Finite Group Databasebeta

← #14662959

Subgroups — #14662959

Order 2816.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#13077178C211yesmaximal, characteristic
2D11×#349C212yesmaximal
3#13066567C211yesmaximal, characteristic, complemented
4#13066566C212yesmaximal, complemented
5C11×#1327C211yesmaximal, characteristic, complemented
6C2×M16×D11C411yescharacteristic
7C2×M16×D11C2211yescharacteristic
8C2×#66925C411yescharacteristic
9C11×#423C2211yescharacteristic
10#10622731C411yescharacteristic
11#10622731C2211yescharacteristic
12#10622537C411yescharacteristic
13D11×M32—22no—
14#10622452—22no—
15#10622452—22no—
16C11×#349C2212yes—
17#10622191C2212yes—
18#10622152—22no—
19C22×C4×D11C2×C411yescharacteristic
20C2×C11×M16C2×C411yescharacteristic
21C2×C11×M16C2311yescharacteristic
22C2×C42×C11C2×C411yescharacteristic
23C2×(C2×D11)⋊C4—21no—
24C2×Dic11⋊C4—21no—
25C2×C4×Dic11C2×C411yescharacteristic
26C2×#4318C2×C411yescharacteristic
27C2×#4318C2×C411yescharacteristic
28M16×D11—42no—
29M16×D11—42no—
30C2×#4313—21no—
31C2×#4313D412yes—
32C2×C8×D11—21no—
33C2×C8×D11D412yes—
34#66925—21no—
35#66925—21no—
36#66925C812yes—
37#66925C812yes—
38C11×M32—22no—
39C11×C4⋊C8—22no—
40Dic11⋊C8—22no—
41Dic11⋊C8—22no—
42#66876—22no—
43C4⋊(C11⋊C8)—22no—
44#66862—42no—
45C16×D11—42no—
46#11456—111nomaximal, Sylow
47C23×D11M1611yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11C22×C411yescharacteristic
50C22×Dic11—21no—
51C22×Dic11M1611yescharacteristic
52C2×C4×D11—22no—
53C2×C4×D11—22no—
54C2×C4×D11C22⋊C411yescharacteristic
55C2×C4×D11C22⋊C411yescharacteristic
56C2×C4×D11C2×C811yescharacteristic
57C2×C4×D11C2×C811yescharacteristic
58C11×M16—41no—
59C11×M16—41no—
60C2×C8×C11—21no—
61C2×C8×C11C2×D412yes—
62C42×C11—21no—
63C42×C11C2×C812yes—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—22no—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68C4×Dic11—21no—
69C4×Dic11C2×C812yes—
70#4318—41no—
71#4318—41no—
72C2×C11⋊C8—21no—
73C2×C11⋊C8C22⋊C412yes—
74#4313—42no—
75#4313—42no—
76C8×D11—22no—
77C8×D11—22no—
78C8×D11—42no—
79C11×C16—42no—
80C11⋊C16—42no—
81#2905—111no—
82C2×#349—112no—
83#1327—111no—
84#1327—112no—
85#1327D1111yescharacteristic, complemented
86C23×C11C2×M1611yescharacteristic
87C22×D11—22no—
88C22×D11—81no—
89C22×D11C22⋊C811yescharacteristic
90C22×D11C22⋊C811yescharacteristic
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—81no—
95C2×C4×C11C2×C22⋊C411yescharacteristic
96C2×C4×C11C22×C811yescharacteristic
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—81no—
100C2×Dic11C22⋊C811yescharacteristic
101C2×Dic11C22⋊C811yescharacteristic
102C4×D11—22no—
103C4×D11—21no—
104C4×D11—21no—
105C4×D11—22no—
106C4×D11#9912yes—
107C4×D11#10112yes—
108C8×C11—22no—
109C8×C11—41no—
110C11⋊C8—22no—
111C11⋊C8—41no—
112C22×M16—111no—
113C22×M16—111no—
114C2×#117—111no—
115C2×M32—222no—
116#424—222no—
117#424—222no—
118#423—111no—
119#423—111no—
