Finite Group Databasebeta

← #14736675

Subgroups — #14736675

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078992C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3Q8×#4318C211yesmaximal, characteristic, complemented
4#13068186C212yesmaximal, complemented
5#13068158C212yesmaximal, complemented
6#13068062C212yesmaximal, complemented
7#13068034C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067283C211yesmaximal, characteristic
11C11×#3104C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4325—21no—
15C2×#66927C2211yescharacteristic
16C11×#484—21no—
17C11×#477C2211yescharacteristic, complemented
18C11×#477C2211yescharacteristic, complemented
19C11×#462C2211yescharacteristic, complemented
20C11×#462C2211yescharacteristic, complemented
21C11×#451—21no—
22C4×C11×Q16—21no—
23C4×C11×Q16—21no—
24C11×#431C2211yescharacteristic
25#10622701C2212yes—
26#10622701C2212yes—
27#10622680—22no—
28#10622640—21no—
29#10622640—21no—
30#10622640C2212yes—
31#10622640C2212yes—
32#10622637—22no—
33#10622637C2212yescomplemented
34Q8×C11⋊C8C2212yescomplemented
35#10622614—21no—
36#10622614—21no—
37C2×#66873—21no—
38#10622537—21no—
39#10622537C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C4×#4318—21no—
42C4×#4318C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622184C2212yescomplemented
45#10622123C2212yes—
46#10622123C2212yes—
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×Q8×C11D411yescharacteristic
50C22×D44—21no—
51C22×D44—21no—
52C22×D44—21no—
53C2×C11×Q16—21no—
54C2×C11×Q16—21no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11D411yescharacteristic
65C4×Q8×C11D411yescharacteristic
66C4×Q8×C11C2311yescharacteristic
67C4×Q8×C11C2311yescharacteristic
68C11×#117—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×#4325—22no—
74C2×#4325—22no—
75C2×#4325—44no—
76C2×#4318—21no—
77C2×#4318D411yescharacteristic
78C2×#4318D411yescharacteristic
79C22×C11⋊C8—21no—
80#66927—21no—
81#66927—21no—
82#66927—21no—
83#66927C2312yes—
84C11×#107—21no—
85C11×#107—21no—
86C11×C4⋊C8C2311yescharacteristic
87C11×C4⋊C8C2311yescharacteristic
88C11×#103—21no—
89C11×#103—21no—
90C11×#103—21no—
91C11×#103—21no—
92C11×C22⋊C8—21no—
93C4×C8×C11—21no—
94#66873—22no—
95#66873—22no—
96#66873—22no—
97#66873—22no—
98#66873—22no—
99#66873—22no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—22no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2312yes—
106#66867—22no—
107#66867D412yes—
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2312yes—
110#19174—111nomaximal, Sylow
111C23×D11—41no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—41no—
117C2×Q8×C11C2×D411yescharacteristic
118C2×Q8×C11C2×D411yescharacteristic
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44—41no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—82no—
135C11×Q16—42no—
136C11×Q16—42no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4C2×D411yescharacteristic
151C11×C4⋊C4C2×D411yescharacteristic
152C11×C22⋊C4—41no—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—41no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11#4111yescharacteristic
161C42×C11C2411yescharacteristic
162#4325—44no—
163#4325—44no—
164#4318—22no—
165#4318—22no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8C2×D412yes—
172#3138—111no—
173#3104D1111yescharacteristic, complemented
174C2×#460—111no—
175Q8×M16—111no—
176#1702—112no—
177#1698—112no—
178#1682—112no—
179#1678—112no—
180#1565—111no—
181#1550—111no—
182#1545—111no—
183C23×C11#12111yescharacteristic
184C22×D11—42no—
185C22×D11—82no—
186C22×D11—82no—
187C22×D11—82no—
188Q8×C11—21no—
189Q8×C11—21no—
190Q8×C11—21no—
191Q8×C11—42no—
192Q8×C11—41no—
193Q8×C11—41no—
194Q8×C11—81no—
195Q8×C11AGL(1,ℤ/8)12yes—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—81no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#13512yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215D44—42no—
216D44—42no—
217D44—42no—
218D44—42no—
219D44—82no—
220D44—82no—
221D44—82no—
222D44—82no—
223C8×C11—41no—
224C8×C11—41no—
225C11⋊C8—22no—
226C11⋊C8—22no—
227C11⋊C8—42no—
228C11⋊C8—42no—
229C22×SD16—221no—
230#533C2×D1111yescharacteristic
231C2×#127—111no—
232C2×C4×Q8C2×D1111yescharacteristic
233#490—222no—
234#486—112no—
235#486—112no—
236#484—21no—
237#477C2×D1111yescharacteristic, complemented
238#477C2×D1111yescharacteristic, complemented
239#462C2×D1111yescharacteristic, complemented
240#462C2×D1111yescharacteristic, complemented
241#460—112no—
242#460—112no—
243#460—221no—
244#460—221no—
245#451—21no—
246#446—112no—
247#446—222no—
248C8×Q8—112no—
249C4×Q16—21no—
250C4×Q16—21no—
251#431C2×D1111yescharacteristic
252#423—111no—
253#423—221no—
254C2×C4⋊C8—111no—
255#418—221no—
256#418—221no—
257C2×#102—221no—
258C4×M16—111no—
259C4×M16—221no—
260#335—112no—
261#334—112no—
262#333—112no—
263#332—112no—
264#331—112no—
