Finite Group Databasebeta

← #14745285

Subgroups — #14745285

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080921C212yesmaximal, complemented
2#13080337C211yesmaximal, characteristic, complemented
3#13068214C211yesmaximal, characteristic, complemented
4#13068161C212yesmaximal, complemented
5#13068002C211yesmaximal, characteristic, complemented
6#13067981C211yesmaximal, characteristic, complemented
7#13067900C212yesmaximal, complemented
8#13067899C212yesmaximal, complemented
9#13067501C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11C11×#3334C211yesmaximal, characteristic, complemented
12C11×#547C2212yes—
13C2×#66965—21no—
14#10623086C2212yes—
15C11×#500C2211yescharacteristic
16C11×#480—22no—
17C11×#474C2212yes—
18C11×#466—21no—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×C11×#107—21no—
22#10622851—22no—
23#10622845—22no—
24#10622696C2212yes—
25#10622694C2212yes—
26#10622692C2212yes—
27#10622662—22no—
28#10622657—22no—
29#10622632C2212yes—
30C4×#4323C2211yescharacteristic
31#10622625C2212yes—
32#10622620C2212yes—
33#10622500—21no—
34#10622396—22no—
35#10622312C2211yescharacteristic
36C8×D44C2211yescharacteristic
37#10622185C2212yes—
38D4⋊(C11⋊C8)C2212yes—
39D4⋊(C11⋊C8)C2211yescharacteristic
40#10622121C2211yescharacteristic
41#10622120C2212yes—
42#10622117C2211yescharacteristic
43#10622096C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C2×C11×#41—22no—
46C2×#4341—22no—
47C2×C11×D8D411yescharacteristic
48C22×C8×C11—21no—
49C11×C4⋊Q8C2312yes—
50C11×#123—42no—
51C11×C22⋊Q8—22no—
52C11×#121—22no—
53C4×D4×C11C2312yes—
54C4×D4×C11C2311yescharacteristic
55C2×C11×C4⋊C4—22no—
56C2×#4325—22no—
57C2×#4324—22no—
58C2×#4323D411yescharacteristic
59#66983—22no—
60C2×C4⋊Dic11—22no—
61C2×#4318—22no—
62#66965—44no—
63C2×Dic44—21no—
64C2×Dic44—21no—
65C2×C8×D11—21no—
66#66950—22no—
67#66939—42no—
68C4×D44C2311yescharacteristic
69#66922C2312yes—
70C11×#107—21no—
71C11×#107—21no—
72C11×#107—22no—
73C11×#107D411yescharacteristic
74C11×C4⋊C8C2311yescharacteristic
75C11×#102—22no—
76C11×#102D412yes—
77C11×C22⋊C8—21no—
78C4×C8×C11C2311yescharacteristic
79#66899—22no—
80#66899—22no—
81#66899—22no—
82#66896—22no—
83#66896D411yescharacteristic
84C22⋊(C11⋊C8)—22no—
85(C2×D11)⋊C8—21no—
86#66874—22no—
87#66873D411yescharacteristic
88#66872—42no—
89#66871—22no—
90#66871D411yescharacteristic
91C4⋊(C11⋊C8)C2311yescharacteristic
92C4⋊(C11⋊C8)C2312yes—
93C4×C11⋊C8C2311yescharacteristic
94C4×C11⋊C8C2311yescharacteristic
95#19902—111nomaximal, Sylow
96C11×#41—44no—
97C11×#41—82no—
98C2×Q8×C11—22no—
99C2×D4×C11—42no—
100C2×D4×C11C2×D412yes—
101C2×D4×C11C2×D411yescharacteristic
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—42no—
105C2×C22⋊D11—42no—
106C22×Dic11—42no—
107#4341—44no—
108#4341—82no—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×Dic22—22no—
112C11×D8—22no—
113C2×C8×C11—21no—
114C2×C8×C11—42no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4C2×D411yescharacteristic
121C11×C4⋊C4C2×D412yes—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—21no—
