Finite Group Databasebeta

← #13074907

Subgroups — #13074907

Order 1408.

804 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 157 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×#66983C212yesmaximal, complemented
2C2×#66948C212yesmaximal, complemented
3C2×#66937C212yesmaximal, complemented
4C11×#385C211yesmaximal, characteristic, complemented
5#10622607C212yesmaximal, complemented
6#10622573C211yesmaximal, characteristic, complemented
7#10622573C211yesmaximal, characteristic, complemented
8#10622284C212yesmaximal, complemented
9#10622281C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C22⋊D11C2212yes—
13C22×D44C2212yes—
14C22×D44C2211yescharacteristic
15C22×D44C2212yes—
16C22×D44C2211yescharacteristic
17C22×C4×D11C2212yes—
18C2×C11×C4⋊C4C2212yes—
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21#66983—28no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×C4⋊Dic11C2212yes—
28C2×Dic11⋊C4C2212yes—
29#66948—28no—
30#66937—28no—
31C11×#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C11⋊#95C2211yescharacteristic
34C24×C11C2311yescharacteristic
35C23×D11C2312yes—
36C23×D11C2312yes—
37C22×C4×C11—24no—
38C22×C4×C11—41no—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C2×C22⋊D11—24no—
44C2×C22⋊D11—24no—
45C2×C22⋊D11—24no—
46C2×C22⋊D11—24no—
47C2×C22⋊D11—42no—
48C2×C22⋊D11—42no—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C2×D44—24no—
52C2×D44—24no—
53C2×D44—24no—
54C2×D44—24no—
55C2×D44—24no—
56C2×D44—42no—
57C2×D44—42no—
58C2×D44—42no—
59C2×D44—41no—
60C2×D44—41no—
61C2×C4×D11—24no—
62C2×C4×D11—24no—
63C2×C4×D11—42no—
64C11×C4⋊C4—24no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4D414yescomplemented
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4D418yescomplemented
72C4⋊Dic11—24no—
73Dic11⋊C4—24no—
74#2675—111nomaximal, Sylow
75C23×C11—22no—
76C23×C11—21no—
77C23×C11—22no—
78C23×C11—21no—
79C23×C11C2×D412yes—
80C23×C11C2411yescharacteristic
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94C22×D11C2×D414yes—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—44no—
104C2×C4×C11C2×D414yes—
105C2×C4×C11C2×D414yes—
106C22⋊D11—48no—
107C22⋊D11—48no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11C2×D414yes—
114D44—48no—
115D44—48no—
116D44—44no—
117D44—44no—
118C4×D11—48no—
119C2×#121—112no—
120C2×#121—112no—
121C2×#121—112no—
122#396—112no—
123#392—111no—
124#392—111no—
125#392—112no—
126#385—112no—
127#385D1111yescharacteristic, complemented
128C22×C11—22no—
129C22×C11—24no—
130C22×C11—42no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11C22×D411yescharacteristic
134C22×C11C22×D412yes—
135C22×C11H(5,𝔽2)11yescharacteristic
136C22×C11H(5,𝔽2)12yes—
137C22×C112−1+411yescharacteristic
138C2×D11—24no—
139C2×D11—24no—
140C2×D11—24no—
141C2×D11—42no—
142C2×D11—42no—
143C2×D11—42no—
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C4×C11—24no—
153C4×C11—24no—
154C4×C11—41no—
155C4×C11—41no—
156Dic11—24no—
157Dic11—42no—
158C22×D4—112no—
159C22×D4—112no—
160C22×D4—111no—
161C22×D4—112no—
162C22×D4—112no—
163C22×D4—111no—
164C23×C4—112no—
165C23×C4C2×D1111yescharacteristic
