Finite Group Databasebeta

← #14763289

Subgroups — #14763289

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C211yesmaximal, characteristic
2#13071023C211yesmaximal, characteristic
3#13069586C214yesmaximal, complemented
4#13069574C214yesmaximal, complemented
5#13068706C212yesmaximal
6#13068702C212yesmaximal
7C22×C11×#125C211yesmaximal, characteristic
8C2×C11×#125—21no—
9C2×C11×#125—21no—
10C2×C11×#125—24no—
11C2×C11×#125C418yescomplemented
12C2×C11×#125C2212yes—
13C2×C11×#125C2212yes—
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×#66979—21no—
20#10622825—21no—
21#10622825C2212yes—
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622549—21no—
24#10622548C2212yes—
25C4×C4⋊Dic11—21no—
26C4×C4⋊Dic11C2212yes—
27#10622539—24no—
28C2×C4⋊(C11⋊C8)C2212yes—
29C2×#66867C2212yes—
30#10622167C2218yes—
31#10622167C2218yes—
32C23×C4×C11—21no—
33C23×C4×C11—21no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×#125—28no—
38C11×#125—28no—
39C11×#125—24no—
40C11×#125—24no—
41C11×#125C2×C418yes—
42C11×#125C2×C418yes—
43C2×C11×C4⋊C4—28no—
44C2×C11×C4⋊C4—28no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2×C414yes—
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D414yes—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64#66979—44no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2314yes—
68C2×C4×Dic11—22no—
69C22×C11⋊C8C2314yes—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C22⋊(C11⋊C8)—24no—
73C4⋊(C11⋊C8)—24no—
74#66867—24no—
75#21838—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—42no—
85C22×C4×C11—44no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11C22⋊C414yes—
89C22×C4×C11C22⋊C414yes—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—24no—
99C11×C4⋊C4—28no—
100C11×C4⋊C4—28no—
101C11×C4⋊C4—28no—
102C11×C4⋊C4—28no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4C22×C414yes—
108C11×C4⋊C4C22×C414yes—
109C42×C11C22⋊C414yes—
110C42×C11C22⋊C414yes—
111C42×C11C22×C412yes—
112C42×C11C22×C412yes—
113C42×C11C2×D412yes—
114C42×C11C2×D412yes—
115C22⋊Dic11—44no—
116C4⋊Dic11—28no—
117C4⋊Dic11—44no—
118C4⋊Dic11—44no—
119C4×Dic11—44no—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—28no—
122C22×#125D1111yescharacteristic
123C2×#432—111no—
124#2285—111no—
125#1992—114no—
126#1989—114no—
127#1824—112no—
128#1823—112no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11C2×C22⋊C412yes—
132C23×C11AGL(1,ℤ/8)12yes—
133C23×C11#13712yes—
134C23×C11C22×D411yescharacteristic
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—28no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—44no—
148C2×C4×C11—48no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—44no—
152C2×C4×C11—48no—
153C2×C4×C11C2×C22⋊C412yes—
154C2×C4×C11C2×C22⋊C412yes—
155C2×C4×C11C2×C22⋊C412yes—
156C2×C4×C11C2×C22⋊C412yes—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C23×C411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C112−1+414yes—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C11⋊C8—44no—
165C2×#125—21no—
166C2×#125—21no—
167C2×#125—24no—
168C2×#125Dic1118yescomplemented
169C2×#125C2×D1112yes—
170C2×#125C2×D1112yes—
171C2×#117—221no—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4C2×D1111yescharacteristic
175C22×C4⋊C4C2×D1111yescharacteristic
176C22×C42C2×D1111yescharacteristic
177#432—224no—
178C2×C4⋊C8—112no—
179C2×C22⋊C8—112no—
180C2×#97—112no—
181#384—112no—
182#382—221no—
183#380—112no—
184#380—221no—
185C4×C4⋊C4—112no—
186C4×C4⋊C4—221no—
187#340—118no—
188#340—118no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11#41714yes—
194C22×C11C22×C22⋊C411yescharacteristic
195C22×C11#53612yes—
