Finite Group Databasebeta

← #13080912

Subgroups — #13080912

Order 1408.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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
1Q8×D44C211yesmaximal, characteristic, complemented
2#10623094C211yesmaximal, characteristic
3C4×C11×SD16C211yesmaximal, characteristic, complemented
4#10622783C212yesmaximal, complemented
5#10622634C211yesmaximal, characteristic, complemented
6#10622632C211yesmaximal, characteristic, complemented
7#10622480C212yesmaximal, complemented
8#10622415C212yesmaximal, complemented
9#10622393C212yesmaximal, complemented
10#10622301C211yesmaximal, characteristic, complemented
11#10622294C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2212yes—
13C2×C11×SD16C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15C4×D4×C11C2211yescharacteristic
16#66991C2212yes—
17C2×#4324C2212yes—
18#66983—21no—
19#66979—21no—
20C2×#4313C2212yes—
21#66950—22no—
22#66950C2212yes—
23#66945C2212yes—
24#66938—22no—
25C4×D44—21no—
26C4×D44C2211yescharacteristic
27#66922—21no—
28#66922C2211yescharacteristic
29#66922C2211yescharacteristic
30C11×#106C2211yescharacteristic
31C11×#103C2211yescharacteristic
32C11×#102C2211yescharacteristic
33C4×C8×C11C2211yescharacteristic
34#66899C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66880C2212yes—
37#66880C2212yes—
38#66874C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11C2311yescharacteristic
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C2×C22⋊D11—22no—
45Q8×D11—24no—
46Q8×D11—42no—
47C2×D44D411yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11C2312yes—
50C2×Dic22—22no—
51C2×Dic22—21no—
52C2×Dic22C2312yes—
53C11×SD16—22no—
54C2×C8×C11C2311yescharacteristic
55C2×C8×C11C2311yescharacteristic
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2311yescharacteristic
58C11×C4⋊C4C2311yescharacteristic
59C11×C22⋊C4—21no—
60C42×C11—21no—
61C42×C11C2311yescharacteristic
62C22⋊Dic11—22no—
63#4324—42no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4D412yes—
67C4⋊Dic11—22no—
68C4⋊Dic11—21no—
69C4⋊Dic11—21no—
70C4⋊Dic11—21no—
71C4⋊Dic11D411yescharacteristic
72C4⋊Dic11C2312yes—
73C4×Dic11—22no—
74C2×C11⋊C8C2312yes—
75#4313—42no—
76#3329—111nomaximal, Sylow
77C23×C11—21no—
78C22×D11C2×D412yes—
79Q8×C11—21no—
80Q8×C11#4112yes—
81D4×C11—21no—
82D4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—42no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C22⋊D11—82no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11C2×D412yes—
94D44—22no—
95C4×D11—22no—
96C4×D11—22no—
97C4×D11—44no—
98Dic22—22no—
99Dic22—22no—
100Dic22—44no—
101Dic22—81no—
102C8×C11—21no—
103C8×C11—21no—
104C11⋊C8—22no—
105#555—111no—
106D4×Q8—111no—
107#487—111no—
108#485—112no—
109#477—111no—
110#468—112no—
111#461—111no—
112#448—112no—
113C4×SD16D1111yescharacteristic, complemented
114#436—111no—
115#419—112no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11C22×D411yescharacteristic
120C2×D11—22no—
121C2×D11—22no—
122C2×D11—22no—
123C4×C11—22no—
124C4×C11—21no—
125C4×C11—41no—
126C4×C11—41no—
127C4×C11#13712yes—
128C4×C11C2×#4111yescharacteristic
129C4×C11H(5,𝔽2)11yescharacteristic
130Dic11—22no—
131Dic11—42no—
132Dic11—42no—
133C22×Q8—112no—
134C2×SD16—112no—
135C2×SD16C2×D1111yescharacteristic
136C2×M16—112no—
137C4⋊Q8—111no—
138C4⋊Q8—111no—
139C4⋊Q8—221no—
140#124—222no—
141C22⋊Q8—112no—
142C22⋊Q8—222no—
143#121—112no—
144#121—221no—
145C4×Q8C2×D1111yescharacteristic
146C4×D4—111no—
147C4×D4—221no—
148C4×D4C2×D1111yescharacteristic
149#117—112no—
150#117—221no—
151#107—112no—
152#106C2×D1111yescharacteristic
153C4⋊C8—111no—
154#103—112no—
155#103—112no—
156#103—112no—
157#103—112no—
158#103C2×D1111yescharacteristic
159#102C2×D1111yescharacteristic
160C22⋊C8—112no—
161C4×C8C2×D1111yescharacteristic
162C2×C11—81no—
163C2×C11#54611yescharacteristic
164C2×C11C2×#13711yescharacteristic
165C2×C11#57711yescharacteristic
166D11—42no—
167C2×Q8—112no—
168C2×Q8—222no—
169C2×Q8—221no—
170C2×Q8—224no—
171C2×Q8—442no—
172C2×Q8C22×D1111yescharacteristic
173C2×D4—111no—
174C2×D4—222no—
175C2×D4C22×D1111yescharacteristic
176C22×C4—21no—
177C22×C4—112no—
178C22×C4—222no—
179SD16—22no—
180SD16—442no—
181M16—442no—
182C2×C8—112no—
183C2×C8C22×D1111yescharacteristic
184C2×C8C22×D1111yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—111no—
187C4⋊C4—112no—
188C4⋊C4—222no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4C22×D1111yescharacteristic
193C4⋊C4C22×D1111yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—112no—
196C22⋊C4—222no—
197C22⋊C4—222no—
198C22⋊C4—222no—
199C42—21no—
200C42—222no—
201C42C22×D1111yescharacteristic
202C11#332911yescharacteristic, complemented, Sylow
203C23—21no—
204C23—112no—
205Q8—21no—
206Q8—222no—
207Q8—222no—
208Q8—444no—
209Q8—881no—
210Q8#433912yes—
211D4—21no—
212D4—21no—
213D4—222no—
214D4—882no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—112no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—444no—
225C2×C4D4×D1111yescharacteristic
226C2×C4D4×D1111yescharacteristic
227C2×C4C23×D1111yescharacteristic
228C8—21no—
229C8—21no—
230C8—222no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—222no—
235C22—222no—
236C22—222no—
237C22C2×D4×D1111yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—41no—
242C4—222no—
243C4—442no—
244C4—442no—
245C4#6696812yes—
246C4C2×#433911yescharacteristic
247C4#6704211yescharacteristic
248C2—81no—
249C2—442no—
250C2#1062308111yescharacteristic
251C2C2×#6696811yescharacteristic
252C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×SD16C2
socleC22×C11C22×D4
prime radical#10623094C2
hypercenterC4×SD16D11
hypocenterC11#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×D44C2semidirect
3. C4×C11×SD16C2semidirect
4. #10622783C2semidirect
5. #10622634C2semidirect
6. #10622632C2semidirect
7. #10622480C2semidirect
8. #10622415C2semidirect
9. #10622393C2semidirect
10. #10622301C2semidirect
11. #10622294C2semidirect
113. C4×SD16D11semidirect
202. C11#3329semidirect

Maximal subgroups

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

subgroupindex
Q8×D442
#106230942
C4×C11×SD162
#106227832
#106226342
#106226322
#106224802
#106224152
#106223932
#106223012
#106222942
#332911