Finite Group Databasebeta

← #14664902

Subgroups — #14664902

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#13072933C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic
3#13066641C214yesmaximal, complemented
4C11×#1460C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic, complemented
7C11×#431—21no—
8#10622833—21no—
9C2×#66898—21no—
10#10622825—21no—
11#10622825—21no—
12#10622825C411yescharacteristic, complemented
13#10622599C412yescomplemented
14#10622562C2212yes—
15#10622559—21no—
16#10622541—21no—
17C11×#323—21no—
18C11×#323C2212yes—
19#10622164C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C22⋊C4D411yescharacteristic
28C2×C11×C22⋊C4C2311yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C22⋊Dic11—21no—
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—41no—
36C2×C4⋊Dic11—41no—
37C2×C4⋊Dic11—41no—
38C2×C4⋊Dic11C2×C412yes—
39C2×Dic11⋊C4—22no—
40C11×C4⋊C8—41no—
41C11×C22⋊C8—22no—
42C4×C8×C11—41no—
43#66898—42no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—41no—
47C11⋊#95C2×C412yes—
48#11899—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—
69C22×Dic11—42no—
70C22×Dic11—82no—
71C2×C8×C11—42no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—41no—
74C11×C22⋊C4—41no—
75C42×C11—21no—
76C42×C11—21no—
77C22⋊Dic11—42no—
78C22⋊Dic11—42no—
79C22⋊Dic11—42no—
80C22⋊Dic11—82no—
81C4⋊Dic11—42no—
82C4⋊Dic11—42no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85C4⋊Dic11—82no—
86Dic11⋊C4—82no—
87#2487—111no—
88#1799—111no—
89#1460D1111yescharacteristic
90#1352—114no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11#10312yes—
100C23×C11C2×C22⋊C411yescharacteristic
101C23×C11C2×SD1611yescharacteristic
102C23×C11C2×Q1611yescharacteristic
103D4×C11—42no—
104D4×C11—42no—
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—42no—
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#9911yescharacteristic
119C2×C4×C11#9911yescharacteristic
120C2×C4×C11#10312yes—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—84no—
128C2×Dic11—82no—
129C2×Dic11—82no—
130C2×Dic11—82no—
131C8×C11—82no—
132C2×C4×D4C2×D1111yescharacteristic
133C22×C4⋊C4—111no—
134#431—21no—
135C2×#99—221no—
136#400—112no—
137#399—112no—
138#389—221no—
139#386—221no—
140#385—221no—
141#380—111no—
142#380—221no—
143#380—221no—
144#342—112no—
145#323—21no—
146#323C2×D1112yes—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—22no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—42no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—42no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—81no—
161C22×C11C2×#9911yescharacteristic
162C22×C11C2×#10311yescharacteristic
163C22×C11#42111yescharacteristic
164C4×C11—21no—
165C4×C11—22no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11#35212yes—
170Dic11—82no—
171Dic11—82no—
172Dic11—162no—
173C22×D4D4411yescharacteristic
174C23×C4—221no—
175C23×C4C4×D1111yescharacteristic
176C23×C4D4411yescharacteristic
177C4×D4—41no—
178C4×D4—41no—
179C2×C4⋊C4—112no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—221no—
182C2×C4⋊C4—222no—
183C2×C4⋊C4—441no—
184C2×C4⋊C4—441no—
185C2×C4⋊C4—441no—
186C2×C4⋊C4C4×D1111yescharacteristic
187C2×C22⋊C4—221no—
188C2×C22⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C22⋊C4C22⋊D1111yescharacteristic
191C2×C22⋊C4C22×D1111yescharacteristic
192C2×C42C22⋊D1111yescharacteristic
193C4⋊C8—41no—
194#99—442no—
195C22⋊C8—22no—
196C4×C8—41no—
197#95—112no—
198#95—222no—
199#95—222no—
200#95—441no—
201C2×C11—21no—
202C2×C11—21no—
203C2×C11—41no—
204C2×C11—42no—
205C2×C11—41no—
206C2×C11#152011yescharacteristic
207C2×C11C2×#35211yescharacteristic
208C2×C11#212811yescharacteristic
209C24(C2×D11)⋊C411yescharacteristic
210C24C2×D4411yescharacteristic
211C2×D4—41no—
212C2×D4—41no—
213C2×D4#431412yes—
214C2×D4Dic4412yes—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—222no—
222C22×C4—222no—
223C22×C4—442no—
224C22×C4—442no—
225C22×C4—882no—
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4C2×C4×D1111yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231C2×C8—42no—
232C4⋊C4—41no—
233C4⋊C4—442no—
234C4⋊C4—442no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C4⋊C4—882no—
238C4⋊C4—882no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—442no—
242C22⋊C4—442no—
243C22⋊C4—442no—
244C22⋊C4—882no—
245C42—21no—
246C42—21no—
247C11#1189911yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23#6688012yes—
257C23C2×#431411yescharacteristic
258C23C2×Dic4411yescharacteristic
259C23C2×(C2×D11)⋊C411yescharacteristic
260D4—42no—
261D4—42no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—81no—
275C2×C4—442no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4—884no—
282C2×C4—882no—
283C2×C4—882no—
284C2×C4—882no—
285C2×C4#6687011yescharacteristic
286C2×C4#6687011yescharacteristic
287C2×C4#6688012yes—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#6687011yescharacteristic
304C22C2×#6688011yescharacteristic
305C22#1062275211yescharacteristic
306C4—21no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—882no—
312C4—882no—
313C4—1762no—
314C4#1062211412yes—
315C2—21no—
316C2—21no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2#1306718911yescharacteristic
321C2C2×#1062211411yescharacteristic
322C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1460C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1460D11
hypocenterC11#11899
LCSG ▷ C22×C4×C11 ▷ C23×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. #13066641C2semidirect
6. C22×C4⋊Dic11C4semidirect
12. #10622825C4semidirect
13. #10622599C4semidirect
247. C11#11899semidirect

Maximal subgroups

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

subgroupindex
#130729332
#130686042
#130666412
C11×#14602
#1189911