Finite Group Databasebeta

← #13130675

Subgroups — #13130675

Order 1664.

592 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C22×Q8×D13C211yesmaximal, characteristic
2C2×#88117C214yesmaximal, complemented
3#11719136C211yesmaximal, characteristic
4D13⋊(C22⋊C8)C211yesmaximal, characteristic
5C22×Q8×C13C411yescharacteristic, complemented
6C2×Q8×D13—28no—
7C2×Q8×D13—21no—
8C2×Q8×D13—21no—
9C2×Q8×D13C412yescomplemented
10C2×Q8×D13C2212yes—
11C22×C4×D13—21no—
12C22×C4×D13C2211yescharacteristic
13C22×Dic26—21no—
14C22×Dic26C411yescharacteristic, complemented
15C2×C22⋊#261—21no—
16C2×C4⋊#261C2212yes—
17C2×D13⋊C8C2212yes—
18C22⋊#1057—21no—
19#88117—28no—
20(C2×#261)⋊C4—21no—
21#88111—21no—
22C23×D13D411yescharacteristic
23C22×#261—22no—
24C2×Q8×C13—24no—
25C2×Q8×C13—21no—
26C2×Q8×C13C2×C412yes—
27C22×C4×C13—21no—
28C22×C4×C13C2×C411yescharacteristic
29C22×Dic13—21no—
30C22×Dic13D411yescharacteristic
31Q8×D13—28no—
32Q8×D13—28no—
33Q8×D13—24no—
34Q8×D13—24no—
35Q8×D13—24no—
36Q8×D13D418yes—
37C2×C4×D13—28no—
38C2×C4×D13—22no—
39C2×C4×D13—22no—
40C2×C4×D13—24no—
41C2×C4×D13C2×C411yescharacteristic
42C2×C4×D13D411yescharacteristic
43C2×C4×D13D411yescharacteristic
44C2×C4×D13C2311yescharacteristic
45C2×Dic26—28no—
46C2×Dic26—21no—
47C2×Dic26—22no—
48C2×Dic26—22no—
49C2×Dic26—24no—
50C2×Dic26C2×C412yes—
51C22⋊#261—42no—
52C2×#1057—22no—
53C4⋊#261—24no—
54D13⋊C8—24no—
55#1787—131nomaximal, Sylow
56C23×C13C22⋊C411yescharacteristic
57C22×D13—22no—
58C22×D13—22no—
59C22×D13C22⋊C411yescharacteristic
60C22×D13SD1612yes—
61C22×D13Q1612yes—
62C22×D13C2×D411yescharacteristic
63C2×#261—42no—
64C2×#261—42no—
65C2×#261—42no—
66Q8×C13—24no—
67Q8×C13—22no—
68Q8×C13C22⋊C414yescomplemented
69C2×C4×C13—24no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13C22⋊C411yescharacteristic
73C2×C4×C13C22×C411yescharacteristic
74C2×Dic13—24no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13C22⋊C411yescharacteristic
78C2×Dic13C2×D411yescharacteristic
79C4×D13—28no—
80C4×D13—28no—
81C4×D13—22no—
82C4×D13—22no—
83C4×D13—22no—
84C4×D13C2×D414yes—
85Dic26—28no—
86Dic26—24no—
87Dic26—22no—
88Dic26—28no—
89Dic26C22⋊C414yescomplemented
90#1057—42no—
91C23×Q8—131no—
92C2×#103—134no—
93C2×C22⋊C8—131no—
94#380—131no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13#10312yescomplemented
98C22×C13C2×C22⋊C411yescharacteristic
99C2×D13—21no—
100C2×D13—21no—
101C2×D13—24no—
102C2×D13—24no—
103C2×D13#10312yescomplemented
104C2×D13#12012yes—
105C2×D13C2×SD1611yescharacteristic
106C2×D13C2×Q1611yescharacteristic
107C2×D13#13712yes—
108#261—82no—
109C4×C13—24no—
110C4×C13—21no—
111C4×C13C2×C22⋊C412yes—
112Dic13—21no—
113Dic13—24no—
114Dic13#12012yes—
115C22×Q8—132no—
116C22×Q8—132no—
117C22×Q8—131no—
118C22×Q8—261no—
119C22×Q8—261no—
120C22×Q8—261no—
121C22×Q8—268no—
122C22×Q8#26111yescharacteristic, complemented
123C23×C4—131no—
124C23×C4—261no—
125C22×C8—132no—
126C2×C4⋊C4—132no—
127C2×C22⋊C4—261no—
128#103—268no—
129C22⋊C8—261no—
130C22⋊C8—261no—
131#95—261no—
132C2×C13—22no—
133C2×C13#37911yescharacteristic
134C2×C13C2×#10311yescharacteristic
135C2×C13#41911yescharacteristic
136D13—22no—
137D13#44812yes—
138D13#45112yes—
139C24—131no—
140C2×Q8—24no—
141C2×Q8—21no—
142C2×Q8—138no—
143C2×Q8—132no—
144C2×Q8—262no—
145C2×Q8—262no—
146C2×Q8—264no—
147C2×Q8—268no—
148C2×Q8—264no—
149C2×Q8—264no—
150C2×Q8—268no—
151C2×Q8—268no—
152C2×Q8—264no—
153C2×Q8—261no—
154C2×Q8C2×#26112yes—
155C22×C4—21no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—264no—
162C22×C4—262no—
163C22×C4—262no—
164C22×C4—268no—
165C22×C4—261no—
166C22×C4—262no—
167C22×C4C2×#26111yescharacteristic
168C2×C8—262no—
169C2×C8—264no—
170C4⋊C4—264no—
171C22⋊C4—522no—
172C13#178711yescharacteristic, complemented, Sylow
173C23—131no—
174C23—132no—
175C23—132no—
176C23—131no—
177C23—262no—
178C23—262no—
179C23C22⋊#26111yescharacteristic
180Q8—24no—
181Q8—22no—
182Q8—134no—
183Q8—268no—
184Q8—268no—
185Q8—264no—
186Q8—262no—
187Q8C22⋊#26114yescomplemented
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—131no—
192C2×C4—134no—
193C2×C4—131no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—268no—
197C2×C4—268no—
198C2×C4—262no—
199C2×C4—264no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4C22⋊#26111yescharacteristic
206C2×C4C22×#26111yescharacteristic
207C8—522no—
208C22—21no—
209C22—21no—
210C22—132no—
211C22—131no—
212C22—131no—
213C22—132no—
214C22—132no—
215C22—264no—
216C22—264no—
217C22—261no—
218C22—261no—
219C22#8811712yescomplemented
220C22C2×C22⋊#26111yescharacteristic
221C4—24no—
222C4—21no—
223C4—132no—
224C4—261no—
225C4—264no—
226C4—1042no—
227C4C2×C22⋊#26112yes—
228C2—22no—
229C2—132no—
230C2—132no—
231C2—262no—
232C2C2×#8811711yescharacteristic
233C2#1171915311yescharacteristic
234C2#1171917111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC22×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC22×Q8#261
hypocenterC13#1787
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#88117C2semidirect
5. C22×Q8×C13C4semidirect
9. C2×Q8×D13C4semidirect
14. C22×Dic26C4semidirect
68. Q8×C13C22⋊C4semidirect
89. Dic26C22⋊C4semidirect
97. C22×C13#103semidirect
103. C2×D13#103semidirect
122. C22×Q8#261semidirect
172. C13#1787semidirect
187. Q8C22⋊#261semidirect
219. C22#88117semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D132
C2×#881172
#117191362
D13⋊(C22⋊C8)2
#178713