Finite Group Databasebeta

← #28399867

Subgroups — #28399867

Order 14464.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C2×#16813653C211yesmaximal, characteristic, complemented
3C22×#14268637C211yesmaximal, characteristic, complemented
4#20298758C214yesmaximal, complemented
5#20298753C214yesmaximal, complemented
6#20298606C211yesmaximal, characteristic, complemented
7#20298592C211yesmaximal, characteristic, complemented
8#20298565C211yesmaximal, characteristic, complemented
9#536×C113C211yesmaximal, characteristic, complemented
10#16813669—24no—
11#16813669—24no—
12C2×#14268647C2212yes—
13C2×#14268647C2211yescharacteristic
14C2×#14268646—22no—
15C2×#14268646—21no—
16C22×Dic226C2212yes—
17C22×Dic226C2211yescharacteristic
18C2×Q8×D113—21no—
19#16813653—24no—
20C2×#14268637—24no—
21C2×#14268637C2212yes—
22C2×#14268637C2214yes—
23C2×#14268634C2212yes—
24C2×#14268631C2211yescharacteristic
25C22×#11744751C2211yescharacteristic
26#16813545C2212yes—
27#16813545C2214yes—
28#16813542C2212yes—
29C22⋊#11744751C2214yes—
30C2×#41×C113C2211yescharacteristic
31C22×Q8×C113C2211yescharacteristic
32C4⋊Q8×C113—21no—
33#124×C113—21no—
34#123×C113—22no—
35C22⋊Q8×C113C2214yes—
36#117×C113C2211yescharacteristic
37#14268647—22no—
38#14268647—24no—
39#14268647—24no—
40#14268647D414yes—
41#14268646—216no—
42#14268646—28no—
43C2×Dic226—22no—
44C2×Dic226—21no—
45C2×Dic226—22no—
46C2×Dic226—24no—
47C2×Dic226—24no—
48C2×Dic226D414yes—
49C2×Dic226C2311yescharacteristic
50C2×Dic226C2312yes—
51Q8×D113—28no—
52C2×D452C2311yescharacteristic
53C2×C22⋊D113—22no—
54C2×C22⋊D113—21no—
55C22×Dic113—22no—
56C22×Dic113—21no—
57C2×C4×D113—22no—
58C2×C4×D113—21no—
59#14268637—28no—
60#14268637—24no—
61#14268634—24no—
62#14268631—22no—
63C2×#11744751—22no—
64C2×#11744751C2312yes—
65C2×#11744751C2312yes—
66#41×C113—22no—
67#41×C113—22no—
68C2×Q8×C113—21no—
69C2×Q8×C113—22no—
70C2×Q8×C113—22no—
71C2×Q8×C113D411yescharacteristic
72C2×Q8×C113C2312yes—
73C2×D4×C113D412yes—
74C2×D4×C113D411yescharacteristic
75C22×C4×C113—21no—
76C22×C4×C113C2312yes—
77C22×C4×C113C2311yescharacteristic
78C4⋊C4×C113—24no—
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—21no—
81C22⋊C4×C113—24no—
82C42×C113—21no—
83C23×C113C2×D412yes—
84C23×C113C2×D411yescharacteristic
85C22×D113—21no—
86Q8×C113—22no—
87Q8×C113—22no—
88Q8×C113—22no—
89Q8×C113—42no—
90D4×C113—24no—
91D4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113—22no—
94C2×C4×C113—22no—
95C2×C4×C113—22no—
96C2×C4×C113—42no—
97C2×C4×C113C2×D412yes—
98C2×C4×C113C2×D412yes—
99C2×C4×C113C2×D412yes—
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2411yescharacteristic
102C22⋊D113—28no—
103C22⋊D113—24no—
104C2×Dic113—28no—
105C2×Dic113—24no—
106C2×Dic113—21no—
107C2×Dic113—22no—
108D452—21no—
109D452C2×D412yes—
110C4×D113—28no—
111C4×D113—24no—
112Dic226—28no—
113Dic226—24no—
114Dic226—22no—
115Dic226—21no—
116Dic226C2×D412yes—
117Dic226C2×D414yes—
118#11744751—22no—
119#11744751—22no—
120C22×C113—22no—
121C22×C113—22no—
122C22×C113—24no—
123C22×C113#12012yes—
124C22×C113C22×D411yescharacteristic
125C2×D113—22no—
126C2×D113—42no—
127C4×C113—22no—
128C4×C113—42no—
129C4×C113—42no—
130C4×C113#12012yes—
131C4×C113C22×D411yescharacteristic
132C4×C113C22×D411yescharacteristic
133Dic113—22no—
134Dic113—24no—
135C2×C113—22no—
136C2×C113—42no—
