Finite Group Databasebeta

← #13074503

Subgroups — #13074503

Order 1408.

620 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 137 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×#66983C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C11×#381C211yesmaximal, characteristic, complemented
4#10622574C212yesmaximal, complemented
5#10622573C212yesmaximal, complemented
6#10622290C211yesmaximal, characteristic, complemented
7#10622285C211yesmaximal, characteristic, complemented
8#10622284C211yesmaximal, characteristic, complemented
9#10622283C212yesmaximal, complemented
10#10622278C212yesmaximal, complemented
11#10622272C211yesmaximal, characteristic, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×C22⋊D11C2212yes—
15C22×D44C2212yes—
16C22×D44C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2211yescharacteristic
20#66983—24no—
21C4×C22⋊D11—24no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2212yes—
30C2×Dic11⋊C4C2211yescharacteristic
31C2×C4×Dic11C2211yescharacteristic
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11×#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2312yes—
39C23×D11C2311yescharacteristic
40C22×C4×C11—42no—
41C22×C4×C11D414yescomplemented
42C22×C4×C11C2312yes—
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—22no—
47C2×C22⋊D11—22no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—22no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11—42no—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2312yes—
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C2×D44—24no—
57C2×D44—22no—
58C2×D44—42no—
59C2×D44—42no—
60C2×D44—42no—
61C2×C4×D11—22no—
62C2×C4×D11—42no—
63C11×C22⋊C4—42no—
64C22⋊Dic11—22no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—42no—
69(C2×D11)⋊C4—42no—
70(C2×D11)⋊C4—42no—
71C4⋊Dic11—22no—
72C4⋊Dic11—42no—
73Dic11⋊C4—22no—
74C4×Dic11—22no—
75#2635—111nomaximal, Sylow
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11C2×D412yes—
81C23×C11C2411yescharacteristic
82C22×D11—21no—
83C22×D11—21no—
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#4112yes—
94C2×C4×C11—22no—
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—22no—
102C2×C4×C11—44no—
103C2×C4×C11C2×D412yes—
104C2×C4×C11C2×D412yes—
105C22⋊D11—28no—
106C22⋊D11—48no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11#4112yes—
117D44—44no—
118D44—48no—
119C4×D11—44no—
120C2×#121—111no—
121C2×C4×D4—111no—
122#400—111no—
123#399—111no—
124#394—112no—
125#394—111no—
126#392—112no—
127#392—111no—
128#388—112no—
129#386—112no—
130#381D1111yescharacteristic, complemented
131C22×C11—22no—
132C22×C11—22no—
133C22×C11—22no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11C22×D411yescharacteristic
137C22×C11C2×#4111yescharacteristic
138C22×C11C2×#4111yescharacteristic
139C22×C11H(5,𝔽2)12yes—
140C22×C11H(5,𝔽2)12yes—
141C2×D11—22no—
142C2×D11—24no—
143C2×D11—41no—
144C2×D11—41no—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C4×C11—22no—
154C4×C11—22no—
155C4×C11—42no—
156C4×C11—42no—
157Dic11—22no—
158Dic11—41no—
159Dic11—41no—
160Dic11—42no—
161C22×D4—111no—
162C22×D4—112no—
163C22×D4—111no—
164C22×D4—112no—
165C23×C4—111no—
166C23×C4C2×D1111yescharacteristic
167#121—224no—
168C4×D4—224no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—112no—
172C2×C22⋊C4—111no—
173C2×C22⋊C4—111no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4—112no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4C2×D1112yes—
180C2×C42—111no—
181#95—112no—
182#95—112no—
183#95C2×D1112yes—
184#95C2×D1111yescharacteristic
185#95C2×D1111yescharacteristic
186C2×C11—42no—
187C2×C11#52511yescharacteristic
188C2×C11#53411yescharacteristic
189C2×C11#53511yescharacteristic
190C2×C11#53812yes—
191C2×C11#54012yes—
192D11—42no—
193D11—82no—
194C24—111no—
195C24—112no—
196C24C22×D1111yescharacteristic
197C2×D4—224no—
198C2×D4—222no—
199C2×D4—222no—
200C2×D4—222no—
201C2×D4—224no—
202C2×D4—222no—
203C2×D4—442no—
204C2×D4—442no—
205C2×D4—442no—
206C2×D4—442no—
207C2×D4—442no—
208C22×C4—42no—
209C22×C4—111no—
210C22×C4—111no—
211C22×C4—112no—
212C22×C4—111no—
213C22×C4—222no—
214C22×C4—442no—
215C22×C4D4414yescomplemented
216C22×C4C22×D1112yes—
217C22×C4C22×D1112yes—
218C22×C4C22×D1111yescharacteristic
219C22×C4C22×D1111yescharacteristic
220C4⋊C4—222no—
221C4⋊C4—222no—
222C4⋊C4—442no—
223C22⋊C4—42no—
224C22⋊C4—224no—
225C22⋊C4—222no—
226C22⋊C4—222no—
227C22⋊C4—224no—
228C22⋊C4—442no—
229C22⋊C4—442no—
230C22⋊C4—442no—
231C42—222no—
232C11#263511yescharacteristic, complemented, Sylow
233C23—22no—
234C23—21no—
235C23—21no—
236C23—22no—
237C23—112no—
238C23—221no—
239C23—222no—
240C23—221no—
241C23—222no—
242C23—222no—
243C23—222no—
244C23—222no—
245C23—222no—
246C23—222no—
247C23—222no—
248C23—222no—
249C23C2×D4412yes—
250C23C23×D1111yescharacteristic
251D4—228no—
252D4—444no—
253D4—448no—
254D4—448no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—44no—
264C2×C4—112no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—444no—
275C2×C4C2×D4412yes—
276C2×C4C2×D4412yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—42no—
281C22—42no—
282C22—222no—
283C22—224no—
284C22—441no—
285C22—441no—
286C22—442no—
287C22—442no—
288C22—442no—
289C22—442no—
290C22—442no—
291C22—442no—
292C22—442no—
293C22—442no—
294C22C22×D4411yescharacteristic
295C22#6703712yes—
296C22#41×D1111yescharacteristic
297C22#41×D1111yescharacteristic
298C22#6704212yes—
299C4—22no—
300C4—22no—
301C4—42no—
302C4—42no—
303C4—222no—
304C4—441no—
305C4—442no—
306C4—441no—
307C2—42no—
308C2—442no—
309C2—882no—
310C2#1062302411yescharacteristic
311C2#1062305511yescharacteristic
312C2#1062305611yescharacteristic
313C2#1062318812yes—
314C2#1062319412yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
hypercenter#381D11
hypocenterC11#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#66983C2semidirect
2. C2×C4×C22⋊D11C2semidirect
3. C11×#381C2semidirect
4. #10622574C2semidirect
5. #10622573C2semidirect
6. #10622290C2semidirect
7. #10622285C2semidirect
8. #10622284C2semidirect
9. #10622283C2semidirect
10. #10622278C2semidirect
11. #10622272C2semidirect
41. C22×C4×C11D4semidirect
130. #381D11semidirect
215. C22×C4D44semidirect
232. C11#2635semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C2×C4×C22⋊D112
C11×#3812
#106225742
#106225732
#106222902
#106222852
#106222842
#106222832
#106222782
#106222722
#263511