Finite Group Databasebeta

← #14664725

Subgroups — #14664725

Order 2816.

314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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#13079197C211yesmaximal, characteristic
2#13070416C211yesmaximal, characteristic
3#13068745C211yesmaximal, characteristic
4#13066629C211yesmaximal, characteristic
5#13066628C211yesmaximal, characteristic
6#13066627C211yesmaximal, characteristic
7C11×#1348C211yesmaximal, characteristic
8#10623153—21no—
9C11×#467C2211yescharacteristic
10Q16×Dic11C411yescharacteristic, complemented
11#10622794C411yescharacteristic, complemented
12#10622729C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14#10622664—21no—
15#10622590—21no—
16#10622487C411yescharacteristic, complemented
17#10622486C411yescharacteristic, complemented
18#10622405—21no—
19#10622403—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#340C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25#10622140—21no—
26Dic11⋊C16—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×C22⋊Q8—21no—
30C2×C11×C4⋊C4—21no—
31Q8×Dic11—21no—
32#66997—21no—
33C2×#4326—21no—
34C2×C4⋊Dic11—21no—
35#66977—21no—
36C2×C4×Dic11D411yescharacteristic
37C22×C11⋊C8D411yescharacteristic
38C2×Dic44C2×C411yescharacteristic
39#66942—41no—
40#66941—21no—
41#66940—21no—
42#66940—41no—
43#66931—41no—
44#66930—41no—
45C2×C11×C16—21no—
46C11×#107C2×C411yescharacteristic
47C11×#103—21no—
48#66899—21no—
49C11⋊#95—41no—
50C11⋊#95—41no—
51#66882C2×C411yescharacteristic
52#66880—21no—
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66874—21no—
59#66871—21no—
60#11859—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—41no—
65C22×Dic11D811yescharacteristic
66C22×Dic11D811yescharacteristic
67C2×Dic22—21no—
68C2×Dic22—41no—
69C11×Q16—41no—
70C2×C8×C11—41no—
71C2×C8×C11C22×C411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C22⋊Dic11—41no—
79#4326—42no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—41no—
90C4×Dic11—41no—
91C4×Dic11C22⋊C411yescharacteristic
92C4×Dic11C22⋊C411yescharacteristic
93C4×Dic11SD1611yescharacteristic
94C4×Dic11SD1611yescharacteristic
95C2×C11⋊C8—41no—
96C2×C11⋊C8C22⋊C411yescharacteristic
97C2×C11⋊C8C22⋊C411yescharacteristic
98Dic44—41no—
99C11×C16—41no—
100C11⋊C16—41no—
101#3170—111no—
102#2163—111no—
103#1835—111no—
104#1348—111no—
105#1348—111no—
106#1348—111no—
107#1348D1111yescharacteristic
108C23×C11C2×D811yescharacteristic
109Q8×C11—41no—
110Q8×C11—41no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11C2×SD1611yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—41no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—81no—
126C2×Dic11—81no—
127C2×Dic11—81no—
128C2×Dic11#10211yescharacteristic
129C2×Dic11#10211yescharacteristic
130C2×Dic11#10211yescharacteristic
131C2×Dic11#10211yescharacteristic
132Dic22—41no—
133Dic22—41no—
134Dic22—82no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#533—221no—
140#500—111no—
141#494—111no—
142#487—221no—
143#467—111no—
144#467—221no—
145#467C2×D1111yescharacteristic
146C4×Q16—111no—
147C4×Q16—111no—
148C4×Q16—221no—
149C2×C4×C8—111no—
150#382—221no—
151C4⋊C16—221no—
152C22⋊C16—111no—
153C22⋊C16C2×D1111yescharacteristic
154#346—221no—
155#340—111no—
156#340—221no—
