Finite Group Databasebeta

← #13120959

Subgroups — #13120959

Order 1664.

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

normal subgroups only

This group has 448 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
1C2×#88143C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic
3C13×#398C211yesmaximal, characteristic
4#11718644C211yesmaximal, characteristic
5#11718641C211yesmaximal, characteristic
6#11718640C212yesmaximal
7#11718637C212yesmaximal
8#11718322C211yesmaximal, characteristic
9#11718317C212yesmaximal
10#11718311C212yesmaximal
11#11718309C211yesmaximal, characteristic
12C22×Dic26C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊Dic13C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×#6101C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2212yes—
28#88143—24no—
29#88142—24no—
30C13×#95C2211yescharacteristic
31C13×#95C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×Dic13C2311yescharacteristic
43C22×Dic13C2312yes—
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C2×Dic26—24no—
49C2×Dic26—42no—
50C2×Dic26—42no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—42no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13—42no—
57#6101—22no—
58#6101—24no—
59#6101—22no—
60#6101—22no—
61#6101—22no—
62#6101—42no—
63#6101—42no—
64C4×Dic13D414yes—
65C4×Dic13Q818yescomplemented
66#2660—131nomaximal, Sylow
67C23×C13C2411yescharacteristic
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13C2×D412yes—
80C2×C4×C13C2×Q814yes—
81C2×Dic13—22no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13C2×D412yes—
94C2×Dic13C2×D412yes—
95C2×Dic13C2×Q814yes—
96C2×Dic13C2×Q814yes—
97Dic26—48no—
98C2×C4⋊Q8—131no—
99C2×#125—131no—
100#398—131no—
101#398—131no—
102#398—131no—
103#398D1311yescharacteristic
104#395—132no—
105#395—132no—
106#384—132no—
107#382—132no—
108#376—131no—
109C22×C13C22×D411yescharacteristic
110C22×C13C22×Q812yes—
111C22×C13H(5,𝔽2)11yescharacteristic
112C22×C13H(5,𝔽2)11yescharacteristic
113C22×C132−1+412yes—
114C4×C13—22no—
115C4×C13—24no—
116C4×C13—42no—
117C4×C13—41no—
118C4×C13—41no—
119Dic13—22no—
120Dic13—24no—
121Dic13—42no—
122Dic13—41no—
123Dic13—41no—
124Dic13C4⋊Q814yes—
125C22×Q8—132no—
126C4⋊Q8—264no—
127#125—264no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4C2×D1311yescharacteristic
139C2×C4⋊C4C2×D1311yescharacteristic
140C2×C4⋊C4C2×D1312yes—
141C2×C42—131no—
142C2×C42—132no—
143#95—132no—
144#95—131no—
145#95—132no—
146#95—132no—
147#95—132no—
148#95C2×D1311yescharacteristic
149#95C2×D1312yes—
150C2×C13C2×C4⋊Q811yescharacteristic
151C2×C13#53511yescharacteristic
152C2×C13#53611yescharacteristic
153C2×C13#54412yes—
154C2×C13#54412yes—
155C2×Q8—264no—
156C2×Q8—522no—
157C2×Q8—522no—
158C22×C4—131no—
159C22×C4—132no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—132no—
163C22×C4—131no—
164C22×C4C22×D1311yescharacteristic
165C22×C4C22×D1312yes—
166C22×C4C22×D1311yescharacteristic
167C22×C4C22×D1311yescharacteristic
168C22×C4C22×D1312yes—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—42no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—264no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—522no—
180C4⋊C4—522no—
181C4⋊C4—522no—
182C42—134no—
183C42—138no—
184C13#266011yescharacteristic, complemented, Sylow
185C23C23×D1311yescharacteristic
186Q8—528no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—132no—
199C2×C4—134no—
200C2×C4—132no—
201C2×C4—134no—
202C2×C4—261no—
203C2×C4—262no—
204C2×C4—261no—
205C2×C4—262no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—262no—
209C2×C4—261no—
210C2×C4—262no—
211C2×C4—261no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4D4×D1312yes—
215C2×C4Q8×D1314yes—
216C22C2×D4×D1311yescharacteristic
217C22#8825111yescharacteristic
218C22C2×Q8×D1312yes—
219C22#8825611yescharacteristic
220C22#8825712yes—
221C4—24no—
222C4—22no—
223C4—41no—
224C4—42no—
225C4—41no—
226C4—134no—
227C4—262no—
228C4—264no—
229C4—521no—
230C4—522no—
231C4—521no—
232C2#1171931211yescharacteristic
233C2#1171932812yes—
234C2#1171935311yescharacteristic
235C2#1171939412yes—
236C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#398C2
hypercenter#398D13
hypocenterC13#2660
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
65. C4×Dic13Q8semidirect
184. C13#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#881432
C2×#881422
C13×#3982
#117186442
#117186412
#117186402
#117186372
#117183222
#117183172
#117183112
#117183092
#266013