Finite Group Databasebeta

← #16788957

Subgroups — #16788957

Order 3328.

204 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 62 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#13130483C211yesmaximal, characteristic
2#13130429C211yesmaximal, characteristic
3#13129862C211yesmaximal, characteristic
4#13129796C211yesmaximal, characteristic
5#13129796C211yesmaximal, characteristic
6#13129755C211yesmaximal, characteristic
7#13116707C211yesmaximal, characteristic
8#11719158—21no—
9Q8×#1057—21no—
10C2×C13×Q32C411yescharacteristic
11Q16×Dic13C2211yescharacteristic
12Q16×Dic13C2211yescharacteristic
13Q8⋊#1057—21no—
14Q8⋊#1057—21no—
15#11718258C2211yescharacteristic
16#11718253C2211yescharacteristic
17#11718253C2211yescharacteristic
18#11718251C2211yescharacteristic
19#11718156C411yescharacteristic
20#11718156C411yescharacteristic
21#11718097C411yescharacteristic
22#11718094C2211yescharacteristic
23C2×C13×Q16C2×C411yescharacteristic
24C2×C13×Q16C2×C411yescharacteristic
25Q8×Dic13—21no—
26Q8×Dic13—21no—
27#88112—41no—
28#88110—41no—
29C4⋊#1057—21no—
30C4⋊#1057—21no—
31C4⋊#1057—41no—
32C4×#1057—41no—
33C4×#1057D411yescharacteristic
34C4×#1057D411yescharacteristic
35C2×#6092—21no—
36C13×Q32—22no—
37C2×C13×C16C2×C411yescharacteristic
38#88075—21no—
39#88075—21no—
40#88058C2×C411yescharacteristic
41#88058C2×C411yescharacteristic
42C8×Dic13C2311yescharacteristic
43C2×#6090C2×C411yescharacteristic
44#12079—131nomaximal, Sylow
45C2×Q8×C13—21no—
46C2×Q8×C13—21no—
47C2×#1057—21no—
48C2×#1057—21no—
49C2×#1057—41no—
50C2×#1057—41no—
51C13×Q16—21no—
52C13×Q16—21no—
53C13×Q16—21no—
54C13×Q16M1612yes—
55C2×C8×C13C22×C411yescharacteristic
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13—41no—
59C4⋊Dic13—41no—
60C4×Dic13—41no—
61C4×Dic13—41no—
62C4×Dic13C2×D411yescharacteristic
63C2×#1055#4111yescharacteristic
64#6092—22no—
65C13×C16—21no—
66#6090—21no—
67#2176—131no—
68#1593—131no—
69#1579—131no—
70#1368—131no—
71#1334—131no—
72#1334—131no—
73#1313—131no—
74Q8×C13—22no—
75Q8×C13—41no—
76Q8×C13—41no—
77Q8×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13C4×D411yescharacteristic
81C2×Dic13—41no—
82C2×Dic13—41no—
83C2×Dic13AGL(1,ℤ/8)11yescharacteristic
84C2×Dic13AGL(1,ℤ/8)11yescharacteristic
85#1057—41no—
86#1057—41no—
87#1057—81no—
88#1057—81no—
89C8×C13C2×M1611yescharacteristic
90C8×C13#13111yescharacteristic
91#1055—21no—
92C2×Q32#26111yescharacteristic
93#446—261no—
94C8×Q8—261no—
95C4×Q16—131no—
96C4×Q16—131no—
97#367—131no—
98#358—131no—
99#358—131no—
100#346—131no—
101#346—131no—
102#334—131no—
103#334—131no—
104Q8⋊C8—261no—
105Q8⋊C8—261no—
106#322—131no—
107C22×C13#44211yescharacteristic
108C4×C13—42no—
109C4×C13—81no—
110C4×C13#43511yescharacteristic
111C4×C13#44311yescharacteristic
112Dic13—21no—
113Dic13—21no—
114Dic13—81no—
115Dic13—81no—
116C2×Q16C2×#26111yescharacteristic
117C2×Q16C2×#26111yescharacteristic
118C4×Q8—261no—
119C4×Q8—261no—
120Q32—22no—
121C2×C16—131no—
122C2×C16—261no—
123C2×C16C2×#26111yescharacteristic
124#107—131no—
125#107—131no—
126C4⋊C8—261no—
127C4⋊C8—261no—
128C4⋊C8—521no—
129C4⋊C8—521no—
130#103—261no—
131#103—261no—
132#97—521no—
133C4×C8—131no—
134C4×C8—131no—
135C4×C8—131no—
136C4×C8—521no—
137C2×C13#158611yescharacteristic
138C2×C13#218011yescharacteristic
139C2×C13#218011yescharacteristic
140C2×Q8—21no—
141C2×Q8—21no—
142Q16—21no—
143Q16—21no—
144Q16—21no—
145Q16#612212yes—
146C2×C8—131no—
147C2×C8—261no—
148C2×C8—261no—
149C2×C8—521no—
150C2×C8—521no—
151C2×C8C22×#26111yescharacteristic
152C4⋊C4—261no—
153C4⋊C4—261no—
154C4⋊C4—521no—
155C4⋊C4—521no—
156C42—131no—
157C42—521no—
158C42—521no—
159C16—21no—
160C16—262no—
161C16—261no—
162C13#1207911yescharacteristic, complemented, Sylow
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—131no—
170C2×C4—131no—
171C2×C4—521no—
172C2×C4—521no—
173C2×C4D4×#26111yescharacteristic
174C8—261no—
175C8—521no—
176C8—521no—
177C8—1041no—
178C8—1041no—
179C8#8823811yescharacteristic
180C8C2×#612211yescharacteristic
181C22#1171910211yescharacteristic
182C4—42no—
183C4—81no—
184C4—261no—
185C4—261no—
186C4—1041no—
187C4—1041no—
188C4#1171910311yescharacteristic
189C4#1171914411yescharacteristic
190C2#1313045711yescharacteristic
191C2#1313124311yescharacteristic
192C2#1313124411yescharacteristic
subgroupG/H
centerC22#11719102
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC2×C13×Q32C4
socle, prime radicalC22×C13#442
cosocleC8×Dic13C23
hypercenterC2×Q32#261
hypocenterC13#12079
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
162. C13#12079semidirect

Maximal subgroups

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

subgroupindex
#131304832
#131304292
#131298622
#131297962
#131297552
#131167072
#1207913