Finite Group Databasebeta

← #14652209

Subgroups — #14652209

Order 2816.

338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic
2#13067388C211yesmaximal, characteristic
3#13067273C211yesmaximal, characteristic
4#13067019C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic
6#13066449C211yesmaximal, characteristic
7C11×#1994C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C43×C11C2211yescharacteristic
11#10622538C2211yescharacteristic
12#10622538C2211yescharacteristic
13C2×C4⋊(C11⋊C8)C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4×C11⋊C8—21no—
16C11×#339—21no—
17C11×#339—21no—
18#10622185C412yescomplemented
19#10622184C412yescomplemented
20Q8⋊(C11⋊C8)—22no—
21#10622162—21no—
22#10622118—22no—
23C2×C11×M16—21no—
24C11×C4⋊Q8C2×C411yescharacteristic
25C11×C4⋊Q8C2×C411yescharacteristic
26C11×#125—21no—
27C11×C22⋊Q8—21no—
28C11×C22⋊Q8—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C11×#117—21no—
32C2×C42×C11—21no—
33C2×C42×C11—21no—
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C22×C11⋊C8—21no—
38C22×C11⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C22⋊(C11⋊C8)—21no—
42C22⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)C2×C412yes—
47C4⋊(C11⋊C8)C2×C412yes—
48C4⋊(C11⋊C8)D412yes—
49C4×C11⋊C8—21no—
50C4×C11⋊C8—21no—
51C4×C11⋊C8—42no—
52#9579—111nomaximal, Sylow
53C2×Q8×C11—21no—
54C2×Q8×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11#4111yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C11×M16—41no—
61C11×M16—41no—
62C2×C8×C11—41no—
63C11×C4⋊C4—21no—
64C11×C4⋊C4—21no—
65C11×C4⋊C4—21no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C22⋊C4—41no—
70C42×C11—24no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—42no—
75C42×C11—41no—
76C42×C11SD1612yes—
77C42×C11C22×C411yescharacteristic
78C42×C11C2×D411yescharacteristic
79C42×C11#4111yescharacteristic
80C42×C11#4111yescharacteristic
81C2×C11⋊C8—22no—
82C2×C11⋊C8—22no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—41no—
89#1994D1111yescharacteristic
90C4×C4⋊C8—111no—
91#1570—111no—
92#1542—111no—
93#1481—111no—
94#1301—111no—
95#1276—111no—
96C23×C11#12311yescharacteristic
97Q8×C11—42no—
98Q8×C11—81no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11#11711yescharacteristic
110C2×C4×C11C4×D411yescharacteristic
111C2×C4×C11C4×D411yescharacteristic
112C2×C4×C11#12111yescharacteristic
113C2×C4×C11#12411yescharacteristic
114C2×C4×C11#12611yescharacteristic
115C2×C4×C11C2×SD1611yescharacteristic
116C2×C4×C11#13511yescharacteristic
117C2×C4×C11#13711yescharacteristic
118C2×C4×C11#13711yescharacteristic
119C8×C11—81no—
120C11⋊C8—42no—
121C11⋊C8—42no—
122C11⋊C8—42no—
123C11⋊C8—81no—
124#533C2×D1111yescharacteristic
125#431—111no—
126#431—111no—
127#423C2×D1111yescharacteristic
128C2×C4⋊C8—111no—
129C2×C4⋊C8—111no—
130C2×C4×C8—221no—
131C43C2×D1111yescharacteristic
132#339—21no—
133#339—21no—
134#336—221no—
135#334—222no—
136#333—112no—
137#332—112no—
138Q8⋊C8—222no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11#38811yescharacteristic
142C22×C11#48311yescharacteristic
143C22×C11#48511yescharacteristic
144C4×C11—24no—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—42no—
149C4×C11—81no—
150C4×C11—81no—
151C4×C11C4×SD1611yescharacteristic
152C4×C11#44111yescharacteristic
153C4×C11#44312yes—
154C4×C11#46111yescharacteristic
155C4×C11#46411yescharacteristic
156C2×M16—21no—
157C22×C8—221no—
158C22×C8—221no—
159C4⋊Q8C4×D1111yescharacteristic
160C4⋊Q8C4×D1111yescharacteristic
161#125—21no—
162C22⋊Q8—21no—
163C22⋊Q8—21no—
164C4×Q8—21no—
165C4×Q8—21no—
166#117—21no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42C22⋊D1111yescharacteristic
170C2×C42C22⋊D1111yescharacteristic
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8—112no—
175C4⋊C8—112no—
176C4⋊C8—112no—
177C4⋊C8—221no—
178C4⋊C8—221no—
179C4⋊C8—221no—
180C22⋊C8—221no—
181C22⋊C8—221no—
182C4×C8—221no—
183C4×C8—221no—
184C4×C8—442no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11#192711yescharacteristic
188C2×C11#193211yescharacteristic
189C2×C11#193711yescharacteristic
190C2×Q8—21no—
191C2×Q8—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4#434111yescharacteristic
195C22×C4#434111yescharacteristic
196C22×C4C2×C22⋊D1111yescharacteristic
197M16—41no—
198M16—41no—
199C2×C8—41no—
200C2×C8—222no—
201C2×C8—222no—
202C2×C8—222no—
203C2×C8—441no—
204C2×C8—441no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8—441no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C22⋊C4—41no—
215C42—24no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—42no—
220C42—41no—
221C42#432512yes—
222C42C2×C4×D1111yescharacteristic
223C42#433911yescharacteristic
224C42D4×D1111yescharacteristic
225C42#434111yescharacteristic
226C11#957911yescharacteristic, complemented, Sylow
227C23#6698811yescharacteristic
228Q8—42no—
229Q8—81no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4#6693011yescharacteristic
241C2×C4#6693211yescharacteristic
242C2×C4(C22⋊D11)⋊C411yescharacteristic
243C2×C4#6693811yescharacteristic
244C2×C4C4×C22⋊D1111yescharacteristic
245C2×C4#6699111yescharacteristic
246C2×C4C2×#432511yescharacteristic
247C2×C4#6699511yescharacteristic
248C2×C4#6700311yescharacteristic
249C2×C4#6700411yescharacteristic
250C8—81no—
251C8—442no—
252C8—442no—
253C8—442no—
254C8—881no—
255C22—21no—
256C22—21no—
257C22#1062255711yescharacteristic
258C22#1062265611yescharacteristic
259C22#1062265811yescharacteristic
260C4—24no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—81no—
266C4—81no—
267C4#1062243712yes—
268C4C4×#432511yescharacteristic
269C4#1062264311yescharacteristic
270C4#1062266711yescharacteristic
271C4#1062269611yescharacteristic
272C2—21no—
273C2—21no—
274C2#1306924711yescharacteristic
275C2#1306928211yescharacteristic
276C2#1306931711yescharacteristic
subgroupG/H
centerC2×C4#66991
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1994C2
socleC22×C11#388
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1994D11
hypocenterC11#9579
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
18. #10622185C4semidirect
19. #10622184C4semidirect
226. C11#9579semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊(C11⋊C8)2
#130673882
#130672732
#130670192
#130665112
#130664492
C11×#19942
#957911