Finite Group Databasebeta

← #15774886

Subgroups — #15774886

Order 3328.

204 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 69 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#13116708C211yesmaximal, characteristic
2#13113746C211yesmaximal, characteristic
3#13113656C211yesmaximal, characteristic
4#13112902C211yesmaximal, characteristic
5#13112807C211yesmaximal, characteristic
6#13112807C211yesmaximal, characteristic
7C13×#1313C211yesmaximal, characteristic
8C2×Dic104C411yescharacteristic
9C4×Dic52C2211yescharacteristic
10C4×Dic52C2211yescharacteristic
11#11718340—21no—
12C8×Dic26—21no—
13C13×#346C2211yescharacteristic
14C13×#346C2211yescharacteristic
15C13×#322C2211yescharacteristic
16#11718097C411yescharacteristic
17#11718095C411yescharacteristic
18#11718095C411yescharacteristic
19#11718049C2211yescharacteristic
20#11718049C2211yescharacteristic
21#11718048—21no—
22#11718048—21no—
23C2×Dic52C2×C411yescharacteristic
24C2×Dic52C2×C411yescharacteristic
25C4×Dic26—21no—
26C4×Dic26—21no—
27C2×C13×C16—21no—
28C2×C13×C16C2×C411yescharacteristic
29C2×C13×C16C2×C411yescharacteristic
30C4×C8×C13D411yescharacteristic
31C4×C8×C13D411yescharacteristic
32C4×C8×C13C2311yescharacteristic
33#88058C2×C411yescharacteristic
34#88058C2×C411yescharacteristic
35#88056—21no—
36#88056—21no—
37#88055—41no—
38#88054—41no—
39#88054—41no—
40C8×Dic13—41no—
41C4⋊#1055—21no—
42C4⋊#1055—21no—
43Dic104—22no—
44#12079—131nomaximal, Sylow
45C2×Dic26—21no—
46C2×Dic26—21no—
47C2×C8×C13—21no—
48C2×C8×C13—21no—
49C2×C8×C13C22×C411yescharacteristic
50C2×C8×C13#4111yescharacteristic
51C42×C13C2×D411yescharacteristic
52C4⋊Dic13—21no—
53C4⋊Dic13—21no—
54#6101—41no—
55#6101—41no—
56C4×Dic13—41no—
57C4×Dic13—41no—
58C2×#1055—41no—
59C2×#1055—41no—
60Dic52—21no—
61Dic52—21no—
62Dic52—21no—
63Dic52M1612yes—
64C13×C16—22no—
65C13×C16—21no—
66C13×C16—21no—
67#2176—131no—
68#1593—131no—
69#1579—131no—
70#1368—131no—
71#1334—131no—
72#1334—131no—
73#1313D1311yescharacteristic
74C2×C4×C13C4×D411yescharacteristic
75C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
76C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
77C2×Dic13—41no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81Dic26—22no—
82Dic26—41no—
83Dic26—41no—
84Dic26—41no—
85C8×C13—21no—
86C8×C13—41no—
87C8×C13—41no—
88C8×C13C2×M1611yescharacteristic
89C8×C13#13111yescharacteristic
90#1055—81no—
91#1055—81no—
92C2×Q32—131no—
93#446—261no—
94C8×Q8—261no—
95C4×Q16—131no—
96C4×Q16—131no—
97#367—131no—
98#358—131no—
99#358—131no—
100#346C2×D1311yescharacteristic
101#346C2×D1311yescharacteristic
102#334—131no—
103#334—131no—
104Q8⋊C8—261no—
105Q8⋊C8—261no—
106#322C2×D1311yescharacteristic
107C22×C13#44211yescharacteristic
108C4×C13—21no—
109C4×C13—21no—
110C4×C13#43511yescharacteristic
111C4×C13#44311yescharacteristic
112Dic13—42no—
113Dic13—81no—
114Dic13—81no—
115Dic13—81no—
116C2×Q16—131no—
117C2×Q16—131no—
118C4×Q8—261no—
119C4×Q8—261no—
120Q32—262no—
121C2×C16—21no—
122C2×C16C4×D1311yescharacteristic
123C2×C16C4×D1311yescharacteristic
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—521no—
134C4×C8D5211yescharacteristic
135C4×C8D5211yescharacteristic
136C4×C8C22×D1311yescharacteristic
137C2×C13#158611yescharacteristic
138C2×C13#218011yescharacteristic
139C2×C13#218011yescharacteristic
140C2×Q8—261no—
141C2×Q8—261no—
142Q16—132no—
143Q16—261no—
144Q16—261no—
145Q16—261no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—521no—
149C2×C8—521no—
150C2×C8C2×C4×D1311yescharacteristic
151C2×C8#612711yescharacteristic
152C4⋊C4—261no—
153C4⋊C4—261no—
154C4⋊C4—521no—
155C4⋊C4—521no—
156C42—521no—
157C42—521no—
158C42C2×D5211yescharacteristic
159C16—22no—
160C16—21no—
161C16—21no—
162C13#1207911yescharacteristic, complemented, Sylow
163Q8—262no—
164Q8—521no—
165Q8—521no—
166Q8—521no—
167C2×C4—521no—
168C2×C4—521no—
169C2×C4—521no—
170C2×C4—521no—
171C2×C4C4×D5211yescharacteristic
172C2×C4#8816211yescharacteristic
173C2×C4#8816211yescharacteristic
174C8—21no—
175C8—41no—
176C8—41no—
177C8—1041no—
178C8—1041no—
179C8M16×D1311yescharacteristic
180C8#8816111yescharacteristic
181C22#1171837211yescharacteristic
182C4—21no—
183C4—21no—
184C4—522no—
185C4—1041no—
186C4—1041no—
187C4—1041no—
188C4#1171836111yescharacteristic
189C4#1171836711yescharacteristic
190C2#1311370211yescharacteristic
191C2#1311672911yescharacteristic
192C2#1311672911yescharacteristic
subgroupG/H
centerC22#11718372
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1313C2
socle, prime radicalC22×C13#442
cosocleC4×C8×C13C23
hypercenter#1313D13
hypocenterC13#12079
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1313

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
#131167082
#131137462
#131136562
#131129022
#131128072
C13×#13132
#1207913