Finite Group Databasebeta

← #14736476

Subgroups — #14736476

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078065C212yesmaximal, complemented
2#13077582C211yesmaximal, characteristic, complemented
3#13068181C212yesmaximal, complemented
4#13068174C212yesmaximal, complemented
5#13068131C211yesmaximal, characteristic, complemented
6#13068126C211yesmaximal, characteristic, complemented
7#13068097C211yesmaximal, characteristic, complemented
8#13068092C211yesmaximal, characteristic, complemented
9C2×#10622095C211yesmaximal, characteristic, complemented
10#13067265C212yesmaximal, complemented
11C11×#3169C211yesmaximal, characteristic, complemented
12C11×#532C2212yes—
13C2×#67003—22no—
14C4×#4339C2211yescharacteristic
15C11×#500C2211yescharacteristic
16C11×#493C2211yescharacteristic
17C11×#486C2212yes—
18C11×#466—21no—
19C11×#466—21no—
20C4×C11×D8—21no—
21C4×C11×D8—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622846—22no—
24#10622724—21no—
25#10622724—21no—
26#10622703C2212yes—
27#10622696C2212yes—
28#10622688C2212yes—
29#10622685C2212yes—
30#10622670—22no—
31#10622667—22no—
32#10622538C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622301C2211yescharacteristic
35#10622301C2211yescharacteristic
36C4×#4313—21no—
37#10622298—21no—
38#10622292C2211yescharacteristic
39#10622292C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622095C2211yescharacteristic
45#10622095C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×#41—22no—
48C2×#4339D411yescharacteristic
49C2×C11×D8—21no—
50C2×C11×D8—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C11×C4⋊Q8C2312yes—
54C11×#127C2312yes—
55C11×#124—22no—
56C11×#121—22no—
57C11×#121—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C42×C11C2311yescharacteristic
61#67003—48no—
62C2×#4326—22no—
63C2×#4325—22no—
64C2×#4324—22no—
65C2×#4323—22no—
66C4×C22⋊D11—21no—
67C4×C22⋊D11—21no—
68#66979D411yescharacteristic
69C22×C11⋊C8—22no—
70C2×#4313—21no—
71C2×#4313—21no—
72C4×D44D411yescharacteristic
73C4×D44C2311yescharacteristic
74#66925—21no—
75C42×D11—21no—
76C4×Dic22D411yescharacteristic
77C4×Dic22C2311yescharacteristic
78C11×#107—21no—
79C11×#107—21no—
80C11×#102—22no—
81C11×#102—22no—
82C4×C8×C11D411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11C2311yescharacteristic
85C4×C8×C11C2311yescharacteristic
86#66899—22no—
87#66899—22no—
88#66896—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—21no—
91(C2×D11)⋊C8—21no—
92(C2×D11)⋊C8—21no—
93#66879—21no—
94#66879—21no—
95Dic11⋊C8—21no—
96Dic11⋊C8—21no—
97C4⋊(C11⋊C8)—22no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4×C11⋊C8—21no—
103#19157—111nomaximal, Sylow
104C11×#41—44no—
105C11×#41—44no—
106C2×Q8×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C2×C22⋊D11—21no—
116#4339—24no—
117C2×D44C2×D411yescharacteristic
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×Dic22C2×D411yescharacteristic
122C11×D8—42no—
123C11×D8—42no—
124C2×C8×C11—22no—
125C2×C8×C11—41no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—42no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—21no—
139#4326—44no—
140#4325—44no—
141#4324—44no—
142#4323—44no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145C4⋊Dic11C2×D411yescharacteristic
146C4⋊Dic11C2×D411yescharacteristic
147Dic11⋊C4—21no—
148Dic11⋊C4—21no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—44no—
157#4313—42no—
158#4313—42no—
159#3169D1111yescharacteristic, complemented
160#3035—112no—
161#2965—111no—
162#1702—112no—
163#1701—112no—
164#1694—111no—
165#1693—111no—
166#1688—111no—
167#1687—111no—
168C2×#334—111no—
169#1540—112no—
170C23×C11—42no—
171C23×C11#12111yescharacteristic
172C22×D11—21no—
173Q8×C11—42no—
174Q8×C11—42no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—82no—
180D4×C11—84no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—84no—
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)14yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C22⋊D11—42no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197D44—22no—
198C4×D11—42no—
199C4×D11—41no—
200C4×D11—41no—
201C4×D11—42no—
202Dic22—22no—
203C8×C11—21no—
204C8×C11—21no—
205C8×C11—21no—
206C8×C11#13512yescomplemented
207C11⋊C8—41no—
208C11⋊C8—42no—
209C11⋊C8—42no—
210C11⋊C8—41no—
211C2×#135—222no—
212#532C2×D1112yes—
213C4×#41—111no—
214#500C2×D1111yescharacteristic
215#493C2×D1111yescharacteristic
216#486C2×D1112yes—
217#466—21no—
218#466—21no—
219#464—222no—
220#463—222no—
221#462—112no—
222#461—112no—
223#460—112no—
224#459—112no—
225#446—111no—
226#446—111no—
227C4×D8—21no—
228C4×D8—21no—
229#436—111no—
230#436—111no—
231#435—221no—
232#435—221no—
