Finite Group Databasebeta

← #16786942

Subgroups — #16786942

Order 3328.

430 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 108 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#13129757C212yesmaximal, complemented
3#13129756C212yesmaximal, complemented
4C2×C8×C22⋊D13C211yesmaximal, characteristic
5C23×C8×C13C411yescharacteristic
6C2×C4×C22⋊D13C411yescharacteristic
7C22×C8×D13C411yescharacteristic
8C2×C22⋊#1055C2211yescharacteristic
9C8×C22⋊D13—22no—
10C8×C22⋊D13—22no—
11C2×#88060C2211yescharacteristic
12C2×#88054C411yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14C22⋊#6092C2214yes—
15#11718260—22no—
16#11718257—22no—
17C23×C4×C13C2×C411yescharacteristic
18C22×C22⋊D13C811yescharacteristic
19C22×C4×D13C2×C411yescharacteristic
20C22×C8×C13—21no—
21C22×C8×C13—21no—
22C22×C8×C13—42no—
23C22×C8×C13C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C2×C22⋊Dic13C811yescharacteristic
26C4×C22⋊D13—22no—
27C4×C22⋊D13—22no—
28C2×#6103C811yescharacteristic
29C2×#6101C811yescharacteristic
30C2×C4×Dic13C2×C411yescharacteristic
31C22×#1055C2×C411yescharacteristic
32C22×#1055C2311yescharacteristic
33C2×C8×D13—21no—
34C2×C8×D13—21no—
35C2×C8×D13—42no—
36C2×#6092—24no—
37C22⋊#1055—22no—
38#88060—22no—
39#88054—22no—
40C8×Dic13D412yes—
41C8×Dic13D412yes—
42#11487—131nomaximal, Sylow
43C24×C13C2×C811yescharacteristic
44C23×D13C2×C811yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—41no—
48C22×C4×C13—41no—
49C22×C4×C13C2×C811yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C2×C22⋊D13—22no—
52C2×C22⋊D13—22no—
53C2×C22⋊D13C1614yescomplemented
54C22×Dic13C2×C811yescharacteristic
55C22×Dic13C2×C811yescharacteristic
56C22×Dic13C2×C811yescharacteristic
57C2×C4×D13—21no—
58C2×C4×D13—21no—
59C2×C4×D13—41no—
60C2×C4×D13—41no—
61C2×C8×C13—22no—
62C2×C8×C13—21no—
63C2×C8×C13—42no—
64C2×C8×C13—42no—
65C2×C8×C13—41no—
66C2×C8×C13C22⋊C411yescharacteristic
67C2×C8×C13C22⋊C411yescharacteristic
68C22⋊Dic13—22no—
69#6103—22no—
70#6101—22no—
71C4×Dic13C22⋊C412yes—
72C4×Dic13M1612yes—
73C2×#1055—21no—
74C2×#1055—41no—
75C2×#1055—41no—
76C2×#1055C2×D412yes—
77C8×D13—42no—
78C8×D13—42no—
79#6092—44no—
80C2×C8×D4—131no—
81#2162—132no—
82#1314—132no—
83#1314—132no—
84C23×C13—21no—
85C23×C13—21no—
86C23×C13—41no—
87C23×C13—41no—
88C23×C13C2×C1612yes—
89C23×C13C22×C811yescharacteristic
90C22×D13—21no—
91C22×D13—21no—
92C22×D13—41no—
93C22×D13—41no—
94C22×D13C2×C1612yes—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13C2×C22⋊C411yescharacteristic
103C2×C4×C13C2×M1611yescharacteristic
104C22⋊D13—28no—
105C2×Dic13—21no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108C2×Dic13C22⋊C812yes—
109C2×Dic13C22⋊C812yes—
110C2×Dic13C2×C1612yes—
111C2×Dic13M3212yes—
112C4×D13—42no—
113C4×D13—41no—
114C4×D13—41no—
115C8×C13—21no—
116C8×C13—41no—
117C8×C13#10012yes—
118#1055—22no—
119#1055—41no—
120C23×C8—131no—
121C23×C8#26111yescharacteristic
122C2×C4×D4—131no—
123C8×D4—262no—
124C8×D4—262no—
125C2×C4⋊C8—131no—
126C2×C22⋊C8—131no—
127C2×C22⋊C8—131no—
128C2×C4×C8—131no—
129C4⋊C16—262no—
130C22⋊C16—134no—
131C4×C16—262no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—22no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13C2×C22⋊C811yescharacteristic
140C22×C13C22×C1611yescharacteristic
