Finite Group Databasebeta

← #14719367

Subgroups — #14719367

Order 2816.

890 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
1C8×#4339C211yesmaximal, characteristic
2#13077572C211yesmaximal, characteristic
3C4×#66960C211yesmaximal, characteristic
4#13066900C211yesmaximal, characteristic, complemented
5#13066898C212yesmaximal, complemented
6#13066895C212yesmaximal, complemented
7M16×C11⋊C8C211yesmaximal, characteristic, complemented
8C8×#4313C212yesmaximal, complemented
9C2×#10622092C211yesmaximal, characteristic, complemented
10D11×#322C212yesmaximal, complemented
11C8×C11×M16C211yesmaximal, characteristic, complemented
12C2×#66960C412yes—
13C4×#4339C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C4×C11×M16C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17#10622735C412yes—
18C8×C22⋊D11C414yes—
19#10622538C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622447C412yes—
23#10622443C412yes—
24(C22⋊D11)⋊C8C414yes—
25#10622321C414yes—
26C4×#4313C2212yes—
27C8×D44C412yes—
28#10622298C2212yes—
29#10622298C2212yes—
30C4×C8×D11C2212yes—
31C4×C8×D11C2212yes—
32C4×C8×D11C2212yes—
33C8×Dic22C412yes—
34C11×#322C2212yes—
35C82×C11C2212yes—
36#10622093C2212yes—
37#10622092C2211yescharacteristic
38#10622092C2212yes—
39#10622092C2211yescharacteristic
40#10622092C2211yescharacteristic
41#10622092C2211yescharacteristic
42C8×C11⋊C8C2212yes—
43C8×C11⋊C8C2212yes—
44C2×#4339C2×C411yescharacteristic
45C2×C11×M16C2×C412yes—
46C22×C8×C11C2×C412yes—
47C2×C42×C11C2311yescharacteristic
48C4×C22⋊D11C2×C412yes—
49C4×C22⋊D11C2×C412yes—
50#66979C2×C411yescharacteristic
51C22×C11⋊C8C2×C412yes—
52C22×C11⋊C8C2×C412yes—
53#66960C8116yescomplemented
54C2×#4313C2×C414yes—
55C2×C8×D11C2×C414yes—
56C2×C8×D11C2×C414yes—
57C2×C8×D11C2×C414yes—
58C4×D44C2×C411yescharacteristic
59C4×D44C2×C411yescharacteristic
60#66925C2×C412yes—
61C42×D11C2312yes—
62C4×Dic22C2×C411yescharacteristic
63C4×Dic22C2×C411yescharacteristic
64C11×C4⋊C8C2×C412yes—
65C11×C22⋊C8C2×C412yes—
66C11×#97C2×C412yes—
67C4×C8×C11C2×C412yes—
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2312yes—
70C4×C8×C11C2312yes—
71C4×C8×C11C2311yescharacteristic
72C22⋊(C11⋊C8)C2×C412yes—
73(C2×D11)⋊C8C2×C414yes—
74(C2×D11)⋊C8C2×C414yes—
75#66879C2×C414yes—
76Dic11⋊C8C2×C414yes—
77Dic11⋊C8C2×C414yes—
78C8×Dic11C2×C414yes—
79C8×Dic11C2×C414yes—
80C8×Dic11C2×C414yes—
81C4⋊(C11⋊C8)C2×C412yes—
82C4×C11⋊C8C2×C412yes—
83C4×C11⋊C8C2×C412yes—
84C4×C11⋊C8C2311yescharacteristic
85C4×C11⋊C8C2311yescharacteristic
86C4×C11⋊C8C2311yescharacteristic
87C4×C11⋊C8C2311yescharacteristic
88C4×C11⋊C8C2312yes—
89#17316—111nomaximal, Sylow
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C2×C22⋊D11C4212yes—
94#4339C2×C818yes—
95C2×D44C4211yescharacteristic
96C2×C4×D11C22×C412yes—
97C2×C4×D11C22×C412yes—
98C2×C4×D11C22×C412yes—
99C2×Dic22C4211yescharacteristic
100C11×M16C2×C818yescomplemented
101C2×C8×C11—42no—
102C2×C8×C11C22×C412yes—
103C2×C8×C11C22×C414yes—
104C2×C8×C11C22×C412yes—
105C2×C8×C11C22×C414yes—
106C42×C11C22×C411yescharacteristic
107C42×C11C22×C411yescharacteristic
