Finite Group Databasebeta

← #28402292

Subgroups — #28402292

Order 14464.

484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16813642C212yesmaximal, complemented
2#20299253C211yesmaximal, characteristic, complemented
3#20298977C211yesmaximal, characteristic, complemented
4#20298837C212yesmaximal, complemented
5#20298803C211yesmaximal, characteristic, complemented
6#20298800C211yesmaximal, characteristic, complemented
7#20298760C212yesmaximal, complemented
8#20298758C212yesmaximal, complemented
9C4×#14268632C211yesmaximal, characteristic, complemented
10D4×#11744751C211yesmaximal, characteristic, complemented
11#547×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2212yes—
13#16813642—28no—
14C2×#14268637C2212yes—
15C2×#14268637C2212yes—
16C2×#14268635C2212yes—
17C2×#14268634C2212yes—
18C2×#14268632C2211yescharacteristic
19C22×#11744751C2212yes—
20#16813622C2211yescharacteristic
21#16813604—22no—
22#16813601C2212yes—
23#16813593—21no—
24C4×D452C2211yescharacteristic
25C4⋊C4×D113—21no—
26#16813555C2211yescharacteristic
27C4⋊#11744751C2211yescharacteristic
28#16813546C2212yes—
29#16813545C2212yes—
30#16813543C2211yescharacteristic
31#16813542C2211yescharacteristic
32C22⋊#11744751C2212yes—
33C4×#11744751C2211yescharacteristic
34C2×#41×C113C2212yes—
35C4⋊Q8×C113C2211yescharacteristic
36#123×C113—22no—
37C22⋊Q8×C113C2212yes—
38#121×C113—21no—
39C4×D4×C113C2211yescharacteristic
40C4×D4×C113C2211yescharacteristic
41C2×C4⋊C4×C113—21no—
42#14268647—24no—
43#14268647—42no—
44C2×Dic226C2312yes—
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—22no—
47C2×C4×D113—21no—
48C2×C4×D113—22no—
49#14268637—24no—
50#14268637—42no—
51#14268635—24no—
52#14268634—24no—
53#14268632D414yescomplemented
54C2×#11744751—24no—
55C2×#11744751C2312yes—
56C2×#11744751C2311yescharacteristic
57C2×#11744751C2311yescharacteristic
58C4⋊Dic113—21no—
59C4⋊Dic113—21no—
60C4⋊Dic113C2311yescharacteristic
61#14268626—22no—
62C22⋊Dic113—22no—
63#14268624—21no—
64#41×C113—24no—
65#41×C113—42no—
66C2×Q8×C113C2312yes—
67C2×D4×C113—22no—
68C2×D4×C113D411yescharacteristic
69C2×D4×C113C2311yescharacteristic
70C22×C4×C113—21no—
71C22×C4×C113—22no—
72C22×C4×C113C2312yes—
73C4⋊C4×C113—21no—
74C4⋊C4×C113—22no—
75C4⋊C4×C113—21no—
76C4⋊C4×C113D411yescharacteristic
77C4⋊C4×C113C2311yescharacteristic
78C22⋊C4×C113—22no—
79C22⋊C4×C113—21no—
80C22⋊C4×C113D412yes—
81C42×C113C2311yescharacteristic
82C23×C113—21no—
83C23×C113C2×D412yes—
84C22×D113—21no—
85Q8×C113—22no—
86Q8×C113—22no—
87D4×C113—22no—
88D4×C113—21no—
89D4×C113—44no—
90D4×C113C2×D412yes—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113—21no—
94C2×C4×C113—22no—
95C2×C4×C113—44no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D411yescharacteristic
98C2×C4×C113C2×D412yes—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2411yescharacteristic
101C22⋊D113—44no—
102C2×Dic113—21no—
103C2×Dic113—22no—
104D452—21no—
105D452C2×D412yes—
106C4×D113—44no—
107C4×D113—42no—
108Dic226—22no—
109Dic226—22no—
110#11744751—22no—
111#11744751—21no—
112#11744751C2×D412yes—
113C22×C113—22no—
114C22×C113—22no—
115C22×C113—22no—
116C22×C113—22no—
117C22×C113—41no—
118C22×C113—41no—
119C22×C113C22×D411yescharacteristic
120C2×D113—22no—
121C2×D113—41no—
122C2×D113—41no—
123C4×C113—22no—
124C4×C113—21no—
125C4×C113—42no—
126C4×C113—41no—
127C4×C113#13512yescomplemented
128C4×C113C22×D411yescharacteristic
129C4×C113H(5,𝔽2)11yescharacteristic
130Dic113—42no—
131Dic113—41no—
132C2×C113—42no—
133C2×C113—42no—
134C2×C113D4211yescharacteristic
