Finite Group Databasebeta

← #13080417

Subgroups — #13080417

Order 1408.

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

normal subgroups only

This group has 444 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
1#10623369C212yesmaximal, complemented
2#10623310C212yesmaximal, complemented
3C11×#456C211yesmaximal, characteristic, complemented
4#10622817C212yesmaximal, complemented
5#10622708C211yesmaximal, characteristic, complemented
6#10622705C211yesmaximal, characteristic, complemented
7#10622439C212yesmaximal, complemented
8#10622437C212yesmaximal, complemented
9#10622368C212yesmaximal, complemented
10C11×2−1+4C2211yescharacteristic
11#67043C2212yes—
12#67040C2211yescharacteristic
13C11×#137C2212yes—
14C11×C4⋊Q8C2211yescharacteristic
15#67004—22no—
16#67004C2212yes—
17#67003—22no—
18#67003C2212yes—
19#67001C2212yes—
20C2×#4326—22no—
21C2×#4326C2212yes—
22C2×#4326C2212yes—
23#66995—22no—
24#66995C2212yes—
25#66971—22no—
26Q16×D11—22no—
27#66969—22no—
28#66968—22no—
29#66962C2212yes—
30#66960C2212yes—
31#66922C2211yescharacteristic
32C11×#104C2212yes—
33C11×#101C2211yescharacteristic
34#66900C2211yescharacteristic
35#66888C2212yes—
36#66886C2212yes—
37#66869C2212yes—
38C4×C11⋊C8C2211yescharacteristic
39C11×#41—22no—
40C11×#41—41no—
41C11×#41C2312yes—
42C2×Q8×C11—22no—
43C2×Q8×C11C2311yescharacteristic
44C2×Q8×C11C2311yescharacteristic
45#4343—22no—
46Q8×D11—22no—
47Q8×D11—22no—
48#4341—22no—
49#4341—42no—
50#4339—22no—
51#4339—41no—
52#4339C2312yes—
53C2×Dic22—22no—
54C2×Dic22C2312yes—
55C11×Q16—22no—
56C11×SD16—22no—
57C11×M16C2312yes—
58C11×C4⋊C4—41no—
59C42×C11C2311yescharacteristic
60#4326—22no—
61#4326—22no—
62#4326—22no—
63#4326—22no—
64#4326—22no—
65#4326—22no—
66#4326D412yes—
67#4325—22no—
68#4325D412yes—
69#4324—22no—
70#4324D412yes—
71#4323D412yes—
72C4⋊Dic11—41no—
73#4318—22no—
74#4318C2312yes—
75C2×C11⋊C8—22no—
76C2×C11⋊C8C2312yes—
77Dic44—22no—
78#4314—22no—
79#4313—22no—
80C8×D11—22no—
81#3293—111nomaximal, Sylow
82Q8×C11—22no—
83Q8×C11—22no—
84Q8×C11—41no—
85Q8×C11C2×D412yes—
86D4×C11—22no—
87D4×C11—41no—
88D4×C11C2×D412yes—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—42no—
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—22no—
96C22⋊D11—42no—
97C2×Dic11—22no—
98C2×Dic11—42no—
99D44—41no—
100D44C2×D412yes—
101C4×D11—22no—
102C4×D11—42no—
103C4×D11—42no—
104Dic22—22no—
105Dic22—22no—
106Dic22—41no—
107Dic22—42no—
108Dic22C2×D412yes—
109C8×C11—22no—
110C11⋊C8—22no—
111C11⋊C8C2×D412yes—
112C11⋊C8C2×D412yes—
113#578—112no—
114#578—112no—
115#494—111no—
116#473—112no—
117#473—112no—
118#456—111no—
119#456—112no—
120#456D1111yescharacteristic, complemented
121#443—112no—
122C22×C11—22no—
123C22×C11H(5,𝔽2)11yescharacteristic
124C2×D11—22no—
125C4×C11—22no—
126C4×C11—22no—
127C4×C11—41no—
128C4×C11—41no—
129C4×C11C22×D412yes—
130Dic11—22no—
131Dic11—42no—
1322−1+4—112no—
1332−1+4—111no—
1342−1+4C2×D1111yescharacteristic
135#137—112no—
136#137—112no—
137#137—112no—
138#137—222no—
139#137—222no—
140#137—222no—
141#137—222no—
142#137C2×D1112yes—
143#135—112no—
144#135—222no—
145#135—222no—
146C2×Q16—112no—
147C2×Q16—112no—
148C2×Q16—222no—
149C2×Q16—222no—
150#131—112no—
151#131—112no—
152C4⋊Q8—111no—
153C4⋊Q8C2×D1111yescharacteristic
154#108—112no—
155#104—112no—
156#104C2×D1112yes—
157#101—111no—
158#101—112no—
159#101C2×D1111yescharacteristic
160C4×C8—111no—
161C2×C11—21no—
162C2×C11—42no—
163C2×C11D4211yescharacteristic
164D11—42no—
165#41—22no—
166#41—41no—
167#41—112no—
168#41—222no—
169#41—222no—
170#41—222no—
171#41—441no—
172#41—442no—
173#41C22×D1112yes—
174C2×Q8—22no—
175C2×Q8—112no—
176C2×Q8—222no—
177C2×Q8—222no—
178C2×Q8—222no—
179C2×Q8C22×D1111yescharacteristic
180C2×Q8C22×D1111yescharacteristic
181Q16—22no—
182Q16—112no—
183Q16—222no—
184Q16—222no—
185Q16—222no—
186Q16—222no—
187Q16—222no—
188Q16—222no—
189Q16—222no—
190SD16—22no—
191SD16—112no—
192SD16—112no—
193SD16—222no—
194SD16—222no—
195SD16—222no—
196D8—112no—
197M16—112no—
198M16—222no—
199M16—222no—
200M16C22×D1112yes—
201C2×C8—112no—
202C2×C8—222no—
203C2×C8—222no—
204C4⋊C4—41no—
205C4⋊C4—441no—
206C42C22×D1111yescharacteristic
207C11#329311yescharacteristic, complemented, Sylow
208Q8—22no—
209Q8—22no—
210Q8—41no—
211Q8—112no—
212Q8—222no—
213Q8—222no—
214Q8—442no—
215Q8—441no—
216Q8D4×D1112yes—
217D4—22no—
218D4—41no—
219D4—112no—
220D4—222no—
221D4—441no—
222D4—442no—
223D4D4×D1112yes—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4—442no—
234C2×C4C23×D1111yescharacteristic
235C8—22no—
236C8—112no—
237C8—112no—
238C8—222no—
239C22—22no—
240C22—222no—
241C22#6703711yescharacteristic
242C4—22no—
243C4—22no—
244C4—41no—
245C4—41no—
246C4—222no—
247C4—442no—
248C4C2×D4×D1112yes—
249C2—21no—
250C2—42no—
251C2—442no—
252C2#1062312111yescharacteristic
subgroupG/H
centerC2#10623121
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#456C2
socleC2×C11D42
hypercenter#456D11
hypocenterC11#3293
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #10623369C2semidirect
2. #10623310C2semidirect
3. C11×#456C2semidirect
4. #10622817C2semidirect
5. #10622708C2semidirect
6. #10622705C2semidirect
7. #10622439C2semidirect
8. #10622437C2semidirect
9. #10622368C2semidirect
120. #456D11semidirect
207. C11#3293semidirect

Maximal subgroups

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

subgroupindex
#106233692
#106233102
C11×#4562
#106228172
#106227082
#106227052
#106224392
#106224372
#106223682
#329311