Finite Group Databasebeta

← #14658453

Subgroups — #14658453

Order 2816.

328 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 83 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#13067405C211yesmaximal, characteristic, complemented
2#13067404C211yesmaximal, characteristic, complemented
3#13067285C211yesmaximal, characteristic
4#13067283C211yesmaximal, characteristic
5#13067283C211yesmaximal, characteristic
6C11⋊#1309C211yesmaximal, characteristic, complemented
7C11×#1574C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622537C2211yescharacteristic
14#10622537C2211yescharacteristic
15C11×#335—21no—
16C11×#334—21no—
17#10622123—21no—
18#10622123—21no—
19#10622123—21no—
20#10622123—21no—
21#10622123—21no—
22#10622123—21no—
23#10622118—21no—
24#10622117—21no—
25#10622096—21no—
26#10622095—21no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—21no—
30C2×C11×M16—21no—
31C2×C42×C11C2311yescharacteristic
32C2×#4318—21no—
33C2×#4318—21no—
34#66927—21no—
35#66927—21no—
36#66927—21no—
37#66927Q812yes—
38C11×C4⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×C4⋊C8D411yescharacteristic
42C11×C4⋊C8D411yescharacteristic
43C11×C4⋊C8D411yescharacteristic
44C11×C22⋊C8—21no—
45C11×C22⋊C8—21no—
46C4×C8×C11—21no—
47C4×C8×C11—21no—
48C22⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)D411yescharacteristic
54C4⋊(C11⋊C8)D411yescharacteristic
55C4×C11⋊C8—21no—
56#10611—111nomaximal, Sylow
57C23×D11—41no—
58C22×C4×C11#4111yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C2×D44—22no—
62C2×D44—22no—
63C2×D44—22no—
64C2×D44—41no—
65C2×D44—41no—
66C2×D44—41no—
67C2×D44—81no—
68C2×D44—81no—
69C2×D44—81no—
70C2×D44—81no—
71C2×D44—81no—
72C2×D44—81no—
73C11×M16—81no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C42×C11C2×D411yescharacteristic
80C42×C11C2×D411yescharacteristic
81C42×C11C2×D411yescharacteristic
82C42×C11C2×Q811yescharacteristic
83#4318—81no—
84#4318—81no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—41no—
89#1574—111no—
90#1574—111no—
91#1574D1111yescharacteristic, complemented
92#1545—111no—
93#1545—111no—
94#1545—111no—
95#1309—111no—
96C23×C11#12611yescharacteristic
97C22×D11—42no—
98C22×D11—82no—
99C22×D11—82no—
100C22×D11—82no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11#12111yescharacteristic
108C2×C4×C11#12111yescharacteristic
109C2×C4×C11#12111yescharacteristic
110C2×C4×C11C22⋊Q811yescharacteristic
111C2×C4×C11C22⋊Q811yescharacteristic
112C2×C4×C11C22⋊Q811yescharacteristic
113D44—82no—
114D44—82no—
115D44—82no—
116D44—81no—
117D44—81no—
118D44—81no—
119D44—81no—
120D44—81no—
121D44—81no—
122C8×C11—41no—
123C8×C11—41no—
124C8×C11—41no—
125C8×C11—41no—
126C8×C11—81no—
127C11⋊C8—41no—
128C11⋊C8—41no—
129C11⋊C8—81no—
130C11⋊C8—81no—
131C2×#127—111no—
132#431—111no—
133#431C2×D1111yescharacteristic
134#431C2×D1111yescharacteristic
135#423—111no—
136#423—111no—
137#423C2×D1111yescharacteristic
138#335—21no—
139#335—221no—
140#335—221no—
141#334—21no—
142#334—221no—
143#334—221no—
144#331—221no—
145#331—221no—
146#331—221no—
147#331—221no—
148#331—221no—
149#331—221no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11#39611yescharacteristic
154C2×D11—82no—
155C2×D11—82no—
156C2×D11—82no—
