Finite Group Databasebeta

← #16782353

Subgroups — #16782353

Order 3328.

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

normal subgroups only

This group has 262 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
1#13130385C211yesmaximal, characteristic
2#13130383C211yesmaximal, characteristic
3#13129676C212yesmaximal
4#13129660C212yesmaximal
5#13114586C211yesmaximal, characteristic
6#11719119C2212yes—
7#11719119C2212yes—
8C2×#88055C2211yescharacteristic
9C2×C8×Dic13C2211yescharacteristic
10#11718593C2211yescharacteristic
11#11718256—21no—
12#11718255—21no—
13#11718254—21no—
14#11718253—21no—
15C13×#336C411yescharacteristic
16#11718142C411yescharacteristic
17#11718142C411yescharacteristic
18#11718116C411yescharacteristic
19C22×C8×C13C2×C411yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C2×C42×C13C2×C411yescharacteristic
22C2×C4×Dic13C2×C411yescharacteristic
23C2×C4×Dic13C2311yescharacteristic
24C22×#1055C2×C411yescharacteristic
25C22×#1055C2×C411yescharacteristic
26C22⋊#1057—22no—
27C22⋊#1057—22no—
28C4⋊#1057—22no—
29C4⋊#1057—22no—
30C4×#1057—22no—
31C4×#1057—22no—
32#88071—21no—
33#88071—21no—
34#88055—21no—
35#88055—21no—
36C8×Dic13D411yescharacteristic
37C8×Dic13D411yescharacteristic
38C8×Dic13Q811yescharacteristic
39C8×Dic13Q811yescharacteristic
40#8782—131nomaximal, Sylow
41C22×C4×C13—21no—
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13—21no—
44C22×Dic13#4111yescharacteristic
45C22×Dic13#4111yescharacteristic
46C2×#1057—42no—
47C2×#1057—42no—
48C2×C8×C13—21no—
49C2×C8×C13—21no—
50C2×C8×C13—21no—
51C2×C8×C13—21no—
52C2×C8×C13—21no—
53C2×C8×C13C4⋊C411yescharacteristic
54C2×C8×C13C4⋊C411yescharacteristic
55C42×C13—21no—
56C42×C13—21no—
57C4×Dic13—21no—
58C4×Dic13—21no—
59C4×Dic13C2×D411yescharacteristic
60C4×Dic13C2×Q811yescharacteristic
61C4×Dic13#4111yescharacteristic
62C4×Dic13#4111yescharacteristic
63C2×#1055—21no—
64C2×#1055—21no—
65C2×#1055—21no—
66C2×#1055—21no—
67C2×#1055—21no—
68C2×#1055C4⋊C411yescharacteristic
69C2×#1055C4⋊C411yescharacteristic
70#1746—131no—
71#1564—131no—
72#1564—131no—
73#1281—132no—
74#1274—132no—
75C23×C13#11711yescharacteristic
76C2×C4×C13—41no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13C2×C4⋊C411yescharacteristic
80C2×C4×C13#11711yescharacteristic
81C2×C4×C13#13111yescharacteristic
82C2×C4×C13#13111yescharacteristic
83C2×C4×C13#13111yescharacteristic
84C2×C4×C13#13111yescharacteristic
85C2×Dic13—41no—
86C2×Dic13—41no—
87C2×Dic13—41no—
88C2×Dic13—41no—
89C2×Dic13—41no—
90C2×Dic13#12411yescharacteristic
91C2×Dic13#12411yescharacteristic
92C2×Dic13#12511yescharacteristic
93C2×Dic13#12511yescharacteristic
94#1057—82no—
95#1057—82no—
96C8×C13—21no—
97C8×C13—21no—
98C8×C13—41no—
99#1055—21no—
100#1055—21no—
101#1055—41no—
102#431—132no—
103#431—132no—
104C2×#97—131no—
105C2×C4×C8—131no—
106#376—131no—
107#336—131no—
108#336—131no—
109#336—131no—
110#336#26111yescharacteristic
111#335—261no—
112#335—261no—
113#334—261no—
114#334—261no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13#38211yescharacteristic
118C22×C13#43311yescharacteristic
119C22×C13#43311yescharacteristic
120C4×C13—81no—
121C4×C13#42411yescharacteristic
122C4×C13#42411yescharacteristic
123C4×C13#43311yescharacteristic
124C4×C13#43311yescharacteristic
125Dic13—21no—
126Dic13—21no—
127Dic13—21no—
128Dic13—21no—
129Dic13—81no—
130C22×C8—131no—
131C22×C8—131no—
132C22×C8C2×#26111yescharacteristic
133C22×C8C2×#26111yescharacteristic
134C2×C42—131no—
135C2×C42—131no—
136C2×C42C2×#26111yescharacteristic
137C4⋊C8—262no—
138C4⋊C8—262no—
139C22⋊C8—262no—
140C22⋊C8—262no—
141#97—261no—
142#97—261no—
143C4×C8—131no—
144C4×C8—131no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8—262no—
148C4×C8—262no—
149#95—261no—
150#95—261no—
151C2×C13—21no—
152C2×C13—21no—
153C2×C13#183211yescharacteristic
154C2×C13#183311yescharacteristic
155C2×C13#183311yescharacteristic
156C22×C4—21no—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—261no—
160C22×C4C22×#26111yescharacteristic
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—261no—
169C2×C8—261no—
170C2×C8—261no—
171C2×C8—261no—
172C2×C8—261no—
173C2×C8—522no—
174C2×C8—522no—
175C2×C8C4⋊#26111yescharacteristic
176C2×C8C4⋊#26111yescharacteristic
177C42—21no—
178C42—21no—
179C42—131no—
180C42—131no—
181C42—131no—
182C42—131no—
183C42—261no—
184C42—261no—
185C13#878211yescharacteristic, complemented, Sylow
186C23#8823711yescharacteristic
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—131no—
194C2×C4—521no—
195C2×C4—521no—
196C2×C4—521no—
197C2×C4—521no—
198C2×C4—521no—
199C2×C4C2×C4⋊#26111yescharacteristic
200C2×C4#8823711yescharacteristic
201C2×C4#8823811yescharacteristic
202C2×C4#8823811yescharacteristic
203C2×C4#8823811yescharacteristic
204C2×C4#8824011yescharacteristic
205C8—21no—
206C8—21no—
207C8—41no—
208C8—261no—
209C8—261no—
210C8—521no—
211C8—1042no—
212C8—1042no—
213C22—21no—
214C22—21no—
215C22#1171906011yescharacteristic
216C22#1171906811yescharacteristic
217C22#1171907711yescharacteristic
218C4—81no—
219C4—261no—
220C4—261no—
221C4—261no—
222C4—261no—
223C4—1041no—
224C4#1171906711yescharacteristic
225C4#1171906811yescharacteristic
226C4#1171907711yescharacteristic
227C4#1171907911yescharacteristic
228C2—21no—
229C2—21no—
230C2#1313075411yescharacteristic
231C2#1313075511yescharacteristic
232C2#1313075611yescharacteristic
subgroupG/H
centerC2×C4#88237
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#336C4
socleC22×C13#382
prime radicalC23×C13#117
cosocleC2×C4×Dic13C23
hypercenter#336#261
hypocenterC13#8782
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
185. C13#8782semidirect

Maximal subgroups

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

subgroupindex
#131303852
#131303832
#131296762
#131296602
#131145862
#878213