Finite Group Databasebeta

← #14642952

Subgroups — #14642952

Order 2816.

378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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#13070159C211yesmaximal, characteristic
2#13070087C211yesmaximal, characteristic
3#13070024C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic
5#13066442C211yesmaximal, characteristic
6#13066439C211yesmaximal, characteristic
7C11×#2806C211yesmaximal, characteristic
8C11×#398—21no—
9C11×#398—21no—
10C11×#395—21no—
11C11×#391—21no—
12C11×#391C2211yescharacteristic
13C11×#391C2211yescharacteristic
14C11×#389—21no—
15C11×#389C2211yescharacteristic
16C11×#387—21no—
17C2×#66899—21no—
18C2×#66899—21no—
19C2×#66872—21no—
20C2×#66871—21no—
21#10622548C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622162C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C22×C11⋊C8—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—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#66899—42no—
55#66899—42no—
56#66872—42no—
57#66871—42no—
58#7809—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11Q1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—41no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—81no—
84C11×C4⋊C4—81no—
85C11×C4⋊C4—81no—
86C11×C4⋊C4—81no—
87C11×C4⋊C4SD1612yes—
88C42×C11—41no—
89C42×C11—81no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2806D1111yescharacteristic
106#2096—111no—
107#2083—111no—
108#2072—111no—
109#1272—111no—
110#1272—111no—
111#1271—111no—
112C23×C11#12011yescharacteristic
113Q8×C11—42no—
114Q8×C11—42no—
115Q8×C11—81no—
116Q8×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11C2×SD1611yescharacteristic
142C2×C4×C11C2×Q1611yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C11⋊C8—42no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C2×#107—221no—
154C2×#106—221no—
155C2×#103—221no—
156C2×#103—221no—
157#398—21no—
158#398—21no—
159#395—21no—
160#391—21no—
161#391C2×D1111yescharacteristic
162#391C2×D1111yescharacteristic
163#389—21no—
164#389C2×D1111yescharacteristic
165#387—21no—
166#384—111no—
167#340—221no—
168#340—221no—
169#336—111no—
170#336—111no—
171#336—111no—
172C22×C11#44811yescharacteristic
173C22×C11#44911yescharacteristic
174C22×C11#45111yescharacteristic
175C22×C11#45311yescharacteristic
176C22×C11#45511yescharacteristic
177C22×C11#45611yescharacteristic
178C22×C11#45811yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—42no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11—81no—
191Dic11—161no—
192C22×Q8C22⋊D1111yescharacteristic
193C22×Q8C22⋊D1111yescharacteristic
194C22×C8—221no—
195C22×C8—221no—
196C22×C8—221no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4C22⋊D1111yescharacteristic
206C2×C4⋊C4C22⋊D1111yescharacteristic
207C2×C4⋊C4C22⋊D1111yescharacteristic
208C2×C4⋊C4C22⋊D1111yescharacteristic
209C2×C42—21no—
210C2×C42C22×D1111yescharacteristic
211#107—442no—
212#106—442no—
213#103—442no—
214#103—442no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223C2×C11#161111yescharacteristic
224C2×C11#161211yescharacteristic
225C2×C11#161411yescharacteristic
226C2×C11#162211yescharacteristic
227C2×C11#164511yescharacteristic
228C2×C11#164811yescharacteristic
229C2×C11#166111yescharacteristic
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8#432612yes—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—441no—
245C22×C4C2×C22⋊D1111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248C2×C8—222no—
249C2×C8—222no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C2×C8—441no—
256C2×C8—441no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4#432512yes—
274C42—41no—
275C42—81no—
276C11#780911yescharacteristic, complemented, Sylow
277C23#6700611yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—881no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4C2×#432511yescharacteristic
310C2×C4#6699511yescharacteristic
311C2×C4#6699511yescharacteristic
312C2×C4C2×#432611yescharacteristic
313C2×C4#6700211yescharacteristic
314C2×C4#6700311yescharacteristic
315C8—442no—
316C8—442no—
317C8—881no—
318C22#1062284011yescharacteristic
319C22#1062284111yescharacteristic
320C22#1062285111yescharacteristic
321C22#1062285411yescharacteristic
322C22#1062285511yescharacteristic
323C22#1062285611yescharacteristic
324C22#1062285911yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—42no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—1761no—
338C2#1306762411yescharacteristic
339C2#1306763011yescharacteristic
340C2#1306764111yescharacteristic
341C2#1306768811yescharacteristic
342C2#1306783711yescharacteristic
343C2#1306785811yescharacteristic
344C2#1306793311yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2806C2
socle, prime radicalC23×C11#120
hypercenter#2806D11
hypocenterC11#7809
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2806

Complements

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

NH ≅ G/Ntype
276. C11#7809semidirect

Maximal subgroups

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

subgroupindex
#130701592
#130700872
#130700242
#130664422
#130664392
C11×#28062
#780911