Finite Group Databasebeta

← #14737301

Subgroups — #14737301

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C211yesmaximal, characteristic, complemented
2#13079531C211yesmaximal, characteristic
3#13078991C211yesmaximal, characteristic, complemented
4#13068177C212yesmaximal, complemented
5#13068149C212yesmaximal, complemented
6#13068053C212yesmaximal, complemented
7#13068025C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067274C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#2935C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C11×#532C2211yescharacteristic
14C2×#66927C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#436C2212yescomplemented
17C11×#435—22no—
18C8×D4×C11C2212yescomplemented
19C2×C11×C4⋊C8C2211yescharacteristic
20C11×#408—21no—
21C4×C11×M16C2211yescharacteristic
22#10622744—21no—
23#10622744—21no—
24#10622707—21no—
25#10622701—21no—
26#10622688—21no—
27#10622686—21no—
28#10622654—22no—
29#10622649—22no—
30#10622632C2212yescomplemented
31#10622628C2212yes—
32#10622628C2212yes—
33#10622621C2212yescomplemented
34#10622538C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622326—22no—
37#10622307C2212yes—
38#10622307C2212yes—
39#10622124C2211yescharacteristic, complemented
40#10622124C2211yescharacteristic, complemented
41#10622123C2212yes—
42#10622123C2212yes—
43#10622119C2211yescharacteristic, complemented
44#10622119C2211yescharacteristic, complemented
45#10622096C2212yescomplemented
46#10622095C2212yescomplemented
47C2×C11×#41—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C11×#131—44no—
52C2×C11×M16—22no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D411yescharacteristic
55C22×C8×C11—21no—
56C22×C8×C11—22no—
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—
67C2×#4323—22no—
68#66979—21no—
69#66977—21no—
70#66977—21no—
71C22×C11⋊C8—21no—
72#66927—21no—
73#66927—21no—
74#66927—21no—
75#66927C2312yes—
76#66923—21no—
77#66922C2311yescharacteristic
78#66922C2311yescharacteristic
79C4×Dic22—21no—
80C4×Dic22—21no—
81C11×C4⋊C8—21no—
82C11×C4⋊C8C2311yescharacteristic
83C11×C4⋊C8C2311yescharacteristic
84C11×C22⋊C8—22no—
85C11×C22⋊C8—22no—
86C11×#97D412yes—
87C4×C8×C11C2312yes—
88#66896—22no—
89C22⋊(C11⋊C8)—21no—
90#66885—22no—
91#66885—22no—
92#66885—22no—
93#66885—22no—
94#66874—22no—
95#66873—22no—
96#66873—22no—
97#66872—22no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4×C11⋊C8—21no—
103#19234—111nomaximal, Sylow
104C23×D11—41no—
105C11×#41—42no—
106C11×#41—42no—
107C2×Q8×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11C2×D412yes—
112C22×C4×C11—22no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44—41no—
122C2×D44—42no—
123C2×D44—42no—
124C2×D44—81no—
125C2×D44—81no—
126C2×D44—82no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C11×M16—22no—
130C11×M16—22no—
131C11×M16—44no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—44no—
135C2×C8×C11—42no—
136C2×C8×C11C2×D412yes—
137C2×C8×C11C2×D412yes—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—41no—
147#4324—82no—
148#4323—82no—
149#4323—82no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156C4×Dic11—41no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—81no—
161#3246—111no—
162#3205—111no—
163#3138—111no—
164#2935D1111yescharacteristic, complemented
165#1701—112no—
166#1697—112no—
167#1681—112no—
168#1677—112no—
169#1565—111no—
170#1542—111no—
171C2×#331—111no—
172C23×C11—22no—
173C23×C11#12111yescharacteristic
174C22×D11—42no—
175C22×D11—82no—
176C22×D11—82no—
177C22×D11—82no—
178Q8×C11—42no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—44no—
182D4×C11—42no—
183D4×C11—81no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#13512yes—
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×Dic11—41no—
199C2×Dic11—41no—
200D44—42no—
201D44—42no—
202D44—42no—
203D44—42no—
204D44—82no—
205D44—82no—
206D44—82no—
207D44—82no—
208Dic22—41no—
209Dic22—41no—
210Dic22—81no—
211C8×C11—22no—
212C8×C11—22no—
213C8×C11—41no—
214C8×C11—41no—
215C11⋊C8—42no—
216C11⋊C8—41no—
217C11⋊C8—41no—
218C2×#131—21no—
219#533—111no—
220#532C2×D1111yescharacteristic
221C2×#127—111no—
222#493—221no—
223#490—222no—
224#486—112no—
225#486—112no—
226#486—221no—
227#476—112no—
228#475—221no—
229#465—222no—
230#461—112no—
231#460—221no—
232#459—112no—
233#459—112no—
234#447—222no—
235#436C2×D1112yescomplemented
236#435—22no—
237C8×D4C2×D1112yescomplemented
238#431—111no—
239C2×C4⋊C8—111no—
240C2×C4⋊C8C2×D1111yescharacteristic
241#418—221no—
242#418—221no—
243#408—21no—
244C4×M16C2×D1111yescharacteristic
245#335—112no—
246#334—112no—
247#333—111no—
248#333—111no—
249#332—111no—
250#332—111no—
251#331—112no—
252#331—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11#46312yes—
259C22×C11C2×#12111yescharacteristic
