Finite Group Databasebeta

← #14641978

Subgroups — #14641978

Order 2816.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×#66922C211yesmaximal, characteristic
2#13068759C211yesmaximal, characteristic
3#13066438C214yesmaximal
4C11×#1767C211yesmaximal, characteristic
5C2×#66922C411yescharacteristic
6C2×C4×Dic22—21no—
7C2×C11×C4⋊C8—21no—
8C2×C11×#97—21no—
9C43×C11C2211yescharacteristic
10#10622548C411yescharacteristic
11C4×C4⋊Dic11—21no—
12C4×C4⋊Dic11C412yes—
13#10622542—21no—
14#10622541—21no—
15#10622541C2212yes—
16C11×#336C2212yes—
17#10622162—21no—
18#10622162—21no—
19#10622162C2212yes—
20C22×Dic22—21no—
21C22×C8×C11—22no—
22C2×C42×C11C2×C411yescharacteristic
23C2×C42×C11C2×C411yescharacteristic
24C2×C42×C11D411yescharacteristic
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11C2×C412yes—
33C2×C4⋊Dic11C2×C412yes—
34C2×Dic11⋊C4—22no—
35C2×C4×Dic11—22no—
36C22×C11⋊C8—22no—
37#66922—24no—
38C4×Dic22—44no—
39C11×C4⋊C8—24no—
40C11×#97—42no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43#7622—111nomaximal, Sylow
44C22×C4×C11C22⋊C411yescharacteristic
45C22×C4×C11C22⋊C411yescharacteristic
46C22×C4×C11C22⋊C411yescharacteristic
47C22×C4×C11C22⋊C411yescharacteristic
48C22×C4×C11C22×C411yescharacteristic
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—22no—
52C22×Dic11—22no—
53C2×Dic22—24no—
54C2×Dic22—42no—
55C2×Dic22—42no—
56C2×C8×C11—24no—
57C2×C8×C11—42no—
58C2×C8×C11—42no—
59C42×C11—22no—
60C42×C11—22no—
61C42×C11—22no—
62C42×C11—22no—
63C42×C11—41no—
64C42×C11—41no—
65C42×C11SD1612yes—
66C42×C11Q1612yes—
67C4⋊Dic11—24no—
68C4⋊Dic11—22no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11M1614yes—
73Dic11⋊C4—44no—
74C4×Dic11—44no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78C4×C4⋊Q8—111no—
79#1839—111no—
80#1767D1111yescharacteristic
81#1271—114no—
82C23×C11C2×C22⋊C411yescharacteristic
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11#10112yes—
98C2×C4×C11#10312yes—
99C2×C4×C11#10312yes—
100C2×C4×C11#10412yes—
101C2×C4×C11C2×M1612yes—
102C2×C4×C11C2×SD1611yescharacteristic
103C2×C4×C11C2×Q1611yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)12yes—
105C2×Dic11—24no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111Dic22—48no—
112C8×C11—44no—
113C11⋊C8—82no—
114C2×C4⋊Q8—111no—
115C2×C4×Q8—221no—
116C2×C4⋊C8—21no—
117C2×#97—21no—
118#391—221no—
119#389—112no—
120#389—221no—
121#384—111no—
122C4×C4⋊C4—112no—
123C4×C4⋊C4—221no—
124C43C2×D1111yescharacteristic
125#336—112no—
126#336—221no—
127#336—221no—
128#336C2×D1112yes—
129C22×C11#40711yescharacteristic
130C22×C11#41011yescharacteristic
131C22×C11C2×#10111yescharacteristic
132C22×C11C2×#10311yescharacteristic
133C22×C11#41811yescharacteristic
134C22×C11C2×#10411yescharacteristic
135C22×C11#42111yescharacteristic
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—22no—
143C4×C11—22no—
144Dic11—44no—
145Dic11—82no—
146C22×Q8—221no—
147C22×C8—22no—
148C22×C8—222no—
149C4⋊Q8—224no—
150C4×Q8—444no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—222no—
157C2×C42—222no—
158C2×C42C4×D1111yescharacteristic
159C2×C42C4×D1111yescharacteristic
160C2×C42D4411yescharacteristic
161C2×C42D4411yescharacteristic
162C2×C42C22⋊D1111yescharacteristic
163C2×C42C22⋊D1111yescharacteristic
164C2×C42C22×D1111yescharacteristic
165C4⋊C8—24no—
166#97—42no—
167#95—222no—
168#95—222no—
169C2×C11#146711yescharacteristic
170C2×C11#148711yescharacteristic
171C2×C11#149011yescharacteristic
172C2×C11#150311yescharacteristic
173C2×C11#151411yescharacteristic
174C2×C11#153111yescharacteristic
175C2×C11#154911yescharacteristic
176C2×Q8—224no—
177C2×Q8—442no—
178C2×Q8—442no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4(C2×D11)⋊C411yescharacteristic
182C22×C4(C2×D11)⋊C411yescharacteristic
183C22×C4(C2×D11)⋊C411yescharacteristic
184C22×C4(C2×D11)⋊C411yescharacteristic
185C22×C4C2×C4×D1111yescharacteristic
186C22×C4C2×D4411yescharacteristic
187C22×C4C2×C22⋊D1111yescharacteristic
188C2×C8—24no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—442no—
192C2×C8—442no—
193C2×C8—442no—
194C4⋊C4—114no—
195C4⋊C4—224no—
196C4⋊C4—222no—
197C4⋊C4—442no—
198C4⋊C4—442no—
199C4⋊C4—442no—
200C4⋊C4—444no—
201C42—22no—
202C42—22no—
203C42—22no—
204C42—22no—
205C42—41no—
206C42—41no—
207C42—444no—
208C42#432412yes—
209C42#432612yes—
210C11#762211yescharacteristic, complemented, Sylow
211C23C2×(C2×D11)⋊C411yescharacteristic
212Q8—448no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—224no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4#6686912yes—
234C2×C4#6687412yes—
235C2×C4#6687412yes—
236C2×C4#6688812yes—
237C2×C4M16×D1112yes—
238C2×C4#6696112yes—
239C2×C4C2×#432411yescharacteristic
240C2×C4C2×#432611yescharacteristic
241C8—44no—
242C8—882no—
243C22C2×#6686911yescharacteristic
244C22C2×#6687411yescharacteristic
245C22#1062261911yescharacteristic
246C22#1062273911yescharacteristic
247C22#1062274411yescharacteristic
248C22C2×#6688811yescharacteristic
249C22#1062275211yescharacteristic
250C4—22no—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—22no—
256C4—22no—
257C4—22no—
258C4—444no—
259C4—882no—
260C2#1306695911yescharacteristic
261C2#1306704411yescharacteristic
262C2#1306706011yescharacteristic
263C2#1306711411yescharacteristic
264C2#1306716411yescharacteristic
265C2#1306723011yescharacteristic
266C2#1306730211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1767C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1767D11
hypocenterC11#7622
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
210. C11#7622semidirect

Maximal subgroups

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

subgroupindex
C4×#669222
#130687592
#130664382
C11×#17672
#762211