Finite Group Databasebeta

← #14751734

Subgroups — #14751734

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622612C211yesmaximal, characteristic
2C2×#10622610C211yesmaximal, characteristic
3C2×#10622610C211yesmaximal, characteristic
4C22×#66867C211yesmaximal, characteristic
5#13068491C214yesmaximal, complemented
6#13068485C214yesmaximal, complemented
7#13068313C211yesmaximal, characteristic
8#13068310C211yesmaximal, characteristic
9C11×#2296C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C11×#389C414yes—
18C11×#385C414yes—
19C4×C11×C4⋊C4C2214yes—
20#10622612C418yescomplemented
21#10622610—24no—
22#10622610C418yescomplemented
23C2×C4⋊(C11⋊C8)C2214yes—
24C2×#66867—24no—
25C2×#66867C2212yes—
26C2×#66867C2212yes—
27C2×#66867C2212yes—
28C2×#66867C2212yes—
29C2×C4×C11⋊C8C2212yes—
30C2×C4×C11⋊C8C2212yes—
31#10622162C2214yes—
32#10622162C2214yes—
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2311yescharacteristic
35C11×#117—22no—
36C11×#117—22no—
37C11×#117C2×C414yes—
38C11×#117C2×C414yes—
39C2×C11×C4⋊C4C2×C412yes—
40C2×C11×C4⋊C4C2×C418yes—
41C2×C11×C4⋊C4C2×C412yes—
42C2×C11×C22⋊C4C2×C412yes—
43C2×C11×C22⋊C4C2×C412yes—
44C2×C42×C11—22no—
45C2×C42×C11—22no—
46C2×C42×C11C2×C412yes—
47C2×C42×C11C2312yes—
48C2×C42×C11C2312yes—
49C2×C42×C11C2312yes—
50C2×#4318—22no—
51C2×#4318—22no—
52C2×#4318—22no—
53C2×#4318—22no—
54C2×#4318C2×C414yes—
55C2×#4318C2×C414yes—
56C22×C11⋊C8—22no—
57C22×C11⋊C8—22no—
58C22×C11⋊C8C2×C414yes—
59C22×C11⋊C8C2×C414yes—
60C22×C11⋊C8D414yes—
61C22×C11⋊C8Q814yes—
62C22×C11⋊C8C2312yes—
63C22×C11⋊C8C2312yes—
64C22×C11⋊C8C2312yes—
65C22×C11⋊C8C2311yescharacteristic
66C22×C11⋊C8C2311yescharacteristic
67C11×#95C2×C418yes—
68C4⋊(C11⋊C8)C2×C4116yescomplemented
69#66867—24no—
70#66867—24no—
71#66867—24no—
72#66867C2×C418yescomplemented
73C4×C11⋊C8—24no—
74C4×C11⋊C8C2×C418yescomplemented
75#20436—111nomaximal, Sylow
76C24×C11C22×C411yescharacteristic
77C22×C4×C11—24no—
78C22×C4×C11—44no—
79C22×C4×C11C22×C414yes—
80C22×C4×C11C22×C414yes—
81C22×C4×C11C22×C414yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C412yes—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×Q812yes—
87C22×C4×C11#4112yes—
88C22×C4×C11#4112yes—
89C22×C4×C11C2411yescharacteristic
90C11×C4⋊C4—24no—
91C11×C4⋊C4—48no—
92C11×C4⋊C4C4218yes—
93C11×C22⋊C4—24no—
94C11×C22⋊C4C4218yes—
95C42×C11—24no—
96C42×C11—22no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—22no—
100C42×C11C22×C414yes—
101C42×C11C22×C414yes—
102#4318—28no—
103#4318—28no—
104C2×C11⋊C8—28no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8C4⋊C4116yescomplemented
112C2×C11⋊C8C22×C414yes—
113C2×C11⋊C8C22×C414yes—
114C2×C11⋊C8C22×C414yes—
115C2×C11⋊C8C22×C412yes—
116C2×C11⋊C8C22×C412yes—
117C2×C11⋊C8C2×D412yes—
118C2×C11⋊C8C2×D412yes—
119C2×C11⋊C8C2×Q812yes—
