Finite Group Databasebeta

← #14719700

Subgroups — #14719700

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077657C212yesmaximal, complemented
2#13066954C214yesmaximal, complemented
3#13066946C214yesmaximal, complemented
4#13066940C212yesmaximal, complemented
5#13066930C212yesmaximal, complemented
6C2×C11×#520C211yesmaximal, characteristic
7C22×C11×#41C411yescharacteristic
8C11×#520—28no—
9C2×C4×Q8×C11C411yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×C4×D4×C11C412yes—
12C2×C4×D4×C11C411yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117C412yes—
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C411yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19#10622820C2218yes—
20#10622625—28no—
21#10622538C2214yes—
22#10622166C2214yes—
23#10622166C2218yes—
24#10622163C2214yes—
25C2×C11×#41—24no—
26C2×C11×#41—24no—
27C2×C11×#41—24no—
28C22×Q8×C11C2×C411yescharacteristic
29C22×D4×C11C2×C412yes—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C412yes—
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2×C412yes—
35C23×C4×C11C2312yes—
36C4×Q8×C11—24no—
37C4×Q8×C11—24no—
38C4×D4×C11—24no—
39C4×D4×C11—28no—
40C4×D4×C11—28no—
41C4×D4×C11D418yes—
42C11×#117—28no—
43C11×#117—24no—
44C2×C11×C4⋊C4—28no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4C2×C412yes—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C4⋊C4C2×C412yes—
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2×C411yescharacteristic
55C2×C11×C22⋊C4C2×C412yes—
56C2×C11×C22⋊C4C2311yescharacteristic
57C2×C42×C11C2×C412yes—
58C2×C42×C11C2×C412yes—
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×#4318—28no—
62C22⋊(C11⋊C8)—28no—
63C22⋊(C11⋊C8)C2318yes—
64C4⋊(C11⋊C8)—24no—
65C4×C11⋊C8—24no—
66#17370—111nomaximal, Sylow
67C24×C11C22×C412yes—
68C24×C11C22×C411yescharacteristic
69C11×#41—232no—
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11M1614yescomplemented
73C2×D4×C11—24no—
74C2×D4×C11—24no—
75C2×D4×C11—24no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11C22⋊C414yes—
79C22×C4×C11—24no—
80C22×C4×C11—22no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—22no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—82no—
87C22×C4×C11—82no—
88C22×C4×C11—82no—
89C22×C4×C11M1614yescomplemented
90C22×C4×C11C22×C412yes—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C412yes—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D418yes—
99C22×C4×C11C2411yescharacteristic
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4C22⋊C414yes—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4C22⋊C418yes—
111C42×C11—24no—
112C42×C11—24no—
113C42×C11—22no—
114C42×C11C2×D414yes—
115#4318—88no—
116C2×C11⋊C8—28no—
117C2×#520D1111yescharacteristic
118#2975—112no—
119#1465—114no—
120#1463—114no—
121#1461—112no—
122#1458—112no—
123C23×C11—21no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—21no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C2×C22⋊C414yes—
132C23×C11C2×M1612yes—
133C23×C11C23×C411yescharacteristic
134Q8×C11—28no—
135D4×C11—216no—
136D4×C11—28no—
137C2×C4×C11—216no—
138C2×C4×C11—22no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—28no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—21no—
146C2×C4×C11—48no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—84no—
154C2×C4×C11—84no—
155C2×C4×C11C2×C22⋊C412yes—
156C2×C4×C11C2×C22⋊C414yes—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C2×M1612yes—
159C2×C4×C11C2×M1614yes—
160C2×C4×C11C2×M1612yes—
161C2×C4×C11C2×M1612yes—
162C2×C4×C11C22×D412yes—
163C11⋊C8—48no—
164C22×#41Dic1111yescharacteristic
165#520—28no—
166C2×C4×Q8Dic1111yescharacteristic
167C2×C4×Q8C2×D1111yescharacteristic
168C2×C4×D4Dic1112yes—
169C2×C4×D4Dic1111yescharacteristic
170C2×C4×D4C2×D1112yes—
171C2×C4×D4C2×D1111yescharacteristic
172C2×#117Dic1112yes—
173C2×#117C2×D1111yescharacteristic
174C22×C4⋊C4Dic1111yescharacteristic
175C22×C4⋊C4C2×D1112yes—
176#436—228no—
177#431—114no—
178#407—118no—
179#324—114no—
180#324—118no—
181#323—114no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—24no—
185C22×C11—22no—
186C22×C11—24no—
187C22×C11—24no—
188C22×C11—42no—
189C22×C11—44no—
190C22×C11—44no—
191C22×C11—42no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11C22×C22⋊C411yescharacteristic
