Finite Group Databasebeta

← #14908265

Subgroups — #14908265

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×D16C211yesmaximal, characteristic, complemented
2C2×#10622514C211yesmaximal, characteristic, complemented
3#13078259C212yesmaximal, complemented
4#13070718C212yesmaximal, complemented
5#13070717C212yesmaximal, complemented
6#13070703C211yesmaximal, characteristic, complemented
7#13070702C211yesmaximal, characteristic, complemented
8#13070699C211yesmaximal, characteristic, complemented
9#13070397C211yesmaximal, characteristic, complemented
10#13070330C212yesmaximal, complemented
11C11×#2215C211yesmaximal, characteristic, complemented
12C2×D8×D11C2212yes—
13C2×#66954C2211yescharacteristic
14#10623138—22no—
15C2×C11×D16C2211yescharacteristic
16C22×C11×C16C2211yescharacteristic, complemented
17C11×#466C2212yescomplemented
18#10622770C2212yescomplemented
19C2×#66890C2212yes—
20#10622728C2212yescomplemented
21C2×#66876C2211yescharacteristic, complemented
22#10622652—22no—
23D11×D16—24no—
24C2×D176C2211yescharacteristic
25#10622514—24no—
26C2×#66862C2211yescharacteristic
27C2×#66862C2211yescharacteristic, complemented
28C2×C16×D11C2211yescharacteristic
29C2×C16×D11C2211yescharacteristic, complemented
30#10622496C2212yescomplemented
31#10622493C2212yes—
32#10622395—22no—
33#10622383—22no—
34C11×#366C2211yescharacteristic, complemented
35C11×#357C2212yescomplemented
36#10622200C2212yescomplemented
37#10622147C2212yescomplemented
38#10622142C2211yescharacteristic, complemented
39#10622129C2212yescomplemented
40#10622128C2212yescomplemented
41C2×D4×D11—22no—
42C2×#4339D411yescharacteristic
43C2×C11×D8C2312yes—
44C22×C8×C11C2311yescharacteristic
45C11×#121—22no—
46#66993—42no—
47#66991—22no—
48#66990—42no—
49C2×#4323—22no—
50#66983—22no—
51C2×#4318D411yescharacteristic
52D8×D11—24no—
53D8×D11—24no—
54C2×D88C2312yes—
55#66954—22no—
56#66954—22no—
57C2×#4313D411yescharacteristic
58C2×#4313D411yescharacteristic
59C2×C8×D11C2311yescharacteristic
60C2×C8×D11C2311yescharacteristic
61#66948—22no—
62#66945—22no—
63#66938—42no—
64#66935—42no—
65C11×D16—22no—
66C2×C11×C16—22no—
67C2×C11×C16C2311yescharacteristic
68C2×C11×C16C2311yescharacteristic
69C11×#107C2312yes—
70C11×#102—22no—
71#66896—22no—
72#66890—24no—
73#66885—22no—
74#66882C2312yes—
75#66876—22no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2311yescharacteristic
78#66873—22no—
79#66872—22no—
80D176—22no—
81#66862—22no—
82#66862—22no—
83C16×D11—22no—
84C16×D11D414yescomplemented
85#33607—111nomaximal, Sylow
86C23×D11—42no—
87C2×D4×C11—22no—
88C2×D4×C11—42no—
89C22×C4×C11C2×D411yescharacteristic
90C2×C22⋊D11—42no—
91C2×C22⋊D11—42no—
92C2×C22⋊D11—42no—
93C2×C22⋊D11D811yescharacteristic
94C2×C22⋊D11D811yescharacteristic
95D4×D11—44no—
96D4×D11—44no—
97#4339—22no—
98#4339—22no—
99C2×D44—22no—
100C2×D44—42no—
101C2×D44D811yescharacteristic
102C2×C4×D11C2×D411yescharacteristic
103C2×C4×D11C2×D411yescharacteristic
104C2×Dic22D811yescharacteristic
105C11×D8—22no—
106C11×D8—22no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2411yescharacteristic
111C11×C4⋊C4—22no—
112C11×C22⋊C4—42no—
113C22⋊Dic11—42no—
114#4323—44no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—42no—
118C4⋊Dic11—22no—
119C4×Dic11—42no—
120#4318—22no—
