Finite Group Databasebeta

← #13074297

Subgroups — #13074297

Order 1408.

576 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 145 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×#66928C211yesmaximal, characteristic, complemented
2C2×#66925C211yesmaximal, characteristic, complemented
3C11×#376C211yesmaximal, characteristic, complemented
4#10622553C212yesmaximal, complemented
5#10622552C212yesmaximal, complemented
6#10622286C211yesmaximal, characteristic, complemented
7#10622285C211yesmaximal, characteristic, complemented
8#10622284C211yesmaximal, characteristic
9#10622283C212yesmaximal, complemented
10#10622278C212yesmaximal, complemented
11#10622269C211yesmaximal, characteristic, complemented
12C22×D44C2212yes—
13C22×D44C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C2×C42×C11C2212yes—
17C2×C42×C11C2211yescharacteristic
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2212yes—
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×C4×Dic11C2211yescharacteristic
30#66928—24no—
31#66925—24no—
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11×#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C23×D11C2312yes—
38C23×D11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×D44—24no—
49C2×D44—22no—
50C2×D44—24no—
51C2×D44—42no—
52C2×D44—42no—
53C2×C4×D11—22no—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×Dic22—22no—
57C2×Dic22—42no—
58C42×C11—24no—
59C42×C11D414yescomplemented
60(C2×D11)⋊C4—24no—
61(C2×D11)⋊C4—22no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—42no—
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71C4×Dic11—22no—
72#2610—111nomaximal, Sylow
73C23×C11C2411yescharacteristic
74C22×D11—21no—
75C22×D11—21no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11#4112yes—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11C2×D412yes—
96C2×C4×C11C2×D412yes—
97C2×C4×C11C2×D412yes—
98C2×C4×C11#4114yes—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11#4112yes—
109D44—48no—
110D44—44no—
111C4×D11—28no—
112Dic22—44no—
113C2×#124—111no—
114C2×#117—111no—
115#395—111no—
116#394—111no—
117#393—111no—
118#392—111no—
119#390—112no—
120#388—112no—
121#388—112no—
122#386—112no—
123#376D1111yescharacteristic, complemented
124C22×C11C22×D411yescharacteristic
125C22×C11C2×#4112yes—
126C22×C11C2×#4111yescharacteristic
127C22×C11C2×#4111yescharacteristic
128C22×C11H(5,𝔽2)12yes—
129C2×D11—22no—
130C2×D11—24no—
131C2×D11—41no—
132C2×D11—41no—
133C2×D11—42no—
134C2×D11—42no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—42no—
139C2×D11—42no—
140C2×D11—42no—
141C4×C11—22no—
142C4×C11—22no—
143C4×C11—22no—
144C4×C11—24no—
145C4×C11—42no—
146Dic11—22no—
147Dic11—41no—
148Dic11—42no—
149Dic11—41no—
150C22×Q8—111no—
151C22×D4—112no—
152C22×D4—111no—
153C23×C4—111no—
154#124—224no—
155#117—224no—
156C2×C4⋊C4—111no—
157C2×C4⋊C4—111no—
158C2×C4⋊C4—112no—
159C2×C22⋊C4—111no—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C42—111no—
168C2×C42C2×D1112yes—
169C2×C42C2×D1111yescharacteristic
170#95—112no—
171#95—112no—
172#95C2×D1112yes—
173#95C2×D1111yescharacteristic
174#95C2×D1111yescharacteristic
175C2×C11#52511yescharacteristic
176C2×C11#53211yescharacteristic
177C2×C11#53511yescharacteristic
178C2×C11#55112yes—
179C2×C11#55512yes—
180D11—42no—
181D11—82no—
182C24—111no—
183C24—112no—
184C2×Q8—222no—
185C2×Q8—442no—
186C2×D4—224no—
187C2×D4—222no—
188C2×D4—224no—
189C2×D4—442no—
190C2×D4—442no—
191C22×C4—111no—
192C22×C4—111no—
193C22×C4—112no—
194C22×C4—111no—
195C22×C4—222no—
196C22×C4—222no—
197C22×C4—222no—
198C22×C4C22×D1112yes—
199C22×C4C22×D1111yescharacteristic
200C22×C4C22×D1111yescharacteristic
201C22×C4C22×D1111yescharacteristic
202C22×C4C22×D1112yes—
203C4⋊C4—222no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C22⋊C4—224no—
207C22⋊C4—222no—
208C22⋊C4—222no—
209C22⋊C4—224no—
210C22⋊C4—224no—
211C22⋊C4—224no—
212C22⋊C4—442no—
213C22⋊C4—442no—
214C42—24no—
215C42—222no—
216C42D4414yescomplemented
217C11#261011yescharacteristic, complemented, Sylow
218C23—112no—
219C23—221no—
220C23—222no—
221C23—221no—
222C23—222no—
223C23—222no—
224C23—222no—
225C23—222no—
226C23—222no—
227C23—222no—
228C23—222no—
229C23—222no—
230C23C23×D1111yescharacteristic
231Q8—444no—
232D4—448no—
233D4—444no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—112no—
244C2×C4—228no—
245C2×C4—221no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4C2×D4412yes—
255C2×C4C2×D4412yes—
256C2×C4C2×D4412yes—
257C2×C4#433914yes—
258C22—222no—
259C22—224no—
260C22—441no—
261C22—441no—
262C22—442no—
263C22—442no—
264C22—442no—
265C22—442no—
266C22—442no—
267C22—442no—
268C22—442no—
269C22—442no—
270C22C22×D4411yescharacteristic
271C22C2×#433912yes—
272C22#41×D1111yescharacteristic
273C22#41×D1111yescharacteristic
274C22#6704212yes—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—24no—
279C4—42no—
280C4—222no—
281C4—441no—
282C4—442no—
283C4—441no—
284C2—442no—
285C2—882no—
286C2#1062300811yescharacteristic
287C2#1062305511yescharacteristic
288C2#1062305611yescharacteristic
289C2#1062305812yes—
290C2#1062306312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#376C2
prime radical#10622284C2
hypercenter#376D11
hypocenterC11#2610
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
1. C2×#66928C2semidirect
2. C2×#66925C2semidirect
3. C11×#376C2semidirect
4. #10622553C2semidirect
5. #10622552C2semidirect
6. #10622286C2semidirect
7. #10622285C2semidirect
9. #10622283C2semidirect
10. #10622278C2semidirect
11. #10622269C2semidirect
59. C42×C11D4semidirect
123. #376D11semidirect
216. C42D44semidirect
217. C11#2610semidirect

Maximal subgroups

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

subgroupindex
C2×#669282
C2×#669252
C11×#3762
#106225532
#106225522
#106222862
#106222852
#106222842
#106222832
#106222782
#106222692
#261011