Finite Group Databasebeta

← #14763282

Subgroups — #14763282

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622538C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13069582C214yesmaximal, complemented
4#13069569C212yesmaximal, complemented
5#13069565C212yesmaximal, complemented
6#13068711C214yesmaximal
7C2×C11×#533C211yesmaximal, characteristic
8C11×#533—24no—
9C11×#533C418yescomplemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#125C2212yes—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8—21no—
15C2×C4×Q8×C11—21no—
16C2×C4×Q8×C11—21no—
17C2×C11×#117C2212yes—
18C22×C42×C11C2211yescharacteristic
19#10622825C2212yes—
20#10622824—21no—
21C4×C22⋊Dic11—21no—
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622550—21no—
24#10622549C2212yes—
25C4×C4⋊Dic11C2212yes—
26#10622545—21no—
27#10622538—24no—
28C2×C4⋊(C11⋊C8)C2212yes—
29C2×C4×C11⋊C8C2212yes—
30#10622167C2218yes—
31#10622167C2218yes—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8C2×C414yes—
40C11×C4⋊Q8C2×C414yes—
41C11×#125—24no—
42C11×#125C2×C418yes—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—28no—
45C4×Q8×C11—28no—
46C4×Q8×C11—28no—
47C11×#117—24no—
48C11×#117C2×C418yes—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—22no—
57C2×C42×C11C2×C414yes—
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D414yes—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64C2×C4⋊Dic11C2314yes—
65C2×C4×Dic11—22no—
66C22×C11⋊C8C2314yes—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C22⋊(C11⋊C8)—24no—
72C4⋊(C11⋊C8)—24no—
73C4×C11⋊C8—24no—
74#21837—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C2×Q8×C11—24no—
77C2×Q8×C11—24no—
78C2×Q8×C11—44no—
79C2×Q8×C11—44no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—42no—
85C22×C4×C11C22⋊C414yes—
86C22×C4×C11C22⋊C414yes—
87C22×C4×C11C22×C412yes—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—24no—
96C11×C4⋊C4—28no—
97C11×C4⋊C4—28no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4C22×C414yes—
103C11×C4⋊C4C22×C414yes—
104C11×C22⋊C4—28no—
105C42×C11—28no—
106C42×C11C22⋊C414yes—
107C42×C11C22⋊C414yes—
108C42×C11C22×C412yes—
109C42×C11C22×C412yes—
110C42×C11C2×D412yes—
111C42×C11C2×D412yes—
112C22⋊Dic11—44no—
113C4⋊Dic11—28no—
114C4×Dic11—44no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—28no—
117C2×#533D1111yescharacteristic
118C2×#431—111no—
119#2283—111no—
120#1991—114no—
121#1988—112no—
122#1987—112no—
123#1825—114no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11C2×C22⋊C412yes—
128C23×C11C22×D411yescharacteristic
129Q8×C11—48no—
130Q8×C11—48no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—28no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—44no—
141C2×C4×C11—44no—
142C2×C4×C11—44no—
143C2×C4×C11C2×C22⋊C412yes—
144C2×C4×C11C2×C22⋊C412yes—
145C2×C4×C11C2×C22⋊C412yes—
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11C2×C22⋊C412yes—
148C2×C4×C11#13514yes—
149C2×C4×C11C23×C411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C112−1+414yes—
152C2×Dic11—44no—
153C2×Dic11—44no—
154C2×Dic11—44no—
155C11⋊C8—44no—
156#533—24no—
157#533Dic1118yescomplemented
158C2×C4⋊Q8C2×D1111yescharacteristic
159C2×C4⋊Q8C2×D1111yescharacteristic
160C2×#125C2×D1112yes—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C4×Q8—21no—
164C2×C4×Q8—21no—
165C2×#117C2×D1112yes—
166C22×C42C2×D1111yescharacteristic
167#431—224no—
168C2×C4⋊C8—112no—
169C2×C22⋊C8—112no—
170C2×C4×C8—112no—
171#383—221no—
172#382—112no—
173#381—221no—
174#380—112no—
175C4×C4⋊C4—112no—
176C4×C22⋊C4—221no—
177#376—221no—
178#340—118no—
179#340—118no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—44no—
