Finite Group Databasebeta

← #14736949

Subgroups — #14736949

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#13079932C211yesmaximal, characteristic, complemented
2#13079923C211yesmaximal, characteristic
3#13078939C211yesmaximal, characteristic, complemented
4#13068191C212yesmaximal, complemented
5#13068177C212yesmaximal, complemented
6#13068039C212yesmaximal, complemented
7#13068025C212yesmaximal, complemented
8C2×#10622095C211yesmaximal, characteristic, complemented
9#13067307C211yesmaximal, characteristic, complemented
10#13067294C211yesmaximal, characteristic, complemented
11C11×#2931C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C11×#532C2211yescharacteristic
14#10623008C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#436—21no—
17C11×#436C2212yes—
18C8×D4×C11—21no—
19C8×D4×C11C2212yes—
20C11×#423C2211yescharacteristic
21C11×#408—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622726—21no—
24#10622726—21no—
25#10622707—21no—
26#10622700—21no—
27#10622688—21no—
28#10622685—21no—
29#10622654—22no—
30#10622651—22no—
31#10622632C2212yes—
32#10622628C2212yes—
33#10622621C2212yes—
34#10622620C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622310—21no—
38#10622310—21no—
39#10622307C2211yescharacteristic
40#10622307C2211yescharacteristic
41#10622294C2211yescharacteristic
42#10622294C2211yescharacteristic
43#10622124C2212yes—
44#10622123C2212yes—
45#10622120C2212yes—
46#10622119C2212yes—
47#10622095C2212yes—
48#10622095C2212yes—
49C2×C11×#41—21no—
50C2×#4339—21no—
51C11×#131—44no—
52C2×C11×M16—21no—
53C2×C11×M16—22no—
54C22×C8×C11—22no—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×#127D411yescharacteristic
59C11×#124—21no—
60C11×#121—21no—
61C11×#121D412yes—
62C4×D4×C11—21no—
63C4×D4×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4324—22no—
66C2×#4323—22no—
67#66983—21no—
68#66983—21no—
69#66979—21no—
70#66977—21no—
71#66977—21no—
72C22×C11⋊C8—21no—
73C22×C11⋊C8—21no—
74#66928—21no—
75#66927C2311yescharacteristic
76C4×D44—21no—
77C4×D44—21no—
78#66923—21no—
79#66922C2311yescharacteristic
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×C22⋊C8—22no—
87C11×C22⋊C8—22no—
88C4×C8×C11D411yescharacteristic
89C4×C8×C11D411yescharacteristic
90C4×C8×C11C2311yescharacteristic
91C4×C8×C11C2311yescharacteristic
92#66896—22no—
93#66896—22no—
94#66885—21no—
95#66885—21no—
96#66885—21no—
97#66885—21no—
98#66880—21no—
99#66880—21no—
100#66880—21no—
101#66880—21no—
102#66874—22no—
103#66873—22no—
104#66872—22no—
105#66871—22no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2312yes—
110#19200—111nomaximal, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11C2×D412yes—
118C22×C4×C11—22no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—41no—
123#4339—42no—
124#4339—42no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C11×M16—44no—
133C11×M16—42no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—44no—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4C2×D412yes—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150C22⋊Dic11—41no—
151#4324—82no—
152#4323—82no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—81no—
167C2×C11⋊C8—81no—
168#3246—111no—
169#3245—111no—
170#3131—111no—
171#2931D1111yescharacteristic, complemented
172#1703—112no—
173#1701—112no—
174#1679—112no—
175#1677—112no—
176C2×#334—111no—
177#1550—111no—
178#1547—111no—
179C23×C11—22no—
180C23×C11#12111yescharacteristic
181C22×D11—41no—
182Q8×C11—42no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11—42no—
186D4×C11—44no—
187D4×C11—42no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#13512yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C22⋊D11—82no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206D44—41no—
207D44—41no—
208D44—41no—
209D44—41no—
210D44—81no—
211C4×D11—82no—
212Dic22—41no—
213Dic22—41no—
214Dic22—41no—
215Dic22—41no—
216Dic22—81no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—42no—
222C11⋊C8—42no—
223C11⋊C8—42no—
224C2×#131—21no—
225#533—111no—
226#532—111no—
227#532C2×D1111yescharacteristic
228#488—221no—
229#488—221no—
230#487—111no—
231#487—111no—
232#486—111no—
233#486—111no—
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—21no—
245#436C2×D1112yes—
246C8×D4—21no—
247C8×D4C2×D1112yes—
248#423C2×D1111yescharacteristic
249C2×C4⋊C8—111no—
250C2×C4⋊C8—111no—
251#416—221no—
252#416—221no—
253#408—21no—
254C2×C4×C8C2×D1111yescharacteristic
255#334—112no—
256#334—112no—
257#333—112no—
258#332—112no—
