Finite Group Databasebeta

← #14664222

Subgroups — #14664222

Order 2816.

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

normal subgroups only

This group has 320 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#13068517C211yesmaximal, characteristic
4#13066635C211yesmaximal, characteristic
5#13066634C211yesmaximal, characteristic
6#13066633C211yesmaximal, characteristic
7C11×#1350C211yesmaximal, characteristic
8#10623153—21no—
9C11×#467C2211yescharacteristic
10Q16×Dic11C411yescharacteristic
11#10622794C411yescharacteristic
12C2×#66886—21no—
13M16×Dic11—21no—
14#10622729C2211yescharacteristic
15C2×C8×Dic11C2211yescharacteristic
16#10622664—21no—
17#10622487C411yescharacteristic
18#10622486C411yescharacteristic
19#10622405—21no—
20#10622403—21no—
21C11×C22⋊C16C2211yescharacteristic
22C11×#341C2211yescharacteristic
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#66886—24no—
50#66882C2×C411yescharacteristic
51#66880—21no—
52#66879—41no—
53C8×Dic11—41no—
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11C2×C411yescharacteristic
56C8×Dic11D411yescharacteristic
57C8×Dic11D411yescharacteristic
58C2×C11⋊C16—21no—
59#66874—21no—
60#66871—21no—
61#11752—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11SD1611yescharacteristic
65C22×Dic11SD1611yescharacteristic
66C2×Dic22—21no—
67C2×Dic22—41no—
68C11×Q16—41no—
69C11×M16—22no—
70C11×M16—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11C22×C411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C22⋊Dic11—41no—
79#4326—42no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82Dic11⋊C4—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87C4×Dic11—41no—
88C4×Dic11—41no—
89C4×Dic11C22⋊C411yescharacteristic
90C4×Dic11C22⋊C411yescharacteristic
91C4×Dic11D811yescharacteristic
92C4×Dic11D811yescharacteristic
93#4318—22no—
94#4318—41no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8C22⋊C411yescharacteristic
98C2×C11⋊C8C22⋊C411yescharacteristic
99Dic44—41no—
100C11×C16—41no—
101C11⋊C16—41no—
102#3170—111no—
103#2163—111no—
104C4×#108—111no—
105#1350—111no—
106#1350—111no—
107#1350—111no—
108#1350D1111yescharacteristic
109C23×C11C2×SD1611yescharacteristic
110Q8×C11—41no—
111Q8×C11—41no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11C2×C22⋊C411yescharacteristic
117C2×C4×C11C2×D811yescharacteristic
118C2×Dic11—22no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11#10211yescharacteristic
123C2×Dic11#10211yescharacteristic
124C2×Dic11#10211yescharacteristic
125C2×Dic11#10211yescharacteristic
126Dic22—41no—
127Dic22—41no—
128Dic22—82no—
129C8×C11—21no—
130C8×C11—21no—
131C8×C11—42no—
132C11⋊C8—21no—
133C11⋊C8—42no—
134C11⋊C8#10412yes—
135#533—221no—
136#500—111no—
137#494—111no—
138#487—221no—
139#467—111no—
140#467—221no—
141#467C2×D1111yescharacteristic
142C4×Q16—111no—
143C4×Q16—111no—
144C4×Q16—221no—
145C2×#108—221no—
146C4×M16—221no—
147C2×C4×C8—111no—
148C4⋊C16—221no—
149C22⋊C16—111no—
150C22⋊C16C2×D1111yescharacteristic
151#346—221no—
152#341—111no—
153#341C2×D1111yescharacteristic
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11C2×#10211yescharacteristic
158C4×C11—21no—
159C4×C11—81no—
160C4×C11—81no—
161C4×C11#41011yescharacteristic
162C4×C11C2×#10411yescharacteristic
163Dic11—21no—
164Dic11—21no—
165Dic11—21no—
166Dic11—81no—
167Dic11—81no—
168Dic11#36212yes—
169C2×Q16—111no—
170C2×Q16—221no—
171C2×Q16C4×D1111yescharacteristic
172C2×M16—21no—
173C2×M16—221no—
174C22×C8—111no—
175C22×C8C22×D1111yescharacteristic
176C4⋊Q8—221no—
177C4⋊Q8—221no—
178#125—441no—
179C22⋊Q8—21no—
180C22⋊Q8—221no—
181C22⋊Q8—441no—
182C4×Q8—221no—
183C4×Q8—221no—
184C4×Q8—441no—
185#117—441no—
186C2×C42—111no—
187C2×C16—21no—
188C2×C16—221no—
189#108—224no—
190#107—111no—
191#107—221no—
192#107C4×D1111yescharacteristic
193#103—21no—
194#103—221no—
195#103—221no—
196#103—221no—
197#97—441no—
198C4×C8—111no—
199C4×C8—111no—
200C4×C8—111no—
201C4×C8—111no—
202C4×C8—441no—
203C2×C11—41no—
204C2×C11#150211yescharacteristic
205C2×C11#214311yescharacteristic
206C2×C11C2×#36211yescharacteristic
207C2×Q8—21no—
208C2×Q8—221no—
209C2×Q8—441no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4D4×D1111yescharacteristic
213Q16—41no—
214Q16—441no—
215Q16—442no—
216M16—22no—
217M16—41no—
218M16—222no—
219M16—441no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—111no—
223C2×C8—111no—
224C2×C8—222no—
225C2×C8—441no—
226C2×C8C2×C4×D1111yescharacteristic
227C2×C8D4×D1111yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—221no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C22⋊C4—41no—
238C22⋊C4—441no—
239C42—111no—
240C42—111no—
241C42—111no—
242C42—111no—
243C42—441no—
244C42—441no—
245C16—41no—
246C16—441no—
247C11#1175211yescharacteristic, complemented, Sylow
248C23SD16×D1111yescharacteristic
249Q8—41no—
250Q8—41no—
251Q8—441no—
252Q8—441no—
253Q8—882no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—111no—
259C2×C4—111no—
260C2×C4—111no—
261C2×C4—111no—
262C2×C4—222no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4C22⋊C4×D1111yescharacteristic
267C2×C4D8×D1111yescharacteristic
268C8—21no—
269C8—21no—
270C8—42no—
271C8—112no—
272C8—221no—
273C8—442no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22D11×#10211yescharacteristic
278C4—21no—
279C4—81no—
280C4—81no—
281C4—112no—
282C4—221no—
283C4—221no—
284C4—221no—
285C4—881no—
286C4—881no—
287C4#1062235311yescharacteristic
288C4D11×#10411yescharacteristic
289C2—41no—
290C2#1306710911yescharacteristic
291C2#1307034211yescharacteristic
292C2D11×#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#11752
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
247. C11#11752semidirect

Maximal subgroups

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

subgroupindex
#130791972
#130704162
#130685172
#130666352
#130666342
#130666332
C11×#13502
#1175211