157C2×D11—164no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11#47111yescharacteristic
162C4×C11#47111yescharacteristic
163C4×C11#47111yescharacteristic
164C4×C11#47211yescharacteristic
165C4×C11#47211yescharacteristic
166C4×C11#47211yescharacteristic
167C22×D4—221no—
168C22×D4—221no—
169C22×D4—221no—
170C2×M16—21no—
171C2×M16—221no—
172C2×M16—221no—
173#127—112no—
174#127—221no—
175#127—221no—
176#127—221no—
177C2×C42C22×D1111yescharacteristic
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8—111no—
181C4⋊C8—111no—
182C4⋊C8—221no—
183C4⋊C8—221no—
184C4⋊C8—221no—
185C4⋊C8—221no—
186C4⋊C8D4411yescharacteristic
187C4⋊C8D4411yescharacteristic
188C4⋊C8C22⋊D1111yescharacteristic
189C4⋊C8C22⋊D1111yescharacteristic
190C22⋊C8—21no—
191C22⋊C8—21no—
192C22⋊C8—221no—
193C4×C8—21no—
194C4×C8—21no—
195C4×C8—221no—
196C2×C11—41no—
197C2×C11#206311yescharacteristic
198C2×C11#206311yescharacteristic
199C2×C11#206311yescharacteristic
200D11—162no—
201C24—441no—
202C2×D4—222no—
203C2×D4—222no—
204C2×D4—222no—
205C2×D4—441no—
206C2×D4—441no—
207C2×D4—441no—
208C2×D4—881no—
209C2×D4—881no—
210C2×D4—881no—
211C2×D4—881no—
212C2×D4—881no—
213C2×D4—881no—
214C22×C4#433911yescharacteristic
215C22×C4#434111yescharacteristic
216C22×C4#434311yescharacteristic
217M16—81no—
218M16—881no—
219M16—881no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—221no—
226C2×C8—221no—
227C2×C8—441no—
228C2×C8—441no—
229C42C2×D4411yescharacteristic
230C42D4×D1111yescharacteristic
231C42Q8×D1111yescharacteristic
232C42C2×C22⋊D1111yescharacteristic
233C11#1061111yescharacteristic, complemented, Sylow
234C23—442no—
235C23—882no—
236C23—882no—
237C23—882no—
238C23#6695111yescharacteristic
239D4—882no—
240D4—882no—
241D4—882no—
242D4—881no—
243D4—881no—
244D4—881no—
245D4—881no—
246D4—881no—
247D4—881no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4#6694811yescharacteristic
255C2×C4#6694911yescharacteristic
256C2×C4#6695011yescharacteristic
257C2×C4#6698311yescharacteristic
258C2×C4#6699211yescharacteristic
259C2×C4#6699911yescharacteristic
260C8—41no—
261C8—41no—
262C8—41no—
263C8—41no—
264C8—81no—
265C8—441no—
266C8—441no—
267C8—881no—
268C8—881no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—882no—
273C22—882no—
274C22—882no—
275C22—1764no—
276C22#1062260711yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4#1062251011yescharacteristic
281C4#1062251111yescharacteristic
282C4#1062275411yescharacteristic
283C4#1062275511yescharacteristic
284C4#1062281211yescharacteristic
285C4#1062281611yescharacteristic
286C2—41no—
287C2—1762no—
288C2#1306997111yescharacteristic
289C2#1306997311yescharacteristic
290C2#1306997511yescharacteristic
subgroupG/H
centerC22#10622607
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1574C2
socleC22×C11#396
prime radicalC2×#66927C22
hypercenter#1574D11
hypocenterC11#10611
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
1. #13067405C2semidirect
2. #13067404C2semidirect
6. C11⋊#1309C2semidirect
7. C11×#1574C2semidirect
91. #1574D11semidirect
233. C11#10611semidirect

Maximal subgroups

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

subgroupindex
#130674052
#130674042
#130672852
#130672832
C11⋊#13092
C11×#15742
#1061111