Finite Group Databasebeta

← #14663086

Subgroups — #14663086

Order 2816.

364 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 83 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#13077333C211yesmaximal, characteristic
2#13070235C212yesmaximal, complemented
3#13066567C211yesmaximal, characteristic, complemented
4#13066553C212yesmaximal, complemented
5C11×#1327C211yesmaximal, characteristic, complemented
6C2×#66960C411yescharacteristic
7C2×#66960C2211yescharacteristic
8#10623008C411yescharacteristic
9C11×#423C2211yescharacteristic
10#10622742C411yescharacteristic
11#10622742C2211yescharacteristic
12C2×#66867C411yescharacteristic
13D11×M32—22no—
14#10622449—22no—
15#10622449—22no—
16C11×#349C2212yes—
17#10622191C2212yes—
18#10622152—22no—
19C2×#4339C2×C411yescharacteristic
20C2×#4339C2×C411yescharacteristic
21C2×C11×M16C2×C411yescharacteristic
22C2×C11×M16C2311yescharacteristic
23C2×C42×C11C2×C411yescharacteristic
24#66983—22no—
25C22×C11⋊C8C2×C411yescharacteristic
26C22×C11⋊C8C2×C411yescharacteristic
27#66960—42no—
28#66960—42no—
29C2×#4313—21no—
30C2×#4313D412yes—
31C2×C8×D11—21no—
32C2×C8×D11D412yes—
33#66928C811yescharacteristic
34#66928C811yescharacteristic
35#66927C811yescharacteristic
36C4×D44—22no—
37#66922C811yescharacteristic
38C11×M32—22no—
39C11×C4⋊C8—22no—
40(C2×D11)⋊C8—22no—
41(C2×D11)⋊C8—22no—
42#66876—22no—
43#66867—21no—
44#66867—21no—
45#66862—42no—
46C16×D11—42no—
47#11486—111nomaximal, Sylow
48C22×C4×C11—21no—
49C22×C4×C11C22×C411yescharacteristic
50C2×C22⋊D11—21no—
51C2×C22⋊D11M1612yes—
52#4339—41no—
53#4339—41no—
54#4339—41no—
55#4339—41no—
56C2×D44—22no—
57C2×D44C2×C811yescharacteristic
58C2×D44C2×C811yescharacteristic
59C2×C4×D11—21no—
60C2×C4×D11C22⋊C412yes—
61C2×Dic22C2×C811yescharacteristic
62C2×Dic22C2×C811yescharacteristic
63C11×M16—41no—
64C11×M16—41no—
65C2×C8×C11—21no—
66C2×C8×C11C2×D412yes—
67C42×C11—21no—
68C42×C11C2×C811yescharacteristic
69C42×C11C2×C811yescharacteristic
70(C2×D11)⋊C4—22no—
71(C2×D11)⋊C4—22no—
72C4⋊Dic11—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—21no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8C22⋊C411yescharacteristic
77C2×C11⋊C8C22⋊C411yescharacteristic
78#4313—42no—
79#4313—42no—
80C8×D11—22no—
81C8×D11—22no—
82C8×D11—42no—
83C11×C16—42no—
84C11⋊C16—42no—
85#2932—111no—
86#2115—112no—
87#1327—111no—
88#1327D1111yescharacteristic, complemented
89#1321—112no—
90C23×C11C2×M1611yescharacteristic
91C22×D11—21no—
92C22×D11C22⋊C812yes—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—81no—
98C2×C4×C11C2×C22⋊C411yescharacteristic
99C2×C4×C11C22×C811yescharacteristic
100C22⋊D11—42no—
101C22⋊D11—42no—
102C2×Dic11—21no—
103C2×Dic11C22⋊C812yes—
104D44—41no—
105D44—41no—
106D44—82no—
107C4×D11—22no—
108C4×D11—22no—
109C4×D11—41no—
110C4×D11—41no—
111Dic22—41no—
112Dic22—41no—
113C8×C11—22no—
114C8×C11—41no—
115C11⋊C8—21no—
116C11⋊C8—41no—
117C11⋊C8#9912yes—
118C2×#131—111no—
119C2×#131—111no—
120#532—111no—
121C2×M32—222no—
122#435—222no—
123#435—222no—
124#423C2×D1111yescharacteristic
