Finite Group Databasebeta

← #16786839

Subgroups — #16786839

Order 3328.

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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#13131198C211yesmaximal, characteristic, complemented
2#13131194C211yesmaximal, characteristic, complemented
3#13129773C212yesmaximal, complemented
4#13129756C212yesmaximal
5C2×#11718381C211yesmaximal, characteristic
6C2×#88180C411yescharacteristic
7C2×C13×C22⋊C8C411yescharacteristic
8C2×C22⋊#1055C2211yescharacteristic
9C2×#88055C411yescharacteristic
10C2×#88054C411yescharacteristic
11C2×#88054C2211yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13#11718381—21no—
14#11718381—21no—
15#11718381—21no—
16#11718381—21no—
17C22⋊#6092C2212yes—
18C22⋊#6092C2212yes—
19#11718260—21no—
20#11718260—21no—
21#11718258—21no—
22#11718257—21no—
23C23×C4×C13C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C22×C8×C13C2×C411yescharacteristic
26C2×C22⋊Dic13C811yescharacteristic
27C2×C22⋊Dic13C811yescharacteristic
28#88180—21no—
29#88180—21no—
30#88180—21no—
31#88180—21no—
32C2×C4⋊Dic13C811yescharacteristic
33C2×C4⋊Dic13C811yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C22×#1055C2311yescharacteristic
38C2×#6092—22no—
39C2×#6092—22no—
40C13×C22⋊C8—21no—
41C13×C22⋊C8—21no—
42C22⋊#1055—21no—
43C22⋊#1055—21no—
44#88055—21no—
45#88055—21no—
46#88054—21no—
47#88054—21no—
48#88054—21no—
49#88054—21no—
50C8×Dic13D411yescharacteristic
51C8×Dic13D411yescharacteristic
52C8×Dic13D411yescharacteristic
53C8×Dic13D411yescharacteristic
54#11461—131nomaximal, Sylow
55C24×C13C2×C811yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13C2×C811yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13C2×C811yescharacteristic
63C22×Dic13C2×C811yescharacteristic
64C22×Dic13C2×C811yescharacteristic
65C22×Dic13C2×C811yescharacteristic
66C2×C8×C13—21no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C2×C8×C13C22⋊C411yescharacteristic
70C2×C8×C13C22⋊C411yescharacteristic
71C22⋊Dic13—21no—
72C22⋊Dic13—21no—
73C22⋊Dic13—21no—
74C22⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13—21no—
77C4⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13C22⋊C411yescharacteristic
82C4×Dic13C22⋊C411yescharacteristic
83C4×Dic13M1611yescharacteristic
84C4×Dic13M1611yescharacteristic
85C2×#1055—21no—
86C2×#1055—41no—
87C2×#1055—41no—
88C2×#1055C2×D411yescharacteristic
89C2×#1055C2×D411yescharacteristic
90#6092—42no—
91#6092—42no—
92C2×#433—131no—
93#2163—131no—
94#2162—131no—
95#1322—132no—
96#1314—132no—
97C23×C13—21no—
98C23×C13—22no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13C22×C811yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13C2×C22⋊C411yescharacteristic
110C2×C4×C13C2×M1611yescharacteristic
111C2×Dic13—22no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—22no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13C22⋊C811yescharacteristic
118C2×Dic13C22⋊C811yescharacteristic
119C2×Dic13C22⋊C811yescharacteristic
120C2×Dic13C22⋊C811yescharacteristic
121C8×C13—21no—
122C8×C13—21no—
123C8×C13—41no—
124#1055—21no—
125#1055—21no—
126#1055—41no—
127C2×#117—131no—
128#433—261no—
129#433—261no—
130#433—261no—
