Finite Group Databasebeta

← #14663183

Subgroups — #14663183

Order 2816.

418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071236C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066559C214yesmaximal, complemented
4C11×#1464C211yesmaximal, characteristic
5C2×C11×#117C2211yescharacteristic
6C2×#66979C411yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C11×#432—21no—
9#10622590C2212yes—
10#10622589C412yes—
11#10622559—21no—
12#10622559—21no—
13#10622541—21no—
14#10622541—21no—
15#10622539—21no—
16C11×#324C2212yes—
17C11×#323—21no—
18#10622166C2212yes—
19#10622163—21no—
20C23×C4×C11C2×C411yescharacteristic
21C23×Dic11—21no—
22C11×#117—41no—
23C11×#117—41no—
24C2×C11×C4⋊C4C2×C411yescharacteristic
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C11×C22⋊C4D411yescharacteristic
27C2×C11×C22⋊C4D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C22⋊Dic11—21no—
31#66979—24no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—41no—
35C2×C4⋊Dic11—41no—
36C2×C4⋊Dic11C2×C412yes—
37C2×Dic11⋊C4—22no—
38C2×Dic11⋊C4—22no—
39C2×C4×Dic11C2×C412yes—
40C11×C4⋊C8—41no—
41C11×C22⋊C8—22no—
42C11×#97—41no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—41no—
47#66867—41no—
48#11515—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C22×C4×C11—22no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—22no—
61C22×Dic11—22no—
62C22×Dic11—42no—
63C22×Dic11—82no—
64C2×C8×C11—42no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—41no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C22⋊Dic11—24no—
74C4⋊Dic11—24no—
75C4⋊Dic11—42no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78Dic11⋊C4—82no—
79Dic11⋊C4—82no—
80C4×Dic11—22no—
81C4×Dic11M1614yes—
82C2×C11⋊C8—42no—
83#2317—111no—
84#1464—111no—
85#1464D1111yescharacteristic
86#1324—114no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—41no—
90C23×C11—41no—
91C23×C11#10112yes—
92C23×C11C2×C22⋊C411yescharacteristic
93C2×C4×C11—24no—
94C2×C4×C11—24no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11#9911yescharacteristic
108C2×C4×C11#9911yescharacteristic
109C2×C4×C11C2×M1612yes—
110C2×Dic11—24no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—84no—
117C8×C11—82no—
118C11⋊C8—82no—
119C2×#117—111no—
120C2×#117C2×D1111yescharacteristic
121C22×C4⋊C4—111no—
122#432—21no—
123#432—221no—
124#389—221no—
125#389—221no—
126#385—221no—
127#385—221no—
128#384—112no—
129#382—112no—
130#324—112no—
131#324C2×D1112yes—
132#323—21no—
133#323—221no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—22no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11#40711yescharacteristic
142C22×C11C2×#9911yescharacteristic
143C22×C11C2×#10111yescharacteristic
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—22no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151Dic11—44no—
152Dic11—82no—
153C23×C4—221no—
154C23×C4C4×D1111yescharacteristic
155#117—41no—
156#117—41no—
157#117—224no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4—221no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—222no—
162C2×C4⋊C4—222no—
163C2×C4⋊C4—441no—
164C2×C4⋊C4—441no—
165C2×C4⋊C4C4×D1111yescharacteristic
166C2×C4⋊C4C22×D1111yescharacteristic
167C2×C22⋊C4—221no—
168C2×C22⋊C4D4411yescharacteristic
169C2×C22⋊C4C22⋊D1111yescharacteristic
170C2×C42—112no—
171C2×C42D4411yescharacteristic
172C2×C42C22⋊D1111yescharacteristic
173C4⋊C8—41no—
174C4⋊C8—441no—
175C22⋊C8—22no—
176C22⋊C8—222no—
177#97—41no—
178#97—441no—
179#95—222no—
180#95—222no—
181C2×C11—21no—
182C2×C11—21no—
183C2×C11—42no—
184C2×C11#146311yescharacteristic
185C2×C11#212911yescharacteristic
186C2×C11#213411yescharacteristic
187C24(C2×D11)⋊C411yescharacteristic
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—222no—
193C22×C4—222no—
194C22×C4—442no—
195C22×C4—882no—
196C22×C4(C2×D11)⋊C411yescharacteristic
197C22×C4(C2×D11)⋊C411yescharacteristic
198C22×C4(C2×D11)⋊C411yescharacteristic
199C22×C4C2×C4×D1111yescharacteristic
200C22×C4C2×D4411yescharacteristic
201C22×C4C2×C22⋊D1111yescharacteristic
202C2×C8—42no—
203C2×C8—442no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—224no—
207C4⋊C4—442no—
208C4⋊C4—441no—
209C4⋊C4—441no—
210C4⋊C4—882no—
211C4⋊C4—882no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—224no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—114no—
220C42—222no—
221C11#1151511yescharacteristic, complemented, Sylow
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23#6688812yes—
227C23C2×(C2×D11)⋊C411yescharacteristic
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—224no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—884no—
249C2×C4#6687011yescharacteristic
250C2×C4#6687011yescharacteristic
251C2×C4M16×D1112yes—
252C8—82no—
253C8—882no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22C2×#6687011yescharacteristic
262C22#1062273911yescharacteristic
263C22C2×#6688811yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—444no—
272C4—882no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#1306694511yescharacteristic
277C2#1307029011yescharacteristic
278C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1464D11
hypocenterC11#11515
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13066559C2semidirect
221. C11#11515semidirect

Maximal subgroups

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

subgroupindex
#130712362
#130669502
#130665592
C11×#14642
#1151511