Finite Group Databasebeta

← #16787054

Subgroups — #16787054

Order 3328.

284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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#13131205C212yesmaximal, complemented
2#13129782C212yesmaximal, complemented
3#13129768C212yesmaximal
4#13123474C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6#11718868C411yescharacteristic
7#11718868C2211yescharacteristic
8#11718661—22no—
9#11718661—22no—
10#11718585C411yescharacteristic
11#11718585C2211yescharacteristic
12C4×#6099C411yescharacteristic
13C4×#6099C2211yescharacteristic
14#11718284C2214yes—
15#11718233—22no—
16#11718232—22no—
17C23×C4×C13C2×C411yescharacteristic
18C13×#117—21no—
19C13×#117—21no—
20C13×#117—22no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C22⋊C4—21no—
23C2×C42×C13C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×#6099C2×C411yescharacteristic
26C2×#6099C2×C411yescharacteristic
27C2×#6099C2×C411yescharacteristic
28C2×#6099C2311yescharacteristic
29#88106—24no—
30C22⋊#1055—22no—
31C22⋊#1055—22no—
32C4⋊#1055—22no—
33C4⋊#1055—22no—
34#88043—21no—
35#88043D412yes—
36C4×#1055—21no—
37C4×#1055D412yes—
38#11522—131nomaximal, Sylow
39C24×C13M1611yescharacteristic
40C22×C4×C13—21no—
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—41no—
45C22×C4×C13—41no—
46C22×C4×C13M1611yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C13×C4⋊C4—22no—
49C13×C4⋊C4—22no—
50C13×C22⋊C4—22no—
51C13×C22⋊C4—22no—
52C42×C13—21no—
53C42×C13—21no—
54C42×C13C22⋊C411yescharacteristic
55C42×C13C22⋊C411yescharacteristic
56C42×C13M1612yes—
57#6099—41no—
58#6099—41no—
59#6099—41no—
60#6099—41no—
61C2×#1055—21no—
62C2×#1055—21no—
63C2×#1055C22⋊C412yes—
64C2×#1055C2×D412yes—
65#6092—44no—
66#2921—131no—
67#2165—132no—
68#1327—132no—
69#1320—132no—
70C23×C13—21no—
71C23×C13—41no—
72C23×C13—81no—
73C23×C13C2×M1611yescharacteristic
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—42no—
81C2×C4×C13—41no—
82C2×C4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13C2×M1611yescharacteristic
88#1055—22no—
89#1055—22no—
90#1055—41no—
91#1055—41no—
92C2×#117#26111yescharacteristic
93#433—262no—
94#433—262no—
95#423—131no—
96#423—131no—
97#407—131no—
98#407—131no—
99C4×M16—131no—
100C4×M16—131no—
101#364—262no—
102#349—134no—
103#347—262no—
104C22×C13—21no—
105C22×C13—41no—
106C22×C13—42no—
107C22×C13—41no—
108C22×C13—82no—
109C22×C13#40711yescharacteristic
110C4×C13—21no—
111C4×C13—41no—
112C4×C13—41no—
113C4×C13—42no—
114C4×C13—41no—
115C4×C13#41011yescharacteristic
116C4×C13#41311yescharacteristic
117C23×C4C2×#26111yescharacteristic
118C2×M16—131no—
119C2×M16—131no—
120C2×M16—131no—
121C2×M16—131no—
122#117—22no—
123#117—21no—
124#117—21no—
125C2×C4⋊C4—21no—
126C2×C22⋊C4—21no—
127C2×C42C2×#26111yescharacteristic
128C2×C42C2×#26111yescharacteristic
129M32—264no—
130C4⋊C8—262no—
131C4⋊C8—262no—
132C22⋊C8—262no—
133C22⋊C8—262no—
134#97—132no—
135#97—261no—
136C4×C8—132no—
137C4×C8—261no—
138C2×C13—21no—
139C2×C13—41no—
140C2×C13—81no—
141C2×C13#146411yescharacteristic
142C24#612211yescharacteristic
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4#612211yescharacteristic
150C22×C4C22×#26111yescharacteristic
151M16—521no—
152M16—521no—
153M16—521no—
154M16—521no—
155C2×C8—132no—
156C2×C8—132no—
157C2×C8—261no—
158C2×C8—261no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C42—21no—
164C42—21no—
165C42#612212yes—
166C42C22⋊#26111yescharacteristic
167C42C22⋊#26111yescharacteristic
168C16—524no—
169C13#1152211yescharacteristic, complemented, Sylow
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×#612211yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4C2×#612211yescharacteristic
187C2×C4C2×C22⋊#26111yescharacteristic
188C8—262no—
189C8—262no—
190C8—521no—
191C8—521no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22#1171916911yescharacteristic
198C4—21no—
199C4—42no—
200C4—41no—
201C4—41no—
202C4—41no—
203C4#1171911611yescharacteristic
204C4#1171913211yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2#1313008711yescharacteristic
subgroupG/H
centerC4#11719116
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC2×C13#1464
prime radicalC24×C13M16
cosocleC2×#6099C23
hypercenterC2×#117#261
hypocenterC13#11522
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #13131205C2semidirect
2. #13129782C2semidirect
169. C13#11522semidirect

Maximal subgroups

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

subgroupindex
#131312052
#131297822
#131297682
#131234742
#1152213