Finite Group Databasebeta

← #14719504

Subgroups — #14719504

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077583C211yesmaximal, characteristic
2C4×#67001C211yesmaximal, characteristic
3#13066919C212yesmaximal, complemented
4#13066911C212yesmaximal, complemented
5#13066906C212yesmaximal, complemented
6#13066906C211yesmaximal, characteristic, complemented
7#13066905C211yesmaximal, characteristic, complemented
8#13066903C212yesmaximal, complemented
9#13066900C211yesmaximal, characteristic, complemented
10C2×#10622092C211yesmaximal, characteristic, complemented
11C11×#2965C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13C2×#67001C412yes—
14C11×#446C412yes—
15C11×#436C412yes—
16C11×#435C414yes—
17C11×#431C2211yescharacteristic
18C11×#431C2212yes—
19C4×C11×M16C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21#10622637C412yes—
22#10622625C412yes—
23#10622624C414yes—
24#10622610C414yes—
25#10622610C412yes—
26#10622538C2211yescharacteristic
27#10622538C2212yes—
28C4×#4318C2211yescharacteristic
29C4×#4318C2212yes—
30C4×#4318C2212yes—
31C2×C4×C11⋊C8C2211yescharacteristic
32C2×C4×C11⋊C8C2212yes—
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622093C2212yes—
35#10622093C2212yes—
36#10622092C2211yescharacteristic
37#10622092C2211yescharacteristic
38#10622092C2211yescharacteristic
39#10622092C2211yescharacteristic
40#10622092C2212yes—
41#10622092C2212yes—
42#10622092C2212yes—
43C8×C11⋊C8C2212yes—
44C2×C11×#41C2×C411yescharacteristic
45C2×C11×M16C2×C414yes—
46C22×C8×C11C2×C412yes—
47C4×Q8×C11C2×C411yescharacteristic
48C4×Q8×C11C2×C411yescharacteristic
49C4×D4×C11C2×C412yes—
50C4×D4×C11C2×C411yescharacteristic
51C4×D4×C11C2×C412yes—
52C4×D4×C11C2×C411yescharacteristic
53C11×#117C2×C412yes—
54C11×#117C2×C411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2312yes—
57#67001—28no—
58C2×#4318C2×C412yes—
59C2×#4318C2×C414yes—
60C2×#4318C2×C414yes—
61C22×C11⋊C8C2×C414yes—
62C22×C11⋊C8C2×C412yes—
63C22×C11⋊C8C2×C412yes—
64C11×C4⋊C8C2×C414yes—
65C11×C4⋊C8C2×C412yes—
66C11×C22⋊C8C2×C412yes—
67C11×C22⋊C8C2×C414yes—
68C11×#97C2×C414yes—
69C4×C8×C11C2×C412yes—
70C4×C8×C11C2312yes—
71C4×C8×C11C2311yescharacteristic
72C4×C8×C11C2311yescharacteristic
73C22⋊(C11⋊C8)C2×C412yes—
74C22⋊(C11⋊C8)C2×C414yes—
75C4⋊(C11⋊C8)C2×C414yes—
76C4⋊(C11⋊C8)C2×C412yes—
77#66867C2×C412yes—
78#66867C2×C414yes—
79#66867C2×C414yes—
80C4×C11⋊C8C2×C414yes—
81C4×C11⋊C8C2×C412yes—
82C4×C11⋊C8C2×C412yes—
83C4×C11⋊C8C2311yescharacteristic
84C4×C11⋊C8C2311yescharacteristic
85C4×C11⋊C8C2312yes—
86C4×C11⋊C8C2311yescharacteristic
87C4×C11⋊C8C2311yescharacteristic
88C4×C11⋊C8C2312yes—
89#17336—111nomaximal, Sylow
90C11×#41—24no—
91C2×Q8×C11C4211yescharacteristic
92C2×D4×C11C4212yes—
93C2×D4×C11C4211yescharacteristic
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C411yescharacteristic
100C11×M16—44no—
101C2×C8×C11—42no—
102C2×C8×C11C22×C412yes—
103C2×C8×C11C22×C412yes—
104C2×C8×C11C22×C414yes—
105C11×C4⋊C4C4212yes—
106C11×C4⋊C4C4212yes—
107C11×C4⋊C4C4211yescharacteristic
108C11×C4⋊C4C4211yescharacteristic
