Finite Group Databasebeta

← #14663302

Subgroups — #14663302

Order 2816.

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

normal subgroups only

This group has 380 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#13072899C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066563C212yesmaximal
4#13066545C212yesmaximal
5C11×#1458C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C22×Dic11⋊C4C411yescharacteristic
8C11×#431—21no—
9#10622824C411yescharacteristic
10#10622595—21no—
11#10622593—21no—
12#10622559C411yescharacteristic
13#10622559C2211yescharacteristic
14#10622556C411yescharacteristic
15#10622556C2211yescharacteristic
16#10622546—21no—
17#10622546—21no—
18#10622539—21no—
19C11×#324—21no—
20C11×#323C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×Dic11C2×C411yescharacteristic
25C23×Dic11C2×C411yescharacteristic
26C11×#117—41no—
27C11×#117—41no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11C2×C411yescharacteristic
35C2×C22⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—41no—
41C2×Dic11⋊C4—41no—
42C11×C4⋊C8—41no—
43C11×C22⋊C8—22no—
44C4×C8×C11—41no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55#66867—41no—
56#11544—111nomaximal, Sylow
57C24×C11C22×C411yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—22no—
73C22×Dic11—41no—
74C22×Dic11—41no—
75C22×Dic11—41no—
76C22×Dic11—42no—
77C2×C8×C11—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C22⋊Dic11—22no—
87C22⋊Dic11—41no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C2×C11⋊C8—42no—
94#2484—111no—
95#1464—111no—
96#1458D1111yescharacteristic
97#1326—112no—
98#1317—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11C2×C22⋊C411yescharacteristic
104C23×C11#13112yes—
105C2×C4×C11—21no—
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—42no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11#9911yescharacteristic
121C2×C4×C11#9911yescharacteristic
122C2×Dic11—22no—
123C2×Dic11—41no—
124C2×Dic11—42no—
125C2×Dic11—41no—
126C2×Dic11—42no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—82no—
137C8×C11—82no—
138C11⋊C8—82no—
139C2×#117C2×D1111yescharacteristic
140C22×C4⋊C4—111no—
141#432—221no—
142#431—21no—
143#400—221no—
144#398—221no—
145#387—221no—
146#387—221no—
147#385—111no—
148#385—111no—
149#381—111no—
150#381—111no—
151#381—111no—
152#324—21no—
153#324—221no—
154#323—112no—
155#323C2×D1112yes—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—22no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11#40811yescharacteristic
164C22×C11C2×#9911yescharacteristic
165C22×C11#41311yescharacteristic
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173Dic11—42no—
174Dic11—81no—
175Dic11—81no—
176Dic11—81no—
177C23×C4—111no—
178C23×C4—111no—
179C23×C4C4×D1111yescharacteristic
180#117—41no—
181#117—41no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—441no—
187C2×C4⋊C4—441no—
188C2×C4⋊C4D4411yescharacteristic
189C2×C4⋊C4C22⋊D1111yescharacteristic
190C2×C22⋊C4—111no—
191C2×C22⋊C4—111no—
192C2×C22⋊C4C4×D1111yescharacteristic
193C2×C22⋊C4C22×D1111yescharacteristic
194C2×C42D4411yescharacteristic
195C2×C42C22⋊D1111yescharacteristic
196C4⋊C8—41no—
197C4⋊C8—441no—
198C22⋊C8—22no—
199C22⋊C8—222no—
200#97—441no—
201C4×C8—41no—
202#95—221no—
203#95—221no—
204#95—221no—
205#95—221no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—42no—
213C2×C11#146811yescharacteristic
214C2×C11#212011yescharacteristic
215C2×C11#212311yescharacteristic
216C24C2×C4×D1111yescharacteristic
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—221no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4—222no—
226C22×C4—442no—
227C22×C4—441no—
228C22×C4—441no—
229C22×C4—441no—
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4C2×D4411yescharacteristic
235C22×C4C2×C22⋊D1111yescharacteristic
236C2×C8—42no—
237C2×C8—442no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—442no—
241C4⋊C4—442no—
242C4⋊C4—442no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—222no—
248C22⋊C4—441no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C11#1154411yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23#6695412yes—
259C23C2×(C2×D11)⋊C411yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—222no—
276C2×C4—441no—
277C2×C4—442no—
278C2×C4—441no—
279C2×C4—442no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—882no—
290C2×C4#6687011yescharacteristic
291C2×C4#6687011yescharacteristic
292C8—82no—
293C8—882no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22C2×#6687011yescharacteristic
302C22#1062272311yescharacteristic
303C22#1062274511yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—442no—
312C4—881no—
313C4—881no—
314C4—881no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1306696211yescharacteristic
319C2#1307025511yescharacteristic
320C2#1307027111yescharacteristic
subgroupG/H
centerC22C2×#66870
commutator, prime radicalC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1458C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#1458D11
hypocenterC11#11544
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
253. C11#11544semidirect

Maximal subgroups

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

subgroupindex
#130728992
#130669502
#130665632
#130665452
C11×#14582
#1154411