Finite Group Databasebeta

← #14737347

Subgroups — #14737347

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic, complemented
2#13079069C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068098C212yesmaximal, complemented
5#13068090C212yesmaximal, complemented
6#13067974C212yesmaximal, complemented
7#13067966C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067265C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#3246C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67002—21no—
15C2×#67002—21no—
16C2×#66927C2211yescharacteristic
17C11×#476—21no—
18C11×#475C2212yescomplemented
19C11×#465—22no—
20C11×#461—21no—
21C11×#460C2212yescomplemented
22C2×C11×C4⋊C8C2211yescharacteristic
23#10622701—21no—
24#10622698—21no—
25#10622698C2212yes—
26#10622686C2212yes—
27#10622671—22no—
28#10622659—22no—
29#10622640C2212yes—
30#10622640C2212yes—
31#10622637—22no—
32#10622637C2212yescomplemented
33Q8×C11⋊C8C2212yescomplemented
34#10622612—21no—
35#10622610—21no—
36#10622538C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622185C2211yescharacteristic, complemented
40#10622185C2211yescharacteristic, complemented
41#10622182C2211yescharacteristic, complemented
42#10622182C2211yescharacteristic, complemented
43#10622123C2212yes—
44#10622123C2212yes—
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C2×C11×#41—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C2×C11×SD16—22no—
52C22×C8×C11—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#125—21no—
58C11×#124—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8D412yes—
61C11×#121—21no—
62C11×#121—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11C2312yes—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C11×#117—21no—
68C2×C42×C11C2311yescharacteristic
69#67002—44no—
70#67002—44no—
71C2×#4325—22no—
72C2×#4325—22no—
73C2×#4325—22no—
74C2×#4325—22no—
75C2×#4323—22no—
76C2×#4323—22no—
77C2×#4318D411yescharacteristic
78C2×#4318D411yescharacteristic
79C22×C11⋊C8—21no—
80#66927—21no—
81#66927—21no—
82#66927—21no—
83#66927C2312yes—
84C11×#106—22no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8C2312yes—
87C11×#103—22no—
88C11×#102—22no—
89C22⋊(C11⋊C8)—21no—
90#66873—22no—
91#66873—22no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)—22no—
94C4⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)C2311yescharacteristic
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99#66867—22no—
100#66867D412yes—
101C4×C11⋊C8—21no—
102C4×C11⋊C8—22no—
103C4×C11⋊C8C2312yes—
104#19238—111nomaximal, Sylow
105C23×D11—41no—
106C11×#41—42no—
107C11×#41—42no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—41no—
123C2×D44—41no—
124C2×D44—41no—
125C2×D44—42no—
126C2×D44—42no—
127C2×D44—81no—
128C2×D44—81no—
129C2×D44—82no—
130C11×SD16—82no—
131C2×C8×C11—22no—
132C2×C8×C11—81no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4C2×D412yes—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C42×C11—22no—
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11#4111yescharacteristic
148C42×C11C2411yescharacteristic
149#4325—44no—
150#4325—44no—
151#4325—82no—
152#4325—82no—
153#4323—44no—
154#4323—44no—
155#4318—22no—
156#4318SD1614yescomplemented
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—42no—
162C2×C11⋊C8C2×D412yes—
163C2×C11⋊C8C2×D412yes—
164#3246D1111yescharacteristic, complemented
165#3208—111no—
166#3151—111no—
167#2962—111no—
168#1688—112no—
169#1686—112no—
170#1668—112no—
171#1666—112no—
172#1565—111no—
173#1540—111no—
174C2×#331—111no—
175C23×C11—41no—
176C23×C11#12111yescharacteristic
177C22×D11—42no—
178C22×D11—82no—
179C22×D11—82no—
180C22×D11—82no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—81no—
186D4×C11—41no—
187D4×C11—41no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—81no—
191D4×C11—82no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—82no—
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11C2×SD1612yes—
203C2×C4×C11AGL(1,ℤ/8)12yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207D44—42no—
208D44—42no—
209D44—42no—
210D44—42no—
211D44—82no—
212D44—82no—
213D44—82no—
214D44—82no—
215C8×C11—42no—
216C11⋊C8—22no—
217C11⋊C8—41no—
218C11⋊C8—41no—
219C11⋊C8—41no—
220C11⋊C8—41no—
221C11⋊C8C2×SD1614yes—
222C2×AGL(1,ℤ/8)—221no—
223C2×AGL(1,ℤ/8)—221no—
224#533C2×D1111yescharacteristic
225#532C2×D1111yescharacteristic
226C2×#127—111no—
227#496—222no—
228#493—112no—
229#492—112no—
230#492—221no—
231#486—221no—
232#476—21no—
233#475C2×D1112yescomplemented
234#465—22no—
235#461—21no—
236#460—112no—
237#460—112no—
238#460C2×D1112yescomplemented
239#450—222no—
240#446—112no—
241#446—222no—
242C8×Q8—112no—
243#431—111no—
244#424—221no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8C2×D1111yescharacteristic
247#405—221no—
248C4×M16—111no—
249#335—112no—
250#334—112no—
251#332—111no—
252#332—111no—
253#331—111no—
254#331—111no—
255#331—112no—