109C11×C22⋊C4C4212yes—
110C11×C22⋊C4C4212yes—
111C11×C22⋊C4C4212yes—
112C42×C11C22×C411yescharacteristic
113C42×C11C22×C412yes—
114C42×C11C22×C411yescharacteristic
115C42×C11C22×C412yes—
116C42×C11C22×C411yescharacteristic
117C42×C11C22×C412yes—
118C42×C11C2411yescharacteristic
119#4318—28no—
120#4318—24no—
121#4318—44no—
122C2×C11⋊C8—28no—
123C2×C11⋊C8—42no—
124C2×C11⋊C8M1618yescomplemented
125C2×C11⋊C8C22×C414yes—
126C2×C11⋊C8C22×C412yes—
127C2×C11⋊C8C22×C412yes—
128C2×C11⋊C8C22×C414yes—
129C2×C11⋊C8C22×C412yes—
130C2×C11⋊C8C22×C412yes—
131#2965—111no—
132#2965D1111yescharacteristic
133C4×#131—111no—
134#1455—112no—
135#1453—112no—
136#1451—112no—
137#1451—111no—
138#1451—112no—
139#1451—111no—
140#1450—111no—
141C2×#322—111no—
142C23×C11C2×C4212yes—
143C23×C11C2×C4211yescharacteristic
144Q8×C11—22no—
145D4×C11—24no—
146D4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11C2×C4211yescharacteristic
153C2×C4×C11C2×C4212yes—
154C2×C4×C11C2×C4211yescharacteristic
155C2×C4×C11C2×C4212yes—
156C2×C4×C11C2×C4212yes—
157C2×C4×C11C2×C4211yescharacteristic
158C2×C4×C11C2×M1614yes—
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C23×C411yescharacteristic
161C2×C4×C11C23×C411yescharacteristic
162C8×C11—22no—
163C8×C11—22no—
164C8×C11—24no—
165C11⋊C8—24no—
166C11⋊C8—22no—
167C11⋊C8—22no—
168C11⋊C8—24no—
169C11⋊C8C2×M1614yes—
170C11⋊C8C2×M1614yes—
171C2×#131—112no—
172C4×#41C2×D1111yescharacteristic
173#446—112no—
174#446Dic1112yes—
175#436—112no—
176#436Dic1112yes—
177#435—114no—
178#435Dic1114yes—
179#431—111no—
180#431—112no—
181#431C2×D1111yescharacteristic
182#431C2×D1112yes—
183#405—112no—
184#405—114no—
185C4×M16—111no—
186C4×M16—112no—
187C4×M16—112no—
188C4×M16C2×D1112yes—
189C2×C4×C8—111no—
190C2×C4×C8—112no—
191C2×C4×C8—111no—
192C2×C4×C8C2×D1111yescharacteristic
193#322—111no—
194#322—111no—
195#322—111no—
196#322—111no—
197#322—112no—
198#322—112no—
199#322—112no—
200#322—112no—
201#322—112no—
202C82—112no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11C4×M1612yes—
209C22×C11C22×C4211yescharacteristic
210C4×C11—22no—
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—21no—
214C4×C11—22no—
215C4×C11C4×M1612yes—
216C4×C11C22×M1612yes—
217C4×C11#56812yes—
218C4×C11#56812yes—
219C2×#41C4×D1111yescharacteristic
220#131—228no—
221C2×M16—114no—
222C2×M16—112no—
223C2×M16—114no—
224C2×M16C2×Dic1114yes—
225C22×C8—112no—
226C22×C8—114no—
227C22×C8—112no—
228C22×C8C2×Dic1112yes—
229C4×Q8C4×D1111yescharacteristic
230C4×Q8C2×Dic1111yescharacteristic
231C4×D4C4×D1112yes—
232C4×D4C4×D1111yescharacteristic
233C4×D4C2×Dic1112yes—
234C4×D4C2×Dic1111yescharacteristic
235#117C4×D1112yes—
236#117C4×D1111yescharacteristic
237C2×C42C22×D1111yescharacteristic
238C2×C42C22×D1112yes—
239C4⋊C8—114no—
240C4⋊C8—112no—
241C4⋊C8C2×Dic1114yes—
242C4⋊C8C2×Dic1112yes—
243C22⋊C8—112no—
244C22⋊C8—114no—
245C22⋊C8C2×Dic1112yes—
246C22⋊C8C2×Dic1114yes—
247#97—114no—
248#97—112no—
249#97—114no—
250#97C2×Dic1114yes—
251C4×C8—112no—
252C4×C8—114no—
253C4×C8—112no—
254C4×C8—111no—
255C4×C8—112no—
