Finite Group Databasebeta

← #13073628

Subgroups — #13073628

Order 1408.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×#66931C212yesmaximal
2C11×#380C211yesmaximal, characteristic
3C4×C22⋊Dic11C211yesmaximal, characteristic
4C2×C11⋊#95C211yesmaximal, characteristic
5#10622597C212yesmaximal, complemented
6#10622592C212yesmaximal, complemented
7#10622559C212yesmaximal
8#10622260C212yesmaximal, complemented
9#10622259C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C22×Dic22C2212yes—
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2212yes—
23#66931—28no—
24C11×#95C2211yescharacteristic
25C11×#95C2211yescharacteristic
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C24×C11C2311yescharacteristic
33C22×C4×C11—42no—
34C22×C4×C11Q814yescomplemented
35C22×C4×C11C2312yes—
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×Dic11—24no—
40C22×Dic11—24no—
41C22×Dic11—42no—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C2×Dic22—24no—
47C2×Dic22—24no—
48C2×Dic22—42no—
49C11×C4⋊C4—42no—
50C11×C22⋊C4—24no—
51C22⋊Dic11D414yes—
52C22⋊Dic11Q814yescomplemented
53C4⋊Dic11—24no—
54Dic11⋊C4—24no—
55Dic11⋊C4—24no—
56Dic11⋊C4—24no—
57Dic11⋊C4—42no—
58C4×Dic11—42no—
59#2549—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—22no—
62C23×C11C2×D412yes—
63C23×C11C2×Q812yes—
64C23×C11C2×Q812yes—
65C23×C11C2411yescharacteristic
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—44no—
75C2×C4×C11C2×Q812yes—
76C2×C4×C11C2×Q812yes—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—48no—
87C2×Dic11C2×D414yes—
88C2×Dic11C2×Q814yes—
89C2×Dic11#4114yes—
90Dic22—48no—
91C2×C22⋊Q8—112no—
92#398—112no—
93#395—112no—
94#391—112no—
95#389—112no—
96#385—112no—
97#380D1111yescharacteristic
98C4×C22⋊C4—111no—
99C2×#95—111no—
100C22×C11—22no—
101C22×C11—22no—
102C22×C11—24no—
103C22×C11—24no—
104C22×C11C4⋊Q814yes—
105C22×C11C22×D411yescharacteristic
106C22×C11C22×Q811yescharacteristic
107C22×C11C22×Q811yescharacteristic
108C22×C11C2×#4112yes—
109C22×C11H(5,𝔽2)12yes—
110C4×C11—22no—
111C4×C11—22no—
112C4×C11—42no—
113C4×C11—42no—
114Dic11—24no—
115Dic11—24no—
116Dic11—24no—
117Dic11—42no—
118C22×Q8—112no—
119C23×C4—112no—
120C23×C4C2×D1111yescharacteristic
121C22⋊Q8—228no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4—112no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4C2×D1112yes—
128C2×C22⋊C4—111no—
129C2×C22⋊C4—111no—
130C2×C22⋊C4C2×D1112yes—
131C2×C42—112no—
132#95—112no—
133#95—111no—
134#95—111no—
135#95—112no—
136#95—112no—
137#95—112no—
138#95C2×D1111yescharacteristic
139#95C2×D1111yescharacteristic
140C2×C11—24no—
141C2×C11C2×C4⋊Q811yescharacteristic
142C2×C11#53311yescharacteristic
143C2×C11#54311yescharacteristic
144C2×C11#54612yes—
145C2×C11#55412yes—
146C24C22×D1111yescharacteristic
147C2×Q8—224no—
148C2×Q8—224no—
149C2×Q8—442no—
150C22×C4—42no—
151C22×C4—112no—
152C22×C4—112no—
153C22×C4—112no—
154C22×C4—112no—
155C22×C4—224no—
156C22×C4—224no—
157C22×C4—442no—
158C22×C4Dic2214yescomplemented
159C22×C4C22×D1112yes—
160C22×C4C22×D1112yes—
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1111yescharacteristic
163C4⋊C4—42no—
164C4⋊C4—224no—
165C4⋊C4—224no—
166C4⋊C4—224no—
167C4⋊C4—224no—
168C4⋊C4—442no—
169C22⋊C4—24no—
170C22⋊C4—114no—
171C22⋊C4—114no—
172C42—442no—
173C11#254911yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23C2×Dic2212yes—
177C23D4×D1112yes—
178C23Q8×D1112yes—
179C23C23×D1111yescharacteristic
180Q8—448no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—114no—
191C2×C4—114no—
192C2×C4—114no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—448no—
203C2×C4C2×Dic2212yes—
204C2×C4C2×Dic2212yes—
205C22—22no—
206C22—22no—
207C22—24no—
208C22—24no—
209C22#6694114yes—
210C22C22×Dic2211yescharacteristic
211C22C2×D4×D1111yescharacteristic
212C22#6703712yes—
213C22C2×Q8×D1111yescharacteristic
214C22#41×D1112yes—
215C4—22no—
216C4—22no—
217C4—42no—
218C4—42no—
219C4—224no—
220C4—224no—
221C4—224no—
222C4—442no—
223C2—24no—
224C2#1062301411yescharacteristic
225C2C2×#6694111yescharacteristic
226C2#1062304811yescharacteristic
227C2#1062314112yes—
228C2#1062316712yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC24×C11C23
hypercenter#380D11
hypocenterC11#2549
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
5. #10622597C2semidirect
6. #10622592C2semidirect
8. #10622260C2semidirect
9. #10622259C2semidirect
34. C22×C4×C11Q8semidirect
52. C22⋊Dic11Q8semidirect
158. C22×C4Dic22semidirect
173. C11#2549semidirect

Maximal subgroups

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

subgroupindex
C2×#669312
C11×#3802
C4×C22⋊Dic112
C2×C11⋊#952
#106225972
#106225922
#106225592
#106222602
#106222592
#254911