166#121—228no—
167#121—228no—
168#121—228no—
169C2×C4⋊C4—112no—
170C2×C4⋊C4—112no—
171C2×C4⋊C4C2×D1112yes—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4C2×D1111yescharacteristic
178C2×C22⋊C4C2×D1111yescharacteristic
179#95—111no—
180#95—111no—
181#95C2×D1112yes—
182C2×C11—42no—
183C2×C11#53711yescharacteristic
184C2×C11#53712yes—
185C2×C11D4212yes—
186C2×C11D4211yescharacteristic
187C2×C11#56011yescharacteristic
188D11—44no—
189D11—82no—
190C24—112no—
191C24—112no—
192C24C22×D1111yescharacteristic
193C2×D4—224no—
194C2×D4—224no—
195C2×D4—224no—
196C2×D4—224no—
197C2×D4—224no—
198C2×D4—224no—
199C2×D4—224no—
200C2×D4—224no—
201C2×D4—224no—
202C2×D4—442no—
203C2×D4—442no—
204C2×D4—441no—
205C2×D4—441no—
206C2×D4—442no—
207C2×D4—442no—
208C2×D4—442no—
209C22×C4—24no—
210C22×C4—41no—
211C22×C4—112no—
212C22×C4—112no—
213C22×C4—224no—
214C22×C4—224no—
215C22×C4—442no—
216C22×C4C22×D1111yescharacteristic
217C22×C4C22×D1111yescharacteristic
218C22×C4C22×D1112yes—
219C22×C4C22×D1112yes—
220C4⋊C4—24no—
221C4⋊C4—224no—
222C4⋊C4—224no—
223C22⋊C4—41no—
224C22⋊C4—118no—
225C22⋊C4—224no—
226C22⋊C4—224no—
227C22⋊C4—224no—
228C22⋊C4—442no—
229C22⋊C4D4414yescomplemented
230C11#267511yescharacteristic, complemented, Sylow
231C23—22no—
232C23—21no—
233C23—21no—
234C23—22no—
235C23—114no—
236C23—222no—
237C23—222no—
238C23—222no—
239C23—222no—
240C23—222no—
241C23—222no—
242C23—222no—
243C23—222no—
244C23—222no—
245C23—222no—
246C23—222no—
247C23—222no—
248C23—222no—
249C23C2×D4412yes—
250C23C23×D1111yescharacteristic
251D4—448no—
252D4—448no—
253D4—444no—
254D4—444no—
255D4—448no—
256D4—448no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—44no—
266C2×C4—114no—
267C2×C4—222no—
268C2×C4—222no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—448no—
273C2×C4C2×D4414yes—
274C2×C4D4×D1114yes—
275C22—22no—
276C22—24no—
277C22—41no—
278C22—42no—
279C22—41no—
280C22—224no—
281C22—224no—
282C22—224no—
283C22—442no—
284C22—442no—
285C22—442no—
286C22—442no—
287C22—442no—
288C22—442no—
289C22—442no—
290C22—442no—
291C22—442no—
292C22—442no—
293C22—442no—
294C22C22×D4411yescharacteristic
295C22C2×D4×D1112yes—
296C22#6703711yescharacteristic
297C22#6704011yescharacteristic
298C22#6704212yes—
299C4—24no—
300C4—24no—
301C4—41no—
302C4—41no—
303C4—224no—
304C4—442no—
305C2—42no—
306C2—444no—
307C2—882no—
308C2#1062304111yescharacteristic
309C2D4×D4412yes—
310C2#1062312111yescharacteristic
311C2#1062316012yes—
312C2#1062319711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
hypercenter#385D11
hypocenterC11#2675
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#66983C2semidirect
2. C2×#66948C2semidirect
3. C2×#66937C2semidirect
4. C11×#385C2semidirect
5. #10622607C2semidirect
6. #10622573C2semidirect
7. #10622573C2semidirect
8. #10622284C2semidirect
9. #10622281C2semidirect
66. C11×C22⋊C4D4semidirect
71. (C2×D11)⋊C4D4semidirect
127. #385D11semidirect
229. C22⋊C4D44semidirect
230. C11#2675semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C2×#669482
C2×#669372
C11×#3852
#106226072
#106225732
#106222842
#106222812
#267511