Finite Group Databasebeta

← #13072241

Subgroups — #13072241

Order 1408.

836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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×#4343C211yesmaximal, characteristic
2C2×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C2×#67000C211yesmaximal, characteristic, complemented
4C2×#66999C211yesmaximal, characteristic, complemented
5#10622843C211yesmaximal, characteristic, complemented
6#10622604C214yesmaximal, complemented
7#10622602C214yesmaximal, complemented
8#10622552C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12C2×#4343—24no—
13C2×#4343—24no—
14C2×#4343—24no—
15C22×D44C2212yes—
16C22×D44C2211yescharacteristic
17C22×C4×D11C2212yes—
18C22×C4×D11C2211yescharacteristic
19C11×C4⋊Q8—24no—
20C2×C11×C4⋊C4C2214yes—
21C2×C42×C11C2211yescharacteristic
22#67000—24no—
23#66999—24no—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2214yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2214yes—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31C11⋊#95C2212yes—
32C11⋊#95C2214yes—
33C23×D11C2312yes—
34C23×D11C2311yescharacteristic
35C2×Q8×C11—22no—
36C2×Q8×C11—22no—
37C2×Q8×C11—22no—
38C2×Q8×C11—22no—
39C2×Q8×C11—22no—
40C2×Q8×C11D414yes—
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2311yescharacteristic
48#4343—232no—
49C2×D44—24no—
50C2×D44—24no—
51C2×D44—22no—
52C2×D44—24no—
53C2×D44—22no—
54C2×D44D414yes—
55C2×C4×D11—24no—
56C2×C4×D11—24no—
57C2×C4×D11—22no—
58C2×C4×D11—24no—
59C2×C4×D11—22no—
60C2×C4×D11D414yes—
61C11×C4⋊C4—28no—
62C42×C11—22no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—28no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—28no—
67C4⋊Dic11—22no—
68Dic11⋊C4—24no—
69C4×Dic11—22no—
70#2432—111nomaximal, Sylow
71C23×C11C2411yescharacteristic
72C22×D11—22no—
73C22×D11—21no—
74C22×D11—22no—
75C22×D11—21no—
76C22×D11—22no—
77C22×D11—24no—
78C22×D11—22no—
79C22×D11—24no—
80C22×D11C2×D414yes—
81C22×D11C2×D412yes—
82Q8×C11—28no—
83Q8×C11—44no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D412yes—
93C2×C4×C11C2×D414yes—
94C2×C4×C11C2×D412yes—
95C2×C4×C11#4114yescomplemented
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—24no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11C2×D412yes—
104D44—216no—
105D44—28no—
106C4×D11—216no—
107C4×D11—28no—
108C22×#41—111no—
109C2×C4⋊Q8D1111yescharacteristic, complemented
110C2×#124—111no—
111C2×C22⋊Q8—111no—
112#394—114no—
113#391—111no—
114#390—111no—
115#385—114no—
116C4×C22⋊C4—111no—
117C22×C11C22×D411yescharacteristic
118C22×C11C22×D411yescharacteristic
119C22×C11C22×D411yescharacteristic
120C22×C11C2×#4112yes—
121C22×C112−1+412yes—
122C2×D11—24no—
123C2×D11—22no—
124C2×D11—22no—
125C2×D11—22no—
126C2×D11—28no—
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—44no—
132C4×C11—24no—
133C4×C11—24no—
134C4×C11—42no—
135C4×C11#12014yes—
136Dic11—22no—
137Dic11—42no—
138Dic11—42no—
139C2×#41—224no—
140C2×#41—224no—
141C2×#41—224no—
142C22×Q8C2×D1111yescharacteristic
143C22×Q8C2×D1111yescharacteristic
144C22×D4—111no—
145C22×D4—112no—
146C23×C4—111no—
147C23×C4—112no—
148C4⋊Q8—24no—
149#124—224no—
150C22⋊Q8—224no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—111no—
153C2×C4⋊C4C2×D1114yes—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—114no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—114no—
158C2×C42—111no—
159C2×C42C2×D1111yescharacteristic
160#95—112no—
161#95—114no—
162C2×C11C2×#12011yescharacteristic
163C2×C11#53211yescharacteristic
164C2×C11#53611yescharacteristic
165C2×C11#54712yes—
166C2×C11#54812yes—
167D11—42no—
168D11—44no—
169C24—111no—
170C24—112no—
171#41—2232no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8C22⋊D1114yes—
178C2×D4—114no—
179C2×D4—224no—
180C2×D4—224no—
181C2×D4—222no—
182C2×D4—224no—
183C2×D4—222no—
184C22×C4—111no—
185C22×C4—114no—
186C22×C4—112no—
187C22×C4—112no—
188C22×C4—224no—
189C22×C4—224no—
190C22×C4—222no—
191C22×C4—224no—
192C22×C4—222no—
193C22×C4C22×D1112yes—
194C22×C4C22×D1112yes—
195C22×C4C22×D1112yes—
196C22×C4C22×D1111yescharacteristic
197C4⋊C4—28no—
198C4⋊C4—224no—
199C4⋊C4—222no—
200C22⋊C4—224no—
201C22⋊C4—228no—
202C22⋊C4—224no—
203C22⋊C4—228no—
204C42—22no—
205C42—222no—
206C11#243211yescharacteristic, complemented, Sylow
207C23—112no—
208C23—114no—
209C23—222no—
210C23—221no—
211C23—222no—
212C23—224no—
213C23—222no—
214C23—224no—
215C23—222no—
216C23—221no—
217C23C23×D1111yescharacteristic
218Q8—28no—
219Q8—44no—
220D4—2216no—
221D4—228no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—112no—
230C2×C4—2216no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—228no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—224no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4D4×D1112yes—
240C2×C4D4×D1112yes—
241C2×C4#434314yescomplemented
242C2×C4C2×C22⋊D1114yes—
243C2×C4C2×C22⋊D1112yes—
244C22—222no—
245C22—222no—
246C22—228no—
247C22—224no—
248C22—222no—
249C22—442no—
250C22—442no—
251C22—442no—
252C22—442no—
253C22—444no—
254C22C2×D4×D1111yescharacteristic
255C22C2×D4×D1111yescharacteristic
256C22C2×#434312yes—
257C22#6704012yes—
258C22C22×C22⋊D1111yescharacteristic
259C4—24no—
260C4—24no—
261C4—42no—
262C4—222no—
263C4—442no—
264C4—442no—
265C4#6699014yes—
266C2—442no—
267C2—444no—
268C2#1062325511yescharacteristic
269C2#1062325611yescharacteristic
270C2#1062325712yes—
271C2C2×#6699011yescharacteristic
272C2#1062334812yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C4⋊Q8C2
prime radicalC22×#4343C2
hypercenterC2×C4⋊Q8D11
hypocenterC11#2432
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C11×C4⋊Q8C2semidirect
3. C2×#67000C2semidirect
4. C2×#66999C2semidirect
5. #10622843C2semidirect
6. #10622604C2semidirect
7. #10622602C2semidirect
8. #10622552C2semidirect
9. C4×(C2×D11)⋊C4C2semidirect
95. C2×C4×C11#41semidirect
109. C2×C4⋊Q8D11semidirect
206. C11#2432semidirect
241. C2×C4#4343semidirect

Maximal subgroups

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

subgroupindex
C22×#43432
C2×C11×C4⋊Q82
C2×#670002
C2×#669992
#106228432
#106226042
#106226022
#106225522
C4×(C2×D11)⋊C42
#243211