Finite Group Databasebeta

← #14763221

Subgroups — #14763221

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2#13071007C212yesmaximal
3#13069599C218yesmaximal
4#13068693C211yesmaximal, characteristic
5#13068691C212yesmaximal
6C11×#1820C211yesmaximal, characteristic
7C2×C11×#117C2211yescharacteristic
8C2×#66979C2211yescharacteristic
9C22×C4×Dic11C2211yescharacteristic
10#10623048—22no—
11#10623048—22no—
12#10623048—22no—
13#10623048—22no—
14C2×#66943C412yescomplemented
15C2×#66941C412yescomplemented
16C2×#66931C2214yes—
17C2×C4×Dic22C414yescomplemented
18C11×#381C2212yes—
19#10622824C2212yes—
20#10622555C2214yes—
21C22⋊C4×Dic11C2214yes—
22#10622264—22no—
23#10622263—22no—
24#10622262—22no—
25#10622261—22no—
26C11×#342C2214yes—
27#10622165C2218yes—
28#10622164C2214yes—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11C2312yes—
31C22×Dic22C2×C414yes—
32C11×#117—22no—
33C11×#117—22no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C22⋊C4C2314yes—
36C2×C11×C22⋊C4C2312yes—
37C2×C42×C11C2×C412yes—
38C2×C22⋊Dic11C2314yes—
39C2×C22⋊Dic11C2312yes—
40#66979—22no—
41#66979—22no—
42C2×C4⋊Dic11C2×C414yes—
43C2×C4⋊Dic11C2×C412yes—
44C2×Dic11⋊C4—24no—
45C2×Dic11⋊C4C2×C414yes—
46C2×Dic11⋊C4C2×C414yes—
47C2×C4×Dic11—24no—
48C2×C4×Dic11C2×C412yes—
49C2×C4×Dic11C2×C412yes—
50C2×C4×Dic11C2×C411yescharacteristic
51C2×C4×Dic11C2×C411yescharacteristic
52C2×C4×Dic11D412yes—
53C2×C4×Dic11D412yes—
54C2×C4×Dic11D412yes—
55C2×C4×Dic11D412yes—
56#66943—22no—
57#66943—22no—
58#66943—22no—
59#66943—22no—
60#66941—22no—
61#66941—22no—
62#66941—22no—
63#66941—22no—
64#66931—24no—
65#66931—24no—
66#66931—24no—
67#66931—24no—
68C4×Dic22—24no—
69C4×Dic22—24no—
70C4×Dic22—24no—
71C4×Dic22—24no—
72C11×#95—22no—
73C11×#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78#21826—111nomaximal, Sylow
79C24×C11C2411yescharacteristic
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C414yes—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D412yes—
87C22×Dic11—24no—
88C22×Dic11—44no—
89C22×Dic11C22×C412yes—
90C22×Dic11C22×C414yes—
91C22×Dic11C22×C412yes—
92C22×Dic11C2×D412yes—
93C22×Dic11C2×D412yes—
94C22×Dic11C2×D412yes—
95C22×Dic11C2×D412yes—
96C2×Dic22—24no—
97C2×Dic22—24no—
98C2×Dic22—48no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—28no—
103C42×C11—24no—
104C22⋊Dic11—24no—
105C22⋊Dic11—28no—
106C4⋊Dic11—24no—
107C4⋊Dic11—24no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110Dic11⋊C4—24no—
111Dic11⋊C4—24no—
112Dic11⋊C4—24no—
113Dic11⋊C4—24no—
114Dic11⋊C4—48no—
115C4×Dic11—24no—
116C4×Dic11—48no—
117C4×Dic11C22⋊C412yes—
118C4×Dic11C22⋊C412yes—
119C4×Dic11C22⋊C412yes—
120C4×Dic11C22⋊C412yes—
121C4×Dic11C22⋊C411yescharacteristic
122C4×Dic11C22⋊C412yes—
123C4×Dic11C22⋊C411yescharacteristic
124C4×Dic11C22⋊C411yescharacteristic
125C4×Dic11C22⋊C412yes—
126C4×Dic11C22⋊C411yescharacteristic
127C2×#533—111no—
128#2283—112no—
129#1996—118no—
130#1820—112no—
131#1820—111no—
132#1820D1111yescharacteristic
133C23×C11—42no—
134C23×C11C23×C411yescharacteristic
135C23×C11C22×D412yes—
136C23×C112−1+414yes—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—44no—
143C2×C4×C11—44no—
144C2×C4×C11—44no—
145C2×C4×C11—44no—
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×Dic11—24no—
150C2×Dic11—24no—
151C2×Dic11—24no—
152C2×Dic11—24no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—44no—
157C2×Dic11—44no—
158C2×Dic11—44no—
159C2×Dic11—44no—
160C2×Dic11C2×C22⋊C412yes—
161C2×Dic11C2×C22⋊C412yes—
162C2×Dic11C2×C22⋊C412yes—
163C2×Dic11C2×C22⋊C412yes—
164Dic22—48no—
165Dic22—48no—
166#533—222no—
167#533—222no—
168#533—222no—
169#533—222no—
170C2×C4⋊Q8—112no—
171C2×#125—112no—
172C2×C22⋊Q8—114no—
173C2×C4×Q8—114no—
174C2×#117—111no—
175C2×#117C2×D1111yescharacteristic