124C11×C22⋊C4—42no—
125C42×C11C2411yescharacteristic
126#4325—82no—
127#4324—44no—
128#4323—22no—
129(C2×D11)⋊C4—21no—
130(C2×D11)⋊C4—42no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—42no—
134C4⋊Dic11C2×D411yescharacteristic
135#4318—82no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8C2×D411yescharacteristic
140C2×C11⋊C8C2×D411yescharacteristic
141Dic44—42no—
142Dic44—81no—
143C8×D11—42no—
144#3334D1111yescharacteristic, complemented
145#3330—112no—
146#3283—111no—
147#1707—111no—
148#1699—112no—
149#1673—111no—
150#1669—111no—
151#1654—112no—
152#1654—112no—
153#1589—111no—
154C8×D8—111no—
155C23×C11—21no—
156C23×C11—22no—
157C22×D11—21no—
158Q8×C11—42no—
159Q8×C11—42no—
160D4×C11—22no—
161D4×C11—21no—
162D4×C11—22no—
163D4×C11—84no—
164D4×C11#13512yescomplemented
165C2×C4×C11—22no—
166C2×C4×C11—21no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—84no—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11H(5,𝔽2)11yescharacteristic
176C22⋊D11—84no—
177C2×Dic11—21no—
178C2×Dic11—42no—
179C2×Dic11—84no—
180D44—21no—
181D44—21no—
182C4×D11—41no—
183C4×D11—41no—
184Dic22—42no—
185Dic22—42no—
186C8×C11—21no—
187C8×C11—41no—
188C8×C11AGL(1,ℤ/8)12yes—
189C11⋊C8—22no—
190C11⋊C8—21no—
191C11⋊C8—21no—
192C11⋊C8—41no—
193C11⋊C8—42no—
194C2×#135—221no—
195#547—112no—
196#547C2×D1112yes—
197#500C2×D1111yescharacteristic
198#498—112no—
199#494—111no—
200#487—112no—
201#484—222no—
202#480—22no—
203#474—112no—
204#474C2×D1112yes—
205#468—222no—
206#467—221no—
207#466—21no—
208#461—112no—
209#461—112no—
210#452—222no—
211#449—222no—
212C4×D8—111no—
213C4×D8C2×D1111yescharacteristic
214#436—112no—
215C8×D4—111no—
216C8×D4C2×D1111yescharacteristic
217C2×#107—21no—
218#417—222no—
219#335—111no—
220#335—111no—
221#332—112no—
222#332—112no—
223D4⋊C8—111no—
224D4⋊C8—112no—
225D4⋊C8—111no—
226C82—111no—
227C22×C11—22no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11D4211yescharacteristic
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C4×C11—21no—
238C4×C11—41no—
239C4×C11—42no—
240C4×C11—82no—
241C4×C11C2×#13511yescharacteristic
242C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C4×C11#57611yescharacteristic
244C4×C11#57711yescharacteristic
245Dic11—41no—
246Dic11—82no—
247C2×#41—22no—
248C2×#41—222no—
249#135—444no—
250C2×Q16—221no—
251C2×Q16—221no—
252C2×SD16—222no—
253C2×SD16—222no—
254C2×D8—111no—
255C2×D8C22⋊D1111yescharacteristic
256C2×M16—222no—
257C22×C8—21no—
258C22×C8—221no—
259C4⋊Q8—112no—
260C4⋊Q8C22×D1112yes—
261#123—42no—
262#123—442no—
263C22⋊Q8—22no—
264C22⋊Q8—222no—
265#121—22no—
266#121—222no—
267C4×D4—111no—
268C4×D4C22×D1111yescharacteristic
269C4×D4C22×D1112yes—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—222no—
272#107—21no—
273#107—21no—
274#107—22no—
275#107—111no—
276#107—222no—
277#107C22⋊D1111yescharacteristic
278#106—442no—
279C4⋊C8—111no—
280C4⋊C8—112no—
281C4⋊C8C22×D1111yescharacteristic
282#103—222no—
283#103—222no—
284#103—222no—
285#103—222no—
286#102—22no—
287#102—111no—
