Finite Group Databasebeta

← #14671240

Subgroups — #14671240

Order 2816.

454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 123 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#13081719C211yesmaximal, characteristic
2#13078271C211yesmaximal, characteristic
3C2×#10622134C212yesmaximal, complemented
4#13066730C212yesmaximal, complemented
5C11×#1813C211yesmaximal, characteristic
6C2×C11×#131C2211yescharacteristic
7#10623356—21no—
8C22×Dic44C2211yescharacteristic
9C2×C11×#108C2212yes—
10C11×#413—21no—
11#10622753—24no—
12#10622750C414yes—
13#10622733—21no—
14#10622729—22no—
15#10622719C2211yescharacteristic
16C2×#66876—22no—
17C2×#66876C2212yes—
18C11×#338—21no—
19#10622134—24no—
20C2×C11×#41D411yescharacteristic
21C22×Dic22—21no—
22C11×#131—22no—
23C11×#131—22no—
24C2×C11×M16—22no—
25C2×C11×M16C2×C412yes—
26C2×C11×M16D411yescharacteristic
27C22×C8×C11D412yes—
28C22×C8×C11C2311yescharacteristic
29#66997—41no—
30#66989—41no—
31#66988—42no—
32#66979—21no—
33#66977—24no—
34C2×Dic44—22no—
35C2×Dic44—22no—
36C2×Dic44—21no—
37C2×Dic44C2×C412yes—
38C11×#108—22no—
39C11×#108—22no—
40C11×#101—41no—
41C11×#100—41no—
42#66882—21no—
43#66881C2×C412yes—
44#66880—24no—
45#66876—24no—
46#66876—22no—
47#66876D414yes—
48C2×C11⋊C16—24no—
49C2×C11⋊C16—22no—
50#13078—111nomaximal, Sylow
51C11×#41—22no—
52C11×#41—22no—
53C2×Q8×C11D811yescharacteristic
54C2×D4×C11D811yescharacteristic
55C2×D4×C11SD1612yes—
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—41no—
59C2×Dic22—22no—
60C2×Dic22—42no—
61C2×Dic22—41no—
62C2×Dic22—42no—
63C11×M16—24no—
64C11×M16—22no—
65C11×M16—42no—
66C11×M16—42no—
67C2×C8×C11—22no—
68C2×C8×C11—22no—
69C2×C8×C11—42no—
70C2×C8×C11C22⋊C412yes—
71C2×C8×C11C22×C411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D412yes—
74C2×C8×C11#4112yes—
75C22⋊Dic11—44no—
76C22⋊Dic11—41no—
77C4⋊Dic11—22no—
78Dic11⋊C4—44no—
79C4×Dic11—41no—
80Dic44—24no—
81Dic44—41no—
82Dic44—41no—
83C11⋊C16—24no—
84#3407—111no—
85#3059—111no—
86C2×#362—112no—
87#1813D1111yescharacteristic
88#1389—112no—
89C23×C11#10212yes—
90C23×C11C2×SD1611yescharacteristic
91Q8×C11—22no—
92D4×C11—24no—
93D4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11#10212yes—
97C2×C4×C11C2×C22⋊C411yescharacteristic
98C2×C4×C11#12112yes—
99C2×C4×C11C2×D811yescharacteristic
100C2×C4×C11#13512yes—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—82no—
104Dic22—42no—
105Dic22—42no—
106Dic22—82no—
107C8×C11—22no—
108C8×C11—82no—
109C8×C11C4×D412yes—
110C8×C11#12011yescharacteristic
111C8×C11#12311yescharacteristic
112C22×Q16—111no—
113C2×#131C2×D1111yescharacteristic
114#536—221no—
115#504—224no—
116C2×M32—112no—
117C2×M32—222no—
118#470—114no—
119#467—222no—
120C2×#108C2×D1112yes—
121#427—111no—
122#419—221no—
123#413—21no—
124#362—224no—
125#338—21no—
126C22×C11—22no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11C2×#10211yescharacteristic
