Finite Group Databasebeta

← #13079786

Subgroups — #13079786

Order 1408.

334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#10623010C211yesmaximal, characteristic
2C2×#66923C211yesmaximal, characteristic, complemented
3C11×#431C211yesmaximal, characteristic, complemented
4#10622460C212yesmaximal, complemented
5#10622442C212yesmaximal, complemented
6#10622349C211yesmaximal, characteristic
7#10622348C211yesmaximal, characteristic
8#10622335C211yesmaximal, characteristic, complemented
9#10622334C211yesmaximal, characteristic, complemented
10#10622310C212yesmaximal, complemented
11#10622296C212yesmaximal, complemented
12C2×C42×C11C2211yescharacteristic
13#66983C2211yescharacteristic
14#66982—21no—
15C4×C22⋊D11—21no—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18#66977C2211yescharacteristic
19C2×Dic11⋊C4—21no—
20C2×Dic11⋊C4—21no—
21#66929—21no—
22#66928C2211yescharacteristic
23C4×D44C2211yescharacteristic
24#66925—21no—
25#66923—21no—
26#66923—21no—
27#66923C2212yes—
28#66923C2212yes—
29#66923C2211yescharacteristic
30C4×Dic22C2211yescharacteristic
31C11×C4⋊C8C2212yes—
32C11×C22⋊C8C2211yescharacteristic
33C11×C22⋊C8C2211yescharacteristic
34C4×C8×C11C2212yes—
35#66885C2212yes—
36#66885C2212yes—
37#66882C2212yes—
38#66882C2212yes—
39#66881C2212yes—
40#66881C2212yes—
41#66880C2212yes—
42#66880C2212yes—
43C22×C4×C11D411yescharacteristic
44C22×C4×C11D411yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—21no—
47C22×Dic11—21no—
48C22×Dic11—21no—
49C2×D44C2311yescharacteristic
50C2×C4×D11—21no—
51C2×Dic22C2311yescharacteristic
52C2×C8×C11C2312yes—
53C2×C8×C11C2312yes—
54C42×C11D411yescharacteristic
55C42×C11D411yescharacteristic
56C42×C11C2311yescharacteristic
57C42×C11C2311yescharacteristic
58C22⋊Dic11—21no—
59(C2×D11)⋊C4—21no—
60(C2×D11)⋊C4—21no—
61(C2×D11)⋊C4—21no—
62(C2×D11)⋊C4—21no—
63C4⋊Dic11—21no—
64C4⋊Dic11—21no—
65C4⋊Dic11C2312yes—
66C4⋊Dic11C2312yes—
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—21no—
70Dic11⋊C4—22no—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73Dic11⋊C4—22no—
74Dic11⋊C4—21no—
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77C4×Dic11—21no—
78#3232—111nomaximal, Sylow
79C23×C11C2×D411yescharacteristic
80C22×D11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—41no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C22⋊D11—42no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98D44—22no—
99C4×D11—42no—
100Dic22—22no—
101C8×C11—22no—
102C8×C11—22no—
103#529—111no—
104C2×#125—111no—
105#499—112no—
106#488—112no—
107#484—111no—
108#483—111no—
109#481—111no—
110#480—111no—
111#479—112no—
112#478—112no—
113#431D1111yescharacteristic, complemented
114C22×C11—21no—
115C22×C11—21no—
116C22×C11#13512yes—
117C22×C11C22×D411yescharacteristic
118C2×D11—41no—
119C2×D11—41no—
120C2×D11—41no—
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C112−1+412yes—
127Dic11—41no—
128Dic11—42no—
129Dic11—41no—
130Dic11—41no—
131Dic11—42no—
132#126—221no—
133#125—112no—
134#125—112no—
135#125—111no—
136#125—221no—
137#125—221no—
138#124—111no—
139#123—221no—
140C22⋊Q8—111no—
141#121—111no—
142C4×Q8—111no—
143C4×D4—111no—
144C4×D4—221no—
145#117—221no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4—221no—
150C2×C42C2×D1111yescharacteristic
151#107—112no—
152#107—112no—
153#106—112no—
154#106—112no—
155C4⋊C8C2×D1112yes—
156#103—112no—
157#103—112no—
158#102—112no—
159#102—112no—
160C22⋊C8C2×D1111yescharacteristic
161C22⋊C8C2×D1111yescharacteristic
162C4×C8C2×D1112yes—
163C2×C11—22no—
164C2×C11#53611yescharacteristic
165C2×C11C2×#13511yescharacteristic
166C2×C11#57511yescharacteristic
167D11—81no—
168C2×Q8—111no—
169C2×D4—111no—
170C2×D4—221no—
171C22×C4—221no—
172C22×C4—221no—
173C22×C4—221no—
174C22×C4D4411yescharacteristic
175C22×C4D4411yescharacteristic
176C22×C4C22×D1111yescharacteristic
177C2×C8C22×D1112yes—
178C2×C8C22×D1112yes—
179C4⋊C4—112no—
180C4⋊C4—112no—
181C4⋊C4—111no—
182C4⋊C4—111no—
183C4⋊C4—221no—
184C4⋊C4—221no—
185C4⋊C4—222no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C22⋊C4—221no—
194C22⋊C4—221no—
195C22⋊C4—221no—
196C22⋊C4—221no—
197C22⋊C4—221no—
198C42—221no—
199C42D4411yescharacteristic
200C42D4411yescharacteristic
201C42C22×D1111yescharacteristic
202C42C22×D1111yescharacteristic
203C11#323211yescharacteristic, complemented, Sylow
204C23—221no—
205C23C2×D4411yescharacteristic
206Q8—222no—
207D4—222no—
208D4—442no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—221no—
213C2×C4—221no—
214C2×C4—221no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—442no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4C2×D4411yescharacteristic
221C2×C4C2×D4411yescharacteristic
222C2×C4C2×D4411yescharacteristic
223C2×C4C2×D4411yescharacteristic
224C2×C4C2×D4411yescharacteristic
225C2×C4C23×D1111yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—441no—
231C22—441no—
232C22—441no—
233C22#6695712yes—
234C22C22×D4411yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—442no—
241C4—441no—
242C4—441no—
243C4—442no—
244C4—441no—
245C4#6704312yes—
246C2—22no—
247C2—881no—
248C2#1062305711yescharacteristic
249C2C2×#6695711yescharacteristic
250C2#1062327911yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#431C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#431D11
hypocenterC11#3232
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×#66923C2semidirect
3. C11×#431C2semidirect
4. #10622460C2semidirect
5. #10622442C2semidirect
8. #10622335C2semidirect
9. #10622334C2semidirect
10. #10622310C2semidirect
11. #10622296C2semidirect
113. #431D11semidirect
203. C11#3232semidirect

Maximal subgroups

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

subgroupindex
#106230102
C2×#669232
C11×#4312
#106224602
#106224422
#106223492
#106223482
#106223352
#106223342
#106223102
#106222962
#323211