260C2×D11—82no—
261C2×D11—82no—
262C2×D11—82no—
263C2×D11—164no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11#46312yes—
269C4×C11C2×#13511yescharacteristic
270C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C11#57611yescharacteristic
272C4×C11#57711yescharacteristic
273Dic11—81no—
274Dic11—81no—
275C2×#41—21no—
276C22×D4—221no—
277C22×D4—221no—
278C22×D4—221no—
279C2×SD16—222no—
280C2×D8—222no—
281C2×D8—222no—
282#131—44no—
283C2×M16—22no—
284C2×M16C22⋊D1111yescharacteristic
285C2×M16C22⋊D1111yescharacteristic
286C22×C8—21no—
287C22×C8—22no—
288C22×C8—221no—
289C4⋊Q8—111no—
290C4⋊Q8—111no—
291C4⋊Q8D4411yescharacteristic
292#127—112no—
293#127—221no—
294#127—221no—
295#127—221no—
296#127D4411yescharacteristic
297#125—221no—
298#124—21no—
299C22⋊Q8—221no—
300C22⋊Q8—221no—
301#121—21no—
302#121D4412yes—
303C4×Q8—221no—
304C4×Q8—221no—
305C4×D4—21no—
306C4×D4C22×D1112yes—
307#117—221no—
308C2×C42C22×D1111yescharacteristic
309#106—222no—
310C4⋊C8—21no—
311C4⋊C8—112no—
312C4⋊C8—111no—
313C4⋊C8—111no—
314C4⋊C8—221no—
315C4⋊C8C22×D1111yescharacteristic
316C4⋊C8C22×D1111yescharacteristic
317#103—222no—
318#102—222no—
319#102—222no—
320#102—222no—
321#102—222no—
322#102—222no—
323#102—222no—
324#102—222no—
325C22⋊C8—22no—
326C22⋊C8—22no—
327C22⋊C8—221no—
328#97C22⋊D1112yes—
329C4×C8—221no—
330C4×C8C22×D1112yes—
331C2×C11—22no—
332C2×C11—82no—
333C2×C11C2×#46311yescharacteristic
334C2×C11#306211yescharacteristic
335C2×C11#306811yescharacteristic
336D11—162no—
337C24—441no—
338#41—42no—
339#41—42no—
340C2×Q8—21no—
341C2×Q8—221no—
342C2×Q8—221no—
343C2×D4—22no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—222no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—442no—
353C2×D4—442no—
354C2×D4—881no—
355C2×D4—881no—
356C2×D4—882no—
357C2×D4C2×D4412yes—
358C22×C4—22no—
359C22×C4C2×D4411yescharacteristic
360C22×C4#433911yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362SD16—882no—
363D8—882no—
364D8—882no—
365M16—22no—
366M16—22no—
367M16—44no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—44no—
371C2×C8—42no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—222no—
375C2×C8—881no—
376C2×C8C2×C22⋊D1112yes—
377C2×C8C2×C22⋊D1112yes—
378C4⋊C4—21no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4C2×D4412yes—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—441no—
389C42—441no—
390C42C2×D4411yescharacteristic
391C42#433911yescharacteristic
392C42C2×C22⋊D1111yescharacteristic
393C42C23×D1111yescharacteristic
394C11#1923411yescharacteristic, complemented, Sylow
395C23—22no—
396C23—442no—
397C23—882no—
398C23—882no—
399C23—882no—
400C23#6698311yescharacteristic
401Q8—42no—
402Q8—441no—
403Q8—441no—
404Q8—881no—
405D4—22no—
406D4—22no—
407D4—44no—
408D4—42no—
409D4—81no—
410D4—442no—
411D4—442no—
412D4—442no—
413D4—442no—
414D4—882no—
415D4—882no—
416D4—882no—
417D4—882no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4#6698311yescharacteristic
427C2×C4#6698311yescharacteristic
428C2×C4#6698311yescharacteristic
429C2×C4#6698512yes—
430C2×C4#6700312yes—
431C2×C4C22×D4411yescharacteristic
432C2×C4C2×#433911yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—22no—
435C8—22no—
436C8—41no—
437C8—41no—
438C8—441no—
439C8—442no—
440C8—441no—
441C22—21no—
442C22—21no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—882no—
447C22—882no—
448C22—882no—
449C22—1764no—
450C22#1062262912yes—
451C22C2×#6698311yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—881no—
457C4—881no—
458C4#1062262912yes—
459C4#1062328211yescharacteristic
460C4#1062328311yescharacteristic
461C4C2×#6698511yescharacteristic
462C4C2×#6700311yescharacteristic
463C2—22no—
464C2—82no—
465C2—1762no—
466C2C2×#1062262911yescharacteristic
467C2#1307829611yescharacteristic
468C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2935C2
socleC22×C11C2×#121
prime radical#13079531C2
hypercenter#2935D11
hypocenterC11#19234
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
3. #13078991C2semidirect
4. #13068177C2semidirect
5. #13068149C2semidirect
6. #13068053C2semidirect
7. #13068025C2semidirect
8. #13067368C2semidirect
9. #13067274C2semidirect
10. C2×#10622123C2semidirect
11. C11×#2935C2semidirect
16. C11×#436C22semidirect
18. C8×D4×C11C22semidirect
30. #10622632C22semidirect
33. #10622621C22semidirect
39. #10622124C22semidirect
40. #10622124C22semidirect
43. #10622119C22semidirect
44. #10622119C22semidirect
45. #10622096C22semidirect
46. #10622095C22semidirect
164. #2935D11semidirect
235. #436C2×D11semidirect
237. C8×D4C2×D11semidirect
394. C11#19234semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130795312
#130789912
#130681772
#130681492
#130680532
#130680252
#130673682
#130672742
C2×#106221232
C11×#29352
#1923411