Finite Group Databasebeta

← #14664153

Subgroups — #14664153

Order 2816.

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

normal subgroups only

This group has 402 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
1#13071907C211yesmaximal, characteristic
2C4×#66900C211yesmaximal, characteristic
3#13066647C212yesmaximal
4#13066623C212yesmaximal
5C11×#1461C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic
8C11×#431—21no—
9#10622842—21no—
10C2×#66900—21no—
11#10622596C411yescharacteristic
12#10622596C2211yescharacteristic
13#10622593—21no—
14#10622592C411yescharacteristic
15#10622592C2211yescharacteristic
16#10622545C411yescharacteristic
17C4×Dic11⋊C4—21no—
18C4×Dic11⋊C4—21no—
19C4×#4318—21no—
20C11×#324—21no—
21C11×#324C2212yes—
22#10622168C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×Dic11⋊C4—21no—
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C2×C4×Dic11—21no—
41C2×#4318—22no—
42C4×Dic22—41no—
43C4×Dic22—41no—
44C11×C4⋊C8—41no—
45C11×C22⋊C8—22no—
46C4×C8×C11—41no—
47#66900—24no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55#66867—41no—
56C4×C11⋊C8—41no—
57#11736—111nomaximal, Sylow
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—41no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C2×Dic22—41no—
73C2×Dic22—42no—
74C2×C8×C11—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C4⋊Dic11—41no—
85Dic11⋊C4—42no—
86Dic11⋊C4—42no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90C4×Dic11—24no—
91C4×Dic11—41no—
92C4×Dic11—41no—
93#4318—24no—
94#4318—42no—
95C2×C11⋊C8—42no—
96#2399—111no—
97C4×#101—111no—
98#1461D1111yescharacteristic
99#1354—112no—
100#1346—112no—
101C23×C11C2×C22⋊C411yescharacteristic
102Q8×C11—44no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11#9911yescharacteristic
118C2×C4×C11#9911yescharacteristic
119C2×C4×C11#10412yes—
120C2×C4×C11#13512yes—
121C2×Dic11—22no—
122C2×Dic11—22no—
123C2×Dic11—22no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133Dic22—42no—
134Dic22—42no—
135C8×C11—82no—
136C11⋊C8—44no—
137C2×C4×Q8—111no—
138C2×C4×Q8C2×D1111yescharacteristic
139#431—21no—
140C2×#101—221no—
141C4×M16—221no—
142#398—111no—
143#398—111no—
144#398—221no—
145#395—111no—
146#395—111no—
147#395—221no—
148C4×C4⋊C4—221no—
149C4×C4⋊C4—221no—
150#376—111no—
151#343—112no—
152#324—21no—
153#324C2×D1112yes—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11C2×#9911yescharacteristic
157C22×C11#41611yescharacteristic
158C22×C11C2×#10411yescharacteristic
159C4×C11—21no—
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11#35612yes—
167Dic11—42no—
168Dic11—42no—
169Dic11—42no—
170Dic11—81no—
171C22×Q8—111no—
172C22×Q8D4411yescharacteristic
173C2×M16—222no—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×Q8—441no—
177C4×Q8—441no—
178C2×C4⋊C4—111no—
179C2×C4⋊C4—221no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—221no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4C4×D1111yescharacteristic
185C2×C4⋊C4C22⋊D1111yescharacteristic
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C42—221no—
188C2×C42—221no—
189C2×C42C4×D1111yescharacteristic
190C2×C42D4411yescharacteristic
191C2×C42C22⋊D1111yescharacteristic
192C4⋊C8—41no—
193#101—224no—
194C22⋊C8—22no—
195#97—441no—
196C4×C8—41no—
197C4×C8—441no—
198#95—111no—
199#95—111no—
200#95—221no—
201#95—221no—
202#95—221no—
203#95—221no—
204#95—221no—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11#150111yescharacteristic
208C2×C11#212011yescharacteristic
209C2×C11C2×#35611yescharacteristic
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—441no—
214C2×Q8—442no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4—221no—
219C22×C4(C2×D11)⋊C411yescharacteristic
220C22×C4(C2×D11)⋊C411yescharacteristic
221C22×C4(C2×D11)⋊C411yescharacteristic
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4C2×C4×D1111yescharacteristic
224C22×C4C2×D4411yescharacteristic
225C22×C4C2×C22⋊D1111yescharacteristic
226M16—224no—
227M16—442no—
228C2×C8—42no—
229C2×C8—442no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—441no—
234C4⋊C4—442no—
235C4⋊C4—442no—
236C4⋊C4—442no—
237C4⋊C4—442no—
238C4⋊C4—442no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—224no—
246C42—441no—
247C42—441no—
248C11#1173611yescharacteristic, complemented, Sylow
249C23C2×(C2×D11)⋊C411yescharacteristic
250Q8—44no—
251Q8—442no—
252Q8—442no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—222no—
268C2×C4—222no—
269C2×C4—222no—
270C2×C4—441no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4—441no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4#6687011yescharacteristic
280C2×C4#6687011yescharacteristic
281C2×C4#6688912yes—
282C2×C4#6695712yes—
283C8—82no—
284C8—444no—
285C22—21no—
286C22—21no—
287C22C2×#6687011yescharacteristic
288C22#1062272611yescharacteristic
289C22C2×#6688911yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—442no—
298C4—442no—
299C4—442no—
300C4—881no—
301C4#1062211612yes—
302C2—21no—
303C2—21no—
304C2#1306710811yescharacteristic
305C2#1307025511yescharacteristic
306C2C2×#1062211611yescharacteristic
subgroupG/H
centerC2×C4#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1461C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1461D11
hypocenterC11#11736
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
248. C11#11736semidirect

Maximal subgroups

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

subgroupindex
#130719072
C4×#669002
#130666472
#130666232
C11×#14612
#1173611