Finite Group Databasebeta

← #16786963

Subgroups — #16786963

Order 3328.

330 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#13131198C212yesmaximal
2#13129773C212yesmaximal
3#13129772C212yesmaximal
4C2×C8×Dic26C211yesmaximal, characteristic
5C2×C4×Dic26C411yescharacteristic
6C2×C4×C8×C13C411yescharacteristic
7C2×#88054C411yescharacteristic
8C2×#88054C2211yescharacteristic
9C2×C8×Dic13C411yescharacteristic
10C2×C8×Dic13C2211yescharacteristic
11C2×C4⋊#1055C2211yescharacteristic
12C8×Dic26—22no—
13C8×Dic26—22no—
14C22⋊#6092C2214yes—
15#11718260—22no—
16#11718258—22no—
17C22×Dic26C811yescharacteristic
18C22×C8×C13C2×C411yescharacteristic
19C22×C8×C13C2×C411yescharacteristic
20C2×C42×C13C2×C411yescharacteristic
21C2×C4⋊Dic13C811yescharacteristic
22C2×#6101C811yescharacteristic
23C2×#6101C811yescharacteristic
24C2×C4×Dic13C2×C411yescharacteristic
25C2×C4×Dic13C2×C411yescharacteristic
26C22×#1055C2×C411yescharacteristic
27C22×#1055C2311yescharacteristic
28C4×Dic26—22no—
29C4×Dic26—22no—
30C2×#6092—24no—
31C4×C8×C13—21no—
32C4×C8×C13—21no—
33#88054—22no—
34#88054—22no—
35C8×Dic13—21no—
36C8×Dic13—21no—
37C8×Dic13D412yes—
38C8×Dic13D412yes—
39C4⋊#1055—22no—
40#11494—131nomaximal, Sylow
41C22×C4×C13C2×C811yescharacteristic
42C22×C4×C13C2×C811yescharacteristic
43C22×C4×C13C22×C411yescharacteristic
44C22×Dic13C2×C811yescharacteristic
45C22×Dic13C2×C811yescharacteristic
46C22×Dic13C2×C811yescharacteristic
47C22×Dic13C2×C811yescharacteristic
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—22no—
51C2×C8×C13—22no—
52C2×C8×C13—21no—
53C2×C8×C13—41no—
54C2×C8×C13C22⋊C411yescharacteristic
55C2×C8×C13C22⋊C411yescharacteristic
56C42×C13—21no—
57C42×C13—21no—
58C4⋊Dic13—22no—
59#6101—22no—
60#6101—22no—
61C4×Dic13—21no—
62C4×Dic13—21no—
63C4×Dic13C22⋊C412yes—
64C4×Dic13M1612yes—
65C2×#1055—21no—
66C2×#1055—41no—
67C2×#1055—41no—
68C2×#1055C2×D412yes—
69#6092—44no—
70C2×C8×Q8—131no—
71#2163—132no—
72#1322—132no—
73#1322—132no—
74C23×C13C22×C811yescharacteristic
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—41no—
81C2×C4×C13M3212yes—
82C2×C4×C13C2×C22⋊C411yescharacteristic
83C2×C4×C13C2×M1611yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—41no—
90C2×Dic13—41no—
91C2×Dic13C22⋊C812yes—
92C2×Dic13C22⋊C812yes—
93C2×Dic13M3212yes—
94Dic26—28no—
95C8×C13—21no—
96C8×C13—41no—
97C8×C13#10112yes—
98#1055—22no—
99#1055—41no—
100C2×C4×Q8—131no—
101C8×Q8—262no—
102C8×Q8—262no—
103C2×C4⋊C8—131no—
104C2×C4⋊C8—131no—
105C2×C4⋊C8—131no—
106C2×C4×C8—131no—
107C2×C4×C8—131no—
108C2×C4×C8#26111yescharacteristic
109C4⋊C16—262no—
110C22⋊C16—134no—
111#346—262no—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13C2×C22⋊C811yescharacteristic
115C22×C13C2×M3211yescharacteristic
116C22×C13C2×M3211yescharacteristic
117C4×C13—22no—
118C4×C13—21no—
119C4×C13—41no—
120C4×C13#41011yescharacteristic
121C4×C13C2×#10111yescharacteristic
122Dic13—22no—
123Dic13—22no—
124Dic13—22no—
125Dic13—41no—
126C22×Q8—131no—
127C22×C8—131no—
128C22×C8—131no—
129C22×C8C2×#26111yescharacteristic
130C22×C8C2×#26111yescharacteristic
131C4×Q8—262no—
132C4×Q8—262no—
133C2×C4⋊C4—131no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—131no—
136C2×C42—131no—
137C2×C42—131no—
138C2×C42C2×#26111yescharacteristic
139C2×C16—264no—
140C4⋊C8—262no—
141C4⋊C8—262no—
142C4⋊C8—262no—
143C4×C8—21no—
144C4×C8—21no—
145C4×C8—132no—
146C4×C8—132no—
147C4×C8—261no—
148C4×C8—261no—
149C2×C13—21no—
150C2×C13—21no—
151C2×C13#146111yescharacteristic
152C2×C13#211211yescharacteristic
153C2×C13#211511yescharacteristic
154C2×Q8—262no—
155C2×Q8—262no—
156C2×Q8—262no—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4D13⋊C811yescharacteristic
162C22×C4D13⋊C811yescharacteristic
163C22×C4C22×#26111yescharacteristic
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8—132no—
168C2×C8—261no—
169C2×C8—521no—
170C2×C8—521no—
171C2×C8C22⋊#26111yescharacteristic
172C2×C8C22⋊#26111yescharacteristic
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C42—21no—
177C42—21no—
178C42—132no—
179C42—132no—
180C42—261no—
181C42—261no—
182C16—524no—
183C13#1149411yescharacteristic, complemented, Sylow
184C23C2×D13⋊C811yescharacteristic
185Q8—268no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—132no—
193C2×C4—132no—
194C2×C4—132no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—521no—
201C2×C4—521no—
202C2×C4#8809812yes—
203C2×C4D13⋊M1611yescharacteristic
204C2×C4C2×C22⋊#26111yescharacteristic
205C8—21no—
206C8—41no—
207C8—262no—
208C8—521no—
209C8#8811312yes—
210C22—21no—
211C22—21no—
212C22C2×#8809811yescharacteristic
213C22D13⋊M3211yescharacteristic
214C22D13⋊(C22⋊C8)11yescharacteristic
215C4—22no—
216C4—21no—
217C4—41no—
218C4—262no—
219C4—262no—
220C4—262no—
221C4—521no—
222C4#1171911611yescharacteristic
223C4C2×#8811311yescharacteristic
224C2—21no—
225C2—21no—
226C2#1313007811yescharacteristic
227C2#1313106411yescharacteristic
228C2#1313107311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutator, prime radicalC23×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×C8×C13C4
socleC22×C13C2×C22⋊C8
cosocleC22×#1055C23
hypercenterC2×C4×C8#261
hypocenterC13#11494
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
183. C13#11494semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131297732
#131297722
C2×C8×Dic262
#1149413