Finite Group Databasebeta

← #13120199

Subgroups — #13120199

Order 1664.

468 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 147 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×#88141C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic
3C13×#400C211yesmaximal, characteristic
4#11718643C211yesmaximal, characteristic
5#11718640C211yesmaximal, characteristic
6#11718317C211yesmaximal, characteristic
7#11718315C212yesmaximal
8#11718313C212yesmaximal
9#11718311C211yesmaximal, characteristic
10#11718308C212yesmaximal
11#11718307C212yesmaximal
12C22×Dic26C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic13C2212yes—
17C2×#6101C2211yescharacteristic
18C2×#6101C2212yes—
19C2×#6101C2211yescharacteristic
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×C4×Dic13C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24C2×C4×Dic13C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26#88141—24no—
27#88141—24no—
28C13×#95C2212yes—
29C13×#95C2212yes—
30C13×#95C2211yescharacteristic
31#88071C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2211yescharacteristic
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—24no—
51C2×Dic26—22no—
52C2×Dic26Q814yescomplemented
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C4⋊Dic13—24no—
56#6101—22no—
57#6101—24no—
58#6101—22no—
59#6101—24no—
60#6101—24no—
61C4×Dic13—22no—
62C4×Dic13—24no—
63C4×Dic13—22no—
64C4×Dic13D414yes—
65#2581—131nomaximal, Sylow
66C23×C13C2411yescharacteristic
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—21no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—24no—
76C2×C4×C13—22no—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2×Q812yes—
79C2×Dic13—21no—
80C2×Dic13—22no—
81C2×Dic13—21no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—21no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13C2×D412yes—
90C2×Dic13C2×D412yes—
91C2×Dic13C2×Q812yes—
92C2×Dic13C2×Q812yes—
93C2×Dic13#4114yes—
94C2×Dic13#4112yes—
95Dic26—28no—
96Dic26—28no—
97C2×C4×Q8—131no—
98C2×C4×Q8—131no—
99#400—131no—
100#400D1311yescharacteristic
101#395—131no—
102#395—131no—
103#391—132no—
104#389—132no—
105#387—132no—
106#387—132no—
107#382—131no—
108C22×C13C22×D411yescharacteristic
109C22×C13C22×Q811yescharacteristic
110C22×C13C2×#4111yescharacteristic
111C22×C13C2×#4112yes—
112C22×C132−1+412yes—
113C4×C13—22no—
114C4×C13—22no—
115C4×C13—41no—
116C4×C13—42no—
117C4×C13—42no—
118Dic13—22no—
119Dic13—24no—
120Dic13—22no—
121Dic13—41no—
122Dic13—42no—
123Dic13C22⋊Q814yes—
124C22×Q8—131no—
125C22×Q8—131no—
126C4×Q8—264no—
127C4×Q8—264no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4C2×D1311yescharacteristic
135C2×C4⋊C4C2×D1311yescharacteristic
136C2×C42—131no—
137C2×C42—131no—
138C2×C42—131no—
139C2×C42—132no—
140#95—132no—
141#95—131no—
142#95—132no—
143#95—132no—
144#95—132no—
145#95—132no—
146#95C2×D1311yescharacteristic
147#95C2×D1312yes—
148#95C2×D1312yes—
149C2×C13C2×C22⋊Q811yescharacteristic
150C2×C13#52511yescharacteristic
151C2×C13#53611yescharacteristic
152C2×C13#55612yes—
153C2×C13#55712yes—
154C2×Q8—134no—
155C2×Q8—262no—
156C2×Q8—262no—
157C2×Q8—264no—
158C2×Q8—262no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—132no—
163C22×C4—132no—
164C22×C4—131no—
165C22×C4C22×D1312yes—
166C22×C4C22×D1312yes—
167C22×C4C22×D1311yescharacteristic
168C22×C4C22×D1311yescharacteristic
169C22×C4C22×D1311yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—262no—
173C4⋊C4—264no—
174C4⋊C4—264no—
175C4⋊C4—264no—
176C4⋊C4—264no—
177C4⋊C4—262no—
178C42—134no—
179C42—262no—
180C42—264no—
181C42—262no—
182C13#258111yescharacteristic, complemented, Sylow
183C23C23×D1311yescharacteristic
184Q8—268no—
185Q8—268no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—132no—
197C2×C4—132no—
198C2×C4—132no—
199C2×C4—132no—
200C2×C4—132no—
201C2×C4—134no—
202C2×C4—261no—
203C2×C4—262no—
204C2×C4—261no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—261no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4D4×D1312yes—
213C2×C4Q8×D1312yes—
214C22C2×D4×D1311yescharacteristic
215C22C2×Q8×D1311yescharacteristic
216C22#41×D1311yescharacteristic
217C22#41×D1312yes—
218C22#8825712yes—
219C4—22no—
220C4—22no—
221C4—41no—
222C4—42no—
223C4—42no—
224C4—134no—
225C4—262no—
226C4—264no—
227C4—262no—
228C4—521no—
229C4—522no—
230C2D13×C22⋊Q811yescharacteristic
231C2#1171936111yescharacteristic
232C2#1171938011yescharacteristic
233C2#1171939012yes—
234C2#1171940712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#400C2
hypercenter#400D13
hypocenterC13#2581
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C2×Dic26Q8semidirect
182. C13#2581semidirect

Maximal subgroups

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

subgroupindex
C2×#881412
C13×#4002
#117186432
#117186402
#117183172
#117183152
#117183132
#117183112
#117183082
#117183072
#258113