Finite Group Databasebeta

← #14643063

Subgroups — #14643063

Order 2816.

358 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 85 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#13075567C211yesmaximal, characteristic
2#13070180C211yesmaximal, characteristic
3#13070180C211yesmaximal, characteristic
4#13070179C211yesmaximal, characteristic
5#13066440C211yesmaximal, characteristic
6#13066440C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×#66943—21no—
9C11×#389C2211yescharacteristic
10#10622597—21no—
11#10622597—21no—
12#10622594—21no—
13#10622548C2211yescharacteristic
14#10622541C2211yescharacteristic
15#10622541C2211yescharacteristic
16#10622274—21no—
17#10622260—21no—
18C11×#336C2211yescharacteristic
19C11×#336C2211yescharacteristic
20#10622189—21no—
21#10622189—21no—
22#10622189—21no—
23#10622189—21no—
24#10622167—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C22×C11⋊C8—21no—
48#66943—42no—
49#66943—42no—
50C11×#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#7827—111nomaximal, Sylow
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—41no—
67C2×C8×C11—41no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4Q1612yes—
78C42×C11—41no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84C4⋊Dic11—42no—
85C4⋊Dic11—42no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11—42no—
89C4⋊Dic11SD1612yes—
90Dic11⋊C4—42no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—81no—
96C4×Dic11—42no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100#2726—111no—
101#2100—111no—
102#2100—111no—
103#2100—111no—
104#1271—111no—
105#1271—111no—
106#1271D1111yescharacteristic
107C23×C11#12011yescharacteristic
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—22no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11C2×Q1611yescharacteristic
122C2×C4×C11#13511yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—22no—
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—41no—
137C2×Dic11—41no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141C8×C11—81no—
142C8×C11—81no—
143C11⋊C8—81no—
144C2×#125—221no—
145#398—221no—
146#398—221no—
147#398—221no—
148#389—111no—
149#389—111no—
150#389—221no—
151#389C2×D1111yescharacteristic
152#387—221no—
153#384—111no—
154#340—221no—
155#340—221no—
156#340—221no—
157#340—221no—
158#340—221no—
159#340—221no—
160#336—111no—
161#336C2×D1111yescharacteristic
162#336C2×D1111yescharacteristic
163C22×C11#45011yescharacteristic
164C22×C11#45111yescharacteristic
165C22×C11#45211yescharacteristic
166C22×C11#45411yescharacteristic
167C22×C11#45411yescharacteristic
168C22×C11#45411yescharacteristic
169C22×C11#45811yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—81no—
178Dic11—42no—
179Dic11—81no—
180Dic11—81no—
181Dic11—81no—
182Dic11—161no—
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—221no—
186#125—442no—
187#125—442no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4D4411yescharacteristic
203C2×C4⋊C4D4411yescharacteristic
204C2×C42—221no—
205C2×C42C22×D1111yescharacteristic
206#95—21no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—221no—
212C2×C11#161511yescharacteristic
213C2×C11#161611yescharacteristic
214C2×C11#161711yescharacteristic
215C2×C11#163511yescharacteristic
216C2×C11#163611yescharacteristic
217C2×C11#163711yescharacteristic
218C2×C11#165811yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—221no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4—441no—
226C22×C4C2×D4411yescharacteristic
227C22×C4D4×D1111yescharacteristic
228C22×C4D4×D1111yescharacteristic
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—441no—
236C2×C8—441no—
237C2×C8—441no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—112no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—442no—
249C4⋊C4—442no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—442no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—881no—
259C4⋊C4Dic4412yes—
260C42—41no—
261C42—442no—
262C11#782711yescharacteristic, complemented, Sylow
263C23#6693511yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—222no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
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—881no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4C2×Dic4411yescharacteristic
292C2×C4#6696211yescharacteristic
293C2×C4#6696411yescharacteristic
294C2×C4SD16×D1111yescharacteristic
295C2×C4#6696911yescharacteristic
296C2×C4#6697111yescharacteristic
297C8—81no—
298C8—81no—
299C8—881no—
300C22#1062235211yescharacteristic
301C22#1062235511yescharacteristic
302C22#1062236611yescharacteristic
303C22#1062238911yescharacteristic
304C22#1062242311yescharacteristic
305C22#1062244011yescharacteristic
306C22#1062244011yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—442no—
316C4—881no—
317C4—881no—
318C4—881no—
319C4—1761no—
320C2#1306765011yescharacteristic
321C2#1306765411yescharacteristic
322C2#1306766011yescharacteristic
323C2#1306776811yescharacteristic
324C2#1306777711yescharacteristic
325C2#1306778411yescharacteristic
326C2#1306791911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socle, prime radicalC23×C11#120
hypercenter#1271D11
hypocenterC11#7827
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
262. C11#7827semidirect

Maximal subgroups

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

subgroupindex
#130755672
#130701802
#130701792
#130664402
C11×#12712
#782711