Finite Group Databasebeta

← #14652799

Subgroups — #14652799

Order 2816.

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

normal subgroups only

This group has 456 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
1#13076979C211yesmaximal, characteristic
2#13068469C211yesmaximal, characteristic
3C2×#10622103C214yesmaximal
4C11×#1745C211yesmaximal, characteristic
5C2×#66923C2212yes—
6C2×C11×#97C2212yes—
7C43×C11C2211yescharacteristic
8#10622549C412yes—
9#10622548C411yescharacteristic
10#10622548C411yescharacteristic
11#10622541—21no—
12#10622541—21no—
13#10622541—21no—
14#10622541—21no—
15C2×C4⋊(C11⋊C8)—21no—
16C2×#66867C2212yes—
17C11×#336—21no—
18C11×#336—21no—
19#10622162—21no—
20#10622103—28no—
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⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
34C2×C4⋊Dic11C2×C412yes—
35C2×Dic11⋊C4—22no—
36C2×Dic11⋊C4—22no—
37C22×C11⋊C8—22no—
38#66923—24no—
39#66923—24no—
40C11×#97—22no—
41C11×#97D414yes—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C4⋊(C11⋊C8)—24no—
45#66867—24no—
46#9690—111nomaximal, Sylow
47C22×C4×C11C22⋊C411yescharacteristic
48C22×C4×C11C22⋊C411yescharacteristic
49C22×C4×C11C22⋊C411yescharacteristic
50C22×C4×C11C22⋊C411yescharacteristic
51C22×C4×C11C22×C411yescharacteristic
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11C2×D411yescharacteristic
54C22×Dic11—22no—
55C22×Dic11—22no—
56C2×C8×C11—24no—
57C2×C8×C11—42no—
58C2×C8×C11—42no—
59C42×C11—22no—
60C42×C11—22no—
61C42×C11—22no—
62C42×C11—41no—
63C42×C11—41no—
64C42×C11—41no—
65C42×C11C2×D412yes—
66C42×C11#4112yes—
67C4⋊Dic11—24no—
68C4⋊Dic11—24no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73Dic11⋊C4—44no—
74Dic11⋊C4—42no—
75Dic11⋊C4—42no—
76C2×C11⋊C8—24no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—42no—
79#2859—111no—
80#1767—111no—
81#1745D1111yescharacteristic
82C2×#330—114no—
83C23×C11C2×C22⋊C411yescharacteristic
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—21no—
98C2×C4×C11—21no—
99C2×C4×C11#10112yes—
100C2×C4×C11#10112yes—
101C2×C4×C11#10412yes—
102C2×C4×C11C4×D412yes—
103C2×C4×C11#12112yes—
104C2×C4×C11#12411yescharacteristic
105C2×C4×C11#12711yescharacteristic
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C8×C11—44no—
113C11⋊C8—44no—
114C2×#125—112no—
115C2×C4⋊C8—221no—
116C2×#97—112no—
117C2×#97C2×D1112yes—
118#389—221no—
119#389—221no—
120#389—221no—
121#389—221no—
122#384—111no—
123#384—111no—
124#382—112no—
125C43C2×D1111yescharacteristic
126#336—21no—
127#336—21no—
128#336—221no—
129#330—228no—
130C22×C11#39011yescharacteristic
131C22×C11C2×#10111yescharacteristic
132C22×C11C2×#10111yescharacteristic
133C22×C11C2×#10411yescharacteristic
134C22×C11#42111yescharacteristic
135C22×C11#42111yescharacteristic
136C22×C11#42111yescharacteristic
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—22no—
142C4×C11—22no—
143C4×C11—22no—
144C4×C11—41no—
145Dic11—82no—
146Dic11—82no—
147C22×C8—22no—
148C22×C8—222no—
149#125—224no—
150#125—224no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4—222no—
158C2×C4⋊C4—222no—
159C2×C42C4×D1111yescharacteristic
160C2×C42C4×D1111yescharacteristic
161C2×C42D4411yescharacteristic
162C2×C42D4411yescharacteristic
163C2×C42C22⋊D1111yescharacteristic
164C2×C42C22⋊D1111yescharacteristic
165C2×C42C22×D1111yescharacteristic
166C4⋊C8—224no—
167#97—22no—
168#97—224no—
169#97D4414yes—
170#95—222no—
171#95—222no—
172C2×C11#152811yescharacteristic
173C2×C11#153111yescharacteristic
174C2×C11#153411yescharacteristic
175C2×C11#153711yescharacteristic
176C2×C11#196311yescharacteristic
177C2×C11#196611yescharacteristic
178C2×C11#198011yescharacteristic
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—224no—
192C2×C8—442no—
193C2×C8—442no—
194C4⋊C4—224no—
195C4⋊C4—224no—
196C4⋊C4—442no—
197C4⋊C4—442no—
198C4⋊C4—442no—
199C4⋊C4—442no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C4⋊C4—444no—
203C42—22no—
204C42—22no—
205C42—22no—
206C42—41no—
207C42—41no—
208C42—41no—
209C42C2×D4412yes—
210C42#433912yes—
211C11#969011yescharacteristic, complemented, Sylow
212C23C2×(C2×D11)⋊C411yescharacteristic
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—21no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4—442no—
234C2×C4#6688812yes—
235C2×C4#6688812yes—
236C2×C4#6688912yes—
237C2×C4C4×D4412yes—
238C2×C4#6692711yescharacteristic
239C2×C4#6692811yescharacteristic
240C2×C4#6698312yes—
241C8—44no—
242C8—444no—
243C22#1062255211yescharacteristic
244C22#1062261811yescharacteristic
245C22#1062261811yescharacteristic
246C22C2×#6688811yescharacteristic
247C22C2×#6688811yescharacteristic
248C22C2×#6688911yescharacteristic
249C22#1062275211yescharacteristic
250C4—22no—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—22no—
256C4—22no—
257C4—41no—
258C4—882no—
259C4—882no—
260C2#1306721911yescharacteristic
261C2#1306723211yescharacteristic
262C2#1306724211yescharacteristic
263C2#1306725311yescharacteristic
264C2#1306944811yescharacteristic
265C2#1306946011yescharacteristic
266C2#1306953511yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1745C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1745D11
hypocenterC11#9690
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
211. C11#9690semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130684692
C2×#106221032
C11×#17452
#969011