Finite Group Databasebeta

← #14810413

Subgroups — #14810413

Order 2816.

1104 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2C2×#10622669C212yesmaximal, complemented
3#13069757C212yesmaximal, complemented
4#13069752C212yesmaximal, complemented
5#13069580C212yesmaximal, complemented
6#13068939C212yesmaximal
7#13068929C212yesmaximal, complemented
8C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9C11×#2850C211yesmaximal, characteristic
10C2×C11×#124C2211yescharacteristic
11C2×C11×C22⋊Q8C2211yescharacteristic
12C2×C11×#121C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×#66979C2212yes—
15C2×#66977—22no—
16#10623001—28no—
17C2×#66923C2212yes—
18C2×#66922C2212yes—
19C2×C4×Dic22—22no—
20C11×#391C2211yescharacteristic
21C11×#390C2211yescharacteristic
22C11×#388—22no—
23C11×#386—22no—
24C11×#382C2211yescharacteristic
25C2×#66899C2214yes—
26C2×#66896C2214yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622669—28no—
29C2×C4×C11⋊C8C2212yes—
30#10622167C2214yes—
31#10622167C2214yes—
32#10622162C2212yes—
33C22×Q8×C11C2311yescharacteristic
34C22×D4×C11—21no—
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11D412yes—
37C23×C4×C11C2311yescharacteristic
38C22×Dic22—22no—
39C11×#124—24no—
40C11×C22⋊Q8—24no—
41C11×#121—24no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C42×C11—24no—
50C2×C42×C11D412yes—
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54#66979—28no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11C2314yes—
57#66977—216no—
58C2×Dic11⋊C4—24no—
59C2×C4×Dic11—22no—
60C22×C11⋊C8C2314yes—
61#66923—24no—
62#66923D418yescomplemented
63#66922—28no—
64C4×Dic22—216no—
65C11×#95—22no—
66C11×#95—22no—
67#66899—28no—
68#66896—28no—
69C22⋊(C11⋊C8)—24no—
70C4×C11⋊C8—24no—
71#25906—111nomaximal, Sylow
72C24×C11—21no—
73C24×C11C2×D411yescharacteristic
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—44no—
81C2×D4×C11—42no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—42no—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D412yes—
93C22×C4×C11#4114yes—
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—24no—
96C2×Dic22—28no—
97C2×Dic22—44no—
98C2×Dic22—44no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—42no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—44no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—44no—
106C42×C11—24no—
107C42×C11—22no—
108C42×C11C2×D414yes—
109C22⋊Dic11—28no—
110C4⋊Dic11—28no—
111C4⋊Dic11—24no—
112C4⋊Dic11C2×D418yes—
113Dic11⋊C4—216no—
114C4×Dic11—28no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—24no—
117C2×C11⋊C8—24no—
118C2×#533—111no—
119C2×#488—112no—
120#2850D1111yescharacteristic
121#2024—112no—
122#2023—112no—
123#1991—112no—
124#1875—112no—
125#1873—112no—
126C4×C22⋊C8—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11#12412yes—
137C23×C11C22×D411yescharacteristic
138Q8×C11—44no—
139D4×C11—44no—
140D4×C11—84no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—28no—
148C2×C4×C11—48no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11#12014yes—
157C2×C4×C11#12412yes—
158C2×C4×C11#13514yes—
159C2×C4×C11C22×D412yes—
160C2×C4×C11C2×#4112yes—
161C2×C4×C112−1+412yes—
162C2×Dic11—28no—
163C2×Dic11—44no—
164C2×Dic11—44no—
165Dic22—416no—
166C11⋊C8—44no—
167#533—228no—
168C2×C4⋊Q8—112no—
169C2×#125—112no—
170C2×#124C2×D1111yescharacteristic
171C2×C22⋊Q8—222no—
172C2×C22⋊Q8C2×D1111yescharacteristic
173C2×#121C2×D1111yescharacteristic
174C2×C4×Q8—222no—
175C2×#117—112no—
176C22×C42C2×D1111yescharacteristic
177#488—228no—
178C2×#103—114no—
179C2×#102—114no—
180C2×C22⋊C8—112no—
181C2×C4×C8—112no—
182#391C2×D1111yescharacteristic
183#390C2×D1111yescharacteristic
184#388—22no—
185#386—22no—
186#382C2×D1111yescharacteristic
187#340—114no—
