Finite Group Databasebeta

← #14910590

Subgroups — #14910590

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D88C211yesmaximal, characteristic, complemented
2#13070841C211yesmaximal, characteristic, complemented
3#13070796C212yesmaximal, complemented
4#13070750C211yesmaximal, characteristic, complemented
5#13070700C212yesmaximal, complemented
6#13070651C211yesmaximal, characteristic, complemented
7#13070527C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10C2×#10622129C212yesmaximal, complemented
11C11×#3334C211yesmaximal, characteristic, complemented
12C11×#547—21no—
13C22×D88C2212yes—
14D4×D44—21no—
15C11×#500C2211yescharacteristic, complemented
16C11×#480—22no—
17C11×#474—21no—
18C11×#466C2212yescomplemented
19C4×C11×D8C2211yescharacteristic, complemented
20C8×D4×C11C2211yescharacteristic
21C2×C11×#107C2212yescomplemented
22C2×#66890C2211yescharacteristic
23C2×#66890C2212yescomplemented
24#10622728C2212yes—
25C22×C11⋊C16C2212yescomplemented
26#10622456—21no—
27#10622345—22no—
28#10622308C2211yescharacteristic
29C4×D88C2211yescharacteristic
30#10622200C2211yescharacteristic, complemented
31C22⋊(C11⋊C16)C2212yescomplemented
32#10622129C2211yescharacteristic
33#10622129C2212yes—
34#10622129C2212yescomplemented
35#10622129C2212yescomplemented
36#10622129C2212yescomplemented
37#10622127C2212yescomplemented
38#10622127C2211yescharacteristic, complemented
39C4⋊(C11⋊C16)C2211yescharacteristic, complemented
40C4×C11⋊C16C2211yescharacteristic, complemented
41C2×C11×#41—41no—
42C2×D4×D11—41no—
43C22×D44—22no—
44C2×C11×D8C2311yescharacteristic
45C22×C8×C11C2312yes—
46C11×C4⋊Q8—21no—
47C11×#123—42no—
48C11×C22⋊Q8—41no—
49C11×#121—22no—
50C4×D4×C11—21no—
51C4×D4×C11D411yescharacteristic
52C2×C11×C4⋊C4—22no—
53#66983—22no—
54C2×D88—24no—
55C2×D88—22no—
56C2×D88—21no—
57C2×D88—42no—
58C2×D88C2312yes—
59C2×D88C2311yescharacteristic
60#66948—41no—
61#66935—42no—
62#66927—21no—
63C4×D44—21no—
64C11×#107—21no—
65C11×#107—22no—
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×C4⋊C8D411yescharacteristic
69C11×#102—21no—
70C11×#102—22no—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2311yescharacteristic
73#66890—22no—
74#66890—42no—
75#66885—22no—
76#66885—21no—
77#66882C2311yescharacteristic
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82#33861—111nomaximal, Sylow
83C23×D11—42no—
84C11×#41—84no—
85C2×Q8×C11—41no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11D811yescharacteristic
89C22×C4×C11—42no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D412yes—
92C2×C22⋊D11—42no—
93D4×D11—84no—
94C2×D44—21no—
95C2×D44—22no—
96C2×D44—44no—
97C2×D44—41no—
98C2×D44—42no—
99C2×D44—41no—
100C2×D44—82no—
101C2×C4×D11—41no—
102C11×D8—21no—
103C11×D8—21no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D412yes—
108C2×C8×C11C2411yescharacteristic
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4D811yescharacteristic
114C11×C22⋊C4—41no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4D812yes—
117C42×C11C2×D411yescharacteristic
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—42no—
120C4⋊Dic11—21no—
