Finite Group Databasebeta

← #13072240

Subgroups — #13072240

Order 1408.

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

normal subgroups only

This group has 836 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×#66997C211yesmaximal, characteristic, complemented
3C2×#66989C211yesmaximal, characteristic, complemented
4C2×#66977C211yesmaximal, characteristic, complemented
5#10622843C211yesmaximal, characteristic, complemented
6#10622835C214yesmaximal, complemented
7#10622834C211yesmaximal, characteristic, complemented
8#10622823C214yesmaximal, complemented
9C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
10C2×C11×#41—24no—
11C2×C11×#41—24no—
12C2×C11×#41—24no—
13C22×Q8×C11C2211yescharacteristic
14C22×D4×C11C2212yes—
15C22×D4×C11C2211yescharacteristic
16C23×C4×C11C2212yes—
17C23×C4×C11C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2214yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2214yes—
23#66997—24no—
24#66989—24no—
25C2×C4⋊Dic11C2211yescharacteristic
26#66977—24no—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2214yes—
29C2×C4×Dic11C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C11⋊#95C2212yes—
32C11⋊#95C2214yes—
33C24×C11C2312yes—
34C24×C11C2311yescharacteristic
35C11×#41—232no—
36C2×Q8×C11—22no—
37C2×Q8×C11—22no—
38C2×Q8×C11D414yes—
39C2×D4×C11—24no—
40C2×D4×C11—24no—
41C2×D4×C11—24no—
42C2×D4×C11—22no—
43C2×D4×C11—22no—
44C2×D4×C11D414yes—
45C22×C4×C11—24no—
46C22×C4×C11—24no—
47C22×C4×C11—24no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11D414yes—
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2312yes—
53C22×C4×C11C2311yescharacteristic
54C22×Dic11C2312yes—
55C22×Dic11C2312yes—
56C22×Dic11C2312yes—
57C22×Dic11C2312yes—
58C2×Dic22—22no—
59C2×Dic22—22no—
60C2×Dic22—22no—
61C22⋊Dic11—24no—
62C22⋊Dic11—28no—
63C22⋊Dic11—24no—
64C22⋊Dic11—28no—
65C4⋊Dic11—22no—
66Dic11⋊C4—24no—
67Dic11⋊C4—28no—
68C4×Dic11—22no—
69C4×Dic11—22no—
70#2432—111nomaximal, Sylow
71C23×C11—22no—
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11—24no—
77C23×C11—22no—
78C23×C11—24no—
79C23×C11C2×D414yes—
80C23×C11C2×D412yes—
81C23×C11C2411yescharacteristic
82Q8×C11—28no—
83D4×C11—216no—
84D4×C11—28no—
85C2×C4×C11—216no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—28no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D414yes—
93C2×C4×C11C2×D412yes—
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×D412yes—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—24no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11#4114yescomplemented
107Dic22—44no—
108C22×#41D1111yescharacteristic
109C2×C4⋊Q8—111no—
110C2×#124—111no—
111C2×C22⋊Q8—111no—
112#394—114no—
113#391—111no—
114#390—111no—
115#385—114no—
116C4×C22⋊C4—111no—
117C22×C11—24no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11—28no—
122C22×C11—42no—
123C22×C11—42no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—44no—
127C22×C11C22×D411yescharacteristic
128C22×C11C22×D411yescharacteristic
129C22×C11C22×D411yescharacteristic
130C22×C11C2×#4112yes—
131C22×C112−1+412yes—
132C4×C11—22no—
133C4×C11—24no—
134C4×C11#12014yes—
135Dic11—24no—
136Dic11—42no—
137Dic11—42no—
138Dic11—42no—
139C2×#41—24no—
140C2×#41—24no—
141C2×#41—24no—
142C22×Q8—111no—
143C22×Q8C2×D1111yescharacteristic
144C22×D4C2×D1112yes—
145C22×D4C2×D1111yescharacteristic
146C23×C4C2×D1112yes—
147C23×C4C2×D1111yescharacteristic
148C4⋊Q8—224no—
149#124—224no—
150C22⋊Q8—224no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—111no—
153C2×C4⋊C4—114no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—114no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—114no—
158C2×C42—111no—
159C2×C42—111no—
160#95—112no—
161#95—114no—
162C2×C11—42no—
163C2×C11—44no—
164C2×C11C2×#12011yescharacteristic
165C2×C11#53211yescharacteristic
166C2×C11#53611yescharacteristic
167C2×C11#54712yes—
168C2×C11#54812yes—
169C24C22×D1112yes—
170C24C22×D1111yescharacteristic
171#41—232no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—222no—
175C2×Q8—222no—
176C2×Q8—222no—
177C2×Q8C22⋊D1114yes—
178C2×D4—24no—
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4C22⋊D1114yes—
184C22×C4—24no—
185C22×C4—24no—
186C22×C4—24no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—112no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—112no—
193C22×C4C22⋊D1114yes—
194C22×C4C22×D1111yescharacteristic
195C22×C4C22×D1112yes—
196C22×C4C22×D1111yescharacteristic
197C4⋊C4—224no—
198C4⋊C4—222no—
199C4⋊C4—228no—
200C22⋊C4—224no—
201C22⋊C4—228no—
202C22⋊C4—224no—
203C22⋊C4—228no—
204C42—222no—
205C42—222no—
206C11#243211yescharacteristic, complemented, Sylow
207C23—24no—
208C23—22no—
209C23—24no—
210C23—22no—
211C23—21no—
212C23—22no—
213C23—22no—
214C23—21no—
215C23C2×C22⋊D1114yes—
216C23C2×C22⋊D1112yes—
217C23C23×D1111yescharacteristic
218Q8—28no—
219Q8—444no—
220D4—216no—
221D4—28no—
222C2×C4—216no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—28no—
228C2×C4—114no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—224no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4C2×C22⋊D1112yes—
240C2×C4C2×C22⋊D1114yes—
241C2×C4C2×C22⋊D1112yes—
242C2×C4C2×C22⋊D1112yes—
243C2×C4C2×C22⋊D1112yes—
244C22—28no—
245C22—22no—
246C22—22no—
247C22—24no—
248C22—22no—
249C22—42no—
250C22—42no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22#41×D1112yes—
255C22#6704312yes—
256C22C22×C22⋊D1111yescharacteristic
257C22C22×C22⋊D1111yescharacteristic
258C22C22×C22⋊D1111yescharacteristic
259C4—22no—
260C4—24no—
261C4—224no—
262C4—442no—
263C4—442no—
264C4—442no—
265C4#6700614yes—
266C2—44no—
267C2—42no—
268C2#1062335512yes—
269C2#1062335611yescharacteristic
270C2#1062336212yes—
271C2#1062336311yescharacteristic
272C2C2×#6700611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC22×C11×#41C2
hypercenterC22×#41D11
hypocenterC11#2432
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
2. C2×#66997C2semidirect
3. C2×#66989C2semidirect
4. C2×#66977C2semidirect
5. #10622843C2semidirect
6. #10622835C2semidirect
7. #10622834C2semidirect
8. #10622823C2semidirect
9. C4×C22⋊Dic11C2semidirect
106. C2×Dic11#41semidirect
206. C11#2432semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#412
C2×#669972
C2×#669892
C2×#669772
#106228432
#106228352
#106228342
#106228232
C4×C22⋊Dic112
#243211