Finite Group Databasebeta

← #13078142

Subgroups — #13078142

Order 1408.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C11×#536C211yesmaximal, characteristic
2C2×#67004C211yesmaximal, characteristic
3C22×#4326C211yesmaximal, characteristic, complemented
4#10623047C211yesmaximal, characteristic, complemented
5#10622846C211yesmaximal, characteristic
6#10622838C211yesmaximal, characteristic, complemented
7#10622703C214yesmaximal, complemented
8#10622667C214yesmaximal, complemented
9#10622612C211yesmaximal, characteristic, complemented
10C2×C11×#41C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C11×C4⋊Q8C2212yes—
14C11×#124C2212yes—
15C11×#123—22no—
16C11×C22⋊Q8—22no—
17C11×#117C2211yescharacteristic
18#67004—24no—
19C2×#4326—24no—
20C2×#4326C2214yes—
21C2×#4326C2212yes—
22C2×#4324C2212yes—
23#66979C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25C22×C11⋊C8C2211yescharacteristic
26#66940—22no—
27#66930—22no—
28C4×Dic22C2214yes—
29#66899C2214yes—
30#66899C2212yes—
31#66896C2212yes—
32C4⋊(C11⋊C8)C2214yes—
33C11×#41—22no—
34C11×#41—22no—
35C2×Q8×C11—21no—
36C2×Q8×C11—22no—
37C2×Q8×C11—22no—
38C2×Q8×C11C2312yes—
39C2×Q8×C11C2311yescharacteristic
40C2×D4×C11—21no—
41C2×D4×C11C2311yescharacteristic
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11C2311yescharacteristic
45C22×Dic11—21no—
46C2×Dic22—21no—
47C2×Dic22—22no—
48C2×Dic22D414yes—
49C2×Dic22C2312yes—
50C11×C4⋊C4—24no—
51C11×C4⋊C4D412yes—
52C11×C22⋊C4—24no—
53C11×C22⋊C4D412yes—
54C42×C11C2312yes—
55C22⋊Dic11—21no—
56#4326—28no—
57#4326—24no—
58#4324—24no—
59C4⋊Dic11C2312yes—
60Dic11⋊C4—24no—
61C4×Dic11—24no—
62C4×Dic11—21no—
63#4318—22no—
64C2×C11⋊C8—22no—
65C2×C11⋊C8C2312yes—
66C2×C11⋊C8C2312yes—
67#3044—111nomaximal, Sylow
68C23×C11—21no—
69C23×C11C2×D411yescharacteristic
70Q8×C11—22no—
71Q8×C11—21no—
72Q8×C11—22no—
73Q8×C11—21no—
74Q8×C11—42no—
75D4×C11—21no—
76D4×C11—21no—
77D4×C11—42no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2×D414yes—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11#4112yes—
86C2×C4×C11C2411yescharacteristic
87C2×Dic11—24no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90Dic22—24no—
91Dic22—22no—
92Dic22C2×D414yes—
93C11⋊C8—22no—
94C11⋊C8—22no—
95C2×#137—111no—
96C22×Q16—111no—
97#536D1111yescharacteristic
98#519—111no—
99#464—114no—
100#462—114no—
101#424—111no—
102#419—111no—
103#416—111no—
104C22×C11—22no—
105C22×C11—41no—
106C22×C11—42no—
107C22×C11#12112yes—
108C22×C11C22×D411yescharacteristic
109C4×C11—24no—
110C4×C11—41no—
111C4×C11—42no—
112C4×C11#12112yes—
113C4×C11C22×D411yescharacteristic
114C4×C11C2×#4111yescharacteristic
115Dic11—24no—
116Dic11—42no—
117C2×#41C2×D1111yescharacteristic
118C22×Q8—111no—
119C22×Q8C2×D1111yescharacteristic
120#137—224no—
121C2×Q16—114no—
122C2×Q16—112no—
123C2×Q16—224no—
124C2×SD16—112no—
125C2×M16—111no—
126C22×C8—111no—
127C4⋊Q8C2×D1112yes—
128#124C2×D1112yes—
129#123—22no—
130C22⋊Q8—22no—
131C4×Q8—114no—
132C4×Q8—222no—
133#117—111no—
134#117—222no—
135#117C2×D1111yescharacteristic
136C4⋊C8—114no—
137#103—112no—
138#103—114no—
139#102—112no—
140C2×C11—22no—
141C2×C11—81no—
142C2×C11C2×#12111yescharacteristic
143C2×C11#57812yes—
144#41—22no—
145#41—22no—
146C2×Q8—21no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—114no—
150C2×Q8—112no—
151C2×Q8—222no—
152C2×Q8—221no—
153C2×Q8C22×D1112yes—
154C2×Q8C22×D1111yescharacteristic
155C2×D4—21no—
156C2×D4C22×D1111yescharacteristic
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—221no—
160C22×C4C22×D1111yescharacteristic
161Q16—228no—
162Q16—224no—
163SD16—224no—
164M16—222no—
165C2×C8—112no—
166C2×C8—112no—
167C2×C8—222no—
168C4⋊C4—24no—
169C4⋊C4—112no—
170C4⋊C4—224no—
171C4⋊C4C22⋊D1112yes—
172C22⋊C4—24no—
173C22⋊C4—221no—
174C22⋊C4C22⋊D1112yes—
175C42—221no—
176C42—224no—
177C42C22×D1112yes—
178C11#304411yescharacteristic, complemented, Sylow
179C23—21no—
180C23C2×C22⋊D1111yescharacteristic
181Q8—22no—
182Q8—21no—
183Q8—22no—
184Q8—21no—
185Q8—42no—
186Q8—114no—
187Q8—224no—
188Q8—222no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—224no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4D4×D1112yes—
200C2×C4#434112yes—
201C2×C4C2×C22⋊D1114yes—
202C2×C4C2×C22⋊D1111yescharacteristic
203C2×C4C23×D1111yescharacteristic
204C8—222no—
205C8—222no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22#6699112yes—
210C22C22×C22⋊D1111yescharacteristic
211C4—24no—
212C4—41no—
213C4—42no—
214C4—224no—
215C4—442no—
216C4#6699112yes—
217C4C2×D4×D1111yescharacteristic
218C4C2×#434111yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#6699111yescharacteristic
222C2#1062336912yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#536C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#536D11
hypocenterC11#3044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
3. C22×#4326C2semidirect
4. #10623047C2semidirect
6. #10622838C2semidirect
7. #10622703C2semidirect
8. #10622667C2semidirect
9. #10622612C2semidirect
178. C11#3044semidirect

Maximal subgroups

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

subgroupindex
C11×#5362
C2×#670042
C22×#43262
#106230472
#106228462
#106228382
#106227032
#106226672
#106226122
#304411