Finite Group Databasebeta

← #28399810

Subgroups — #28399810

Order 14464.

738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×Q8×D113C211yesmaximal, characteristic, complemented
2C2×#16813655C211yesmaximal, characteristic, complemented
3C2×#16813653C211yesmaximal, characteristic, complemented
4#20299110C211yesmaximal, characteristic
5#20298755C214yesmaximal, complemented
6#20298738C214yesmaximal, complemented
7#20298606C211yesmaximal, characteristic, complemented
8#20298561C211yesmaximal, characteristic, complemented
9#419×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C22×Dic226—21no—
12C22×Dic226C2211yescharacteristic
13C2×Q8×D113—24no—
14C2×Q8×D113—22no—
15C2×Q8×D113—24no—
16C2×Q8×D113C2214yes—
17C22×C4×D113—21no—
18C22×C4×D113C2211yescharacteristic
19#16813655—24no—
20#16813653—24no—
21C2×Dic452C2212yescomplemented
22C2×#14268637C2212yescomplemented
23C2×#14268636C2212yescomplemented
24C2×#14268634C2212yescomplemented
25C2×#14268631C2211yescharacteristic
26#16813606—21no—
27#16813602C2212yes—
28#16813597C2212yes—
29#16813592—21no—
30C4×D452—22no—
31#16813545C2214yescomplemented
32#16813534C2214yes—
33C22×Q8×C113C2211yescharacteristic
34C2×M16×C113C2211yescharacteristic
35#117×C113C2211yescharacteristic
36#103×C113C2214yescomplemented
37C23×D113D411yescharacteristic
38#14268647—22no—
39#14268647—22no—
40C2×Dic226—28no—
41C2×Dic226—21no—
42C2×Dic226—22no—
43C2×Dic226—24no—
44C2×Dic226D414yescomplemented
45C2×Dic226C2311yescharacteristic
46C2×Dic226C2312yes—
47Q8×D113—216no—
48Q8×D113—28no—
49Q8×D113—28no—
50C2×D452—22no—
51C2×D452C2311yescharacteristic
52C2×C22⋊D113—21no—
53C22×Dic113—21no—
54C22×Dic113D411yescharacteristic
55C2×C4×D113—28no—
56C2×C4×D113—24no—
57C2×C4×D113—22no—
58C2×C4×D113—22no—
59C2×C4×D113—21no—
60C2×C4×D113D412yes—
61C2×C4×D113C2312yes—
62Dic452—24no—
63#14268637—24no—
64#14268636—24no—
65#14268634—24no—
66#14268631—22no—
67C2×#11744751C2312yes—
68C4⋊Dic113—22no—
69#14268624—22no—
70#14268624—22no—
71C2×Q8×C113—22no—
72C2×Q8×C113—21no—
73C2×Q8×C113D414yescomplemented
74C2×Q8×C113C2312yes—
75C22×C4×C113—21no—
76C22×C4×C113C2311yescharacteristic
77M16×C113—22no—
78C2×C8×C113C2312yes—
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—21no—
81C42×C113—21no—
82C23×C113C2×D411yescharacteristic
83C22×D113—22no—
84C22×D113—24no—
85C22×D113—21no—
86C22×D113C2×D412yes—
87Q8×C113—24no—
88Q8×C113—22no—
89Q8×C113C2×D414yes—
90C2×C4×C113—24no—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D412yes—
95C2×C4×C113C2×D412yes—
96C2×C4×C113C2411yescharacteristic
97C22⋊D113—42no—
98C2×Dic113—24no—
99C2×Dic113—22no—
100C2×Dic113—22no—
101C2×Dic113—21no—
102C2×Dic113C2×D412yes—
103D452—21no—
104D452—21no—
105D452—44no—
106C4×D113—216no—
107C4×D113—24no—
108C4×D113—22no—
109C4×D113—22no—
110C4×D113—42no—
111Dic226—216no—
112Dic226—24no—
113Dic226—22no—
114Dic226—21no—
115Dic226—21no—
116Dic226C2×D414yes—
117C8×C113—22no—
118#11744751—22no—
119C22×C113—22no—
120C22×C113#12012yes—
121C22×C113C22×D411yescharacteristic
122C2×D113—28no—
123C2×D113—22no—
124C2×D113—22no—
125C2×D113—41no—
126C2×D113—42no—
127C2×D113#13714yescomplemented
128C4×C113—24no—
129C4×C113—42no—
130C4×C113#12012yes—
131C4×C113C22×D411yescharacteristic
132C4×C113C22×D411yescharacteristic
133Dic113—22no—
134Dic113—24no—
135Dic113—41no—
136C2×C113—22no—
137C2×C113C2×#12011yescharacteristic
138C2×C113C2×#13712yes—
139D113—24no—
140D113—81no—
141#3004—1131nomaximal, Sylow
142C113#300411yescharacteristic, complemented, Sylow
