Finite Group Databasebeta

← #14664448

Subgroups — #14664448

Order 2816.

502 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074366C211yesmaximal, characteristic
2#13068693C211yesmaximal, characteristic, complemented
3#13066614C214yesmaximal, complemented
4C11×#1464C211yesmaximal, characteristic, complemented
5C2×C11×#117C2211yescharacteristic
6C2×#66983—21no—
7C2×#66927C411yescharacteristic, complemented
8C11×#432—21no—
9#10622824—21no—
10#10622604—21no—
11#10622604C412yescomplemented
12#10622573—21no—
13#10622573C2212yes—
14#10622552—21no—
15#10622549C411yescharacteristic, complemented
16C11×#324—21no—
17C11×#323C2212yes—
18#10622164—21no—
19#10622164C2212yes—
20C23×C4×C11D411yescharacteristic
21C22×C22⋊D11—22no—
22C22×D44—21no—
23C22×D44—21no—
24C22×D44C2×C412yes—
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C11×C22⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—22no—
34#66983—44no—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×C4⋊Dic11—21no—
39#66927—41no—
40#66927—41no—
41C11×C4⋊C8—41no—
42C11×C22⋊C8—22no—
43C11×#97—41no—
44C11⋊#95—21no—
45C11⋊#95—41no—
46C11⋊#95—41no—
47C11⋊#95C2×C412yes—
48#11800—111nomaximal, Sylow
49C24×C11C2×D411yescharacteristic
50C23×D11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—41no—
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C2×C22⋊D11—44no—
62C2×C22⋊D11—82no—
63C2×C22⋊D11—82no—
64C22×Dic11—22no—
65C22×Dic11—42no—
66C2×D44—42no—
67C2×D44—42no—
68C2×D44—42no—
69C2×D44—42no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—82no—
73C2×D44—82no—
74C2×C8×C11—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—41no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C22⋊Dic11—42no—
84C22⋊Dic11—42no—
85(C2×D11)⋊C4—44no—
86(C2×D11)⋊C4—82no—
87(C2×D11)⋊C4—82no—
88C4⋊Dic11—42no—
89#2619—111no—
90#1820—111no—
91#1464D1111yescharacteristic, complemented
92#1343—114no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11C2×C22⋊C411yescharacteristic
98C23×C11AGL(1,ℤ/8)12yes—
99C22×D11—42no—
100C22×D11—42no—
101C22×D11—42no—
102C22×D11—42no—
103C22×D11—42no—
104C22×D11—42no—
105C22×D11—42no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
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—21no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11#9911yescharacteristic
122C2×C4×C11#9911yescharacteristic
123C22⋊D11—88no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—82no—
128C2×Dic11—82no—
129C2×Dic11—82no—
130D44—82no—
131D44—82no—
132D44—84no—
133D44—84no—
134C8×C11—82no—
135C2×#127—111no—
136C2×#121—221no—
137C2×#117C2×D1111yescharacteristic
138#432—21no—
139#394—112no—
140#394—221no—
141#392—112no—
142#392—221no—
143#390—221no—
144#382—111no—
145#381—221no—
146#342—112no—
147#342—221no—
148#324—21no—
149#323C2×D1112yes—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—22no—
153C22×C11—42no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—81no—
157C22×C11C2×#9911yescharacteristic
158C22×C11#41811yescharacteristic
159C22×C11#42111yescharacteristic
160C2×D11—82no—
161C2×D11—82no—
162C2×D11—82no—
163C2×D11—82no—
164C2×D11—82no—
165C2×D11—82no—
166C2×D11—82no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174Dic11—82no—
175Dic11—162no—
176C22×D4—112no—
177C22×D4—222no—
178C22×D4—221no—
179C22×D4—221no—
180C23×C4D4411yescharacteristic
181#127—441no—
182#127—441no—
183#121—444no—
184#117—41no—
185#117—41no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4C4×D1111yescharacteristic
188C2×C4⋊C4C22⋊D1111yescharacteristic
189C2×C22⋊C4—222no—
190C2×C22⋊C4—222no—
191C2×C22⋊C4—222no—
192C2×C22⋊C4—222no—
193C2×C22⋊C4D4411yescharacteristic
194C2×C22⋊C4C22×D1111yescharacteristic
195C2×C42C4×D1111yescharacteristic
196C2×C42C22⋊D1111yescharacteristic
197C4⋊C8—41no—
198C22⋊C8—22no—
199#97—41no—
200#95—112no—
201#95—221no—
202#95—441no—
203#95—441no—
204C2×C11—21no—
205C2×C11—21no—
206C2×C11—42no—
207C2×C11#151011yescharacteristic
208C2×C11#212211yescharacteristic
209C2×C11#212811yescharacteristic
210D11—162no—
211C24—222no—
212C24C2×D4411yescharacteristic
213C2×D4—442no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—444no—
218C2×D4—441no—
219C2×D4—441no—
220C2×D4—882no—
221C2×D4—882no—
222C2×D4—882no—
223C2×D4—882no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—222no—
229C22×C4—442no—
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4C2×C4×D1111yescharacteristic
235C22×C4C2×C22⋊D1111yescharacteristic
236C2×C8—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—442no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—444no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C22⋊C4—882no—
246C22⋊C4—882no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C11#1180011yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—442no—
257C23—442no—
258C23—442no—
259C23—442no—
260C23—442no—
261C23—442no—
262C23—442no—
263C23#6696112yes—
264C23C2×(C2×D11)⋊C411yescharacteristic
265D4—882no—
266D4—882no—
267D4—884no—
268D4—884no—
269D4—888no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—882no—
289C2×C4—882no—
290C2×C4—882no—
291C2×C4#6687011yescharacteristic
292C2×C4#6687011yescharacteristic
293C8—82no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—81no—
301C22—882no—
302C22—882no—
303C22—882no—
304C22—882no—
305C22—882no—
306C22—882no—
307C22—882no—
308C22C2×#6687011yescharacteristic
309C22#1062274411yescharacteristic
310C22#1062275211yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—882no—
319C4—1762no—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—1762no—
324C2#1306714611yescharacteristic
325C2#1307026711yescharacteristic
326C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radical#13074366C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1464D11
hypocenterC11#11800
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13068693C2semidirect
3. #13066614C2semidirect
4. C11×#1464C2semidirect
7. C2×#66927C4semidirect
11. #10622604C4semidirect
15. #10622549C4semidirect
91. #1464D11semidirect
251. C11#11800semidirect

Maximal subgroups

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

subgroupindex
#130743662
#130686932
#130666142
C11×#14642
#1180011