Finite Group Databasebeta

← #14810422

Subgroups — #14810422

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic, complemented
2C2×#10622669C212yesmaximal, complemented
3#13069767C212yesmaximal, complemented
4#13069762C212yesmaximal, complemented
5#13069580C212yesmaximal, complemented
6#13068934C212yesmaximal
7#13068924C212yesmaximal, complemented
8C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9C11×#2850C211yesmaximal, characteristic
10C2×C11×#124C2211yescharacteristic
11C2×C11×C22⋊Q8C2211yescharacteristic
12C2×C11×#121C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×Dic11⋊C4—22no—
16C2×#66923—22no—
17C2×#66923—28no—
18C2×#66923C2212yes—
19C2×#66923C2212yes—
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
38C23×Dic11—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×C4⋊Dic11—22no—
54C2×C4⋊Dic11—28no—
55C2×C4⋊Dic11C2314yes—
56C2×Dic11⋊C4—216no—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4—24no—
59C22×C11⋊C8C2314yes—
60#66923—216no—
61#66923—24no—
62#66923—28no—
63#66923D418yescomplemented
64C11×#95—22no—
65C11×#95—22no—
66#66899—28no—
67#66896—28no—
68C22⋊(C11⋊C8)—24no—
69C4×C11⋊C8—24no—
70#25907—111nomaximal, Sylow
71C24×C11—21no—
72C24×C11C2×D411yescharacteristic
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—42no—
80C2×D4×C11—44no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—42no—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4114yes—
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—28no—
95C22×Dic11—24no—
96C22×Dic11—44no—
97C22×Dic11—44no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—42no—
101C11×C22⋊C4—44no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—44no—
104C11×C22⋊C4—42no—
105C42×C11—24no—
106C42×C11—22no—
107C42×C11C2×D414yes—
108C4⋊Dic11—28no—
109C4⋊Dic11—24no—
110C4⋊Dic11C2×D418yes—
111Dic11⋊C4—216no—
112Dic11⋊C4—216no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—24no—
115C2×C11⋊C8—24no—
116C22×#125—111no—
117C2×#488—112no—
118#2850D1111yescharacteristic
119#2026—112no—
120#2025—112no—
121#1991—112no—
122#1874—112no—
123#1872—112no—
124C4×C22⋊C8—111no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—22no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11#12412yes—
134C23×C11#13514yes—
135C23×C11C22×D411yescharacteristic
136Q8×C11—44no—
137D4×C11—44no—
138D4×C11—84no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—28no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—48no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11#12014yes—
156C2×C4×C11#12412yes—
157C2×C4×C11C22×D412yes—
158C2×C4×C11C2×#4112yes—
159C2×C4×C112−1+412yes—
160C2×Dic11—28no—
161C2×Dic11—416no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C11⋊C8—44no—
165C2×#125—112no—
166C2×#125—112no—
167C2×#125—228no—
168C2×#125—222no—
169C2×#124C2×D1111yescharacteristic
170C2×C22⋊Q8C2×D1111yescharacteristic
171C2×#121C2×D1111yescharacteristic
172C22×C4⋊C4—112no—
173C22×C4⋊C4—222no—
174C22×C42C2×D1111yescharacteristic
175#488—228no—
176C2×#103—114no—
177C2×#102—114no—
178C2×C22⋊C8—112no—
179C2×C4×C8—112no—
180#391C2×D1111yescharacteristic
181#390C2×D1111yescharacteristic
182#388—22no—
183#386—22no—
184#382C2×D1111yescharacteristic
185#340—114no—
186#340—114no—
187#336—112no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—24no—
191C22×C11—24no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11#48814yescomplemented
198C22×C11C2×#12011yescharacteristic
199C22×C11C2×#12411yescharacteristic
200C22×C11#53611yescharacteristic
201C22×C11C2×#13512yes—
202C22×C11#57512yes—
203C4×C11—22no—
204C4×C11—24no—
