Finite Group Databasebeta

← #14666844

Subgroups — #14666844

Order 2816.

332 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 59 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#13076885C211yesmaximal, characteristic
2#13067658C211yesmaximal, characteristic
3#13067590C211yesmaximal, characteristic
4#13066645C211yesmaximal, characteristic
5#13066642C211yesmaximal, characteristic
6#13066562C211yesmaximal, characteristic
7C11×#2060C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#428—21no—
10C11×#384C2211yescharacteristic
11#10622663—21no—
12#10622657—21no—
13#10622599—21no—
14#10622599C2211yescharacteristic
15#10622597—21no—
16#10622597—21no—
17#10622597—21no—
18#10622592—21no—
19#10622592C2211yescharacteristic
20#10622550—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23#10622176—21no—
24#10622176—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×Dic22D411yescharacteristic
28C2×C11×M16—21no—
29C11×C4⋊Q8—41no—
30C11×#125—41no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×#117—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×#4326—41no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C11×#107—41no—
46C11×#106—41no—
47#66899—41no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—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—
76C11×M16—22no—
77C11×M16—41no—
78C2×C8×C11—41no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—81no—
88C11×C4⋊C4—81no—
89C11×C22⋊C4—41no—
90C42×C11—21no—
91C42×C11—41no—
92C42×C11Q1612yescomplemented
93#4326—82no—
94C4⋊Dic11—41no—
95C4⋊Dic11—81no—
96Dic11⋊C4—81no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101#2843—111no—
102#2060D1111yescharacteristic
103#1617—111no—
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—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
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×C11C2×Q1611yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—42no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138Dic22—42no—
139Dic22—81no—
140C8×C11—42no—
141C11⋊C8—81no—
142C11⋊C8—81no—
143#544C2×D1111yescharacteristic
144#484—221no—
145#451—221no—
146#428—21no—
147#400—111no—
148#400—221no—
149#398—221no—
150#398—221no—
151#398—221no—
152#395—111no—
153#395—221no—
154#384C2×D1111yescharacteristic
155#383—221no—
156#343C2×D1111yescharacteristic
157#339—21no—
158#328—221no—
159#328—221no—
160#324—111no—
161#324—111no—
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—42no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—81no—
173C4×C11—81no—
174C4×C11—81no—
175Dic11—81no—
176Dic11—81no—
177Dic11—81no—
178Dic11—81no—
179C22×Q8—111no—
180C2×Q16—441no—
181C2×M16—21no—
182C4⋊Q8—41no—
183#125—41no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186#117—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—111no—
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×C42C22⋊D1111yescharacteristic
197#107—41no—
198#107—441no—
199#106—41no—
200#103—441no—
201#103—441no—
202C22⋊C8—221no—
203C22⋊C8—221no—
204#95—111no—
205#95—111no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—221no—
212#95—221no—
213#95—221no—
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—22no—
234M16—41no—
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—81no—
247C4⋊C4—81no—
248C4⋊C4—441no—
249C4⋊C4—881no—
250C4⋊C4—881no—
251C4⋊C4—881no—
252C4⋊C4—881no—
253C22⋊C4—41no—
254C42—21no—
255C42—41no—
256C42#432612yescomplemented
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—22no—
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—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—442no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4C2×#432611yescharacteristic
289C2×C4#6700411yescharacteristic
290C8—42no—
291C8—881no—
292C8—881no—
293C22—21no—
294C22—21no—
295C22#1062264511yescharacteristic
296C22#1062266311yescharacteristic
297C22#1062270811yescharacteristic
298C4—21no—
299C4—21no—
300C4—42no—
301C4—41no—
302C4—41no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4—881no—
307C4—881no—
308C4—881no—
309C4—881no—
310C2—21no—
311C2—21no—
312C2#1306758911yescharacteristic
313C2#1307062211yescharacteristic
314C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2060C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2060D11
hypocenterC11#12259
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
92. C42×C11Q16semidirect
256. C42#4326semidirect
257. C11#12259semidirect

Maximal subgroups

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

subgroupindex
#130768852
#130676582
#130675902
#130666452
#130666422
#130665622
C11×#20602
#1225911