Finite Group Databasebeta

← #14737262

Subgroups — #14737262

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#13079737C211yesmaximal, characteristic, complemented
3#13077362C211yesmaximal, characteristic, complemented
4#13068102C212yesmaximal, complemented
5#13068078C212yesmaximal, complemented
6#13067978C212yesmaximal, complemented
7#13067954C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067265C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3152C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×#137—21no—
14C11×#532C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#66960—21no—
17#10623008C2211yescharacteristic
18C11×#497—22no—
19C11×#494C2212yes—
20C11×#492C2212yes—
21C4×C11×M16C2211yescharacteristic
22#10622742—21no—
23#10622701—21no—
24#10622700C2212yes—
25#10622700C2212yes—
26#10622700C2212yes—
27#10622691—21no—
28#10622685C2212yes—
29#10622651—22no—
30#10622628—21no—
31#10622620—21no—
32#10622580—22no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622319—22no—
37#10622301C2212yes—
38C8×D44C2212yes—
39#10622185C2211yescharacteristic
40#10622185C2211yescharacteristic
41#10622185C2212yes—
42#10622185C2212yes—
43#10622182C2211yescharacteristic
44#10622182C2211yescharacteristic
45#10622096C2212yes—
46#10622095C2212yes—
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C2×#4339—21no—
50C11×#137—44no—
51C11×#137—44no—
52C2×C11×Q16—22no—
53C2×C11×Q16—22no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C2×C11×M16D411yescharacteristic
57C2×C11×M16D411yescharacteristic
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2311yescharacteristic
63C11×#127C2311yescharacteristic
64C11×#124—21no—
65C11×#121—21no—
66C11×#121—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4323—22no—
73#66983—21no—
74#66983D412yes—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77#66960—44no—
78C2×#4313—22no—
79C2×C8×D11—22no—
80#66928—21no—
81#66927D411yescharacteristic
82C4×D44—21no—
83C4×D44C2312yes—
84#66922D411yescharacteristic
85C11×#97D412yes—
86C4×C8×C11C2312yes—
87#66896—22no—
88C22⋊(C11⋊C8)—21no—
89(C2×D11)⋊C8—22no—
90(C2×D11)⋊C8—22no—
91#66873—22no—
92#66873—22no—
93#66873—22no—
94#66871—22no—
95#66871—22no—
96#66871—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
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×Q8×C11—22no—
110C2×Q8×C11—41no—
111C2×Q8×C11—42no—
112C2×Q8×C11—42no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—22no—
123#4339—42no—
124#4339—42no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44C2×D412yes—
128C2×C4×D11—22no—
129C2×Dic22—21no—
130C11×Q16—44no—
131C11×Q16—44no—
132C11×SD16—44no—
133C11×SD16—44no—
134C11×M16—22no—
135C11×M16D814yescomplemented
136C2×C8×C11C2×D412yes—
137C2×C8×C11C2×D412yes—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150#4323—82no—
151(C2×D11)⋊C4—22no—
152(C2×D11)⋊C4—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11C2×D412yes—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—42no—
161C2×C11⋊C8—81no—
162#4313—44no—
163C8×D11—44no—
164#3245—111no—
165#3226—111no—
166#3152D1111yescharacteristic, complemented
167#2935—111no—
168#1689—112no—
169#1685—112no—
170#1669—112no—
171#1665—112no—
172#1565—111no—
173#1540—111no—
174C2×#332—111no—
175C23×C11—41no—
176C23×C11#12111yescharacteristic
177C22×D11—22no—
178Q8×C11—42no—
179Q8×C11—41no—
180Q8×C11—42no—
181Q8×C11—41no—
182Q8×C11—82no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—41no—
186D4×C11—41no—
187D4×C11—81no—
188D4×C11—82no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—82no—
195C2×C4×C11—82no—
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11C2×D812yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C22⋊D11—44no—
205C2×Dic11—22no—
206D44—22no—
207D44—22no—
208D44—42no—
209D44—81no—
210C4×D11—42no—
211C4×D11—42no—
212Dic22—42no—
213C8×C11—22no—
214C8×C11C2×D814yes—
215C11⋊C8—41no—
216C11⋊C8—41no—
217C11⋊C8—41no—
218C11⋊C8—42no—
219C11⋊C8—41no—
220C2×#137—21no—
221C2×#137—21no—
222C2×#131—221no—
223#532—111no—
224#532C2×D1111yescharacteristic
225C2×C4⋊Q8C2×D1111yescharacteristic
226#500—221no—
227#497—22no—
228#494C2×D1112yes—
229#492C2×D1112yes—
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#436—112no—
240#435—222no—
241C8×D4—112no—
242#431—111no—
243C2×C4⋊C8—111no—
244C2×C4⋊C8—111no—
245#408—221no—
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—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11#45912yes—
