Finite Group Databasebeta

← #13076573

Subgroups — #13076573

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#389C211yesmaximal, characteristic
2#10622597C211yesmaximal, characteristic
3#10622596C211yesmaximal, characteristic
4#10622593C211yesmaximal, characteristic
5#10622592C211yesmaximal, characteristic
6#10622591C211yesmaximal, characteristic
7#10622587C211yesmaximal, characteristic
8#10622585C211yesmaximal, characteristic
9#10622585C211yesmaximal, characteristic
10#10622546C211yesmaximal, characteristic
11#10622542C211yesmaximal, characteristic
12#10622270C211yesmaximal, characteristic
13#10622269C211yesmaximal, characteristic
14#10622259C211yesmaximal, characteristic
15#10622259C211yesmaximal, characteristic
16C22×Dic22C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C42×C11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×C4×Dic11C2211yescharacteristic
34C2×C4×Dic11C2211yescharacteristic
35C11×#95C2211yescharacteristic
36C11×#95C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C11⋊#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C2×Dic22—22no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×Dic22—41no—
70C2×Dic22—41no—
71C2×Dic22Q814yescomplemented
72C11×C4⋊C4—22no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C42×C11—41no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79Dic11⋊C4—22no—
80Dic11⋊C4—41no—
81Dic11⋊C4—41no—
82Dic11⋊C4—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4Q814yescomplemented
87C4×Dic11—41no—
88C4×Dic11—41no—
89#2806—111nomaximal, Sylow
90C23×C11C2411yescharacteristic
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
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—21no—
109C2×C4×C11C2×Q812yes—
110C2×C4×C11C2×Q812yes—
111C2×C4×C11#4112yes—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11C2×Q812yes—
133C2×Dic11C2×Q812yes—
134C2×Dic11C2×Q812yes—
135C2×Dic11C2×Q812yes—
136Dic22—44no—
137Dic22—44no—
138#398—111no—
139#398—111no—
140#398—111no—
141#398—111no—
142#395—111no—
143#395—111no—
144#391—111no—
145#391—111no—
146#391—111no—
147#391—111no—
148#389—111no—
149#389—111no—
150#389D1111yescharacteristic
151#387—111no—
152#387—111no—
153C22×C11C22×Q811yescharacteristic
154C22×C11C22×Q811yescharacteristic
155C22×C11C2×#4111yescharacteristic
156C22×C11H(5,𝔽2)11yescharacteristic
157C22×C11H(5,𝔽2)11yescharacteristic
158C22×C11H(5,𝔽2)11yescharacteristic
159C22×C112−1+411yescharacteristic
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167Dic11—22no—
168Dic11—22no—
169Dic11—22no—
170Dic11—22no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C22×Q8—111no—
176C22×Q8—111no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—111no—
179C2×C4⋊C4—111no—
180C2×C4⋊C4—111no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4C2×D1111yescharacteristic
188C2×C4⋊C4C2×D1111yescharacteristic
189C2×C4⋊C4C2×D1111yescharacteristic
190C2×C4⋊C4C2×D1111yescharacteristic
191C2×C42—111no—
192C2×C42—111no—
193C2×C42C2×D1111yescharacteristic
194#95—111no—
195#95—111no—
196#95—111no—
197#95—111no—
198#95—111no—
199#95—111no—
200#95—111no—
201#95—111no—
202#95—111no—
203#95—111no—
204#95—111no—
205#95—111no—
206#95—111no—
207#95—111no—
208#95C2×D1111yescharacteristic
209#95C2×D1111yescharacteristic
210C2×C11#53811yescharacteristic
211C2×C11#54311yescharacteristic
212C2×C11#54411yescharacteristic
213C2×C11#55411yescharacteristic
214C2×C11#55711yescharacteristic
215C2×C11Q8211yescharacteristic
216C2×C11#56211yescharacteristic
217C2×Q8—114no—
218C2×Q8—222no—
219C2×Q8—441no—
220C2×Q8—441no—
221C2×Q8—441no—
222C2×Q8—441no—
223C22×C4—111no—
224C22×C4—111no—
225C22×C4—111no—
226C22×C4—111no—
227C22×C4—111no—
228C22×C4—111no—
229C22×C4—111no—
230C22×C4—111no—
231C22×C4C22×D1111yescharacteristic
232C22×C4C22×D1111yescharacteristic
233C22×C4C22×D1111yescharacteristic
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1111yescharacteristic
236C22×C4C22×D1111yescharacteristic
237C22×C4C22×D1111yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—114no—
243C4⋊C4—222no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C4⋊C4—441no—
252C42—41no—
253C42—441no—
254C42—441no—
255C11#280611yescharacteristic, complemented, Sylow
256C23C23×D1111yescharacteristic
257Q8—444no—
258Q8—444no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—112no—
278C2×C4—112no—
279C2×C4—112no—
280C2×C4—112no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4#433912yes—
302C2×C4Q8×D1112yes—
303C2×C4Q8×D1112yes—
304C22C2×#433911yescharacteristic
305C22#6703711yescharacteristic
306C22#6703711yescharacteristic
307C22C2×Q8×D1111yescharacteristic
308C22C2×Q8×D1111yescharacteristic
309C22#6704211yescharacteristic
310C22#6704311yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—222no—
319C4—222no—
320C4—222no—
321C4—222no—
322C4—441no—
323C4—441no—
324C4—441no—
325C4—441no—
326C2#1062304211yescharacteristic
327C2#1062309111yescharacteristic
328C2#1062309811yescharacteristic
329C2#1062315211yescharacteristic
330C2#1062316511yescharacteristic
331C2#1062322011yescharacteristic
332C2#1062325311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#389C2
hypercenter#389D11
hypocenterC11#2806
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
71. C2×Dic22Q8semidirect
86. Dic11⋊C4Q8semidirect
255. C11#2806semidirect

Maximal subgroups

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

subgroupindex
C11×#3892
#106225972
#106225962
#106225932
#106225922
#106225912
#106225872
#106225852
#106225462
#106225422
#106222702
#106222692
#106222592
#280611