Finite Group Databasebeta

← #14647339

Subgroups — #14647339

Order 2816.

498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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#13068608C211yesmaximal, characteristic
2#13066937C211yesmaximal, characteristic
3#13066519C212yesmaximal, complemented
4#13066474C212yesmaximal, complemented
5C11×#2349C211yesmaximal, characteristic
6C2×C4×D4×C11—21no—
7C2×C4×D4×C11C2211yescharacteristic
8C11×#389—21no—
9C11×#385—22no—
10C11×#382C2211yescharacteristic
11C11×#380C412yes—
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×C11×#95C412yes—
14C2×#66897—21no—
15#10622538C2212yes—
16#10622537C2212yes—
17#10622168—21no—
18#10622163—22no—
19C22×D4×C11D411yescharacteristic
20C23×C4×C11—22no—
21C23×C4×C11C2×C412yes—
22C4×D4×C11—22no—
23C4×D4×C11—22no—
24C4×D4×C11—42no—
25C4×D4×C11—42no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4D412yes—
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C2×#4318—22no—
35C11×#95—22no—
36C11×#95—21no—
37C11×#95C2×C411yescharacteristic
38C11×#95C2×C412yes—
39C11×#95C2×C411yescharacteristic
40#66897—42no—
41C22⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—22no—
45C4×C11⋊C8—22no—
46#8764—111nomaximal, Sylow
47C24×C11C22⋊C412yes—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11D812yes—
51C2×D4×C11SD1612yes—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—21no—
57C22×C4×C11—44no—
58C22×C4×C11—44no—
59C22×C4×C11—82no—
60C22×C4×C11—82no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×C4⋊C4—22no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—82no—
70C11×C22⋊C4—24no—
71C11×C22⋊C4—44no—
72C42×C11—41no—
73C42×C11—41no—
74C42×C11#4112yes—
75C42×C11#4112yes—
76#4318—42no—
77#4318—42no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80#2349D1111yescharacteristic
81#1800—111no—
82#1460—111no—
83#1303—112no—
84#1286—112no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11#10214yes—
90C23×C11C2×C22⋊C411yescharacteristic
91D4×C11—24no—
92D4×C11—24no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—82no—
107C2×C4×C11—82no—
108C2×C4×C11—88no—
109C2×C4×C11#11711yescharacteristic
110C2×C4×C11#11711yescharacteristic
111C2×C4×C11#12312yes—
112C2×C4×C11#12312yes—
113C2×C4×C11C2×D811yescharacteristic
114C2×C4×C11C2×SD1611yescharacteristic
115C2×C4×C11#13712yes—
116C11⋊C8—82no—
117C11⋊C8—82no—
118C2×C4×D4—21no—
119C2×C4×D4C2×D1111yescharacteristic
120#431—112no—
121#423—112no—
122C2×#100—221no—
123#389—21no—
124#385—22no—
125#382C2×D1111yescharacteristic
126#380Dic1112yes—
127C4×C4⋊C4C2×D1111yescharacteristic
128C2×#95Dic1112yes—
129#343—221no—
130#323—222no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—24no—
134C22×C11—44no—
135C22×C11—44no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11#38111yescharacteristic
139C22×C11C2×#10211yescharacteristic
140C22×C11#41911yescharacteristic
141C4×C11—22no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—42no—
145C4×C11—42no—
146C4×C11—81no—
147C4×C11—82no—
148C4×C11#48012yes—
149C4×C11#48312yes—
150C22×D4C22⋊D1111yescharacteristic
151C23×C4—22no—
152C23×C4C2×Dic1112yes—
153C2×M16—222no—
154C4×D4—22no—
155C4×D4—22no—
156C4×D4—42no—
157C4×D4—42no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4C22⋊D1111yescharacteristic
162C2×C22⋊C4—22no—
163C2×C22⋊C4C22⋊D1112yes—
164C2×C42—21no—
165C2×C42C22×D1111yescharacteristic
166C4⋊C8—222no—
167C4⋊C8—222no—
168C4⋊C8—222no—
169#100—442no—
170C22⋊C8—222no—
171C4×C8—222no—
172#95—22no—
173#95—21no—
174#95C2×Dic1111yescharacteristic
175#95C2×Dic1112yes—
176#95C2×Dic1111yescharacteristic
177C2×C11—21no—
178C2×C11—21no—
179C2×C11—44no—
180C2×C11#182311yescharacteristic
181C2×C11#182711yescharacteristic
182C2×C11#182911yescharacteristic
183C24C22⋊Dic1112yes—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4#432312yes—
187C2×D4#432412yes—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—44no—
194C22×C4—44no—
195C22×C4—82no—
196C22×C4—82no—
197C22×C4C22⋊Dic1112yes—
198C22×C4C22×Dic1111yescharacteristic
199C22×C4C2×C22⋊D1111yescharacteristic
200C22×C4C2×C22⋊D1111yescharacteristic
201M16—442no—
202M16—442no—
203C2×C8—442no—
204C2×C8—442no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—82no—
210C22⋊C4—24no—
211C22⋊C4—44no—
212C42—41no—
213C42—41no—
214C42#433912yes—
215C42#433912yes—
216C11#876411yescharacteristic, complemented, Sylow
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23#6689614yes—
222C23C2×C22⋊Dic1111yescharacteristic
223D4—24no—
224D4—24no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—88no—
241C2×C4#6697911yescharacteristic
242C2×C4#6697911yescharacteristic
243C2×C4#6698212yes—
244C2×C4#6698212yes—
245C2×C4C2×#432311yescharacteristic
246C2×C4C2×#432411yescharacteristic
247C2×C4#6699512yes—
248C8—882no—
249C8—882no—
250C22—21no—
251C22—21no—
252C22—24no—
253C22—44no—
254C22—44no—
255C22—42no—
256C22—42no—
257C22#1062282411yescharacteristic
258C22C2×#6689611yescharacteristic
259C22#1062283811yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—82no—
266C4—81no—
267C4#1062258012yes—
268C4#1062258412yes—
269C2—21no—
270C2—21no—
271C2—44no—
272C2#1306870211yescharacteristic
273C2#1306872011yescharacteristic
274C2#1306872711yescharacteristic
subgroupG/H
centerC22#10622824
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2349C2
socleC22×C11#381
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#2349D11
hypocenterC11#8764
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #13066519C2semidirect
4. #13066474C2semidirect
216. C11#8764semidirect

Maximal subgroups

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

subgroupindex
#130686082
#130669372
#130665192
#130664742
C11×#23492
#876411