121D88—22no—
122D88—21no—
123D88—22no—
124D88—44no—
125D88—81no—
126D88#4112yescomplemented
127C11⋊C16—21no—
128C11⋊C16—21no—
129C11⋊C16—22no—
130#3334D1111yescharacteristic, complemented
131D4×D8—111no—
132#2240—111no—
133#2232—112no—
134#2224—111no—
135#2215—112no—
136#2206—111no—
137#2184—112no—
138C4×D16—111no—
139D4×C16—111no—
140C2×#357—112no—
141C23×C11—41no—
142C23×C11C2×D812yes—
143C22×D11—41no—
144C22×D11—42no—
145C22×D11—84no—
146C22×D11—84no—
147C22×D11—162no—
148Q8×C11—82no—
149D4×C11—41no—
150D4×C11—41no—
151D4×C11—84no—
152D4×C11D1614yescomplemented
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—84no—
158C2×C4×C11—82no—
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×D812yes—
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C22⋊D11—84no—
164C2×Dic11—41no—
165D44—22no—
166D44—42no—
167D44—41no—
168D44—42no—
169D44—84no—
170D44—82no—
171D44—161no—
172C4×D11—82no—
173C8×C11—22no—
174C8×C11—21no—
175C8×C11C2×#4111yescharacteristic
176C8×C11H(5,𝔽2)11yescharacteristic
177C22×D8—112no—
178#547—21no—
179D42—221no—
180C2×D16—111no—
181C2×D16—112no—
182C22×C16—112no—
183#500C2×D1111yescharacteristic, complemented
184#493—111no—
185#480—22no—
186#474—21no—
187#466—112no—
188#466C2×D1112yescomplemented
189#459—221no—
190#447—222no—
191C4×D8—111no—
192C4×D8C2×D1111yescharacteristic, complemented
193C8×D4C2×D1111yescharacteristic
194C2×#107C2×D1112yescomplemented
195#366—111no—
196#366—112no—
197C4⋊C16—111no—
198#357—111no—
199#357—111no—
200#357—112no—
201#357—112no—
202#357—112no—
203#357—112no—
204C22⋊C16—112no—
205C4×C16—111no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11C2×D1614yes—
212C22×C11C22×D811yescharacteristic
213C2×D11—42no—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—82no—
219C2×D11—168no—
220C4×C11—21no—
221C4×C11—22no—
222C4×C11—81no—
223C4×C11—82no—
224C4×C11C2×D1612yes—
225C4×C11#54611yescharacteristic
226C4×C11#57711yescharacteristic
227Dic11—81no—
228C2×#41—41no—
229C22×D4—222no—
230C22×D4—441no—
231C2×D8—111no—
232C2×D8—112no—
233C2×D8—224no—
234C2×D8—222no—
235C2×D8—221no—
236C2×D8—442no—
237C2×D8C22×D1111yescharacteristic
238C22×C8C22×D1112yes—
239C4⋊Q8—21no—
240#127—221no—
241#123—42no—
242C22⋊Q8—41no—
243#121—22no—
244#121—222no—
245#121—441no—
246#120—442no—
247C4×D4—21no—
248C4×D4—221no—
249C4×D4C22⋊D1111yescharacteristic
250C2×C4⋊C4—22no—
251D16—222no—
252D16—442no—
253C2×C16—111no—
254C2×C16—111no—
255C2×C16—112no—
256C2×C16—442no—
257#107—22no—
258#107—21no—
259#107—111no—
260#107C22×D1111yescharacteristic
261#107C22×D1112yes—
262C4⋊C8C22⋊D1111yescharacteristic
263#102—21no—
264#102—22no—
265#102—221no—
266#102—222no—
267C22⋊C8C22⋊D1112yes—
268C4×C8C22×D1111yescharacteristic
269C2×C11—24no—
270C2×C11—161no—
271C2×C11#329411yescharacteristic
272C2×C11C22×D1611yescharacteristic
273C2×C11#341611yescharacteristic
274D11—82no—
275D11—162no—
276C24—442no—
277#41—84no—
278C2×Q8—41no—
279C2×D4—21no—
280C2×D4—42no—
281C2×D4—221no—
282C2×D4—222no—
283C2×D4—444no—
284C2×D4—442no—
285C2×D4—442no—
286C2×D4—441no—
287C2×D4—441no—
288C2×D4—882no—
289C2×D4—884no—