108C42×C11C22×C411yescharacteristic
109C42×C11C2411yescharacteristic
110C22⋊Dic11C4212yes—
111(C2×D11)⋊C4C4212yes—
112(C2×D11)⋊C4C4212yes—
113C4⋊Dic11C4211yescharacteristic
114C4⋊Dic11C4211yescharacteristic
115Dic11⋊C4C4212yes—
116Dic11⋊C4C4212yes—
117C4×Dic11C22×C412yes—
118C4×Dic11C22×C412yes—
119C4×Dic11C22×C412yes—
120C2×C11⋊C8—42no—
121C2×C11⋊C8C2×C818yescomplemented
122C2×C11⋊C8C22×C412yes—
123C2×C11⋊C8C22×C412yes—
124C2×C11⋊C8C22×C414yes—
125C2×C11⋊C8C22×C412yes—
126C2×C11⋊C8C22×C412yes—
127#4313C2×C8116yescomplemented
128C8×D11—44no—
129C8×D11—44no—
130C8×D11C2×C8116yescomplemented
131C8×#41—111no—
132C8×#41—111no—
133C4×#131—111no—
134#1450—111no—
135#1450—112no—
136C8×M16—111no—
137C8×M16—112no—
138C8×M16—112no—
139C8×M16D1111yescharacteristic, complemented
140C2×#322—111no—
141C2×#322—112no—
142C23×C11C2×C4211yescharacteristic
143C22×D11C2×C4212yes—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11C2×C4211yescharacteristic
147C2×C4×C11C2×C4211yescharacteristic
148C2×C4×C11C2×C4211yescharacteristic
149C2×C4×C11C22×C814yes—
150C2×C4×C11C23×C411yescharacteristic
151C2×C4×C11C23×C411yescharacteristic
152C2×C4×C11C23×C411yescharacteristic
153C22⋊D11C4×C818yes—
154C2×Dic11C2×C4212yes—
155C2×Dic11C2×C4212yes—
156C2×Dic11C2×C4212yes—
157D44C4×C814yes—
158C4×D11—24no—
159C4×D11—24no—
160C4×D11C22×C818yes—
161Dic22C4×C814yes—
162C8×C11—22no—
163C8×C11—24no—
164C8×C11—22no—
165C8×C11C22×C818yes—
166C11⋊C8—22no—
167C11⋊C8—24no—
168C11⋊C8—22no—
169C11⋊C8C22×C814yes—
170C11⋊C8C22×C814yes—
171C2×#131—112no—
172C4×#41—111no—
173C8×Q8—112no—
174C8×Q8—112no—
175C8×D4—114no—
176C8×D4—112no—
177C8×D4—114no—
178C8×D4—112no—
179#431—111no—
180#431—112no—
181#431—112no—
182#431C2×D1111yescharacteristic
183#405—112no—
184#405—114no—
185C4×M16—112no—
186C4×M16C2×D1111yescharacteristic
187C2×C4×C8—111no—
188C2×C4×C8—111no—
189C2×C4×C8—112no—
190C2×C4×C8—112no—
191C2×C4×C8—112no—
192C2×C4×C8C2×D1111yescharacteristic
193#322—111no—
194#322—111no—
195#322—111no—
196#322—112no—
197#322—111no—
198#322—112no—
199#322C2×D1112yes—
200C82—112no—
201C82—112no—
202C82C2×D1112yes—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11C2×C4×C812yes—
206C22×C11C22×C4211yescharacteristic
207C2×D11—22no—
208C2×D11—22no—
209C2×D11C2×C4×C814yes—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11C2×C4×C812yes—
213C4×C11C23×C812yes—
214C4×C11#56812yes—
215C4×C11#56812yes—
216Dic11—22no—
217Dic11—22no—
218Dic11C2×C4×C814yes—
219C2×#41—111no—
220#131—1116no—
221C2×M16—114no—
222C2×M16C4×D1112yes—
223C22×C8—112no—
224C22×C8—114no—
225C22×C8—112no—
226C22×C8—114no—
227C22×C8—114no—
228C22×C8C4×D1112yes—
229C4×Q8—111no—
230C4×Q8—111no—
231C4×D4—112no—
232C4×D4—112no—
233C4×D4—111no—
234C4×D4—111no—
235#117—111no—
236#117—112no—
237C2×C42—112no—
238C2×C42C22×D1111yescharacteristic
239C4⋊C8—114no—
240C4⋊C8—114no—
241C4⋊C8—112no—
242C4⋊C8C4×D1112yes—
243C22⋊C8—112no—
244C22⋊C8—114no—
245C22⋊C8—114no—
246C22⋊C8C4×D1112yes—
247#97—114no—
248#97C4×D1112yes—
249C4×C8—114no—
250C4×C8—114no—
251C4×C8—114no—
252C4×C8—112no—
253C4×C8—112no—
254C4×C8—111no—
