Finite Group Databasebeta

← #14910433

Subgroups — #14910433

Order 2816.

718 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×#10622532C211yesmaximal, characteristic, complemented
2C22×D176C211yesmaximal, characteristic, complemented
3#13080298C212yesmaximal, complemented
4#13070878C211yesmaximal, characteristic, complemented
5#13070703C211yesmaximal, characteristic, complemented
6#13070674C212yesmaximal, complemented
7#13070544C212yesmaximal, complemented
8#13070542C212yesmaximal, complemented
9#13070462C211yesmaximal, characteristic, complemented
10C16×C22⋊D11C211yesmaximal, characteristic, complemented
11C11×#2216C211yesmaximal, characteristic, complemented
12C2×#66972C2212yescomplemented
13C22×D88C2212yes—
14#10623161—22no—
15C2×C11×Q32C2211yescharacteristic, complemented
16C22×C11×C16C2211yescharacteristic
17C11×#467C2212yes—
18#10622804C2212yescomplemented
19C2×#66892C2212yescomplemented
20C2×#66892C2212yescomplemented
21C8×C22⋊D11C2211yescharacteristic
22#10622659—22no—
23#10622532—24no—
24C2×D176—24no—
25C2×D176C2211yescharacteristic
26C2×D176C2212yes—
27C2×D176C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic, complemented
29#10622496C2212yescomplemented
30#10622485C2212yescomplemented
31#10622432—22no—
32#10622424—22no—
33C11×#366C2211yescharacteristic, complemented
34C11×#358C2212yescomplemented
35C22⋊(C11⋊C16)C2211yescharacteristic
36(C2×D11)⋊C16C2211yescharacteristic, complemented
37Dic11⋊C16C2211yescharacteristic, complemented
38C16×Dic11C2211yescharacteristic, complemented
39#10622129C2212yescomplemented
40#10622129C2212yescomplemented
41C2×#4343—22no—
42C22×D44—22no—
43C2×C11×Q16C2312yes—
44C22×C8×C11C2311yescharacteristic
45C11×C22⋊Q8—22no—
46#67000—22no—
47C2×#4325—22no—
48C2×#4325—22no—
49C4×C22⋊D11D411yescharacteristic
50#66972—24no—
51#66972—42no—
52C2×D88—24no—
53C2×D88—22no—
54C2×D88—42no—
55C2×D88C2312yes—
56C2×D88C2312yes—
57C2×C8×D11C2311yescharacteristic
58#66948—22no—
59#66948—42no—
60#66947—42no—
61#66946—22no—
62#66935—42no—
63C22⋊C4×D11—42no—
64C11×Q32—22no—
65C2×C11×C16—22no—
66C2×C11×C16C2311yescharacteristic
67C2×C11×C16C2311yescharacteristic
68C11×#107C2312yes—
69C11×#103—22no—
70C22⋊(C11⋊C8)D411yescharacteristic
71#66892—24no—
72#66892—42no—
73(C2×D11)⋊C8D411yescharacteristic
74Dic11⋊C8D411yescharacteristic
75C8×Dic11C2311yescharacteristic
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2311yescharacteristic
78#66873—22no—
79#66873—22no—
80D176—24no—
81D176—22no—
82D176D414yescomplemented
83C16×D11—22no—
84#33846—111nomaximal, Sylow
85C23×D11—42no—
86C2×Q8×C11—22no—
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11D811yescharacteristic
89#4343—44no—
90#4343—82no—
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—44no—
94C2×D44—42no—
95C2×D44—42no—
96C2×D44—42no—
97C2×D44—82no—
98C2×C4×D11—42no—
99C2×C4×D11—42no—
100C2×C4×D11C2×D411yescharacteristic
101C11×Q16—22no—
102C11×Q16—22no—
103C2×C8×C11—21no—
104C2×C8×C11—21no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—22no—
108C11×C4⋊C4—42no—
109C11×C22⋊C4—42no—
110C22⋊Dic11D811yescharacteristic
111#4325—44no—
112#4325—82no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4D811yescharacteristic
