Finite Group Databasebeta

← #13081668

Subgroups — #13081668

Order 1408.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623244C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3C11×#460C211yesmaximal, characteristic
4#10622780C212yesmaximal, complemented
5#10622775C212yesmaximal, complemented
6#10622689C211yesmaximal, characteristic
7C4×#4326C211yesmaximal, characteristic, complemented
8#10622462C211yesmaximal, characteristic, complemented
9#10622444C211yesmaximal, characteristic, complemented
10#10622380C212yesmaximal, complemented
11#10622370C212yesmaximal, complemented
12C2×C11×SD16C2212yes—
13C11×#127C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15#66997C2212yes—
16C2×#4326C2211yescharacteristic
17#66989—21no—
18#66989C2212yes—
19#66988—22no—
20D4×Dic11—21no—
21D4×Dic11C2212yes—
22C2×#4324C2212yes—
23C2×#4324C2212yes—
24C2×Dic44C2212yes—
25#66942—22no—
26#66940C2212yes—
27#66923—21no—
28#66922C2211yescharacteristic
29C4×Dic22—21no—
30C4×Dic22C2211yescharacteristic
31C4×Dic22C2211yescharacteristic
32C11×C4⋊C8C2211yescharacteristic
33C11×#102C2212yes—
34#66899C2211yescharacteristic
35#66880C2212yes—
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66874C2211yescharacteristic
39#66871C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11C2311yescharacteristic
42C2×D4×C11—21no—
43C2×D4×C11—21no—
44C2×D4×C11C2312yes—
45C22×Dic11—22no—
46C2×Dic22D411yescharacteristic
47C2×Dic22C2311yescharacteristic
48C2×Dic22C2312yes—
49C11×SD16—42no—
50C2×C8×C11C2312yes—
51C11×C4⋊C4—21no—
52C11×C4⋊C4C2311yescharacteristic
53C42×C11—21no—
54C42×C11C2311yescharacteristic
55C22⋊Dic11—22no—
56C22⋊Dic11—22no—
57C22⋊Dic11—22no—
58#4326—22no—
59#4324—24no—
60#4324—42no—
61C4⋊Dic11—21no—
62C4⋊Dic11—21no—
63C4⋊Dic11D411yescharacteristic
64C4⋊Dic11C2311yescharacteristic
65Dic11⋊C4—22no—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—21no—
69Dic11⋊C4D412yes—
70C4×Dic11—22no—
71C4×Dic11—21no—
72C4×Dic11C2312yes—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75Dic44—42no—
76#3400—111nomaximal, Sylow
77C23×C11—22no—
78Q8×C11—21no—
79Q8×C11—21no—
80D4×C11—22no—
81D4×C11—22no—
82D4×C11—42no—
83D4×C11—81no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2411yescharacteristic
89C2×Dic11—22no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—82no—
93C2×Dic11C2×D412yes—
94C2×Dic11C2×D412yes—
95Dic22—22no—
96Dic22—22no—
97Dic22—21no—
98Dic22—21no—
99Dic22—22no—
100C8×C11—22no—
101C11⋊C8—21no—
102C11⋊C8#4112yes—
103#559—111no—
104#557—111no—
105#497—112no—
106#492—111no—
107#464—112no—
108#462—111no—
109#461—112no—
110#460D1111yescharacteristic
111#446—111no—
112#440—112no—
113C4×Q16—111no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11—42no—
117C22×C11C22×D411yescharacteristic
118C4×C11—21no—
119C4×C11—41no—
120C4×C11—41no—
121C4×C11#13712yes—
122C4×C11C2×#4111yescharacteristic
123C4×C11H(5,𝔽2)11yescharacteristic
124Dic11—22no—
125Dic11—22no—
126Dic11—42no—
127Dic11—41no—
128Dic11—41no—
129C2×Q16—111no—
130C2×Q16—112no—
131C2×SD16—112no—
132C2×SD16—112no—
133C2×SD16C2×D1112yes—
134C4⋊Q8—112no—
135C4⋊Q8—111no—
136#127C2×D1111yescharacteristic
137#125—221no—
138#125—222no—
139#124—112no—
140#124—221no—
141#123—222no—
142C4×Q8—111no—
143C4×Q8—112no—
144C4×Q8—111no—
145C4×Q8—221no—
146C4×Q8C2×D1111yescharacteristic
147C4×D4—112no—
148C4×D4—221no—
149#107—111no—
150C4⋊C8—112no—
151C4⋊C8C2×D1111yescharacteristic
152#103—111no—
153#103—112no—
154#103—111no—
155#102C2×D1112yes—
156#97—112no—
157C4×C8—111no—
158C2×C11—82no—
159C2×C11#55011yescharacteristic
160C2×C11C2×#13711yescharacteristic
161C2×C11#57711yescharacteristic
162C2×Q8—111no—
163C2×Q8—111no—
164C2×Q8—112no—
165C2×Q8C22×D1111yescharacteristic
166C2×D4—21no—
167C2×D4—21no—
168C2×D4C22×D1112yes—
169C22×C4—222no—
170Q16—222no—
171Q16—442no—
172SD16—42no—
173SD16—224no—
174SD16—442no—
175C2×C8—111no—
176C2×C8—111no—
177C2×C8C22×D1112yes—
178C4⋊C4—21no—
179C4⋊C4—111no—
180C4⋊C4—112no—
181C4⋊C4—111no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—222no—
185C4⋊C4—221no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C4⋊C4C22×D1111yescharacteristic
189C22⋊C4—222no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C42—21no—
193C42—112no—
194C42—222no—
195C42—221no—
196C42C22×D1111yescharacteristic
197C11#340011yescharacteristic, complemented, Sylow
198C23—22no—
199Q8—21no—
200Q8—21no—
201Q8—222no—
202Q8—222no—
203Q8—221no—
204Q8—222no—
205Q8—221no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—112no—
213C2×C4—112no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—222no—
217C2×C4—882no—
218C2×C4D4×D1111yescharacteristic
219C2×C4D4×D1111yescharacteristic
220C2×C4C23×D1111yescharacteristic
221C8—22no—
222C8—112no—
223C8—221no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22C2×D4×D1111yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—222no—
232C4—222no—
233C4—441no—
234C4—441no—
235C4—442no—
236C4#6696812yes—
237C4#6703711yescharacteristic
238C4#41×D1111yescharacteristic
239C2—82no—
240C2#1062313011yescharacteristic
241C2C2×#6696811yescharacteristic
242C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#460C2
socleC22×C11C22×D4
prime radicalC11×#127C22
hypercenter#460D11
hypocenterC11#3400
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #10623098C2semidirect
4. #10622780C2semidirect
5. #10622775C2semidirect
7. C4×#4326C2semidirect
8. #10622462C2semidirect
9. #10622444C2semidirect
10. #10622380C2semidirect
11. #10622370C2semidirect
197. C11#3400semidirect

Maximal subgroups

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

subgroupindex
#106232442
#106230982
C11×#4602
#106227802
#106227752
#106226892
C4×#43262
#106224622
#106224442
#106223802
#106223702
#340011