Finite Group Databasebeta

← #14664458

Subgroups — #14664458

Order 2816.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#10622596C211yesmaximal, characteristic
2#13066946C211yesmaximal, characteristic
3#13066621C214yesmaximal, complemented
4C11×#1821C211yesmaximal, characteristic
5C22×C11×C4⋊C4C2211yescharacteristic
6C22×C4⋊Dic11C411yescharacteristic
7C22×Dic11⋊C4—21no—
8C11×#407—21no—
9C2×C11⋊#95—21no—
10C2×C11⋊#95C411yescharacteristic
11#10622820—21no—
12#10622596—21no—
13#10622596—21no—
14#10622596C412yes—
15#10622596C2212yes—
16C11×#343—21no—
17C11×#343C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C2×C11×M16—22no—
26C2×C11×C4⋊C4—41no—
27C2×C11×C4⋊C4—41no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—41no—
34C2×C4⋊Dic11—41no—
35C2×C4⋊Dic11C2×C412yes—
36C2×Dic11⋊C4—22no—
37C2×Dic11⋊C4—22no—
38C2×Dic11⋊C4—44no—
39C2×#4318—41no—
40C11×C22⋊C8—41no—
41C11×C22⋊C8—41no—
42C11⋊#95—22no—
43C11⋊#95—21no—
44C11⋊#95—22no—
45C11⋊#95C2×C412yes—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)—41no—
48#11803—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11—41no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—24no—
67C22×Dic11—22no—
68C22×Dic11—22no—
69C22×Dic11—42no—
70C22×Dic11—42no—
71C22×Dic11—42no—
72C22×Dic11—42no—
73C22×Dic11—41no—
74C22×Dic11—41no—
75C11×M16—42no—
76C11×M16—42no—
77C2×C8×C11—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C4⋊Dic11—42no—
83C4⋊Dic11—42no—
84Dic11⋊C4—44no—
85Dic11⋊C4—44no—
86#4318—82no—
87C2×C11⋊C8—42no—
88C2×#398—111no—
89#1821D1111yescharacteristic
90#1463—111no—
91#1346—114no—
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11#9911yescharacteristic
97C23×C11#9911yescharacteristic
98C23×C11C2×C22⋊C411yescharacteristic
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—81no—
118C2×C4×C11AGL(1,ℤ/8)12yes—
119C2×Dic11—24no—
120C2×Dic11—48no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—82no—
127C2×Dic11—82no—
128C8×C11—82no—
129C11⋊C8—82no—
130C22×C4⋊C4—111no—
131C22×C4⋊C4—221no—
132C22×C4⋊C4C2×D1111yescharacteristic
133#407—21no—
134#407—221no—
135#398—112no—
136#398—112no—
137#398—221no—
138#398—221no—
139C2×#95—111no—
140C2×#95—221no—
141#343—21no—
142#343C2×D1112yes—
143#324—112no—
144#324—221no—
145C22×C11—24no—
146C22×C11—24no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11#35212yes—
154C22×C11#35612yes—
155C22×C11C2×#9911yescharacteristic
156C22×C11#41811yescharacteristic
157C22×C11#42111yescharacteristic
158C4×C11—22no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164Dic11—44no—
165Dic11—82no—
166C23×C4—221no—
167C23×C4—221no—
168C23×C4C4×D1111yescharacteristic
169C23×C4D4411yescharacteristic
170C23×C4C22⋊D1111yescharacteristic
171C2×M16—22no—
172C2×M16—441no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—112no—
176C2×C4⋊C4—221no—
177C2×C4⋊C4—222no—
178C2×C4⋊C4—222no—
179C2×C4⋊C4—441no—
180C2×C4⋊C4—441no—
181C2×C4⋊C4—444no—
182C2×C4⋊C4C4×D1111yescharacteristic
183C2×C4⋊C4D4411yescharacteristic
184C2×C4⋊C4C22⋊D1111yescharacteristic
185C2×C4⋊C4C22×D1111yescharacteristic
186C22⋊C8—41no—
187C22⋊C8—41no—
188C22⋊C8—222no—
189C22⋊C8—441no—
190#95—112no—
191#95—221no—
192#95—222no—
193#95—222no—
194C2×C11—21no—
195C2×C11—22no—
196C2×C11—22no—
197C2×C11—21no—
198C2×C11#151011yescharacteristic
199C2×C11C2×#35211yescharacteristic
200C2×C11C2×#35611yescharacteristic
201C24(C2×D11)⋊C411yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—41no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—224no—
213C22×C4—222no—
214C22×C4—222no—
215C22×C4—442no—
216C22×C4—442no—
217C22×C4—442no—
218C22×C4—442no—
219C22×C4—441no—
220C22×C4—441no—
221C22×C4(C2×D11)⋊C411yescharacteristic
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4C2×C4×D1111yescharacteristic
225C22×C4C2×D4411yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227M16—42no—
228M16—42no—
229M16—882no—
230C2×C8—42no—
231C2×C8—442no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—442no—
237C4⋊C4—444no—
238C4⋊C4—442no—
239C4⋊C4—444no—
240C11#1180311yescharacteristic, complemented, Sylow
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23#6687011yescharacteristic
246C23#6687011yescharacteristic
247C23C2×(C2×D11)⋊C411yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—224no—
268C2×C4—448no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—882no—
275C2×C4—882no—
276C2×C4#6700212yes—
277C8—82no—
278C8—882no—
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22#1062211412yes—
288C22#1062211612yes—
289C22C2×#6687011yescharacteristic
290C22#1062261411yescharacteristic
291C22#1062261811yescharacteristic
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—444no—
299C4—882no—
300C2—21no—
301C2—21no—
302C2—22no—
303C2—22no—
304C2#1306714411yescharacteristic
305C2C2×#1062211411yescharacteristic
306C2C2×#1062211611yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1821C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1821D11
hypocenterC11#11803
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #13066621C2semidirect
240. C11#11803semidirect

Maximal subgroups

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

subgroupindex
C2×#106225962
#130669462
#130666212
C11×#18212
#1180311