118Dic11⋊C4D811yescharacteristic
119C4×Dic11C2×D411yescharacteristic
120C2×C11⋊C8C2×D411yescharacteristic
121C2×C11⋊C8C2×D411yescharacteristic
122D88—22no—
123D88—22no—
124D88—22no—
125D88—44no—
126D88C2×D414yes—
127C8×D11—21no—
128C8×D11—21no—
129C11×C16—21no—
130C11×C16C2×D412yes—
131C11⋊C16—21no—
132C11⋊C16—21no—
133C2×#508—111no—
134C22×D16—111no—
135#3280—112no—
136#2249—111no—
137#2216D1111yescharacteristic, complemented
138#2215—111no—
139#2210—112no—
140#2187—112no—
141#2186—112no—
142C4×D16—111no—
143D4×C16—111no—
144C23×C11C2×D811yescharacteristic
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—84no—
148C22×D11—84no—
149C22×D11—162no—
150C22×D11C2×D811yescharacteristic
151Q8×C11—42no—
152Q8×C11—42no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C22⋊D11—22no—
160C2×Dic11C2×D811yescharacteristic
161C2×Dic11C2×D811yescharacteristic
162C2×Dic11C2×D811yescharacteristic
163D44—24no—
164D44—42no—
165D44—42no—
166D44—42no—
167D44—84no—
168D44—84no—
169D44—162no—
170C4×D11—21no—
171C4×D11—21no—
172C4×D11—84no—
173C4×D11—162no—
174C8×C11—21no—
175C8×C11C22×D411yescharacteristic
176C8×C11H(5,𝔽2)11yescharacteristic
177C11⋊C8—21no—
178C11⋊C8—21no—
179C2×#135—112no—
180C22×D8—112no—
181#546—222no—
182#508—224no—
183C2×Q32C2×D1111yescharacteristic, complemented
184C2×SD32—112no—
185C2×SD32—112no—
186C2×D16—111no—
187C2×D16—112no—
188C2×D16—111no—
189C2×D16—224no—
190C22×C16—111no—
191C22×C16C2×D1111yescharacteristic
192#495—112no—
193#467C2×D1112yes—
194#466—112no—
195#463—222no—
196#450—222no—
197#449—222no—
198C4×D8—112no—
199C8×D4—111no—
200#366C2×D1111yescharacteristic, complemented
201C4⋊C16—111no—
202#358C2×D1112yescomplemented
203#357—112no—
204#357—112no—
205C22⋊C16—111no—
206C22⋊C16—111no—
207C4×C16—111no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11#50812yescomplemented
211C22×C11C22×D811yescharacteristic
212C2×D11—21no—
213C2×D11—21no—
214C2×D11—21no—
215C2×D11—44no—
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—82no—
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—168no—
222C4×C11—21no—
223C4×C11—82no—
224C4×C11—82no—
225C4×C11D4211yescharacteristic
226C4×C11#57611yescharacteristic
227Dic11—21no—
228Dic11—21no—
229Dic11—21no—
230C2×#41—222no—
231C22×D4—222no—
232#135—224no—
233#135—442no—
234C2×Q16C22×D1112yes—
235C2×SD16—222no—
236C2×SD16—222no—
237C2×D8—112no—
238C2×D8—112no—
239C2×D8—224no—
240C2×D8—222no—
241C2×D8—442no—
242C22×C8—111no—
243C22×C8C22×D1111yescharacteristic
244#124—222no—
245#123—442no—
246C22⋊Q8—22no—
247#121—222no—
248#121—442no—
249#120—442no—
250C4×D4—111no—
251C4×D4—222no—
252C2×C22⋊C4—442no—
253Q32—22no—
254SD32—224no—
255SD32—442no—
256D16—114no—
257D16—224no—
258D16—222no—
259C2×C16—22no—
260C2×C16—111no—
261C2×C16—111no—
262C2×C16—222no—
263C2×C16C22×D1111yescharacteristic
264C2×C16C22×D1111yescharacteristic
265#107C22×D1112yes—
266C4⋊C8—111no—
267#103—22no—
268#102—222no—
269#102—222no—
270C22⋊C8—111no—
271C22⋊C8—111no—
272C4×C8—111no—
273C2×C11—22no—
274C2×C11D4×D811yescharacteristic
275C2×C11C2×#50811yescharacteristic
276C2×C11#341511yescharacteristic
277D11—41no—
278D11—84no—
279D11—162no—
280C24—442no—
281#41—444no—
282#41—882no—
283C2×Q8—22no—
284C2×D4—111no—
