Finite Group Databasebeta

← #15772129

Subgroups — #15772129

Order 3328.

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

normal subgroups only

This group has 314 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#13123479C211yesmaximal, characteristic
2#13116632C212yesmaximal, complemented
3#13112778C211yesmaximal, characteristic, complemented
4#13112761C212yesmaximal
5C13×#1323C211yesmaximal, characteristic, complemented
6#11719227C411yescharacteristic
7C13×#424C2211yescharacteristic
8#11718790C411yescharacteristic
9M16×Dic13C411yescharacteristic
10#11718771C2211yescharacteristic
11C2×C8×Dic13C2211yescharacteristic
12#11718660C411yescharacteristic
13#11718501—22no—
14#11718494—22no—
15C13×C22⋊C16C2212yes—
16C22⋊#6090C2212yes—
17#11718093—22no—
18C16×Dic13—22no—
19C2×#6127C2×C411yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C22×C8×C13C2311yescharacteristic
22C13×#117C2×C411yescharacteristic
23C2×C4×Dic13C2×C411yescharacteristic
24C2×#6099C2×C411yescharacteristic
25C22×#1055C2×C411yescharacteristic
26#88147C812yes—
27#88141C812yes—
28#88135—22no—
29#88126—21no—
30C42×D13—21no—
31C2×C13×C16—22no—
32C13×C4⋊C8—22no—
33#88060—22no—
34#88060—22no—
35#88055—21no—
36C8×Dic13—21no—
37C8×Dic13D412yes—
38C8×Dic13D412yes—
39C2×#6090—22no—
40C4⋊#1055—22no—
41#11462—131nomaximal, Sylow
42C22×C4×C13C22×C411yescharacteristic
43C2×C22⋊D13—21no—
44C22×Dic13M1612yes—
45#6127—41no—
46#6127—41no—
47C2×D52C2×C811yescharacteristic
48C2×C4×D13—21no—
49C2×C4×D13—22no—
50C2×Dic26C2×C811yescharacteristic
51C13×M16—41no—
52C2×C8×C13—21no—
53C2×C8×C13—41no—
54C2×C8×C13C2×D412yes—
55C13×C4⋊C4C2×C812yes—
56C13×C22⋊C4—21no—
57C42×C13—21no—
58#6103—22no—
59#6101—22no—
60C4×Dic13—22no—
61C4×Dic13C22⋊C411yescharacteristic
62C4×Dic13C22⋊C411yescharacteristic
63C4×Dic13C2×C812yes—
64#6099—41no—
65C2×#1055—21no—
66C2×#1055—41no—
67C2×#1055C22⋊C412yes—
68C13×C16—42no—
69#6090—42no—
70#2922—131no—
71#2162—132no—
72#1323—131no—
73#1323D1311yescharacteristic, complemented
74#1315—132no—
75C23×C13C2×M1611yescharacteristic
76C22×D13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13C2×C22⋊C411yescharacteristic
81C2×C4×C13C22×C811yescharacteristic
82C22⋊D13—42no—
83C2×Dic13—24no—
84C2×Dic13—21no—
85C2×Dic13C22⋊C812yes—
86C2×Dic13C22⋊C812yes—
87D52—41no—
88C4×D13—41no—
89C4×D13—41no—
90C4×D13—44no—
91Dic26—41no—
92C8×C13—22no—
93C8×C13—41no—
94#1055—22no—
95#1055—41no—
96C4×#41—131no—
97#433—262no—
98#431—262no—
99#424—131no—
100#424C2×D1311yescharacteristic
101#408—131no—
102#408—131no—
103C4×M16—131no—
104C2×C4×C8—131no—
105C4⋊C16—262no—
106C22⋊C16—132no—
107C22⋊C16C2×D1312yes—
108C4×C16—262no—
109C22×C13—22no—
110C22×C13—21no—
111C22×C13C2×C22⋊C811yescharacteristic
112C2×D13—42no—
113C2×D13—41no—
114C4×C13—21no—
115C4×C13—42no—
116C4×C13#41011yescharacteristic
117C4×C13#41311yescharacteristic
118Dic13—22no—
119Dic13—41no—
120Dic13#35014yes—
121C2×#41—131no—
122C2×M16—131no—
123C2×M16C4×D1311yescharacteristic
124C22×C8—131no—
125C22×C8C22×D1311yescharacteristic
126C4×Q8—132no—
127C4×D4—132no—
128C4×D4—262no—
129#117—261no—
130#117C4×D1311yescharacteristic
131C2×C42—131no—
132C2×C42—261no—
133C2×C16—22no—
134C2×C16—262no—
135C4⋊C8—22no—
136C4⋊C8—262no—
137C22⋊C8—262no—
138C22⋊C8—262no—
139#97—261no—
140C4×C8—132no—
141C4×C8—132no—
142C4×C8—261no—
143C2×C13—41no—
144C2×C13#145811yescharacteristic
145C2×C13C2×#35012yes—
146D13—81no—
147#41—521no—
148#41—521no—
149C2×Q8—131no—
150C2×D4—131no—
151C2×D4—261no—
152C22×C4—132no—
153C22×C4—262no—
154C22×C4—261no—
155C22×C4C2×C4×D1311yescharacteristic
156M16—41no—
157M16—521no—
158C2×C8—21no—
159C2×C8—41no—
160C2×C8—132no—
161C2×C8—261no—
162C2×C8—521no—
163C2×C8D4×D1312yes—
164C4⋊C4—262no—
165C4⋊C4C8×D1312yes—
166C22⋊C4—21no—
167C22⋊C4—262no—
168C42—21no—
169C42—131no—
170C42—131no—
171C42—132no—
172C42—262no—
173C16—42no—
174C16—522no—
175C13#1146211yescharacteristic, complemented, Sylow
176C23—261no—
177C23M16×D1311yescharacteristic
178Q8—521no—
179D4—521no—
180D4—522no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—132no—
185C2×C4—132no—
186C2×C4—264no—
187C2×C4—261no—
188C2×C4—524no—
189C2×C4—521no—
190C2×C4—521no—
191C2×C4C22⋊C4×D1311yescharacteristic
192C2×C4C2×C8×D1311yescharacteristic
193C8—22no—
194C8—41no—
195C8—262no—
196C8—521no—
197C22—22no—
198C22—21no—
199C22—522no—
200C22—521no—
201C22D13×C22⋊C811yescharacteristic
202C4—21no—
203C4—42no—
204C4—134no—
205C4—262no—
206C4—521no—
207C4#1171840111yescharacteristic
208C4#1171841211yescharacteristic
209C2—41no—
210C2—1041no—
211C2#1311314911yescharacteristic
212C2D13×#35012yes—
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1323C2
socleC22×C13C2×C22⋊C8
prime radicalC2×#6127C2×C4
cosocleC22×C8×C13C23
hypercenter#1323D13
hypocenterC13#11462
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #13116632C2semidirect
3. #13112778C2semidirect
5. C13×#1323C2semidirect
73. #1323D13semidirect
175. C13#11462semidirect

Maximal subgroups

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

subgroupindex
#131234792
#131166322
#131127782
#131127612
C13×#13232
#1146213