharacteristic
135D113—41no—
136#3283—1131nomaximal, Sylow
137C113#328311yescharacteristic, complemented, Sylow
138C2×#135—1131no—
139C2×#135D11311yescharacteristic, complemented
140#547—1132no—
141#494—1131no—
142#467—1131no—
143#467—1131no—
144#461—1132no—
145#452—1132no—
146#452—1132no—
147C4×D8—1131no—
148C8×D4—1131no—
149C2×#41—1132no—
150C2×#41C2×D11312yes—
151#135—24no—
152#135—2264no—
153C2×Q16—1132no—
154C2×Q16—1131no—
155C2×Q16C2×D11311yescharacteristic
156C2×SD16—1132no—
157C2×SD16C2×D11312yes—
158C2×D8C2×D11311yescharacteristic
159C22×C8—1131no—
160C22×C8C2×D11311yescharacteristic
161C4⋊Q8—1132no—
162#123—2262no—
163#123—2262no—
164C22⋊Q8—1132no—
165C22⋊Q8—1132no—
166#121—2262no—
167C4×D4—1131no—
168C4×D4—1132no—
169C2×C4⋊C4—2262no—
170#107—1131no—
171C4⋊C8—1131no—
172#103—1132no—
173#103—1132no—
174#102—1132no—
175C22⋊C8—1131no—
176C22⋊C8—1131no—
177C4×C8—1131no—
178#41—24no—
179#41—42no—
180#41—4522no—
181#41—2264no—
182C2×Q8—1132no—
183C2×Q8C22×D11312yes—
184C2×D4—22no—
185C2×D4—1131no—
186C2×D4—2262no—
187C2×D4C22×D11312yes—
188C22×C4—22no—
189C22×C4—1131no—
190C22×C4—2262no—
191C22×C4—2262no—
192C22×C4C22×D11311yescharacteristic
193Q16—22no—
194Q16—4522no—
195Q16—2262no—
196SD16—24no—
197SD16—2264no—
198D8C22⋊D11314yescomplemented
199C2×C8—22no—
200C2×C8—1131no—
201C2×C8—1131no—
202C2×C8—2262no—
203C2×C8C22×D11311yescharacteristic
204C2×C8C22×D11311yescharacteristic
205C4⋊C4—1131no—
206C4⋊C4—1132no—
207C4⋊C4—2262no—
208C4⋊C4—2262no—
209C4⋊C4—2262no—
210C4⋊C4—2262no—
211C22⋊C4—1131no—
212C22⋊C4—1131no—
213C22⋊C4—2262no—
214C22⋊C4—2262no—
215C22⋊C4—2262no—
216C42—1131no—
217C23—22no—
218C23—1131no—
219C23D4×D11311yescharacteristic
220Q8—22no—
221Q8—22no—
222Q8—2262no—
223Q8—2262no—
224D4—22no—
225D4—44no—
226D4—4524no—
227D4—2262no—
228D4C2×C22⋊D11314yes—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—44no—
233C2×C4—1131no—
234C2×C4—1131no—
235C2×C4—1131no—
236C2×C4—4524no—
237C2×C4—4524no—
238C2×C4—2262no—
239C2×C4—2262no—
240C2×C4—2261no—
241C2×C4—2261no—
242C2×C4D4×D11311yescharacteristic
243C2×C4C23×D11311yescharacteristic
244C8—21no—
245C8—2261no—
246C8—2261no—
247C8C2×C22⋊D11312yes—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—24no—
252C22—42no—
253C22—42no—
254C22—2261no—
255C22—2261no—
256C22—2261no—
257C22C2×D4×D11311yescharacteristic
258C4—21no—
259C4—42no—
260C4—1132no—
261C4—4522no—
262C4—4522no—
263C4—2261no—
264C4—2261no—
265C4C22×C22⋊D11311yescharacteristic
266C4#1681366711yescharacteristic
267C2—41no—
268C2—44no—
269C2—4521no—
270C2D4×C22⋊D11311yescharacteristic
271C2#135×D11311yescharacteristic
272C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#135×C113C2
socleC22×C113C22×D4
hypercenterC2×#135D113
hypocenterC113#3283
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#16813641C2semidirect
2. #20299247C2semidirect
3. #20298976C2semidirect
4. #20298839C2semidirect
5. #20298836C2semidirect
6. #20298801C2semidirect
7. #20298760C2semidirect
8. #20298757C2semidirect
9. D8×Dic113C2semidirect
10. C8×C22⋊D113C2semidirect
11. C2×#135×C113C2semidirect
76. D8×C113D4semidirect
129. Dic113#135semidirect
137. C113#3283semidirect
139. C2×#135D113semidirect
198. D8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136412
#202992472
#202989762
#202988392
#202988362
#202988012
#202987602
#202987572
D8×Dic1132
C8×C22⋊D1132
C2×#135×C1132
#3283113