Finite Group Databasebeta

← #15779284

Subgroups — #15779284

Order 3328.

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

normal subgroups only

This group has 234 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#13116601C211yesmaximal, characteristic
2#13116594C211yesmaximal, characteristic
3#13114591C211yesmaximal, characteristic
4#13112924C211yesmaximal, characteristic
5#13112922C211yesmaximal, characteristic
6#13112921C211yesmaximal, characteristic
7C13×#1379C211yesmaximal, characteristic
8C2×C13×M32C2211yescharacteristic
9C22×C13×C16C2211yescharacteristic
10C13×#405C2211yescharacteristic
11#11718762C2211yescharacteristic
12#11718762C2211yescharacteristic
13C2×#88052C2211yescharacteristic
14C2×#88052C2211yescharacteristic
15#11718152C411yescharacteristic
16#11718149C411yescharacteristic
17#11718123C411yescharacteristic
18#11718123C411yescharacteristic
19#11718103—22no—
20#11718093—22no—
21C2×C13×M16C2×C411yescharacteristic
22C22×C8×C13C2311yescharacteristic
23C13×#117C2×C411yescharacteristic
24#88180C2×C411yescharacteristic
25#88180C2×C411yescharacteristic
26C2×#6099C2×C411yescharacteristic
27C2×#6099C2×C411yescharacteristic
28C13×M32—21no—
29C13×M32—21no—
30C2×C13×C16—21no—
31C2×C13×C16—21no—
32C2×C13×C16—21no—
33C2×C13×C16—21no—
34C13×#97—21no—
35C4×C8×C13—21no—
36#88055—21no—
37#88055Q812yes—
38C8×Dic13—21no—
39C8×Dic13D412yes—
40#88052—21no—
41#88052—21no—
42#88052—21no—
43#88052—21no—
44C2×#6090—21no—
45C2×#6090—21no—
46#12885—131nomaximal, Sylow
47C22×C4×C13C22×C411yescharacteristic
48C13×M16—21no—
49C13×M16—21no—
50C2×C8×C13—21no—
51C2×C8×C13C2×D411yescharacteristic
52C2×C8×C13C2×Q811yescharacteristic
53C2×C8×C13#4111yescharacteristic
54C2×C8×C13#4111yescharacteristic
55C2×C8×C13#4111yescharacteristic
56C2×C8×C13#4111yescharacteristic
57C13×C4⋊C4—21no—
58C13×C22⋊C4—21no—
59C42×C13—21no—
60C22⋊Dic13—21no—
61C22⋊Dic13—21no—
62C4⋊Dic13—21no—
63C4⋊Dic13—21no—
64C4×Dic13—21no—
65C4×Dic13C4⋊C412yes—
66#6099—21no—
67#6099—21no—
68#6099—21no—
69#6099—21no—
70C2×#1055—21no—
71C2×#1055C4⋊C412yes—
72C13×C16—41no—
73C13×C16—41no—
74#6090—41no—
75#6090—41no—
76#2153—131no—
77#2151—131no—
78#1747—131no—
79#1379—131no—
80#1379D1311yescharacteristic
81#1378—131no—
82#1378—131no—
83C23×C13#13111yescharacteristic
84C2×C4×C13—41no—
85C2×C4×C13C2×C4⋊C411yescharacteristic
86C2×C4×C13#11711yescharacteristic
87C2×C4×C13#11711yescharacteristic
88C2×C4×C13#13111yescharacteristic
89C2×C4×C13#13111yescharacteristic
90C2×C4×C13#13111yescharacteristic
91C2×Dic13—22no—
92C2×Dic13—41no—
93C8×C13—41no—
94C8×C13#12411yescharacteristic
95C8×C13#12411yescharacteristic
96C8×C13#12511yescharacteristic
97C8×C13#12511yescharacteristic
98#1055—22no—
99#1055—41no—
100C2×M32—131no—
101C2×M32—131no—
102C2×M32C2×D1311yescharacteristic
103C22×C16C2×D1311yescharacteristic
104#405—131no—
105#405—131no—