255C4×C8—111no—
256C4×C8—112no—
257C4×C8—111no—
258C4×C8—111no—
259C4×C8C4×D1112yes—
260C4×C8C22×D1112yes—
261C4×C8C22×D1112yes—
262C4×C8C22×D1111yescharacteristic
263C4×C8C22×D1111yescharacteristic
264C2×C11—22no—
265C2×C11C22×C4×C811yescharacteristic
266C2×C11#287511yescharacteristic
267C2×C11#287511yescharacteristic
268D11—24no—
269#41—118no—
270C2×Q8—111no—
271C2×D4—112no—
272C2×D4—111no—
273C22×C4—112no—
274C22×C4—112no—
275C22×C4—112no—
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4C2×C4×D1111yescharacteristic
279M16—1116no—
280M16C8×D1118yescomplemented
281C2×C8—42no—
282C2×C8—118no—
283C2×C8—112no—
284C2×C8—112no—
285C2×C8—1116no—
286C2×C8—112no—
287C2×C8—114no—
288C2×C8—112no—
289C2×C8—444no—
290C2×C8—444no—
291C2×C8—442no—
292C2×C8C2×C4×D1112yes—
293C2×C8C2×C4×D1114yes—
294C2×C8C2×C4×D1112yes—
295C2×C8C2×C4×D1114yes—
296C4⋊C4—112no—
297C4⋊C4—112no—
298C4⋊C4—111no—
299C4⋊C4—111no—
300C22⋊C4—112no—
301C22⋊C4—112no—
302C22⋊C4—112no—
303C42—112no—
304C42—112no—
305C42—112no—
306C42C2×C4×D1111yescharacteristic
307C42C2×C4×D1111yescharacteristic
308C42C2×C4×D1111yescharacteristic
309C42C23×D1111yescharacteristic
310C11#1731611yescharacteristic, complemented, Sylow
311C23—112no—
312C23C42×D1111yescharacteristic
313Q8—114no—
314D4—118no—
315D4—114no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—112no—
319C2×C4—118no—
320C2×C4—112no—
321C2×C4—112no—
322C2×C4—224no—
323C2×C4—224no—
324C2×C4C42×D1111yescharacteristic
325C2×C4C42×D1111yescharacteristic
326C2×C4C42×D1111yescharacteristic
327C2×C4C2×C8×D1114yes—
328C2×C4C22×C4×D1111yescharacteristic
329C2×C4C22×C4×D1111yescharacteristic
330C2×C4C22×C4×D1111yescharacteristic
331C8—22no—
332C8—22no—
333C8—24no—
334C8—114no—
335C8—114no—
336C8—224no—
337C8—222no—
338C8—222no—
339C8C2×C8×D1118yes—
340C22—21no—
341C22—21no—
342C22—114no—
343C22—222no—
344C22—222no—
345C22C4×C8×D1112yes—
346C22C2×C42×D1111yescharacteristic
347C4—21no—
348C4—21no—
349C4—114no—
350C4—222no—
351C4—222no—
352C4C4×C8×D1112yes—
353C4C22×C8×D1112yes—
354C4#1062327612yes—
355C4#1062328112yes—
356C2—22no—
357C2—224no—
358C2C2×C4×C8×D1111yescharacteristic
359C2#1307704311yescharacteristic
360C2#1307704511yescharacteristic
subgroupG/H
center, FrattiniC42C23×D11
commutatorC2×C11C22×C4×C8
FittingC8×C11×M16C2
socleC22×C11C22×C42
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenterC8×M16D11
hypocenterC11#17316
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
4. #13066900C2semidirect
5. #13066898C2semidirect
6. #13066895C2semidirect
7. M16×C11⋊C8C2semidirect
8. C8×#4313C2semidirect
9. C2×#10622092C2semidirect
10. D11×#322C2semidirect
11. C8×C11×M16C2semidirect
53. #66960C8semidirect
100. C11×M16C2×C8semidirect
121. C2×C11⋊C8C2×C8semidirect
127. #4313C2×C8semidirect
130. C8×D11C2×C8semidirect
139. C8×M16D11semidirect
280. M16C8×D11semidirect
310. C11#17316semidirect

Maximal subgroups

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

subgroupindex
C8×#43392
#130775722
C4×#669602
#130669002
#130668982
#130668952
M16×C11⋊C82
C8×#43132
C2×#106220922
D11×#3222
C8×C11×M162
#1731611