Finite Group Databasebeta

← #15774720

Subgroups — #15774720

Order 3328.

206 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 89 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#13116744C211yesmaximal, characteristic
2C16×Dic26C211yesmaximal, characteristic
3C8×Dic52C211yesmaximal, characteristic
4#13112906C211yesmaximal, characteristic
5#13112816C211yesmaximal, characteristic
6#13112816C211yesmaximal, characteristic
7C13×#1311C211yesmaximal, characteristic
8C4×Dic52C411yescharacteristic
9C8×Dic26C2211yescharacteristic
10C8×Dic26C2211yescharacteristic
11C4×C13×C16C2211yescharacteristic
12C4×C13×C16C2211yescharacteristic
13C82×C13C2211yescharacteristic
14#11718094—21no—
15#11718093—21no—
16#11718093—21no—
17C16×Dic13—21no—
18C4⋊#6090C2211yescharacteristic
19C4⋊#6090C2211yescharacteristic
20#11718050C411yescharacteristic
21#11718048C411yescharacteristic
22#11718048C411yescharacteristic
23C2×Dic52C811yescharacteristic
24C4×Dic26C2×C411yescharacteristic
25C4×Dic26C2×C411yescharacteristic
26C2×C13×C16—21no—
27C2×C13×C16D411yescharacteristic
28C2×C13×C16D411yescharacteristic
29C4×C8×C13C2×C411yescharacteristic
30C4×C8×C13C2×C411yescharacteristic
31C4×C8×C13C2311yescharacteristic
32#88058C811yescharacteristic
33#88056C811yescharacteristic
34#88056C811yescharacteristic
35#88054—21no—
36#88054—21no—
37C8×Dic13—21no—
38C8×Dic13—21no—
39C2×#6090—21no—
40C2×#6090—21no—
41C4⋊#1055C2×C411yescharacteristic
42C4⋊#1055C2×C411yescharacteristic
43#12053—131nomaximal, Sylow
44C2×Dic26C2×C811yescharacteristic
45C2×Dic26C2×C811yescharacteristic
46C2×C8×C13—21no—
47C2×C8×C13C2×C811yescharacteristic
48C2×C8×C13C2×C811yescharacteristic
49C2×C8×C13C2×D411yescharacteristic
50C2×C8×C13#4111yescharacteristic
51C42×C13C22×C411yescharacteristic
52C4⋊Dic13C2×C811yescharacteristic
53C4⋊Dic13C2×C811yescharacteristic
54#6101—21no—
55#6101—21no—
56C4×Dic13—21no—
57C4×Dic13—21no—
58C2×#1055—21no—
59C2×#1055—21no—
60Dic52—22no—
61C13×C16—22no—
62C13×C16—21no—
63C13×C16Q1612yescomplemented
64#6090—41no—
65#6090—41no—
66#2183—131no—
67Q8×C16—131no—
68C8×Q16—131no—
69#1370—131no—
70Q8⋊C16—131no—
71Q8⋊C16—131no—
72#1311D1311yescharacteristic
73C2×C4×C13C4×D411yescharacteristic
74C2×C4×C13C22×C811yescharacteristic
75C2×C4×C13#13111yescharacteristic
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80Dic26—21no—
81Dic26—21no—
82Dic26—21no—
83Dic26M3212yes—
84C8×C13—21no—
85C8×C13—21no—
86C8×C13—21no—
87C8×C13—41no—
88C8×C13C2×Q1611yescharacteristic
89C8×C13#13511yescharacteristic
90#1055—41no—
91#1055—41no—
92C8×Q8—131no—
93C8×Q8—131no—
94C4×Q16—131no—
95C4⋊C16—131no—
96C4⋊C16—131no—
97C4⋊C16—261no—
98C4⋊C16—261no—
99#346—261no—
100C4×C16—261no—
101C4×C16C2×D1311yescharacteristic
102C4×C16C2×D1311yescharacteristic
103#335—131no—
104Q8⋊C8—131no—
105Q8⋊C8—131no—
106C82C2×D1311yescharacteristic
107C22×C13C8×D411yescharacteristic
108C4×C13—21no—
109C4×C13C4×Q1611yescharacteristic
110C4×C13#44311yescharacteristic
111C4×C13C2×M3211yescharacteristic
112C4×C13#50411yescharacteristic
113Dic13—22no—
114Dic13—41no—
115Dic13—41no—
116Dic13—41no—
117C2×Q16—131no—
118C4×Q8—131no—
119C4×Q8—131no—
120C2×C16—21no—
121C2×C16—261no—
122C2×C16—261no—
123C2×C16D5211yescharacteristic
124C2×C16D5211yescharacteristic
125#107—131no—
126C4⋊C8—131no—
127C4⋊C8—131no—
128C4⋊C8—261no—
129C4⋊C8—261no—
130#103—131no—
131#103—131no—
132C4×C8—261no—
133C4×C8—261no—
134C4×C8C4×D1311yescharacteristic
135C4×C8C4×D1311yescharacteristic
136C4×C8C22×D1311yescharacteristic
137C2×C13C8×Q1611yescharacteristic
138C2×C13#216811yescharacteristic
139C2×C13#217111yescharacteristic
140C2×Q8—131no—
141C2×Q8—131no—
142Q16—262no—
143C2×C8—21no—
144C2×C8—261no—
145C2×C8—261no—
146C2×C8C8×D1311yescharacteristic
147C2×C8C8×D1311yescharacteristic
148C2×C8C2×D5211yescharacteristic
149C2×C8#612711yescharacteristic
150C4⋊C4—131no—
151C4⋊C4—131no—
152C4⋊C4—261no—
153C4⋊C4—261no—
154C42—261no—
155C42—261no—
156C42C2×C4×D1311yescharacteristic
157C16—22no—
158C16—21no—
159C16—521no—
160C16—521no—
161C16Dic5212yescomplemented
162C13#1205311yescharacteristic, complemented, Sylow
163Q8—132no—
164Q8—261no—
165Q8—261no—
166Q8—261no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—261no—
170C2×C4—261no—
171C2×C4C4×D5211yescharacteristic
172C2×C4C2×C8×D1311yescharacteristic
173C2×C4#8815511yescharacteristic
174C8—21no—
175C8—21no—
176C8—21no—
177C8—41no—
178C8—521no—
179C8—521no—
180C8#8815811yescharacteristic
181C8C2×Dic5211yescharacteristic
182C22C8×D5211yescharacteristic
183C4—21no—
184C4—262no—
185C4—521no—
186C4—521no—
187C4—521no—
188C4C4×Dic5211yescharacteristic
189C4#1171836111yescharacteristic
190C4D13×M3211yescharacteristic
191C4#1171856811yescharacteristic
192C2C8×Dic5211yescharacteristic
193C2#1311666311yescharacteristic
194C2#1311667911yescharacteristic
subgroupG/H
centerC2×C8C2×D52
commutatorC2×C4×C13C22×C8
FrattiniC4×C8C22×D13
FittingC13×#1311C2
socle, prime radicalC22×C13C8×D4
cosocleC4×C8×C13C23
hypercenter#1311D13
hypocenterC13#12053
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C16 ◁ #1311

Complements

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

NH ≅ G/Ntype
63. C13×C16Q16semidirect
161. C16Dic52semidirect
162. C13#12053semidirect

Maximal subgroups

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

subgroupindex
#131167442
C16×Dic262
C8×Dic522
#131129062
#131128162
C13×#13112
#1205313