Finite Group Databasebeta

← #14763258

Subgroups — #14763258

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic
2C2×#10622538C211yesmaximal, characteristic
3#13069576C214yesmaximal, complemented
4#13069564C214yesmaximal, complemented
5#13068704C214yesmaximal
6C11×#2285C211yesmaximal, characteristic
7C23×Dic22—21no—
8C2×C11×#117—21no—
9C22×C42×C11C2211yescharacteristic
10C22×C4⋊Dic11—21no—
11C22×C4⋊Dic11C2212yes—
12C2×#66922—24no—
13C2×#66922—21no—
14C2×#66922—21no—
15C2×#66922C418yescomplemented
16C2×#66922C2212yes—
17C2×#66922C2212yes—
18C11×#384C2212yes—
19C11×#382—21no—
20C11×#380—21no—
21C11×#380C2212yes—
22C4×C11×C4⋊C4—21no—
23C4×C11×C4⋊C4C2212yes—
24C2×C22⋊(C11⋊C8)C2212yes—
25#10622538—24no—
26C2×C4⋊(C11⋊C8)C2212yes—
27C2×C4×C11⋊C8C2212yes—
28#10622167C22116yes—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—22no—
33C22×Dic22—28no—
34C22×Dic22—22no—
35C22×Dic22—22no—
36C22×Dic22—48no—
37C11×#117—44no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4C2314yes—
41C2×C11×C22⋊C4—22no—
42C2×C42×C11—22no—
43C2×C42×C11C2×C414yes—
44C2×C42×C11D414yes—
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—28no—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2×C418yes—
55C2×C4⋊Dic11C2314yes—
56C22×C11⋊C8C2314yes—
57#66922—28no—
58#66922—28no—
59#66922—24no—
60#66922—24no—
61#66922C2×C418yes—
62#66922C2×C418yes—
63C11×#95—22no—
64C11×#95—22no—
65C22⋊(C11⋊C8)—24no—
66C4⋊(C11⋊C8)—24no—
67C4×C11⋊C8—24no—
68#21834—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11C22⋊C414yes—
74C22×C4×C11C22⋊C414yes—
75C22×C4×C11SD1614yes—
76C22×C4×C11Q1614yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—28no—
86C22×Dic11—24no—
87C22×Dic11—48no—
88C2×Dic22—28no—
89C2×Dic22—28no—
90C2×Dic22—48no—
91C2×Dic22—432no—
92C2×Dic22—48no—
93C11×C4⋊C4—28no—
94C11×C4⋊C4—44no—
95C11×C4⋊C4—44no—
96C11×C22⋊C4—44no—
97C42×C11—44no—
98C42×C11C22⋊C414yes—
99C42×C11C22⋊C414yes—
100C42×C11C22×C412yes—
101C42×C11C22×C412yes—
102C42×C11C2×D412yes—
103C42×C11C2×D412yes—
104C4⋊Dic11—28no—
105C4⋊Dic11—28no—
106C4⋊Dic11—28no—
107C4⋊Dic11—24no—
108C4⋊Dic11C22×C418yes—
109C2×C11⋊C8—24no—
110C2×C11⋊C8—28no—
111C22×C4⋊Q8—111no—
112C2×#431—111no—
113#2285D1111yescharacteristic
114#1990—114no—
115#1987—114no—
116#1824—114no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11C2×C22⋊C412yes—
120C23×C11C2×SD1612yes—
121C23×C11C2×Q1612yes—
122C23×C11C22×D411yescharacteristic
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—28no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11#103116yes—
132C2×C4×C11C2×C22⋊C412yes—
133C2×C4×C11C2×C22⋊C412yes—
134C2×C4×C11C2×C22⋊C412yes—
135C2×C4×C11C2×C22⋊C412yes—
136C2×C4×C11C2×C22⋊C412yes—
137C2×C4×C11C2×SD1612yes—
138C2×C4×C11C2×SD1612yes—
139C2×C4×C11C2×Q1612yes—
140C2×C4×C11C2×Q1612yes—
141C2×C4×C11AGL(1,ℤ/8)14yes—
142C2×C4×C11C23×C411yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C112−1+414yes—
145C2×Dic11—28no—
146C2×Dic11—416no—
147C2×Dic11—48no—
148Dic22—416no—
149Dic22—416no—
150C11⋊C8—44no—
151C23×Q8—221no—
152C2×C4⋊Q8—112no—
153C2×C4⋊Q8—112no—
154C2×C4⋊Q8—118no—
155C2×C4⋊Q8—224no—
156C2×C4⋊Q8—221no—
157C2×C4⋊Q8—221no—
158C2×#117—21no—
159C22×C4⋊C4—112no—
160C22×C4⋊C4—221no—
161C22×C42C2×D1111yescharacteristic
162#431—224no—
163C2×C4⋊C8—112no—
164C2×C22⋊C8—112no—
165C2×C4×C8—112no—
166#384C2×D1112yes—
167#382—21no—
168#380—21no—
169#380C2×D1112yes—
170C4×C4⋊C4—21no—
171C4×C4⋊C4C2×D1112yes—
172#340—1116no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—24no—
176C22×C11—24no—
177C22×C11C2×#10314yes—
178C22×C11C22×C22⋊C411yescharacteristic
179C22×C11#53612yes—
180C22×C11C22×SD1611yescharacteristic
181C22×C11C22×Q1611yescharacteristic
182C22×C11C2×AGL(1,ℤ/8)12yes—
183C4×C11—22no—
184C4×C11—22no—