157#340C2×D1111yescharacteristic
158C22×C11—21no—
159C22×C11—21no—
160C22×C11C2×#10211yescharacteristic
161C22×C11#51011yescharacteristic
162C22×C11#51011yescharacteristic
163C4×C11—21no—
164C4×C11—81no—
165C4×C11—81no—
166C4×C11—161no—
167C4×C11#41011yescharacteristic
168C4×C11#42111yescharacteristic
169Dic11—21no—
170Dic11—21no—
171Dic11—21no—
172Dic11—21no—
173Dic11—81no—
174Dic11—81no—
175Dic11—161no—
176C2×Q16—111no—
177C2×Q16—221no—
178C2×Q16C4×D1111yescharacteristic
179C22×C8—111no—
180C22×C8C22×D1111yescharacteristic
181C4⋊Q8—221no—
182C4⋊Q8—221no—
183#125—441no—
184C22⋊Q8—21no—
185C22⋊Q8—221no—
186C22⋊Q8—441no—
187C4×Q8—221no—
188C4×Q8—221no—
189C4×Q8—441no—
190#117—441no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—221no—
193C2×C42—111no—
194C2×C16—21no—
195C2×C16—221no—
196#107—111no—
197#107—221no—
198#107C4×D1111yescharacteristic
199#103—21no—
200#103—221no—
201#103—221no—
202#103—221no—
203C4×C8—111no—
204C4×C8—111no—
205C4×C8—111no—
206C4×C8—111no—
207#95—441no—
208#95—441no—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11#151711yescharacteristic
212C2×C11#214111yescharacteristic
213C2×C11#214511yescharacteristic
214C2×Q8—21no—
215C2×Q8—221no—
216C2×Q8—441no—
217C22×C4—41no—
218C22×C4—111no—
219C22×C4—111no—
220C22×C4—441no—
221C22×C4D4×D1111yescharacteristic
222Q16—41no—
223Q16—441no—
224Q16—442no—
225C2×C8—41no—
226C2×C8—111no—
227C2×C8—111no—
228C2×C8—441no—
229C2×C8C2×C4×D1111yescharacteristic
230C2×C8D4×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—221no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C4⋊C4—441no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C22⋊C4—41no—
245C22⋊C4—441no—
246C42—111no—
247C42—111no—
248C42—111no—
249C42—111no—
250C42—441no—
251C42—441no—
252C16—41no—
253C16—441no—
254C11#1185911yescharacteristic, complemented, Sylow
255C23D8×D1111yescharacteristic
256Q8—41no—
257Q8—41no—
258Q8—441no—
259Q8—441no—
260Q8—882no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—111no—
269C2×C4—111no—
270C2×C4—111no—
271C2×C4—111no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—881no—
278C2×C4—881no—
279C2×C4—881no—
280C2×C4C22⋊C4×D1111yescharacteristic
281C2×C4SD16×D1111yescharacteristic
282C8—21no—
283C8—21no—
284C8—221no—
285C8—221no—
286C22—21no—
287C22—21no—
288C22D11×#10211yescharacteristic
289C22#1062252811yescharacteristic
290C22#1062253111yescharacteristic
291C4—21no—
292C4—81no—
293C4—81no—
294C4—161no—
295C4—221no—
296C4—221no—
297C4—221no—
298C4—221no—
299C4—881no—
300C4—881no—
301C4—1761no—
302C4#1062235311yescharacteristic
303C4#1062243411yescharacteristic
304C2—21no—
305C2—21no—
306C2#1306717411yescharacteristic
307C2#1307033411yescharacteristic
308C2#1307035011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1348C2
socleC22×C11C2×#102
prime radicalC23×C11C2×D8
cosocleC22×C8×C11C23
hypercenter#1348D11
hypocenterC11#11859
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
10. Q16×Dic11C4semidirect
11. #10622794C4semidirect
16. #10622487C4semidirect
17. #10622486C4semidirect
254. C11#11859semidirect

Maximal subgroups

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

subgroupindex
#130791972
#130704162
#130687452
#130666292
#130666282
#130666272
C11×#13482
#1185911