Finite Group Databasebeta

← #14663420

Subgroups — #14663420

Order 2816.

424 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 95 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#13066954C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic
3#13066560C214yesmaximal, complemented
4C11×#2563C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×D4×C11C2211yescharacteristic
7C11×#393—21no—
8C11×#393—21no—
9C11×#390C412yes—
10C11×#382C2212yes—
11C11×#380—21no—
12C11×#380—21no—
13C4×C11×C4⋊C4C411yescharacteristic
14#10622820—21no—
15C2×C22⋊(C11⋊C8)—21no—
16#10622166C2212yes—
17#10622166C2212yes—
18#10622163—21no—
19#10622163—21no—
20C22×Q8×C11—21no—
21C22×D4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C4×D4×C11—41no—
27C4×D4×C11—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11C2×C412yes—
37C2×C42×C11C2×C411yescharacteristic
38C2×#4318—41no—
39C22×C11⋊C8—41no—
40C11×#95—21no—
41C11×#95—22no—
42C11×#95—22no—
43C22⋊(C11⋊C8)—22no—
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—41no—
46C22⋊(C11⋊C8)—41no—
47#11569—111nomaximal, Sylow
48C24×C11C22⋊C411yescharacteristic
49C24×C11C22⋊C411yescharacteristic
50C2×Q8×C11—42no—
51C2×Q8×C11—82no—
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C11×C4⋊C4—41no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—41no—
74C11×C22⋊C4—41no—
75C11×C22⋊C4—82no—
76C11×C22⋊C4—82no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—24no—
80#4318—82no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—82no—
84#2563D1111yescharacteristic
85#1465—111no—
86#1459—111no—
87#1324—114no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—41no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11#10112yes—
98C23×C11C2×C22⋊C411yescharacteristic
99Q8×C11—84no—
100D4×C11—44no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11#9911yescharacteristic
121C2×C4×C11#9911yescharacteristic
122C2×C4×C11#13112yes—
123C11⋊C8—82no—
124C11⋊C8—82no—
125C2×C4⋊Q8Dic1111yescharacteristic
126C2×C4×D4C2×D1111yescharacteristic
127#407—221no—
128C2×C22⋊C8—221no—
129#393—21no—
130#393—21no—
131#390Dic1112yes—
132#382C2×D1112yes—
133#380—21no—
134#380—21no—
135C4×C4⋊C4Dic1111yescharacteristic
136#324—112no—
137#324—112no—
138#323—221no—
139#323—221no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—22no—
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—81no—
152C22×C11#40811yescharacteristic
153C22×C11C2×#9911yescharacteristic
154C22×C11C2×#10111yescharacteristic
155C4×C11—21no—
156C4×C11—22no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—82no—
161C4×C11—82no—
162C4×C11#35412yes—
163C22×Q8—21no—
164C22×D4C2×Dic1111yescharacteristic
165C23×C4C22⋊D1111yescharacteristic
166C23×C4C22⋊D1111yescharacteristic
167C2×M16—441no—
168C22×C8—441no—
169C4⋊Q8—41no—
170C4⋊Q8—41no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4C2×Dic1112yes—
176C2×C4⋊C4C22×D1111yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4C22⋊D1111yescharacteristic
180C2×C22⋊C4C22⋊D1111yescharacteristic
181C2×C42C2×Dic1112yes—
182C2×C42C2×Dic1111yescharacteristic
183C22⋊C8—222no—
184C22⋊C8—222no—
185C22⋊C8—441no—
186C22⋊C8—441no—
187#95—21no—
188#95—22no—
189#95—22no—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11—42no—
193C2×C11—81no—
194C2×C11#147211yescharacteristic
195C2×C11C2×#35411yescharacteristic
196C2×C11#213411yescharacteristic
197C24C22⋊Dic1111yescharacteristic
198C24C22⋊Dic1111yescharacteristic
199C2×Q8—42no—
200C2×Q8—82no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4C22⋊Dic1111yescharacteristic
213C22×C4C22⋊Dic1111yescharacteristic
214C22×C4C22×Dic1111yescharacteristic
215C22×C4C2×C22⋊D1111yescharacteristic
216C22×C4C2×C22⋊D1111yescharacteristic
217M16—882no—
218C2×C8—442no—
219C2×C8—442no—
220C2×C8—882no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—82no—
229C22⋊C4—82no—
230C42—21no—
231C42—21no—
232C42—24no—
233C11#1156911yescharacteristic, complemented, Sylow
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23#6690012yes—
244C23C2×C22⋊Dic1111yescharacteristic
245Q8—84no—
246D4—44no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4#6689811yescharacteristic
267C2×C4#6689811yescharacteristic
268C2×C4#6700112yes—
269C8—882no—
270C8—882no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22C2×#6689811yescharacteristic
284C22C2×#6690011yescharacteristic
285C22#1062284711yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4#1062217912yes—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1306698011yescharacteristic
299C2C2×#1062217911yescharacteristic
300C2#1307030811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2563C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2563D11
hypocenterC11#11569
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
3. #13066560C2semidirect
233. C11#11569semidirect

Maximal subgroups

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

subgroupindex
#130669542
#130669342
#130665602
C11×#25632
#1156911