120C2×C11⋊C8C2×Q812yes—
121C2×#424—111no—
122C2×#405—111no—
123C2×#405—111no—
124C22×#97—111no—
125#2296D1111yescharacteristic
126#1771—114no—
127#1770—114no—
128#1729—111no—
129#1728—111no—
130C23×C11—24no—
131C23×C11C2×C4212yes—
132C23×C11C4×D412yes—
133C23×C11C4×Q812yes—
134C23×C11C23×C411yescharacteristic
135C2×C4×C11—28no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—28no—
140C2×C4×C11—24no—
141C2×C4×C11—48no—
142C2×C4×C11C2×C4218yes—
143C2×C4×C11C2×C4212yes—
144C2×C4×C11C2×C4⋊C414yes—
145C2×C4×C11#11714yes—
146C2×C4×C11C4×D414yes—
147C2×C4×C11C4×D412yes—
148C2×C4×C11C4×Q814yes—
149C2×C4×C11C4×Q812yes—
150C2×C4×C11C23×C411yescharacteristic
151C2×C4×C11C23×C411yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C2×C4×C11C22×Q811yescharacteristic
154C2×C4×C11C2×#4111yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C11⋊C8—24no—
157C11⋊C8—24no—
158C11⋊C8—24no—
159C11⋊C8C2×C4⋊C414yes—
160C11⋊C8C2×C4⋊C414yes—
161C22×M16—111no—
162C22×M16—111no—
163C23×C8—111no—
164C23×C8—111no—
165C2×#117C2×D1111yescharacteristic
166C2×#117C2×D1111yescharacteristic
167C22×C42C2×D1111yescharacteristic
168#424—118no—
169C2×C4⋊C8—114no—
170#405—118no—
171#405—224no—
172C2×#97—112no—
173C2×#97—112no—
174C2×#97—112no—
175C2×#97—112no—
176C2×#97—224no—
177C2×C4×C8—112no—
178C2×C4×C8—112no—
179#389Dic1114yes—
180#385Dic1114yes—
181C4×C4⋊C4C2×D1114yes—
182#336—114no—
183#336—114no—
184C22×C11—24no—
185C22×C11—24no—
186C22×C11—24no—
187C22×C11C4×C4⋊C414yes—
188C22×C11C22×C4211yescharacteristic
189C22×C11C2×C4×D411yescharacteristic
190C22×C11C2×C4×Q811yescharacteristic
191C22×C11#56814yes—
192C4×C11—28no—
193C4×C11—44no—
194C4×C11—44no—
195C4×C11C4×C4⋊C414yes—
196C4×C11C22×C4⋊C411yescharacteristic
197C4×C11C2×#11711yescharacteristic
198C4×C11C2×C4×D411yescharacteristic
199C4×C11C2×C4×Q811yescharacteristic
200C23×C4C2×Dic1112yes—
201C23×C4C22×D1111yescharacteristic
202C2×M16—114no—
203C2×M16—114no—
204C2×M16—222no—
205C2×M16—222no—
206C2×M16—222no—
207C2×M16—222no—
208C22×C8—114no—
209C22×C8—114no—
210C22×C8—114no—
211C22×C8—111no—
212C22×C8—111no—
213C22×C8—114no—
214C22×C8—112no—
215C22×C8—112no—
216C22×C8—112no—
217C22×C8—222no—
218C22×C8—222no—
219#117—22no—
220#117—22no—
221#117C4×D1114yes—
222#117C4×D1114yes—
223C2×C4⋊C4C2×Dic1112yes—
224C2×C4⋊C4C2×Dic1118yes—
225C2×C4⋊C4C2×Dic1112yes—
226C2×C22⋊C4C2×Dic1112yes—
227C2×C22⋊C4C2×Dic1112yes—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42C2×Dic1112yes—
231C2×C42C22×D1112yes—
232C2×C42C22×D1112yes—
233C2×C42C22×D1112yes—
234C4⋊C8—1116no—
235#97—118no—
236#97—224no—
237#97—224no—
238#97—224no—
239C4×C8—118no—
240C4×C8—224no—
241#95C2×Dic1118yes—
242C2×C11—24no—
243C2×C11C2×C4×C4⋊C411yescharacteristic
244C2×C11#287512yes—
245C2×C11#293012yes—
246C2×C11#296112yes—
247C24C22×Dic1111yescharacteristic
