Finite Group Databasebeta

← #14645853

Subgroups — #14645853

Order 2816.

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

normal subgroups only

This group has 868 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
1C2×#10623244C211yesmaximal, characteristic
2#13068618C212yesmaximal, complemented
3C2×#10622182C211yesmaximal, characteristic
4C2×#10622094C212yesmaximal, complemented
5C11×#1957C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×#66989—22no—
8C2×#66988—22no—
9C2×D4×Dic11—22no—
10#10623244—22no—
11#10623244—24no—
12#10623244C414yescomplemented
13C2×C4×Dic22C2212yes—
14C2×C11×#102—22no—
15C2×C4×C8×C11C2211yescharacteristic
16C11×#384C2211yescharacteristic
17C2×#66874—22no—
18C2×C4⋊(C11⋊C8)C2212yes—
19#10622182—22no—
20#10622167—22no—
21#10622094—24no—
22C22×D4×C11—22no—
23C22×D4×C11D412yes—
24C23×Dic11—22no—
25C22×Dic22D412yes—
26C22×C8×C11—21no—
27C11×#127—22no—
28C11×#127C2×C412yes—
29C11×#127D412yes—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—24no—
34C2×C22⋊Dic11—22no—
35#66989—28no—
36#66989—28no—
37#66988—28no—
38#66988—28no—
39D4×Dic11—28no—
40D4×Dic11—28no—
41C2×C4⋊Dic11D412yes—
42C2×Dic11⋊C4—22no—
43C2×C4×Dic11—22no—
44C22×C11⋊C8—22no—
45C4×Dic22—22no—
46C4×Dic22—22no—
47C4×Dic22C2×C414yes—
48C4×Dic22D414yes—
49C11×#102—44no—
50C4×C8×C11—22no—
51#66874—44no—
52C4⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#8445—111nomaximal, Sylow
55C24×C11—22no—
56C2×D4×C11—24no—
57C2×D4×C11—24no—
58C2×D4×C11—22no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11C22⋊C414yes—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×Dic11—28no—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—82no—
73C22×Dic11—82no—
74C2×Dic22—22no—
75C2×Dic22—22no—
76C2×Dic22—22no—
77C2×Dic22—22no—
78C2×Dic22—22no—
79C2×Dic22C22⋊C414yes—
80C2×C8×C11—22no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—42no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D412yes—
89C22⋊Dic11—216no—
90C22⋊Dic11—28no—
91C4⋊Dic11—22no—
92C4⋊Dic11C22⋊C414yes—
93Dic11⋊C4—24no—
94Dic11⋊C4—24no—
95C4×Dic11—24no—
96C4×Dic11—24no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99C2×C11⋊C8—42no—
100C2×#559—111no—
101#1957D1111yescharacteristic
102#1803—112no—
103C2×#331—111no—
104C2×Q8⋊C8—112no—
105C23×C11—24no—
106C23×C11—44no—
107C23×C11—44no—
108C23×C11—42no—
109C23×C11—42no—
110C23×C11#12011yescharacteristic
111D4×C11—44no—
112D4×C11—44no—
113D4×C11—44no—
114D4×C11—44no—
115D4×C11—44no—
116D4×C11—82no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—82no—
120C2×C4×C11—81no—
121C2×C4×C11C2×C22⋊C412yes—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11#12012yes—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#13512yes—
126C2×C4×C11#13512yes—
127C2×C4×C11AGL(1,ℤ/8)12yes—
128C2×C4×C11#13712yes—
129C2×Dic11—24no—
130C2×Dic11—24no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—88no—
136Dic22—24no—
137Dic22—24no—
138Dic22—42no—
139Dic22—42no—
140C8×C11—42no—
141C11⋊C8—82no—
142#559—114no—
143#559—224no—
144#559—222no—
145C2×#127C2×D1111yescharacteristic
146C2×#124—222no—
147C2×#123—222no—
148C2×C4×Q8—112no—
149C2×C4×D4—222no—
150C2×C4⋊C8—112no—
151C2×#103—222no—
152C2×#102—22no—
153C2×C4×C8C2×D1111yescharacteristic
154#384C2×D1111yescharacteristic
155#340—222no—
156#331—222no—
157Q8⋊C8—224no—
158C22×C11—44no—
159C22×C11—48no—
160C22×C11—82no—
161C22×C11—82no—
162C22×C11—84no—
163C22×C11#37911yescharacteristic
