Finite Group Databasebeta

← #16786831

Subgroups — #16786831

Order 3328.

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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#13131194C212yesmaximal, complemented
2#13129773C212yesmaximal, complemented
3#13129756C212yesmaximal
4C2×#11718379C211yesmaximal, characteristic
5C22×C4×Dic13C411yescharacteristic
6C2×C13×C22⋊C8C411yescharacteristic
7C2×C22⋊#1055C2211yescharacteristic
8C2×#88054C411yescharacteristic
9C2×#88054C2211yescharacteristic
10C2×C8×Dic13C411yescharacteristic
11C2×C8×Dic13C2211yescharacteristic
12#11718379—22no—
13#11718379—22no—
14C22⋊#6092C2214yes—
15#11718260—22no—
16#11718257—22no—
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13C811yescharacteristic
19C23×Dic13C811yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22C2×C4×Dic13—21no—
23C2×C4×Dic13—21no—
24C2×C4×Dic13—21no—
25C2×C4×Dic13—21no—
26C2×C4×Dic13C811yescharacteristic
27C2×C4×Dic13C811yescharacteristic
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13C2×C411yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C22×#1055C2311yescharacteristic
32C2×#6092—24no—
33C13×C22⋊C8—22no—
34C22⋊#1055—22no—
35#88054—22no—
36#88054—22no—
37C8×Dic13—21no—
38C8×Dic13—21no—
39C8×Dic13D412yes—
40C8×Dic13D412yes—
41#11459—131nomaximal, Sylow
42C24×C13C2×C811yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—41no—
46C22×C4×C13—41no—
47C22×C4×C13C2×C811yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—21no—
50C22×Dic13—21no—
51C22×Dic13—22no—
52C22×Dic13—21no—
53C22×Dic13—21no—
54C22×Dic13—42no—
55C22×Dic13C1614yescomplemented
56C22×Dic13C2×C811yescharacteristic
57C22×Dic13C2×C811yescharacteristic
58C22×Dic13C2×C811yescharacteristic
59C22×Dic13C2×C811yescharacteristic
60C2×C8×C13—21no—
61C2×C8×C13—41no—
62C2×C8×C13—41no—
63C2×C8×C13C22⋊C412yes—
64C4×Dic13—21no—
65C4×Dic13—21no—
66C4×Dic13—21no—
67C4×Dic13—21no—
68C4×Dic13—21no—
69C4×Dic13—21no—
70C4×Dic13C22⋊C411yescharacteristic
71C4×Dic13C22⋊C411yescharacteristic
72C4×Dic13M1611yescharacteristic
73C4×Dic13M1611yescharacteristic
74C2×#1055—21no—
75C2×#1055—41no—
76C2×#1055—41no—
77C2×#1055C2×D412yes—
78#6092—44no—
79C2×#431—131no—
80#2162—132no—
81#1322—132no—
82#1314—132no—
83C23×C13—21no—
84C23×C13—21no—
85C23×C13—41no—
86C23×C13—41no—
87C23×C13C2×C1612yes—
88C23×C13C22×C811yescharacteristic
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×C4×C13C2×M1611yescharacteristic
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—24no—
101C2×Dic13—24no—
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—41no—
107C2×Dic13C22⋊C811yescharacteristic
108C2×Dic13C22⋊C811yescharacteristic
109C2×Dic13C22⋊C811yescharacteristic
110C2×Dic13C22⋊C811yescharacteristic
111C2×Dic13C2×C1612yes—
112C2×Dic13C2×C1612yes—
113C2×Dic13M3212yes—
114C8×C13—22no—
115C8×C13—41no—
116#1055—22no—
117#1055—41no—
118C22×C42—131no—
119#431—262no—
120#431—262no—
121C2×C4⋊C8—131no—
122C2×C4⋊C8—131no—
123C2×C22⋊C8—131no—
124C2×C22⋊C8#26111yescharacteristic
125C2×C4×C8—131no—
126C2×C4×C8—131no—
127C4⋊C16—262no—
128C22⋊C16—134no—
129C4×C16—262no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—22no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13C2×C22⋊C811yescharacteristic
