Finite Group Databasebeta

← #16777350

Subgroups — #16777350

Order 3328.

276 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 52 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#13130737C211yesmaximal, characteristic
2#13130089C211yesmaximal, characteristic
3#13114605C211yesmaximal, characteristic
4C2×#88126C2211yescharacteristic
5#11719128—21no—
6#11719126—21no—
7C2×C13×#97C411yescharacteristic
8C2×#88060—21no—
9C2×C4×#1055C411yescharacteristic
10#11718291—21no—
11#11718291C412yes—
12#11718287C412yes—
13#11718286—21no—
14#11718142—21no—
15C22×C4×D13D411yescharacteristic
16C2×#6122—22no—
17C22×C8×C13—21no—
18C2×C42×C13C2×C411yescharacteristic
19C2×#6103C2×C411yescharacteristic
20C2×#6103Q811yescharacteristic
21C2×#6101C2×C411yescharacteristic
22C2×#6101D411yescharacteristic
23C2×C4×Dic13D411yescharacteristic
24C22×#1055—21no—
25#88126—41no—
26#88126—41no—
27C22⋊#1057—22no—
28#88112—41no—
29#88111—41no—
30#88111—41no—
31#88110—41no—
32C13×#97—41no—
33#88060—24no—
34C4×#1055—41no—
35#7216—131nomaximal, Sylow
36C23×D13C4⋊C411yescharacteristic
37C22×C4×C13C4211yescharacteristic
38C22×C4×C13C22⋊C411yescharacteristic
39C22×C4×C13C4⋊C411yescharacteristic
40C22×Dic13C22⋊C411yescharacteristic
41C22×Dic13C22⋊C411yescharacteristic
42C22×Dic13C4⋊C411yescharacteristic
43C2×C4×D13—21no—
44C2×C4×D13—21no—
45C2×C4×D13—22no—
46C2×C4×D13—41no—
47#6122—42no—
48#6122—42no—
49C2×#1057—42no—
50C2×#1057—42no—
51C2×C8×C13—22no—
52C2×C8×C13—41no—
53C2×C8×C13—41no—
54C42×C13—21no—
55C42×C13—21no—
56#6103—41no—
57#6103—41no—
58#6101—41no—
59#6101—41no—
60C4×Dic13—21no—
61C4×Dic13—21no—
62C2×#1055—22no—
63C2×#1055—41no—
64C2×#1055—41no—
65#1822—131no—
66#1750—131no—
67#1464—131no—
68C23×C13#9511yescharacteristic
69C22×D13—21no—
70C22×D13—21no—
71C22×D13—21no—
72C22×D13—41no—
73C22×D13—41no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13#9911yescharacteristic
81C2×C4×C13#9911yescharacteristic
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—41no—
87C2×Dic13—41no—
88C2×Dic13#10412yes—
89C4×D13—42no—
90C4×D13—42no—
91#1057—82no—
92#1057—82no—
93C8×C13—42no—
94#1055—42no—
95C2×#117—131no—
96#432—261no—
97#407—261no—
98C2×C22⋊C8—261no—
99C2×#97#26111yescharacteristic
100C2×C4×C8—131no—
101#343—132no—
102#343—261no—
103#336—261no—
104#324—261no—
105#323—132no—
106C22×C13—21no—
107C22×C13—21no—
108C22×C13H(3,ℤ/4)11yescharacteristic
109C22×C13#33911yescharacteristic
110C22×C13#34211yescharacteristic
111C2×D13—42no—
112C2×D13—41no—
113C2×D13—41no—
114C2×D13—41no—
115C2×D13—81no—
116C4×C13—21no—
117C4×C13—21no—
118C4×C13—41no—
119C4×C13—41no—
120Dic13—22no—
121Dic13—41no—
122Dic13—41no—
123C23×C4—131no—
124C2×M16—262no—
125C22×C8—21no—
126C22×C8—261no—
127#117—521no—
128#117—521no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—131no—
131C2×C22⋊C4—131no—
132C2×C22⋊C4—131no—
133C2×C42—131no—
134C2×C42C2×#26111yescharacteristic
135C4⋊C8—521no—
136C22⋊C8—264no—
137C22⋊C8—262no—
138C22⋊C8—521no—
139C22⋊C8—521no—
140#97—41no—
141#97—521no—
142C4×C8—521no—
143C2×C13—21no—
144C2×C13—21no—
145C2×C13#128411yescharacteristic
146C2×C13#139211yescharacteristic
147C2×C13#139511yescharacteristic
148D13—81no—
149C24—131no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—262no—
154C22×C4—261no—
155C22×C4—261no—
156C22×C4—521no—
157C22×C4C4×#26111yescharacteristic
158C22×C4C4⋊#26111yescharacteristic
159C22×C4C22⋊#26111yescharacteristic
160M16—522no—
161M16—522no—
162C2×C8—22no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—262no—
166C2×C8—521no—
167C2×C8—521no—
168C2×C8—522no—
169C2×C8—522no—
170C4⋊C4—521no—
171C4⋊C4—521no—
172C22⋊C4—521no—
173C22⋊C4—521no—
174C42—21no—
175C42—21no—
176C42—261no—
177C42—261no—
178C13#721611yescharacteristic, complemented, Sylow
179C23—261no—
180C23—261no—
181C23—261no—
182C23—521no—
183C23—521no—
184C23(C2×#261)⋊C411yescharacteristic
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—132no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—521no—
199C2×C4—521no—
200C2×C4#8810711yescharacteristic
201C2×C4#8811911yescharacteristic
202C8—42no—
203C8—522no—
204C8—1042no—
205C8—1042no—
206C22—21no—
207C22—21no—
208C22—522no—
209C22—521no—
210C22—521no—
211C22—521no—
212C22—1041no—
213C22#1171823411yescharacteristic
214C22#1171823511yescharacteristic
215C22#1171828911yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—262no—
221C4—521no—
222C4—521no—
223C2—21no—
224C2—21no—
225C2—1041no—
226C2#1312968411yescharacteristic
227C2#1312992811yescharacteristic
228C2#1312993711yescharacteristic
subgroupG/H
centerC22#11718289
commutatorC22×C4×C13C42
FrattiniC2×C42C2×#261
FittingC2×C13×#97C4
socleC22×C13#342
prime radicalC23×D13C4⋊C4
cosocleC2×#88126C22
hypercenterC2×#97#261
hypocenterC13#7216
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
178. C13#7216semidirect

Maximal subgroups

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

subgroupindex
#131307372
#131300892
#131146052
#721613