121C2×C11⋊C8C2×D411yescharacteristic
122C2×C11⋊C8C2×D411yescharacteristic
123D88—22no—
124D88—22no—
125#4313—22no—
126#4313—22no—
127C8×D11—21no—
128C8×D11—21no—
129C8×D11C2×D412yes—
130C8×D11#4112yes—
131C11×C16—21no—
132C11×C16C2×D412yes—
133C11⋊C16—21no—
134C11⋊C16C2×D412yes—
135C22×D16—111no—
136C2×#504—111no—
137#3058—112no—
138#2218—112no—
139#2218—112no—
140#2215—111no—
141#2215—111no—
142#2215—111no—
143#2215D1111yescharacteristic, complemented
144#2158—111no—
145#2140—112no—
146C23×C11—42no—
147C23×C11C2×D811yescharacteristic
148C22×D11—42no—
149C22×D11—84no—
150C22×D11—162no—
151C22×D11—162no—
152C22×D11C2×D811yescharacteristic
153C22×D11C2×D811yescharacteristic
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—162no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—42no—
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C22⋊D11—22no—
163C22⋊D11—22no—
164C22⋊D11—84no—
165C22⋊D11—162no—
166C22⋊D11—162no—
167C2×Dic11—42no—
168C2×Dic11C2×D811yescharacteristic
169C2×Dic11C2×D811yescharacteristic
170D44—22no—
171D44—42no—
172D44—42no—
173D44—162no—
174C4×D11—21no—
175C4×D11—21no—
176C4×D11#12112yes—
177C4×D11#13512yes—
178Dic22—22no—
179C8×C11—21no—
180C8×C11C22×D411yescharacteristic
181C8×C11C2×#4111yescharacteristic
182C11⋊C8—21no—
183C11⋊C8#12112yes—
184C22×D8—112no—
185C2×#131—111no—
186#535—222no—
187C2×D16—112no—
188C2×D16—111no—
189C2×D16—224no—
190C2×D16C2×D1111yescharacteristic
191#504—224no—
192C2×M32—111no—
193C2×M32—111no—
194C2×M32—111no—
195C22×C16—111no—
196C22×C16—111no—
197C22×C16C2×D1111yescharacteristic, complemented
198#469—222no—
199#469—222no—
200#466—112no—
201#466—112no—
202#466—112no—
203#466C2×D1112yescomplemented
204#427—112no—
205#418—222no—
206#367—112no—
207#366—111no—
208#366C2×D1111yescharacteristic, complemented
209#357—112no—
210#357—112no—
211#357—112no—
212#357C2×D1112yescomplemented
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—82no—
217C22×C11—82no—
218C22×C11—82no—
219C22×C11C22×D811yescharacteristic
220C2×D11—21no—
221C2×D11—21no—
222C2×D11—21no—
223C2×D11—21no—
224C2×D11—21no—
225C2×D11—82no—
226C2×D11—82no—
227C2×D11—82no—
228C2×D11—168no—
229C2×D11#46612yes—
230C4×C11—21no—
231C4×C11—82no—
232C4×C11C2×#12111yescharacteristic
233C4×C11C2×#13511yescharacteristic
234Dic11—21no—
235Dic11—82no—
236Dic11#46612yes—
237C2×#41—111no—
238C22×D4—222no—
239C2×D8—112no—
240C2×D8—224no—
241C2×D8—224no—
242C2×D8—222no—
243C2×D8C22×D1112yes—
244#131—222no—
245#131—222no—
246C2×M16—111no—
247C2×M16—111no—
248C2×M16—111no—
249C22×C8—111no—
250C22×C8—111no—
251C22×C8C22×D1111yescharacteristic
252#127—442no—
253#124—442no—
254#121—22no—
255#121—222no—
256#121—222no—
257#121—222no—
258#120—442no—
259#120—442no—
260#117—222no—
261D16—22no—
262D16—224no—
263D16—222no—
264M32—222no—
265M32—222no—
266M32—222no—
267C2×C16—22no—
268C2×C16—111no—
269C2×C16—114no—
270C2×C16—111no—
271C2×C16—222no—
272C2×C16C22×D1111yescharacteristic
273C2×C16C22×D1111yescharacteristic
274#107—112no—
275#107C22×D1112yes—
276#106—222no—
277#102—22no—
278#102—222no—
279#102—222no—
280#102—222no—
281C2×C11—41no—
282C2×C11—162no—
283C2×C11C2×#46611yescharacteristic
284C2×C11#341511yescharacteristic
285C2×C11#341511yescharacteristic
286D11—22no—
287D11—41no—
288D11—162no—
289C24—442no—
