Finite Group Databasebeta

← #14664751

Subgroups — #14664751

Order 2816.

300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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#13068752C211yesmaximal, characteristic
4#13066635C211yesmaximal, characteristic
5#13066634C211yesmaximal, characteristic
6#13066633C211yesmaximal, characteristic
7C11×#1350C211yesmaximal, characteristic
8#10623153—21no—
9C11×#467C2211yescharacteristic
10Q16×Dic11C411yescharacteristic
11#10622794C411yescharacteristic
12#10622731—21no—
13#10622729C2211yescharacteristic
14C2×C8×Dic11C2211yescharacteristic
15#10622664—21no—
16#10622487C411yescharacteristic
17#10622486C411yescharacteristic
18#10622405—21no—
19#10622403—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#341C2211yescharacteristic
22#10622196—21no—
23#10622190C2211yescharacteristic
24C22⋊(C11⋊C16)C2211yescharacteristic
25#10622140—21no—
26Dic11⋊C16—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C2×C11×M16—21no—
29C22×C8×C11C2311yescharacteristic
30C11×C22⋊Q8—21no—
31Q8×Dic11—21no—
32#66997—21no—
33C2×#4326—21no—
34#66977—21no—
35C2×C4×Dic11D411yescharacteristic
36C2×#4318—21no—
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—
49#66882C2×C411yescharacteristic
50#66880—21no—
51Dic11⋊C8—41no—
52Dic11⋊C8—41no—
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66874—21no—
59#66871—21no—
60#11865—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11SD1611yescharacteristic
64C22×Dic11SD1611yescharacteristic
65C2×Dic22—21no—
66C2×Dic22—41no—
67C11×Q16—41no—
68C11×M16—41no—
69C11×M16—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C22⋊C4—41no—
77C22⋊Dic11—41no—
78#4326—42no—
79C4⋊Dic11—21no—
80C4⋊Dic11—41no—
81Dic11⋊C4—41no—
82Dic11⋊C4—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86C4×Dic11—41no—
87C4×Dic11—41no—
88C4×Dic11C22⋊C411yescharacteristic
89C4×Dic11C22⋊C411yescharacteristic
90C4×Dic11D811yescharacteristic
91C4×Dic11D811yescharacteristic
92#4318—41no—
93#4318—41no—
94C2×C11⋊C8—41no—
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#1837—111no—
104#1350—111no—
105#1350—111no—
106#1350—111no—
107#1350D1111yescharacteristic
108C23×C11C2×SD1611yescharacteristic
109Q8×C11—41no—
110Q8×C11—41no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11C2×D811yescharacteristic
117C2×Dic11—22no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11#10211yescharacteristic
122C2×Dic11#10211yescharacteristic
123C2×Dic11#10211yescharacteristic
124C2×Dic11#10211yescharacteristic
125Dic22—41no—
126Dic22—41no—
127Dic22—82no—
128C8×C11—21no—
129C8×C11—21no—
130C8×C11—81no—
131C11⋊C8—21no—
132C11⋊C8—21no—
133C11⋊C8—81no—
134#533—221no—
135#500—111no—
136#494—111no—
137#487—221no—
138#467—111no—
139#467—221no—
140#467C2×D1111yescharacteristic
141C4×Q16—111no—
142C4×Q16—111no—
143C4×Q16—221no—
144#423—221no—
145C2×C4×C8—111no—
146C4⋊C16—221no—
147C22⋊C16—111no—
148C22⋊C16C2×D1111yescharacteristic
149#346—221no—
150#341—111no—
151#341—221no—
152#341C2×D1111yescharacteristic
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11C2×#10211yescharacteristic
157C4×C11—21no—
158C4×C11—81no—
159C4×C11—81no—
160C4×C11#41011yescharacteristic
161C4×C11#42111yescharacteristic
162Dic11—21no—
163Dic11—21no—
164Dic11—21no—
165Dic11—81no—
166Dic11—81no—
167Dic11#36212yes—
168C2×Q16—111no—
169C2×Q16—221no—
170C2×Q16C4×D1111yescharacteristic
171C2×M16—21no—
172C2×M16—221no—
173C22×C8—111no—
174C22×C8C22×D1111yescharacteristic
175C4⋊Q8—221no—
176C4⋊Q8—221no—
177#125—441no—
178C22⋊Q8—21no—
179C22⋊Q8—221no—
180C22⋊Q8—441no—
181C4×Q8—221no—
182C4×Q8—221no—
183C4×Q8—441no—
184#117—441no—
185C2×C42—111no—
186C2×C16—21no—
187C2×C16—221no—
188#107—111no—
189#107—221no—
190#107C4×D1111yescharacteristic
191C4⋊C8—441no—
192C4⋊C8—441no—
193#103—21no—
194#103—221no—
195#103—221no—
196#103—221no—
197C4×C8—111no—
198C4×C8—111no—
199C4×C8—111no—
200C4×C8—111no—
201C2×C11—41no—
202C2×C11#151711yescharacteristic
203C2×C11#214311yescharacteristic
204C2×C11C2×#36211yescharacteristic
205C2×Q8—21no—
206C2×Q8—221no—
207C2×Q8—441no—
208C22×C4—111no—
209C22×C4—111no—
210C22×C4D4×D1111yescharacteristic
211Q16—41no—
212Q16—441no—
213Q16—442no—
214M16—41no—
215M16—41no—
216M16—441no—
217M16—441no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—111no—
221C2×C8—111no—
222C2×C8—441no—
223C2×C8—441no—
224C2×C8C2×C4×D1111yescharacteristic
225C2×C8D4×D1111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—41no—
228C4⋊C4—221no—
229C4⋊C4—441no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C22⋊C4—41no—
236C22⋊C4—441no—
237C42—111no—
238C42—111no—
239C42—111no—
240C42—111no—
241C42—441no—
242C42—441no—
243C16—41no—
244C16—441no—
245C11#1186511yescharacteristic, complemented, Sylow
246C23SD16×D1111yescharacteristic
247Q8—41no—
248Q8—41no—
249Q8—441no—
250Q8—441no—
251Q8—882no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—111no—
257C2×C4—111no—
258C2×C4—111no—
259C2×C4—111no—
260C2×C4—222no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4C22⋊C4×D1111yescharacteristic
265C2×C4D8×D1111yescharacteristic
266C8—21no—
267C8—21no—
268C8—81no—
269C8—221no—
270C8—221no—
271C8—881no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22D11×#10211yescharacteristic
276C4—21no—
277C4—81no—
278C4—81no—
279C4—112no—
280C4—221no—
281C4—221no—
282C4—221no—
283C4—881no—
284C4—881no—
285C4#1062235311yescharacteristic
286C4#1062243411yescharacteristic
287C2—41no—
288C2#1306717411yescharacteristic
289C2#1307034211yescharacteristic
290C2D11×#36211yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1350C2
socleC22×C11C2×#102
prime radicalC23×C11C2×SD16
cosocleC22×C8×C11C23
hypercenter#1350D11
hypocenterC11#11865
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
245. C11#11865semidirect

Maximal subgroups

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

subgroupindex
#130791972
#130704162
#130687522
#130666352
#130666342
#130666332
C11×#13502
#1186511