Finite Group Databasebeta

← #14736956

Subgroups — #14736956

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic, complemented
2#13079923C211yesmaximal, characteristic
3#13077329C211yesmaximal, characteristic, complemented
4#13068160C212yesmaximal, complemented
5#13068146C212yesmaximal, complemented
6#13068064C212yesmaximal, complemented
7#13068050C212yesmaximal, complemented
8C2×#10622096C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067293C211yesmaximal, characteristic, complemented
11C11×#3131C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#66954—21no—
15#10623008C2211yescharacteristic
16C11×#488—21no—
17C11×#488—21no—
18C11×#487C2211yescharacteristic
19C11×#487C2211yescharacteristic
20C11×#486C2211yescharacteristic
21C11×#486C2211yescharacteristic
22C11×#416—21no—
23C11×#416—21no—
24C2×C4×C8×C11C2211yescharacteristic
25#10622723—21no—
26#10622700C2212yes—
27#10622697C2212yes—
28#10622696C2212yes—
29#10622685C2212yes—
30#10622661—22no—
31#10622651—22no—
32#10622640—21no—
33#10622633—21no—
34#10622628—21no—
35#10622620—21no—
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622301—21no—
40#10622301C2212yes—
41C8×D44—21no—
42C8×D44C2212yes—
43#10622185C2212yes—
44#10622185C2212yes—
45#10622184C2212yes—
46#10622182C2212yes—
47#10622096C2212yes—
48#10622096C2212yes—
49C2×C11×#41—21no—
50C2×#4339—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#125—21no—
58C11×#124—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C11×#121—21no—
62C11×#121—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C11×#117—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4325—22no—
70C2×#4323—22no—
71#66983—21no—
72#66983D412yes—
73C2×#4318—21no—
74C22×C11⋊C8—21no—
75C22×C11⋊C8—21no—
76#66954—44no—
77C2×#4313—22no—
78C2×C8×D11—22no—
79#66928—21no—
80#66927D411yescharacteristic
81C4×D44—21no—
82C4×D44C2312yes—
83#66922D411yescharacteristic
84C11×#103—21no—
85C11×#103—21no—
86C11×#103—21no—
87C11×#103—21no—
88C11×#102—21no—
89C11×#102—21no—
90C11×#102—21no—
91C11×#102—21no—
92C4×C8×C11D411yescharacteristic
93C4×C8×C11D411yescharacteristic
94C4×C8×C11C2311yescharacteristic
95C4×C8×C11C2311yescharacteristic
96#66899—22no—
97#66896—22no—
98(C2×D11)⋊C8—22no—
99(C2×D11)⋊C8—22no—
100#66873—22no—
101#66873—22no—
102#66872—22no—
103#66871—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2312yes—
110#19201—111nomaximal, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C2×C22⋊D11—22no—
125#4339—42no—
126#4339—42no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44C2×D412yes—
130C2×C4×D11—22no—
131C2×Dic22—21no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C42×C11—41no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11#4111yescharacteristic
153C42×C11C2411yescharacteristic
154#4325—82no—
155#4323—82no—
156(C2×D11)⋊C4—22no—
157(C2×D11)⋊C4—22no—
158C4⋊Dic11—21no—
159C4⋊Dic11C2×D412yes—
160#4318—42no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—81no—
165C2×C11⋊C8—81no—
166#4313—44no—
167C8×D11—44no—
168#3246—111no—
169#3245—111no—
170#3131D1111yescharacteristic, complemented
171#2931—111no—
172#1699—112no—
173#1697—112no—
174#1683—112no—
175#1681—112no—
176C2×#335—111no—
177#1550—111no—
178#1547—111no—
179C23×C11—41no—
180C23×C11#12111yescharacteristic
181C22×D11—22no—
182Q8×C11—41no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—81no—
187D4×C11—41no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—81no—
192D4×C11—82no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—82no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#13512yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C22⋊D11—44no—
209C2×Dic11—22no—
210D44—22no—
211D44—22no—
212D44—42no—
213D44—42no—
214C4×D11—42no—
215C4×D11—42no—
216Dic22—42no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—21no—
220C8×C11—21no—
221C11⋊C8—42no—
222C11⋊C8—42no—
223C11⋊C8—42no—
224C2×#131—221no—
225#533C2×D1111yescharacteristic
226#532—111no—
227#532C2×D1111yescharacteristic
228#488—21no—
229#488—21no—
230#487C2×D1111yescharacteristic
231#487C2×D1111yescharacteristic
232#486C2×D1111yescharacteristic
233#486C2×D1111yescharacteristic
234#476—112no—
235#475—221no—
236#474—112no—
237#474—221no—
238#466—222no—
239#465—222no—
240#461—112no—
241#460—221no—
242#459—112no—
243#459—221no—
244#436—112no—
245#436—221no—
246C8×D4—112no—
247C8×D4—221no—
248#423—111no—
249C2×C4⋊C8—111no—
250C2×C4⋊C8—111no—
251#416—21no—
252#416—21no—
253#408—221no—
254C2×C4×C8C2×D1111yescharacteristic
255#335—112no—
256#335—112no—
257#333—112no—
258#332—112no—
