Finite Group Databasebeta

← #13073776

Subgroups — #13073776

Order 1408.

532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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×D4×Dic11C211yesmaximal, characteristic
2C2×#66942C211yesmaximal, characteristic, complemented
3C11×#394C211yesmaximal, characteristic
4#10622835C211yesmaximal, characteristic
5#10622599C211yesmaximal, characteristic, complemented
6#10622564C212yesmaximal, complemented
7#10622557C212yesmaximal, complemented
8#10622555C212yesmaximal, complemented
9#10622555C212yesmaximal, complemented
10#10622272C211yesmaximal, characteristic, complemented
11#10622262C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×Dic11C2212yes—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C11×C22⋊C4C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20D4×Dic11—24no—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2212yes—
29C2×C4×Dic11C2211yescharacteristic
30#66942—24no—
31C11×#95C2211yescharacteristic
32C11⋊#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C2×D4×C11—24no—
39C2×D4×C11—22no—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×Dic11—24no—
45C22×Dic11—24no—
46C22×Dic11—24no—
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C11×C4⋊C4—22no—
54C11×C22⋊C4—24no—
55C11×C22⋊C4—42no—
56C22⋊Dic11—24no—
57C22⋊Dic11—24no—
58C22⋊Dic11—42no—
59C4⋊Dic11—22no—
60C4⋊Dic11—22no—
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—24no—
65Dic11⋊C4—22no—
66C4×Dic11—42no—
67C4×Dic11D414yes—
68#2562—111nomaximal, Sylow
69C23×C11—22no—
70C23×C11—22no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11#4114yes—
76C23×C11C2411yescharacteristic
77D4×C11—28no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11C2×D412yes—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—48no—
102C2×Dic11C2×D412yes—
103C2×Dic11C2×D412yes—
104C2×Dic11#4114yes—
105C2×#125—111no—
106C2×C4×D4—111no—
107#400—111no—
108#400—111no—
109#394—111no—
110#394D1111yescharacteristic
111#388—112no—
112#388—112no—
113#380—112no—
114#380—112no—
115C4×C4⋊C4—111no—
116C22×C11—24no—
117C22×C11—24no—
118C22×C11—24no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11C22×D411yescharacteristic
124C22×C11C2×#4112yes—
125C22×C11C2×#4112yes—
126C22×C11H(5,𝔽2)11yescharacteristic
127C22×C112−1+411yescharacteristic
128C4×C11—22no—
129C4×C11—41no—
130C4×C11—41no—
131C4×C11—42no—
132Dic11—22no—
133Dic11—41no—
134Dic11—42no—
135Dic11—41no—
136Dic11—42no—
137Dic11#12414yes—
138C22×D4C2×D1111yescharacteristic
139C23×C4—112no—
140#125—224no—
141C4×D4—224no—
142C2×C4⋊C4—111no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4—111no—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C22⋊C4—112no—
151C2×C22⋊C4—112no—
152C2×C22⋊C4—112no—
153C2×C22⋊C4C2×D1112yes—
154C2×C22⋊C4C2×D1112yes—
155C2×C42—111no—
156C2×C42—112no—
157#95—111no—
158#95—112no—
159#95—112no—
160#95—112no—
161#95—112no—
162#95C2×D1111yescharacteristic
163C2×C11—44no—
164C2×C11#52511yescharacteristic
165C2×C11C2×#12411yescharacteristic
166C2×C11#53711yescharacteristic
167C2×C11#55212yes—
168C2×C11#55312yes—
169C24C22×D1112yes—
170C2×D4—24no—
171C2×D4—22no—
172C22×C4—111no—
173C22×C4—111no—
174C22×C4—112no—
175C22×C4—112no—
176C22×C4—111no—
177C22×C4—111no—
178C22×C4—224no—
179C22×C4—224no—
180C22×C4—224no—
181C22×C4C22×D1112yes—
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1111yescharacteristic
184C22×C4C22×D1111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—224no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C22⋊C4—24no—
194C22⋊C4—42no—
195C22⋊C4—224no—
196C22⋊C4—224no—
197C22⋊C4—442no—
198C42—114no—
199C42—442no—
200C11#256211yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23#434114yes—
208C23C23×D1111yescharacteristic
209D4—28no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—112no—
220C2×C4—114no—
221C2×C4—112no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—222no—
225C2×C4—221no—
226C2×C4—221no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—221no—
235C2×C4—448no—
236C2×C4D4×D1112yes—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D1111yescharacteristic
245C22C2×#434112yes—
246C22#6703711yescharacteristic
247C22#41×D1112yes—
248C22#6704311yescharacteristic
249C4—22no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—114no—
254C4—222no—
255C4—441no—
256C4—442no—
257C4—441no—
258C4—442no—
259C2—44no—
260C2#1062311711yescharacteristic
261C2#1062313212yes—
262C2#1062313911yescharacteristic
263C2#1062318112yes—
264C2D11×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC22×D4×C11C22
hypercenter#394D11
hypocenterC11#2562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#66942C2semidirect
5. #10622599C2semidirect
6. #10622564C2semidirect
7. #10622557C2semidirect
8. #10622555C2semidirect
9. #10622555C2semidirect
10. #10622272C2semidirect
11. #10622262C2semidirect
200. C11#2562semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
C2×#669422
C11×#3942
#106228352
#106225992
#106225642
#106225572
#106225552
#106222722
#106222622
#256211