Finite Group Databasebeta

← #14666845

Subgroups — #14666845

Order 2816.

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

normal subgroups only

This group has 332 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#13076886C211yesmaximal, characteristic
2#13069958C211yesmaximal, characteristic
3#13067590C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic
5#13066643C211yesmaximal, characteristic
6#13066561C211yesmaximal, characteristic
7C11×#1617C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#484—21no—
10C11×#400C2211yescharacteristic
11#10622663—21no—
12#10622608—21no—
13#10622596—21no—
14#10622592C2211yescharacteristic
15#10622589C2211yescharacteristic
16#10622274—21no—
17#10622271—21no—
18#10622270—21no—
19#10622269—21no—
20#10622264—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×Dic22D411yescharacteristic
28C11×C4⋊Q8—41no—
29C11×#125—41no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×#117—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×#4326—41no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—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
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66874—41no—
60#66872—41no—
61#66871—41no—
62#12259—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×Dic22—41no—
75C2×Dic22—81no—
76C2×C8×C11—41no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C42×C11—41no—
87#4326—82no—
88C4⋊Dic11—41no—
89C4⋊Dic11—81no—
90C4⋊Dic11—81no—
91Dic11⋊C4—81no—
92Dic11⋊C4—81no—
93Dic11⋊C4—81no—
94Dic11⋊C4—81no—
95C4×Dic11—21no—
96C4×Dic11Q1612yescomplemented
97#4318—22no—
98#4318—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101#2843—111no—
102#2060—111no—
103#1617D1111yescharacteristic
104#1605—111no—
105#1354—111no—
106#1353—111no—
107#1325—111no—
108C23×C11#12011yescharacteristic
109Q8×C11—81no—
110Q8×C11—81no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
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—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—
138Dic22—42no—
139Dic22—81no—
140C8×C11—81no—
141C11⋊C8—42no—
142C11⋊C8—81no—
143#544C2×D1111yescharacteristic
144#484—21no—
145#451—221no—
146#428—221no—
147#400—221no—
148#400C2×D1111yescharacteristic
149#398—221no—
150#398—221no—
151#398—221no—
152#395—111no—
153#395—221no—
154#384—111no—
155#383—221no—
156#343—111no—
157#339—221no—
158#328—21no—
159#328—221no—
160#324—111no—
161#324C2×D1111yescharacteristic
162C22×C11—21no—
163C22×C11—21no—
164C22×C11#45111yescharacteristic
165C22×C11#45611yescharacteristic
166C22×C11B(4,𝔽2)11yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—81no—
172C4×C11—81no—
173C4×C11—81no—
174C4×C11—81no—
175Dic11—42no—
176Dic11—81no—
177Dic11—81no—
178Dic11—81no—
179C22×Q8—111no—
180C2×Q16—441no—
181C2×M16—221no—
182C4⋊Q8—41no—
183#125—41no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186#117—21no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4C22⋊D1111yescharacteristic
195C2×C4⋊C4C22×D1111yescharacteristic
196C2×C42—111no—
197#107—41no—
198#107—441no—
199#106—441no—
200#103—41no—
201#103—441no—
202C22⋊C8—21no—
203C22⋊C8—221no—
204#95—21no—
205#95—21no—
206#95—111no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—221no—
212#95—221no—
213#95C22⋊D1111yescharacteristic
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#160511yescharacteristic
217C2×C11#220011yescharacteristic
218C2×C11#220311yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—441no—
222C2×Q8—881no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4D4×D1111yescharacteristic
230C22×C4D4×D1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232Q16—882no—
233M16—222no—
234M16—441no—
235C2×C8—41no—
236C2×C8—441no—
237C2×C8—441no—
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—441no—
247C4⋊C4—881no—
248C4⋊C4—881no—
249C4⋊C4—881no—
250C4⋊C4—881no—
251C4⋊C4—881no—
252C4⋊C4—881no—
253C22⋊C4—41no—
254C42—41no—
255C42—112no—
256C42—221no—
257C11#1225911yescharacteristic, complemented, Sylow
258C23#6699011yescharacteristic
259Q8—81no—
260Q8—81no—
261Q8—442no—
262Q8—881no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
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×C4Q16×D1111yescharacteristic
289C2×C4#6697111yescharacteristic
290C8—81no—
291C8—442no—
292C8—881no—
293C22—21no—
294C22—21no—
295C22#1062264511yescharacteristic
296C22#1062279911yescharacteristic
297C22#1062281811yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—81no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4—442no—
307C4—881no—
308C4—881no—
309C4—881no—
310C2—21no—
311C2—21no—
312C2#1306758811yescharacteristic
313C2#1307062011yescharacteristic
314C2#1307063611yescharacteristic
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#12259
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
96. C4×Dic11Q16semidirect
257. C11#12259semidirect

Maximal subgroups

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

subgroupindex
#130768862
#130699582
#130675902
#130666472
#130666432
#130665612
C11×#16172
#1225911