131#433—261no—
132C2×C4⋊C8—131no—
133C2×C4⋊C8—131no—
134C2×C22⋊C8—131no—
135C2×C22⋊C8#26111yescharacteristic
136C2×#97—131no—
137C2×C4×C8—131no—
138C4⋊C16—261no—
139C4⋊C16—261no—
140C22⋊C16—132no—
141C22⋊C16—132no—
142#346—261no—
143C4×C16—261no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—82no—
150C22×C13C2×C22⋊C811yescharacteristic
151C22×C13#50412yes—
152C4×C13—21no—
153C4×C13—41no—
154C4×C13#41011yescharacteristic
155C4×C13#41311yescharacteristic
156Dic13—21no—
157Dic13—21no—
158Dic13—21no—
159Dic13—21no—
160Dic13—41no—
161Dic13—41no—
162C23×C4C2×#26111yescharacteristic
163C22×C8—131no—
164C22×C8—131no—
165C22×C8C2×#26111yescharacteristic
166C22×C8C2×#26111yescharacteristic
167#117—261no—
168#117—261no—
169#117—261no—
170#117—261no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—131no—
173C2×C22⋊C4—131no—
174C2×C22⋊C4—131no—
175C2×C42—131no—
176C2×C42—131no—
177C2×C16—262no—
178C2×C16—262no—
179C4⋊C8—261no—
180C4⋊C8—261no—
181C4⋊C8—261no—
182C4⋊C8—261no—
183C22⋊C8—21no—
184C22⋊C8—21no—
185C22⋊C8—261no—
186C22⋊C8—261no—
187#97—261no—
188#97—261no—
189C4×C8—131no—
190C4×C8—131no—
191C4×C8—131no—
192C4×C8—131no—
193C2×C13—22no—
194C2×C13—81no—
195C2×C13#145811yescharacteristic
196C2×C13#211311yescharacteristic
197C2×C13#211511yescharacteristic
198C24D13⋊C811yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4D13⋊C811yescharacteristic
208C22×C4C22×#26111yescharacteristic
209C2×C8—21no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—131no—
213C2×C8—131no—
214C2×C8—261no—
215C2×C8—521no—
216C2×C8—521no—
217C2×C8C22⋊#26111yescharacteristic
218C2×C8C22⋊#26111yescharacteristic
219C4⋊C4—261no—
220C4⋊C4—261no—
221C4⋊C4—261no—
222C4⋊C4—261no—
223C22⋊C4—261no—
224C22⋊C4—261no—
225C22⋊C4—261no—
226C22⋊C4—261no—
227C42—131no—
228C42—131no—
229C42—131no—
230C42—131no—
231C42—261no—
232C42—261no—
233C16—522no—
234C16—522no—
235C13#1146111yescharacteristic, complemented, Sylow
236C23—21no—
237C23—22no—
238C23—41no—
239C23—41no—
240C23C2×D13⋊C811yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—131no—
249C2×C4—131no—
250C2×C4—131no—
251C2×C4—131no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4D13⋊M1611yescharacteristic
259C2×C4C2×C22⋊#26111yescharacteristic
260C8—21no—
261C8—21no—
262C8—41no—
263C8—261no—
264C8—261no—
265C8—521no—
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—82no—
272C22#1171909612yes—
273C22D13⋊(C22⋊C8)11yescharacteristic
274C4—21no—
275C4—41no—
276C4—261no—
277C4—261no—
278C4—261no—
279C4—261no—
280C4—521no—
281C4—521no—
282C4#1171914211yescharacteristic
283C4#1171914811yescharacteristic
284C2—22no—
285C2—81no—
286C2#1313006811yescharacteristic
287C2#1313106711yescharacteristic
288C2#1313107311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊C8C4
socleC22×C13C2×C22⋊C8
prime radicalC24×C13C2×C8
cosocleC22×#1055C23
hypercenterC2×C22⋊C8#261
hypocenterC13#11461
LCSG ▷ C23×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. #13131198C2semidirect
2. #13131194C2semidirect
3. #13129773C2semidirect
235. C13#11461semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131311942
#131297732
#131297562
C2×#117183812
#1146113