Finite Group Databasebeta

← #13119813

Subgroups — #13119813

Order 1664.

576 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 165 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×C13×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#88201C211yesmaximal, characteristic
3C2×#88201C211yesmaximal, characteristic
4C2×Q8×Dic13C211yesmaximal, characteristic, complemented
5#11718891C211yesmaximal, characteristic, complemented
6#11718655C214yesmaximal, complemented
7#11718651C214yesmaximal, complemented
8#11718600C211yesmaximal, characteristic
9C4×#6101C211yesmaximal, characteristic, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×Q8×C13C2211yescharacteristic
12C22×D52C2211yescharacteristic
13C13×C4⋊Q8—24no—
14C2×C13×C4⋊C4C2214yes—
15C2×C42×C13C2211yescharacteristic
16#88201—24no—
17#88201—24no—
18Q8×Dic13—24no—
19C2×#6103C2212yes—
20C2×#6103C2214yes—
21C2×#6103C2212yes—
22C2×#6103C2214yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28C2×C4×Dic13C2211yescharacteristic
29#88071C2212yes—
30#88071C2214yes—
31C23×D13C2312yes—
32C2×Q8×C13—22no—
33C2×Q8×C13—22no—
34C2×Q8×C13—22no—
35C2×Q8×C13—22no—
36C2×Q8×C13—22no—
37C2×Q8×C13D414yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C2×D52—22no—
47C2×D52—22no—
48C2×D52—22no—
49C13×C4⋊C4—28no—
50C42×C13—22no—
51#6103—28no—
52#6103—28no—
53#6103—24no—
54#6103—24no—
55C4⋊Dic13—22no—
56C4⋊Dic13—24no—
57#6101—24no—
58C4×Dic13—22no—
59C4×Dic13—24no—
60C4×Dic13D414yes—
61#2545—131nomaximal, Sylow
62C23×C13C2411yescharacteristic
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—24no—
66C22×D13—22no—
67C22×D13—24no—
68Q8×C13—28no—
69Q8×C13—44no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13C2×D414yes—
78C2×C4×C13C2×D412yes—
79C2×C4×C13C2×D412yes—
80C2×C4×C13#4114yes—
81C2×C4×C13#4112yes—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—24no—
88C2×Dic13—22no—
89C2×Dic13C2×D412yes—
90C2×Dic13C2×D412yes—
91D52—44no—
92C2×C4⋊Q8D1311yescharacteristic, complemented
93C2×#124—131no—
94C2×#124—131no—
95C2×C4×Q8—131no—
96#396—134no—
97#391—131no—
98#390—131no—
99#388—134no—
100C4×C4⋊C4—131no—
101C22×C13C22×D411yescharacteristic
102C22×C13C22×D411yescharacteristic
103C22×C13C2×#4111yescharacteristic
104C22×C13C2×#4112yes—
105C22×C132−1+412yes—
106C2×D13—42no—
107C2×D13—42no—
108C2×D13—42no—
109C2×D13—44no—
110C2×D13—44no—
111C4×C13—24no—
112C4×C13—24no—
113C4×C13—42no—
114C4×C13#12114yes—
115Dic13—22no—
116Dic13—22no—
117Dic13—42no—
118Dic13—42no—
119C22×Q8C2×D1311yescharacteristic
120C22×Q8C2×D1311yescharacteristic
121C22×D4—131no—
122C4⋊Q8—24no—
123#124—264no—
124#124—264no—
125C4×Q8—264no—
126C2×C4⋊C4—131no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4C2×D1314yes—
130C2×C22⋊C4—132no—
131C2×C22⋊C4—134no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—134no—
134C2×C42—131no—
135C2×C42—132no—
136C2×C42—131no—
137C2×C42C2×D1311yescharacteristic
138#95—132no—
139#95—134no—
140C2×C13C2×#12111yescharacteristic
141C2×C13#53211yescharacteristic
142C2×C13#53611yescharacteristic
143C2×C13#54812yes—
144C2×C13#55612yes—
145D13—82no—
146C24—132no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8C22⋊D1314yes—
153C2×D4—262no—
154C2×D4—262no—
155C2×D4—262no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4C22×D1312yes—
161C22×C4C22×D1312yes—
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—28no—
165C4⋊C4—264no—
166C4⋊C4—262no—
167C4⋊C4—264no—
168C22⋊C4—264no—
169C22⋊C4—264no—
170C22⋊C4—268no—
171C22⋊C4—268no—
172C42—22no—
173C42—134no—
174C42—264no—
175C42—262no—
176C13#254511yescharacteristic, complemented, Sylow
177C23—262no—
178C23—262no—
179C23—264no—
180C23—264no—
181C23—262no—
182C23C23×D1311yescharacteristic
183Q8—28no—
184Q8—44no—
185D4—524no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—132no—
194C2×C4—132no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—264no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4D4×D1312yes—
203C2×C4#612912yes—
204C2×C4#613114yes—
205C2×C4C2×C22⋊D1314yes—
206C2×C4C2×C22⋊D1312yes—
207C22—522no—
208C22—522no—
209C22—524no—
210C22—522no—
211C22—524no—
212C22C2×D4×D1311yescharacteristic
213C22C2×#612911yescharacteristic
214C22C2×#613112yes—
215C22#8825412yes—
216C22C22×C22⋊D1311yescharacteristic
217C4—24no—
218C4—24no—
219C4—42no—
220C4—262no—
221C4—262no—
222C4—522no—
223C4—522no—
224C4#8819314yes—
225C2—1042no—
226C2#1171942911yescharacteristic
227C2#1171943011yescharacteristic
228C2#1171943712yes—
229C2C2×#8819311yescharacteristic
230C2#1171952212yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C4⋊Q8C2
prime radicalC22×D52C22
hypercenterC2×C4⋊Q8D13
hypocenterC13#2545
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C4⋊Q8C2semidirect
4. C2×Q8×Dic13C2semidirect
5. #11718891C2semidirect
6. #11718655C2semidirect
7. #11718651C2semidirect
9. C4×#6101C2semidirect
92. C2×C4⋊Q8D13semidirect
176. C13#2545semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C4⋊Q82
C2×#882012
C2×Q8×Dic132
#117188912
#117186552
#117186512
#117186002
C4×#61012
#254513