Finite Group Databasebeta

← #14658603

Subgroups — #14658603

Order 2816.

330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068627C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13067008C211yesmaximal, characteristic
4#13066513C211yesmaximal, characteristic, complemented
5#13066476C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1571C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66887—21no—
13C2×#66885—21no—
14#10622549C2211yescharacteristic
15#10622538C2211yescharacteristic
16#10622537C2211yescharacteristic
17C11×#335—22no—
18#10622192—21no—
19#10622189—21no—
20#10622097—22no—
21C22×D44D411yescharacteristic
22C22×C4×D11—21no—
23C2×C11×M16—21no—
24C22×C8×C11—21no—
25C2×C42×C11C2311yescharacteristic
26C2×(C2×D11)⋊C4—21no—
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11D411yescharacteristic
29C2×#4318—21no—
30C4×D44—21no—
31C4×D44—21no—
32C4×D44—21no—
33C4×D44—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C4⋊C8—21no—
38C11×C4⋊C8—21no—
39C11×C22⋊C8—21no—
40C4×C8×C11D412yes—
41C11⋊#95—21no—
42C11⋊#95—21no—
43C22⋊(C11⋊C8)—21no—
44#66887—42no—
45#66885—42no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4×C11⋊C8—21no—
50#10638—111nomaximal, Sylow
51C23×D11—21no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×Dic11—21no—
56C22×Dic11—41no—
57C2×D44—21no—
58C2×D44—21no—
59C2×D44—21no—
60C2×D44—21no—
61C2×D44—21no—
62C2×D44Q1612yes—
63C2×C4×D11—41no—
64C2×C4×D11—41no—
65C2×C4×D11—82no—
66C11×M16—41no—
67C11×M16—41no—
68C2×C8×C11—22no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C42×C11C2×D411yescharacteristic
74C42×C11#4111yescharacteristic
75C42×C11#4111yescharacteristic
76C42×C11#4111yescharacteristic
77(C2×D11)⋊C4—41no—
78(C2×D11)⋊C4—41no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83#4318—41no—
84#4318—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87#1804—111no—
88#1800—111no—
89#1571D1111yescharacteristic, complemented
90#1478—111no—
91#1301—111no—
92#1286—111no—
93#1286—111no—
94C23×C11#12311yescharacteristic
95C22×D11—22no—
96C22×D11—41no—
97C22×D11—41no—
98C22×D11—81no—
99C22×D11—81no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11#12311yescharacteristic
104C2×C4×C11#12311yescharacteristic
105C2×C4×C11#12411yescharacteristic
106C2×C4×C11#12611yescharacteristic
107C2×C4×C11#12611yescharacteristic
108C2×C4×C11C2×Q1611yescharacteristic
109C2×C4×C11#13511yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×Dic11—41no—
113C2×Dic11—81no—
114C2×Dic11—81no—
115C2×Dic11—81no—
116C2×Dic11—81no—
117D44—22no—
118D44—22no—
119D44—41no—
120D44—41no—
121C4×D11—82no—
122C4×D11—82no—
123C8×C11—42no—
124C8×C11—81no—
125C8×C11—81no—
126C11⋊C8—81no—
127C11⋊C8—81no—
128C2×C4×D4—111no—
129#431—111no—
130#431C2×D1111yescharacteristic
131#423—111no—
132#423C2×D1111yescharacteristic
133C2×C4⋊C8C2×D1111yescharacteristic
134C2×#102—221no—
135C2×#100—221no—
136#382—111no—
137#343—221no—
138#340—221no—
139#335—22no—
140D4⋊C8—222no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11#39711yescharacteristic
144C22×C11#48211yescharacteristic
145C22×C11#48411yescharacteristic
146C2×D11—42no—
147C2×D11—82no—
148C2×D11—81no—
149C2×D11—81no—
150C2×D11—82no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11#46711yescharacteristic