143C23×Q8—1131no—
144C2×#137—1131no—
145C2×#137—1131no—
146#525—1131no—
147#451—1134no—
148#448—1134no—
149#419—1131no—
150#419D11311yescharacteristic, complemented
151#407—1131no—
152C2×#41—1131no—
153C22×Q8—1134no—
154C22×Q8—1131no—
155C22×Q8—2261no—
156C22×Q8—2262no—
157C22×Q8—2264no—
158C22×Q8—2264no—
159C22×Q8C2×D11311yescharacteristic
160C23×C4—1131no—
161C23×C4—2261no—
162#137—2264no—
163#137—2264no—
164C2×Q16—1132no—
165C2×Q16—1132no—
166C2×SD16—1132no—
167C2×SD16—1132no—
168C2×M16—1131no—
169C2×M16C2×D11311yescharacteristic
170#123—2261no—
171C22⋊Q8—1132no—
172#121—1132no—
173#120—2261no—
174C4×D4—2262no—
175#117C2×D11311yescharacteristic
176#103—1134no—
177#103C2×D11314yescomplemented
178C22⋊C8—1134no—
179C24—1131no—
180#41—2262no—
181#41—2262no—
182C2×Q8—22no—
183C2×Q8—21no—
184C2×Q8—1134no—
185C2×Q8—1132no—
186C2×Q8—1131no—
187C2×Q8—2264no—
188C2×Q8—2268no—
189C2×Q8—2268no—
190C2×Q8—22616no—
191C2×Q8—2268no—
192C2×Q8—2261no—
193C2×Q8—2262no—
194C2×Q8D45214yescomplemented
195C2×Q8C22×D11312yes—
196C2×D4—1131no—
197C2×D4—2262no—
198C2×D4—2261no—
199C22×C4—21no—
200C22×C4—1131no—
201C22×C4—1132no—
202C22×C4—1132no—
203C22×C4—2264no—
204C22×C4—2268no—
205C22×C4—2261no—
206C22×C4—2261no—
207C22×C4—2262no—
208C22×C4—2262no—
209C22×C4C22×D11311yescharacteristic
210Q16—2264no—
211Q16—2264no—
212SD16—2264no—
213SD16—2264no—
214M16—22no—
215M16—2262no—
216C2×C8—1132no—
217C2×C8C22×D11312yes—
218C4⋊C4—2262no—
219C4⋊C4C22×D11312yes—
220C22⋊C4—21no—
221C22⋊C4—2262no—
222C22⋊C4—2262no—
223C42—21no—
224C23—1132no—
225C23—2264no—
226C23—2261no—
227C23—2262no—
228C23D4×D11311yescharacteristic
229Q8—24no—
230Q8—22no—
231Q8—1134no—
232Q8—22616no—
233Q8—2261no—
234Q8—2261no—
235Q8—2264no—
236Q8—2262no—
237Q8C2×D45214yes—
238D4—4524no—
239D4—4522no—
240D4—2261no—
241D4—2261no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—1132no—
246C2×C4—4522no—
247C2×C4—22616no—
248C2×C4—2261no—
249C2×C4—2262no—
250C2×C4—2264no—
251C2×C4—2262no—
252C2×C4—2264no—
253C2×C4—2262no—
254C2×C4—2262no—
255C2×C4D4×D11311yescharacteristic
256C2×C4D4×D11312yes—
257C2×C4C2×D45212yes—
258C2×C4C23×D11311yescharacteristic
259C8—22no—
260C8—2262no—
261C22—22no—
262C22—1134no—
263C22—4521no—
264C22—4522no—
265C22—2268no—
266C22—2262no—
267C22—2262no—
268C22#1681359212yes—
269C22C2×D4×D11311yescharacteristic
270C4—24no—
271C4—42no—
272C4—4521no—
273C4—2262no—
274C4—2264no—
275C4#1681359212yes—
276C4C2×D4×D11311yescharacteristic
277C4C22×D45211yescharacteristic
278C2—22no—
279C2—9041no—
280C2—2264no—
281C2C2×#1681359211yescharacteristic
282C2#137×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#419×C113C2
socleC22×C113C22×D4
prime radical#20299110C2
hypercenter#419D113
hypocenterC113#3004
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D113C2semidirect
2. C2×#16813655C2semidirect
3. C2×#16813653C2semidirect
5. #20298755C2semidirect
6. #20298738C2semidirect
7. #20298606C2semidirect
8. #20298561C2semidirect
9. #419×C113C2semidirect
21. C2×Dic452C22semidirect
22. C2×#14268637C22semidirect
23. C2×#14268636C22semidirect
24. C2×#14268634C22semidirect
31. #16813545C22semidirect
36. #103×C113C22semidirect
44. C2×Dic226D4semidirect
73. C2×Q8×C113D4semidirect
127. C2×D113#137semidirect
142. C113#3004semidirect
150. #419D113semidirect
177. #103C2×D113semidirect
194. C2×Q8D452semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D1132
C2×#168136552
C2×#168136532
#202991102
#202987552
#202987382
#202986062
#202985612
#419×C1132
#3004113