137C2×C113C2×#12011yescharacteristic
138C2×C113#57812yes—
139D113—42no—
140#3011—1131nomaximal, Sylow
141C113#301111yescharacteristic, complemented, Sylow
142C2×2−1+4—1131no—
143C2×#137—1131no—
144C22×Q16—1131no—
145#536D11311yescharacteristic, complemented
146#452—1134no—
147#451—1134no—
148#419—1131no—
149#416—1131no—
150#408—1131no—
1512−1+4—2264no—
1522−1+4—2264no—
153C2×#41—1131no—
154C2×#41—1132no—
155C2×#41—2262no—
156C2×#41—2261no—
157C2×#41C2×D11311yescharacteristic
158C22×Q8—1131no—
159C22×Q8—1132no—
160C22×Q8—2261no—
161C22×Q8C2×D11311yescharacteristic
162#137—2264no—
163C2×Q16—1134no—
164C2×Q16—1132no—
165C2×Q16—2264no—
166C2×SD16—1132no—
167C2×M16—1131no—
168C22×C8—1131no—
169C4⋊Q8—21no—
170#124—21no—
171#123—22no—
172C22⋊Q8C2×D11314yes—
173#117C2×D11311yescharacteristic
174#103—1132no—
175#103—1134no—
176#102—1132no—
177C22⋊C8—1134no—
178#41—22no—
179#41—22no—
180#41—1134no—
181#41—2264no—
182#41—2264no—
183#41—22616no—
184#41—2268no—
185#41—2262no—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—1134no—
190C2×Q8—1132no—
191C2×Q8—1131no—
192C2×Q8—2264no—
193C2×Q8—2264no—
194C2×Q8—2268no—
195C2×Q8—2262no—
196C2×Q8—2262no—
197C2×Q8—2261no—
198C2×Q8C22⋊D11311yescharacteristic
199C2×Q8C22×D11312yes—
200C2×D4—1131no—
201C2×D4—2262no—
202C2×D4—2261no—
203C2×D4C22⋊D11312yes—
204C2×D4C22⋊D11311yescharacteristic
205C22×C4—21no—
206C22×C4—2262no—
207C22×C4—2261no—
208C22×C4—2262no—
209C22×C4—2261no—
210C22×C4C22×D11312yes—
211C22×C4C22×D11311yescharacteristic
212Q16—2268no—
213Q16—2264no—
214SD16—2264no—
215M16—2262no—
216C2×C8—1132no—
217C2×C8—1132no—
218C2×C8—2262no—
219C4⋊C4—24no—
220C4⋊C4C22×D11312yes—
221C22⋊C4—21no—
222C22⋊C4—24no—
223C42—21no—
224C23—2261no—
225C23C2×C22⋊D11312yes—
226C23C2×C22⋊D11311yescharacteristic
227Q8—22no—
228Q8—22no—
229Q8—22no—
230Q8—42no—
231Q8—1134no—
232Q8—1132no—
233Q8—2268no—
234Q8—2264no—
235Q8—2262no—
236Q8—2261no—
237D4—24no—
238D4—22no—
239D4—1132no—
240D4—2268no—
241D4—2264no—
242D4—2261no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—2268no—
249C2×C4—2268no—
250C2×C4—2264no—
251C2×C4—2262no—
252C2×C4—2261no—
253C2×C4—2264no—
254C2×C4D4×D11312yes—
255C2×C4D4×D11312yes—
256C2×C4C2×C22⋊D11312yes—
257C2×C4C2×C22⋊D11311yescharacteristic
258C2×C4C23×D11311yescharacteristic
259C8—2262no—
260C8—2262no—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—4522no—
265C22—2262no—
266C22#1681359012yes—
267C22C22×C22⋊D11311yescharacteristic
268C4—22no—
269C4—42no—
270C4—42no—
271C4—2264no—
272C4—2262no—
273C4#1681359012yes—
274C4C2×D4×D11311yescharacteristic
275C4C2×D4×D11311yescharacteristic
276C2—22no—
277C2—42no—
278C2—4522no—
279C2C2×#1681359011yescharacteristic
280C2#2029941312yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#536×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813669C2
hypercenter#536D113
hypocenterC113#3011
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#16813653C2semidirect
3. C22×#14268637C2semidirect
4. #20298758C2semidirect
5. #20298753C2semidirect
6. #20298606C2semidirect
7. #20298592C2semidirect
8. #20298565C2semidirect
9. #536×C113C2semidirect
141. C113#3011semidirect
145. #536D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136692
C2×#168136532
C22×#142686372
#202987582
#202987532
#202986062
#202985922
#202985652
#536×C1132
#3011113