256#331—112no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11#46012yes—
263C22×C11C2×#12111yescharacteristic
264C2×D11—82no—
265C2×D11—82no—
266C2×D11—82no—
267C2×D11—164no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11#46012yes—
275C4×C11C22×SD1611yescharacteristic
276C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C11#57611yescharacteristic
278C4×C11#57711yescharacteristic
279C2×#41—21no—
280C22×D4—221no—
281C22×D4—221no—
282C22×D4—221no—
283AGL(1,ℤ/8)—444no—
284AGL(1,ℤ/8)—444no—
285C2×SD16—22no—
286C2×SD16—222no—
287C2×SD16—222no—
288C2×SD16—222no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×D8—222no—
292C2×M16—111no—
293C2×M16—111no—
294C22×C8—21no—
295C22×C8—221no—
296C4⋊Q8C22⋊D1111yescharacteristic
297C4⋊Q8C22⋊D1111yescharacteristic
298C4⋊Q8C22×D1111yescharacteristic
299#127—112no—
300#127—221no—
301#127—221no—
302#127—221no—
303#127C22×D1111yescharacteristic
304#125—21no—
305#124—21no—
306C22⋊Q8—21no—
307C22⋊Q8C22⋊D1112yes—
308#121—21no—
309#121—21no—
310C4×Q8—21no—
311C4×Q8C22×D1112yes—
312C4×D4—21no—
313C4×D4—21no—
314#117—21no—
315C2×C42C22×D1111yescharacteristic
316#106—22no—
317C4⋊C8—21no—
318C4⋊C8—111no—
319C4⋊C8—111no—
320C4⋊C8—111no—
321C4⋊C8—111no—
322C4⋊C8—222no—
323C4⋊C8—222no—
324C4⋊C8—221no—
325C4⋊C8C22×D1112yes—
326#103—22no—
327#102—22no—
328#102—222no—
329#102—222no—
330C22⋊C8—221no—
331#97—112no—
332#97—222no—
333C4×C8—112no—
334C4×C8—222no—
335C4×C8—221no—
336C2×C11—22no—
337C2×C11—161no—
338C2×C11C2×#46011yescharacteristic
339C2×C11#306211yescharacteristic
340C2×C11#306811yescharacteristic
341D11—162no—
342C24—441no—
343#41—42no—
344#41—42no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8C2×C22⋊D1112yes—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—442no—
356C2×D4—442no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—881no—
361C2×D4—881no—
362C2×D4—882no—
363C22×C4—41no—
364C22×C4D4×D1111yescharacteristic
365C22×C4#434111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367SD16—82no—
368SD16—444no—
369SD16—444no—
370SD16—882no—
371SD16—882no—
372D8—444no—
373D8—444no—
374M16—114no—
375M16—222no—
376C2×C8—22no—
377C2×C8—81no—
378C2×C8—112no—
379C2×C8—112no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—442no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4C2×C22⋊D1112yes—
393C22⋊C4—22no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C42—22no—
397C42D4×D1111yescharacteristic
398C42#434111yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1923811yescharacteristic, complemented, Sylow
402C23—41no—
403C23—442no—
404C23—882no—
405C23—882no—
406C23—882no—
407C23#6699211yescharacteristic
408Q8—22no—
409Q8—22no—
410Q8—41no—
411Q8—41no—
412Q8—81no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—41no—
417D4—81no—
418D4—82no—
419D4—442no—
420D4—442no—
421D4—442no—
422D4—442no—
423D4—882no—
424D4—882no—
425D4—882no—
426D4—882no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—82no—
434C2×C4SD16×D1112yes—
435C2×C4#6696712yes—
436C2×C4#6699211yescharacteristic
437C2×C4#6699211yescharacteristic
438C2×C4#6699211yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C2×C4C2×#434111yescharacteristic
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—42no—
443C8—114no—
444C8—222no—
445C8—441no—
446C8—441no—
447C8—441no—
448C8—441no—
449C22—21no—
450C22—21no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—882no—
455C22—882no—
456C22—882no—
457C22—1764no—
458C22#1062277612yes—
459C22C2×#6699211yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—42no—
465C4—81no—
466C4#1062277612yes—
467C4C2×SD16×D1111yescharacteristic
468C4C2×#6696711yescharacteristic
469C4#1062336611yescharacteristic
470C4#1062336811yescharacteristic
471C2—22no—
472C2—161no—
473C2—1762no—
474C2C2×#1062277611yescharacteristic
475C2#1307829811yescharacteristic
476C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3246C2
socleC22×C11C2×#121
prime radical#13079069C2
hypercenter#3246D11
hypocenterC11#19238
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

Complements

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

NH ≅ G/Ntype
1. #13079554C2semidirect
3. #13077565C2semidirect
4. #13068098C2semidirect
5. #13068090C2semidirect
6. #13067974C2semidirect
7. #13067966C2semidirect
8. #13067366C2semidirect
9. #13067265C2semidirect
10. C2×#10622123C2semidirect
11. C11×#3246C2semidirect
18. C11×#475C22semidirect
21. C11×#460C22semidirect
32. #10622637C22semidirect
33. Q8×C11⋊C8C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
41. #10622182C22semidirect
42. #10622182C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
156. #4318SD16semidirect
164. #3246D11semidirect
233. #475C2×D11semidirect
238. #460C2×D11semidirect
401. C11#19238semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130790692
#130775652
#130680982
#130680902
#130679742
#130679662
#130673662
#130672652
C2×#106221232
C11×#32462
#1923811