196C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
197C22×C11C2×#13711yescharacteristic
198C22×C11#57512yes—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—44no—
205C4×C11—44no—
206C4×C11#51912yes—
207C4×C11#53612yes—
208Dic11—84no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4C22⋊D1111yescharacteristic
212C23×C4C22⋊D1111yescharacteristic
213C23×C4C22×D1111yescharacteristic
214C22×C8—114no—
215#125—28no—
216#125—28no—
217#125—24no—
218#125—24no—
219#125C2×Dic1118yes—
220#125C2×Dic1118yes—
221#117—444no—
222C2×C4⋊C4—28no—
223C2×C4⋊C4—28no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—114no—
233C2×C4⋊C4—222no—
234C2×C4⋊C4—222no—
235C2×C4⋊C4C2×Dic1114yes—
236C2×C4⋊C4C2×Dic1114yes—
237C2×C4⋊C4C22×D1112yes—
238C2×C4⋊C4C22×D1112yes—
239C2×C22⋊C4—222no—
240C2×C42—222no—
241C2×C42C2×Dic1114yes—
242C2×C42C22⋊D1111yescharacteristic
243C2×C42C22⋊D1111yescharacteristic
244C2×C42C22⋊D1114yes—
245C2×C42C22×D1111yescharacteristic
246C2×C42C22×D1111yescharacteristic
247C4⋊C8—224no—
248C22⋊C8—224no—
249#97—224no—
250#95—222no—
251#95—222no—
252C2×C11—24no—
253C2×C11#231011yescharacteristic
254C2×C11C2×#41711yescharacteristic
255C2×C11#289611yescharacteristic
256C2×C11#323412yes—
257C2×C11#323612yes—
258C24C2×C22⋊D1111yescharacteristic
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—42no—
267C22×C4—44no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—224no—
271C22×C4C22⋊Dic1114yes—
272C22×C4C22⋊Dic1114yes—
273C22×C4C22×Dic1112yes—
274C22×C4C2×C22⋊D1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279C22×C4C2×C22⋊D1112yes—
280C22×C4C23×D1111yescharacteristic
281C2×C8—228no—
282C2×C8—224no—
283C4⋊C4—28no—
284C4⋊C4—28no—
285C4⋊C4—28no—
286C4⋊C4—28no—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—228no—
292C4⋊C4—444no—
293C4⋊C4—444no—
294C4⋊C4C22×Dic1114yes—
295C4⋊C4C22×Dic1114yes—
296C22⋊C4—444no—
297C42—444no—
298C42C22⋊Dic1114yes—
299C42C22⋊Dic1114yes—
300C42C22×Dic1112yes—
301C42C22×Dic1112yes—
302C42C2×C22⋊D1112yes—
303C42C2×C22⋊D1112yes—
304C11#2183811yescharacteristic, complemented, Sylow
305C23—22no—
306C23—22no—
307C23#6700212yes—
308C23#6700412yes—
309C23C2×C22⋊Dic1112yes—
310C23C22×C22⋊D1111yescharacteristic
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—28no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—44no—
324C2×C4—48no—
325C2×C4—42no—
326C2×C4—44no—
327C2×C4—42no—
328C2×C4—48no—
329C2×C4—444no—
330C2×C4—444no—
331C2×C4—444no—
332C2×C4C2×C22⋊Dic1112yes—
333C2×C4C2×C22⋊Dic1112yes—
334C2×C4C2×C22⋊Dic1112yes—
335C2×C4C2×C22⋊Dic1112yes—
336C2×C4C2×C22⋊Dic1112yes—
337C2×C4#6704014yes—
338C2×C4C23×Dic1111yescharacteristic
339C2×C4C22×C22⋊D1111yescharacteristic
340C8—444no—
341C22—24no—
342C22—22no—
343C22—22no—
344C22—24no—
345C22#1062284514yes—
346C22#1062334712yes—
347C22C2×#6700211yescharacteristic
348C22#1062335312yes—
349C22C2×#6700411yescharacteristic
350C22C22×C22⋊Dic1111yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—44no—
357C4—44no—
358C4—884no—
359C4#1062334312yes—
360C4#1062334712yes—
361C2—24no—
362C2#1307120211yescharacteristic
363C2C2×#1062284511yescharacteristic
364C2#1307713511yescharacteristic
365C2#1307980612yes—
366C2#1307982212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#125C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×#125D11
hypocenterC11#21838
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
3. #13069586C2semidirect
4. #13069574C2semidirect
11. C2×C11×#125C4semidirect
168. C2×#125Dic11semidirect
304. C11#21838semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130710232
#130695862
#130695742
#130687062
#130687022
C22×C11×#1252
#2183811