Finite Group Databasebeta

← #14907164

Subgroups — #14907164

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C211yesmaximal, characteristic
2#13077493C211yesmaximal, characteristic, complemented
3#13070490C212yesmaximal, complemented
4#13070485C212yesmaximal, complemented
5C4×#66892C212yesmaximal, complemented
6C4×#66891C212yesmaximal, complemented
7C2×#10622128C211yesmaximal, characteristic, complemented
8#13070328C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic, complemented
10#13070213C211yesmaximal, characteristic, complemented
11C11×#2951C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C11×#520—21no—
14C2×#66957C2211yescharacteristic
15#10623054—21no—
16C11×#440—22no—
17C4×C11×Q16C2212yes—
18C4×C11×D8C2212yes—
19C2×C11×#107C2211yescharacteristic
20C11×#417—21no—
21C11×#405C2211yescharacteristic
22#10622807C418yescomplemented
23C2×#66893C2211yescharacteristic
24C2×#66892C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622746—21no—
28C2×#66882C2211yescharacteristic
29C2×#66876C2211yescharacteristic
30C22×C11⋊C16C2211yescharacteristic
31#10622323—22no—
32C4×Dic44C2212yes—
33C4×D88C2212yes—
34#10622202C2212yes—
35#10622200C2212yes—
36#10622130C2212yes—
37#10622129C2212yes—
38#10622128C2212yes—
39#10622128C2212yes—
40#10622099C2212yes—
41C4×C11⋊C16C2212yes—
42C2×C11×#41—21no—
43C2×#4339—21no—
44C11×#135—22no—
45C11×#135C2×C414yescomplemented
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—21no—
48C2×C11×D8C2311yescharacteristic
49C2×C11×M16D411yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—22no—
52C4×D4×C11—22no—
53C4×D4×C11—42no—
54C11×#117—41no—
55C11×#117D411yescharacteristic
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—41no—
58C2×C4⋊Dic11—21no—
59C2×Dic44C2311yescharacteristic
60#66957—22no—
61#66957C2×C414yescomplemented
62C2×D88C2311yescharacteristic
63C2×#4314—21no—
64#66945—41no—
65C4⋊C4×D11—41no—
66(C22⋊D11)⋊C4—42no—
67C4×D44—22no—
68C4×Dic22—22no—
69C11×#107—21no—
70C11×#107C2312yes—
71C11×#103—22no—
72C11×#102—22no—
73C11×#97D412yes—
74C4×C8×C11C2312yes—
75#66893C2×C414yescomplemented
76#66892C2×C414yescomplemented
77#66891C2×C414yescomplemented
78#66890C2×C414yescomplemented
79#66885—22no—
80#66882—21no—
81#66882C2312yes—
82#66880—22no—
83#66876—22no—
84C2×C11⋊C16C2×C414yescomplemented
85C2×C11⋊C16C2312yes—
86C2×C11⋊C16C2311yescharacteristic
87C2×C11⋊C16C2311yescharacteristic
88#33460—111nomaximal, Sylow
89C11×#41—24no—
90C11×#41—42no—
91C2×Q8×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—42no—
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—41no—
99C22×Dic11—41no—
100#4339—24no—
101#4339—42no—
102C2×D44—21no—
103C2×C4×D11—41no—
104C2×C4×D11—42no—
105C2×Dic22—21no—
106C11×Q16—21no—
107C11×Q16C22×C412yes—
108C11×SD16—24no—
109C11×D8—21no—
110C11×D8C22×C412yes—
111C11×M16—22no—
112C2×C8×C11C22×C412yes—
113C2×C8×C11C2×D412yes—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11#4112yes—
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—22no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4D811yescharacteristic