259#332—112no—
260#331—112no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11#46312yes—
267C22×C11C2×#12111yescharacteristic
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11#46312yes—
278C4×C11C2×#13511yescharacteristic
279C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C11#57611yescharacteristic
281C4×C11#57811yescharacteristic
282Dic11—42no—
283C2×#41—21no—
284C2×#41—221no—
285C2×SD16—222no—
286C2×D8—222no—
287#131—444no—
288C2×M16—221no—
289C2×M16—222no—
290C22×C8—221no—
291C22×C8—221no—
292C22×C8—222no—
293C22×C8C22⋊D1111yescharacteristic
294C22×C8C22⋊D1111yescharacteristic
295C4⋊Q8—111no—
296C4⋊Q8C22×D1111yescharacteristic
297C4⋊Q8C22×D1111yescharacteristic
298C4⋊Q8C22×D1111yescharacteristic
299#127—111no—
300#127C22×D1111yescharacteristic
301#125—21no—
302#124—21no—
303#124—221no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306#121—21no—
307#121—21no—
308#121—112no—
309#121—221no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—112no—
315C4×D4—221no—
316#117—21no—
317C2×C42C22×D1111yescharacteristic
318#107—222no—
319#106—222no—
320C4⋊C8—112no—
321C4⋊C8—112no—
322C4⋊C8—112no—
323C4⋊C8—221no—
324C4⋊C8—221no—
325C4⋊C8—221no—
326#103—21no—
327#103—21no—
328#103—21no—
329#103—21no—
330#103—222no—
331#102—21no—
332#102—21no—
333#102—21no—
334#102—21no—
335#102—222no—
336#102—222no—
337#102—222no—
338C22⋊C8—222no—
339C22⋊C8—222no—
340C4×C8C22⋊D1111yescharacteristic
341C4×C8C22⋊D1111yescharacteristic
342C4×C8C22×D1111yescharacteristic
343C4×C8C22×D1111yescharacteristic
344C2×C11—22no—
345C2×C11—161no—
346C2×C11C2×#46311yescharacteristic
347C2×C11#306111yescharacteristic
348C2×C11#306711yescharacteristic
349D11—82no—
350#41—42no—
351#41—42no—
352#41—442no—
353#41—442no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—221no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—112no—
363C2×D4—222no—
364C2×D4—221no—
365C2×D4—221no—
366C22×C4—41no—
367C22×C4—222no—
368C22×C4D4×D1111yescharacteristic
369C22×C4#434111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371SD16—882no—
372D8—882no—
373M16—444no—
374M16—442no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8—222no—
380C2×C8—444no—
381C2×C8—881no—
382C2×C8—881no—
383C2×C8C2×C22⋊D1111yescharacteristic
384C2×C8C2×C22⋊D1111yescharacteristic
385C2×C8C2×C22⋊D1111yescharacteristic
386C2×C8C2×C22⋊D1111yescharacteristic
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—112no—
396C4⋊C4—221no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C42—41no—
403C42D4×D1111yescharacteristic
404C42#434111yescharacteristic
405C42C2×C22⋊D1111yescharacteristic
406C42C23×D1111yescharacteristic
407C11#1920111yescharacteristic, complemented, Sylow
408C23—41no—
409C23—222no—
410C23#6699111yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—81no—
416Q8—442no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—81no—
422D4—82no—
423D4—222no—
424D4—222no—
425D4—442no—
426D4—444no—
427D4—442no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—222no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4#6699111yescharacteristic
439C2×C4#6699111yescharacteristic
440C2×C4#6699111yescharacteristic
441C2×C4#6700212yes—
442C2×C4#6700312yes—
443C2×C4C2×D4×D1111yescharacteristic
444C2×C4C2×#434111yescharacteristic
445C2×C4C22×C22⋊D1111yescharacteristic
446C8—21no—
447C8—21no—
448C8—21no—
449C8—21no—
450C8—442no—
451C8—442no—
452C8—442no—
453C22—21no—
454C22—21no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—442no—
459C22—442no—
460C22—442no—
461C22#1062267012yes—
462C22C2×#6699111yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—442no—
470C4#1062267012yes—
471C4#1062330011yescharacteristic
472C4#1062330211yescharacteristic
473C4C2×#6700211yescharacteristic
474C4C2×#6700311yescharacteristic
475C2—22no—
476C2—161no—
477C2—882no—
478C2C2×#1062267011yescharacteristic
479C2#1307828211yescharacteristic
480C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3131C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#3131D11
hypocenterC11#19201
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #13079928C2semidirect
3. #13077329C2semidirect
4. #13068160C2semidirect
5. #13068146C2semidirect
6. #13068064C2semidirect
7. #13068050C2semidirect
8. C2×#10622096C2semidirect
9. #13067306C2semidirect
10. #13067293C2semidirect
11. C11×#3131C2semidirect
170. #3131D11semidirect
407. C11#19201semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130799232
#130773292
#130681602
#130681462
#130680642
#130680502
C2×#106220962
#130673062
#130672932
C11×#31312
#1920111