156C4×C11#46911yescharacteristic
157C4×C11#48211yescharacteristic
158C4×C11#48411yescharacteristic
159Dic11—81no—
160Dic11—161no—
161C22×D4—111no—
162C23×C4—221no—
163C2×M16—21no—
164C2×M16—221no—
165C22×C8—21no—
166C4×D4—221no—
167C4×D4—221no—
168C4×D4—221no—
169C4×D4—221no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—221no—
172C2×C22⋊C4—221no—
173C2×C42C22×D1111yescharacteristic
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181C4⋊C8—221no—
182#102—442no—
183#100—442no—
184C22⋊C8—21no—
185C22⋊C8—221no—
186C4×C8—221no—
187C4×C8C22⋊D1112yes—
188#95—221no—
189#95—221no—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11#207611yescharacteristic
193C2×C11#208011yescharacteristic
194C2×C11#208111yescharacteristic
195D11—82no—
196C24—221no—
197C2×D4—112no—
198C2×D4—221no—
199C2×D4—221no—
200C2×D4—221no—
201C2×D4—221no—
202C2×D4—221no—
203C22×C4—221no—
204C22×C4—441no—
205C22×C4—441no—
206C22×C4—441no—
207C22×C4—882no—
208C22×C4#433911yescharacteristic
209C22×C4D4×D1111yescharacteristic
210C22×C4#434311yescharacteristic
211M16—41no—
212M16—41no—
213M16—441no—
214M16—441no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—441no—
221C2×C8—441no—
222C4⋊C4—221no—
223C4⋊C4—221no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C22⋊C4—441no—
227C22⋊C4—441no—
228C42#433911yescharacteristic
229C42#434111yescharacteristic
230C42#434311yescharacteristic
231C42C2×C22⋊D1111yescharacteristic
232C11#1063811yescharacteristic, complemented, Sylow
233C23—222no—
234C23—441no—
235C23—441no—
236C23—881no—
237C23—881no—
238C23#6694711yescharacteristic
239D4—222no—
240D4—222no—
241D4—441no—
242D4—441no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—441no—
246C2×C4—882no—
247C2×C4—882no—
248C2×C4—881no—
249C2×C4—881no—
250C2×C4—881no—
251C2×C4—881no—
252C2×C4#6694711yescharacteristic
253C2×C4#6695111yescharacteristic
254C2×C4#6695111yescharacteristic
255C2×C4#6696411yescharacteristic
256C2×C4#6696411yescharacteristic
257C2×C4Q16×D1111yescharacteristic
258C2×C4#6697211yescharacteristic
259C2×C4#6698211yescharacteristic
260C2×C4#6699111yescharacteristic
261C2×C4#6700011yescharacteristic
262C8—42no—
263C8—81no—
264C8—81no—
265C8—881no—
266C8—881no—
267C22—21no—
268C22—21no—
269C22—442no—
270C22—882no—
271C22—882no—
272C22—881no—
273C22—881no—
274C22#1062249711yescharacteristic
275C22#1062249811yescharacteristic
276C22#1062260611yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—881no—
282C4—1761no—
283C4#1062249711yescharacteristic
284C4#1062249811yescharacteristic
285C4#1062277211yescharacteristic
286C4#1062280111yescharacteristic
287C2—21no—
288C2—21no—
289C2—882no—
290C2#1307004511yescharacteristic
291C2#1307006711yescharacteristic
292C2#1307007411yescharacteristic
subgroupG/H
centerC22#10622606
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1571C2
socleC22×C11#397
prime radicalC22×D44D4
hypercenter#1571D11
hypocenterC11#10638
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
4. #13066513C2semidirect
5. #13066476C2semidirect
6. #13066475C2semidirect
7. C11×#1571C2semidirect
89. #1571D11semidirect
232. C11#10638semidirect

Maximal subgroups

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

subgroupindex
#130686272
#130686052
#130670082
#130665132
#130664762
#130664752
C11×#15712
#1063811