290C2×D4#432311yescharacteristic
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—441no—
294C22×C4C2×C22⋊D1112yes—
295D8—21no—
296D8—21no—
297D8—112no—
298D8—222no—
299D8—221no—
300D8—222no—
301D8—444no—
302D8—881no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8C2×C22⋊D1111yescharacteristic
306C2×C8C2×C22⋊D1112yes—
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—221no—
313C4⋊C4#432311yescharacteristic
314C22⋊C4—41no—
315C22⋊C4—42no—
316C22⋊C4—441no—
317C22⋊C4—442no—
318C22⋊C4#432312yes—
319C42C2×C22⋊D1111yescharacteristic
320C16—221no—
321C16—221no—
322C16—222no—
323C11#3386111yescharacteristic, complemented, Sylow
324C23—41no—
325C23—441no—
326C23—442no—
327C23—884no—
328C23—884no—
329C23—1762no—
330C23C2×#432312yes—
331Q8—82no—
332D4—41no—
333D4—41no—
334D4—84no—
335D4—222no—
336D4—442no—
337D4—441no—
338D4—442no—
339D4—884no—
340D4—884no—
341D4—882no—
342D4—1761no—
343D4#6689014yescomplemented
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—84no—
349C2×C4—82no—
350C2×C4—441no—
351C2×C4—882no—
352C2×C4C2×#432311yescharacteristic
353C2×C4C2×#432312yes—
354C2×C4C2×#432311yescharacteristic
355C2×C4C22×C22⋊D1111yescharacteristic
356C8—22no—
357C8—21no—
358C8#41×D1111yescharacteristic
359C8#6704211yescharacteristic
360C22—22no—
361C22—22no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—442no—
366C22—881no—
367C22—881no—
368C22—882no—
369C22—882no—
370C22—882no—
371C22—1768no—
372C22C2×#6689014yes—
373C22C22×#432311yescharacteristic
374C4—22no—
375C4—21no—
376C4—81no—
377C4—82no—
378C4—881no—
379C4C2×#6689012yes—
380C4#1062336011yescharacteristic
381C4#1062336811yescharacteristic
382C2—24no—
383C2—161no—
384C2—882no—
385C2—1762no—
386C2#1308042311yescharacteristic
387C2C22×#6689011yescharacteristic
388C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3334C2
socleC22×C11C22×D8
hypercenter#3334D11
hypocenterC11#33861
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. D4×D88C2semidirect
2. #13070841C2semidirect
3. #13070796C2semidirect
4. #13070750C2semidirect
5. #13070700C2semidirect
6. #13070651C2semidirect
7. #13070527C2semidirect
8. C4×#66890C2semidirect
9. D4×C11⋊C16C2semidirect
10. C2×#10622129C2semidirect
11. C11×#3334C2semidirect
15. C11×#500C22semidirect
18. C11×#466C22semidirect
19. C4×C11×D8C22semidirect
21. C2×C11×#107C22semidirect
23. C2×#66890C22semidirect
25. C22×C11⋊C16C22semidirect
30. #10622200C22semidirect
31. C22⋊(C11⋊C16)C22semidirect
34. #10622129C22semidirect
35. #10622129C22semidirect
36. #10622129C22semidirect
37. #10622127C22semidirect
38. #10622127C22semidirect
39. C4⋊(C11⋊C16)C22semidirect
40. C4×C11⋊C16C22semidirect
126. D88#41semidirect
130. #3334D11semidirect
152. D4×C11D16semidirect
183. #500C2×D11semidirect
188. #466C2×D11semidirect
192. C4×D8C2×D11semidirect
194. C2×#107C2×D11semidirect
323. C11#33861semidirect
343. D4#66890semidirect

Maximal subgroups

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

subgroupindex
D4×D882
#130708412
#130707962
#130707502
#130707002
#130706512
#130705272
C4×#668902
D4×C11⋊C162
C2×#106221292
C11×#33342
#3386111