Finite Group Databasebeta

← #13078143

Subgroups — #13078143

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
1C22×C11×Q16C211yesmaximal, characteristic, complemented
2#10623347C211yesmaximal, characteristic
3#10623343C211yesmaximal, characteristic, complemented
4C2×#66995C211yesmaximal, characteristic
5#10622838C211yesmaximal, characteristic, complemented
6#10622798C214yesmaximal, complemented
7#10622795C214yesmaximal, complemented
8#10622726C211yesmaximal, characteristic
9#10622715C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12C2×#4339C2211yescharacteristic
13C2×C11×Q16—24no—
14C2×C11×Q16C2214yes—
15C22×C8×C11C2211yescharacteristic
16#67000C2212yes—
17#66999—22no—
18Q8×Dic11—22no—
19Q8×Dic11C2214yes—
20#66997C2212yes—
21C2×#4326C2212yes—
22#66995—24no—
23C2×#4325C2212yes—
24#66982—22no—
25#66979—22no—
26#66979C2211yescharacteristic
27#66979C2211yescharacteristic
28C2×#4318C2211yescharacteristic
29#66899C2214yes—
30#66885C2212yes—
31#66880C2212yes—
32Dic11⋊C8C2214yes—
33C2×Q8×C11—21no—
34C2×Q8×C11—21no—
35C2×Q8×C11—22no—
36C2×Q8×C11—22no—
37C2×Q8×C11—22no—
38C2×Q8×C11D414yes—
39C2×Q8×C11C2312yes—
40C2×Q8×C11C2312yes—
41C22×C4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—21no—
45#4339—22no—
46#4339—22no—
47C2×D44C2311yescharacteristic
48C2×C4×D11—21no—
49C2×Dic22C2311yescharacteristic
50C11×Q16—28no—
51C2×C8×C11—22no—
52C2×C8×C11C2312yes—
53C22⋊Dic11—21no—
54C22⋊Dic11D412yes—
55#4326—24no—
56#4325—24no—
57(C2×D11)⋊C4—24no—
58C4⋊Dic11—24no—
59C4⋊Dic11D412yes—
60C4⋊Dic11C2312yes—
61Dic11⋊C4—24no—
62C4×Dic11—24no—
63C4×Dic11—21no—
64C4×Dic11C2312yes—
65#4318—22no—
66C2×C11⋊C8C2312yes—
67#3044—111nomaximal, Sylow
68C23×C11C2×D411yescharacteristic
69C22×D11—21no—
70Q8×C11—24no—
71Q8×C11—22no—
72Q8×C11—22no—
73Q8×C11—22no—
74Q8×C11—42no—
75Q8×C11C2×D414yes—
76C2×C4×C11—24no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—42no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D412yes—
82C2×C4×C11#4112yes—
83C2×C4×C11C2411yescharacteristic
84C22⋊D11—42no—
85C2×Dic11—22no—
86C2×Dic11—21no—
87C2×Dic11C2×D414yes—
88D44—21no—
89D44—21no—
90C4×D11—42no—
91Dic22—21no—
92Dic22—21no—
93C8×C11—22no—
94C11⋊C8—22no—
95C2×#137—111no—
96C22×Q16D1111yescharacteristic, complemented
97#536—111no—
98#519—111no—
99#464—114no—
100#462—114no—
101#424—111no—
102#419—111no—
103#416—111no—
104C22×C11—22no—
105C22×C11#12112yes—
106C22×C11C22×D411yescharacteristic
107C2×D11—41no—
108C2×D11—42no—
109C4×C11—24no—
110C4×C11—42no—
111C4×C11#12112yes—
112C4×C11C22×D411yescharacteristic
113C4×C11C2×#4111yescharacteristic
114Dic11—24no—
115Dic11—41no—
116Dic11—42no—
117C2×#41—111no—
118C22×Q8C2×D1111yescharacteristic
119C22×Q8C2×D1111yescharacteristic
120#137—224no—
121C2×Q16—24no—
122C2×Q16—112no—
123C2×Q16C2×D1114yes—
124C2×SD16—112no—
125C2×M16—111no—
126C22×C8C2×D1111yescharacteristic
127C4⋊Q8—112no—
128#124—112no—
129#123—222no—
130C22⋊Q8—222no—
131C4×Q8—114no—
132C4×Q8—222no—
133#117—111no—
134#117—111no—
135#117—222no—
136C4⋊C8—114no—
137#103—114no—
138#103—112no—
139#102—112no—
140C2×C11—22no—
141C2×C11C2×#12111yescharacteristic
142C2×C11#57812yes—
143D11—81no—
144#41—222no—
145#41—222no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—111no—
152C2×Q8C22⋊D1114yes—
153C2×Q8C22×D1112yes—
154C2×Q8C22×D1112yes—
155C2×D4—111no—
156C2×D4—221no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—221no—
160C22×C4C22×D1111yescharacteristic
161Q16—28no—
162Q16—224no—
163SD16—224no—
164M16—222no—
165C2×C8—22no—
166C2×C8—112no—
167C2×C8C22×D1112yes—
168C4⋊C4—112no—
169C4⋊C4—112no—
170C4⋊C4—224no—
171C4⋊C4—224no—
172C22⋊C4—112no—
173C22⋊C4—224no—
174C22⋊C4—221no—
175C42—112no—
176C42—224no—
177C42—221no—
178C11#304411yescharacteristic, complemented, Sylow
179C23—221no—
180C23D4×D1111yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—22no—
184Q8—22no—
185Q8—42no—
186Q8—221no—
187Q8—221no—
188Q8C2×C22⋊D1114yes—
189D4—221no—
190D4—221no—
191D4—442no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—114no—
197C2×C4—222no—
198C2×C4—221no—
199C2×C4—442no—
200C2×C4D4×D1111yescharacteristic
201C2×C4#434112yes—
202C2×C4C2×C22⋊D1112yes—
203C2×C4C23×D1111yescharacteristic
204C8—22no—
205C8—222no—
206C22—22no—
207C22—442no—
208C22—441no—
209C22#6699212yes—
210C22C2×D4×D1111yescharacteristic
211C4—24no—
212C4—42no—
213C4—224no—
214C4—442no—
215C4—441no—
216C4#6699212yes—
217C4C2×#434111yescharacteristic
218C4C22×C22⋊D1111yescharacteristic
219C2—22no—
220C2—881no—
221C2#1062329712yes—
222C2C2×#6699211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC22×C11×Q16C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenterC22×Q16D11
hypocenterC11#3044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C22×C11×Q16C2semidirect
3. #10623343C2semidirect
5. #10622838C2semidirect
6. #10622798C2semidirect
7. #10622795C2semidirect
9. #10622715C2semidirect
96. C22×Q16D11semidirect
178. C11#3044semidirect

Maximal subgroups

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

subgroupindex
C22×C11×Q162
#106233472
#106233432
C2×#669952
#106228382
#106227982
#106227952
#106227262
#106227152
#304411