106#405C2×D1311yescharacteristic
107#364—262no—
108C4⋊C16—262no—
109#338—131no—
110H(3,ℤ/4)—131no—
111H(3,ℤ/4)—131no—
112H(3,ℤ/4)—131no—
113C22×C13—41no—
114C22×C13#42411yescharacteristic
115C22×C13#43311yescharacteristic
116C22×C13#43311yescharacteristic
117C4×C13—81no—
118C4×C13#38211yescharacteristic
119C4×C13#42411yescharacteristic
120C4×C13#43311yescharacteristic
121C4×C13#43311yescharacteristic
122Dic13—42no—
123Dic13—81no—
124C2×M16—131no—
125C2×M16—131no—
126C2×M16C4×D1311yescharacteristic
127C22×C8C22×D1311yescharacteristic
128#117—131no—
129#117—131no—
130#117C4×D1311yescharacteristic
131M32—21no—
132M32—21no—
133M32—261no—
134M32—261no—
135M32—261no—
136M32—261no—
137C2×C16—21no—
138C2×C16—21no—
139C2×C16—21no—
140C2×C16—21no—
141C2×C16—261no—
142C2×C16—261no—
143#97—21no—
144#97—132no—
145#97—261no—
146C4×C8—21no—
147C4×C8—132no—
148C4×C8—261no—
149C2×C13—21no—
150C2×C13—21no—
151C2×C13—21no—
152C2×C13#183211yescharacteristic
153C22×C4C2×C4×D1311yescharacteristic
154M16—21no—
155M16—21no—
156M16—261no—
157M16—261no—
158M16—261no—
159M16—261no—
160C2×C8—21no—
161C2×C8—132no—
162C2×C8—261no—
163C2×C8#612711yescharacteristic
164C2×C8#612711yescharacteristic
165C2×C8D4×D1311yescharacteristic
166C2×C8#612911yescharacteristic
167C2×C8#612911yescharacteristic
168C2×C8Q8×D1311yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—261no—
171C4⋊C4—261no—
172C22⋊C4—21no—
173C22⋊C4—261no—
174C22⋊C4—261no—
175C42—21no—
176C42—132no—
177C42—261no—
178C16—41no—
179C16—41no—
180C16—521no—
181C16—521no—
182C13#1288511yescharacteristic, complemented, Sylow
183C23#8816111yescharacteristic
184C2×C4—41no—
185C2×C4—262no—
186C2×C4—521no—
187C2×C4#8812611yescharacteristic
188C2×C4#8813111yescharacteristic
189C2×C4C4⋊C4×D1311yescharacteristic
190C2×C4#8815511yescharacteristic
191C2×C4#8815511yescharacteristic
192C2×C4#8816111yescharacteristic
193C8—41no—
194C8—262no—
195C8—521no—
196C8#8813911yescharacteristic
197C8#8813911yescharacteristic
198C8#8814311yescharacteristic
199C8#8814311yescharacteristic
200C22—41no—
201C22#1171837011yescharacteristic
202C22#1171838111yescharacteristic
203C22#1171850011yescharacteristic
204C4—81no—
205C4—522no—
206C4—1041no—
207C4#1171831111yescharacteristic
208C4#1171835111yescharacteristic
209C4#1171838111yescharacteristic
210C4#1171850011yescharacteristic
211C2—21no—
212C2—21no—
213C2—21no—
214C2#1311495411yescharacteristic
subgroupG/H
centerC8#88139
commutatorC22×C4×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1379C2
socleC2×C13#1832
prime radicalC23×C13#131
cosocleC22×C8×C13C23
hypercenter#1379D13
hypocenterC13#12885
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
182. C13#12885semidirect

Maximal subgroups

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

subgroupindex
#131166012
#131165942
#131145912
#131129242
#131129222
#131129212
C13×#13792
#1288513