285C2×D4—222no—
286C2×D4—222no—
287C2×D4—444no—
288C2×D4—442no—
289C2×D4—442no—
290C2×D4—442no—
291C2×D4—882no—
292C22×C4—111no—
293C22×C4—442no—
294C22×C4—442no—
295C22×C4D4×D1111yescharacteristic
296Q16—22no—
297Q16—22no—
298SD16—444no—
299SD16—882no—
300D8—114no—
301D8—222no—
302D8—222no—
303D8—222no—
304D8—444no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—111no—
308C2×C8—111no—
309C2×C8—221no—
310C2×C8—221no—
311C2×C8D4×D1111yescharacteristic
312C2×C8C23×D1111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—42no—
315C4⋊C4—111no—
316C22⋊C4—42no—
317C22⋊C4—111no—
318C22⋊C4—111no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—442no—
322C22⋊C4—442no—
323C42—111no—
324C16—21no—
325C16—221no—
326C16—221no—
327C16D4×D1112yes—
328C11#3384611yescharacteristic, complemented, Sylow
329C23—111no—
330C23—442no—
331C23—442no—
332C23—884no—
333C23—884no—
334C23—1762no—
335C23D8×D1111yescharacteristic
336Q8—42no—
337Q8—42no—
338D4—222no—
339D4—224no—
340D4—442no—
341D4—442no—
342D4—442no—
343D4—884no—
344D4—884no—
345D4—1762no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—111no—
351C2×C4—111no—
352C2×C4—111no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—884no—
356C2×C4—1762no—
357C2×C4D8×D1111yescharacteristic
358C2×C4C2×D4×D1111yescharacteristic
359C8—21no—
360C8—221no—
361C8—221no—
362C8C2×D4×D1111yescharacteristic
363C8#6704211yescharacteristic
364C22—21no—
365C22—21no—
366C22—221no—
367C22—221no—
368C22—221no—
369C22—444no—
370C22—882no—
371C22—882no—
372C22—882no—
373C22—882no—
374C22—882no—
375C22—1768no—
376C22#1062253212yescomplemented
377C22C2×D8×D1111yescharacteristic
378C4—21no—
379C4—82no—
380C4—82no—
381C4—221no—
382C4—221no—
383C4—221no—
384C4#1062314011yescharacteristic
385C4#1062330011yescharacteristic
386C2—22no—
387C2—441no—
388C2—884no—
389C2—1762no—
390C2#1308029011yescharacteristic
391C2C2×#1062253211yescharacteristic
392C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2216C2
socleC22×C11C22×D8
hypercenter#2216D11
hypocenterC11#33846
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
1. C2×#10622532C2semidirect
2. C22×D176C2semidirect
3. #13080298C2semidirect
4. #13070878C2semidirect
5. #13070703C2semidirect
6. #13070674C2semidirect
7. #13070544C2semidirect
8. #13070542C2semidirect
9. #13070462C2semidirect
10. C16×C22⋊D11C2semidirect
11. C11×#2216C2semidirect
12. C2×#66972C22semidirect
15. C2×C11×Q32C22semidirect
18. #10622804C22semidirect
19. C2×#66892C22semidirect
20. C2×#66892C22semidirect
28. C2×C16×D11C22semidirect
29. #10622496C22semidirect
30. #10622485C22semidirect
33. C11×#366C22semidirect
34. C11×#358C22semidirect
36. (C2×D11)⋊C16C22semidirect
37. Dic11⋊C16C22semidirect
38. C16×Dic11C22semidirect
39. #10622129C22semidirect
40. #10622129C22semidirect
82. D176D4semidirect
137. #2216D11semidirect
183. C2×Q32C2×D11semidirect
200. #366C2×D11semidirect
202. #358C2×D11semidirect
210. C22×C11#508semidirect
328. C11#33846semidirect
376. C22#10622532semidirect

Maximal subgroups

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

subgroupindex
C2×#106225322
C22×D1762
#130802982
#130708782
#130707032
#130706742
#130705442
#130705422
#130704622
C16×C22⋊D112
C11×#22162
#3384611