Finite Group Databasebeta

← #14670346

Subgroups — #14670346

Order 2816.

402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077204C211yesmaximal, characteristic
2#13070389C211yesmaximal, characteristic, complemented
3#13070388C211yesmaximal, characteristic, complemented
4C2×#10622152C211yesmaximal, characteristic
5#13068655C211yesmaximal, characteristic
6#13066730C211yesmaximal, characteristic, complemented
7C11×#1389C211yesmaximal, characteristic, complemented
8C22×#4313C2211yescharacteristic
9D11×#117—21no—
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C11×#427C2211yescharacteristic
13#10622739—21no—
14C2×#66883C2211yescharacteristic
15#10622719C2211yescharacteristic
16C2×#66876C2211yescharacteristic
17#10622611—21no—
18#10622494—22no—
19#10622474—22no—
20#10622196—21no—
21#10622152C414yescomplemented
22#10622151—22no—
23#10622125—22no—
24C22×C4×D11D411yescharacteristic
25C2×C11×M16—21no—
26C22×C8×C11C2311yescharacteristic
27C11×#117—21no—
28#66979—21no—
29C2×#4318—21no—
30C22×C11⋊C8D411yescharacteristic
31C2×#4313—21no—
32C2×#4313—21no—
33C2×#4313—21no—
34C2×#4313—21no—
35C2×#4313C2×C412yes—
36C2×#4313Q812yes—
37#66945—22no—
38C4⋊C4×D11—22no—
39C22⋊C4×D11—41no—
40#66930—41no—
41#66925—41no—
42C42×D11—41no—
43C11×M32—21no—
44C11×M32C2×C412yescomplemented
45C2×C11×C16—21no—
46C11×#108—21no—
47C11×#108—21no—
48C11×#107—21no—
49C11×#106D412yes—
50(C2×D11)⋊C8—42no—
51#66883—21no—
52#66883—21no—
53#66882—21no—
54#66881D412yes—
55#66876—21no—
56#66876C2×C412yescomplemented
57C2×C11⋊C16—21no—
58#66872—22no—
59#66871—22no—
60#12932—111nomaximal, Sylow
61C23×D11SD1611yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11SD1611yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11—42no—
69C2×C4×D11C4⋊C412yes—
70C2×C4×D11SD1612yes—
71C11×M16—41no—
72C11×M16—41no—
73C2×C8×C11—41no—
74C2×C8×C11C22×C411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11C2×Q811yescharacteristic
78C2×C8×C11#4111yescharacteristic
79C2×C8×C11#4111yescharacteristic
80C11×C4⋊C4—22no—
81C11×C22⋊C4—41no—
82C42×C11—41no—
83C22⋊Dic11—41no—
84(C2×D11)⋊C4—42no—
85C4⋊Dic11—22no—
86Dic11⋊C4—42no—
87C4×Dic11—42no—
88C4×Dic11—41no—
89#4318—41no—
90#4318—41no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8C4⋊C412yes—
95#4313—22no—
96#4313—22no—
97#4313—22no—
98#4313—22no—
99C11×C16—22no—
100C11⋊C16—22no—
101#2911—111no—
102#2155—111no—
103#2155—111no—
104C2×#349—111no—
105#1811—111no—
106#1389—111no—
107#1389D1111yescharacteristic, complemented
108C23×C11C2×SD1611yescharacteristic
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—81no—
112C22×D11#10612yes—
113C2×C4×C11—42no—
114C2×C4×C11C2×C4⋊C411yescharacteristic
115C2×C4×C11#12011yescharacteristic
116C2×C4×C11#12311yescharacteristic
117C2×C4×C11C2×SD1611yescharacteristic
118C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C11#13711yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—42no—
123C2×Dic11#10612yes—
124C4×D11—22no—
125C4×D11—22no—
126C4×D11—22no—
127C4×D11—22no—
128C4×D11—84no—
129C8×C11—81no—
130C8×C11C4×D411yescharacteristic
131C8×C11C4×D411yescharacteristic
132C8×C11C22⋊Q811yescharacteristic
133C8×C11C22⋊Q811yescharacteristic
134C11⋊C8—22no—
135C11⋊C8—81no—
136C22×M16—111no—
137C2×#117—221no—
138C2×M32—111no—
139C2×M32C2×D1111yescharacteristic
140C2×#108—111no—
141C2×#108C2×D1111yescharacteristic
142#428—222no—
143#428—222no—
144#427—111no—
145#427—221no—
146#427C2×D1111yescharacteristic
147#407—221no—
148#365—222no—
149#365—222no—
150#349—114no—
151#341—221no—
152C22×C11—41no—
153C22×C11C2×#10611yescharacteristic
154C22×C11#45011yescharacteristic