205C4×C11—42no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11#54814yes—
210Dic11—48no—
211C22×Q8C22×D1111yescharacteristic
212C22×D4—21no—
213C22×D4C22×D1111yescharacteristic
214C23×C4—222no—
215C23×C4C22⋊D1112yes—
216C23×C4C22×D1111yescharacteristic
217C22×C8—114no—
218#125—118no—
219#125—228no—
220#125—2216no—
221#125—224no—
222#124—24no—
223C22⋊Q8—24no—
224#121—24no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—114no—
227C2×C4⋊C4—228no—
228C2×C4⋊C4—2216no—
229C2×C4⋊C4—222no—
230C2×C4⋊C4—224no—
231C2×C4⋊C4—224no—
232C2×C4⋊C4C22×D1111yescharacteristic
233C2×C4⋊C4C22×D1111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C42—24no—
239C2×C42C22⋊D1112yes—
240C2×C42C22×D1111yescharacteristic
241C2×C42C22×D1111yescharacteristic
242#103—228no—
243#102—228no—
244C22⋊C8—224no—
245C4×C8—224no—
246#95—22no—
247#95—22no—
248C2×C11—24no—
249C2×C11—161no—
250C2×C11#243611yescharacteristic
251C2×C11#300212yes—
252C2×C11C2×#48811yescharacteristic
253C2×C11#314211yescharacteristic
254C2×C11#323212yes—
255C24—21no—
256C24C2×C22⋊D1111yescharacteristic
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—42no—
264C2×D4—44no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—42no—
273C22×C4—228no—
274C22×C4—224no—
275C22×C4—444no—
276C22×C4—444no—
277C22×C4#434114yes—
278C22×C4C2×C22⋊D1112yes—
279C22×C4C2×C22⋊D1111yescharacteristic
280C22×C4C2×C22⋊D1112yes—
281C22×C4C23×D1111yescharacteristic
282C2×C8—224no—
283C2×C8—224no—
284C2×C8—224no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—42no—
288C4⋊C4—118no—
289C4⋊C4—2216no—
290C4⋊C4—228no—
291C4⋊C4—2216no—
292C4⋊C4—224no—
293C22⋊C4—44no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—44no—
297C42—24no—
298C42—22no—
299C42D4×D1114yes—
300C11#2590711yescharacteristic, complemented, Sylow
301C23—21no—
302C23—22no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23—42no—
307C23—42no—
308C23—41no—
309C23#6698912yes—
310C23#6700314yes—
311C23C22×C22⋊D1111yescharacteristic
312Q8—44no—
313D4—44no—
314D4—84no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—28no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—48no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—228no—
332C2×C4—4416no—
333C2×C4—444no—
334C2×C4—444no—
335C2×C4#6698912yes—
336C2×C4#6699014yes—
337C2×C4C2×D4×D1112yes—
338C2×C4C2×#434112yes—
339C2×C4#6704312yes—
340C8—444no—
341C22—24no—
342C22—22no—
343C22—24no—
344C22—22no—
345C22—82no—
346C22—81no—
347C22—81no—
348C22—82no—
349C22—81no—
350C22#1062266914yescomplemented
351C22C2×#6698911yescharacteristic
352C22C2×#6699011yescharacteristic
353C22C2×#6700312yes—
354C22#1062335312yes—
355C22#1062335611yescharacteristic
356C4—24no—
357C4—22no—
358C4—42no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4—448no—
363C4#1062312914yes—
364C2—24no—
365C2—161no—
366C2#1307227511yescharacteristic
367C2#1307783212yes—
368C2C2×#1062266911yescharacteristic
369C2#1307901611yescharacteristic
370C2#1307978012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2850C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2850D11
hypocenterC11#25907
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. C22×#66923C2semidirect
2. C2×#10622669C2semidirect
3. #13069767C2semidirect
4. #13069762C2semidirect
5. #13069580C2semidirect
7. #13068924C2semidirect
8. C4×C22⋊(C11⋊C8)C2semidirect
63. #66923D4semidirect
197. C22×C11#488semidirect
300. C11#25907semidirect
350. C22#10622669semidirect

Maximal subgroups

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

subgroupindex
C22×#669232
C2×#106226692
#130697672
#130697622
#130695802
#130689342
#130689242
C4×C22⋊(C11⋊C8)2
C11×#28502
#2590711