Finite Group Databasebeta

← #14737268

Subgroups — #14737268

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic
2#13079734C211yesmaximal, characteristic, complemented
3#13079075C211yesmaximal, characteristic, complemented
4#13068105C212yesmaximal, complemented
5#13068081C212yesmaximal, complemented
6#13067981C212yesmaximal, complemented
7#13067957C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067266C211yesmaximal, characteristic, complemented
10C2×#10622120C211yesmaximal, characteristic, complemented
11C11×#2935C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C11×#532C2211yescharacteristic
14C2×#66962—21no—
15C2×#66962—21no—
16#10623008C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C11×#436C2212yes—
19C11×#435—22no—
20C8×D4×C11C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#408—21no—
23C4×C11×M16C2211yescharacteristic
24#10622700—21no—
25#10622691—21no—
26#10622685—21no—
27#10622683—21no—
28#10622651—22no—
29#10622646—22no—
30#10622628C2212yes—
31#10622620C2212yes—
32#10622620C2212yes—
33#10622620C2212yes—
34#10622538C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622328—22no—
37#10622312C2212yes—
38#10622306C2212yes—
39#10622123C2211yescharacteristic
40#10622123C2211yescharacteristic
41#10622120C2211yescharacteristic
42#10622120C2211yescharacteristic
43#10622120C2212yes—
44#10622120C2212yes—
45#10622096C2212yes—
46#10622095C2212yes—
47C2×C11×#41—21no—
48C2×#4339—21no—
49C22×Dic22—21no—
50C11×#131—44no—
51C2×C11×M16—22no—
52C2×C11×M16D411yescharacteristic
53C2×C11×M16D411yescharacteristic
54C22×C8×C11—21no—
55C22×C8×C11—22no—
56C11×C4⋊Q8D411yescharacteristic
57C11×#127D411yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121D412yes—
61C4×D4×C11—21no—
62C4×D4×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4323—22no—
65#66983—21no—
66#66983—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C22×C11⋊C8—21no—
70#66962—44no—
71#66962—44no—
72C2×Dic44—22no—
73C2×Dic44—22no—
74C2×#4314—22no—
75C2×#4314—22no—
76#66928—21no—
77#66927C2311yescharacteristic
78C4×D44—21no—
79C4×D44—21no—
80#66922—21no—
81#66922—21no—
82#66922—21no—
83#66922C2312yes—
84#66922C2311yescharacteristic
85C11×C4⋊C8—21no—
86C11×C4⋊C8C2311yescharacteristic
87C11×C4⋊C8C2311yescharacteristic
88C11×C22⋊C8—22no—
89C11×C22⋊C8—22no—
90C11×#97D412yes—
91C4×C8×C11C2312yes—
92#66896—22no—
93#66896—22no—
94#66896—22no—
95C22⋊(C11⋊C8)—21no—
96#66873—22no—
97#66871—22no—
98#66871—22no—
99#66871—22no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4×C11⋊C8—21no—
105#19231—111nomaximal, Sylow
106C11×#41—42no—
107C11×#41—42no—
108C2×Q8×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11C2×D412yes—
113C22×C4×C11—22no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—41no—
118C22×Dic11—41no—
119#4339—42no—
120#4339—42no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×C4×D11—41no—
125C2×Dic22—22no—
126C2×Dic22—21no—
127C2×Dic22—41no—
128C2×Dic22—42no—
129C2×Dic22—42no—
130C11×M16—22no—
131C11×M16—44no—
132C11×M16D814yescomplemented
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—44no—
136C2×C8×C11—42no—
137C2×C8×C11C2×D412yes—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—21no—
140C11×C4⋊C4C2×D412yes—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147#4323—82no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—41no—
155C4⋊Dic11—41no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—81no—
160Dic44—44no—
161Dic44—44no—
162#4314—44no—
163#4314—44no—
164#3245—111no—
165#3226—111no—
166#3152—111no—
167#2935D1111yescharacteristic, complemented
168#1689—112no—
169#1685—112no—
170#1669—112no—
171#1665—112no—
172#1565—111no—
173#1540—111no—
174C2×#332—111no—
175C23×C11—22no—
176C23×C11#12111yescharacteristic
177C22×D11—41no—
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×C11C2×D812yes—
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C22⋊D11—82no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—82no—
202D44—41no—
203D44—41no—
204D44—41no—
205D44—41no—
206D44—81no—
207C4×D11—82no—
208Dic22—42no—
209Dic22—41no—
210Dic22—42no—
211Dic22—41no—
212Dic22—82no—
213C8×C11—22no—
214C8×C11—41no—
215C8×C11—41no—
216C8×C11C2×D814yes—
217C11⋊C8—41no—
218C11⋊C8—42no—
219C11⋊C8—41no—
220C2×#137—221no—
221C2×#137—221no—
222C2×#131—21no—
223#532—111no—
224#532C2×D1111yescharacteristic
225C2×C4⋊Q8—111no—
226#500—221no—
227#497—222no—
228#494—112no—
229#492—112no—
230#486—221no—
231#480—222no—
232#474—112no—
233#474—112no—
234#474—112no—
235#474—221no—
236#466—222no—
237#459—112no—
238#459—221no—
239#436C2×D1112yes—
240#435—22no—
241C8×D4C2×D1112yes—
242#431—111no—
243C2×C4⋊C8—111no—
244C2×C4⋊C8C2×D1111yescharacteristic
245#408—21no—
246C4×M16C2×D1111yescharacteristic