290#41—222no—
291#41—222no—
292C2×Q8—111no—
293C2×D4—22no—
294C2×D4—42no—
295C2×D4—111no—
296C2×D4—111no—
297C2×D4—111no—
298C2×D4—222no—
299C2×D4—442no—
300C2×D4—444no—
301C2×D4—444no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—442no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4D4×D1111yescharacteristic
308D8—22no—
309D8—22no—
310D8—222no—
311D8—222no—
312D8—444no—
313M16—222no—
314M16—222no—
315M16—222no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—111no—
319C2×C8—112no—
320C2×C8—112no—
321C2×C8—111no—
322C2×C8—221no—
323C2×C8—221no—
324C2×C8D4×D1111yescharacteristic
325C2×C8C23×D1111yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—222no—
328C22⋊C4—42no—
329C22⋊C4—442no—
330C22⋊C4—442no—
331C22⋊C4—442no—
332C22⋊C4—442no—
333C42—442no—
334C16—21no—
335C16—112no—
336C16—221no—
337C16D4×D1112yes—
338C11#3360711yescharacteristic, complemented, Sylow
339C23—42no—
340C23—111no—
341C23—111no—
342C23—442no—
343C23—884no—
344C23—1762no—
345C23—1762no—
346C23D8×D1111yescharacteristic
347Q8—222no—
348D4—42no—
349D4—42no—
350D4—162no—
351D4—222no—
352D4—222no—
353D4—222no—
354D4—442no—
355D4—442no—
356D4—884no—
357D4—1762no—
358D4—1762no—
359D4—1762no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—111no—
364C2×C4—112no—
365C2×C4—112no—
366C2×C4—111no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—442no—
370C2×C4D8×D1111yescharacteristic
371C2×C4C2×D4×D1111yescharacteristic
372C8—21no—
373C8—112no—
374C8—221no—
375C8C2×D4×D1111yescharacteristic
376C8#41×D1111yescharacteristic
377C22—21no—
378C22—21no—
379C22—21no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—112no—
384C22—221no—
385C22—221no—
386C22—221no—
387C22—221no—
388C22—221no—
389C22—882no—
390C22—882no—
391C22—882no—
392C22—1768no—
393C22C2×D8×D1111yescharacteristic
394C4—21no—
395C4—82no—
396C4—112no—
397C4—221no—
398C4—882no—
399C4D11×#12111yescharacteristic
400C4D11×#13511yescharacteristic
401C2—41no—
402C2—162no—
403C2—222no—
404C2—441no—
405C2—1762no—
406C2D11×#46611yescharacteristic
407C2#1308175311yescharacteristic
408C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33607
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. C2×D11×D16C2semidirect
2. C2×#10622514C2semidirect
3. #13078259C2semidirect
4. #13070718C2semidirect
5. #13070717C2semidirect
6. #13070703C2semidirect
7. #13070702C2semidirect
8. #13070699C2semidirect
9. #13070397C2semidirect
10. #13070330C2semidirect
11. C11×#2215C2semidirect
16. C22×C11×C16C22semidirect
17. C11×#466C22semidirect
18. #10622770C22semidirect
20. #10622728C22semidirect
21. C2×#66876C22semidirect
27. C2×#66862C22semidirect
29. C2×C16×D11C22semidirect
30. #10622496C22semidirect
34. C11×#366C22semidirect
35. C11×#357C22semidirect
36. #10622200C22semidirect
37. #10622147C22semidirect
38. #10622142C22semidirect
39. #10622129C22semidirect
40. #10622128C22semidirect
84. C16×D11D4semidirect
143. #2215D11semidirect
197. C22×C16C2×D11semidirect
203. #466C2×D11semidirect
208. #366C2×D11semidirect
212. #357C2×D11semidirect
338. C11#33607semidirect

Maximal subgroups

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

subgroupindex
C2×D11×D162
C2×#106225142
#130782592
#130707182
#130707172
#130707032
#130707022
#130706992
#130703972
#130703302
C11×#22152
#3360711