185C4×C11—84no—
186C4×C11C2×#10314yes—
187C4×C11C2×#10314yes—
188C4×C11#41814yes—
189C4×C11#51912yes—
190C4×C11#53612yes—
191Dic11—48no—
192C22×Q8—228no—
193C22×Q8—222no—
194C22×Q8—222no—
195C22×Q8—448no—
196C23×C4—222no—
197C23×C4C22⋊D1111yescharacteristic
198C23×C4C22⋊D1111yescharacteristic
199C23×C4C22×D1111yescharacteristic
200C22×C8—114no—
201C4⋊Q8—118no—
202C4⋊Q8—118no—
203C4⋊Q8—228no—
204C4⋊Q8—228no—
205C4⋊Q8—224no—
206C4⋊Q8—224no—
207#117—44no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—118no—
211C2×C4⋊C4—114no—
212C2×C4⋊C4—228no—
213C2×C4⋊C4—224no—
214C2×C4⋊C4—222no—
215C2×C4⋊C4—222no—
216C2×C4⋊C4—222no—
217C2×C4⋊C4C22×D1114yes—
218C2×C22⋊C4—22no—
219C2×C42—22no—
220C2×C42C4×D1114yes—
221C2×C42D4414yes—
222C2×C42C22⋊D1111yescharacteristic
223C2×C42C22⋊D1111yescharacteristic
224C2×C42C22×D1111yescharacteristic
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—224no—
227C22⋊C8—224no—
228C4×C8—224no—
229#95—22no—
230#95—22no—
231C2×C11—24no—
232C2×C11#231011yescharacteristic
233C2×C11C22×#10311yescharacteristic
234C2×C11C2×#41811yescharacteristic
235C2×C11#322712yes—
236C2×C11#323012yes—
237C24C2×C22⋊D1111yescharacteristic
238C2×Q8—228no—
239C2×Q8—228no—
240C2×Q8—448no—
241C2×Q8—4432no—
242C2×Q8—448no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—228no—
247C22×C4—224no—
248C22×C4—448no—
249C22×C4(C2×D11)⋊C414yes—
250C22×C4(C2×D11)⋊C414yes—
251C22×C4#432414yes—
252C22×C4#432614yes—
253C22×C4C2×C4×D1112yes—
254C22×C4C2×D4412yes—
255C22×C4C2×C22⋊D1111yescharacteristic
256C22×C4C2×C22⋊D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260C22×C4C23×D1111yescharacteristic
261C2×C8—224no—
262C2×C8—228no—
263C4⋊C4—28no—
264C4⋊C4—44no—
265C4⋊C4—44no—
266C4⋊C4—118no—
267C4⋊C4—228no—
268C4⋊C4—228no—
269C4⋊C4—228no—
270C4⋊C4—224no—
271C22⋊C4—44no—
272C42—44no—
273C42(C2×D11)⋊C414yes—
274C42(C2×D11)⋊C414yes—
275C42C2×C4×D1112yes—
276C42C2×C4×D1112yes—
277C42C2×D4412yes—
278C42C2×D4412yes—
279C11#2183411yescharacteristic, complemented, Sylow
280C23—22no—
281C23—22no—
282C23C2×(C2×D11)⋊C412yes—
283C23C2×#432412yes—
284C23C2×#432612yes—
285C23C22×C22⋊D1111yescharacteristic
286Q8—4416no—
287Q8—4416no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—28no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—228no—
297C2×C4—4416no—
298C2×C4—448no—
299C2×C4#66874116yes—
300C2×C4C2×(C2×D11)⋊C412yes—
301C2×C4C2×(C2×D11)⋊C412yes—
302C2×C4C2×(C2×D11)⋊C412yes—
303C2×C4C2×(C2×D11)⋊C412yes—
304C2×C4C2×(C2×D11)⋊C412yes—
305C2×C4C2×#432412yes—
306C2×C4C2×#432412yes—
307C2×C4C2×#432612yes—
308C2×C4C2×#432612yes—
309C2×C4#6700214yes—
310C2×C4C22×C4×D1111yescharacteristic
311C2×C4C22×D4411yescharacteristic
312C2×C4#6704314yes—
313C8—444no—
314C22—22no—
315C22—22no—
316C22—24no—
317C22—24no—
318C22C2×#6687414yes—
319C22C22×(C2×D11)⋊C411yescharacteristic
320C22C22×#432411yescharacteristic
321C22C22×#432611yescharacteristic
322C22C2×#6700212yes—
323C22#1062335612yes—
324C4—22no—
325C4—22no—
326C4—84no—
327C4—448no—
328C4C2×#6687414yes—
329C4C2×#6687414yes—
330C4#1062261414yes—
331C4#1062304712yes—
332C4#1062305712yes—
333C2—24no—
334C2#1307120011yescharacteristic
335C2C22×#6687411yescharacteristic
336C2C2×#1062261411yescharacteristic
337C2#1307974112yes—
338C2#1307976412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2285C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2285D11
hypocenterC11#21834
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
3. #13069576C2semidirect
4. #13069564C2semidirect
15. C2×#66922C4semidirect
279. C11#21834semidirect

Maximal subgroups

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

subgroupindex
C22×#669222
C2×#106225382
#130695762
#130695642
#130687042
C11×#22852
#2183411