265#331—112no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11#46412yes—
269C22×C11C2×#12111yescharacteristic
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—164no—
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11#46412yes—
284C4×C11C2×#13511yescharacteristic
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11C2×#13711yescharacteristic
287C4×C11#57511yescharacteristic
288C22×Q8C22⋊D1111yescharacteristic
289C22×D4—221no—
290C22×D4—221no—
291C22×D4—221no—
292C2×Q16—21no—
293C2×Q16—21no—
294C2×SD16—222no—
295C2×SD16—222no—
296C2×SD16—444no—
297C2×M16—111no—
298C2×M16—111no—
299C2×M16—221no—
300C22×C8—221no—
301C4⋊Q8C22×D1111yescharacteristic
302C4⋊Q8C22×D1111yescharacteristic
303#127—112no—
304#127—221no—
305#127—221no—
306#127—221no—
307#125—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8C22⋊D1111yescharacteristic
315C4×Q8C22⋊D1111yescharacteristic
316C4×Q8C22×D1111yescharacteristic
317C4×Q8C22×D1111yescharacteristic
318#117—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C42—21no—
322C2×C42C22×D1111yescharacteristic
323#107—21no—
324#107—21no—
325C4⋊C8—112no—
326C4⋊C8—112no—
327C4⋊C8—222no—
328C4⋊C8—222no—
329C4⋊C8—221no—
330C4⋊C8—221no—
331C4⋊C8C22×D1111yescharacteristic
332C4⋊C8C22×D1111yescharacteristic
333#103—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#102—222no—
338#102—222no—
339#102—222no—
340#102—222no—
341#102—222no—
342#102—222no—
343C22⋊C8—21no—
344#97—112no—
345#97—222no—
346C4×C8—21no—
347C4×C8—112no—
348C4×C8—222no—
349C2×C11—22no—
350C2×C11C2×#46411yescharacteristic
351C2×C11#305511yescharacteristic
352C2×C11#306811yescharacteristic
353D11—162no—
354C24—441no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—41no—
360C2×Q8C2×C22⋊D1111yescharacteristic
361C2×Q8C2×C22⋊D1111yescharacteristic
362C2×D4—222no—
363C2×D4—222no—
364C2×D4—222no—
365C2×D4—442no—
366C2×D4—442no—
367C2×D4—442no—
368C2×D4—442no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C2×D4—882no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4D4×D1111yescharacteristic
376C22×C4#434111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378Q16—42no—
379Q16—42no—
380SD16—444no—
381SD16—444no—
382M16—222no—
383M16—222no—
384M16—442no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—112no—
388C2×C8—112no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—442no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C2×C22⋊D1111yescharacteristic
404C4⋊C4C2×C22⋊D1111yescharacteristic
405C22⋊C4—41no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—41no—
411C42D4×D1111yescharacteristic
412C42#434111yescharacteristic
413C42C2×C22⋊D1111yescharacteristic
414C42C23×D1111yescharacteristic
415C11#1917411yescharacteristic, complemented, Sylow
416C23—442no—
417C23—882no—
418C23—882no—
419C23—882no—
420C23#6699211yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—21no—
424Q8—42no—
425Q8—41no—
426Q8—41no—
427Q8—81no—
428Q8#6700212yes—
429D4—442no—
430D4—442no—
431D4—442no—
432D4—442no—
433D4—882no—
434D4—882no—
435D4—882no—
436D4—882no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—81no—
448C2×C4#6697112yes—
449C2×C4#6697212yes—
450C2×C4#6699211yescharacteristic
451C2×C4#6699211yescharacteristic
452C2×C4#6699211yescharacteristic
453C2×C4C2×D4×D1111yescharacteristic
454C2×C4C2×#434111yescharacteristic
455C2×C4C22×C22⋊D1111yescharacteristic
456C8—41no—
457C8—41no—
458C8—222no—
459C8—222no—
460C8—442no—
461C8—442no—
462C22—21no—
463C22—21no—
464C22—882no—
465C22—882no—
466C22—882no—
467C22—1764no—
468C22#1062279812yes—
469C22C2×#6699211yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—81no—
479C4#1062279812yes—
480C4C2×#6697111yescharacteristic
481C4C2×#6697211yescharacteristic
482C4C2×#6700211yescharacteristic
483C4#1062335311yescharacteristic
484C2—22no—
485C2—1762no—
486C2C2×#1062279811yescharacteristic
487C2#1307823711yescharacteristic
488C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3104C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#3104D11
hypocenterC11#19174
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. Q8×#4318C2semidirect
4. #13068186C2semidirect
5. #13068158C2semidirect
6. #13068062C2semidirect
7. #13068034C2semidirect
8. #13067369C2semidirect
9. #13067306C2semidirect
11. C11×#3104C2semidirect
17. C11×#477C22semidirect
18. C11×#477C22semidirect
19. C11×#462C22semidirect
20. C11×#462C22semidirect
33. #10622637C22semidirect
34. Q8×C11⋊C8C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
173. #3104D11semidirect
237. #477C2×D11semidirect
238. #477C2×D11semidirect
239. #462C2×D11semidirect
240. #462C2×D11semidirect
415. C11#19174semidirect

Maximal subgroups

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

subgroupindex
#130789922
C2×#106226402
Q8×#43182
#130681862
#130681582
#130680622
#130680342
#130673692
#130673062
#130672832
C11×#31042
#1917411