Finite Group Databasebeta

← #13120717

Subgroups — #13120717

Order 1664.

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

normal subgroups only

This group has 416 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×#88144C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic
3C13×#398C211yesmaximal, characteristic
4#11718647C211yesmaximal, characteristic
5#11718642C212yesmaximal
6#11718641C211yesmaximal, characteristic
7#11718640C212yesmaximal
8#11718320C211yesmaximal, characteristic
9#11718319C212yesmaximal
10#11718316C212yesmaximal
11#11718312C211yesmaximal, characteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C4⋊Dic13C2212yes—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×#6101C2211yescharacteristic
19C2×#6101C2211yescharacteristic
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×C4×Dic13C2211yescharacteristic
23C2×C4×Dic13C2211yescharacteristic
24C2×C4×Dic13C2211yescharacteristic
25#88144—24no—
26#88141—24no—
27C13×#95C2211yescharacteristic
28C13×#95C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2211yescharacteristic
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—22no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—24no—
54C4⋊Dic13—22no—
55C4⋊Dic13—24no—
56#6101—22no—
57#6101—22no—
58#6101—24no—
59#6101—24no—
60C4×Dic13—22no—
61C4×Dic13—22no—
62C4×Dic13D414yes—
63#2634—131nomaximal, Sylow
64C23×C13C2411yescharacteristic
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
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×C13C2×D412yes—
77C2×C4×C13#4112yes—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13—22no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13C2×D412yes—
91C2×Dic13C2×D412yes—
92C2×Dic13#4112yes—
93Dic26—28no—
94C2×#125—131no—
95C2×C4×Q8—131no—
96#400—131no—
97#400—132no—
98#400—131no—
99#398—131no—
100#398D1311yescharacteristic
101#395—132no—
102#387—132no—
103#387—132no—
104#383—131no—
105C22×C13C22×D411yescharacteristic
106C22×C13C2×#4111yescharacteristic
107C22×C13C2×#4111yescharacteristic
108C22×C132−1+412yes—
109C22×C132−1+412yes—
110C4×C13—22no—
111C4×C13—22no—
112C4×C13—42no—
113C4×C13—41no—
114C4×C13—42no—
115Dic13—22no—
116Dic13—22no—
117Dic13—22no—
118Dic13—42no—
119Dic13—41no—
120Dic13—42no—
121C22×Q8—131no—
122#125—264no—
123C4×Q8—264no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4—131no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—132no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4C2×D1311yescharacteristic
131C2×C4⋊C4C2×D1311yescharacteristic
132C2×C4⋊C4C2×D1312yes—
133C2×C42—131no—
134C2×C42—131no—
135C2×C42—131no—
136#95—132no—
137#95—132no—
138#95—131no—
139#95—132no—
140#95—132no—
141#95—132no—
142#95—132no—
143#95—132no—
144#95C2×D1311yescharacteristic
145#95C2×D1312yes—
146C2×C13#52511yescharacteristic
147C2×C13#53611yescharacteristic
148C2×C13#53611yescharacteristic
149C2×C13#54112yes—
150C2×C13#54112yes—
151C2×Q8—262no—
152C2×Q8—262no—
153C2×Q8—262no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—131no—
157C22×C4—132no—
158C22×C4—131no—
159C22×C4—132no—
160C22×C4C22×D1312yes—
161C22×C4C22×D1311yescharacteristic
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1311yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—24no—
168C4⋊C4—262no—
169C4⋊C4—264no—
170C4⋊C4—264no—
171C4⋊C4—264no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C42—134no—
175C42—262no—
176C42—262no—
177C13#263411yescharacteristic, complemented, Sylow
178C23C23×D1311yescharacteristic
179Q8—268no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—132no—
192C2×C4—132no—
193C2×C4—132no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—262no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—262no—
201C2×C4—264no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4D4×D1312yes—
207C2×C4#612912yes—
208C22C2×D4×D1311yescharacteristic
209C22C2×#612911yescharacteristic
210C22#8825412yes—
211C22#41×D1311yescharacteristic
212C22#8825712yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—42no—
217C4—41no—
218C4—262no—
219C4—262no—
220C4—262no—
221C4—522no—
222C4—521no—
223C4—522no—
224C2#1171931111yescharacteristic
225C2#1171933012yes—
226C2#1171935311yescharacteristic
227C2#1171940112yes—
228C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#398C2
hypercenter#398D13
hypocenterC13#2634
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
177. C13#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#881442
C2×#881412
C13×#3982
#117186472
#117186422
#117186412
#117186402
#117183202
#117183192
#117183162
#117183122
#263413