Finite Group Databasebeta

← #14664906

Subgroups — #14664906

Order 2816.

452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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#13073789C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic
3#13066638C214yesmaximal, complemented
4C11×#1459C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic, complemented
7C2×C11×C22⋊C8—21no—
8#10622834—21no—
9C2×#66898—21no—
10#10622825—21no—
11#10622825—21no—
12#10622825—21no—
13#10622590—21no—
14#10622560C412yescomplemented
15#10622560C2212yes—
16C4×C4⋊Dic11C411yescharacteristic, complemented
17C11×#324—21no—
18C11×#323C2212yes—
19#10622164C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×Dic22C2×C412yes—
24C22×C8×C11—41no—
25C4×D4×C11—41no—
26C4×D4×C11—41no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C22⋊C4C2×C411yescharacteristic
29C2×C11×C22⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—41no—
38C2×C4×Dic11—21no—
39#66922—41no—
40#66922—41no—
41C11×C22⋊C8—22no—
42C11×C22⋊C8—41no—
43#66898—42no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—41no—
47C11⋊#95C2×C412yes—
48#11900—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C2×D411yescharacteristic
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11SD1612yes—
54C2×D4×C11Q1612yes—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11—42no—
69C2×Dic22—42no—
70C2×Dic22—82no—
71C2×C8×C11—42no—
72C2×C8×C11—82no—
73C11×C4⋊C4—41no—
74C11×C22⋊C4—41no—
75C11×C22⋊C4—41no—
76C42×C11—21no—
77C42×C11—21no—
78C22⋊Dic11—42no—
79C22⋊Dic11—42no—
80C22⋊Dic11—82no—
81C22⋊Dic11—82no—
82C4⋊Dic11—42no—
83C4⋊Dic11—42no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—82no—
87C4×Dic11—42no—
88#2563—111no—
89#1799—111no—
90#1459D1111yescharacteristic
91#1351—114no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11#10312yes—
101C23×C11C2×C22⋊C411yescharacteristic
102C23×C11C2×SD1611yescharacteristic
103C23×C11C2×Q1611yescharacteristic
104D4×C11—42no—
105D4×C11—42no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11#9911yescharacteristic
120C2×C4×C11#9911yescharacteristic
121C2×C4×C11#10312yes—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—82no—
129C2×Dic11—82no—
130C2×Dic11—82no—
131Dic22—84no—
132C8×C11—82no—
133C2×C4⋊Q8—111no—
134C2×C4×D4C2×D1111yescharacteristic
135C2×#99—221no—
136C2×C22⋊C8—21no—
137#393—112no—
138#393—112no—
139#390—221no—
140#382—221no—
141#380—221no—
142#380—221no—
143#380—221no—
144C4×C4⋊C4—111no—
145#342—112no—
146#324—21no—
147#323C2×D1112yes—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—22no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—42no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—81no—
161C22×C11—81no—
162C22×C11C2×#9911yescharacteristic
163C22×C11C2×#10311yescharacteristic
164C22×C11#42111yescharacteristic
165C4×C11—21no—
166C4×C11—22no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11#35412yes—
171Dic11—82no—
172Dic11—82no—
173Dic11—162no—
174C22×Q8—112no—
175C22×D4D4411yescharacteristic
176C23×C4D4411yescharacteristic
177C23×C4C22⋊D1111yescharacteristic
178C22×C8—41no—
179C4⋊Q8—441no—
180C4⋊Q8—441no—
181C4×D4—41no—
182C4×D4—41no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—441no—
187C2×C4⋊C4C22⋊D1111yescharacteristic
188C2×C22⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C22⋊C4—222no—
191C2×C22⋊C4C4×D1111yescharacteristic
192C2×C22⋊C4C22×D1111yescharacteristic
193C2×C42—221no—
194C2×C42C4×D1111yescharacteristic
195#99—442no—
196C22⋊C8—22no—
197C22⋊C8—41no—
198#95—112no—
199#95—222no—
200#95—222no—
201#95—441no—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11—41no—
205C2×C11—42no—
206C2×C11—41no—
207C2×C11#152011yescharacteristic
208C2×C11#212211yescharacteristic
209C2×C11C2×#35411yescharacteristic
210C24(C2×D11)⋊C411yescharacteristic
211C24C2×D4411yescharacteristic
212C2×Q8—442no—
213C2×Q8—882no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4#431412yes—
217C2×D4Dic4412yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—222no—
225C22×C4—222no—
226C22×C4—442no—
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4(C2×D11)⋊C411yescharacteristic
230C22×C4C2×C4×D1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—42no—
233C2×C8—82no—
234C4⋊C4—41no—
235C4⋊C4—442no—
236C4⋊C4—442no—
237C4⋊C4—441no—
238C4⋊C4—441no—
239C4⋊C4—882no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—442no—
243C22⋊C4—442no—
244C22⋊C4—882no—
245C22⋊C4—882no—
246C42—21no—
247C42—21no—
248C42—442no—
249C11#1190011yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23#6688012yes—
259C23C2×#431411yescharacteristic
260C23C2×Dic4411yescharacteristic
261C23C2×(C2×D11)⋊C411yescharacteristic
262Q8—884no—
263D4—42no—
264D4—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—882no—
285C2×C4—882no—
286C2×C4—882no—
287C2×C4#6687011yescharacteristic
288C2×C4#6687011yescharacteristic
289C2×C4#6688012yes—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—22no—
295C22—21no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22—81no—
305C22C2×#6687011yescharacteristic
306C22C2×#6688011yescharacteristic
307C22#1062275211yescharacteristic
308C4—22no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—882no—
314C4—882no—
315C4—1762no—
316C4#1062211112yes—
317C2—21no—
318C2—21no—
319C2—41no—
320C2—42no—
321C2—41no—
322C2#1306718911yescharacteristic
323C2#1307026711yescharacteristic
324C2C2×#1062211111yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1459C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1459D11
hypocenterC11#11900
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13066638C2semidirect
6. C2×#66922C4semidirect
14. #10622560C4semidirect
16. C4×C4⋊Dic11C4semidirect
249. C11#11900semidirect

Maximal subgroups

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

subgroupindex
#130737892
#130686042
#130666382
C11×#14592
#1190011