188#340—114no—
189#336—112no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11C2×#12011yescharacteristic
201C22×C11C2×#12411yescharacteristic
202C22×C11#53611yescharacteristic
203C22×C11C2×#13512yes—
204C22×C11#57512yes—
205C4×C11—22no—
206C4×C11—24no—
207C4×C11—24no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11#54814yes—
212Dic11—48no—
213C22×Q8—222no—
214C22×Q8C22×D1111yescharacteristic
215C22×D4—21no—
216C22×D4C22×D1111yescharacteristic
217C23×C4C22⋊D1112yes—
218C23×C4C22×D1111yescharacteristic
219C22×C8—114no—
220C4⋊Q8—228no—
221#125—118no—
222#125—224no—
223#124—24no—
224C22⋊Q8—24no—
225C22⋊Q8—2216no—
226#121—24no—
227C4×Q8—2216no—
228#117—228no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—114no—
231C2×C4⋊C4—224no—
232C2×C4⋊C4—222no—
233C2×C4⋊C4C22×D1111yescharacteristic
234C2×C4⋊C4C22×D1111yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—222no—
240C2×C42—24no—
241C2×C42—222no—
242C2×C42C22⋊D1112yes—
243C2×C42C22×D1111yescharacteristic
244C2×C42C22×D1111yescharacteristic
245#103—228no—
246#102—228no—
247C22⋊C8—224no—
248C4×C8—224no—
249#95—22no—
250#95—22no—
251C2×C11—42no—
252C2×C11—161no—
253C2×C11#243611yescharacteristic
254C2×C11#300212yes—
255C2×C11#313111yescharacteristic
256C2×C11#314011yescharacteristic
257C2×C11#323312yes—
258C24—21no—
259C24C2×C22⋊D1111yescharacteristic
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—228no—
264C2×Q8—444no—
265C2×Q8—444no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—44no—
270C2×D4—42no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—224no—
280C22×C4#434114yes—
281C22×C4C2×C22⋊D1111yescharacteristic
282C22×C4C2×C22⋊D1112yes—
283C22×C4C2×C22⋊D1112yes—
284C22×C4C23×D1111yescharacteristic
285C2×C8—224no—
286C2×C8—224no—
287C2×C8—224no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—42no—
291C4⋊C4—118no—
292C4⋊C4—228no—
293C4⋊C4—2216no—
294C4⋊C4—224no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—44no—
298C22⋊C4—44no—
299C22⋊C4—228no—
300C42—24no—
301C42—22no—
302C42—228no—
303C42D4×D1114yes—
304C11#2590611yescharacteristic, complemented, Sylow
305C23—21no—
306C23—22no—
307C23—22no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23#6698912yes—
315C23C22×C22⋊D1111yescharacteristic
316Q8—44no—
317Q8—4416no—
318D4—44no—
319D4—84no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—28no—
327C2×C4—48no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—228no—
336C2×C4—444no—
337C2×C4—444no—
338C2×C4#6698912yes—
339C2×C4#6699014yes—
340C2×C4#6700314yes—
341C2×C4C2×D4×D1112yes—
342C2×C4C2×#434112yes—
343C2×C4#6704312yes—
344C8—444no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—42no—
349C22—42no—
350C22—82no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—82no—
355C22C2×#6698911yescharacteristic
356C22C2×#6699011yescharacteristic
357C22C2×#6700312yes—
358C22#1062335312yes—
359C22#1062335611yescharacteristic
360C4—24no—
361C4—24no—
362C4—22no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—448no—
367C4#1062312914yes—
368C2—42no—
369C2—161no—
370C2#1307227511yescharacteristic
371C2#1307783212yes—
372C2#1307893811yescharacteristic
373C2#1307900211yescharacteristic
374C2#1307979112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2850C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2850D11
hypocenterC11#25906
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. C2×#10622669C2semidirect
3. #13069757C2semidirect
4. #13069752C2semidirect
5. #13069580C2semidirect
7. #13068929C2semidirect
8. C4×C22⋊(C11⋊C8)C2semidirect
62. #66923D4semidirect
304. C11#25906semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106226692
#130697572
#130697522
#130695802
#130689392
#130689292
C4×C22⋊(C11⋊C8)2
C11×#28502
#2590611