Finite Group Databasebeta

← #14658582

Subgroups — #14658582

Order 2816.

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

normal subgroups only

This group has 346 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#13069439C211yesmaximal, characteristic
2#13068756C211yesmaximal, characteristic, complemented
3#13067285C211yesmaximal, characteristic
4#13067283C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic, complemented
6#13066460C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66927C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66873—21no—
13C2×#66873—21no—
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17#10622196—21no—
18#10622196—21no—
19#10622123—22no—
20#10622123—22no—
21C22×D44—21no—
22C22×D44—21no—
23C22×D44—21no—
24C2×C11×M16—21no—
25C2×C11×C4⋊C4—21no—
26C2×C42×C11C2311yescharacteristic
27C2×#4318—21no—
28C22×C11⋊C8D411yescharacteristic
29C22×C11⋊C8D411yescharacteristic
30#66927—21no—
31#66927—21no—
32#66927—21no—
33#66927D412yes—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11—21no—
39C11×#95—21no—
40C11×#95—21no—
41C22⋊(C11⋊C8)—21no—
42#66873—42no—
43#66873—42no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47#66867—21no—
48#66867—21no—
49C4×C11⋊C8—21no—
50#10634—111nomaximal, Sylow
51C23×D11—41no—
52C22×C4×C11—41no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C2×D44—22no—
57C2×D44—22no—
58C2×D44—22no—
59C2×D44—41no—
60C2×D44—41no—
61C2×D44—41no—
62C2×D44—41no—
63C2×D44—41no—
64C2×D44—41no—
65C2×D44—41no—
66C2×D44—82no—
67C2×D44—82no—
68C11×M16—41no—
69C11×M16—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C42×C11C2×D411yescharacteristic
75C42×C11#4111yescharacteristic
76C42×C11#4111yescharacteristic
77C42×C11#4111yescharacteristic
78#4318—41no—
79#4318—41no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—21no—
83C2×C11⋊C8—21no—
84C2×C11⋊C8—21no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—41no—
88#1961—111no—
89#1838—111no—
90#1545—111no—
91#1545—111no—
92#1286—111no—
93#1286D1111yescharacteristic, complemented
94#1281—111no—
95C23×C11#12411yescharacteristic
96C22×D11—42no—
97C22×D11—82no—
98C22×D11—82no—
99C22×D11—81no—
100C22×D11—81no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—81no—
104C2×C4×C11—81no—
105C2×C4×C11—81no—
106C2×C4×C11#12111yescharacteristic
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11#12311yescharacteristic
109C2×C4×C11#12311yescharacteristic
110C2×C4×C11#12611yescharacteristic
111C2×C4×C11#12611yescharacteristic
112C2×C4×C11#13511yescharacteristic
113C2×C4×C11#13511yescharacteristic
114C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
116D44—42no—
117D44—42no—
118D44—82no—
119D44—82no—
120D44—82no—
121D44—82no—
122D44—81no—
123D44—81no—
124C8×C11—81no—
125C8×C11—81no—
126C11⋊C8—41no—
127C11⋊C8—41no—
128C11⋊C8—81no—
129C11⋊C8—81no—
130C2×#127—111no—
131#431—111no—
132#431C2×D1111yescharacteristic
133#423—111no—
134#423C2×D1111yescharacteristic
135C2×#102—221no—
136C2×#102—221no—
137C2×#97—111no—
138#382C2×D1111yescharacteristic
139#341—221no—
140#341—221no—
141#331—222no—
142#331—222no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11#39711yescharacteristic
146C22×C11#48811yescharacteristic
147C22×C11#49011yescharacteristic
148C2×D11—82no—
149C2×D11—82no—
150C2×D11—82no—
151C2×D11—162no—
152C2×D11—162no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—161no—
158C4×C11#46311yescharacteristic
159C4×C11#46311yescharacteristic
160C4×C11#48211yescharacteristic
161C4×C11#48211yescharacteristic
162C22×D4—221no—
163C22×D4—221no—
164C22×D4—221no—
165C2×M16—21no—
166C2×M16—221no—
167C22×C8—111no—
168C22×C8—111no—
169#127—112no—
170#127—221no—
171#127—221no—
172#127—221no—
173C2×C4⋊C4—21no—
174C2×C42C22×D1111yescharacteristic
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—221no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181#102—442no—
182#102—442no—
183C22⋊C8—21no—
184C22⋊C8—221no—
185#97—221no—
186#97—221no—
187C4×C8—21no—
188C4×C8—221no—
189#95—21no—
190#95—21no—
191C2×C11—21no—
192C2×C11—21no—
193C2×C11#207311yescharacteristic
194C2×C11#208111yescharacteristic
195C2×C11#208111yescharacteristic
196D11—162no—
197C24—441no—
198C2×D4—222no—
199C2×D4—222no—
200C2×D4—222no—
201C2×D4—441no—
202C2×D4—441no—
203C2×D4—441no—
204C2×D4—441no—
205C2×D4—441no—
206C2×D4—441no—
207C2×D4—441no—
208C2×D4—882no—
209C2×D4—882no—
210C22×C4—41no—
211C22×C4#433911yescharacteristic
212C22×C4D4×D1111yescharacteristic
213C22×C4#434111yescharacteristic
214M16—41no—
215M16—41no—
216M16—441no—
217M16—441no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—221no—
221C2×C8—221no—
222C2×C8—221no—
223C2×C8—221no—
224C2×C8—221no—
225C2×C8—221no—
226C2×C8—441no—
227C2×C8—441no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C42#433911yescharacteristic
231C42#433911yescharacteristic
232C42D4×D1111yescharacteristic
233C42#434311yescharacteristic
234C11#1063411yescharacteristic, complemented, Sylow
235C23—442no—
236C23—882no—
237C23—882no—
238C23—881no—
239C23—881no—
240C23#6693811yescharacteristic
241D4—442no—
242D4—442no—
243D4—882no—
244D4—882no—
245D4—882no—
246D4—882no—
247D4—881no—
248D4—881no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4#6692911yescharacteristic
255C2×C4#6693611yescharacteristic
256C2×C4#6693711yescharacteristic
257C2×C4#6694711yescharacteristic
258C2×C4#6694711yescharacteristic
259C2×C4#6695111yescharacteristic
260C2×C4#6696411yescharacteristic
261C2×C4#6696711yescharacteristic
262C2×C4#6696911yescharacteristic
263C2×C4#6697211yescharacteristic
264C8—81no—
265C8—81no—
266C8—441no—
267C8—441no—
268C8—881no—
269C8—881no—
270C22—21no—
271C22—21no—
272C22—882no—
273C22—882no—
274C22—882no—
275C22—1762no—
276C22—1762no—
277C22#1062228811yescharacteristic
278C22#1062237711yescharacteristic
279C22#1062241311yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—161no—
285C4#1062240011yescharacteristic
286C4#1062243211yescharacteristic
287C4#1062247911yescharacteristic
288C4#1062249811yescharacteristic
289C2—21no—
290C2—21no—
291C2—1762no—
292C2#1307003311yescharacteristic
293C2#1307007811yescharacteristic
294C2#1307007911yescharacteristic
subgroupG/H
centerC22#10622288
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#397
prime radicalC2×#66927C22
hypercenter#1286D11
hypocenterC11#10634
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
2. #13068756C2semidirect
5. #13066474C2semidirect
6. #13066460C2semidirect
7. C11×#1286C2semidirect
93. #1286D11semidirect
234. C11#10634semidirect

Maximal subgroups

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

subgroupindex
#130694392
#130687562
#130672852
#130672832
#130664742
#130664602
C11×#12862
#1063411