184C22×C11C22×C22⋊C411yescharacteristic
185C22×C11#53612yes—
186C22×C11C2×#13512yes—
187C22×C11#57512yes—
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—22no—
192C4×C11—44no—
193C4×C11—44no—
194C4×C11#41614yes—
195C4×C11#51912yes—
196C4×C11#53612yes—
197Dic11—84no—
198C22×Q8—21no—
199C22×Q8—21no—
200C23×C4C22⋊D1111yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22×D1111yescharacteristic
203C22×C8—114no—
204C4⋊Q8—22no—
205C4⋊Q8—22no—
206C4⋊Q8C2×Dic1114yes—
207C4⋊Q8C2×Dic1114yes—
208#125—24no—
209#125C2×Dic1118yes—
210C22⋊Q8—28no—
211C22⋊Q8—28no—
212C4×Q8—28no—
213C4×Q8—28no—
214#117—24no—
215#117C2×Dic1118yes—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—114no—
221C2×C4⋊C4C22×D1112yes—
222C2×C4⋊C4C22×D1112yes—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—222no—
225C2×C42—22no—
226C2×C42—222no—
227C2×C42C2×Dic1114yes—
228C2×C42C22⋊D1111yescharacteristic
229C2×C42C22⋊D1111yescharacteristic
230C2×C42C22⋊D1114yes—
231C2×C42C22×D1111yescharacteristic
232C2×C42C22×D1111yescharacteristic
233C4⋊C8—224no—
234C22⋊C8—224no—
235C4×C8—224no—
236#95—222no—
237#95—222no—
238#95—222no—
239#95—222no—
240C2×C11—42no—
241C2×C11#231011yescharacteristic
242C2×C11C2×#41611yescharacteristic
243C2×C11#289611yescharacteristic
244C2×C11#323314yes—
245C24C2×C22⋊D1111yescharacteristic
246C2×Q8—24no—
247C2×Q8—24no—
248C2×Q8—44no—
249C2×Q8—44no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—42no—
255C22×C4—224no—
256C22×C4C22⋊Dic1114yes—
257C22×C4C22⋊Dic1114yes—
258C22×C4C22×Dic1112yes—
259C22×C4C2×C22⋊D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C2×C22⋊D1112yes—
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C23×D1111yescharacteristic
266C2×C8—228no—
267C2×C8—224no—
268C4⋊C4—28no—
269C4⋊C4—28no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—228no—
275C4⋊C4C22×Dic1114yes—
276C4⋊C4C22×Dic1114yes—
277C22⋊C4—28no—
278C22⋊C4—444no—
279C42—28no—
280C42—444no—
281C42C22⋊Dic1114yes—
282C42C22⋊Dic1114yes—
283C42C22×Dic1112yes—
284C42C22×Dic1112yes—
285C42C2×C22⋊D1112yes—
286C42C2×C22⋊D1112yes—
287C11#2183711yescharacteristic, complemented, Sylow
288C23—22no—
289C23—22no—
290C23—22no—
291C23C2×C22⋊Dic1112yes—
292C23C22×C22⋊D1111yescharacteristic
293Q8—48no—
294Q8—48no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—28no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—444no—
308C2×C4—444no—
309C2×C4—444no—
310C2×C4#6700314yes—
311C2×C4C2×C22⋊Dic1112yes—
312C2×C4C2×C22⋊Dic1112yes—
313C2×C4C2×C22⋊Dic1112yes—
314C2×C4C2×C22⋊Dic1112yes—
315C2×C4C2×C22⋊Dic1112yes—
316C2×C4#6704014yes—
317C2×C4C23×Dic1111yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—444no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—44no—
324C22#1062334712yes—
325C22C2×#6700312yes—
326C22#1062335312yes—
327C22C22×C22⋊Dic1111yescharacteristic
328C4—22no—
329C4—22no—
330C4—22no—
331C4—22no—
332C4—44no—
333C4—44no—
334C4—884no—
335C4#1062284614yes—
336C4#1062334312yes—
337C4#1062334712yes—
338C2—42no—
339C2#1307120211yescharacteristic
340C2C2×#1062284611yescharacteristic
341C2#1307713511yescharacteristic
342C2#1307979514yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#533D11
hypocenterC11#21837
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. #13069582C2semidirect
4. #13069569C2semidirect
5. #13069565C2semidirect
9. C11×#533C4semidirect
157. #533Dic11semidirect
287. C11#21837semidirect

Maximal subgroups

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

subgroupindex
C2×#106225382
#130710142
#130695822
#130695692
#130695652
#130687112
C2×C11×#5332
#2183711