176C22×C42—111no—
177#383—222no—
178#382—222no—
179#381—112no—
180#381C2×D1112yes—
181#380—114no—
182C4×C4⋊C4—222no—
183C4×C22⋊C4—114no—
184#376—222no—
185#342—114no—
186#342—118no—
187#342C2×D1114yes—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—44no—
192C22×C11C22×C22⋊C411yescharacteristic
193C22×C11#51912yes—
194C22×C11#53614yes—
195C4×C11—22no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—44no—
199C4×C11—84no—
200Dic11—22no—
201Dic11—22no—
202Dic11—22no—
203Dic11—44no—
204Dic11—84no—
205Dic11#41014yes—
206C22×Q8—114no—
207C23×C4—112no—
208C23×C4C22×D1111yescharacteristic
209C4⋊Q8—222no—
210C4⋊Q8—222no—
211C4⋊Q8—222no—
212C4⋊Q8—222no—
213#125—222no—
214#125—222no—
215#125—222no—
216#125—222no—
217C22⋊Q8—224no—
218C22⋊Q8—224no—
219C22⋊Q8—224no—
220C22⋊Q8—224no—
221C4×Q8—224no—
222C4×Q8—224no—
223C4×Q8—224no—
224C4×Q8—224no—
225#117—22no—
226#117—22no—
227#117—222no—
228#117—222no—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—114no—
231C2×C4⋊C4—114no—
232C2×C4⋊C4—114no—
233C2×C4⋊C4—224no—
234C2×C4⋊C4C4×D1112yes—
235C2×C22⋊C4—112no—
236C2×C22⋊C4—114no—
237C2×C22⋊C4C22×D1114yes—
238C2×C22⋊C4C22×D1112yes—
239C2×C42—112no—
240C2×C42—111no—
241C2×C42—111no—
242C2×C42—112no—
243C2×C42—112no—
244C2×C42—112no—
245C2×C42—112no—
246C2×C42—112no—
247C2×C42—224no—
248C2×C42C4×D1112yes—
249#95—22no—
250#95—22no—
251#95—224no—
252#95—224no—
253#95—222no—
254#95—222no—
255C2×C11—24no—
256C2×C11—22no—
257C2×C11#231011yescharacteristic
258C2×C11C2×#41012yes—
259C24C23×D1111yescharacteristic
260C2×Q8—224no—
261C2×Q8—224no—
262C2×Q8—448no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—112no—
266C22×C4—112no—
267C22×C4—112no—
268C22×C4—112no—
269C22×C4—112no—
270C22×C4—112no—
271C22×C4—114no—
272C22×C4—224no—
273C22×C4—444no—
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4C2×C4×D1111yescharacteristic
276C22×C4C2×C4×D1114yes—
277C22×C4D4×D1112yes—
278C22×C4D4×D1112yes—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—224no—
282C4⋊C4—224no—
283C4⋊C4—224no—
284C4⋊C4—224no—
285C4⋊C4—224no—
286C4⋊C4—224no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—448no—
290C22⋊C4—24no—
291C22⋊C4—28no—
292C22⋊C4—224no—
293C22⋊C4—228no—
294C42—24no—
295C42—112no—
296C42—112no—
297C42—112no—
298C42—112no—
299C42—111no—
300C42—112no—
301C42—111no—
302C42—111no—
303C42—112no—
304C42—111no—
305C42—224no—
306C42—448no—
307C11#2182611yescharacteristic, complemented, Sylow
308C23—42no—
309C23C22×C4×D1111yescharacteristic
310C23C2×D4×D1112yes—
311C23#6704314yes—
312Q8—448no—
313Q8—448no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—112no—
324C2×C4—112no—
325C2×C4—112no—
326C2×C4—112no—
327C2×C4—224no—
328C2×C4—224no—
329C2×C4—224no—
330C2×C4—224no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—444no—
335C2×C4—444no—
336C2×C4—444no—
337C2×C4—444no—
338C2×C4C22⋊C4×D1112yes—
339C2×C4C22⋊C4×D1111yescharacteristic
340C2×C4C22⋊C4×D1111yescharacteristic
341C22—22no—
342C22—22no—
343C22—22no—
344C22—44no—
345C22C2×C22⋊C4×D1111yescharacteristic
346C22#1062304712yes—
347C22#1062317914yes—
348C4—22no—
349C4—21no—
350C4—21no—
351C4—44no—
352C4—84no—
353C4—114no—
354C4—222no—
355C4—222no—
356C4—222no—
357C4—444no—
358C4—884no—
359C2—24no—
360C2—22no—
361C2#1307120111yescharacteristic
362C2D11×#41012yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1820C2
socleC22×C11C22×C22⋊C4
prime radical, cosocleC24×C11C24
hypercenter#1820D11
hypocenterC11#21826
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
14. C2×#66943C4semidirect
15. C2×#66941C4semidirect
17. C2×C4×Dic22C4semidirect
307. C11#21826semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
#130710072
#130695992
#130686932
#130686912
C11×#18202
#2182611