121C11×C4⋊C4D811yescharacteristic
122C11×C22⋊C4—42no—
123C11×C22⋊C4D812yes—
124C42×C11—42no—
125C42×C11C2×D412yes—
126(C2×D11)⋊C4—42no—
127C4⋊Dic11—22no—
128C4⋊Dic11—41no—
129Dic11⋊C4—42no—
130C4×Dic11—42no—
131Dic44—21no—
132Dic44C22×C412yes—
133D88—21no—
134D88C22×C412yes—
135#4314—24no—
136C11⋊C16—22no—
137C11⋊C16C22×C412yes—
138C11⋊C16C22×C412yes—
139C2×#508—111no—
140#2951—111no—
141#2951D1111yescharacteristic, complemented
142#2177—112no—
143#2176—112no—
144C4×SD32—112no—
145C4×SD32—112no—
146C2×#367—111no—
147#2139—111no—
148#2139—111no—
149#2108—111no—
150C23×C11—41no—
151C23×C11C2×D811yescharacteristic
152C22×D11—41no—
153Q8×C11—22no—
154Q8×C11—41no—
155D4×C11—22no—
156D4×C11—44no—
157D4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—162no—
162C2×C4×C11—161no—
163C2×C4×C11C4×D412yes—
164C2×C4×C11C2×D812yes—
165C2×C4×C11C2×D812yes—
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11#13512yes—
168C2×C4×C11C22×D411yescharacteristic
169C22⋊D11—44no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—161no—
173D44—22no—
174D44—41no—
175C4×D11—44no—
176C4×D11—162no—
177Dic22—22no—
178Dic22—41no—
179C8×C11—22no—
180C8×C11C4×D412yes—
181C8×C11C23×C411yescharacteristic
182C8×C11C2×#4111yescharacteristic
183C2×#135—111no—
184C2×#135C2×D1111yescharacteristic
185#520—21no—
186#520—221no—
187#508—118no—
188C2×Q32—111no—
189C2×SD32—111no—
190C2×SD32—111no—
191C2×D16—111no—
192C2×M32—111no—
193C22×C16—111no—
194#440—22no—
195#440—222no—
196C4×Q16—112no—
197C4×Q16C2×D1112yes—
198C4×D8—112no—
199C4×D8C2×D1112yes—
200C2×#107—111no—
201C2×#107C2×D1111yescharacteristic
202#417—21no—
203#417—221no—
204#405C2×D1111yescharacteristic
205#367—112no—
206#367—112no—
207#358—112no—
208#358—112no—
209#357—112no—
210#357—112no—
211#346—112no—
212C4×C16—112no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—42no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11C4×D812yes—
219C22×C11C22×D811yescharacteristic
220C2×D11—42no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—22no—
224C4×C11—22no—
225C4×C11—42no—
226C4×C11—82no—
227C4×C11C4×D812yes—
228C4×C11C2×C4×D411yescharacteristic
229C4×C11C2×#13511yescharacteristic
230Dic11—42no—
231Dic11—82no—
232C2×#41—21no—
233C2×#41—221no—
234#135—22no—
235#135—114no—
236#135—222no—
237#135C4×D1114yescomplemented
238C2×Q16—111no—
239C2×Q16C22×D1111yescharacteristic
240C2×SD16—21no—
241C2×SD16—221no—
242C2×D8—111no—
243C2×D8C22×D1111yescharacteristic
244C2×M16C22⋊D1111yescharacteristic
245C22×C8C22×D1111yescharacteristic
246C4×Q8—22no—
247C4×Q8—222no—
248C4×D4—22no—
249C4×D4—42no—
250C4×D4—222no—
251C4×D4—442no—
252#117—41no—
253#117—441no—
254#117C22⋊D1111yescharacteristic
255C2×C4⋊C4—21no—
256C2×C4⋊C4—41no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—441no—
259Q32—114no—
260SD32—114no—
261SD32—114no—
262D16—114no—
263M32—222no—
264C2×C16—114no—
265C2×C16—111no—
266C2×C16—111no—
267C2×C16—112no—
268#107—21no—
269#107—112no—
270#107—221no—
271#107C22×D1112yes—
272#103—22no—
273#103—222no—
274#102—22no—
275#102—222no—
276#97C22⋊D1112yes—
277C4×C8C22×D1112yes—