125#408—111no—
126#408—111no—
127C2×#97—111no—
128#349—112no—
129#349—222no—
130#349C2×D1112yes—
131C22×C11—21no—
132C22×C11—41no—
133C22×C11C2×C22⋊C811yescharacteristic
134C2×D11—22no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—41no—
138C4×C11—21no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11C2×#9911yescharacteristic
142C4×C11#41311yescharacteristic
143Dic11—22no—
144Dic11—41no—
145C2×#41—111no—
146C2×#41—111no—
147#131—442no—
148#131—442no—
149C2×M16—112no—
150C2×M16—221no—
151C2×M16C4×D1111yescharacteristic
152C2×M16C22×D1111yescharacteristic
153C22×C8—111no—
154C22×C8—112no—
155C22×C8—111no—
156C22×C8—221no—
157C4⋊Q8—111no—
158#127—111no—
159#124—111no—
160#124—111no—
161#121—222no—
162C4×D4—222no—
163C2×C42C4×D1111yescharacteristic
164M32—22no—
165M32—222no—
166M32—442no—
167C2×C16—442no—
168C4⋊C8—22no—
169C22⋊C8—222no—
170C22⋊C8—222no—
171#97—221no—
172#97—221no—
173C2×C11—21no—
174C2×C11—41no—
175C2×C11#145911yescharacteristic
176D11—42no—
177D11—81no—
178#41—441no—
179#41—441no—
180#41—441no—
181#41—441no—
182C2×Q8—111no—
183C2×Q8—111no—
184C2×D4—112no—
185C2×D4—111no—
186C2×D4—111no—
187C2×D4—222no—
188C2×D4—221no—
189C22×C4—21no—
190C22×C4—112no—
191C22×C4—221no—
192C22×C4C2×C4×D1111yescharacteristic
193M16—41no—
194M16—41no—
195M16—442no—
196M16—442no—
197C2×C8—21no—
198C2×C8—111no—
199C2×C8—111no—
200C2×C8—222no—
201C2×C8—222no—
202C2×C8—222no—
203C2×C8—221no—
204C2×C8—442no—
205C2×C8—441no—
206C2×C8D4×D1112yes—
207C4⋊C4—222no—
208C22⋊C4—222no—
209C22⋊C4—222no—
210C42—21no—
211C42C8×D1111yescharacteristic
212C42C8×D1111yescharacteristic
213C16—42no—
214C16—442no—
215C11#1148611yescharacteristic, complemented, Sylow
216C23—112no—
217C23—221no—
218C23M16×D1111yescharacteristic
219Q8—441no—
220Q8—441no—
221D4—441no—
222D4—441no—
223D4—442no—
224D4—442no—
225D4—882no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—81no—
231C2×C4—112no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—221no—
235C2×C4—441no—
236C2×C4—441no—
237C2×C4C22⋊C4×D1111yescharacteristic
238C2×C4C2×C8×D1111yescharacteristic
239C8—22no—
240C8—41no—
241C8—112no—
242C8—221no—
243C8—441no—
244C22—21no—
245C22—41no—
246C22—222no—
247C22—442no—
248C22—442no—
249C22—441no—
250C22D11×C22⋊C811yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—222no—
255C4—441no—
256C4D11×#9911yescharacteristic
257C4#1062236411yescharacteristic
258C2—21no—
259C2—41no—
260C2—442no—
261C2—881no—
262C2#1306693311yescharacteristic
subgroupG/H
centerC4D11×#99
commutatorC2×C4×C11C22×C8
FrattiniC2×M16C22×D11
FittingC11×#1327C2
socleC2×C11#1459
prime radical#10623008C4
cosocleC2×C11×M16C23
hypercenter#1327D11
hypocenterC11#11486
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #13070235C2semidirect
3. #13066567C2semidirect
4. #13066553C2semidirect
5. C11×#1327C2semidirect
88. #1327D11semidirect
215. C11#11486semidirect

Maximal subgroups

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

subgroupindex
#130773332
#130702352
#130665672
#130665532
C11×#13272
#1148611