Finite Group Databasebeta

← #14664681

Subgroups — #14664681

Order 2816.

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

normal subgroups only

This group has 376 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#13068699C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066646C212yesmaximal, complemented
4#13066622C212yesmaximal, complemented
5C11×#2599C211yesmaximal, characteristic
6C2×C4×Q8×C11C411yescharacteristic
7C2×C11×#117C2211yescharacteristic
8C11×#398C2211yescharacteristic
9C11×#397C411yescharacteristic
10C11×#395C2211yescharacteristic
11C11×#393C411yescharacteristic
12C11×#388—21no—
13C11×#387—21no—
14C11×#387—21no—
15C11×#385—21no—
16C11×#383C411yescharacteristic
17#10622820—21no—
18#10622538—21no—
19#10622168—21no—
20#10622168C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C22×Q8×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×#4318—22no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95C2×C411yescharacteristic
50C11×#95C2×C411yescharacteristic
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—41no—
53C22⋊(C11⋊C8)—41no—
54C4⋊(C11⋊C8)—41no—
55C4×C11⋊C8—41no—
56#11849—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C2×Q8×C11—42no—
59C2×Q8×C11—41no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—42no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—42no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—42no—
90#4318—42no—
91#4318—42no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94#2599D1111yescharacteristic
95#1822—111no—
96#1458—111no—
97#1354—112no—
98#1346—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11C2×C22⋊C411yescharacteristic
105Q8×C11—42no—
106Q8×C11—42no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#9911yescharacteristic
135C2×C4×C11#13512yes—
136C11⋊C8—82no—
137C11⋊C8—82no—
138C2×C4×Q8Dic1111yescharacteristic
139C2×#117C2×D1111yescharacteristic
140#431—221no—
141#407—221no—
142#398C2×D1111yescharacteristic
143#397Dic1111yescharacteristic
144#395C2×D1111yescharacteristic
145#393Dic1111yescharacteristic
146#388—21no—
147#387—21no—
148#387—21no—
149#385—21no—
150#383Dic1111yescharacteristic
151#343—112no—
152#343—221no—
153#324—112no—
154#323—221no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—42no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—81no—
162C22×C11C2×#9911yescharacteristic
163C22×C11#41611yescharacteristic
164C22×C11#42111yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—42no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—81no—
174C4×C11—81no—
175C4×C11—81no—
176C22×Q8C2×Dic1111yescharacteristic
177C23×C4C22⋊D1111yescharacteristic
178C2×M16—222no—
179C4×Q8—41no—
180C4×Q8—41no—
181#117—41no—
182#117—41no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×Dic1111yescharacteristic
187C2×C4⋊C4C22⋊D1111yescharacteristic
188C2×C4⋊C4C22×D1111yescharacteristic
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4C2×Dic1111yescharacteristic
192C2×C22⋊C4C22⋊D1111yescharacteristic
193C2×C42—21no—
194C2×C42C2×Dic1111yescharacteristic
195C2×C42C22⋊D1111yescharacteristic
196C4⋊C8—441no—
197C22⋊C8—222no—
198C22⋊C8—441no—
199C22⋊C8—441no—
200C4×C8—441no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95C2×Dic1111yescharacteristic
208#95C2×Dic1111yescharacteristic
209C2×C11—21no—
210C2×C11—21no—
211C2×C11—81no—
212C2×C11#151611yescharacteristic
213C2×C11#212011yescharacteristic
214C2×C11#213511yescharacteristic
215C24C22⋊Dic1111yescharacteristic
216C2×Q8—42no—
217C2×Q8—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4C22⋊Dic1111yescharacteristic
227C22×C4C22⋊Dic1111yescharacteristic
228C22×C4C22⋊Dic1111yescharacteristic
229C22×C4C22×Dic1111yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232M16—442no—
233M16—442no—
234C2×C8—442no—
235C2×C8—442no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—42no—
252C11#1184911yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C22⋊Dic1111yescharacteristic
259Q8—42no—
260Q8—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4#6689811yescharacteristic
288C2×C4#6689811yescharacteristic
289C2×C4#6700312yes—
290C8—882no—
291C8—882no—
292C22—21no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22C2×#6689811yescharacteristic
300C22#1062284611yescharacteristic
301C22#1062284911yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—42no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—81no—
311C4—81no—
312C4—81no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2#1306717211yescharacteristic
317C2#1307025711yescharacteristic
318C2#1307031111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2599C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2599D11
hypocenterC11#11849
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2599

Complements

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

NH ≅ G/Ntype
3. #13066646C2semidirect
4. #13066622C2semidirect
252. C11#11849semidirect

Maximal subgroups

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

subgroupindex
#130686992
#130669302
#130666462
#130666222
C11×#25992
#1184911