164C22×C11#44912yes—
165C22×C11#45212yes—
166C22×C11#45311yescharacteristic
167C22×C11#45511yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—161no—
171C4×C11#41612yes—
172C4×C11#41712yes—
173C4×C11#44912yes—
174C4×C11#45212yes—
175Dic11—44no—
176Dic11—44no—
177C22×Q8—112no—
178C22×D4—22no—
179C22×D4C22⋊D1112yes—
180C23×C4—222no—
181C22×C8—21no—
182C22×C8—222no—
183#127—22no—
184#127C4×D1112yes—
185#127D4412yes—
186#124—228no—
187#124—228no—
188#123—228no—
189#123—228no—
190C4×Q8—114no—
191C4×Q8—114no—
192C4×Q8—222no—
193C4×Q8—222no—
194C4×D4—228no—
195C4×D4—228no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—112no—
199C2×C4⋊C4—222no—
200C2×C22⋊C4—224no—
201C2×C22⋊C4—222no—
202C2×C42—222no—
203C2×C42C22×D1111yescharacteristic
204C4⋊C8—222no—
205C4⋊C8—222no—
206#103—444no—
207#102—44no—
208C4×C8—22no—
209C2×C11—84no—
210C2×C11#162011yescharacteristic
211C2×C11#163011yescharacteristic
212C2×C11#164012yes—
213C2×C11#178812yes—
214C2×C11#179211yescharacteristic
215C24—22no—
216C2×Q8—114no—
217C2×Q8—222no—
218C2×Q8—222no—
219C2×Q8—222no—
220C2×Q8—222no—
221C2×Q8—222no—
222C2×D4—24no—
223C2×D4—24no—
224C2×D4—22no—
225C2×D4—42no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—42no—
230C2×D4—42no—
231C2×D4(C2×D11)⋊C414yes—
232C22×C4—41no—
233C22×C4—222no—
234C22×C4—222no—
235C22×C4—228no—
236C22×C4—882no—
237C22×C4—882no—
238C22×C4D4×D1112yes—
239C22×C4C2×C22⋊D1111yescharacteristic
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—442no—
244C2×C8—442no—
245C2×C8—442no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—114no—
250C4⋊C4—222no—
251C4⋊C4—224no—
252C4⋊C4—224no—
253C22⋊C4—2216no—
254C22⋊C4—228no—
255C42—224no—
256C42—224no—
257C42C2×C4×D1111yescharacteristic
258C42C2×D4411yescharacteristic
259C42D4×D1112yes—
260C11#844511yescharacteristic, complemented, Sylow
261C23—24no—
262C23—44no—
263C23—44no—
264C23—42no—
265C23—42no—
266C23#6699011yescharacteristic
267Q8—224no—
268Q8—224no—
269Q8—442no—
270Q8—442no—
271D4—44no—
272D4—44no—
273D4—44no—
274D4—44no—
275D4—44no—
276D4—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—82no—
280C2×C4—81no—
281C2×C4—224no—
282C2×C4—224no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—888no—
288C2×C4C22⋊C4×D1112yes—
289C2×C4#6693512yes—
290C2×C4#6696412yes—
291C2×C4#6696512yes—
292C2×C4#6696812yes—
293C2×C4#6696912yes—
294C2×C4C2×(C2×D11)⋊C411yescharacteristic
295C2×C4#6699011yescharacteristic
296C8—42no—
297C8—882no—
298C22—48no—
299C22—44no—
300C22—84no—
301C22—82no—
302C22—82no—
303C22#1062256811yescharacteristic
304C22#1062267411yescharacteristic
305C22#1062269011yescharacteristic
306C22#1062277112yes—
307C22#1062278612yes—
308C4—21no—
309C4—21no—
310C4—161no—
311C4—444no—
312C4—444no—
313C4#1062238412yes—
314C4#1062238512yes—
315C4#1062239412yes—
316C4#1062239612yes—
317C2—84no—
318C2#1306767311yescharacteristic
319C2#1306773511yescharacteristic
320C2#1306779912yes—
321C2#1306855312yes—
322C2#1306856911yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1957C2
socleC23×C11#120
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#1957D11
hypocenterC11#8445
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13068618C2semidirect
4. C2×#10622094C2semidirect
12. #10623244C4semidirect
260. C11#8445semidirect

Maximal subgroups

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

subgroupindex
C2×#106232442
#130686182
C2×#106221822
C2×#106220942
C11×#19572
#844511