Finite Group Databasebeta

← #13074751

Subgroups — #13074751

Order 1408.

598 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 129 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×#66991C211yesmaximal, characteristic, complemented
2C2×#66947C211yesmaximal, characteristic, complemented
3C11×#394C211yesmaximal, characteristic, complemented
4#10622836C211yesmaximal, characteristic, complemented
5#10622596C211yesmaximal, characteristic, complemented
6#10622573C212yesmaximal, complemented
7#10622572C212yesmaximal, complemented
8#10622570C212yesmaximal, complemented
9#10622557C212yesmaximal, complemented
10#10622287C211yesmaximal, characteristic, complemented
11#10622279C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×C22⋊D11C2212yes—
15C22×D44C2211yescharacteristic
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22#66991—24no—
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2212yes—
32#66947—24no—
33C11×#95C2211yescharacteristic
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C23×D11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C2×D4×C11—22no—
41C2×D4×C11—42no—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—42no—
49C2×C22⋊D11—42no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11—42no—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2312yes—
56C2×D44—22no—
57C2×D44—42no—
58C2×C4×D11—42no—
59C2×C4×D11D414yescomplemented
60C11×C4⋊C4—22no—
61C11×C22⋊C4—42no—
62C11×C22⋊C4—42no—
63C22⋊Dic11—24no—
64C22⋊Dic11—24no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—42no—
70C4⋊Dic11—22no—
71Dic11⋊C4—22no—
72Dic11⋊C4—42no—
73C4×Dic11—42no—
74#2661—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—21no—
86C22×D11—21no—
87C22×D11—21no—
88C22×D11—22no—
89C22×D11—21no—
90C22×D11—22no—
91C22×D11—21no—
92C22×D11C2×D412yes—
93D4×C11—44no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11C2×D412yes—
104C22⋊D11—48no—
105C22⋊D11—48no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11C2×D412yes—
115C2×Dic11#4114yes—
116D44—44no—
117C4×D11—44no—
118C2×#123—111no—
119C2×#121—111no—
120#398—111no—
121#397—111no—
122#394—112no—
123#394D1111yescharacteristic, complemented
124#392—111no—
125#392—112no—
126#390—112no—
127#388—112no—
128C4×C22⋊C4—111no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11C22×D411yescharacteristic
137C22×C11C2×#4112yes—
138C22×C11H(5,𝔽2)12yes—
139C22×C11H(5,𝔽2)11yescharacteristic
140C22×C11H(5,𝔽2)11yescharacteristic
141C2×D11—22no—
142C2×D11—22no—
143C2×D11—22no—
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—41no—
147C2×D11—41no—
148C2×D11—41no—
149C2×D11—42no—
150C2×D11—42no—
151C4×C11—22no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11—42no—
155Dic11—22no—
156Dic11—24no—
157Dic11—41no—
158Dic11—42no—
159C22×D4—112no—
160C22×D4—112no—
161C22×D4—111no—
162C22×D4C2×D1111yescharacteristic
163C23×C4—111no—
164#123—224no—
165#121—224no—
166C2×C4⋊C4—111no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—112no—
169C2×C4⋊C4C2×D1111yescharacteristic
170C2×C22⋊C4—112no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—111no—
173C2×C22⋊C4—111no—
174C2×C22⋊C4—111no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4C2×D1112yes—
178C2×C22⋊C4C2×D1112yes—
179C2×C42—112no—
180#95—111no—
181#95—112no—
182#95—112no—
183#95C2×D1111yescharacteristic
184C2×C11—82no—
185C2×C11#53211yescharacteristic
186C2×C11#53411yescharacteristic
187C2×C11#53511yescharacteristic
188C2×C11#53812yes—
189C2×C11#54012yes—
190D11—42no—
191D11—81no—
192C24—111no—
193C24—111no—
194C24C22×D1112yes—
195C2×D4—22no—
196C2×D4—42no—
197C2×D4—222no—
198C2×D4—224no—
199C2×D4—224no—
200C2×D4—442no—
201C2×D4—442no—
202C2×D4—442no—
203C2×D4—442no—
204C2×D4—442no—
205C22×C4—112no—
206C22×C4—111no—
207C22×C4—114no—
208C22×C4—111no—
209C22×C4—112no—
210C22×C4—442no—
211C22×C4C22×D1111yescharacteristic
212C22×C4C22×D1112yes—
213C22×C4C22×D1111yescharacteristic
214C22×C4C22×D1111yescharacteristic
215C4⋊C4—22no—
216C4⋊C4—222no—
217C4⋊C4—222no—
218C4⋊C4—442no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—222no—
222C22⋊C4—224no—
223C22⋊C4—222no—
224C22⋊C4—224no—
225C22⋊C4—224no—
226C22⋊C4—222no—
227C22⋊C4—442no—
228C42—442no—
229C11#266111yescharacteristic, complemented, Sylow
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—112no—
238C23—222no—
239C23—221no—
240C23—222no—
241C23—221no—
242C23—221no—
243C23—221no—
244C23—222no—
245C23—222no—
246C23—221no—
247C23C23×D1111yescharacteristic
248D4—44no—
249D4—444no—
250D4—448no—
251D4—448no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—112no—
262C2×C4—114no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—221no—
267C2×C4—222no—
268C2×C4—222no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—444no—
272C2×C4D4×D1112yes—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—222no—
281C22—222no—
282C22—222no—
283C22—442no—
284C22—442no—
285C22—441no—
286C22—441no—
287C22—442no—
288C22—442no—
289C22—441no—
290C22C2×D4×D1111yescharacteristic
291C22#6703712yes—
292C22#6703711yescharacteristic
293C22#41×D1112yes—
294C22#6704211yescharacteristic
295C4—22no—
296C4—41no—
297C4—41no—
298C4—42no—
299C4—222no—
300C4—224no—
301C4—442no—
302C4—441no—
303C2—82no—
304C2—442no—
305C2—881no—
306C2#1062312011yescharacteristic
307C2#1062313811yescharacteristic
308C2#1062314612yes—
309C2#1062318812yes—
310C2#1062319911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
hypercenter#394D11
hypocenterC11#2661
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#66991C2semidirect
2. C2×#66947C2semidirect
3. C11×#394C2semidirect
4. #10622836C2semidirect
5. #10622596C2semidirect
6. #10622573C2semidirect
7. #10622572C2semidirect
8. #10622570C2semidirect
9. #10622557C2semidirect
10. #10622287C2semidirect
11. #10622279C2semidirect
59. C2×C4×D11D4semidirect
123. #394D11semidirect
229. C11#2661semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×#669472
C11×#3942
#106228362
#106225962
#106225732
#106225722
#106225702
#106225572
#106222872
#106222792
#266111