Finite Group Databasebeta

← #13120711

Subgroups — #13120711

Order 1664.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×Q8×Dic13C211yesmaximal, characteristic
2C2×#88143C211yesmaximal, characteristic
3C13×#395C211yesmaximal, characteristic
4#11718890C211yesmaximal, characteristic
5#11718647C211yesmaximal, characteristic
6#11718645C212yesmaximal
7#11718642C212yesmaximal
8#11718321C212yesmaximal
9#11718320C211yesmaximal, characteristic
10#11718313C212yesmaximal
11#11718312C211yesmaximal, characteristic
12C22×Q8×C13C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2212yes—
15Q8×Dic13—24no—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊Dic13C2212yes—
19C2×#6101C2211yescharacteristic
20C2×#6101C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×#6101C2211yescharacteristic
23C2×#6101C2212yes—
24C2×C4×Dic13C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26#88143—24no—
27C13×#95C2211yescharacteristic
28C13×#95C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2211yescharacteristic
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C2×Q8×C13—22no—
38C2×Q8×C13—24no—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C13×C4⋊C4—22no—
51C13×C4⋊C4—24no—
52C4⋊Dic13—22no—
53C4⋊Dic13—22no—
54C4⋊Dic13—24no—
55#6101—22no—
56#6101—24no—
57#6101—22no—
58#6101—22no—
59#6101—22no—
60C4×Dic13—24no—
61C4×Dic13D414yes—
62#2634—131nomaximal, Sylow
63C23×C13C2411yescharacteristic
64Q8×C13—28no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13C2×D412yes—
77C2×C4×C13#4114yes—
78C2×Dic13—21no—
79C2×Dic13—22no—
80C2×Dic13—21no—
81C2×Dic13—22no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13C2×D412yes—
92C2×Dic13C2×D412yes—
93C2×#125—131no—
94C2×C4×Q8—131no—
95#400—131no—
96#400—131no—
97#400—132no—
98#398—132no—
99#395—131no—
100#395D1311yescharacteristic
101#387—132no—
102#387—132no—
103#383—131no—
104C22×C13C22×D411yescharacteristic
105C22×C13C2×#4112yes—
106C22×C132−1+412yes—
107C22×C132−1+411yescharacteristic
108C22×C132−1+411yescharacteristic
109C4×C13—22no—
110C4×C13—24no—
111C4×C13—41no—
112C4×C13—41no—
113C4×C13—42no—
114Dic13—22no—
115Dic13—22no—
116Dic13—41no—
117Dic13—42no—
118Dic13—41no—
119Dic13—42no—
120C22×Q8C2×D1311yescharacteristic
121#125—264no—
122C4×Q8—264no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4—131no—
126C2×C4⋊C4—131no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4C2×D1311yescharacteristic
132C2×C4⋊C4C2×D1312yes—
133C2×C42—131no—
134C2×C42—132no—
135#95—132no—
136#95—131no—
137#95—132no—
138#95—132no—
139#95—132no—
140#95—132no—
141#95—132no—
142#95—132no—
143#95C2×D1311yescharacteristic
144#95C2×D1312yes—
145C2×C13#52511yescharacteristic
146C2×C13#53611yescharacteristic
147C2×C13#53611yescharacteristic
148C2×C13#54112yes—
149C2×C13#54112yes—
150C2×Q8—22no—
151C2×Q8—24no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—132no—
155C22×C4—132no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4C22×D1312yes—
159C22×C4C22×D1311yescharacteristic
160C22×C4C22×D1311yescharacteristic
161C22×C4C22×D1311yescharacteristic
162C22×C4C22×D1312yes—
163C4⋊C4—22no—
164C4⋊C4—24no—
165C4⋊C4—264no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—264no—
173C42—134no—
174C42—264no—
175C13#263411yescharacteristic, complemented, Sylow
176C23C23×D1311yescharacteristic
177Q8—28no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—132no—
190C2×C4—132no—
191C2×C4—262no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—262no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—264no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—261no—
203C2×C4—261no—
204C2×C4D4×D1312yes—
205C2×C4#612914yes—
206C22C2×D4×D1311yescharacteristic
207C22C2×#612912yes—
208C22#8825412yes—
209C22#8825411yescharacteristic
210C22#8825711yescharacteristic
211C4—22no—
212C4—24no—
213C4—41no—
214C4—42no—
215C4—41no—
216C4—262no—
217C4—262no—
218C4—522no—
219C4—522no—
220C4—521no—
221C4—521no—
222C2#1171929111yescharacteristic
223C2#1171933012yes—
224C2#1171933311yescharacteristic
225C2#1171942911yescharacteristic
226C2#1171943612yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2634
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
175. C13#2634semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
C2×#881432
C13×#3952
#117188902
#117186472
#117186452
#117186422
#117183212
#117183202
#117183132
#117183122
#263413