Finite Group Databasebeta

← #14642910

Subgroups — #14642910

Order 2816.

338 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 83 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#13070174C211yesmaximal, characteristic
2#13070092C211yesmaximal, characteristic
3#13070087C211yesmaximal, characteristic
4#13066439C211yesmaximal, characteristic
5#13066439C211yesmaximal, characteristic
6#13066439C211yesmaximal, characteristic
7C11×#2810C211yesmaximal, characteristic
8C11×#400—21no—
9C11×#400—21no—
10C11×#400—21no—
11C11×#389C2211yescharacteristic
12C11×#389C2211yescharacteristic
13C11×#389C2211yescharacteristic
14C11×#387—21no—
15C11×#387—21no—
16C11×#387—21no—
17C2×#66872—21no—
18C2×#66871—21no—
19#10622548C2211yescharacteristic
20#10622167—21no—
21#10622167—21no—
22#10622167—21no—
23#10622167—21no—
24#10622162C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54#66872—42no—
55#66871—42no—
56#7803—111nomaximal, Sylow
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—41no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
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⋊C4—41no—
82C42×C11—41no—
83C42×C11—81no—
84C4⋊Dic11—42no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—22no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98#2810D1111yescharacteristic
99#2099—111no—
100#2084—111no—
101#2083—111no—
102#1271—111no—
103#1271—111no—
104#1271—111no—
105C23×C11#12011yescharacteristic
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—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C11⋊C8—42no—
140C11⋊C8—42no—
141C11⋊C8—81no—
142C2×#107—221no—
143C2×#106—221no—
144#400—21no—
145#400—21no—
146#400—21no—
147#389C2×D1111yescharacteristic
148#389C2×D1111yescharacteristic
149#389C2×D1111yescharacteristic
150#387—21no—
151#387—21no—
152#387—21no—
153#384—111no—
154#340—221no—
155#340—221no—
156#340—221no—
157#340—221no—
158#336—111no—
159#336—111no—
160#336—111no—
161C22×C11#44911yescharacteristic
162C22×C11#44911yescharacteristic
163C22×C11#45211yescharacteristic
164C22×C11#45411yescharacteristic
165C22×C11#45611yescharacteristic
166C22×C11#45611yescharacteristic
167C22×C11#45811yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—81no—
175C4×C11—81no—
176C4×C11—81no—
177C4×C11—81no—
178C4×C11—81no—
179C4×C11—81no—
180Dic11—161no—
181C22×C8—221no—
182C22×C8—221no—
183C22×C8—221no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4C22⋊D1111yescharacteristic
191C2×C4⋊C4C22⋊D1111yescharacteristic
192C2×C4⋊C4C22⋊D1111yescharacteristic
193C2×C4⋊C4C22⋊D1111yescharacteristic
194C2×C4⋊C4C22⋊D1111yescharacteristic
195C2×C4⋊C4C22⋊D1111yescharacteristic
196C2×C42—21no—
197C2×C42C22×D1111yescharacteristic
198#107—442no—
199#106—442no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C11#160911yescharacteristic
211C2×C11#160911yescharacteristic
212C2×C11#161511yescharacteristic
213C2×C11#162811yescharacteristic
214C2×C11#165011yescharacteristic
215C2×C11#165211yescharacteristic
216C2×C11#166311yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—441no—
224C22×C4C2×C22⋊D1111yescharacteristic
225C22×C4C2×C22⋊D1111yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227C2×C8—222no—
228C2×C8—222no—
229C2×C8—441no—
230C2×C8—441no—
231C2×C8—441no—
232C2×C8—441no—
233C2×C8—441no—
234C2×C8—441no—
235C2×C8—441no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—442no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C42—41no—
257C42—81no—
258C11#780311yescharacteristic, complemented, Sylow
259C23#6700611yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—881no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4#6700211yescharacteristic
288C2×C4#6700211yescharacteristic
289C2×C4#6700311yescharacteristic
290C2×C4#6700311yescharacteristic
291C2×C4#6700311yescharacteristic
292C2×C4#6700411yescharacteristic
293C8—442no—
294C8—442no—
295C8—881no—
296C22#1062285111yescharacteristic
297C22#1062285111yescharacteristic
298C22#1062285211yescharacteristic
299C22#1062285611yescharacteristic
300C22#1062285811yescharacteristic
301C22#1062285911yescharacteristic
302C22#1062285911yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—1761no—
316C2#1306761311yescharacteristic
317C2#1306761311yescharacteristic
318C2#1306764711yescharacteristic
319C2#1306772611yescharacteristic
320C2#1306787211yescharacteristic
321C2#1306788611yescharacteristic
322C2#1306794411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2810C2
socle, prime radicalC23×C11#120
hypercenter#2810D11
hypocenterC11#7803
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2810

Complements

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

NH ≅ G/Ntype
258. C11#7803semidirect

Maximal subgroups

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

subgroupindex
#130701742
#130700922
#130700872
#130664392
C11×#28102
#780311