278C2×C11—22no—
279C2×C11—82no—
280C2×C11C2×C4×D811yescharacteristic
281C2×C11#341611yescharacteristic
282C2×C11#341611yescharacteristic
283D11—82no—
284#41—24no—
285#41—42no—
286#41—224no—
287#41—442no—
288C2×Q8—21no—
289C2×Q8—221no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—42no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4—442no—
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—21no—
302Q16—112no—
303Q16—221no—
304Q16C2×C4×D1112yes—
305SD16—24no—
306SD16—224no—
307D8—21no—
308D8—112no—
309D8—221no—
310D8C2×C4×D1112yes—
311M16—22no—
312C2×C8C2×C4×D1112yes—
313C2×C8#433912yes—
314C2×C8C2×C22⋊D1112yes—
315C2×C8C2×C22⋊D1111yescharacteristic
316C2×C8C23×D1111yescharacteristic
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—222no—
321C4⋊C4—441no—
322C4⋊C4—442no—
323C4⋊C4#432311yescharacteristic
324C4⋊C4#432311yescharacteristic
325C22⋊C4—42no—
326C22⋊C4—442no—
327C22⋊C4#432312yes—
328C42—42no—
329C42—442no—
330C42C2×C22⋊D1112yes—
331C16—112no—
332C16—112no—
333C16—222no—
334C11#3346011yescharacteristic, complemented, Sylow
335C23—41no—
336C23—441no—
337C23C2×#432311yescharacteristic
338Q8—22no—
339Q8—41no—
340Q8—222no—
341Q8—441no—
342D4—22no—
343D4—44no—
344D4—41no—
345D4—222no—
346D4—444no—
347D4—441no—
348C2×C4—41no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—162no—
352C2×C4—161no—
353C2×C4—441no—
354C2×C4—444no—
355C2×C4—442no—
356C2×C4—1762no—
357C2×C4—1761no—
358C2×C4C4×C22⋊D1112yes—
359C2×C4C2×#432312yes—
360C2×C4C2×#432312yes—
361C2×C4C2×#432311yescharacteristic
362C2×C4#6700312yes—
363C2×C4C22×C22⋊D1111yescharacteristic
364C8—22no—
365C8C4×C22⋊D1112yes—
366C8C22×C4×D1111yescharacteristic
367C8C2×#433911yescharacteristic
368C22—21no—
369C22—21no—
370C22—42no—
371C22—81no—
372C22—81no—
373C22—442no—
374C22—881no—
375C22—881no—
376C22C4×#432312yes—
377C22C22×#432311yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—82no—
382C4—442no—
383C4—882no—
384C4C4×#432312yes—
385C4C2×C4×C22⋊D1111yescharacteristic
386C4C2×#6700311yescharacteristic
387C2—22no—
388C2—82no—
389C2—882no—
390C2C2×C4×#432311yescharacteristic
391C2#1308176011yescharacteristic
392C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2951C2
socleC22×C11C22×D8
prime radicalC2×#10622807C2
cosocleC2×C8×C11C24
hypercenter#2951D11
hypocenterC11#33460
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
2. #13077493C2semidirect
3. #13070490C2semidirect
4. #13070485C2semidirect
5. C4×#66892C2semidirect
6. C4×#66891C2semidirect
7. C2×#10622128C2semidirect
8. #13070328C2semidirect
9. #13070326C2semidirect
10. #13070213C2semidirect
11. C11×#2951C2semidirect
22. #10622807C4semidirect
45. C11×#135C2×C4semidirect
61. #66957C2×C4semidirect
75. #66893C2×C4semidirect
76. #66892C2×C4semidirect
77. #66891C2×C4semidirect
78. #66890C2×C4semidirect
84. C2×C11⋊C16C2×C4semidirect
141. #2951D11semidirect
237. #135C4×D11semidirect
334. C11#33460semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
#130774932
#130704902
#130704852
C4×#668922
C4×#668912
C2×#106221282
#130703282
#130703262
#130702132
C11×#29512
#3346011