Finite Group Databasebeta

← #13072933

Subgroups — #13072933

Order 1408.

584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 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×C4×D4×C11C211yesmaximal, characteristic
2C22×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#10622833C212yesmaximal
4#10622825C212yesmaximal, complemented
5#10622825C211yesmaximal, characteristic, complemented
6#10622599C212yesmaximal, complemented
7#10622562C212yesmaximal, complemented
8#10622559C212yesmaximal, complemented
9#10622541C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C23×C4×C11C2211yescharacteristic
13C23×Dic11C2212yes—
14C4×D4×C11—24no—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C42×C11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2214yes—
21C2×C4⋊Dic11—24no—
22C2×C4⋊Dic11C2212yes—
23C2×C4⋊Dic11C2212yes—
24C2×C4⋊Dic11C2212yes—
25C2×Dic11⋊C4C2214yes—
26C11⋊#95C2214yes—
27C11⋊#95C2214yes—
28C11⋊#95C2212yes—
29C24×C11C2311yescharacteristic
30C24×C11C2311yescharacteristic
31C2×D4×C11—22no—
32C2×D4×C11—22no—
33C2×D4×C11Q814yes—
34C22×C4×C11—24no—
35C22×C4×C11—22no—
36C22×C4×C11—24no—
37C22×C4×C11D414yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×Dic11—24no—
44C22×Dic11—44no—
45C22×Dic11C2314yes—
46C22×Dic11C2314yes—
47C11×C4⋊C4—22no—
48C11×C22⋊C4—22no—
49C11×C22⋊C4—22no—
50C42×C11—22no—
51C22⋊Dic11—24no—
52C22⋊Dic11—44no—
53C4⋊Dic11—24no—
54C4⋊Dic11—24no—
55C4⋊Dic11—24no—
56Dic11⋊C4—44no—
57#2487—111nomaximal, Sylow
58C23×C11—22no—
59C23×C11—22no—
60C23×C11—21no—
61C23×C11—22no—
62C23×C11—21no—
63C23×C11—22no—
64C23×C11C2×D412yes—
65C23×C11C2×Q812yes—
66C23×C11C2×Q812yes—
67C23×C11#4112yes—
68C23×C11C2411yescharacteristic
69D4×C11—28no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—21no—
73C2×C4×C11—28no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—44no—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×Q812yes—
82C2×C4×C11#4114yes—
83C2×Dic11—24no—
84C2×Dic11—24no—
85C2×Dic11—24no—
86C2×Dic11—24no—
87C2×Dic11—24no—
88C2×Dic11—24no—
89C2×Dic11—48no—
90C2×C4×D4D1111yescharacteristic
91C22×C4⋊C4—111no—
92#400—112no—
93#399—112no—
94#389—112no—
95#386—112no—
96#385—112no—
97#380—112no—
98#380—111no—
99C22×C11—22no—
100C22×C11—22no—
101C22×C11—24no—
102C22×C11—24no—
103C22×C11—22no—
104C22×C11—24no—
105C22×C11—41no—
106C22×C11—41no—
107C22×C11—42no—
108C22×C11C22⋊Q814yes—
109C22×C11C22×D411yescharacteristic
110C22×C11C22×Q811yescharacteristic
111C22×C11C2×#4111yescharacteristic
112C22×C11C2×#4112yes—
113C22×C11H(5,𝔽2)12yes—
114C4×C11—22no—
115C4×C11—22no—
116C4×C11—41no—
117C4×C11—41no—
118C4×C11#12314yes—
119Dic11—44no—
120Dic11—44no—
121C22×D4C2×D1111yescharacteristic
122C23×C4—112no—
123C23×C4C2×D1111yescharacteristic
124C23×C4C2×D1111yescharacteristic
125C4×D4—24no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4—114no—
130C2×C4⋊C4—224no—
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C22⋊C4—112no—
133C2×C22⋊C4—114no—
134C2×C22⋊C4C2×D1111yescharacteristic
135C2×C22⋊C4C2×D1111yescharacteristic
136C2×C42C2×D1111yescharacteristic
137#95—114no—
138#95—112no—
139#95—114no—
140C2×C11—24no—
141C2×C11—42no—
142C2×C11C2×C22⋊Q811yescharacteristic
143C2×C11C2×#12311yescharacteristic
144C2×C11#53511yescharacteristic
145C2×C11#55312yes—
146C2×C11#55412yes—
147C24C22×D1111yescharacteristic
148C24C22×D1111yescharacteristic
149C2×D4—22no—
150C2×D4—22no—
151C2×D4Dic2214yes—
152C22×C4—24no—
153C22×C4—24no—
154C22×C4—22no—
155C22×C4—114no—
156C22×C4—114no—
157C22×C4—224no—
158C22×C4—444no—
159C22×C4C22⋊D1114yes—
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1111yescharacteristic
163C22×C4C22×D1111yescharacteristic
164C22×C4C22×D1111yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—224no—
167C4⋊C4—224no—
168C4⋊C4—224no—
169C4⋊C4—444no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—224no—
173C22⋊C4—444no—
174C42—22no—
175C11#248711yescharacteristic, complemented, Sylow
176C23—22no—
177C23—22no—
178C23—21no—
179C23—22no—
180C23—22no—
181C23—21no—
182C23C2×Dic2212yes—
183C23C2×Dic2212yes—
184C23#433912yes—
185C23C2×C22⋊D1112yes—
186C23C23×D1111yescharacteristic
187D4—28no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—44no—
197C2×C4—224no—
198C2×C4—224no—
199C2×C4—224no—
200C2×C4—224no—
201C2×C4—224no—
202C2×C4—224no—
203C2×C4—448no—
204C2×C4C2×Dic2212yes—
205C2×C4#434114yes—
206C2×C4C2×C22⋊D1112yes—
207C2×C4C2×C22⋊D1112yes—
208C22—22no—
209C22—24no—
210C22—24no—
211C22—22no—
212C22—22no—
213C22—24no—
214C22—41no—
215C22—42no—
216C22—41no—
217C22#6697714yes—
218C22C22×Dic2211yescharacteristic
219C22C2×#433911yescharacteristic
220C22C2×#434112yes—
221C22#6704212yes—
222C22C22×C22⋊D1111yescharacteristic
223C4—22no—
224C4—22no—
225C4—41no—
226C4—41no—
227C4—444no—
228C4—444no—
229C4#6698814yes—
230C2—24no—
231C2—42no—
232C2#1062307412yes—
233C2#1062309612yes—
234C2C2×#6697711yescharacteristic
235C2C2×#6698811yescharacteristic
236C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radicalC22×D4×C11C22
hypercenterC2×C4×D4D11
hypocenterC11#2487
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic11C2semidirect
4. #10622825C2semidirect
5. #10622825C2semidirect
6. #10622599C2semidirect
7. #10622562C2semidirect
8. #10622559C2semidirect
9. #10622541C2semidirect
175. C11#2487semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C22×C4⋊Dic112
#106228332
#106228252
#106225992
#106225622
#106225592
#106225412
#248711