195C22×C11C22×M1611yescharacteristic
196C22×C11C22×M1611yescharacteristic
197C4×C11—22no—
198C4×C11—24no—
199C4×C11—22no—
200C4×C11—24no—
201C4×C11—22no—
202C4×C11—42no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11#40714yes—
206C2×#41—24no—
207C2×#41—24no—
208C2×#41—24no—
209C22×Q8C2×Dic1111yescharacteristic
210C22×D4C2×Dic1112yes—
211C22×D4C2×Dic1111yescharacteristic
212C23×C4C2×Dic1112yes—
213C23×C4C2×Dic1111yescharacteristic
214C23×C4C2×Dic1112yes—
215C23×C4C2×Dic1112yes—
216C23×C4C22×D1112yes—
217C2×M16—228no—
218C4×Q8—24no—
219C4×Q8—24no—
220C4×D4—24no—
221C4×D4—28no—
222C4×D4—28no—
223C4×D4C22⋊D1118yes—
224#117—28no—
225#117—24no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4C2×Dic1112yes—
229C2×C4⋊C4C2×Dic1111yescharacteristic
230C2×C4⋊C4C2×Dic1112yes—
231C2×C4⋊C4C2×Dic1111yescharacteristic
232C2×C4⋊C4C2×Dic1111yescharacteristic
233C2×C4⋊C4C22×D1111yescharacteristic
234C2×C4⋊C4C22×D1112yes—
235C2×C22⋊C4C2×Dic1112yes—
236C2×C22⋊C4C2×Dic1111yescharacteristic
237C2×C22⋊C4C2×Dic1112yes—
238C2×C22⋊C4C22×D1111yescharacteristic
239C2×C42C2×Dic1112yes—
240C2×C42C2×Dic1112yes—
241C2×C42C2×Dic1111yescharacteristic
242C2×C42C22×D1111yescharacteristic
243C4⋊C8—224no—
244C22⋊C8—118no—
245C22⋊C8—228no—
246C4×C8—224no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—44no—
250C2×C11—42no—
251C2×C11C2×#40711yescharacteristic
252C2×C11#288311yescharacteristic
253C2×C11#288911yescharacteristic
254C24C22×Dic1111yescharacteristic
255C24C22×Dic1112yes—
256#41—232no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8#431814yescomplemented
260C2×D4—24no—
261C2×D4—24no—
262C2×D4—24no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4C22⋊Dic1114yes—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—82no—
274C22×C4—82no—
275C22×C4—82no—
276C22×C4#431814yescomplemented
277C22×C4C22×Dic1112yes—
278C22×C4C22×Dic1111yescharacteristic
279C22×C4C22×Dic1111yescharacteristic
280C22×C4C22×Dic1112yes—
281C22×C4C22×Dic1111yescharacteristic
282C22×C4C22×Dic1111yescharacteristic
283C22×C4C22×Dic1112yes—
284C22×C4C22×Dic1111yescharacteristic
285C22×C4C2×C22⋊D1118yes—
286C22×C4C23×D1111yescharacteristic
287M16—888no—
288C2×C8—228no—
289C4⋊C4—24no—
290C4⋊C4—24no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—24no—
295C4⋊C4C22⋊Dic1114yes—
296C22⋊C4—24no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4C22⋊Dic1118yes—
300C42—24no—
301C42—24no—
302C42—22no—
303C42C2×C22⋊D1114yes—
304C11#1737011yescharacteristic, complemented, Sylow
305C23—21no—
306C23—22no—
307C23—22no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—41no—
312C23—41no—
313C23C2×#431812yes—
314C23C2×C22⋊Dic1114yes—
315C23C23×Dic1111yescharacteristic
316Q8—28no—
317D4—216no—
318D4—28no—
319C2×C4—216no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—28no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—48no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—84no—
336C2×C4—84no—
337C2×C4C2×#431812yes—
338C2×C4C2×#431814yes—
339C2×C4C2×#431812yes—
340C2×C4C2×#431812yes—
341C2×C4C2×C22⋊Dic1112yes—
342C2×C4C2×C22⋊Dic1114yes—
343C2×C4C2×C22⋊Dic1112yes—
344C2×C4C22×C22⋊D1112yes—
345C8—448no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—24no—
350C22—24no—
351C22—24no—
352C22—42no—
353C22—44no—
354C22—44no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22C22×#431811yescharacteristic
359C22C22×#431811yescharacteristic
360C22C22×C22⋊Dic1111yescharacteristic
361C4—22no—
362C4—24no—
363C4—22no—
364C4—24no—
365C4—22no—
366C4—42no—
367C4—41no—
368C4—41no—
369C4#1062282014yes—
370C2—21no—
371C2—21no—
372C2—44no—
373C2—42no—
374C2C2×#1062282011yescharacteristic
375C2#1307707711yescharacteristic
376C2#1307709911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#520C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C11×#41C4
cosocleC22×C4×C11C24
hypercenterC2×#520D11
hypocenterC11#17370
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13077657C2semidirect
2. #13066954C2semidirect
3. #13066946C2semidirect
4. #13066940C2semidirect
5. #13066930C2semidirect
72. C2×Q8×C11M16semidirect
89. C22×C4×C11M16semidirect
259. C2×Q8#4318semidirect
276. C22×C4#4318semidirect
304. C11#17370semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130669542
#130669462
#130669402
#130669302
C2×C11×#5202
#1737011