Finite Group Databasebeta

← #15772254

Subgroups — #15772254

Order 3328.

342 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11718491C211yesmaximal, characteristic
2#13116632C212yesmaximal
3#13112776C211yesmaximal, characteristic
4#13112775C212yesmaximal
5C13×#1322C211yesmaximal, characteristic
6C2×C4×Dic26C411yescharacteristic
7C2×C13×C4⋊C8C2211yescharacteristic
8C2×#88054C411yescharacteristic
9C2×#88054C2211yescharacteristic
10C2×C8×Dic13C411yescharacteristic
11C2×C8×Dic13C2211yescharacteristic
12C2×C4×#1055C411yescharacteristic
13#11718491—22no—
14#11718491—22no—
15C13×C22⋊C16C2212yes—
16C22⋊#6090C2212yes—
17#11718093—22no—
18C16×Dic13—22no—
19C22×Dic26C811yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C22×C8×C13C2311yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×C4⋊Dic13C811yescharacteristic
24C2×#6101C811yescharacteristic
25C2×#6101C811yescharacteristic
26C2×C4×Dic13C2×C411yescharacteristic
27C2×C4×Dic13C2×C411yescharacteristic
28C22×#1055C2×C411yescharacteristic
29C22×#1055C2×C411yescharacteristic
30C4×Dic26—22no—
31C4×Dic26—22no—
32C2×C13×C16—22no—
33C13×C4⋊C8—22no—
34#88054—22no—
35#88054—22no—
36C8×Dic13—21no—
37C8×Dic13—21no—
38C8×Dic13D412yes—
39C8×Dic13D412yes—
40C2×#6090—22no—
41C4×#1055—21no—
42C4×#1055—21no—
43#11493—131nomaximal, Sylow
44C22×C4×C13C2×C811yescharacteristic
45C22×C4×C13C2×C811yescharacteristic
46C22×C4×C13C22×C411yescharacteristic
47C22×Dic13C2×C811yescharacteristic
48C22×Dic13C2×C811yescharacteristic
49C22×Dic13C2×C811yescharacteristic
50C22×Dic13C2×C811yescharacteristic
51C2×Dic26—22no—
52C2×Dic26—22no—
53C2×Dic26C1614yescomplemented
54C2×C8×C13—21no—
55C2×C8×C13—41no—
56C2×C8×C13—41no—
57C2×C8×C13C2×D412yes—
58C42×C13—21no—
59C42×C13—21no—
60C4⋊Dic13—22no—
61#6101—22no—
62#6101—22no—
63C4×Dic13—21no—
64C4×Dic13—21no—
65C4×Dic13C22⋊C412yes—
66C4×Dic13M1612yes—
67C2×#1055—22no—
68C2×#1055—21no—
69C2×#1055—41no—
70C2×#1055C22⋊C411yescharacteristic
71C2×#1055C22⋊C411yescharacteristic
72C13×C16—42no—
73#6090—42no—
74C2×C8×Q8—131no—
75#2162—132no—
76#1322—131no—
77#1322—132no—
78#1322D1311yescharacteristic
79C23×C13C22×C811yescharacteristic
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—41no—
86C2×C4×C13C2×C1612yes—
87C2×C4×C13C2×C22⋊C411yescharacteristic
88C2×C4×C13C2×M1611yescharacteristic
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—41no—
93C2×Dic13—41no—
94C2×Dic13C22⋊C812yes—
95C2×Dic13C22⋊C812yes—
96C2×Dic13C2×C1612yes—
97C2×Dic13C2×C1612yes—
98C2×Dic13M3212yes—
99Dic26—28no—
100C8×C13—22no—
101C8×C13—41no—
102#1055—21no—
103#1055—41no—
104#1055#10112yes—
105C2×C4×Q8—131no—
106C8×Q8—262no—
107C8×Q8—262no—
108C2×C4⋊C8—131no—
109C2×C4⋊C8—131no—
110C2×C4⋊C8C2×D1311yescharacteristic
111C2×C4×C8—131no—
112C2×C4×C8—131no—
113C2×C4×C8—131no—
114C4⋊C16—262no—
115C22⋊C16—132no—
116C22⋊C16C2×D1312yes—