261C22×C11C2×#12111yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—81no—
269C4×C11—82no—
270C4×C11#45912yes—
271C4×C11C22×D811yescharacteristic
272C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C4×C11#57711yescharacteristic
274C4×C11#57811yescharacteristic
275Dic11—42no—
276C2×#41—21no—
277C2×#41—221no—
278C22×Q8—21no—
279#137—44no—
280#137—44no—
281C2×Q16—22no—
282C2×Q16—22no—
283C2×SD16—22no—
284C2×SD16—22no—
285C2×D8—222no—
286#131—444no—
287C2×M16—222no—
288C2×M16C22⋊D1111yescharacteristic
289C2×M16C22⋊D1111yescharacteristic
290C22×C8—221no—
291C22×C8—221no—
292C22×C8—222no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—111no—
297C4⋊Q8C22×D1112yes—
298C4⋊Q8C22×D1111yescharacteristic
299#127—111no—
300#127C22×D1111yescharacteristic
301#124—21no—
302#124—221no—
303#121—21no—
304#121—21no—
305#121—112no—
306#121—221no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—112no—
310C4×D4—221no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C42C22×D1111yescharacteristic
314#107—222no—
315#107—222no—
316#107—222no—
317C4⋊C8—111no—
318C4⋊C8—111no—
319C4⋊C8—111no—
320C4⋊C8—111no—
321C4⋊C8—112no—
322C4⋊C8—221no—
323C4⋊C8—221no—
324#102—222no—
325#102—222no—
326#102—222no—
327#102—222no—
328C22⋊C8—221no—
329C22⋊C8—222no—
330C22⋊C8—222no—
331#97C22⋊D1112yes—
332C4×C8—221no—
333C4×C8C22×D1112yes—
334C2×C11—22no—
335C2×C11—161no—
336C2×C11C2×#45911yescharacteristic
337C2×C11#306311yescharacteristic
338C2×C11#306911yescharacteristic
339D11—82no—
340#41—42no—
341#41—42no—
342#41—442no—
343#41—442no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—41no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8—221no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—41no—
354C2×D4—112no—
355C2×D4—222no—
356C2×D4—221no—
357C2×D4—221no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—222no—
361C22×C4D4×D1111yescharacteristic
362C22×C4#434111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364Q16—44no—
365Q16—44no—
366SD16—44no—
367SD16—44no—
368D8—882no—
369M16—22no—
370M16—444no—
371M16#432314yescomplemented
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—222no—
375C2×C8—221no—
376C2×C8—221no—
377C2×C8—442no—
378C2×C8—444no—
379C2×C8—881no—
380C2×C8C2×C22⋊D1112yes—
381C2×C8C2×C22⋊D1112yes—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—112no—
389C4⋊C4—221no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—222no—
393C22⋊C4—222no—
394C42D4×D1111yescharacteristic
395C42#434111yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C42C23×D1111yescharacteristic
398C11#1923111yescharacteristic, complemented, Sylow
399C23—41no—
400C23—222no—
401C23#6699111yescharacteristic
402Q8—42no—
403Q8—41no—
404Q8—42no—
405Q8—41no—
406Q8—82no—
407Q8—442no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—81no—
413D4—82no—
414D4—222no—
415D4—222no—
416D4—444no—
417D4—442no—
418D4—881no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—222no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4C2×#432312yes—
430C2×C4#6698512yes—
431C2×C4#6699111yescharacteristic
432C2×C4#6699111yescharacteristic
433C2×C4#6699111yescharacteristic
434C2×C4C2×D4×D1111yescharacteristic
435C2×C4C2×#434111yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—22no—
438C8—442no—
439C8—441no—
440C8—441no—
441C8—441no—
442C8—441no—
443C8C2×#432314yes—
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—442no—
450C22—442no—
451C22—442no—
452C22#1062268512yes—
453C22C2×#6699111yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—82no—
459C4—442no—
460C4#1062268512yes—
461C4#1062330911yescharacteristic
462C4#1062331011yescharacteristic
463C4C22×#432311yescharacteristic
464C4C2×#6698511yescharacteristic
465C2—22no—
466C2—161no—
467C2—882no—
468C2C2×#1062268511yescharacteristic
469C2#1307830111yescharacteristic
470C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3152C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#3152D11
hypocenterC11#19231
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. #13079737C2semidirect
3. #13077362C2semidirect
4. #13068102C2semidirect
5. #13068078C2semidirect
6. #13067978C2semidirect
7. #13067954C2semidirect
8. #13067368C2semidirect
9. #13067265C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3152C2semidirect
135. C11×M16D8semidirect
166. #3152D11semidirect
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
#130797372
#130773622
#130681022
#130680782
#130679782
#130679542
#130673682
#130672652
C2×#106221852
C11×#31522
#1923111