Finite Group Databasebeta

← #14669224

Subgroups — #14669224

Order 2816.

890 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 155 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#13083327C211yesmaximal, characteristic
2#13070245C212yesmaximal, complemented
3C2×#10622146C212yesmaximal, complemented
4#13070237C211yesmaximal, characteristic, complemented
5C11×#2113C211yesmaximal, characteristic, complemented
6#10623453C411yescharacteristic
7C2×C11×#131C2211yescharacteristic
8#10623350C411yescharacteristic
9#10623281—24no—
10D11×#131—24no—
11#10623276—22no—
12#10623276C412yes—
13C2×#66954—22no—
14C2×#66954C2212yes—
15C2×C11×M32C2211yescharacteristic, complemented
16C22×C11×C16C2211yescharacteristic, complemented
17C2×#66876C2212yescomplemented
18C11×C22⋊C16—22no—
19#10622191—22no—
20#10622153—24no—
21#10622146—24no—
22C2×C11×#41C2×C411yescharacteristic
23#67043—22no—
24#67042—22no—
25#41×D11—24no—
26#67040C812yes—
27#67037—22no—
28#67037C812yes—
29C2×#4339—22no—
30C2×#4339C2×C412yes—
31C11×#131—22no—
32C11×#131—22no—
33C2×C11×M16C2×C411yescharacteristic
34C2×C11×M16D412yes—
35C22×C8×C11D412yes—
36C22×C8×C11C2311yescharacteristic
37#67001—24no—
38C2×#4318—22no—
39C2×#4318C2×C412yes—
40#66960—28no—
41#66960—24no—
42M16×D11—28no—
43M16×D11—24no—
44#66954—24no—
45#66954—24no—
46#66954—24no—
47#66954—22no—
48#66954—22no—
49#66954D414yes—
50#66954D414yes—
51C2×#4313—24no—
52C2×#4313—22no—
53C2×C8×D11—24no—
54C2×C8×D11—22no—
55C11×M32—22no—
56C2×C11×C16—21no—
57C2×C11×C16—22no—
58C2×C11×C16—21no—
59#66876—22no—
60#66876—22no—
61C2×C11⋊C16—22no—
62#12685—111nomaximal, Sylow
63C11×#41—22no—
64C11×#41—22no—
65C2×Q8×C11C2×C811yescharacteristic
66C2×D4×C11C2×C811yescharacteristic
67C2×D4×C11M1612yes—
68C22×C4×C11C22⋊C412yes—
69C22×C4×C11C22×C411yescharacteristic
70C2×C22⋊D11—24no—
71C2×C22⋊D11—22no—
72#4343—24no—
73Q8×D11—24no—
74#4341—28no—
75#4341—24no—
76D4×D11—28no—
77D4×D11—24no—
78#4339—24no—
79#4339—24no—
80#4339—24no—
81#4339—22no—
82#4339—22no—
83#4339C22⋊C414yes—
84#4339C2×C814yes—
85C2×D44—22no—
86C2×D44M1612yes—
87C2×C4×D11—24no—
88C2×C4×D11—22no—
89C2×Dic22—22no—
90C2×Dic22M1612yes—
91C11×M16—24no—
92C11×M16—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11C22⋊C412yes—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D412yes—
98C2×C8×C11C2×D412yes—
99C2×C8×C11C2×D411yescharacteristic
100#4318—24no—
101#4318—22no—
102#4318C22⋊C414yes—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—22no—
105#4313—28no—
106#4313—24no—
107#4313—24no—
108C8×D11—28no—
109C8×D11—24no—
110C8×D11—24no—
111C11×C16—41no—
112C11×C16—41no—
113C11⋊C16—42no—
114#3573—111no—
115#2117—112no—
116C2×#350—112no—
117#2115—111no—
118#2113D1111yescharacteristic, complemented
119C23×C11C22⋊C812yes—
120C23×C11C2×M1611yescharacteristic
121C22×D11—24no—
122C22×D11—22no—
123Q8×C11—22no—
124D4×C11—24no—
125D4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11C22⋊C812yes—
129C2×C4×C11C2×C22⋊C412yes—
130C2×C4×C11C2×C22⋊C411yescharacteristic
131C2×C4×C11C22×C811yescharacteristic
132C2×C4×C11C2×M1612yes—
133C22⋊D11—28no—
134C22⋊D11—24no—
135C22⋊D11—24no—
136C2×Dic11—24no—
137C2×Dic11—22no—
138D44—24no—
139D44—22no—
140D44C22⋊C814yes—
141C4×D11—28no—
142C4×D11—24no—
143C4×D11—24no—
144Dic22—24no—
145Dic22—22no—
146Dic22C22⋊C814yes—
147C8×C11—22no—
148C8×C11#12012yes—
149C8×C11#12011yescharacteristic
150C8×C11#12011yescharacteristic
151C11⋊C8—24no—
152#585—111no—
153#568—111no—
154#568—112no—
155#568—224no—
156#568—222no—
157C2×#131—112no—
158C2×#131—224no—
159C2×#131—222no—
160C2×#131C2×D1111yescharacteristic
161C2×M32—112no—
162C2×M32C2×D1111yescharacteristic, complemented
163C22×C16C2×D1111yescharacteristic, complemented
164#350—224no—
165#350—224no—
166#349—222no—
