Finite Group Databasebeta

← #14754112

Subgroups — #14754112

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068759C212yesmaximal, complemented
2#13068733C212yesmaximal, complemented
3#13068687C212yesmaximal
4#13068600C212yesmaximal
5#13068473C212yesmaximal, complemented
6#13068378C211yesmaximal, characteristic
7C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
8#13068368C212yesmaximal, complemented
9C4×C11×#117C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C4×C11×C4⋊C4C412yes—
14C4×C11×C4⋊C4C412yes—
15C4×C11×C22⋊C4C412yes—
16C4×C11×C22⋊C4C412yes—
17C11×#376C2211yescharacteristic
18C11×#376C2211yescharacteristic
19C43×C11C2211yescharacteristic
20C43×C11C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22C2×C22⋊(C11⋊C8)C2212yes—
23C2×C4⋊(C11⋊C8)C2214yes—
24C2×#66867C2212yes—
25C2×C4×C11⋊C8C2212yes—
26#10622162C2214yes—
27#10622162C2214yes—
28#10622162C2212yes—
29#10622162C2212yes—
30#10622162C2214yes—
31C23×C4×C11C2×C412yes—
32C23×C4×C11C2311yescharacteristic
33C11×#117—24no—
34C11×#117—24no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C412yes—
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4C2×C412yes—
41C2×C42×C11—24no—
42C2×C42×C11C2×C412yes—
43C2×C42×C11C2×C412yes—
44C2×C42×C11C2×C412yes—
45C2×C42×C11C2×C412yes—
46C2×C42×C11C2×C412yes—
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C22×C11⋊C8C2314yes—
54C22×C11⋊C8C2314yes—
55C11×#95C2×C412yes—
56C11×#95C2×C412yes—
57C11×#95C2×C412yes—
58C11×#95C2×C412yes—
59C22⋊(C11⋊C8)—24no—
60C22⋊(C11⋊C8)—24no—
61C4⋊(C11⋊C8)—28no—
62#66867—24no—
63C4×C11⋊C8—24no—
64#20784—111nomaximal, Sylow
65C24×C11C22×C411yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—42no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C412yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C22×C412yes—
80C22×C4×C11#4114yes—
81C22×C4×C11C2411yescharacteristic
82C11×C4⋊C4—24no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—24no—
88C42×C11—24no—
89C42×C11—24no—
90C42×C11—24no—
91C42×C11—22no—
92C42×C11—22no—
93C42×C11—22no—
94C42×C11—22no—
95C42×C11—42no—
96C42×C11—42no—
97C42×C11#4114yes—
98C42×C11#4114yes—
99C2×C11⋊C8—24no—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—24no—
102C2×C11⋊C8—24no—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—24no—
105C4×#117D1111yescharacteristic
106#1839—112no—
107#1831—112no—
108#1818—112no—
109#1798—112no—
110#1768—112no—
111#1749—111no—
112C4×C22⋊C8—111no—
113#1746—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—22no—
117C23×C11—22no—
118C23×C11#11712yes—
119C23×C11C23×C411yescharacteristic
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—28no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—48no—
141C2×C4×C11#11714yes—
142C2×C4×C11#11714yes—
143C2×C4×C11#11712yes—
144C2×C4×C11#13114yes—
145C2×C4×C11C2×#4112yes—
146C2×C4×C11C2×#4112yes—
147C2×C4×C11C2×#4112yes—
148C11⋊C8—44no—
149C11⋊C8—44no—
150C2×#117C2×D1111yescharacteristic
151C2×#117C2×D1111yescharacteristic
152C22×C42C2×D1111yescharacteristic
153C2×C4⋊C8—114no—
154C2×C22⋊C8—112no—
155C2×C22⋊C8—112no—
156C2×#97—112no—
157C2×C4×C8—112no—
158C4×C4⋊C4Dic1112yes—
159C4×C4⋊C4Dic1112yes—
160C4×C22⋊C4Dic1112yes—
161C4×C22⋊C4Dic1112yes—
162#376C2×D1111yescharacteristic
163#376C2×D1111yescharacteristic
164C43C2×D1111yescharacteristic
165C43C2×D1111yescharacteristic
166#336—114no—
167#336—114no—
168#336—114no—
169#336—112no—
170#336—112no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11C2×#11711yescharacteristic
