Finite Group Databasebeta

← #14763237

Subgroups — #14763237

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic
2#13077245C212yesmaximal
3#13069607C218yesmaximal, complemented
4#13068696C211yesmaximal, characteristic
5#13068694C212yesmaximal
6C11×#1821C211yesmaximal, characteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C4⋊Dic11C412yes—
9C22×C4⋊Dic11C2211yescharacteristic
10C22×Dic11⋊C4C412yes—
11C22×C4×Dic11C2211yescharacteristic
12C2×#66943—22no—
13C2×#66943—22no—
14C2×#66943—22no—
15C2×#66943—22no—
16C2×#66943C414yes—
17C2×#66943C2214yes—
18C11×#407C2212yes—
19#10622820C2212yes—
20#10622731C2214yes—
21M16×Dic11C2214yes—
22#10622332—22no—
23#10622332—22no—
24#10622331—22no—
25#10622331—22no—
26C11×#343C2214yes—
27#10622192C2218yes—
28#10622168C2214yes—
29C23×C4×C11C2×C412yes—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11C2×C412yes—
32C23×Dic11C2×C411yescharacteristic
33C23×Dic11C2×C411yescharacteristic
34C2×C11×M16C2314yes—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C11×C4⋊C4C2312yes—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—24no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11—22no—
44C2×C4⋊Dic11C2×C412yes—
45C2×C4⋊Dic11C2×C418yes—
46C2×C4⋊Dic11C2312yes—
47C2×Dic11⋊C4—24no—
48C2×Dic11⋊C4—22no—
49C2×Dic11⋊C4—22no—
50C2×Dic11⋊C4C2×C418yes—
51C2×C4×Dic11C2×C412yes—
52C2×C4×Dic11D412yes—
53C2×C4×Dic11D412yes—
54C2×C4×Dic11D412yes—
55C2×C4×Dic11D412yes—
56C2×C4×Dic11C2312yes—
57C2×#4318C2314yes—
58#66943—24no—
59#66943—24no—
60#66943—24no—
61#66943—24no—
62#66943—24no—
63#66943—24no—
64#66943—24no—
65#66943—24no—
66C11×C22⋊C8—22no—
67C11×C22⋊C8—22no—
68C22⋊(C11⋊C8)—22no—
69C22⋊(C11⋊C8)—22no—
70#66879—24no—
71Dic11⋊C8—24no—
72Dic11⋊C8—24no—
73C8×Dic11—24no—
74#21830—111nomaximal, Sylow
75C24×C11C22×C411yescharacteristic
76C22×C4×C11—24no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—44no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C22×C414yes—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11—22no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89C22×Dic11—44no—
90C22×Dic11C22⋊C412yes—
91C22×Dic11C22⋊C412yes—
92C22×Dic11C22⋊C411yescharacteristic
93C22×Dic11C22⋊C411yescharacteristic
94C22×Dic11C22⋊C411yescharacteristic
95C22×Dic11C22⋊C411yescharacteristic
96C22×Dic11C22×C414yes—
97C22×Dic11C22×C412yes—
98C22×Dic11C22×C412yes—
99C11×M16—28no—
100C2×C8×C11—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C4⋊Dic11—28no—
104C4⋊Dic11—28no—
105C4⋊Dic11—24no—
106C4⋊Dic11—24no—
107Dic11⋊C4—28no—
108Dic11⋊C4—28no—
109C4×Dic11C22⋊C412yes—
110C4×Dic11C22⋊C412yes—
111C4×Dic11C22⋊C412yes—
112C4×Dic11C22⋊C412yes—
113C4×Dic11C2×D412yes—
114C4×Dic11C2×D412yes—
115C4×Dic11C2×D412yes—
116C4×Dic11C2×D412yes—
117#4318—28no—
118C2×C11⋊C8—24no—
119C22×#125—111no—
120#2920—112no—
121#1998—118no—
122#1821—112no—
123#1821—111no—
124#1821D1111yescharacteristic
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11C2×C22⋊C411yescharacteristic
130C23×C11C23×C411yescharacteristic
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—44no—
136C2×C4×C11—44no—
137C2×C4×C11—44no—
138C2×C4×C11C2×C22⋊C412yes—
139C2×C4×C11C22×D412yes—
140C2×C4×C112−1+414yes—
141C2×Dic11—24no—
142C2×Dic11—24no—
143C2×Dic11—24no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—44no—
151C2×Dic11—44no—
152C2×Dic11—44no—
153C2×Dic11C2×C22⋊C412yes—
154C2×Dic11C2×C22⋊C412yes—
155C2×Dic11C2×C22⋊C412yes—
156C2×Dic11C2×C22⋊C412yes—
157C8×C11—44no—
158C11⋊C8—44no—
159C2×#125—114no—
160C2×#125—114no—
161C2×#125—222no—
162C2×#125—222no—
163C2×#125—222no—
164C2×#125—222no—
165C22×C4⋊C4—111no—
166C22×C4⋊C4—112no—
167C22×C4⋊C4—112no—
168C22×C4⋊C4C2×D1111yescharacteristic
169C22×C42—111no—
