Finite Group Databasebeta

← #13078281

Subgroups — #13078281

Order 1408.

484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#66965C211yesmaximal, characteristic, complemented
2C2×#66954C211yesmaximal, characteristic, complemented
3#10623139C212yesmaximal, complemented
4C11×#466C211yesmaximal, characteristic, complemented
5#10622770C211yesmaximal, characteristic, complemented
6#10622729C211yesmaximal, characteristic, complemented
7#10622655C212yesmaximal, complemented
8#10622500C211yesmaximal, characteristic, complemented
9D11×#107C211yesmaximal, characteristic, complemented
10#10622393C212yesmaximal, complemented
11#10622384C212yesmaximal, complemented
12C2×#4341C2212yes—
13C2×#4339C2211yescharacteristic
14C2×C11×D8C2211yescharacteristic
15C22×C8×C11C2211yescharacteristic
16C11×#121C2212yes—
17#66992—22no—
18#66991—22no—
19#66991C2212yes—
20C2×#4324C2212yes—
21#66977C2212yes—
22C2×#4318C2211yescharacteristic
23#66965—24no—
24C2×Dic44C2211yescharacteristic
25#66954—24no—
26C2×#4313C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66950C2212yes—
31C4⋊C4×D11C2212yes—
32#66937—22no—
33#66931—22no—
34C11×#107C2211yescharacteristic
35C11×#102C2212yes—
36#66896C2212yes—
37#66882C2211yescharacteristic
38#66880C2212yes—
39#66874C2212yes—
40#66871C2212yes—
41C2×D4×C11—22no—
42C2×D4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—22no—
45C2×C22⋊D11—22no—
46C2×C22⋊D11D411yescharacteristic
47C2×C22⋊D11D411yescharacteristic
48C22×Dic11—22no—
49#4341—24no—
50#4341—24no—
51#4339—22no—
52#4339—22no—
53C2×D44D411yescharacteristic
54C2×C4×D11—22no—
55C2×C4×D11C2311yescharacteristic
56C2×C4×D11C2311yescharacteristic
57C2×Dic22D411yescharacteristic
58C2×Dic22C2312yes—
59C11×D8—22no—
60C2×C8×C11—22no—
61C2×C8×C11C2311yescharacteristic
62C2×C8×C11C2311yescharacteristic
63C11×C4⋊C4C2312yes—
64C11×C22⋊C4—22no—
65C22⋊Dic11—22no—
66C22⋊Dic11—22no—
67#4324—24no—
68(C2×D11)⋊C4—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11C2312yes—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73#4318—22no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76Dic44—22no—
77#4313—22no—
78#4313—22no—
79C8×D11—22no—
80C8×D11D414yescomplemented
81#3061—111nomaximal, Sylow
82C23×C11—22no—
83C23×C11C2×D411yescharacteristic
84C22×D11C2×D411yescharacteristic
85C22×D11C2×D411yescharacteristic
86D4×C11—22no—
87D4×C11—22no—
88D4×C11—82no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2411yescharacteristic
94C22⋊D11—22no—
95C22⋊D11—22no—
96C22⋊D11—44no—
97C22⋊D11—82no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—44no—
101C2×Dic11C2×D411yescharacteristic
102C2×Dic11C2×D411yescharacteristic
103D44—22no—
104C4×D11—21no—
105C4×D11—21no—
106C4×D11—82no—
107C4×D11C2×D412yes—
108C4×D11#4112yes—
109Dic22—22no—
110Dic22—22no—
111Dic22—22no—
112C8×C11—21no—
113C8×C11C2×D412yes—
114C11⋊C8—21no—
115C11⋊C8C2×D412yes—
116C2×#135—111no—
117C2×#131—111no—
118#537—112no—
119#468—112no—
120#468—112no—
121#467—111no—
122#467—111no—
123#466—111no—
124#466D1111yescharacteristic, complemented
125C2×#107—111no—
126#417—112no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11C22×D411yescharacteristic
134C2×D11—21no—
135C2×D11—21no—
136C2×D11—21no—
137C2×D11—21no—
138C2×D11—21no—
139C2×D11#12112yes—
140C4×C11—21no—