117C4×C16—262no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13C2×C22⋊C811yescharacteristic
121C22×C13C22×C1611yescharacteristic
122C22×C13C2×M3211yescharacteristic
123C4×C13—22no—
124C4×C13—21no—
125C4×C13—41no—
126C4×C13#41011yescharacteristic
127C4×C13C2×#10111yescharacteristic
128Dic13—22no—
129Dic13—22no—
130Dic13—41no—
131Dic13C22⋊C1614yes—
132C22×Q8—131no—
133C22×C8—131no—
134C22×C8—131no—
135C22×C8C4×D1311yescharacteristic
136C22×C8C22×D1311yescharacteristic
137C4×Q8—262no—
138C4×Q8—262no—
139C2×C4⋊C4—131no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—131no—
142C2×C42—131no—
143C2×C42—131no—
144C2×C42C4×D1311yescharacteristic
145C2×C16—22no—
146C2×C16—262no—
147C4⋊C8—22no—
148C4⋊C8—262no—
149C4⋊C8—262no—
150C4×C8—132no—
151C4×C8—132no—
152C4×C8—261no—
153C4×C8—261no—
154C4×C8—261no—
155C4×C8—261no—
156C2×C13—21no—
157C2×C13—21no—
158C2×C13#146111yescharacteristic
159C2×C13C2×C22⋊C1611yescharacteristic
160C2×C13#211511yescharacteristic
161C2×Q8—134no—
162C2×Q8—262no—
163C2×Q8—262no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4C8×D1311yescharacteristic
169C22×C4C8×D1311yescharacteristic
170C22×C4C2×C4×D1311yescharacteristic
171C2×C8—21no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—131no—
175C2×C8—131no—
176C2×C8—262no—
177C2×C8—261no—
178C2×C8—521no—
179C2×C8D4×D1312yes—
180C4⋊C4—262no—
181C4⋊C4—262no—
182C4⋊C4—262no—
183C42—21no—
184C42—21no—
185C42—132no—
186C42—132no—
187C42—261no—
188C42—261no—
189C16—42no—
190C16—522no—
191C13#1149311yescharacteristic, complemented, Sylow
192C23C2×C8×D1311yescharacteristic
193Q8—268no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—132no—
201C2×C4—132no—
202C2×C4—132no—
203C2×C4—132no—
204C2×C4—132no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—521no—
209C2×C4—521no—
210C2×C4C16×D1312yes—
211C2×C4C22⋊C4×D1311yescharacteristic
212C2×C4M16×D1311yescharacteristic
213C8—22no—
214C8—41no—
215C8—132no—
216C8—261no—
217C8—521no—
218C22—21no—
219C22—21no—
220C22D13×C22⋊C811yescharacteristic
221C22C2×C16×D1311yescharacteristic
222C22D13×M3211yescharacteristic
223C4—22no—
224C4—21no—
225C4—41no—
226C4—134no—
227C4—262no—
228C4—262no—
229C4—521no—
230C4#1171840111yescharacteristic
231C4D13×#10111yescharacteristic
232C2—21no—
233C2—21no—
234C2#1311315811yescharacteristic
235C2D13×C22⋊C1611yescharacteristic
236C2#1311645511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C22×C16
FrattiniC22×C8C22×D13
FittingC13×#1322C2
socleC22×C13C2×C22⋊C8
prime radicalC23×C13C22×C8
cosocleC22×C8×C13C23
hypercenter#1322D13
hypocenterC13#11493
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
53. C2×Dic26C16semidirect
191. C13#11493semidirect

Maximal subgroups

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

subgroupindex
C2×#117184912
#131166322
#131127762
#131127752
C13×#13222
#1149313