Finite Group Databasebeta

← #14658597

Subgroups — #14658597

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#13068623C211yesmaximal, characteristic
2#13068605C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic, complemented
4#13067008C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66887—21no—
13C2×#66873—21no—
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17#10622192—21no—
18#10622167—21no—
19#10622097—22no—
20#10622096—22no—
21C22×D44D411yescharacteristic
22C22×C4×D11—21no—
23C2×C11×M16—21no—
24C2×C11×C4⋊C4—21no—
25C2×C42×C11C2311yescharacteristic
26C2×(C2×D11)⋊C4—21no—
27C2×C4⋊Dic11D411yescharacteristic
28C2×#4318—21no—
29C22×C11⋊C8—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×C22⋊C8—21no—
38C4×C8×C11D412yes—
39C11×#95—21no—
40C11×#95—21no—
41C22⋊(C11⋊C8)—21no—
42#66887—42no—
43#66873—42no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4×C11⋊C8—21no—
50#10637—111nomaximal, Sylow
51C23×D11—21no—
52C22×C4×C11—41no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C22×Dic11—21no—
57C2×D44—21no—
58C2×D44—21no—
59C2×D44—21no—
60C2×D44—21no—
61C2×D44—21no—
62C2×D44D812yes—
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—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C42×C11C2×D411yescharacteristic
73C42×C11#4111yescharacteristic
74C42×C11#4111yescharacteristic
75C42×C11#4111yescharacteristic
76(C2×D11)⋊C4—41no—
77(C2×D11)⋊C4—41no—
78C4⋊Dic11—21no—
79C4⋊Dic11—21no—
80#4318—41no—
81#4318—41no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87#1804—111no—
88#1800—111no—
89#1571—111no—
90#1478—111no—
91#1301—111no—
92#1286—111no—
93#1286D1111yescharacteristic, complemented
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—81no—
103C2×C4×C11—81no—
104C2×C4×C11—81no—
105C2×C4×C11#12111yescharacteristic
106C2×C4×C11#12311yescharacteristic
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11#12411yescharacteristic
109C2×C4×C11#12611yescharacteristic
110C2×C4×C11#12611yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11#13511yescharacteristic
113C2×C4×C11#13711yescharacteristic
114C2×C4×C11#13711yescharacteristic
115C2×Dic11—41no—
116C2×Dic11—81no—
117D44—22no—
118D44—22no—
119D44—41no—
120D44—41no—
121C4×D11—82no—
122C4×D11—82no—
123C8×C11—42no—
124C8×C11—81no—
125C11⋊C8—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⋊C8—111no—
134C2×#102—221no—
135C2×#100—221no—
136#382C2×D1111yescharacteristic
137#343—221no—
138#340—221no—
139#335—222no—
140D4⋊C8—222no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11#39711yescharacteristic
144C22×C11#48011yescharacteristic
145C22×C11#48511yescharacteristic
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—161no—
156C4×C11#46611yescharacteristic
157C4×C11#47011yescharacteristic
158C4×C11#48011yescharacteristic
159C4×C11#48511yescharacteristic
160Dic11—81no—
161C22×D4—111no—
162C23×C4—221no—
163C2×M16—21no—
164C2×M16—221no—
165C22×C8—221no—
166C4×D4—221no—
167C4×D4—221no—
168C4×D4—221no—
169C4×D4—221no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—111no—
172C2×C22⋊C4—221no—
173C2×C42C22×D1111yescharacteristic
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—221no—
178C4⋊C8—221no—
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×C8D4412yes—
188#95—21no—
189#95—21no—
190C2×C11—21no—
191C2×C11—21no—
192C2×C11#207511yescharacteristic
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—41no—
204C22×C4—221no—
205C22×C4—441no—
206C22×C4—441no—
207C22×C4—882no—
208C22×C4#433911yescharacteristic
209C22×C4D4×D1111yescharacteristic
210C22×C4#434111yescharacteristic
211M16—41no—
212M16—41no—
213M16—441no—
214M16—441no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—441no—
218C2×C8—441no—
219C2×C8—441no—
220C2×C8—441no—
221C2×C8—441no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—221no—
225C4⋊C4—221no—
226C22⋊C4—441no—
227C22⋊C4—441no—
228C42C2×D4411yescharacteristic
229C42#433911yescharacteristic
230C42#434111yescharacteristic
231C42#434311yescharacteristic
232C11#1063711yescharacteristic, complemented, Sylow
233C23—222no—
234C23—441no—
235C23—441no—
236C23—881no—
237C23—881no—
238C23#6693611yescharacteristic
239D4—222no—
240D4—222no—
241D4—441no—
242D4—441no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—441no—
249C2×C4—882no—
250C2×C4—882no—
251C2×C4—881no—
252C2×C4#6692811yescharacteristic
253C2×C4#6693611yescharacteristic
254C2×C4#6693911yescharacteristic
255C2×C4#6694811yescharacteristic
256C2×C4#6695111yescharacteristic
257C2×C4#6695111yescharacteristic
258C2×C4D8×D1111yescharacteristic
259C2×C4#6696811yescharacteristic
260C2×C4#6696811yescharacteristic
261C2×C4#6697211yescharacteristic
262C8—42no—
263C8—81no—
264C8—881no—
265C8—881no—
266C8—881no—
267C22—21no—
268C22—21no—
269C22—442no—
270C22—882no—
271C22—882no—
272C22—881no—
273C22—881no—
274C22#1062228711yescharacteristic
275C22#1062238711yescharacteristic
276C22#1062242711yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—161no—
282C4—881no—
283C4#1062238711yescharacteristic
284C4#1062242711yescharacteristic
285C4#1062248111yescharacteristic
286C4#1062249611yescharacteristic
287C2—21no—
288C2—21no—
289C2—882no—
290C2#1307004111yescharacteristic
291C2#1307006811yescharacteristic
292C2#1307007511yescharacteristic
subgroupG/H
centerC22#10622287
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#397
prime radicalC22×D44D4
hypercenter#1286D11
hypocenterC11#10637
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
3. #13067391C2semidirect
5. #13066511C2semidirect
6. #13066474C2semidirect
7. C11×#1286C2semidirect
93. #1286D11semidirect
232. C11#10637semidirect

Maximal subgroups

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

subgroupindex
#130686232
#130686052
#130673912
#130670082
#130665112
#130664742
C11×#12862
#1063711