288#102—111no—
289#102—222no—
290#102C22⋊D1112yes—
291C22⋊C8—21no—
292C22⋊C8—222no—
293C22⋊C8—221no—
294C4×C8—111no—
295C4×C8—111no—
296C4×C8C22×D1111yescharacteristic
297C2×C11—42no—
298C2×C11—82no—
299C2×C11#327211yescharacteristic
300C2×C11#328011yescharacteristic
301C2×C11#329311yescharacteristic
302D11—81no—
303#41—44no—
304#41—82no—
305#41—444no—
306#41—882no—
307C2×Q8—22no—
308C2×Q8—222no—
309C2×D4—42no—
310C2×D4—111no—
311C2×D4—442no—
312C2×D4D4×D1111yescharacteristic
313C2×D4C2×C22⋊D1112yes—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—221no—
318C22×C4—442no—
319Q16—442no—
320Q16—881no—
321SD16—444no—
322SD16—882no—
323D8—22no—
324D8—222no—
325M16—882no—
326C2×C8—21no—
327C2×C8—42no—
328C2×C8—111no—
329C2×C8—111no—
330C2×C8—221no—
331C2×C8—222no—
332C2×C8—221no—
333C2×C8—442no—
334C2×C8C2×C22⋊D1111yescharacteristic
335C2×C8C2×C22⋊D1111yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—42no—
339C4⋊C4—111no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—442no—
343C4⋊C4D4×D1111yescharacteristic
344C4⋊C4C2×C22⋊D1112yes—
345C22⋊C4—21no—
346C22⋊C4—22no—
347C22⋊C4—42no—
348C22⋊C4—221no—
349C22⋊C4—442no—
350C42C23×D1111yescharacteristic
351C11#1990211yescharacteristic, complemented, Sylow
352C23—21no—
353C23—22no—
354C23—221no—
355Q8—42no—
356Q8—42no—
357Q8—442no—
358Q8—442no—
359D4—21no—
360D4—22no—
361D4—22no—
362D4—84no—
363D4—221no—
364D4—221no—
365D4—884no—
366D4#6696512yescomplemented
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—84no—
375C2×C4—221no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—884no—
380C2×C4C2×D4×D1111yescharacteristic
381C2×C4#6703711yescharacteristic
382C2×C4C22×C22⋊D1111yescharacteristic
383C8—21no—
384C8—41no—
385C8—222no—
386C8—221no—
387C8—221no—
388C8—442no—
389C8—441no—
390C8#6700212yes—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—441no—
398C22—441no—
399C22—441no—
400C22D4×C22⋊D1111yescharacteristic
401C4—21no—
402C4—41no—
403C4—42no—
404C4—82no—
405C4—441no—
406C4—882no—
407C4C2×#6696511yescharacteristic
408C4#1062328811yescharacteristic
409C4C2×#6700211yescharacteristic
410C4#1062336811yescharacteristic
411C2—42no—
412C2—82no—
413C2—881no—
414C2#1308021611yescharacteristic
415C2#1308030111yescharacteristic
416C2#1308041811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3334C2
socleC22×C11D42
hypercenter#3334D11
hypocenterC11#19902
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13080921C2semidirect
2. #13080337C2semidirect
3. #13068214C2semidirect
4. #13068161C2semidirect
5. #13068002C2semidirect
6. #13067981C2semidirect
7. #13067900C2semidirect
8. #13067899C2semidirect
9. #13067501C2semidirect
10. C8×#4323C2semidirect
11. C11×#3334C2semidirect
144. #3334D11semidirect
164. D4×C11#135semidirect
351. C11#19902semidirect
366. D4#66965semidirect

Maximal subgroups

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

subgroupindex
#130809212
#130803372
#130682142
#130681612
#130680022
#130679812
#130679002
#130678992
#130675012
C8×#43232
C11×#33342
#1990211