Finite Group Databasebeta

← #13072025

Subgroups — #13072025

Order 1408.

610 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 153 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×#66982C211yesmaximal, characteristic
2C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
3C2×#66939C211yesmaximal, characteristic
4C2×#66930C211yesmaximal, characteristic, complemented
5C11×#381C211yesmaximal, characteristic, complemented
6#10622571C211yesmaximal, characteristic
7#10622559C211yesmaximal, characteristic, complemented
8#10622289C212yesmaximal, complemented
9#10622282C212yesmaximal, complemented
10#10622270C212yesmaximal, complemented
11#10622260C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C23×Dic11C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic11C2211yescharacteristic
19#66982—24no—
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×Dic11⋊C4—24no—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2212yes—
32C2×C4×Dic11C2212yes—
33#66939—24no—
34#66930—24no—
35C11×#95C2212yes—
36C11×#95C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2311yescharacteristic
40C23×D11C2311yescharacteristic
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—22no—
49C2×C22⋊D11—22no—
50C2×C22⋊D11—22no—
51C22×Dic11—24no—
52C22×Dic11—22no—
53C22×Dic11—22no—
54C22×Dic11—22no—
55C22×Dic11D414yes—
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2312yes—
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2312yes—
61C11×C22⋊C4—22no—
62C11×C22⋊C4—22no—
63C22⋊Dic11D414yes—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—24no—
68C4⋊Dic11—22no—
69C4⋊Dic11—22no—
70Dic11⋊C4—24no—
71Dic11⋊C4—24no—
72Dic11⋊C4—24no—
73Dic11⋊C4—24no—
74Dic11⋊C4—24no—
75C4×Dic11—24no—
76#2413—111nomaximal, Sylow
77C23×C11—22no—
78C23×C11—22no—
79C23×C11C2×D412yes—
80C23×C11C2×D412yes—
81C23×C11#4112yes—
82C23×C11C2411yescharacteristic
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—22no—
86C22×D11—21no—
87C22×D11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—44no—
99C22⋊D11—44no—
100C2×Dic11—28no—
101C2×Dic11—28no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11C2×D414yes—
114C2×Dic11C2×D412yes—
115C2×Dic11C2×D412yes—
116C2×Dic11#4114yes—
117C2×#123—111no—
118C2×#123—111no—
119C2×#117—111no—
120C22×C4⋊C4—111no—
121#398—112no—
122#396—112no—
123#389—112no—
124#388—112no—
125#386—111no—
126#385—111no—
127#381D1111yescharacteristic, complemented
128C22×C11—22no—
129C22×C11—22no—
130C22×C11—24no—
131C22×C11—24no—
132C22×C11#12114yes—
133C22×C11C22×D411yescharacteristic
134C22×C11C22×D411yescharacteristic
135C22×C11C2×#4111yescharacteristic
136C22×C11C2×#4112yes—
137C22×C112−1+412yes—
138C2×D11—41no—
139C2×D11—41no—
140C2×D11—41no—
141C2×D11—42no—
142C2×D11—42no—
143C4×C11—42no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—42no—
147Dic11—22no—
148Dic11—22no—
149Dic11—24no—
150Dic11—24no—
151Dic11—41no—
152C22×D4—111no—
153C23×C4—111no—
154C23×C4—111no—
155C23×C4C2×D1111yescharacteristic
156#123—224no—
157#123—224no—
158#117—224no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—112no—
162C2×C4⋊C4—111no—
163C2×C4⋊C4—112no—
164C2×C4⋊C4—111no—
165C2×C4⋊C4—112no—
166C2×C4⋊C4—224no—
167C2×C22⋊C4—111no—
168C2×C22⋊C4—111no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4—111no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4C2×D1111yescharacteristic
173C2×C22⋊C4C2×D1111yescharacteristic
174C2×C42—112no—
175#95—112no—
176#95—112no—
177#95C2×D1112yes—
178#95C2×D1112yes—
179C2×C11—24no—
180C2×C11C2×#12111yescharacteristic
181C2×C11#52511yescharacteristic
182C2×C11#53611yescharacteristic
183C2×C11#54712yes—
184C2×C11#55212yes—
185D11—81no—
186C24—111no—
187C24C22×D1111yescharacteristic
188C2×D4—222no—
189C2×D4—222no—
190C2×D4—222no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—114no—
195C22×C4—112no—
196C22×C4—112no—
197C22×C4—111no—
198C22×C4—111no—
199C22×C4—111no—
200C22×C4—224no—
201C22×C4—222no—
202C22×C4—222no—
203C22×C4—222no—
204C22×C4C22×D1111yescharacteristic
205C22×C4C22×D1112yes—
206C22×C4C22×D1111yescharacteristic
207C22×C4C22×D1112yes—
208C4⋊C4—224no—
209C4⋊C4—224no—
210C4⋊C4—224no—
211C4⋊C4—224no—
212C4⋊C4—222no—
213C4⋊C4—222no—
214C4⋊C4—224no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—114no—
218C22⋊C4—222no—
219C22⋊C4—222no—
220C22⋊C4—224no—
221C22⋊C4—224no—
222C42—224no—
223C11#241311yescharacteristic, complemented, Sylow
224C23—22no—
225C23—22no—
226C23—221no—
227C23—221no—
228C23—221no—
229C23—222no—
230C23—222no—
231C23#433912yes—
232C23D4×D1112yes—
233C23D4×D1112yes—
234C23C23×D1111yescharacteristic
235D4—444no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—44no—
247C2×C4—114no—
248C2×C4—112no—
249C2×C4—112no—
250C2×C4—114no—
251C2×C4—228no—
252C2×C4—228no—
253C2×C4—221no—
254C2×C4—221no—
255C2×C4—221no—
256C2×C4—221no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—221no—
262C2×C4—221no—
263C2×C4—221no—
264C22—24no—
265C22—22no—
266C22—24no—
267C22—22no—
268C22—441no—
269C22—442no—
270C22—441no—
271C22—442no—
272C22—441no—
273C22#6693714yes—
274C22C2×#433911yescharacteristic
275C22C2×D4×D1111yescharacteristic
276C22C2×D4×D1111yescharacteristic
277C22#41×D1112yes—
278C22#6704312yes—
279C4—42no—
280C4—41no—
281C4—42no—
282C4—41no—
283C4—222no—
284C4—222no—
285C4—224no—
286C4—224no—
287C4—441no—
288C2—24no—
289C2—881no—
290C2C2×#6693711yescharacteristic
291C2#1062306212yes—
292C2#1062317911yescharacteristic
293C2#1062318612yes—
294C2#1062318711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC22×C22⋊D11C22
hypercenter#381D11
hypocenterC11#2413
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×Dic11⋊C4C2semidirect
4. C2×#66930C2semidirect
5. C11×#381C2semidirect
7. #10622559C2semidirect
8. #10622289C2semidirect
9. #10622282C2semidirect
10. #10622270C2semidirect
11. #10622260C2semidirect
127. #381D11semidirect
223. C11#2413semidirect

Maximal subgroups

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

subgroupindex
C2×#669822
C22×Dic11⋊C42
C2×#669392
C2×#669302
C11×#3812
#106225712
#106225592
#106222892
#106222822
#106222702
#106222602
#241311