141C22×C13C2×M3211yescharacteristic
142C2×D13—22no—
143C2×D13—42no—
144C2×D13—41no—
145C2×D13—41no—
146C2×D13—42no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13#41011yescharacteristic
150C4×C13C2×#10011yescharacteristic
151Dic13—22no—
152Dic13—41no—
153Dic13C22⋊C1614yes—
154C22×D4—131no—
155C23×C4—131no—
156C23×C4C2×#26111yescharacteristic
157C22×C8—21no—
158C22×C8—21no—
159C22×C8—42no—
160C22×C8—131no—
161C22×C8—131no—
162C22×C8—261no—
163C22×C8—261no—
164C22×C8—522no—
165C22×C8C2×#26111yescharacteristic
166C22×C8C2×#26111yescharacteristic
167C4×D4—262no—
168C4×D4—262no—
169C2×C4⋊C4—131no—
170C2×C22⋊C4—131no—
171C2×C22⋊C4—131no—
172C2×C42—131no—
173C2×C16—264no—
174C4⋊C8—262no—
175C22⋊C8—262no—
176C22⋊C8—262no—
177C4×C8—132no—
178C4×C8—132no—
179C2×C13—21no—
180C2×C13—21no—
181C2×C13—42no—
182C2×C13#146011yescharacteristic
183C2×C13C2×C22⋊C1611yescharacteristic
184C2×C13#211511yescharacteristic
185D13—42no—
186C24—131no—
187C24D13⋊C811yescharacteristic
188C2×D4—134no—
189C2×D4—262no—
190C2×D4—262no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—261no—
199C22×C4—261no—
200C22×C4—521no—
201C22×C4—521no—
202C22×C4D13⋊C811yescharacteristic
203C22×C4C22×#26111yescharacteristic
204C2×C8—22no—
205C2×C8—21no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—41no—
209C2×C8—132no—
210C2×C8—261no—
211C2×C8—522no—
212C2×C8—521no—
213C2×C8—522no—
214C2×C8—521no—
215C2×C8C22⋊#26111yescharacteristic
216C2×C8C22⋊#26111yescharacteristic
217C4⋊C4—262no—
218C22⋊C4—262no—
219C22⋊C4—262no—
220C42—132no—
221C42—132no—
222C16—524no—
223C13#1148711yescharacteristic, complemented, Sylow
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23—132no—
229C23—261no—
230C23—261no—
231C23—521no—
232C23—521no—
233C23D13⋊C1612yes—
234C23C2×D13⋊C811yescharacteristic
235D4—268no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—132no—
244C2×C4—132no—
245C2×C4—132no—
246C2×C4—132no—
247C2×C4—261no—
248C2×C4—522no—
249C2×C4—521no—
250C2×C4—521no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4D13⋊M1611yescharacteristic
254C2×C4C2×C22⋊#26111yescharacteristic
255C8—21no—
256C8—41no—
257C8—262no—
258C8—521no—
259C8#8812112yes—
260C22—21no—
261C22—21no—
262C22—22no—
263C22—42no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—262no—
268C22—522no—
269C22—522no—
270C22—521no—
271C22—521no—
272C22C2×D13⋊C1611yescharacteristic
273C22D13⋊M3211yescharacteristic
274C22D13⋊(C22⋊C8)11yescharacteristic
275C4—21no—
276C4—41no—
277C4—134no—
278C4—262no—
279C4—521no—
280C4#1171911611yescharacteristic
281C4C2×#8812111yescharacteristic
282C2—21no—
283C2—21no—
284C2—42no—
285C2—522no—
286C2#1313007511yescharacteristic
287C2D13⋊(C22⋊C16)11yescharacteristic
288C2#1313107311yescharacteristic
subgroupG/H
centerC2×C8C22⋊#261
commutatorC22×C13C22×C16
FrattiniC22×C4C22×#261
FittingC23×C8×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC22×C22⋊D13C8
cosocleC22×#1055C23
hypercenterC23×C8#261
hypocenterC13#11487
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #13131194C2semidirect
2. #13129757C2semidirect
3. #13129756C2semidirect
53. C2×C22⋊D13C16semidirect
223. C13#11487semidirect

Maximal subgroups

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

subgroupindex
#131311942
#131297572
#131297562
C2×C8×C22⋊D132
#1148713