Finite Group Databasebeta

← #13118126

Subgroups — #13118126

Order 1664.

504 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 167 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×#88141C211yesmaximal, characteristic
3C13×#395C211yesmaximal, characteristic
4#11718890C211yesmaximal, characteristic
5#11718645C212yesmaximal
6#11718644C211yesmaximal, characteristic
7C4⋊C4×Dic13C212yesmaximal
8#11718322C211yesmaximal, characteristic
9#11718317C212yesmaximal
10#11718310C212yesmaximal
11#11718309C211yesmaximal, characteristic
12C22×Q8×C13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16Q8×Dic13—24no—
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2212yes—
20C2×#6101C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×C4×Dic13C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28C2×C4×Dic13C2212yes—
29#88141—24no—
30C13×#95C2211yescharacteristic
31C13×#95C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C2×Q8×C13—22no—
38C2×Q8×C13—24no—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2312yes—
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C2×Dic26—22no—
51C2×Dic26—22no—
52C2×Dic26—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—24no—
55C4⋊Dic13—22no—
56C4⋊Dic13—24no—
57C4⋊Dic13—24no—
58#6101—22no—
59#6101—24no—
60#6101—24no—
61#6101—22no—
62C4×Dic13—22no—
63C4×Dic13—22no—
64C4×Dic13—24no—
65C4×Dic13D414yes—
66C4×Dic13Q818yescomplemented
67#2399—131nomaximal, Sylow
68C23×C13C2411yescharacteristic
69Q8×C13—28no—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13C2×D412yes—
80C2×C4×C13C2×Q814yes—
81C2×C4×C13#4114yes—
82C2×C4×C13#4112yes—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13C2×D412yes—
95C2×Dic13C2×D412yes—
96C2×Dic13C2×Q814yes—
97C2×Dic13C2×Q814yes—
98C2×Dic13#4112yes—
99Dic26—28no—
100C2×C4×Q8—131no—
101C2×C4×Q8—131no—
102#398—131no—
103#398—132no—
104#398—131no—
105#395—131no—
106#395—132no—
107#395D1311yescharacteristic
108C4×C4⋊C4—132no—
109C4×C4⋊C4—132no—
110#376—131no—
111C22×C13C22×D411yescharacteristic
112C22×C13C22×Q812yes—
113C22×C13C2×#4112yes—
114C22×C13C2×#4111yescharacteristic
115C22×C13C2×#4111yescharacteristic
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—24no—
119C4×C13—24no—
120C4×C13—41no—
121Dic13—22no—
122Dic13—22no—
123Dic13—24no—
124Dic13—41no—
125Dic13—42no—
126Dic13C4⋊Q814yes—
127C22×Q8—131no—
128C22×Q8C2×D1311yescharacteristic
129C4×Q8—264no—
130C4×Q8—264no—
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×D1312yes—
140C2×C42—131no—
141C2×C42—132no—
142C2×C42—131no—
143C2×C42—132no—
144C2×C42—131no—
145#95—131no—
146#95—132no—
147#95—132no—
148#95—132no—
149#95—132no—
150#95C2×D1311yescharacteristic
151#95C2×D1312yes—
152C2×C13#52511yescharacteristic
153C2×C13#52511yescharacteristic
154C2×C13C2×C4⋊Q811yescharacteristic
155C2×C13#53312yes—
156C2×C13#53312yes—
157C2×Q8—22no—
158C2×Q8—24no—
159C2×Q8—262no—
160C2×Q8—262no—
161C2×Q8—262no—
162C22×C4—131no—
163C22×C4—132no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—132no—
168C22×C4C22×D1311yescharacteristic
169C22×C4C22×D1311yescharacteristic
170C22×C4C22×D1312yes—
171C22×C4C22×D1312yes—
172C22×C4C22×D1311yescharacteristic
173C4⋊C4—22no—
174C4⋊C4—24no—
175C4⋊C4—262no—
176C4⋊C4—264no—
177C4⋊C4—264no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—264no—
181C4⋊C4—264no—
182C42—134no—
183C42—138no—
184C42—262no—
185C42—264no—
186C42—262no—
187C13#239911yescharacteristic, complemented, Sylow
188C23C23×D1311yescharacteristic
189Q8—28no—
190Q8—268no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—132no—
201C2×C4—134no—
202C2×C4—132no—
203C2×C4—134no—
204C2×C4—132no—
205C2×C4—261no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—261no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4D4×D1312yes—
217C2×C4#612914yes—
218C2×C4Q8×D1314yes—
219C2×C4#613112yes—
220C22C2×D4×D1311yescharacteristic
221C22C2×#612912yes—
222C22C2×Q8×D1312yes—
223C22C2×#613111yescharacteristic
224C22#41×D1311yescharacteristic
225C4—22no—
226C4—24no—
227C4—24no—
228C4—22no—
229C4—41no—
230C4—134no—
231C4—264no—
232C4—262no—
233C4—262no—
234C4—521no—
235C4—522no—
236C2#1171929111yescharacteristic
237C2#1171932712yes—
238C2#1171933211yescharacteristic
239C2D13×C4⋊Q811yescharacteristic
240C2#1171943312yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2399
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
66. C4×Dic13Q8semidirect
187. C13#2399semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
C2×#881412
C13×#3952
#117188902
#117186452
#117186442
C4⋊C4×Dic132
#117183222
#117183172
#117183102
#117183092
#239913