248C22×C4—24no—
249C22×C4—44no—
250C22×C4C2×C4×D1112yes—
251C22×C4C2×C4×D1112yes—
252C22×C4D4×D1112yes—
253C22×C4#434112yes—
254C22×C4Q8×D1112yes—
255C22×C4#434312yes—
256C22×C4C22×Dic1114yes—
257C22×C4C22×Dic1114yes—
258C22×C4C22×Dic1114yes—
259C22×C4C22×Dic1111yescharacteristic
260C22×C4C23×D1111yescharacteristic
261M16—228no—
262M16—228no—
263C2×C8—1116no—
264C2×C8—112no—
265C2×C8—112no—
266C2×C8—112no—
267C2×C8—112no—
268C2×C8—112no—
269C2×C8—112no—
270C2×C8—114no—
271C2×C8—114no—
272C2×C8—114no—
273C2×C8—228no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—222no—
278C2×C8—222no—
279C2×C8—222no—
280C4⋊C4—24no—
281C4⋊C4—48no—
282C4⋊C4C4×Dic1118yes—
283C22⋊C4—24no—
284C22⋊C4C4×Dic1118yes—
285C42—24no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42C2×C4×D1114yes—
291C42C2×C4×D1114yes—
292C11#2043611yescharacteristic, complemented, Sylow
293C23—24no—
294C23C2×C4×Dic1112yes—
295C23D4×Dic1112yes—
296C23Q8×Dic1112yes—
297C23C23×Dic1111yescharacteristic
298C2×C4—28no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—28no—
303C2×C4—24no—
304C2×C4—48no—
305C2×C4#6694014yes—
306C2×C4C4⋊C4×D1114yes—
307C2×C4#6694514yes—
308C2×C4#6694614yes—
309C2×C4C2×C4×Dic1118yes—
310C2×C4C2×C4×Dic1112yes—
311C2×C4D4×Dic1112yes—
312C2×C4Q8×Dic1112yes—
313C2×C4C22×C4×D1111yescharacteristic
314C2×C4C22×C4×D1111yescharacteristic
315C2×C4C2×D4×D1111yescharacteristic
316C2×C4C2×#434111yescharacteristic
317C2×C4C2×Q8×D1111yescharacteristic
318C2×C4C2×#434311yescharacteristic
319C8—114no—
320C8—114no—
321C8—224no—
322C8—224no—
323C8—224no—
324C22—24no—
325C22—24no—
326C22—24no—
327C22C4⋊C4×Dic1114yes—
328C22C22×C4×Dic1111yescharacteristic
329C22C2×D4×Dic1111yescharacteristic
330C22C2×Q8×Dic1111yescharacteristic
331C22#1062335014yes—
332C4—28no—
333C4—44no—
334C4—44no—
335C4C4⋊C4×Dic1114yes—
336C4C2×#6694011yescharacteristic
337C4C2×C4⋊C4×D1111yescharacteristic
338C4C2×#6694511yescharacteristic
339C4C2×#6694611yescharacteristic
340C2—24no—
341C2C2×C4⋊C4×Dic1111yescharacteristic
342C2#1307704412yes—
343C2#1307732012yes—
344C2#1307755712yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#2296C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#2296D11
hypocenterC11#20436
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2296

Complements

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

NH ≅ G/Ntype
5. #13068491C2semidirect
6. #13068485C2semidirect
20. #10622612C4semidirect
22. #10622610C4semidirect
68. C4⋊(C11⋊C8)C2×C4semidirect
72. #66867C2×C4semidirect
74. C4×C11⋊C8C2×C4semidirect
111. C2×C11⋊C8C4⋊C4semidirect
292. C11#20436semidirect

Maximal subgroups

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

subgroupindex
C2×#106226122
C2×#106226102
C22×#668672
#130684912
#130684852
#130683132
#130683102
C11×#22962
#2043611