167C22⋊C16—22no—
168C22×C11—22no—
169C22×C11—41no—
170C22×C11—42no—
171C22×C11C2×C22⋊C811yescharacteristic
172C22×C11#40712yes—
173C2×D11—24no—
174C2×D11—82no—
175C2×D11—84no—
176C4×C11—22no—
177C4×C11#37911yescharacteristic
178C4×C11C2×C22⋊C812yes—
179C4×C11#40711yescharacteristic
180Dic11—24no—
1812−1+4—112no—
1822−1+4—222no—
183H(5,𝔽2)—112no—
184H(5,𝔽2)—222no—
185H(5,𝔽2)—222no—
186C2×#41—112no—
187C2×#41—224no—
188C2×#41—222no—
189C2×#41C4×D1111yescharacteristic
190#131—22no—
191#131—22no—
192#131—114no—
193#131—114no—
194#131—224no—
195#131—224no—
196#131—224no—
197#131—228no—
198#131—224no—
199#131—224no—
200#131—222no—
201#131—222no—
202C2×M16—112no—
203C2×M16—224no—
204C2×M16—224no—
205C2×M16—228no—
206C2×M16—222no—
207C2×M16—222no—
208C2×M16C4×D1111yescharacteristic
209C2×M16D4412yes—
210C22×C8—224no—
211C22×C8—222no—
212C22×C8C22⋊D1112yes—
213C22×C8C22×D1111yescharacteristic
214M32—22no—
215M32—222no—
216M32—222no—
217C2×C16—22no—
218C2×C16—21no—
219C2×C16—21no—
220C2×C16—222no—
221C2×C11—22no—
222C2×C11—21no—
223C2×C11—42no—
224C2×C11#177911yescharacteristic
225D11—44no—
226#41—22no—
227#41—22no—
228#41—114no—
229#41—114no—
230#41—224no—
231#41—224no—
232#41—224no—
233#41—228no—
234#41—224no—
235#41—224no—
236#41—222no—
237#41—222no—
238C2×Q8—112no—
239C2×Q8—222no—
240C2×Q8—224no—
241C2×Q8C8×D1111yescharacteristic
242C2×D4—112no—
243C2×D4—222no—
244C2×D4—224no—
245C2×D4—228no—
246C2×D4—224no—
247C2×D4—222no—
248C2×D4C8×D1111yescharacteristic
249C2×D4#431312yes—
250C22×C4—224no—
251C22×C4—222no—
252C22×C4(C2×D11)⋊C412yes—
253C22×C4C2×C4×D1111yescharacteristic
254M16—22no—
255M16—24no—
256M16—114no—
257M16—228no—
258M16—224no—
259M16—222no—
260M16—224no—
261M16—224no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—228no—
265C2×C8—224no—
266C2×C8—222no—
267C2×C8—224no—
268C2×C8—224no—
269C2×C8(C2×D11)⋊C412yes—
270C2×C8C2×D4411yescharacteristic
271C2×C8D4×D1112yes—
272C2×C8D4×D1112yes—
273C2×C8C2×C22⋊D1111yescharacteristic
274C16—41no—
275C16—41no—
276C16—442no—
277C11#1268511yescharacteristic, complemented, Sylow
278C23—224no—
279C23—222no—
280C23(C2×D11)⋊C812yes—
281C23C2×#431311yescharacteristic
282Q8—22no—
283Q8—114no—
284Q8—224no—
285Q8—222no—
286D4—24no—
287D4—22no—
288D4—114no—
289D4—224no—
290D4—228no—
291D4—224no—
292D4—224no—
293D4—222no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—228no—
297C2×C4—224no—
298C2×C4—222no—
299C2×C4—224no—
300C2×C4—224no—
301C2×C4(C2×D11)⋊C812yes—
302C2×C4C22⋊C4×D1112yes—
303C2×C4C2×C8×D1111yescharacteristic
304C2×C4M16×D1112yes—
305C2×C4C2×(C2×D11)⋊C411yescharacteristic
306C8—22no—
307C8—224no—
308C8#6693512yes—
309C8#6699011yescharacteristic
310C8#6699011yescharacteristic
311C22—22no—
312C22—41no—
313C22—42no—
314C22—224no—
315C22—882no—
316C22—884no—
317C22#1062233912yes—
318C22C2×(C2×D11)⋊C811yescharacteristic
319C4—22no—
320C4—224no—
321C4D11×C22⋊C812yes—
322C4#1062256811yescharacteristic
323C4#1062273911yescharacteristic
324C2—21no—
325C2—22no—
326C2—42no—
327C2—444no—
328C2#1306852511yescharacteristic
subgroupG/H
centerC8#66990
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2113C2
socleC2×C11#1779
prime radical#10623453C4
cosocleC22×C8×C11C23
hypercenter#2113D11
hypocenterC11#12685
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. #13070245C2semidirect
3. C2×#10622146C2semidirect
4. #13070237C2semidirect
5. C11×#2113C2semidirect
15. C2×C11×M32C22semidirect
16. C22×C11×C16C22semidirect
17. C2×#66876C22semidirect
118. #2113D11semidirect
162. C2×M32C2×D11semidirect
163. C22×C16C2×D11semidirect
277. C11#12685semidirect

Maximal subgroups

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

subgroupindex
#130833272
#130702452
C2×#106221462
#130702372
C11×#21132
#1268511