259#332—112no—
260#331—112no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11#46312yes—
267C22×C11C2×#12111yescharacteristic
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11#46312yes—
276C4×C11C2×#13511yescharacteristic
277C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
278C4×C11#57711yescharacteristic
279C4×C11#57711yescharacteristic
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283C2×#41—21no—
284C2×#41—221no—
285C2×SD16—222no—
286C2×D8—222no—
287#131—44no—
288C2×M16—21no—
289C2×M16—22no—
290C22×C8—22no—
291C22×C8—221no—
292C22×C8—221no—
293C22×C8C22⋊D1111yescharacteristic
294C22×C8C22⋊D1111yescharacteristic
295C4⋊Q8—111no—
296C4⋊Q8—111no—
297C4⋊Q8—111no—
298C4⋊Q8D4411yescharacteristic
299#127—111no—
300#127D4411yescharacteristic
301#125—221no—
302#124—21no—
303#124—221no—
304C22⋊Q8—221no—
305C22⋊Q8—221no—
306#121—21no—
307#121—221no—
308#121—221no—
309#121D4412yes—
310C4×Q8—221no—
311C4×Q8—221no—
312C4×D4—21no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4C22×D1112yes—
316#117—221no—
317C2×C42C22×D1111yescharacteristic
318#107—222no—
319#106—222no—
320C4⋊C8—21no—
321C4⋊C8—112no—
322C4⋊C8—112no—
323C4⋊C8—221no—
324C4⋊C8—221no—
325C4⋊C8C22×D1112yes—
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330#103—222no—
331#102—222no—
332#102—222no—
333#102—221no—
334#102—221no—
335#102—221no—
336#102—221no—
337#102—222no—
338C22⋊C8—22no—
339C22⋊C8—22no—
340C4×C8C22⋊D1111yescharacteristic
341C4×C8C22⋊D1111yescharacteristic
342C4×C8C22×D1111yescharacteristic
343C4×C8C22×D1111yescharacteristic
344C2×C11—22no—
345C2×C11—82no—
346C2×C11C2×#46311yescharacteristic
347C2×C11#306011yescharacteristic
348C2×C11#306711yescharacteristic
349D11—161no—
350#41—42no—
351#41—42no—
352#41—442no—
353#41—442no—
354C2×Q8—21no—
355C2×Q8—221no—
356C2×Q8—221no—
357C2×Q8—221no—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—221no—
362C2×D4—221no—
363C2×D4—221no—
364C2×D4—441no—
365C2×D4C2×D4412yes—
366C22×C4—22no—
367C22×C4—441no—
368C22×C4C2×D4411yescharacteristic
369C22×C4#433911yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371SD16—882no—
372D8—882no—
373M16—44no—
374M16—42no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—44no—
379C2×C8—222no—
380C2×C8—222no—
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—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4C2×D4412yes—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—441no—
403C42C2×D4411yescharacteristic
404C42#433911yescharacteristic
405C42C2×C22⋊D1111yescharacteristic
406C42C23×D1111yescharacteristic
407C11#1920011yescharacteristic, complemented, Sylow
408C23—22no—
409C23—441no—
410C23#6698311yescharacteristic
411Q8—42no—
412Q8—441no—
413Q8—441no—
414Q8—441no—
415Q8—441no—
416Q8—881no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—44no—
421D4—42no—
422D4—441no—
423D4—441no—
424D4—441no—
425D4—441no—
426D4—881no—
427D4—882no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—882no—
438C2×C4#6698311yescharacteristic
439C2×C4#6698311yescharacteristic
440C2×C4#6698311yescharacteristic
441C2×C4#6698512yes—
442C2×C4#6700312yes—
443C2×C4C22×D4411yescharacteristic
444C2×C4C2×#433911yescharacteristic
445C2×C4C22×C22⋊D1111yescharacteristic
446C8—21no—
447C8—21no—
448C8—21no—
449C8—21no—
450C8—42no—
451C8—442no—
452C8—442no—
453C22—21no—
454C22—21no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22#1062262912yes—
462C22C2×#6698311yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—881no—
468C4—881no—
469C4—881no—
470C4#1062262912yes—
471C4#1062328211yescharacteristic
472C4#1062328211yescharacteristic
473C4C2×#6698511yescharacteristic
474C4C2×#6700311yescharacteristic
475C2—22no—
476C2—82no—
477C2—1761no—
478C2C2×#1062262911yescharacteristic
479C2#1307827811yescharacteristic
480C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2931C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#2931D11
hypocenterC11#19200
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2931

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
3. #13078939C2semidirect
4. #13068191C2semidirect
5. #13068177C2semidirect
6. #13068039C2semidirect
7. #13068025C2semidirect
8. C2×#10622095C2semidirect
9. #13067307C2semidirect
10. #13067294C2semidirect
11. C11×#2931C2semidirect
171. #2931D11semidirect
407. C11#19200semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130799232
#130789392
#130681912
#130681772
#130680392
#130680252
C2×#106220952
#130673072
#130672942
C11×#29312
#1920011