247#335—112no—
248#334—112no—
249#332—112no—
250#332—112no—
251#332—111no—
252#332—111no—
253#331—111no—
254#331—111no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11#45912yes—
261C22×C11C2×#12111yescharacteristic
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11#45912yes—
270C4×C11C22×D811yescharacteristic
271C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C11#57711yescharacteristic
273C4×C11#57811yescharacteristic
274Dic11—82no—
275Dic11—81no—
276C2×#41—21no—
277C2×#41—221no—
278C22×Q8—221no—
279#137—444no—
280#137—444no—
281C2×Q16—222no—
282C2×Q16—222no—
283C2×SD16—222no—
284C2×SD16—222no—
285C2×D8—222no—
286#131—44no—
287C2×M16—22no—
288C2×M16C22⋊D1111yescharacteristic
289C2×M16C22⋊D1111yescharacteristic
290C22×C8—21no—
291C22×C8—22no—
292C22×C8—221no—
293C4⋊Q8—112no—
294C4⋊Q8—111no—
295C4⋊Q8—221no—
296C4⋊Q8—221no—
297C4⋊Q8—221no—
298C4⋊Q8D4411yescharacteristic
299#127—111no—
300#127D4411yescharacteristic
301#124—21no—
302#124—221no—
303#121—21no—
304#121—221no—
305#121—221no—
306#121D4412yes—
307C4×D4—21no—
308C4×D4—221no—
309C4×D4—221no—
310C4×D4C22×D1112yes—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C42C22×D1111yescharacteristic
314#107—222no—
315#107—222no—
316#107—222no—
317C4⋊C8—21no—
318C4⋊C8—111no—
319C4⋊C8—111no—
320C4⋊C8—112no—
321C4⋊C8—221no—
322C4⋊C8C22×D1111yescharacteristic
323C4⋊C8C22×D1111yescharacteristic
324#102—222no—
325#102—222no—
326#102—222no—
327#102—222no—
328C22⋊C8—22no—
329C22⋊C8—22no—
330C22⋊C8—221no—
331#97C22⋊D1112yes—
332C4×C8—221no—
333C4×C8C22×D1112yes—
334C2×C11—22no—
335C2×C11—82no—
336C2×C11C2×#45911yescharacteristic
337C2×C11#306311yescharacteristic
338C2×C11#306911yescharacteristic
339D11—161no—
340#41—42no—
341#41—42no—
342#41—442no—
343#41—442no—
344C2×Q8—21no—
345C2×Q8—221no—
346C2×Q8—222no—
347C2×Q8—441no—
348C2×Q8—442no—
349C2×Q8—442no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—441no—
357C2×D4C2×D4412yes—
358C22×C4—22no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4C2×D4411yescharacteristic
362C22×C4#433911yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364Q16—444no—
365Q16—444no—
366SD16—444no—
367SD16—444no—
368D8—882no—
369M16—22no—
370M16—44no—
371M16#432314yescomplemented
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—42no—
375C2×C8—44no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—222no—
379C2×C8—881no—
380C2×C8C2×C22⋊D1112yes—
381C2×C8C2×C22⋊D1112yes—
382C4⋊C4—21no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—221no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4C2×D4412yes—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C42C2×D4411yescharacteristic
395C42#433911yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C42C23×D1111yescharacteristic
398C11#1923111yescharacteristic, complemented, Sylow
399C23—22no—
400C23—441no—
401C23#6698311yescharacteristic
402Q8—42no—
403Q8—442no—
404Q8—441no—
405Q8—442no—
406Q8—441no—
407Q8—882no—
408D4—22no—
409D4—22no—
410D4—44no—
411D4—42no—
412D4—81no—
413D4—441no—
414D4—441no—
415D4—441no—
416D4—441no—
417D4—881no—
418D4—882no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—441no—
426C2×C4—442no—
427C2×C4—882no—
428C2×C4—882no—
429C2×C4#6698311yescharacteristic
430C2×C4#6698311yescharacteristic
431C2×C4#6698311yescharacteristic
432C2×C4C2×#432312yes—
433C2×C4#6700212yes—
434C2×C4C22×D4411yescharacteristic
435C2×C4C2×#433911yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—22no—
438C8—41no—
439C8—41no—
440C8—442no—
441C8—441no—
442C8—441no—
443C8C2×#432314yes—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22#1062262812yes—
453C22C2×#6698311yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—42no—
458C4—881no—
459C4—882no—
460C4#1062262812yes—
461C4#1062328211yescharacteristic
462C4#1062328411yescharacteristic
463C4C22×#432311yescharacteristic
464C4C2×#6700211yescharacteristic
465C2—22no—
466C2—82no—
467C2—1761no—
468C2C2×#1062262811yescharacteristic
469C2#1307830711yescharacteristic
470C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2935C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#2935D11
hypocenterC11#19231
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
2. #13079734C2semidirect
3. #13079075C2semidirect
4. #13068105C2semidirect
5. #13068081C2semidirect
6. #13067981C2semidirect
7. #13067957C2semidirect
8. #13067368C2semidirect
9. #13067266C2semidirect
10. C2×#10622120C2semidirect
11. C11×#2935C2semidirect
132. C11×M16D8semidirect
167. #2935D11semidirect
371. M16#4323semidirect
398. C11#19231semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130797342
#130790752
#130681052
#130680812
#130679812
#130679572
#130673682
#130672662
C2×#106221202
C11×#29352
#1923111