233#431—111no—
234#431—221no—
235C2×C4⋊C8—112no—
236#416—222no—
237C4×M16—221no—
238C2×C4×C8C2×D1111yescharacteristic
239#334—111no—
240#334—111no—
241#334—112no—
242#332—112no—
243#332—112no—
244#331—112no—
245#331—112no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11#46912yes—
252C22×C11C2×#12111yescharacteristic
253C2×D11—41no—
254C2×D11—41no—
255C2×D11—41no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—82no—
260C4×C11#46912yes—
261C4×C11C2×#13511yescharacteristic
262C4×C11C2×AGL(1,ℤ/8)12yes—
263C4×C11#57511yescharacteristic
264Dic11—41no—
265Dic11—41no—
266Dic11—41no—
267C2×#41—22no—
268C2×#41—111no—
269#135—448no—
270C2×Q16—222no—
271C2×SD16—222no—
272C2×SD16—222no—
273C2×D8—21no—
274C2×D8—21no—
275C2×D8—222no—
276C2×M16—221no—
277C2×M16—221no—
278C22×C8—222no—
279C22×C8C22⋊D1111yescharacteristic
280C22×C8C22⋊D1111yescharacteristic
281C4⋊Q8C22×D1112yes—
282#127C22×D1112yes—
283#124—22no—
284#121—22no—
285#121—22no—
286C4×Q8—111no—
287C4×Q8—111no—
288C4×D4—22no—
289C4×D4—22no—
290C4×D4—111no—
291C4×D4—111no—
292C4×D4—221no—
293C4×D4—221no—
294#117—111no—
295#117—221no—
296C2×C42—221no—
297C2×C42C22×D1111yescharacteristic
298#107—21no—
299#107—21no—
300C4⋊C8—111no—
301C4⋊C8—111no—
302C4⋊C8—112no—
303C4⋊C8—112no—
304C4⋊C8—221no—
305C4⋊C8—221no—
306C4⋊C8—222no—
307#103—222no—
308#103—222no—
309#102—22no—
310#102—22no—
311#102—222no—
312#102—222no—
313C22⋊C8—221no—
314C22⋊C8—221no—
315C22⋊C8—221no—
316#97—221no—
317#97—221no—
318C4×C8—221no—
319C4×C8C22⋊D1111yescharacteristic
320C4×C8C22⋊D1111yescharacteristic
321C4×C8C22×D1111yescharacteristic
322C4×C8C22×D1111yescharacteristic
323C2×C11—22no—
324C2×C11—162no—
325C2×C11#303511yescharacteristic
326C2×C11C2×#46911yescharacteristic
327C2×C11#306711yescharacteristic
328D11—81no—
329#41—44no—
330#41—44no—
331#41—224no—
332C2×Q8—22no—
333C2×Q8—111no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—42no—
338C2×D4—111no—
339C2×D4—221no—
340C22×C4—42no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4D4×D1111yescharacteristic
345C22×C4#434111yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347Q16—444no—
348SD16—444no—
349SD16—444no—
350D8—42no—
351D8—42no—
352D8—444no—
353M16—442no—
354M16—442no—
355C2×C8—22no—
356C2×C8—41no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8—444no—
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C2×C8C2×C22⋊D1111yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—111no—
369C4⋊C4—111no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—221no—
375C22⋊C4—221no—
376C22⋊C4—221no—
377C42—221no—
378C42—221no—
379C42—221no—
380C42D4×D1111yescharacteristic
381C42#434111yescharacteristic
382C42C2×C22⋊D1111yescharacteristic
383C42C23×D1111yescharacteristic
384C11#1915711yescharacteristic, complemented, Sylow
385C23—42no—
386C23—221no—
387C23#6699111yescharacteristic
388Q8—42no—
389Q8—42no—
390Q8—222no—
391D4—42no—
392D4—42no—
393D4—42no—
394D4—42no—
395D4—82no—
396D4—84no—
397D4—222no—
398D4—442no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—84no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4#6696414yes—
412C2×C4#6699111yescharacteristic
413C2×C4#6699111yescharacteristic
414C2×C4#6699111yescharacteristic
415C2×C4C2×D4×D1111yescharacteristic
416C2×C4C2×#434111yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—442no—
422C8—442no—
423C8—441no—
424C8—441no—
425C8#6700312yescomplemented
426C22—21no—
427C22—21no—
428C22—82no—
429C22—82no—
430C22—82no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22#1062277212yes—
435C22C2×#6699111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—82no—
440C4—441no—
441C4—441no—
442C4—441no—
443C4#1062277212yes—
444C4C2×#6696412yes—
445C4C2×#6700311yescharacteristic
446C4#1062335311yescharacteristic
447C2—22no—
448C2—162no—
449C2—881no—
450C2#1307806511yescharacteristic
451C2C2×#1062277211yescharacteristic
452C2#1307833211yescharacteristic
subgroupG/H
centerC2×C4#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19157
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13078065C2semidirect
2. #13077582C2semidirect
3. #13068181C2semidirect
4. #13068174C2semidirect
5. #13068131C2semidirect
6. #13068126C2semidirect
7. #13068097C2semidirect
8. #13068092C2semidirect
9. C2×#10622095C2semidirect
10. #13067265C2semidirect
11. C11×#3169C2semidirect
159. #3169D11semidirect
206. C8×C11#135semidirect
384. C11#19157semidirect
425. C8#67003semidirect

Maximal subgroups

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

subgroupindex
#130780652
#130775822
#130681812
#130681742
#130681312
#130681262
#130680972
#130680922
C2×#106220952
#130672652
C11×#31692
#1915711