Finite Group Databasebeta

← #14652213

Subgroups — #14652213

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
1#13069593C211yesmaximal, characteristic
2C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic
3#13067387C211yesmaximal, characteristic
4#13067271C211yesmaximal, characteristic
5#13067020C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic
7C11×#1276C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C43×C11C2211yescharacteristic
12#10622537C2211yescharacteristic
13C2×C4⋊(C11⋊C8)C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4×C11⋊C8—21no—
16#10622162—21no—
17#10622161—21no—
18#10622161—21no—
19#10622120C412yescomplemented
20#10622119C412yescomplemented
21#10622095—22no—
22#10622094—22no—
23C2×C42×C11—21no—
24C2×C42×C11—21no—
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28#66979—21no—
29#66977—21no—
30#66977—21no—
31C2×#4318—21no—
32C22×C11⋊C8—21no—
33C22×C11⋊C8—21no—
34#66923—21no—
35#66922C2×C411yescharacteristic
36#66922C2×C411yescharacteristic
37C4×Dic22—21no—
38C4×Dic22—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8C2×C412yes—
41C11×C22⋊C8—21no—
42C11×C22⋊C8—21no—
43C4×C8×C11—21no—
44C4×C8×C11—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)C2×C412yes—
50C4⋊(C11⋊C8)D412yes—
51C4×C11⋊C8—42no—
52#9579—111nomaximal, Sylow
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11#4111yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C2×Dic22—21no—
59C2×Dic22—21no—
60C2×C8×C11—22no—
61C2×C8×C11—41no—
62C42×C11—24no—
63C42×C11—21no—
64C42×C11—21no—
65C42×C11—21no—
66C42×C11—42no—
67C42×C11SD1612yes—
68C42×C11C22×C411yescharacteristic
69C42×C11C2×D411yescharacteristic
70C42×C11#4111yescharacteristic
71C42×C11#4111yescharacteristic
72C22⋊Dic11—41no—
73C4⋊Dic11—21no—
74C4⋊Dic11—21no—
75C4⋊Dic11—21no—
76C4⋊Dic11—21no—
77Dic11⋊C4—41no—
78Dic11⋊C4—41no—
79C4×Dic11—41no—
80#4318—41no—
81#4318—41no—
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#1994—111no—
90C4×C4⋊C8—111no—
91#1570—111no—
92#1542—111no—
93#1481—111no—
94#1301—111no—
95#1276D1111yescharacteristic
96C23×C11#12311yescharacteristic
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11#11711yescharacteristic
106C2×C4×C11C4×D411yescharacteristic
107C2×C4×C11C4×D411yescharacteristic
108C2×C4×C11#12111yescharacteristic
109C2×C4×C11#12411yescharacteristic
110C2×C4×C11#12611yescharacteristic
111C2×C4×C11C2×SD1611yescharacteristic
112C2×C4×C11#13511yescharacteristic
113C2×C4×C11#13711yescharacteristic
114C2×C4×C11#13711yescharacteristic
115C2×Dic11—41no—
116C2×Dic11—41no—
117Dic22—42no—
118Dic22—81no—
119C8×C11—42no—
120C8×C11—81no—
121C11⋊C8—42no—
122C11⋊C8—42no—
123C11⋊C8—81no—
124#533—111no—
125#431C2×D1111yescharacteristic
126#431C2×D1111yescharacteristic
127#423—111no—
128C2×C4⋊C8—111no—
129C2×C4⋊C8—111no—
130C2×C4×C8—221no—
131C43C2×D1111yescharacteristic
132#339—221no—
133#339—221no—
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×C11C4×SD1611yescharacteristic
150C4×C11#44111yescharacteristic
151C4×C11#44312yes—
152C4×C11#46111yescharacteristic
153C4×C11#46411yescharacteristic
154Dic11—81no—
155Dic11—81no—
156C2×M16—221no—
157C22×C8—221no—
158C22×C8—221no—
159C4⋊Q8—111no—
160C4⋊Q8—111no—
161#125—221no—
162C22⋊Q8—221no—
163C22⋊Q8—221no—
164C4×Q8—221no—
165C4×Q8—221no—
166#117—221no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42D4411yescharacteristic
170C2×C42D4411yescharacteristic
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—21no—
173C4⋊C8—112no—
174C4⋊C8—112no—
175C4⋊C8—221no—
176C4⋊C8—221no—
177C4⋊C8—221no—
178C4⋊C8—221no—
179C4⋊C8C4×D1112yes—
180C22⋊C8—21no—
181C22⋊C8—21no—
182C4×C8—21no—
183C4×C8—21no—
184C4×C8—442no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11#192711yescharacteristic
188C2×C11#193211yescharacteristic
189C2×C11#193711yescharacteristic
190C2×Q8—221no—
191C2×Q8—221no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C2×D4411yescharacteristic
195C22×C4#434111yescharacteristic
196C22×C4#434111yescharacteristic
197M16—441no—
198M16—441no—
199C2×C8—22no—
200C2×C8—41no—
201C2×C8—222no—
202C2×C8—222no—
203C2×C8—441no—
204C2×C8—441no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8—441no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C4⋊C4—221no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C22⋊C4—441no—
215C42—24no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—42no—
220C42—441no—
221C42#431412yes—
222C42C2×C4×D1111yescharacteristic
223C42#433911yescharacteristic
224C42D4×D1111yescharacteristic
225C42#434311yescharacteristic
226C11#957911yescharacteristic, complemented, Sylow
227C23#6693911yescharacteristic
228Q8—442no—
229Q8—881no—
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—441no—
239C2×C4—441no—
240C2×C4C4×D4411yescharacteristic
241C2×C4(C22⋊D11)⋊C411yescharacteristic
242C2×C4#6693811yescharacteristic
243C2×C4#6694511yescharacteristic
244C2×C4#6694811yescharacteristic
245C2×C4#6695111yescharacteristic
246C2×C4C2×#431411yescharacteristic
247C2×C4#6695711yescharacteristic
248C2×C4#6696211yescharacteristic
249C2×C4#6696211yescharacteristic
250C8—42no—
251C8—81no—
252C8—442no—
253C8—442no—
254C8—881no—
255C22—21no—
256C22—21no—
257C22#1062228311yescharacteristic
258C22#1062233411yescharacteristic
259C22#1062233611yescharacteristic
260C4—24no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—881no—
266C4—881no—
267C4C4×#431411yescharacteristic
268C4#1062232911yescharacteristic
269C4#1062243712yes—
270C4#1062245411yescharacteristic
271C4#1062245811yescharacteristic
272C2—21no—
273C2—21no—
274C2#1306925111yescharacteristic
275C2#1306928611yescharacteristic
276C2#1306932111yescharacteristic
subgroupG/H
centerC2×C4#66948
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#388
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1276D11
hypocenterC11#9579
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
19. #10622120C4semidirect
20. #10622119C4semidirect
226. C11#9579semidirect

Maximal subgroups

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

subgroupindex
#130695932
C4×C4⋊(C11⋊C8)2
#130673872
#130672712
#130670202
#130665122
C11×#12762
#957911