138C22×C13C22×C1611yescharacteristic
139C22×C13C2×M3211yescharacteristic
140C4×C13—21no—
141C4×C13—41no—
142C4×C13#41011yescharacteristic
143C4×C13#41311yescharacteristic
144Dic13—22no—
145Dic13—21no—
146Dic13—41no—
147Dic13C22⋊C1612yes—
148Dic13C22⋊C1612yes—
149Dic13#34912yes—
150C23×C4—131no—
151C23×C4—131no—
152C23×C4C2×#26111yescharacteristic
153C22×C8—131no—
154C22×C8—131no—
155C22×C8C2×#26111yescharacteristic
156C22×C8C2×#26111yescharacteristic
157C2×C42—131no—
158C2×C42—131no—
159C2×C42—131no—
160C2×C42—131no—
161C2×C42—261no—
162C2×C42—261no—
163C2×C42—261no—
164C2×C42—261no—
165C2×C16—264no—
166C4⋊C8—262no—
167C4⋊C8—262no—
168C22⋊C8—22no—
169C22⋊C8—262no—
170C4×C8—132no—
171C4×C8—132no—
172C4×C8—261no—
173C4×C8—261no—
174C2×C13—21no—
175C2×C13—21no—
176C2×C13—42no—
177C2×C13#145811yescharacteristic
178C2×C13C2×C22⋊C1611yescharacteristic
179C2×C13C2×#34911yescharacteristic
180C24D13⋊C811yescharacteristic
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—131no—
186C22×C4—134no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—131no—
190C22×C4—261no—
191C22×C4—261no—
192C22×C4—262no—
193C22×C4—261no—
194C22×C4—261no—
195C22×C4—522no—
196C22×C4D13⋊C811yescharacteristic
197C22×C4C22×#26111yescharacteristic
198C2×C8—21no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—132no—
202C2×C8—261no—
203C2×C8—521no—
204C2×C8—521no—
205C2×C8C22⋊#26112yes—
206C42—131no—
207C42—131no—
208C42—131no—
209C42—131no—
210C42—261no—
211C42—261no—
212C42—261no—
213C42—261no—
214C42—261no—
215C42—261no—
216C16—524no—
217C13#1145911yescharacteristic, complemented, Sylow
218C23—21no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23D13⋊C1612yes—
223C23C2×D13⋊C811yescharacteristic
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—132no—
232C2×C4—132no—
233C2×C4—131no—
234C2×C4—131no—
235C2×C4—131no—
236C2×C4—132no—
237C2×C4—131no—
238C2×C4—264no—
239C2×C4—264no—
240C2×C4—262no—
241C2×C4—261no—
242C2×C4—261no—
243C2×C4—261no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—521no—
247C2×C4D13⋊M1611yescharacteristic
248C2×C4C2×C22⋊#26111yescharacteristic
249C8—22no—
250C8—41no—
251C8—262no—
252C8—521no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22—41no—
260C22C2×D13⋊C1611yescharacteristic
261C22D13⋊M3211yescharacteristic
262C22D13⋊(C22⋊C8)11yescharacteristic
263C4—21no—
264C4—41no—
265C4—132no—
266C4—132no—
267C4—132no—
268C4—262no—
269C4—261no—
270C4—521no—
271C4#1171914211yescharacteristic
272C4#1171914811yescharacteristic
273C2—21no—
274C2—21no—
275C2—42no—
276C2#1313006811yescharacteristic
277C2D13⋊(C22⋊C16)11yescharacteristic
278C2D13⋊#34911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC22×C13C22×C16
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊C8C4
socleC22×C13C2×C22⋊C8
prime radicalC24×C13C2×C8
cosocleC22×#1055C23
hypercenterC2×C22⋊C8#261
hypocenterC13#11459
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #13131194C2semidirect
2. #13129773C2semidirect
55. C22×Dic13C16semidirect
217. C13#11459semidirect

Maximal subgroups

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

subgroupindex
#131311942
#131297732
#131297562
C2×#117183792
#1145913