Finite Group Databasebeta

← #14664365

Subgroups — #14664365

Order 2816.

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

normal subgroups only

This group has 482 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#13073615C211yesmaximal, characteristic
2C4×#66900C211yesmaximal, characteristic, complemented
3#13066620C214yesmaximal, complemented
4C11×#1467C211yesmaximal, characteristic, complemented
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#67000—21no—
7C2×#66927C411yescharacteristic
8C11×#432—21no—
9C2×#66900—21no—
10#10622604C412yes—
11#10622604C2212yes—
12#10622601—21no—
13#10622552—21no—
14#10622552—21no—
15C4×C4⋊Dic11C411yescharacteristic
16C4×#4318—21no—
17C11×#324—21no—
18C11×#324C2212yes—
19#10622168C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×D44—21no—
22C22×D44—21no—
23C22×D44C2×C412yes—
24C4×Q8×C11—41no—
25C4×Q8×C11—41no—
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32#67000—44no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×C4⋊Dic11—21no—
38C2×C4×Dic11—21no—
39C2×#4318—22no—
40#66927—41no—
41#66927—41no—
42C11×C4⋊C8—41no—
43C11×C22⋊C8—22no—
44C11×#97—41no—
45#66900—24no—
46C11⋊#95C2×C412yes—
47#66867—41no—
48C4×C11⋊C8—41no—
49#11781—111nomaximal, Sylow
50C23×D11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—41no—
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22×C411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—22no—
62C2×D44—42no—
63C2×D44—42no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—41no—
68C2×D44—41no—
69C2×D44—42no—
70C2×D44—82no—
71C2×C8×C11—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81(C2×D11)⋊C4—44no—
82(C2×D11)⋊C4—44no—
83(C2×D11)⋊C4—82no—
84(C2×D11)⋊C4—82no—
85C4⋊Dic11—42no—
86C4×Dic11—42no—
87#4318—24no—
88#4318—42no—
89C2×C11⋊C8—42no—
90#2548—111no—
91C4×#101—111no—
92#1467D1111yescharacteristic, complemented
93#1345—114no—
94C23×C11C2×C22⋊C411yescharacteristic
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98C22×D11—42no—
99C22×D11—42no—
100C22×D11—42no—
101C22×D11—42no—
102Q8×C11—44no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11#9911yescharacteristic
118C2×C4×C11#9911yescharacteristic
119C2×C4×C11#10412yes—
120C2×C4×C11AGL(1,ℤ/8)12yes—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124D44—82no—
125D44—84no—
126D44—84no—
127D44—82no—
128C8×C11—82no—
129C11⋊C8—44no—
130C2×#127—111no—
131C2×#124—221no—
132C2×C4×Q8C2×D1111yescharacteristic
133#432—21no—
134C2×#101—221no—
135C4×M16—221no—
136#394—112no—
137#394—112no—
138#390—221no—
139#390—221no—
140#390—221no—
141C4×C4⋊C4—111no—
142#343—112no—
143#324—21no—
144#324C2×D1112yes—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11C2×#9911yescharacteristic
148C22×C11#41811yescharacteristic
149C22×C11C2×#10411yescharacteristic
150C2×D11—82no—
151C2×D11—82no—
152C2×D11—82no—
153C2×D11—82no—
154C2×D11—82no—
155C2×D11—82no—
156C2×D11—82no—
157C4×C11—21no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11#35512yes—
165Dic11—82no—
166C22×Q8D4411yescharacteristic
167C22×D4—112no—
168C22×D4—221no—
169C22×D4—221no—
170C2×M16—222no—
171#127—441no—
172#127—441no—
173#124—444no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—221no—
177C2×C4⋊C4C4×D1111yescharacteristic
178C2×C4⋊C4C22⋊D1111yescharacteristic
179C2×C4⋊C4C22×D1111yescharacteristic
180C2×C22⋊C4—222no—
181C2×C22⋊C4—222no—
182C2×C22⋊C4—222no—
183C2×C22⋊C4—222no—
184C2×C42—221no—
185C2×C42C4×D1111yescharacteristic
186C2×C42D4411yescharacteristic
187C2×C42C22⋊D1111yescharacteristic
188C4⋊C8—41no—
189#101—224no—
190C22⋊C8—22no—
191#97—41no—
192#97—441no—
193C4×C8—441no—
194#95—112no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11#150711yescharacteristic
198C2×C11#212211yescharacteristic
199C2×C11C2×#35511yescharacteristic
200D11—162no—
201C24—222no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C2×D4—442no—
206C2×D4—442no—
207C2×D4—442no—
208C2×D4—442no—
209C2×D4—442no—
210C2×D4—441no—
211C2×D4—441no—
212C2×D4—442no—
213C2×D4—882no—
214C22×C4—222no—
215C22×C4(C2×D11)⋊C411yescharacteristic
216C22×C4(C2×D11)⋊C411yescharacteristic
217C22×C4(C2×D11)⋊C411yescharacteristic
218C22×C4(C2×D11)⋊C411yescharacteristic
219C22×C4C2×C4×D1111yescharacteristic
220C22×C4C2×D4411yescharacteristic
221C22×C4C2×C22⋊D1111yescharacteristic
222M16—224no—
223M16—442no—
224C2×C8—42no—
225C2×C8—442no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—442no—
230C22⋊C4—444no—
231C22⋊C4—444no—
232C22⋊C4—882no—
233C22⋊C4—882no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—442no—
241C11#1178111yescharacteristic, complemented, Sylow
242C23—442no—
243C23—442no—
244C23—442no—
245C23—442no—
246C23—442no—
247C23—442no—
248C23—442no—
249C23C2×(C2×D11)⋊C411yescharacteristic
250Q8—44no—
251D4—884no—
252D4—882no—
253D4—884no—
254D4—882no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4—442no—
272C2×C4#6687011yescharacteristic
273C2×C4#6687011yescharacteristic
274C2×C4#6688912yes—
275C2×C4#6696112yes—
276C8—82no—
277C8—444no—
278C22—21no—
279C22—21no—
280C22—882no—
281C22—882no—
282C22—882no—
283C22—882no—
284C22—882no—
285C22—882no—
286C22—882no—
287C22C2×#6687011yescharacteristic
288C22#1062274411yescharacteristic
289C22C2×#6688911yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—882no—
298C4#1062211512yes—
299C2—21no—
300C2—21no—
301C2—1762no—
302C2#1306713311yescharacteristic
303C2#1307026511yescharacteristic
304C2C2×#1062211511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1467C2
socleC22×C11C2×#99
prime radicalC2×#66927C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1467D11
hypocenterC11#11781
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. C4×#66900C2semidirect
3. #13066620C2semidirect
4. C11×#1467C2semidirect
92. #1467D11semidirect
241. C11#11781semidirect

Maximal subgroups

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

subgroupindex
#130736152
C4×#669002
#130666202
C11×#14672
#1178111