Finite Group Databasebeta

← #13071947

Subgroups — #13071947

Order 1408.

864 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 185 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
1C22×C11×#41C211yesmaximal, characteristic
2C2×#66988C212yesmaximal, complemented
3C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#10622842C212yesmaximal, complemented
5#10622835C212yesmaximal, complemented
6#10622833C212yesmaximal, complemented
7#10622824C211yesmaximal, characteristic, complemented
8#10622823C214yesmaximal, complemented
9C2×C11×#41—28no—
10C2×C11×#41—24no—
11C22×Q8×C11C2211yescharacteristic
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C23×C4×C11C2212yes—
15C23×C4×C11C2211yescharacteristic
16C23×Dic11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C2×C22⋊Dic11C2214yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2214yes—
21#66988—28no—
22C2×Dic11⋊C4—24no—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2214yes—
26C11⋊#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2212yes—
29C24×C11C2312yes—
30C24×C11C2311yescharacteristic
31C11×#41—232no—
32C2×Q8×C11—24no—
33C2×Q8×C11—22no—
34C2×D4×C11—24no—
35C2×D4×C11—24no—
36C2×D4×C11—24no—
37C2×D4×C11—22no—
38C2×D4×C11D418yes—
39C22×C4×C11—24no—
40C22×C4×C11—24no—
41C22×C4×C11—24no—
42C22×C4×C11—24no—
43C22×C4×C11D414yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—24no—
48C22×Dic11—22no—
49C22×Dic11—22no—
50C22×Dic11—24no—
51C22×Dic11C2314yes—
52C22×Dic11C2312yes—
53C22×Dic11C2312yes—
54C22⋊Dic11—28no—
55C22⋊Dic11—28no—
56C22⋊Dic11—24no—
57Dic11⋊C4—24no—
58Dic11⋊C4—24no—
59Dic11⋊C4—28no—
60#2406—111nomaximal, Sylow
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—24no—
66C23×C11—24no—
67C23×C11C2×D414yes—
68C23×C11C2×D414yes—
69C23×C11C2×D412yes—
70C23×C11C2411yescharacteristic
71Q8×C11—28no—
72D4×C11—28no—
73D4×C11—216no—
74C2×C4×C11—216no—
75C2×C4×C11—28no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×D414yes—
82C2×C4×C11C2×D412yes—
83C2×Dic11—28no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—24no—
88C2×Dic11—24no—
89C2×Dic11—24no—
90C2×Dic11—24no—
91C2×Dic11—44no—
92C2×Dic11#4114yescomplemented
93C22×#41D1111yescharacteristic
94C2×#123—112no—
95C22×C4⋊C4—111no—
96#395—112no—
97#394—112no—
98#386—112no—
99#385—114no—
100#381—111no—
101C22×C11—22no—
102C22×C11—22no—
103C22×C11—28no—
104C22×C11—24no—
105C22×C11—28no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11—44no—
109C22×C11#12014yes—
110C22×C11C22×D411yescharacteristic
111C22×C11C22×D412yes—
112C22×C11C2×#4112yes—
113C22×C112−1+412yes—
114C4×C11—22no—
115C4×C11—24no—
116C4×C11—22no—
117Dic11—24no—
118Dic11—42no—
119Dic11—44no—
120C2×#41—28no—
121C2×#41—24no—
122C22×Q8C2×D1111yescharacteristic
123C22×D4C2×D1111yescharacteristic
124C22×D4C2×D1112yes—
125C23×C4—111no—
126C23×C4—111no—
127C23×C4C2×D1112yes—
128C23×C4C2×D1111yescharacteristic
129#123—228no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—114no—
133C2×C4⋊C4—224no—
134C2×C22⋊C4—112no—
135C2×C22⋊C4—114no—
136C2×C22⋊C4—114no—
137#95—112no—
138#95—112no—
139#95—114no—
140C2×C11—24no—
141C2×C11—44no—
142C2×C11C2×#12011yescharacteristic
143C2×C11#52511yescharacteristic
144C2×C11#53611yescharacteristic
145C2×C11#54714yes—
146C24C22×D1112yes—
147C24C22×D1111yescharacteristic
148#41—232no—
149C2×Q8—24no—
150C2×Q8—22no—
151C2×D4—24no—
152C2×D4—24no—
153C2×D4—24no—
154C2×D4—22no—
155C2×D4C22⋊D1118yes—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—112no—
161C22×C4—114no—
162C22×C4—112no—
163C22×C4—224no—
164C22×C4—222no—
165C22×C4—222no—
166C22×C4—224no—
167C22×C4C22⋊D1114yes—
168C22×C4C22×D1111yescharacteristic
169C22×C4C22×D1112yes—
170C22×C4C22×D1111yescharacteristic
171C4⋊C4—224no—
172C4⋊C4—224no—
173C4⋊C4—228no—
174C22⋊C4—228no—
175C22⋊C4—224no—
176C22⋊C4—228no—
177C11#240611yescharacteristic, complemented, Sylow
178C23—22no—
179C23—22no—
180C23—24no—
181C23—24no—
182C23—22no—
183C23—22no—
184C23C2×C22⋊D1114yes—
185C23C2×C22⋊D1114yes—
186C23C2×C22⋊D1112yes—
187C23C23×D1111yescharacteristic
188Q8—28no—
189D4—28no—
190D4—216no—
191C2×C4—216no—
192C2×C4—28no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—114no—
198C2×C4—228no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—224no—
202C2×C4—224no—
203C2×C4—224no—
204C2×C4—224no—
205C2×C4—222no—
206C2×C4—444no—
207C2×C4C2×C22⋊D1112yes—
208C2×C4C2×C22⋊D1114yes—
209C2×C4C2×C22⋊D1112yes—
210C22—28no—
211C22—22no—
212C22—22no—
213C22—28no—
214C22—24no—
215C22—44no—
216C22—42no—
217C22—42no—
218C22#6700614yes—
219C22#41×D1112yes—
220C22#6704312yes—
221C22C22×C22⋊D1112yes—
222C22C22×C22⋊D1111yescharacteristic
223C4—22no—
224C4—24no—
225C4—22no—
226C4—224no—
227C4—444no—
228C4—442no—
229C2—24no—
230C2—44no—
231C2#1062335514yes—
232C2#1062335611yescharacteristic
233C2#1062335911yescharacteristic
234C2C2×#6700611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC22×C11×#41C2
hypercenterC22×#41D11
hypocenterC11#2406
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
2. C2×#66988C2semidirect
3. C22×Dic11⋊C4C2semidirect
4. #10622842C2semidirect
5. #10622835C2semidirect
6. #10622833C2semidirect
7. #10622824C2semidirect
8. #10622823C2semidirect
92. C2×Dic11#41semidirect
177. C11#2406semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#412
C2×#669882
C22×Dic11⋊C42
#106228422
#106228352
#106228332
#106228242
#106228232
#240611