Finite Group Databasebeta

← #13074183

Subgroups — #13074183

Order 1408.

604 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 135 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×#66946C211yesmaximal, characteristic, complemented
2C2×#66930C211yesmaximal, characteristic, complemented
3C11×#399C211yesmaximal, characteristic, complemented
4#10622603C212yesmaximal, complemented
5#10622602C212yesmaximal, complemented
6#10622595C211yesmaximal, characteristic, complemented
7#10622573C211yesmaximal, characteristic
8#10622571C212yesmaximal, complemented
9#10622569C212yesmaximal, complemented
10#10622285C211yesmaximal, characteristic, complemented
11#10622264C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2212yes—
13C23×Dic11C2211yescharacteristic
14C22×D44C2211yescharacteristic
15C22×C4×D11C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28C2×C4×Dic11C2211yescharacteristic
29#66946—24no—
30#66930—24no—
31C11×#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C2×C22⋊D11—24no—
44C2×C22⋊D11—24no—
45C2×C22⋊D11—42no—
46C22×Dic11—22no—
47C22×Dic11—22no—
48C22×Dic11—22no—
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C2×D44—24no—
55C2×D44—22no—
56C2×C4×D11—24no—
57C2×C4×D11—42no—
58C2×C4×D11—42no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—42no—
61C11×C22⋊C4—22no—
62C11×C22⋊C4—42no—
63C22⋊Dic11—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—42no—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70C4×Dic11—22no—
71C4×Dic11D414yescomplemented
72#2598—111nomaximal, Sylow
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11#4112yes—
78C23×C11C2411yescharacteristic
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11#4114yes—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
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—
96C22⋊D11—48no—
97C2×Dic11—28no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11C2×D412yes—
109C2×Dic11C2×D412yes—
110C2×Dic11#4112yes—
111D44—28no—
112C4×D11—48no—
113C2×C4×D4—111no—
114C2×#117—111no—
115#400—111no—
116#399D1111yescharacteristic, complemented
117#394—111no—
118#392—111no—
119#388—112no—
120#386—112no—
121#386—112no—
122#385—112no—
123#383—111no—
124C22×C11—22no—
125C22×C11—24no—
126C22×C11—41no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11C22×D411yescharacteristic
130C22×C11C2×#4111yescharacteristic
131C22×C11C2×#4112yes—
132C22×C11C2×#4111yescharacteristic
133C22×C11H(5,𝔽2)12yes—
134C2×D11—24no—
135C2×D11—24no—
136C2×D11—24no—
137C2×D11—42no—
138C2×D11—42no—
139C2×D11—42no—
140C2×D11—42no—
141C4×C11—22no—
142C4×C11—41no—
143C4×C11—42no—
144C4×C11—42no—
145Dic11—22no—
146Dic11—22no—
147Dic11—22no—
148Dic11—41no—
149Dic11—42no—
150C22×D4—112no—
151C22×D4—111no—
152C23×C4—111no—
153C23×C4—112no—
154C4×D4—224no—
155#117—224no—
156C2×C4⋊C4—111no—
157C2×C4⋊C4—111no—
158C2×C4⋊C4C2×D1111yescharacteristic
159C2×C4⋊C4C2×D1112yes—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4C2×D1111yescharacteristic
166C2×C22⋊C4C2×D1112yes—
167C2×C42—111no—
168C2×C42—111no—
169#95—112no—
170#95—112no—
171#95—111no—
172#95—112no—
173#95—112no—
174#95C2×D1111yescharacteristic
175C2×C11—42no—
176C2×C11#52511yescharacteristic
177C2×C11#52511yescharacteristic
178C2×C11#53511yescharacteristic
179C2×C11#55112yes—
180C2×C11#55312yes—
181D11—44no—
182C24—112no—
183C24C22×D1111yescharacteristic
184C2×D4—224no—
185C2×D4—224no—
186C2×D4—224no—
187C2×D4—222no—
188C2×D4—442no—
189C22×C4—111no—
190C22×C4—111no—
191C22×C4—111no—
192C22×C4—112no—
193C22×C4—111no—
194C22×C4—224no—
195C22×C4—222no—
196C22×C4—222no—
197C22×C4—222no—
198C22×C4—442no—
199C22×C4—442no—
200C22×C4C22×D1112yes—
201C22×C4C22×D1112yes—
202C22×C4C22×D1111yescharacteristic
203C22×C4C22×D1111yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—222no—
207C4⋊C4—222no—
208C22⋊C4—22no—
209C22⋊C4—42no—
210C22⋊C4—224no—
211C22⋊C4—224no—
212C22⋊C4—224no—
213C22⋊C4—222no—
214C22⋊C4—442no—
215C42—114no—
216C42—222no—
217C11#259811yescharacteristic, complemented, Sylow
218C23—21no—
219C23—22no—
220C23—21no—
221C23—22no—
222C23—114no—
223C23—222no—
224C23—222no—
225C23—222no—
226C23—222no—
227C23—222no—
228C23—222no—
229C23#434312yes—
230C23C23×D1111yescharacteristic
231D4—228no—
232D4—448no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—112no—
243C2×C4—112no—
244C2×C4—112no—
245C2×C4—228no—
246C2×C4—221no—
247C2×C4—222no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4—221no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—448no—
257C2×C4D4×D1112yes—
258C22—22no—
259C22—24no—
260C22—41no—
261C22—41no—
262C22—42no—
263C22—224no—
264C22—224no—
265C22—224no—
266C22—442no—
267C22—442no—
268C22—442no—
269C22—442no—
270C22C2×D4×D1111yescharacteristic
271C22#6703712yes—
272C22C2×#434311yescharacteristic
273C22#41×D1111yescharacteristic
274C22#41×D1112yes—
275C4—22no—
276C4—42no—
277C4—41no—
278C4—42no—
279C4—222no—
280C4—222no—
281C4—222no—
282C4—442no—
283C4—441no—
284C2—42no—
285C2—444no—
286C2#1062315811yescharacteristic
287C2#1062316812yes—
288C2#1062318711yescharacteristic
289C2#1062319212yes—
290C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radical#10622573C2
hypercenter#399D11
hypocenterC11#2598
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66946C2semidirect
2. C2×#66930C2semidirect
3. C11×#399C2semidirect
4. #10622603C2semidirect
5. #10622602C2semidirect
6. #10622595C2semidirect
8. #10622571C2semidirect
9. #10622569C2semidirect
10. #10622285C2semidirect
11. #10622264C2semidirect
71. C4×Dic11D4semidirect
116. #399D11semidirect
217. C11#2598semidirect

Maximal subgroups

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

subgroupindex
C2×#669462
C2×#669302
C11×#3992
#106226032
#106226022
#106225952
#106225732
#106225712
#106225692
#106222852
#106222642
#259811