Finite Group Databasebeta

← #14666831

Subgroups — #14666831

Order 2816.

342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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#13073854C211yesmaximal, characteristic
2#13069958C211yesmaximal, characteristic
3#13067658C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic
5#13066643C211yesmaximal, characteristic
6#13066561C211yesmaximal, characteristic
7C11×#1617C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#484—21no—
10C11×#400C2211yescharacteristic
11#10622657—21no—
12#10622608—21no—
13#10622599C2211yescharacteristic
14#10622589C2211yescharacteristic
15#10622585—21no—
16#10622273—21no—
17#10622263—21no—
18#10622263—21no—
19#10622262—21no—
20#10622260—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C11×C4⋊Q8—41no—
28C11×#125—41no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—21no—
31C11×#117—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C4⋊Dic11D411yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11—21no—
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45C11×#107—41no—
46C11×#103—41no—
47C11×C22⋊C8—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95D411yescharacteristic
51#66899—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66872—41no—
60#66871—41no—
61#66871—41no—
62#12257—111nomaximal, Sylow
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×C8×C11—41no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—81no—
92C4×Dic11—21no—
93C4×Dic11—42no—
94C4×Dic11—42no—
95C4×Dic11Q1612yes—
96#4318—22no—
97#4318—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100#2571—111no—
101#2060—111no—
102#1617—111no—
103#1617D1111yescharacteristic
104#1353—111no—
105#1353—111no—
106#1325—111no—
107C23×C11#12011yescharacteristic
108Q8×C11—81no—
109Q8×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
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×C11C2×Q1611yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
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—
138C8×C11—81no—
139C11⋊C8—42no—
140C11⋊C8—81no—
141#544C2×D1111yescharacteristic
142#484—21no—
143#484—221no—
144#428—221no—
145#400—111no—
146#400—221no—
147#400C2×D1111yescharacteristic
148#389—221no—
149#389—221no—
150#384—111no—
151#382—221no—
152#382—221no—
153C4×C4⋊C4—221no—
154#343—111no—
155#339—221no—
156#328—21no—
157#328—221no—
158#324—111no—
159#324C2×D1111yescharacteristic
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#45111yescharacteristic
163C22×C11#45611yescharacteristic
164C22×C11B(4,𝔽2)11yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—81no—
170C4×C11—81no—
171C4×C11—81no—
172C4×C11—81no—
173Dic11—24no—
174Dic11—81no—
175Dic11—81no—
176Dic11—81no—
177C2×M16—221no—
178C4⋊Q8—41no—
179#125—41no—
180C22⋊Q8—21no—
181C22⋊Q8—21no—
182#117—21no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4C22⋊D1111yescharacteristic
191C2×C4⋊C4C22×D1111yescharacteristic
192C2×C42—111no—
193C2×C42—221no—
194C2×C42—221no—
195#107—41no—
196#107—441no—
197#107—441no—
198#106—441no—
199#103—41no—
200#103—441no—
201C22⋊C8—21no—
202C22⋊C8—221no—
203#95—21no—
204#95—21no—
205#95—111no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95C22⋊D1111yescharacteristic
212C2×C11—21no—
213C2×C11—21no—
214C2×C11#160511yescharacteristic
215C2×C11#219811yescharacteristic
216C2×C11#220411yescharacteristic
217C2×Q8—21no—
218C2×Q8—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—221no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4D4×D1111yescharacteristic
226C22×C4D4×D1111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—222no—
229M16—441no—
230C2×C8—41no—
231C2×C8—441no—
232C2×C8—441no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4—442no—
244C4⋊C4—442no—
245C4⋊C4—442no—
246C4⋊C4—442no—
247C4⋊C4—881no—
248C22⋊C4—41no—
249C42—41no—
250C42—112no—
251C42—221no—
252C42—442no—
253C42—442no—
254C11#1225711yescharacteristic, complemented, Sylow
255C23#6699011yescharacteristic
256Q8—81no—
257Q8—81no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4Q16×D1111yescharacteristic
285C2×C4#6697111yescharacteristic
286C8—81no—
287C8—442no—
288C8—881no—
289C22—21no—
290C22—21no—
291C22#1062264511yescharacteristic
292C22#1062279911yescharacteristic
293C22#1062281811yescharacteristic
294C4—21no—
295C4—21no—
296C4—41no—
297C4—41no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—224no—
303C4—881no—
304C4—881no—
305C4—881no—
306C2—21no—
307C2—21no—
308C2#1306758811yescharacteristic
309C2#1307061011yescharacteristic
310C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1617C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1617D11
hypocenterC11#12257
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1617

Complements

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

NH ≅ G/Ntype
254. C11#12257semidirect

Maximal subgroups

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

subgroupindex
#130738542
#130699582
#130676582
#130666442
#130666432
#130665612
C11×#16172
#1225711