130C22×C11#46512yes—
131C4×C11—22no—
132C4×C11#38611yescharacteristic
133C4×C11#41611yescharacteristic
134C4×C11#46612yes—
135Dic11—82no—
136Dic11—82no—
137C2×#41C22⋊D1111yescharacteristic
138C22×Q8—221no—
139C2×Q16—112no—
140C2×Q16—221no—
141C2×Q16—222no—
142C2×Q16—222no—
143#131—22no—
144#131—22no—
145C2×M16—22no—
146C2×M16C4×D1112yes—
147C2×M16C22⋊D1111yescharacteristic
148C22×C8D4412yes—
149C22×C8C22×D1111yescharacteristic
150C4⋊Q8—441no—
151#124—441no—
152#123—442no—
153C22⋊Q8—224no—
154#117—221no—
155M32—114no—
156M32—224no—
157M32—222no—
158C2×C16—224no—
159C2×C16—222no—
160#108—22no—
161#108—22no—
162#107—221no—
163#106—112no—
164#103—224no—
165#101—41no—
166#100—41no—
167C2×C11—21no—
168C2×C11—22no—
169C2×C11—42no—
170C2×C11#189311yescharacteristic
171#41—22no—
172#41—22no—
173C2×Q8—222no—
174C2×Q8—441no—
175C2×Q8—442no—
176C2×Q8—442no—
177C2×Q8#432311yescharacteristic
178C2×D4#432311yescharacteristic
179C2×D4#432512yes—
180C22×C4—441no—
181C22×C4(C2×D11)⋊C412yes—
182C22×C4C2×C22⋊D1111yescharacteristic
183Q16—224no—
184Q16—441no—
185Q16—441no—
186M16—22no—
187M16—24no—
188M16—42no—
189M16—42no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—42no—
193C2×C8(C2×D11)⋊C412yes—
194C2×C8C2×C4×D1111yescharacteristic
195C2×C8C2×D4411yescharacteristic
196C2×C8D4×D1112yes—
197C2×C8#434112yes—
198C4⋊C4—222no—
199C4⋊C4—444no—
200C22⋊C4—444no—
201C22⋊C4—441no—
202C42—441no—
203C16—224no—
204C11#1307811yescharacteristic, complemented, Sylow
205C23#6687312yes—
206C23C2×#432511yescharacteristic
207Q8—22no—
208Q8—442no—
209Q8—442no—
210Q8—882no—
211D4—24no—
212D4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—442no—
216C2×C4—442no—
217C2×C4—882no—
218C2×C4#6687312yes—
219C2×C4C2×(C2×D11)⋊C411yescharacteristic
220C2×C4C2×#432311yescharacteristic
221C2×C4#6699212yes—
222C2×C4#6700312yes—
223C8—22no—
224C8—82no—
225C8(C22⋊D11)⋊C412yes—
226C8#6693511yescharacteristic
227C8#6693911yescharacteristic
228C22—22no—
229C22—41no—
230C22—42no—
231C22C2×#6687311yescharacteristic
232C22#1062266112yes—
233C4—22no—
234C4—882no—
235C4—882no—
236C4#1062257111yescharacteristic
237C4#1062261511yescharacteristic
238C4#1062265112yes—
239C2—21no—
240C2—22no—
241C2—42no—
242C2#1306904211yescharacteristic
subgroupG/H
centerC2#13069042
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1813C2
socleC2×C11#1893
prime radicalC2×C11×#41D4
cosocleC22×C8×C11C23
hypercenter#1813D11
hypocenterC11#13078
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #1813

Complements

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

NH ≅ G/Ntype
3. C2×#10622134C2semidirect
4. #13066730C2semidirect
204. C11#13078semidirect

Maximal subgroups

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

subgroupindex
#130817192
#130782712
C2×#106221342
#130667302
C11×#18132
#1307811