155C22×C11#48311yescharacteristic
156C2×D11—22no—
157C2×D11—42no—
158C2×D11—42no—
159C2×D11—81no—
160C4×C11—82no—
161C4×C11#38511yescharacteristic
162C4×C11#42811yescharacteristic
163C4×C11#44811yescharacteristic
164C4×C11#48111yescharacteristic
165Dic11—22no—
166Dic11—82no—
167C23×C4—111no—
168C2×M16—21no—
169C2×M16—112no—
170C2×M16—112no—
171C2×M16—221no—
172C2×M16—221no—
173C2×M16—221no—
174C2×M16—221no—
175C2×M16—221no—
176C22×C8—111no—
177C22×C8C22×D1111yescharacteristic
178#117—21no—
179#117—222no—
180#117—221no—
181#117—441no—
182#117—441no—
183C2×C4⋊C4—222no—
184C2×C22⋊C4—441no—
185C2×C42—441no—
186M32—21no—
187M32—112no—
188M32—221no—
189M32C4×D1112yescomplemented
190C2×C16—21no—
191C2×C16—221no—
192#108—21no—
193#108—21no—
194#108—221no—
195#108—221no—
196#107—21no—
197#107—222no—
198#107—221no—
199#106—112no—
200#106—222no—
201#106D4412yes—
202C22⋊C8—442no—
203C2×C11—21no—
204C2×C11—21no—
205C2×C11—21no—
206C2×C11#185311yescharacteristic
207D11—42no—
208C24—111no—
209C22×C4—111no—
210C22×C4—112no—
211C22×C4—112no—
212C22×C4—221no—
213C22×C4—221no—
214C22×C4—221no—
215C22×C4—221no—
216C22×C4—442no—
217C22×C4D4×D1111yescharacteristic
218M16—41no—
219M16—41no—
220M16—222no—
221M16—222no—
222M16—222no—
223M16—222no—
224M16—441no—
225M16—441no—
226C2×C8—41no—
227C2×C8—112no—
228C2×C8—221no—
229C2×C8—221no—
230C2×C8—441no—
231C2×C8C2×C4×D1111yescharacteristic
232C2×C8C2×D4411yescharacteristic
233C2×C8#433911yescharacteristic
234C2×C8D4×D1111yescharacteristic
235C2×C8#434111yescharacteristic
236C2×C8Q8×D1111yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—222no—
239C4⋊C4—442no—
240C22⋊C4—41no—
241C22⋊C4—442no—
242C22⋊C4—441no—
243C42—41no—
244C42—442no—
245C42—441no—
246C16—22no—
247C16—222no—
248C11#1293211yescharacteristic, complemented, Sylow
249C23—112no—
250C23—221no—
251C23—221no—
252C23—881no—
253C23SD16×D1111yescharacteristic
254C2×C4—42no—
255C2×C4—112no—
256C2×C4—221no—
257C2×C4—221no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—442no—
263C2×C4—884no—
264C2×C4#6693511yescharacteristic
265C2×C4#6693611yescharacteristic
266C2×C4C4⋊C4×D1111yescharacteristic
267C2×C4#6696411yescharacteristic
268C2×C4SD16×D1111yescharacteristic
269C2×C4#6697111yescharacteristic
270C8—81no—
271C8—222no—
272C8—881no—
273C8C4×D4411yescharacteristic
274C8(C22⋊D11)⋊C411yescharacteristic
275C8#6694911yescharacteristic
276C8#6695011yescharacteristic
277C22—41no—
278C22—222no—
279C22—442no—
280C22—442no—
281C22—881no—
282C22#1062238911yescharacteristic
283C22#1062241811yescharacteristic
284C22D11×#10611yescharacteristic
285C4—82no—
286C4—222no—
287C4—882no—
288C4#1062228111yescharacteristic
289C4#1062239011yescharacteristic
290C4#1062241911yescharacteristic
291C4#1062249411yescharacteristic
292C2—21no—
293C2—21no—
294C2—21no—
295C2—442no—
296C2#1306881011yescharacteristic
subgroupG/H
centerC4#10622390
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1389C2
socleC2×C11#1853
prime radicalC23×D11SD16
cosocleC22×C8×C11C23
hypercenter#1389D11
hypocenterC11#12932
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1389

Complements

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

NH ≅ G/Ntype
2. #13070389C2semidirect
3. #13070388C2semidirect
6. #13066730C2semidirect
7. C11×#1389C2semidirect
21. #10622152C4semidirect
44. C11×M32C2×C4semidirect
56. #66876C2×C4semidirect
107. #1389D11semidirect
189. M32C4×D11semidirect
248. C11#12932semidirect

Maximal subgroups

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

subgroupindex
#130772042
#130703892
#130703882
C2×#106221522
#130686552
#130667302
C11×#13892
#1293211