120#423—111no—
121#423C2×D1111yescharacteristic
122#349—112no—
123#349—222no—
124#349C2×D1112yes—
125C22×C11—21no—
126C22×C11—41no—
127C22×C11C2×C22⋊C811yescharacteristic
128C2×D11—21no—
129C2×D11—41no—
130C2×D11—41no—
131C2×D11—82no—
132C2×D11#32412yes—
133C4×C11—21no—
134C4×C11—42no—
135C4×C11C2×#9911yescharacteristic
136C4×C11C2×#10111yescharacteristic
137Dic11—21no—
138Dic11—42no—
139Dic11#32412yes—
140C23×C4—111no—
141C2×M16—111no—
142C2×M16—112no—
143C2×M16—111no—
144C2×M16—221no—
145C2×M16—442no—
146C2×M16—442no—
147C2×M16C4×D1111yescharacteristic
148C2×M16C22×D1111yescharacteristic
149C22×C8—112no—
150C22×C8—221no—
151#117—112no—
152#117—112no—
153#117—221no—
154#117—221no—
155C2×C4⋊C4—221no—
156C2×C22⋊C4—221no—
157C2×C42—111no—
158C2×C42C4×D1111yescharacteristic
159M32—22no—
160M32—222no—
161M32—442no—
162C2×C16—442no—
163C4⋊C8—22no—
164C4⋊C8—222no—
165C4⋊C8—222no—
166C4⋊C8—222no—
167C2×C11—21no—
168C2×C11—41no—
169C2×C11C2×#32411yescharacteristic
170D11—22no—
171D11—41no—
172C24—111no—
173C22×C4—21no—
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—111no—
177C22×C4—111no—
178C22×C4—111no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4—221no—
182C22×C4C2×C4×D1111yescharacteristic
183M16—41no—
184M16—41no—
185M16—442no—
186M16—442no—
187M16—441no—
188M16—441no—
189C2×C8—21no—
190C2×C8—112no—
191C2×C8—222no—
192C2×C8—222no—
193C2×C8—221no—
194C2×C8—442no—
195C2×C8D4×D1112yes—
196C4⋊C4—222no—
197C4⋊C4—222no—
198C22⋊C4—222no—
199C22⋊C4—222no—
200C42—21no—
201C42—112no—
202C42—221no—
203C42C8×D1112yes—
204C16—42no—
205C16—442no—
206C11#1145611yescharacteristic, complemented, Sylow
207C23—111no—
208C23—111no—
209C23—222no—
210C23—881no—
211C23M16×D1111yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—81no—
216C2×C4—111no—
217C2×C4—112no—
218C2×C4—112no—
219C2×C4—111no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—222no—
226C2×C4—881no—
227C2×C4C22⋊C4×D1111yescharacteristic
228C2×C4C2×C8×D1111yescharacteristic
229C8—22no—
230C8—41no—
231C8—222no—
232C8—441no—
233C22—21no—
234C22—41no—
235C22—112no—
236C22—221no—
237C22—441no—
238C22—441no—
239C22—882no—
240C22D11×C22⋊C811yescharacteristic
241C4—21no—
242C4—42no—
243C4—112no—
244C4—221no—
245C4—442no—
246C4D11×#9911yescharacteristic
247C4D11×#10111yescharacteristic
248C2—21no—
249C2—41no—
250C2—222no—
251C2—441no—
252C2D11×#32411yescharacteristic
subgroupG/H
centerC4D11×#99
commutatorC2×C4×C11C22×C8
FrattiniC2×M16C22×D11
FittingC11×#1327C2
socleC2×C11C2×#324
prime radicalC23×D11M16
cosocleC2×C11×M16C23
hypercenter#1327D11
hypocenterC11#11456
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
3. #13066567C2semidirect
4. #13066566C2semidirect
5. C11×#1327C2semidirect
85. #1327D11semidirect
206. C11#11456semidirect

Maximal subgroups

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

subgroupindex
#130771782
D11×#3492
#130665672
#130665662
C11×#13272
#1145611