Finite Group Databasebeta

← #13074403

Subgroups — #13074403

Order 1408.

526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#66947C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C11×#400C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic, complemented
5#10622599C211yesmaximal, characteristic, complemented
6#10622290C211yesmaximal, characteristic, complemented
7#10622288C212yesmaximal, complemented
8#10622281C212yesmaximal, complemented
9#10622278C212yesmaximal
10#10622277C211yesmaximal, characteristic, complemented
11#10622270C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×C4×D11C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28#66947—24no—
29C4⋊C4×D11—24no—
30C11×#95C2212yes—
31C11×#95C2211yescharacteristic
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×D44—22no—
49C2×D44—24no—
50C2×C4×D11—24no—
51C2×C4×D11—24no—
52C2×C4×D11—42no—
53C2×C4×D11—42no—
54C2×C4×D11D414yes—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—42no—
62(C2×D11)⋊C4—42no—
63C4⋊Dic11—22no—
64C4⋊Dic11—42no—
65Dic11⋊C4—24no—
66Dic11⋊C4—22no—
67Dic11⋊C4—42no—
68#2623—111nomaximal, Sylow
69C23×C11C2411yescharacteristic
70C22×D11—22no—
71C22×D11—21no—
72C22×D11—21no—
73C22×D11—21no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—21no—
77C22×D11—21no—
78C22×D11C2×D412yes—
79C22×D11#4114yes—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11C2×D412yes—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11C2×D412yes—
103D44—44no—
104C4×D11—28no—
105C4×D11—48no—
106C2×#123—111no—
107C22×C4⋊C4—111no—
108#400—111no—
109#400D1111yescharacteristic, complemented
110#399—111no—
111#399—111no—
112#398—112no—
113#397—112no—
114#386—112no—
115#385—112no—
116#381—111no—
117C22×C11C22×D411yescharacteristic
118C22×C11C2×#4112yes—
119C22×C11H(5,𝔽2)12yes—
120C22×C112−1+411yescharacteristic
121C22×C112−1+411yescharacteristic
122C2×D11—22no—
123C2×D11—22no—
124C2×D11—24no—
125C2×D11—24no—
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—41no—
129C2×D11—42no—
130C2×D11—42no—
131C2×D11#12314yes—
132C4×C11—22no—
133C4×C11—41no—
134C4×C11—42no—
135C4×C11—41no—
136C4×C11—42no—
137Dic11—22no—
138Dic11—42no—
139Dic11—41no—
140Dic11—42no—
141C22×D4—111no—
142C23×C4—111no—
143C23×C4—112no—
144#123—224no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—224no—
151C2×C4⋊C4C2×D1111yescharacteristic
152C2×C4⋊C4C2×D1111yescharacteristic
153C2×C22⋊C4—111no—
154C2×C22⋊C4—111no—
155C2×C22⋊C4—111no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159#95—112no—
160#95—111no—
161#95—112no—
162#95—112no—
163#95C2×D1111yescharacteristic
164#95C2×D1112yes—
165#95C2×D1112yes—
166C2×C11C2×#12311yescharacteristic
167C2×C11#53511yescharacteristic
168C2×C11#53611yescharacteristic
169C2×C11#53912yes—
170C2×C11#53912yes—
171D11—24no—
172D11—81no—
173C24—111no—
174C24—111no—
175C2×D4—222no—
176C2×D4—224no—
177C22×C4—111no—
178C22×C4—114no—
179C22×C4—112no—
180C22×C4—112no—
181C22×C4—111no—
182C22×C4—224no—
183C22×C4—224no—
184C22×C4—442no—
185C22×C4—442no—
186C22×C4C22×D1111yescharacteristic
187C22×C4C22×D1111yescharacteristic
188C22×C4C22×D1112yes—
189C22×C4C22×D1112yes—
190C22×C4C22×D1111yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—224no—
194C4⋊C4—222no—
195C4⋊C4—222no—
196C4⋊C4—442no—
197C4⋊C4—442no—
198C22⋊C4—222no—
199C22⋊C4—222no—
200C22⋊C4—224no—
201C22⋊C4—222no—
202C22⋊C4—442no—
203C22⋊C4—442no—
204C11#262311yescharacteristic, complemented, Sylow
205C23—112no—
206C23—114no—
207C23—221no—
208C23—222no—
209C23—221no—
210C23—221no—
211C23—221no—
212C23—222no—
213C23—222no—
214C23—221no—
215C23C23×D1111yescharacteristic
216D4—444no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—112no—
230C2×C4—228no—
231C2×C4—222no—
232C2×C4—221no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—448no—
241C2×C4D4×D1112yes—
242C22—114no—
243C22—224no—
244C22—222no—
245C22—222no—
246C22—224no—
247C22—442no—
248C22—441no—
249C22—441no—
250C22—441no—
251C22—442no—
252C22C2×D4×D1111yescharacteristic
253C22#6704011yescharacteristic
254C22#41×D1112yes—
255C22#6704212yes—
256C22#6704311yescharacteristic
257C4—22no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—42no—
262C4—222no—
263C4—442no—
264C4—441no—
265C4—442no—
266C2—224no—
267C2—881no—
268C2#1062315911yescharacteristic
269C2D11×#12311yescharacteristic
270C2#1062320511yescharacteristic
271C2#1062322312yes—
272C2#1062323812yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC22×D44C22
hypercenter#400D11
hypocenterC11#2623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D11C2semidirect
3. C11×#400C2semidirect
4. #10622605C2semidirect
5. #10622599C2semidirect
6. #10622290C2semidirect
7. #10622288C2semidirect
8. #10622281C2semidirect
10. #10622277C2semidirect
11. #10622270C2semidirect
109. #400D11semidirect
204. C11#2623semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C2×C4⋊C4×D112
C11×#4002
#106226052
#106225992
#106222902
#106222882
#106222812
#106222782
#106222772
#106222702
#262311