Finite Group Databasebeta

← #16787470

Subgroups — #16787470

Order 3328.

334 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 102 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#13131197C211yesmaximal, characteristic
2#13131193C211yesmaximal, characteristic
3#13129803C214yesmaximal, complemented
4C2×#11718491C211yesmaximal, characteristic
5C2×C4×Dic26C411yescharacteristic
6C2×C13×C4⋊C8C411yescharacteristic
7C2×#88054—21no—
8C2×C8×Dic13—21no—
9C2×C4×#1055C2211yescharacteristic
10#11718491—21no—
11#11718491—21no—
12#11718491C412yes—
13#11718491C2212yes—
14C22⋊#6092—21no—
15C22⋊#6092—21no—
16#11718231—21no—
17C4⋊#6092—21no—
18C4⋊#6092C2212yes—
19C4×#6092C2212yes—
20C22×Dic26C811yescharacteristic
21C22×C8×C13—21no—
22C2×C42×C13C2×C411yescharacteristic
23C2×C4⋊Dic13C811yescharacteristic
24C2×#6101—21no—
25C2×C4×Dic13—21no—
26C22×#1055D411yescharacteristic
27C22×#1055D411yescharacteristic
28C4×Dic26—21no—
29C4×Dic26—21no—
30C4×Dic26C812yes—
31C4×Dic26C2×C412yes—
32C2×#6092—22no—
33C2×#6092—22no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8C2×C412yes—
36#88054—22no—
37#88054—22no—
38C8×Dic13—22no—
39C8×Dic13—22no—
40C4×#1055C2×C411yescharacteristic
41C4×#1055D411yescharacteristic
42C4×#1055D411yescharacteristic
43C4×#1055C2311yescharacteristic
44#11639—131nomaximal, Sylow
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C2×C811yescharacteristic
47C22×C4×C13M1611yescharacteristic
48C22×Dic13—21no—
49C22×Dic13—21no—
50C2×Dic26—21no—
51C2×Dic26—24no—
52C2×Dic26C2×C812yes—
53C2×C8×C13—22no—
54C2×C8×C13—42no—
55C42×C13C22⋊C411yescharacteristic
56C42×C13C2×C811yescharacteristic
57C42×C13M1611yescharacteristic
58C42×C13C22×C411yescharacteristic
59C4⋊Dic13—21no—
60C4⋊Dic13C2×C812yes—
61#6101—22no—
62#6101—22no—
63C4×Dic13—22no—
64C4×Dic13—22no—
65C2×#1055—22no—
66C2×#1055—41no—
67C2×#1055C22⋊C411yescharacteristic
68C2×#1055C22⋊C411yescharacteristic
69C2×#1055C2×D411yescharacteristic
70C2×#1055C2×D411yescharacteristic
71#6092—42no—
72#6092—42no—
73C2×C8×Q8—131no—
74#2163—131no—
75#2162—131no—
76Q8⋊C16—134no—
77C23×C13C22⋊C811yescharacteristic
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13C22⋊C811yescharacteristic
83C2×C4×C13C22⋊C811yescharacteristic
84C2×C4×C13C22⋊C811yescharacteristic
85C2×C4×C13C2×C22⋊C411yescharacteristic
86C2×C4×C13C22×C811yescharacteristic
87C2×C4×C13C2×M1611yescharacteristic
88C2×Dic13—24no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—42no—
92Dic26—24no—
93Dic26—22no—
94Dic26M3214yes—
95C8×C13—42no—
96#1055—21no—
97#1055—21no—
98#1055—21no—
99#1055#13712yes—
100C2×C4×Q8—131no—
101C8×Q8—132no—
102C8×Q8—132no—
103C8×Q8—261no—
104C8×Q8—261no—
105C2×C4⋊C8—261no—
106C2×C4⋊C8#26111yescharacteristic
107C2×C4×C8—131no—
108C2×C4×C8—261no—
109C4⋊C16—132no—
110C4⋊C16—261no—
111C22⋊C16—261no—
112C22⋊C16—261no—
113#346—261no—
114C4×C16—132no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13#35012yes—
118C22×C13C2×C22⋊C811yescharacteristic
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13#41911yescharacteristic
124C4×C13#42111yescharacteristic
125C4×C13C2×M3212yes—
126Dic13—24no—
127Dic13—42no—
128C22×Q8—131no—
129C22×C8—21no—
130C22×C8—131no—
131C22×C8—131no—
132C4×Q8—132no—
133C4×Q8—132no—
134C4×Q8—261no—
135C4×Q8—261no—
136C2×C4⋊C4—131no—
137C2×C4⋊C4—261no—
138C2×C42—261no—
139C2×C42C2×#26111yescharacteristic
140C2×C16—262no—
141C2×C16—262no—
142C4⋊C8—21no—
143C4⋊C8—262no—
144C4⋊C8—262no—
145C4⋊C8C2×#26112yes—
146C4×C8—131no—
147C4×C8—131no—
148C4×C8—131no—
149C4×C8—131no—
150C4×C8—262no—
151C4×C8—262no—
152C2×C13—22no—
153C2×C13#147911yescharacteristic
154C2×C13#211211yescharacteristic
155C2×C13C2×#35011yescharacteristic
156C2×Q8—132no—
157C2×Q8—264no—
158C2×Q8—261no—
159C22×C4—261no—
160C22×C4—261no—
161C22×C4D13⋊C811yescharacteristic
162C22×C4#611811yescharacteristic
163C22×C4C22⋊#26111yescharacteristic
164C2×C8—22no—
165C2×C8—42no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—131no—
170C2×C8—262no—
171C2×C8—521no—
172C4⋊C4—132no—
173C4⋊C4—261no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C42—262no—
177C42—262no—
178C42D13⋊C811yescharacteristic
179C42#611811yescharacteristic
180C42C22⋊#26111yescharacteristic
181C42C22×#26111yescharacteristic
182C16—522no—
183C16—522no—
184C13#1163911yescharacteristic, complemented, Sylow
185C23#8811111yescharacteristic
186Q8—134no—
187Q8—264no—
188Q8—262no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—264no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—522no—
197C2×C4#8811111yescharacteristic
198C2×C4#8811111yescharacteristic
199C2×C4#8811111yescharacteristic
200C2×C4C2×D13⋊C811yescharacteristic
201C2×C4C2×#611811yescharacteristic
202C2×C4C2×C22⋊#26111yescharacteristic
203C8—42no—
204C8—132no—
205C8—261no—
206C8—261no—
207C8—261no—
208C22—21no—
209C22—21no—
210C22#1171827012yes—
211C22C2×#8811111yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—264no—
217C4—522no—
218C4D13⋊M3212yes—
219C4#1171914011yescharacteristic
220C4#1171915311yescharacteristic
221C2—22no—
222C2#1313014011yescharacteristic
223C2#1313106511yescharacteristic
224C2C2×#1171827011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC42C22×#261
FittingC2×C13×C4⋊C8C4
socleC22×C13C2×C22⋊C8
prime radicalC23×C13C22⋊C8
cosocleC4×#1055C23
hypercenterC2×C4⋊C8#261
hypocenterC13#11639
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #13129803C2semidirect
184. C13#11639semidirect

Maximal subgroups

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

subgroupindex
#131311972
#131311932
#131298032
C2×#117184912
#1163913