Finite Group Databasebeta

← #16777342

Subgroups — #16777342

Order 3328.

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

normal subgroups only

This group has 290 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#13130733C211yesmaximal, characteristic
2#13130089C211yesmaximal, characteristic
3#13114605C211yesmaximal, characteristic
4C2×#88126C2211yescharacteristic
5#11719135—21no—
6#11719128—21no—
7C2×C13×#97C411yescharacteristic, complemented
8C2×#88060—21no—
9C2×C4×#1055C411yescharacteristic, complemented
10#11718289—21no—
11#11718289C412yes—
12#11718287—21no—
13#11718286C412yescomplemented
14#11718142—21no—
15C22×C4×D13D411yescharacteristic
16C2×C22⋊#261—22no—
17C22×C8×C13—21no—
18C2×C42×C13C2×C411yescharacteristic
19C2×#6103C2×C411yescharacteristic
20C2×#6103D411yescharacteristic
21C2×#6101C2×C411yescharacteristic
22C2×#6101Q811yescharacteristic
23C2×C4×Dic13D411yescharacteristic
24C22×#1055—21no—
25#88126—41no—
26#88126—41no—
27C22⋊#1057—22no—
28(C2×#261)⋊C4—41no—
29(C2×#261)⋊C4—41no—
30#88112—41no—
31#88110—41no—
32C13×#97—41no—
33#88060—24no—
34C4×#1055—41no—
35#7214—131nomaximal, Sylow
36C23×D13C22⋊C411yescharacteristic
37C22×#261—42no—
38C22×C4×C13C4211yescharacteristic
39C22×C4×C13C22⋊C411yescharacteristic
40C22×C4×C13C4⋊C411yescharacteristic
41C22×Dic13C22⋊C411yescharacteristic
42C22×Dic13C4⋊C411yescharacteristic
43C22×Dic13C4⋊C411yescharacteristic
44C2×C4×D13—22no—
45C2×C4×D13—21no—
46C2×C4×D13—21no—
47C2×C4×D13—41no—
48C22⋊#261—42no—
49C22⋊#261—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#1820—131no—
66#1750—131no—
67#1464—131no—
68C23×C13#9511yescharacteristic
69C22×D13—21no—
70C22×D13—21no—
71C22×D13—41no—
72C22×D13—41no—
73C22×D13#10412yes—
74C2×#261—82no—
75C2×#261—82no—
76C2×#261—82no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—41no—
82C2×C4×C13—41no—
83C2×C4×C13#9911yescharacteristic
84C2×C4×C13#9911yescharacteristic
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—41no—
91C2×Dic13—41no—
92C4×D13—42no—
93C4×D13—42no—
94#1057—82no—
95C8×C13—42no—
96#1055—42no—
97C2×#117—131no—
98#432—261no—
99C2×C22⋊C8—261no—
100C2×#97#26111yescharacteristic, complemented
101C2×C4×C8—131no—
102#381—261no—
103#342—132no—
104#342—261no—
105#336—261no—
106#324—132no—
107#323—261no—
108C22×C13—21no—
109C22×C13—21no—
110C22×C13H(3,ℤ/4)11yescharacteristic
111C22×C13#33911yescharacteristic
112C22×C13#34211yescharacteristic
113C2×D13—22no—
114C2×D13—41no—
115C2×D13—41no—
116C2×D13—42no—
117C2×D13—81no—
118#261—162no—
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—41no—
122C4×C13—41no—
123Dic13—41no—
124Dic13—41no—
125Dic13—41no—
126C23×C4—131no—
127C22×C8—21no—
128C22×C8—261no—
129#117—521no—
130#117—521no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—131no—
133C2×C22⋊C4—131no—
134C2×C22⋊C4—131no—
135C2×C22⋊C4—262no—
136C2×C42—131no—
137C2×C42C2×#26111yescharacteristic
138C4⋊C8—521no—
139C22⋊C8—264no—
140C22⋊C8—262no—
141#97—41no—
142#97—521no—
143C4×C8—521no—
144#95—521no—
145#95—521no—
146C2×C13—21no—
147C2×C13—21no—
148C2×C13#128411yescharacteristic
149C2×C13#139111yescharacteristic
150C2×C13#139511yescharacteristic
151D13—42no—
152C24—131no—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—262no—
157C22×C4—261no—
158C22×C4—261no—
159C22×C4—521no—
160C22×C4—522no—
161C22×C4C4×#26111yescharacteristic
162C22×C4C4⋊#26111yescharacteristic
163C22×C4C22⋊#26111yescharacteristic
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—262no—
168C2×C8—521no—
169C2×C8—521no—
170C2×C8—522no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C22⋊C4—521no—
174C22⋊C4—521no—
175C22⋊C4—522no—
176C22⋊C4—522no—
177C42—21no—
178C42—21no—
179C42—261no—
180C42—261no—
181C13#721411yescharacteristic, complemented, Sylow
182C23—132no—
183C23—261no—
184C23—261no—
185C23—521no—
186C23—521no—
187C23(C2×#261)⋊C411yescharacteristic
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—522no—
200C2×C4—522no—
201C2×C4—521no—
202C2×C4—521no—
203C2×C4—1042no—
204C2×C4—1042no—
205C2×C4—1042no—
206C2×C4#8810711yescharacteristic
207C2×C4#8811911yescharacteristic
208C8—42no—
209C8—522no—
210C8—1042no—
211C22—21no—
212C22—21no—
213C22—262no—
214C22—522no—
215C22—521no—
216C22—521no—
217C22—1041no—
218C22#1171823411yescharacteristic
219C22#1171823511yescharacteristic
220C22#1171828911yescharacteristic
221C4—21no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—521no—
226C4—521no—
227C4—521no—
228C4—2082no—
229C2—21no—
230C2—21no—
231C2—522no—
232C2#1312968411yescharacteristic
233C2#1312992511yescharacteristic
234C2#1312993711yescharacteristic
subgroupG/H
centerC22#11718289
commutatorC22×C4×C13C42
FrattiniC2×C42C2×#261
FittingC2×C13×#97C4
socleC22×C13#342
prime radicalC23×D13C22⋊C4
cosocleC2×#88126C22
hypercenterC2×#97#261
hypocenterC13#7214
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
7. C2×C13×#97C4semidirect
9. C2×C4×#1055C4semidirect
13. #11718286C4semidirect
100. C2×#97#261semidirect
181. C13#7214semidirect

Maximal subgroups

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

subgroupindex
#131307332
#131300892
#131146052
#721413