170#432—222no—
171#432—222no—
172#431—222no—
173#431—222no—
174#423—114no—
175#407—112no—
176#407C2×D1112yes—
177C4×M16—114no—
178#343—118no—
179#343—114no—
180#343C2×D1114yes—
181C22×C11—28no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11#41312yes—
189C22×C11#41312yes—
190C22×C11C22×C22⋊C411yescharacteristic
191C22×C11#51912yes—
192C4×C11—22no—
193C4×C11—44no—
194C4×C11#53614yes—
195Dic11—22no—
196Dic11—22no—
197Dic11—22no—
198Dic11—22no—
199Dic11—44no—
200C23×C4—111no—
201C23×C4—111no—
202C23×C4—112no—
203C23×C4C4×D1112yes—
204C23×C4C22×D1111yescharacteristic
205C2×M16—114no—
206C2×M16C22×D1114yes—
207#125—224no—
208#125—224no—
209#125—224no—
210#125—224no—
211#125—224no—
212#125—224no—
213#125—224no—
214#125—224no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—118no—
218C2×C4⋊C4—118no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—112no—
221C2×C4⋊C4—224no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4—224no—
225C2×C4⋊C4—222no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4—222no—
228C2×C4⋊C4—222no—
229C2×C4⋊C4C4×D1112yes—
230C2×C4⋊C4C22×D1112yes—
231C2×C42—112no—
232C2×C42—112no—
233C2×C42—112no—
234C2×C42—112no—
235C2×C42—112no—
236C2×C42—112no—
237C4⋊C8—224no—
238C4⋊C8—224no—
239C22⋊C8—22no—
240C22⋊C8—22no—
241C22⋊C8—222no—
242C22⋊C8—222no—
243#97—224no—
244C4×C8—224no—
245C2×C11—22no—
246C2×C11—22no—
247C2×C11—22no—
248C2×C11#231011yescharacteristic
249C2×C11C2×#41311yescharacteristic
250C2×C11C2×#41311yescharacteristic
251C24C2×C4×D1111yescharacteristic
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—44no—
256C22×C4—112no—
257C22×C4—112no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—112no—
263C22×C4—112no—
264C22×C4—114no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4—442no—
268C22×C4—442no—
269C22×C4—444no—
270C22×C4C2×C4×D1111yescharacteristic
271C22×C4C2×C4×D1114yes—
272C22×C4D4×D1112yes—
273C22×C4D4×D1112yes—
274C22×C4C23×D1111yescharacteristic
275M16—28no—
276M16—228no—
277C2×C8—24no—
278C2×C8—224no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—228no—
282C4⋊C4—228no—
283C4⋊C4—228no—
284C4⋊C4—228no—
285C4⋊C4—224no—
286C4⋊C4—224no—
287C42—112no—
288C42—112no—
289C42—112no—
290C42—112no—
291C42—112no—
292C42—112no—
293C42—112no—
294C42—112no—
295C11#2183011yescharacteristic, complemented, Sylow
296C23—22no—
297C23—22no—
298C23—22no—
299C23C22⋊C4×D1111yescharacteristic
300C23C22⋊C4×D1111yescharacteristic
301C23C22×C4×D1111yescharacteristic
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—112no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—112no—
313C2×C4—224no—
314C2×C4—224no—
315C2×C4—224no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—442no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—442no—
322C2×C4—444no—
323C2×C4—444no—
324C2×C4—444no—
325C2×C4C22⋊C4×D1112yes—
326C2×C4C2×D4×D1112yes—
327C2×C4#6704314yes—
328C8—44no—
329C8—444no—
330C22—28no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22#1062235812yes—
338C22#1062236412yes—
339C22C2×C22⋊C4×D1111yescharacteristic
340C22#1062304712yes—
341C4—22no—
342C4—44no—
343C4—222no—
344C4—222no—
345C4—222no—
346C4—222no—
347C4—444no—
348C4#1062317914yes—
349C2—22no—
350C2—22no—
351C2—22no—
352C2#1307120111yescharacteristic
353C2C2×#1062235811yescharacteristic
354C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1821C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1821D11
hypocenterC11#21830
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #13069607C2semidirect
295. C11#21830semidirect

Maximal subgroups

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

subgroupindex
C22×#669432
#130772452
#130696072
#130686962
#130686942
C11×#18212
#2183011