Finite Group Databasebeta

← #14663463

Subgroups — #14663463

Order 2816.

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

normal subgroups only

This group has 424 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#13072933C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066563C214yesmaximal, complemented
4C11×#1460C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic
7C11×#431—21no—
8#10622833C412yes—
9#10622825—21no—
10#10622825C411yescharacteristic
11#10622820—21no—
12#10622599—21no—
13#10622562—21no—
14#10622559C2212yes—
15#10622541—21no—
16C11×#323—21no—
17C11×#323C2212yes—
18#10622166—21no—
19#10622163C2212yes—
20C22×D4×C11C2×C411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11C2×C412yes—
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4D411yescharacteristic
28C2×C11×C22⋊C4C2311yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C22⋊Dic11—22no—
31C2×C22⋊Dic11C2×C412yes—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—41no—
36C2×C4⋊Dic11—41no—
37C2×Dic11⋊C4—22no—
38C2×#4318—41no—
39C11×C4⋊C8—41no—
40C11×C22⋊C8—22no—
41C4×C8×C11—41no—
42C11⋊#95—22no—
43C11⋊#95—21no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)—41no—
47#11579—111nomaximal, Sylow
48C24×C11C22⋊C411yescharacteristic
49C24×C11C22×C411yescharacteristic
50C2×D4×C11—22no—
51C2×D4×C11—22no—
52C2×D4×C11—41no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—42no—
58C22×C4×C11—42no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—22no—
65C22×Dic11—22no—
66C22×Dic11—42no—
67C22×Dic11—82no—
68C2×C8×C11—42no—
69C11×C4⋊C4—41no—
70C11×C22⋊C4—41no—
71C11×C22⋊C4—41no—
72C42×C11—21no—
73C42×C11—21no—
74C22⋊Dic11—24no—
75C22⋊Dic11—82no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80Dic11⋊C4—82no—
81#4318—82no—
82C2×C11⋊C8—42no—
83#2487—111no—
84#1465—111no—
85#1460D1111yescharacteristic
86#1326—114no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11C2×C22⋊C411yescharacteristic
97C23×C11#13112yes—
98D4×C11—44no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—81no—
112C2×C4×C11#9911yescharacteristic
113C2×C4×C11#9911yescharacteristic
114C2×C4×C11#10112yes—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—84no—
122C8×C11—82no—
123C11⋊C8—82no—
124C2×C4×D4C2×D1111yescharacteristic
125C22×C4⋊C4—111no—
126#431—21no—
127#407—221no—
128#400—221no—
129#399—221no—
130#389—221no—
131#386—112no—
132#385—112no—
133#380—111no—
134#380—221no—
135#324—221no—
136#323—21no—
137#323—112no—
138#323C2×D1112yes—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—22no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—81no—
151C22×C11#40811yescharacteristic
152C22×C11C2×#9911yescharacteristic
153C22×C11C2×#10111yescharacteristic
154C4×C11—21no—
155C4×C11—22no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11#35212yes—
160Dic11—82no—
161Dic11—82no—
162C22×D4C4×D1111yescharacteristic
163C23×C4—112no—
164C23×C4C4×D1111yescharacteristic
165C23×C4D4411yescharacteristic
166C2×M16—441no—
167C4×D4—41no—
168C4×D4—41no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—222no—
173C2×C4⋊C4—441no—
174C2×C4⋊C4—441no—
175C2×C4⋊C4D4411yescharacteristic
176C2×C22⋊C4—112no—
177C2×C22⋊C4—222no—
178C2×C22⋊C4C22⋊D1111yescharacteristic
179C2×C22⋊C4C22×D1111yescharacteristic
180C2×C42C22⋊D1111yescharacteristic
181C4⋊C8—41no—
182C22⋊C8—22no—
183C22⋊C8—222no—
184C22⋊C8—441no—
185C4×C8—41no—
186#95—221no—
187#95—222no—
188#95—222no—
189C2×C11—21no—
190C2×C11—21no—
191C2×C11—42no—
192C2×C11—81no—
193C2×C11#147211yescharacteristic
194C2×C11C2×#35211yescharacteristic
195C2×C11#212211yescharacteristic
196C24(C2×D11)⋊C411yescharacteristic
197C24C2×C4×D1111yescharacteristic
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—222no—
208C22×C4—222no—
209C22×C4—442no—
210C22×C4—882no—
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4(C2×D11)⋊C411yescharacteristic
213C22×C4(C2×D11)⋊C411yescharacteristic
214C22×C4C2×D4411yescharacteristic
215C22×C4C2×C22⋊D1111yescharacteristic
216M16—882no—
217C2×C8—42no—
218C2×C8—442no—
219C4⋊C4—41no—
220C4⋊C4—442no—
221C4⋊C4—442no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—882no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—224no—
228C22⋊C4—882no—
229C42—21no—
230C42—21no—
231C11#1157911yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23#6695412yes—
242C23C2×(C2×D11)⋊C411yescharacteristic
243D4—44no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—81no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4—442no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—884no—
264C2×C4#6687011yescharacteristic
265C2×C4#6687011yescharacteristic
266C2×C4#6688812yes—
267C8—82no—
268C8—882no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22C2×#6687011yescharacteristic
282C22#1062272311yescharacteristic
283C22C2×#6688811yescharacteristic
284C4—21no—
285C4—22no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—882no—
290C4—882no—
291C4#1062211412yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—81no—
296C2#1306697911yescharacteristic
297C2C2×#1062211411yescharacteristic
298C2#1307026511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1460C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1460D11
hypocenterC11#11579
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #13066563C2semidirect
231. C11#11579semidirect

Maximal subgroups

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

subgroupindex
#130729332
#130669542
#130665632
C11×#14602
#1157911