177C22×C11C2×#11711yescharacteristic
178C22×C11C2×#11711yescharacteristic
179C22×C11C2×#13112yes—
180C22×C11#56812yes—
181C4×C11—24no—
182C4×C11—24no—
183C4×C11—24no—
184C4×C11—22no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—42no—
190C4×C11#52914yes—
191C23×C4C2×Dic1112yes—
192C23×C4C22×D1111yescharacteristic
193C22×C8—114no—
194C22×C8—114no—
195#117—24no—
196#117—24no—
197C2×C4⋊C4C2×Dic1111yescharacteristic
198C2×C4⋊C4C2×Dic1111yescharacteristic
199C2×C4⋊C4C2×Dic1112yes—
200C2×C22⋊C4C2×Dic1111yescharacteristic
201C2×C22⋊C4C2×Dic1111yescharacteristic
202C2×C22⋊C4C2×Dic1112yes—
203C2×C42—24no—
204C2×C42C2×Dic1112yes—
205C2×C42C2×Dic1112yes—
206C2×C42C2×Dic1112yes—
207C2×C42C2×Dic1112yes—
208C2×C42C2×Dic1112yes—
209C2×C42C22×D1111yescharacteristic
210C2×C42C22×D1111yescharacteristic
211C2×C42C22×D1111yescharacteristic
212C2×C42C22×D1111yescharacteristic
213C2×C42C22×D1111yescharacteristic
214C2×C42C22×D1111yescharacteristic
215C4⋊C8—228no—
216C22⋊C8—224no—
217C22⋊C8—224no—
218#97—224no—
219C4×C8—224no—
220#95C2×Dic1112yes—
221#95C2×Dic1112yes—
222#95C2×Dic1112yes—
223#95C2×Dic1112yes—
224C2×C11—42no—
225C2×C11#228311yescharacteristic
226C2×C11#292211yescharacteristic
227C2×C11#292311yescharacteristic
228C2×C11#292412yes—
229C2×C11#292512yes—
230C24C22×Dic1111yescharacteristic
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—42no—
236C22×C4#433914yes—
237C22×C4C22×Dic1111yescharacteristic
238C22×C4C22×Dic1111yescharacteristic
239C22×C4C22×Dic1112yes—
240C22×C4C22×Dic1111yescharacteristic
241C22×C4C22×Dic1111yescharacteristic
242C22×C4C22×Dic1112yes—
243C22×C4C22×Dic1112yes—
244C22×C4C22×Dic1111yescharacteristic
245C22×C4C22×Dic1112yes—
246C22×C4C23×D1111yescharacteristic
247C2×C8—224no—
248C2×C8—224no—
249C2×C8—224no—
250C2×C8—224no—
251C2×C8—224no—
252C2×C8—224no—
253C4⋊C4—24no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—24no—
259C42—24no—
260C42—24no—
261C42—24no—
262C42—22no—
263C42—22no—
264C42—22no—
265C42—22no—
266C42—42no—
267C42—42no—
268C42#433914yes—
269C42#433914yes—
270C11#2078411yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—22no—
274C23—22no—
275C23#6697912yes—
276C23C23×Dic1111yescharacteristic
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—28no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—48no—
298C2×C4#6697914yes—
299C2×C4#6697914yes—
300C2×C4#6697912yes—
301C2×C4#6700114yes—
302C2×C4C2×#433912yes—
303C2×C4C2×#433912yes—
304C2×C4C2×#433912yes—
305C8—444no—
306C8—444no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—42no—
311C22—42no—
312C22C2×#6697911yescharacteristic
313C22C2×#6697911yescharacteristic
314C22C2×#6697911yescharacteristic
315C22C2×#6700112yes—
316C22#1062335012yes—
317C4—24no—
318C4—24no—
319C4—24no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—42no—
326C4#1062301014yes—
327C2—42no—
328C2#1307101411yescharacteristic
329C2#1307726011yescharacteristic
330C2#1307726711yescharacteristic
331C2#1307727412yes—
332C2#1307728212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#117C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC4×#117D11
hypocenterC11#20784
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
1. #13068759C2semidirect
2. #13068733C2semidirect
5. #13068473C2semidirect
8. #13068368C2semidirect
270. C11#20784semidirect

Maximal subgroups

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

subgroupindex
#130687592
#130687332
#130686872
#130686002
#130684732
#130683782
C4×C22⋊(C11⋊C8)2
#130683682
C4×C11×#1172
#2078411