135C2×C113C2×#13511yescharacteristic
136C2×C113#57811yescharacteristic
137D113—42no—
138#3283—1131nomaximal, Sylow
139C113#328311yescharacteristic, complemented, Sylow
140C2×#135—1132no—
141#547—1131no—
142#547D11311yescharacteristic, complemented
143#494—1131no—
144#467—1132no—
145#461—1131no—
146#461—1131no—
147#452—1132no—
148#452—1132no—
149C4×D8—1131no—
150C8×D4—1131no—
151C2×#41—1132no—
152C2×#41C2×D11312yes—
153#135—2268no—
154C2×Q16—1132no—
155C2×Q16—1132no—
156C2×SD16—1132no—
157C2×SD16—1132no—
158C2×D8—1131no—
159C22×C8—1132no—
160C4⋊Q8—1131no—
161C4⋊Q8C2×D11311yescharacteristic
162#123—22no—
163#123—2262no—
164C22⋊Q8—1132no—
165C22⋊Q8C2×D11312yes—
166#121—21no—
167#121—2261no—
168C4×D4—1131no—
169C4×D4C2×D11311yescharacteristic
170C4×D4C2×D11311yescharacteristic
171C2×C4⋊C4—21no—
172C2×C4⋊C4—2261no—
173#107—1131no—
174C4⋊C8—1131no—
175#103—1132no—
176#103—1132no—
177#102—1131no—
178#102—1131no—
179C22⋊C8—1132no—
180C4×C8—1131no—
181#41—24no—
182#41—42no—
183#41—4522no—
184#41—2264no—
185C2×Q8—1132no—
186C2×Q8C22×D11312yes—
187C2×D4—22no—
188C2×D4—1131no—
189C2×D4—2262no—
190C2×D4C22⋊D11311yescharacteristic
191C2×D4C22×D11311yescharacteristic
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—2261no—
195C22×C4—2262no—
196C22×C4C22×D11312yes—
197Q16—4522no—
198Q16—2264no—
199SD16—2264no—
200SD16—2264no—
201D8—1134no—
202C2×C8—1131no—
203C2×C8—1131no—
204C2×C8—1132no—
205C2×C8—2264no—
206C4⋊C4—21no—
207C4⋊C4—22no—
208C4⋊C4—21no—
209C4⋊C4—1131no—
210C4⋊C4—2261no—
211C4⋊C4—2262no—
212C4⋊C4—2261no—
213C4⋊C4C22⋊D11311yescharacteristic
214C4⋊C4C22×D11311yescharacteristic
215C22⋊C4—22no—
216C22⋊C4—21no—
217C22⋊C4—2262no—
218C22⋊C4—2261no—
219C22⋊C4C22⋊D11312yes—
220C42C22×D11311yescharacteristic
221C23—21no—
222C23—2261no—
223C23C2×C22⋊D11312yes—
224Q8—22no—
225Q8—22no—
226Q8—2262no—
227Q8—2262no—
228D4—22no—
229D4—21no—
230D4—44no—
231D4—1132no—
232D4—4524no—
233D4—2261no—
234D4D4×D11312yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—44no—
240C2×C4—42no—
241C2×C4—4524no—
242C2×C4—4522no—
243C2×C4—2261no—
244C2×C4—2262no—
245C2×C4C2×C22⋊D11311yescharacteristic
246C2×C4C2×C22⋊D11312yes—
247C2×C4C2×C22⋊D11311yescharacteristic
248C2×C4C23×D11311yescharacteristic
249C8—1132no—
250C8—2262no—
251C8—2261no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—4521no—
259C22—4521no—
260C22—2262no—
261C22C22×C22⋊D11311yescharacteristic
262C4—21no—
263C4—22no—
264C4—41no—
265C4—42no—
266C4—4521no—
267C4—4522no—
268C4#1681364212yescomplemented
269C4C2×D4×D11311yescharacteristic
270C4#1681366711yescharacteristic
271C2—42no—
272C2—42no—
273C2—4522no—
274C2D4×C22⋊D11311yescharacteristic
275C2C2×#1681364211yescharacteristic
276C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#547×C113C2
socleC22×C113C22×D4
hypercenter#547D113
hypocenterC113#3283
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#16813642C2semidirect
2. #20299253C2semidirect
3. #20298977C2semidirect
4. #20298837C2semidirect
5. #20298803C2semidirect
6. #20298800C2semidirect
7. #20298760C2semidirect
8. #20298758C2semidirect
9. C4×#14268632C2semidirect
10. D4×#11744751C2semidirect
11. #547×C113C2semidirect
53. #14268632D4semidirect
127. C4×C113#135semidirect
139. C113#3283semidirect
142. #547D113semidirect
268. C4#16813642semidirect

Maximal subgroups

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

subgroupindex
C2×#168136422
#202992532
#202989772
#202988372
#202988032
#202988002
#202987602
#202987582
C4×#142686322
D4×#117447512
#547×C1132
#3283113