Finite Group Databasebeta

← #16782223

Subgroups — #16782223

Order 3328.

418 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×#11718285C212yesmaximal
2#13129679C214yesmaximal
3#13117437C211yesmaximal, characteristic
4C22×C4⋊Dic13C2211yescharacteristic
5C2×C22⋊#1057C2214yes—
6C13×#381C411yescharacteristic
7#11718872C411yescharacteristic
8#11718603C412yes—
9C22⋊C4×Dic13C2212yes—
10#11718315—22no—
11#11718314—22no—
12#11718285—22no—
13#11718285—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13C2×C411yescharacteristic
16C23×Dic13C2311yescharacteristic
17C22×#1057—24no—
18C2×C13×C22⋊C4C2×C412yes—
19C2×C22⋊Dic13C2×C412yes—
20C2×C4⋊Dic13—24no—
21C2×C4⋊Dic13D412yes—
22C2×C4⋊Dic13D412yes—
23C2×#6101—22no—
24C2×C4×Dic13—22no—
25C22⋊#1057—24no—
26C22⋊#1057—24no—
27C13×#95—21no—
28C13×#95—21no—
29#88071—21no—
30#88071—21no—
31#88071—22no—
32#88071—22no—
33#8737—131nomaximal, Sylow
34C24×C13C22×C411yescharacteristic
35C22×C4×C13—22no—
36C22×C4×C13—24no—
37C22×C4×C13—22no—
38C22×C4×C13C22⋊C411yescharacteristic
39C22×C4×C13C22⋊C411yescharacteristic
40C22×Dic13—22no—
41C22×Dic13—22no—
42C22×Dic13—81no—
43C22×Dic13—81no—
44C22×Dic13C22⋊C412yes—
45C22×Dic13C2×D412yes—
46C22×Dic13#4114yes—
47C2×#1057—44no—
48C2×#1057—84no—
49C13×C22⋊C4—24no—
50C22⋊Dic13—24no—
51C4⋊Dic13—24no—
52C4⋊Dic13—24no—
53#6101—82no—
54C4×Dic13—82no—
55#2313—131no—
56C2×#324—132no—
57#1282—134no—
58C23×C13—41no—
59C23×C13—41no—
60C23×C13C2×C22⋊C411yescharacteristic
61C23×C13#11712yes—
62C23×C13#13114yes—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—44no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×Dic13—22no—
72C2×Dic13—42no—
73C2×Dic13—44no—
74C2×Dic13—42no—
75C2×Dic13—42no—
76C2×Dic13—42no—
77C2×Dic13—42no—
78C2×Dic13—82no—
79C2×Dic13#12314yes—
80#1057—84no—
81C22×C4⋊C4—131no—
82C2×C22⋊C8—134no—
83#387—262no—
84#387—262no—
85#381—131no—
86#381#26111yescharacteristic
87#380—132no—
88C4×C22⋊C4—132no—
89#324—262no—
90#324—262no—
91C22×C13—21no—
92C22×C13—22no—
93C22×C13—21no—
94C22×C13—22no—
95C22×C13—44no—
96C22×C13#38111yescharacteristic
97C22×C13#40812yes—
98C22×C13#43314yes—
99C4×C13—41no—
100C4×C13—41no—
101C4×C13—82no—
102Dic13—24no—
103Dic13—42no—
104Dic13—82no—
105C23×C4—131no—
106C23×C4—131no—
107C23×C4C2×#26111yescharacteristic
108C22×C8—264no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—264no—
112C2×C4⋊C4—262no—
113C2×C22⋊C4—132no—
114C2×C22⋊C4C2×#26112yes—
115C2×C42—262no—
116C22⋊C8—264no—
117C22⋊C8—264no—
118#95—21no—
119#95—21no—
120#95—262no—
121#95—262no—
122#95—261no—
123#95—261no—
124C2×C13—22no—
125C2×C13—24no—
126C2×C13#181811yescharacteristic
127C2×C13#182811yescharacteristic
128C2×C13#183011yescharacteristic
129C24C22×#26111yescharacteristic
130C22×C4—22no—
131C22×C4—24no—
132C22×C4—22no—
133C22×C4—134no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—262no—
137C22×C4—262no—
138C22×C4—1041no—
139C22×C4—1041no—
140C22×C4C22⋊#26111yescharacteristic
141C22×C4C22⋊#26111yescharacteristic
142C2×C8—524no—
143C2×C8—1044no—
144C4⋊C4—264no—
145C4⋊C4—264no—
146C4⋊C4—1042no—
147C22⋊C4—24no—
148C22⋊C4—264no—
149C42—1042no—
150C13#873711yescharacteristic, complemented, Sylow
151C23—41no—
152C23—41no—
153C23#8823712yes—
154C23#8823814yes—
155C23C2×C22⋊#26111yescharacteristic
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—134no—
165C2×C4—262no—
166C2×C4—522no—
167C2×C4—524no—
168C2×C4—522no—
169C2×C4—522no—
170C2×C4—522no—
171C2×C4—522no—
172C2×C4—1042no—
173C8—1044no—
174C22—21no—
175C22—22no—
176C22—21no—
177C22—22no—
178C22—44no—
179C22#1171906814yes—
180C22#1171913511yescharacteristic
181C22#1171914612yes—
182C4—41no—
183C4—41no—
184C4—82no—
185C4—264no—
186C4—522no—
187C4—1042no—
188C2—22no—
189C2—24no—
190C2#1313072911yescharacteristic
191C2#1313074811yescharacteristic
192C2#1313075011yescharacteristic
subgroupG/H
centerC22#11719135
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC13×#381C4
socleC22×C13#381
cosocleC23×Dic13C23
hypercenter#381#261
hypocenterC13#8737
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
150. C13#8737semidirect

Maximal subgroups

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

subgroupindex
C2×#117182852
#131296792
#131174372
#873713