Finite Group Databasebeta

← #15749910

Subgroups — #15749910

Order 3328.

304 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 95 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#13116447C211yesmaximal, characteristic
2C8×C22⋊Dic13C211yesmaximal, characteristic
3C2×C13×C22⋊C16C211yesmaximal, characteristic
4C23×C8×C13C2211yescharacteristic
5C22×C13×C16—21no—
6C4×C22⋊Dic13C411yescharacteristic
7C2×C22⋊#1055C411yescharacteristic
8C2×C8×Dic13—21no—
9C2×#88052C412yescomplemented
10C13×C22⋊C16—21no—
11C13×C22⋊C16C412yescomplemented
12#11718142—21no—
13C22⋊#6090—21no—
14C22⋊#6090—21no—
15C23×C4×C13C2×C411yescharacteristic
16C22×C8×C13—42no—
17C22×C8×C13C2×C411yescharacteristic
18C22×C8×C13C2×C411yescharacteristic
19C22×C8×C13D411yescharacteristic
20C22×C8×C13D411yescharacteristic
21C22×C8×C13D411yescharacteristic
22C22×C8×C13Q811yescharacteristic
23C2×C22⋊Dic13—21no—
24C2×C4×Dic13—21no—
25C22×#1055—21no—
26C2×C13×C16—22no—
27C2×C13×C16—42no—
28#88071C812yes—
29C22⋊#1055—21no—
30C22⋊#1055C812yes—
31C8×Dic13—42no—
32#88052—42no—
33C2×#6090—22no—
34#7202—131nomaximal, Sylow
35C24×C13M1611yescharacteristic
36C22×C4×C13—41no—
37C22×C4×C13—41no—
38C22×C4×C13C4211yescharacteristic
39C22×C4×C13C22⋊C411yescharacteristic
40C22×C4×C13C4⋊C411yescharacteristic
41C22×C4×C13C2×C811yescharacteristic
42C22×C4×C13C2×C811yescharacteristic
43C22×C4×C13M1611yescharacteristic
44C22×Dic13—22no—
45C2×C8×C13—22no—
46C2×C8×C13—22no—
47C2×C8×C13—22no—
48C2×C8×C13—41no—
49C2×C8×C13—41no—
50C2×C8×C13—41no—
51C2×C8×C13C22⋊C411yescharacteristic
52C2×C8×C13C22⋊C411yescharacteristic
53C2×C8×C13C4⋊C411yescharacteristic
54C2×C8×C13C4⋊C411yescharacteristic
55C22⋊Dic13—24no—
56C4×Dic13—41no—
57C4×Dic13—41no—
58C2×#1055—22no—
59C2×#1055—41no—
60C2×#1055—41no—
61C13×C16—42no—
62#6090—42no—
63#2112—131no—
64C2×C22⋊C16D1311yescharacteristic
65C8×C22⋊C4—131no—
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—41no—
69C23×C13#9711yescharacteristic
70C23×C13C22⋊C811yescharacteristic
71C23×C13C4⋊C811yescharacteristic
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13#9511yescharacteristic
82C2×C4×C13C4×C811yescharacteristic
83C2×C4×C13C22⋊C811yescharacteristic
84C2×C4×C13C4⋊C811yescharacteristic
85C2×Dic13—24no—
86C2×Dic13—42no—
87C2×Dic13—42no—
88C8×C13—21no—
89C8×C13—21no—
90C8×C13—21no—
91C8×C13#9912yes—
92#1055—42no—
93C23×C8C2×D1311yescharacteristic
94C2×M32—132no—
95C22×C16—21no—
96C2×C22⋊C8—131no—
97C2×C4×C8—261no—
98C4×C22⋊C4—131no—
99C22⋊C16—21no—
100C22⋊C16—261no—
101C22⋊C16—261no—
102C22⋊C16Dic1312yescomplemented
103#336—261no—
104C22×C13—21no—
105C22×C13—21no—
106C22×C13—21no—
107C22×C13—21no—
108C22×C13—21no—
109C22×C13—21no—
110C22×C13—21no—
111C22×C13—44no—
112C22×C13#33611yescharacteristic
113C22×C13#35012yes—
114C22×C13#36412yes—
115C4×C13—21no—
116C4×C13—21no—
117C4×C13—21no—
118C4×C13#34211yescharacteristic
119C4×C13#34411yescharacteristic
120Dic13—44no—
121C23×C4C4×D1311yescharacteristic
122C22×C8—42no—
123C22×C8—261no—
124C22×C8Dic2611yescharacteristic
125C22×C8C4×D1311yescharacteristic
126C22×C8D5211yescharacteristic
127C22×C8C2×Dic1311yescharacteristic
128C22×C8C22⋊D1311yescharacteristic
129C22×C8C22⋊D1311yescharacteristic
130C2×C22⋊C4—261no—
131C2×C42—261no—
132M32—522no—
133C2×C16—22no—
134C2×C16—42no—
135C2×C16—262no—
136C22⋊C8—132no—
137C22⋊C8—261no—
138C4×C8—522no—
139#95—132no—
140C2×C13—22no—
141C2×C13—22no—
142C2×C13—41no—
143C2×C13#128211yescharacteristic
144C2×C13#137611yescharacteristic
145C2×C13#137911yescharacteristic
146C24#609411yescharacteristic
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—262no—
150C22×C4C8×D1311yescharacteristic
151C22×C4C8×D1311yescharacteristic
152C22×C4#609411yescharacteristic
153C22×C4C4×Dic1311yescharacteristic
154C22×C4#610111yescharacteristic
155C22×C4#610311yescharacteristic
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—262no—
163C2×C8—521no—
164C2×C8—521no—
165C2×C8#610111yescharacteristic
166C2×C8C4⋊Dic1311yescharacteristic
167C2×C8#610311yescharacteristic
168C2×C8C22⋊Dic1311yescharacteristic
169C22⋊C4—264no—
170C42—521no—
171C42—521no—
172C16—42no—
173C16—522no—
174C13#720211yescharacteristic, complemented, Sylow
175C23—22no—
176C23—22no—
177C23—41no—
178C23#8805411yescharacteristic
179C23#8805511yescharacteristic
180C23#8806011yescharacteristic
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—264no—
191C2×C4—522no—
192C2×C4—522no—
193C2×C4C8×Dic1311yescharacteristic
194C2×C4#8805411yescharacteristic
195C2×C4#8806011yescharacteristic
196C2×C4#8807111yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—522no—
201C8#8804612yes—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22#1171810012yes—
211C22#1171810312yes—
212C22#1171814211yescharacteristic
213C4—21no—
214C4—21no—
215C4—21no—
216C4—524no—
217C4#1171811911yescharacteristic
218C4#1171815111yescharacteristic
219C2—22no—
220C2—22no—
221C2—41no—
222C2#1311268211yescharacteristic
223C2#1311291711yescharacteristic
224C2#1311292411yescharacteristic
subgroupG/H
centerC2×C8#6103
commutatorC2×C4×C13C4×C8
FrattiniC23×C8C2×D13
FittingC2×C13×C22⋊C16C2
socleC22×C13#336
prime radicalC24×C13M16
cosocleC23×C8×C13C22
hypercenterC2×C22⋊C16D13
hypocenterC13#7202
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
9. C2×#88052C4semidirect
11. C13×C22⋊C16C4semidirect
102. C22⋊C16Dic13semidirect
174. C13#7202semidirect

Maximal subgroups

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

subgroupindex
#131164472
C8×C22⋊Dic132
C2×C13×C22⋊C162
#720213