Finite Group Databasebeta

← #13074558

Subgroups — #13074558

Order 1408.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 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×#66993C211yesmaximal, characteristic
2C2×#66942C211yesmaximal, characteristic, complemented
3C11×#394C211yesmaximal, characteristic, complemented
4#10622835C211yesmaximal, characteristic, complemented
5#10622604C211yesmaximal, characteristic, complemented
6#10622574C212yesmaximal, complemented
7#10622572C212yesmaximal, complemented
8#10622570C212yesmaximal, complemented
9#10622570C212yesmaximal, complemented
10#10622285C211yesmaximal, characteristic, complemented
11#10622261C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×C22⋊D11C2212yes—
15C22×D44C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21#66993—24no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×C4×Dic11C2212yes—
32C2×C4×Dic11C2211yescharacteristic
33#66942—24no—
34C11×#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C24×C11C2312yes—
38C23×D11C2312yes—
39C2×D4×C11—22no—
40C2×D4×C11—42no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—24no—
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—42no—
50C2×C22⋊D11—42no—
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C2×D44—22no—
57C2×D44—42no—
58C11×C4⋊C4—22no—
59C11×C22⋊C4—42no—
60C11×C22⋊C4—42no—
61C22⋊Dic11—42no—
62C22⋊Dic11—42no—
63(C2×D11)⋊C4—42no—
64(C2×D11)⋊C4—42no—
65(C2×D11)⋊C4—42no—
66(C2×D11)⋊C4—42no—
67C4⋊Dic11—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71Dic11⋊C4—22no—
72C4×Dic11—24no—
73C4×Dic11D414yes—
74#2641—111nomaximal, Sylow
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11C2411yescharacteristic
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90D4×C11—44no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11C2×D412yes—
101C22⋊D11—48no—
102C22⋊D11—48no—
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—21no—
113C2×Dic11C2×D412yes—
114C2×Dic11C2×D412yes—
115C2×Dic11#4114yes—
116D44—44no—
117C2×#127—111no—
118C2×#125—111no—
119#394—111no—
120#394—111no—
121#394—112no—
122#394—112no—
123#394—111no—
124#394D1111yescharacteristic, complemented
125#390—112no—
126#390—112no—
127#376—111no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11C22×D411yescharacteristic
136C22×C11C2×#4112yes—
137C22×C11H(5,𝔽2)12yes—
138C22×C11H(5,𝔽2)11yescharacteristic
139C22×C11H(5,𝔽2)11yescharacteristic
140C2×D11—42no—
141C2×D11—42no—
142C2×D11—42no—
143C2×D11—42no—
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—42no—
147C4×C11—22no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—42no—
151Dic11—22no—
152Dic11—41no—
153Dic11—41no—
154Dic11—42no—
155Dic11#12414yes—
156C22×D4—112no—
157C22×D4—112no—
158C22×D4—111no—
159C22×D4C2×D1111yescharacteristic
160#127—224no—
161#125—224no—
162C2×C4⋊C4—111no—
163C2×C4⋊C4—111no—
164C2×C4⋊C4—111no—
165C2×C4⋊C4—111no—
166C2×C4⋊C4—111no—
167C2×C4⋊C4C2×D1111yescharacteristic
168C2×C22⋊C4—112no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4C2×D1112yes—
175C2×C22⋊C4C2×D1112yes—
176C2×C42—111no—
177C2×C42—112no—
178#95—112no—
179#95—111no—
180#95C2×D1111yescharacteristic
181C2×C11—82no—
182C2×C11C2×#12411yescharacteristic
183C2×C11#53511yescharacteristic
184C2×C11#53511yescharacteristic
185C2×C11#54012yes—
186C2×C11#54012yes—
187D11—82no—
188C24—112no—
189C24C22×D1112yes—
190C2×D4—22no—
191C2×D4—42no—
192C2×D4—224no—
193C2×D4—224no—
194C2×D4—224no—
195C2×D4—224no—
196C2×D4—222no—
197C2×D4—442no—
198C2×D4—442no—
199C2×D4—442no—
200C22×C4—111no—
201C22×C4—111no—
202C22×C4—112no—
203C22×C4—111no—
204C22×C4—111no—
205C22×C4C22×D1112yes—
206C22×C4C22×D1111yescharacteristic
207C22×C4C22×D1111yescharacteristic
208C22×C4C22×D1111yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—222no—
211C4⋊C4—222no—
212C4⋊C4—222no—
213C4⋊C4—222no—
214C4⋊C4—222no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—442no—
218C22⋊C4—442no—
219C22⋊C4—442no—
220C22⋊C4—442no—
221C22⋊C4—442no—
222C22⋊C4—442no—
223C42—114no—
224C42—224no—
225C11#264111yescharacteristic, complemented, Sylow
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—222no—
234C23—222no—
235C23—222no—
236C23—222no—
237C23—222no—
238C23—222no—
239C23—222no—
240C23C23×D1111yescharacteristic
241D4—44no—
242D4—444no—
243D4—448no—
244D4—448no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—112no—
255C2×C4—114no—
256C2×C4—112no—
257C2×C4—221no—
258C2×C4—221no—
259C2×C4—221no—
260C2×C4—221no—
261C2×C4—222no—
262C2×C4—221no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—221no—
266C2×C4—222no—
267C2×C4D4×D1112yes—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—442no—
276C22—442no—
277C22—442no—
278C22—442no—
279C22—442no—
280C22—442no—
281C22—442no—
282C22C2×D4×D1111yescharacteristic
283C22#6703712yes—
284C22#6703711yescharacteristic
285C22#41×D1112yes—
286C22#6704211yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—114no—
292C4—222no—
293C4—441no—
294C4—441no—
295C4—442no—
296C2—82no—
297C2—882no—
298C2#1062312311yescharacteristic
299C2#1062313811yescharacteristic
300C2#1062314612yes—
301C2#1062319412yes—
302C2D11×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC2×#66993C2
hypercenter#394D11
hypocenterC11#2641
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66942C2semidirect
3. C11×#394C2semidirect
4. #10622835C2semidirect
5. #10622604C2semidirect
6. #10622574C2semidirect
7. #10622572C2semidirect
8. #10622570C2semidirect
9. #10622570C2semidirect
10. #10622285C2semidirect
11. #10622261C2semidirect
124. #394D11semidirect
225. C11#2641semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669422
C11×#3942
#106228352
#106226042
#106225742
#106225722
#106225702
#106222852
#106222612
#264111