141C4×C11—42no—
142C4×C11C22×D411yescharacteristic
143C4×C11C2×#4111yescharacteristic
144Dic11—21no—
145Dic11—42no—
146Dic11—42no—
147Dic11#12112yes—
148C2×#41—111no—
149C2×#41—112no—
150#135—224no—
151C2×Q16—111no—
152C2×SD16—112no—
153C2×D8C2×D1111yescharacteristic
154#131—224no—
155C2×M16—111no—
156C2×M16—111no—
157C2×M16—111no—
158C22×C8—111no—
159C22×C8—111no—
160C22×C8C2×D1111yescharacteristic
161C22⋊Q8—112no—
162C22⋊Q8—112no—
163C22⋊Q8—222no—
164#121—112no—
165#121—222no—
166#121—222no—
167#121—222no—
168#121C2×D1112yes—
169C2×C4⋊C4—112no—
170#107—111no—
171#107—112no—
172#107C2×D1111yescharacteristic
173#103—112no—
174#103—112no—
175#102—112no—
176#102C2×D1112yes—
177C2×C11—41no—
178C2×C11—82no—
179C2×C11C2×#12111yescharacteristic
180C2×C11#57611yescharacteristic
181C2×C11#57811yescharacteristic
182D11—22no—
183D11—41no—
184#41—222no—
185#41—222no—
186#41—224no—
187#41—224no—
188C2×Q8—111no—
189C2×Q8—112no—
190C2×D4—22no—
191C2×D4—111no—
192C2×D4—111no—
193C2×D4—111no—
194C2×D4—222no—
195C2×D4—222no—
196C2×D4C22×D1112yes—
197C22×C4—111no—
198C22×C4—111no—
199C22×C4—222no—
200C22×C4—222no—
201C22×C4C22×D1111yescharacteristic
202Q16—222no—
203SD16—224no—
204D8—22no—
205M16—222no—
206M16—222no—
207M16—222no—
208C2×C8—22no—
209C2×C8—111no—
210C2×C8—114no—
211C2×C8—111no—
212C2×C8—222no—
213C2×C8C22×D1111yescharacteristic
214C2×C8C22×D1111yescharacteristic
215C4⋊C4—112no—
216C4⋊C4—222no—
217C4⋊C4—222no—
218C4⋊C4—222no—
219C4⋊C4C22×D1112yes—
220C22⋊C4—22no—
221C22⋊C4—222no—
222C22⋊C4—222no—
223C22⋊C4—222no—
224C11#306111yescharacteristic, complemented, Sylow
225C23—22no—
226C23—111no—
227C23—111no—
228C23D4×D1111yescharacteristic
229Q8—222no—
230Q8—222no—
231Q8—222no—
232D4—22no—
233D4—22no—
234D4—82no—
235D4—222no—
236D4—222no—
237D4—222no—
238D4—444no—
239D4—882no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—111no—
244C2×C4—112no—
245C2×C4—112no—
246C2×C4—111no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—444no—
252C2×C4—882no—
253C2×C4D4×D1111yescharacteristic
254C2×C4C23×D1111yescharacteristic
255C8—21no—
256C8—112no—
257C8—221no—
258C8D4×D1112yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—112no—
266C22—221no—
267C22—221no—
268C22—221no—
269C22—221no—
270C22—221no—
271C22C2×D4×D1111yescharacteristic
272C4—21no—
273C4—42no—
274C4—112no—
275C4—221no—
276C4—442no—
277C4—442no—
278C4C2×D4×D1111yescharacteristic
279C4#41×D1111yescharacteristic
280C2—41no—
281C2—82no—
282C2—222no—
283C2—441no—
284C2D11×#12111yescharacteristic
285C2#1062328811yescharacteristic
286C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#466C2
socleC22×C11C22×D4
hypercenter#466D11
hypocenterC11#3061
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#66965C2semidirect
2. C2×#66954C2semidirect
3. #10623139C2semidirect
4. C11×#466C2semidirect
5. #10622770C2semidirect
6. #10622729C2semidirect
7. #10622655C2semidirect
8. #10622500C2semidirect
9. D11×#107C2semidirect
10. #10622393C2semidirect
11. #10622384C2semidirect
80. C8×D11D4semidirect
124. #466D11semidirect
224. C11#3061semidirect

Maximal subgroups

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

subgroupindex
C2×#669652
C2×#669542
#106231392
C11×#4662
#106227702
#106227292
#106226552
#106225002
D11×#1072
#106223932
#106223842
#306111