256C4×C8—111no—
257C4×C8—111no—
258C4×C8—112no—
259C4×C8—111no—
260C4×C8C2×Dic1112yes—
261C4×C8C22×D1112yes—
262C4×C8C22×D1111yescharacteristic
263C4×C8C22×D1111yescharacteristic
264C2×C11—22no—
265C2×C11—42no—
266C2×C11C2×C4×M1611yescharacteristic
267C2×C11#287511yescharacteristic
268C2×C11#287511yescharacteristic
269#41—24no—
270C2×Q8C4×Dic1111yescharacteristic
271C2×D4C4×Dic1112yes—
272C2×D4C4×Dic1111yescharacteristic
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4C2×C4×D1112yes—
275C22×C4C2×C4×D1112yes—
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4C22×Dic1111yescharacteristic
278C22×C4C22×Dic1112yes—
279M16—44no—
280M16—228no—
281M16—224no—
282M16—444no—
283C2×C8—42no—
284C2×C8—118no—
285C2×C8—112no—
286C2×C8—112no—
287C2×C8—114no—
288C2×C8—112no—
289C2×C8—112no—
290C2×C8—114no—
291C2×C8—228no—
292C2×C8—442no—
293C2×C8C22×Dic1112yes—
294C2×C8C22×Dic1112yes—
295C2×C8C22×Dic1114yes—
296C4⋊C4C4×Dic1112yes—
297C4⋊C4C4×Dic1111yescharacteristic
298C4⋊C4C4×Dic1112yes—
299C4⋊C4C4×Dic1111yescharacteristic
300C22⋊C4C4×Dic1112yes—
301C22⋊C4C4×Dic1112yes—
302C22⋊C4C4×Dic1112yes—
303C42C2×C4×D1111yescharacteristic
304C42C2×C4×D1112yes—
305C42C2×C4×D1111yescharacteristic
306C42C2×C4×D1112yes—
307C42C22×Dic1111yescharacteristic
308C42C22×Dic1112yes—
309C42C23×D1111yescharacteristic
310C11#1733611yescharacteristic, complemented, Sylow
311C23C2×C4×Dic1112yes—
312C23C2×C4×Dic1111yescharacteristic
313Q8—22no—
314D4—24no—
315D4—22no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4M16×D1114yes—
322C2×C4C2×C4×Dic1111yescharacteristic
323C2×C4C2×C4×Dic1112yes—
324C2×C4C2×C4×Dic1111yescharacteristic
325C2×C4C2×C4×Dic1112yes—
326C2×C4C2×C4×Dic1112yes—
327C2×C4C2×C4×Dic1111yescharacteristic
328C2×C4C22×C4×D1111yescharacteristic
329C2×C4C22×C4×D1111yescharacteristic
330C2×C4C23×Dic1111yescharacteristic
331C8—22no—
332C8—22no—
333C8—24no—
334C8—114no—
335C8—114no—
336C8—224no—
337C8—222no—
338C8—222no—
339C8—224no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22M16×Dic1112yes—
346C22C22×C4×Dic1111yescharacteristic
347C4—22no—
348C4—21no—
349C4—22no—
350C4—21no—
351C4—22no—
352C4M16×Dic1112yes—
353C4C2×M16×D1112yes—
354C4#1062328112yes—
355C4#1062335012yes—
356C2—22no—
357C2—42no—
358C2C2×M16×Dic1111yescharacteristic
359C2#1307704211yescharacteristic
360C2#1307704411yescharacteristic
subgroupG/H
center, FrattiniC42C23×D11
commutator, socleC22×C11C22×C42
FittingC11×#2965C2
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#2965D11
hypocenterC11#17336
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
3. #13066919C2semidirect
4. #13066911C2semidirect
5. #13066906C2semidirect
6. #13066906C2semidirect
7. #13066905C2semidirect
8. #13066903C2semidirect
9. #13066900C2semidirect
10. C2×#10622092C2semidirect
124. C2×C11⋊C8M16semidirect
310. C11#17336semidirect

Maximal subgroups

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

subgroupindex
#130775832
C4×#670012
#130669192
#130669112
#130669062
#130669052
#130669032
#130669002
C2×#106220922
C11×#29652
#1733611