Finite Group Databasebeta

← #13073105

Subgroups — #13073105

Order 1408.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66948C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C11×#382C211yesmaximal, characteristic, complemented
4#10622601C211yesmaximal, characteristic, complemented
5#10622590C211yesmaximal, characteristic, complemented
6#10622552C211yesmaximal, characteristic, complemented
7C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
8#10622288C214yesmaximal, complemented
9#10622278C214yesmaximal, complemented
10C22×D44C2212yes—
11C22×D44C2211yescharacteristic
12C22×C4×D11C2211yescharacteristic
13C22×C4×D11C2212yes—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C42×C11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×(C2×D11)⋊C4C2214yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24#66948—24no—
25C4⋊C4×D11—24no—
26C11×#95C2214yes—
27C11⋊#95C2214yes—
28C11⋊#95C2212yes—
29C23×D11C2312yes—
30C23×D11C2311yescharacteristic
31C22×C4×C11C2312yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×Dic11C2312yes—
36C22×Dic11C2312yes—
37C22×Dic11C2311yescharacteristic
38C2×D44—24no—
39C2×D44—28no—
40C2×D44—22no—
41C2×D44—22no—
42C2×D44—22no—
43C2×C4×D11—24no—
44C2×C4×D11—22no—
45C2×C4×D11—22no—
46C2×C4×D11—44no—
47C2×C4×D11D414yes—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—22no—
50C42×C11—22no—
51(C2×D11)⋊C4—24no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—44no—
54(C2×D11)⋊C4—44no—
55C4⋊Dic11—22no—
56Dic11⋊C4—24no—
57C4×Dic11—22no—
58#2504—111nomaximal, Sylow
59C23×C11C2411yescharacteristic
60C22×D11—21no—
61C22×D11—21no—
62C22×D11—22no—
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—22no—
66C22×D11—24no—
67C22×D11—24no—
68C22×D11C2×D412yes—
69C22×D11#4114yes—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—24no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11#4112yes—
79C2×C4×C11#4112yes—
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—24no—
87C2×Dic11C2×D412yes—
88D44—48no—
89D44—44no—
90C4×D11—28no—
91C4×D11—48no—
92C2×#121—111no—
93C22×C4⋊C4—111no—
94#397—114no—
95#390—111no—
96#390—111no—
97#386—114no—
98#382—111no—
99#382D1111yescharacteristic, complemented
100C4×C22⋊C4—111no—
101C22×C11C22×D411yescharacteristic
102C22×C11C2×#4111yescharacteristic
103C22×C11C2×#4111yescharacteristic
104C22×C11C2×#4112yes—
105C22×C11H(5,𝔽2)12yes—
106C2×D11—22no—
107C2×D11—22no—
108C2×D11—24no—
109C2×D11—24no—
110C2×D11—42no—
111C2×D11—42no—
112C2×D11—42no—
113C2×D11—44no—
114C2×D11—44no—
115C2×D11#12414yes—
116C4×C11—42no—
117C4×C11—42no—
118C4×C11—42no—
119C4×C11#12314yes—
120Dic11—22no—
121Dic11—42no—
122Dic11—42no—
123C22×D4—112no—
124C22×D4—111no—
125C23×C4—111no—
126C23×C4—112no—
127#121—224no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4—224no—
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C4⋊C4C2×D1111yescharacteristic
133C2×C22⋊C4—112no—
134C2×C22⋊C4—112no—
135C2×C22⋊C4—114no—
136C2×C22⋊C4—114no—
137C2×C42—111no—
138C2×C42C2×D1111yescharacteristic
139#95—112no—
140#95—114no—
141#95C2×D1114yes—
142C2×C11C2×#12311yescharacteristic
143C2×C11C2×#12411yescharacteristic
144C2×C11#53511yescharacteristic
145C2×C11#55312yes—
146C2×C11#55312yes—
147D11—24no—
148D11—82no—
149C24—111no—
150C24—112no—
151C2×D4—224no—
152C2×D4—228no—
153C2×D4—222no—
154C2×D4—222no—
155C2×D4—222no—
156C22×C4—111no—
157C22×C4—114no—
158C22×C4—112no—
159C22×C4—112no—
160C22×C4—224no—
161C22×C4—222no—
162C22×C4—222no—
163C22×C4—444no—
164C22×C4C22×D1112yes—
165C22×C4C22×D1112yes—
166C22×C4C22×D1112yes—
167C22×C4C22×D1111yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—224no—
171C4⋊C4—222no—
172C22⋊C4—224no—
173C22⋊C4—224no—
174C22⋊C4—444no—
175C22⋊C4—444no—
176C42—22no—
177C42—222no—
178C11#250411yescharacteristic, complemented, Sylow
179C23—112no—
180C23—114no—
181C23—221no—
182C23—221no—
183C23—222no—
184C23—222no—
185C23—222no—
186C23—222no—
187C23—224no—
188C23—224no—
189C23C23×D1111yescharacteristic
190D4—448no—
191D4—444no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—112no—
200C2×C4—221no—
201C2×C4—221no—
202C2×C4—228no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—224no—
208C2×C4—448no—
209C2×C4#433912yes—
210C2×C4D4×D1112yes—
211C2×C4#434312yes—
212C22—114no—
213C22—222no—
214C22—224no—
215C22—222no—
216C22—224no—
217C22—442no—
218C22—444no—
219C22—442no—
220C22—442no—
221C22—444no—
222C22C2×#433911yescharacteristic
223C22C2×D4×D1111yescharacteristic
224C22C2×#434311yescharacteristic
225C22#41×D1112yes—
226C22#6704212yes—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—222no—
231C4—442no—
232C4—442no—
233C4#6694714yes—
234C2—224no—
235C2—882no—
236C2C2×#6694711yescharacteristic
237C2#1062306112yes—
238C2D11×#12411yescharacteristic
239C2#1062320511yescharacteristic
240C2#1062322612yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
prime radicalC2×#66948C2
hypercenter#382D11
hypocenterC11#2504
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D11C2semidirect
3. C11×#382C2semidirect
4. #10622601C2semidirect
5. #10622590C2semidirect
6. #10622552C2semidirect
7. C4×(C2×D11)⋊C4C2semidirect
8. #10622288C2semidirect
9. #10622278C2semidirect
99. #382D11semidirect
178. C11#2504semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×C4⋊C4×D112
C11×#3822
#106226012
#106225902
#106225522
C4×(C2×D11)⋊C42
#106222882
#106222782
#250411