Finite Group Databasebeta

← #14642987

Subgroups — #14642987

Order 2816.

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

normal subgroups only

This group has 374 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#13070173C211yesmaximal, characteristic
3#13070093C211yesmaximal, characteristic
4#13066439C211yesmaximal, characteristic
5#13066438C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#2084C211yesmaximal, characteristic
8C2×#66943—21no—
9C2×C11×#106—21no—
10C11×#389C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622597—21no—
13#10622597—21no—
14#10622594—21no—
15C2×#66872—21no—
16#10622541C2211yescharacteristic
17#10622541C2211yescharacteristic
18#10622274—21no—
19#10622260—21no—
20C11×#340—21no—
21C11×#336C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C8×C11—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48#66943—42no—
49#66943—42no—
50C11×#106—42no—
51C11×#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66872—42no—
58#7815—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C2×C8×C11—22no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4SD1612yes—
82C42×C11—41no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—42no—
89C4⋊Dic11—42no—
90C4⋊Dic11SD1612yes—
91Dic11⋊C4—42no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—81no—
97C4×Dic11—42no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2726—111no—
105#2099—111no—
106#2084—111no—
107#2084D1111yescharacteristic
108#1271—111no—
109#1271—111no—
110#1271—111no—
111C23×C11#12011yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C8×C11—42no—
146C11⋊C8—42no—
147C11⋊C8—81no—
148C2×#125—221no—
149C2×#106—21no—
150C2×#106—221no—
151#398—221no—
152#398—221no—
153#398—221no—
154#389—111no—
155#389—111no—
156#389—221no—
157#389C2×D1111yescharacteristic
158#387—221no—
159#384C2×D1111yescharacteristic
160#340—21no—
161#340—221no—
162#340—221no—
163#340—221no—
164#336—111no—
165#336—111no—
166#336C2×D1111yescharacteristic
167C22×C11#44811yescharacteristic
168C22×C11#44911yescharacteristic
169C22×C11#45011yescharacteristic
170C22×C11#45411yescharacteristic
171C22×C11#45611yescharacteristic
172C22×C11#45611yescharacteristic
173C22×C11#45811yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—42no—
181C4×C11—81no—
182C4×C11—161no—
183Dic11—42no—
184Dic11—81no—
185Dic11—81no—
186Dic11—81no—
187C22×C8—21no—
188C22×C8—221no—
189C22×C8—221no—
190#125—442no—
191#125—442no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4C22⋊D1111yescharacteristic
207C2×C4⋊C4C22⋊D1111yescharacteristic
208C2×C42—221no—
209C2×C42C22×D1111yescharacteristic
210#106—42no—
211#106—442no—
212#95—21no—
213#95—221no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95—221no—
218C2×C11#160911yescharacteristic
219C2×C11#161111yescharacteristic
220C2×C11#161611yescharacteristic
221C2×C11#162611yescharacteristic
222C2×C11#165111yescharacteristic
223C2×C11#165411yescharacteristic
224C2×C11#166311yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4D4×D1111yescharacteristic
233C22×C4D4×D1111yescharacteristic
234C22×C4C2×C22⋊D1111yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—222no—
239C2×C8—441no—
240C2×C8—441no—
241C2×C8—441no—
242C2×C8—441no—
243C2×C8—441no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—112no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—442no—
260C4⋊C4—442no—
261C4⋊C4—442no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—881no—
267C4⋊C4#432412yes—
268C42—41no—
269C42—442no—
270C11#781511yescharacteristic, complemented, Sylow
271C23#6699011yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—222no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4SD16×D1111yescharacteristic
300C2×C4#6696711yescharacteristic
301C2×C4#6696711yescharacteristic
302C2×C4#6696911yescharacteristic
303C2×C4C2×#432411yescharacteristic
304C2×C4#6700411yescharacteristic
305C8—42no—
306C8—442no—
307C8—881no—
308C22#1062265311yescharacteristic
309C22#1062266611yescharacteristic
310C22#1062270811yescharacteristic
311C22#1062278211yescharacteristic
312C22#1062278511yescharacteristic
313C22#1062281411yescharacteristic
314C22#1062281811yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—161no—
324C4—442no—
325C4—881no—
326C4—881no—
327C4—881no—
328C2#1306761211yescharacteristic
329C2#1306762311yescharacteristic
330C2#1306765111yescharacteristic
331C2#1306771111yescharacteristic
332C2#1306787711yescharacteristic
333C2#1306789711yescharacteristic
334C2#1306794311yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2084C2
socle, prime radicalC23×C11#120
hypercenter#2084D11
hypocenterC11#7815
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
270. C11#7815semidirect

Maximal subgroups

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

subgroupindex
#130755672
#130701732
#130700932
#130664392
#130664382
C11×#20842
#781511