Finite Group Databasebeta

← #14738515

Subgroups — #14738515

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079843C211yesmaximal, characteristic, complemented
2C2×#10622689C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068086C212yesmaximal, complemented
5#13068079C212yesmaximal, complemented
6#13067962C212yesmaximal, complemented
7#13067955C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067332C211yesmaximal, characteristic, complemented
10#13067330C211yesmaximal, characteristic, complemented
11C11×#3217C211yesmaximal, characteristic
12C2×C11×#127C2211yescharacteristic
13C11×#529C2211yescharacteristic
14C22×#4324—21no—
15C22×#4324—21no—
16C2×#66922C2211yescharacteristic
17C11×#496—21no—
18C11×#490—21no—
19C11×#460C2212yes—
20C11×#459C2212yes—
21C11×#450—21no—
22C11×#447—21no—
23C11×#432C2211yescharacteristic
24#10622689—21no—
25#10622689—21no—
26#10622689C2212yes—
27#10622689C2212yes—
28#10622678—21no—
29#10622668—21no—
30#10622657—21no—
31#10622647—21no—
32#10622637C2211yescharacteristic, complemented
33Q8×C11⋊C8C2211yescharacteristic, complemented
34#10622633C2212yescomplemented
35#10622625C2211yescharacteristic, complemented
36#10622624—21no—
37D4×C11⋊C8—21no—
38D4×C11⋊C8C2211yescharacteristic, complemented
39#10622620C2212yescomplemented
40#10622613—21no—
41#10622610—21no—
42#10622539C2211yescharacteristic
43#10622539C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622182C2212yes—
46#10622182C2212yes—
47#10622124C2212yescomplemented
48#10622124C2212yescomplemented
49#10622118C2212yescomplemented
50#10622117C2212yescomplemented
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×Dic22—21no—
55C2×C11×SD16—22no—
56C2×C11×D8—22no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2312yes—
61C11×#126—21no—
62C11×#125D411yescharacteristic
63C11×#124D411yescharacteristic
64C11×#123—21no—
65C11×C22⋊Q8D411yescharacteristic
66C11×#121D411yescharacteristic
67C4×Q8×C11C2311yescharacteristic
68C4×D4×C11—21no—
69C4×D4×C11C2311yescharacteristic
70C11×#117—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4324—22no—
73C2×#4324—22no—
74C2×#4324—22no—
75C2×#4324—22no—
76C2×#4324—44no—
77C2×#4324—44no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×#4318—21no—
81C22×C11⋊C8—21no—
82C22×C11⋊C8D411yescharacteristic
83C22×C11⋊C8D411yescharacteristic
84#66922—21no—
85#66922—21no—
86#66922—21no—
87#66922C2312yes—
88C11×C4⋊C8C2312yes—
89C11×#102—22no—
90C11×#102—22no—
91C11×C22⋊C8—21no—
92C11×#97—21no—
93#66899—22no—
94#66896—22no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99#66872—22no—
100#66871—22no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2311yescharacteristic
105C4⋊(C11⋊C8)C2311yescharacteristic
106#66867—21no—
107#66867—21no—
108#66867—21no—
109C4×C11⋊C8—21no—
110C4×C11⋊C8D411yescharacteristic
111C4×C11⋊C8D411yescharacteristic
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2311yescharacteristic
114#19352—111nomaximal, Sylow
115C24×C11—41no—
116C2×Q8×C11C2×D411yescharacteristic
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—82no—
127C2×D4×C11—82no—
128C2×D4×C11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C22×Dic11—41no—
134C2×Dic22—22no—
135C2×Dic22—42no—
136C2×Dic22—42no—
137C2×Dic22—41no—
138C11×SD16—82no—
139C11×D8—82no—
140C2×C8×C11—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4C2×D411yescharacteristic
146C11×C4⋊C4C2×D411yescharacteristic
147C11×C22⋊C4—21no—
148C11×C22⋊C4—21no—
149C11×C22⋊C4—21no—
150C11×C22⋊C4—21no—
151C11×C22⋊C4—21no—
152C42×C11—21no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11#4111yescharacteristic
156C42×C11C2411yescharacteristic
157#4324—44no—
158#4324—44no—
159#4324—44no—
160#4324—44no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165#4318—42no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176#3239—111no—
177#3217D1111yescharacteristic
178C2×#492—111no—
179#2966—111no—
180#1686—112no—
181#1685—112no—
182#1666—112no—
183#1665—112no—
184#1568—111no—
185#1556—111no—
186#1555—111no—
187C23×C11—21no—
188C23×C11—42no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11—82no—
192C23×C11#12111yescharacteristic
193Q8×C11—22no—
194D4×C11—22no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—82no—
201D4×C11—82no—
202D4×C11—82no—
203D4×C11—82no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×Dic11—42no—
220C2×Dic11—82no—
221Dic22—42no—
222Dic22—42no—
223Dic22—82no—
224C8×C11—42no—
225C11⋊C8—21no—
226C11⋊C8—21no—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C11⋊C8—42no—
230C11⋊C8AGL(1,ℤ/8)12yes—
231C11⋊C8AGL(1,ℤ/8)12yes—
232C22×SD16—221no—
233C22×SD16—221no—
234C2×C4⋊Q8—111no—
235C2×#127C2×D1111yescharacteristic
236#529C2×D1111yescharacteristic
237#501—221no—
238#496—21no—
239#492—112no—
240#492—112no—
241#492—221no—
242#492—221no—
243#490—21no—
244#489—221no—
245#484—221no—
246#481—221no—
247#475—112no—
248#474—112no—
249#460C2×D1112yes—
250#459C2×D1112yes—
251#450—21no—
252#447—21no—
253#446—111no—
254C8×Q8—111no—
255#436—111no—
256#435—221no—
257C8×D4—111no—
258C8×D4—221no—
259#433—221no—
260#432—111no—
261#432—111no—
262#432C2×D1111yescharacteristic
263#405—221no—
264C2×C4×C8—111no—
265#335—112no—
266#334—112no—
267#332—112no—
268#332—112no—
269#331—112no—
270#331—112no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11—164no—
280C22×C11#47112yes—
281C22×C11C2×#12111yescharacteristic
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—41no—
289C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C11#57712yes—
292Dic11—82no—
293C22×Q8—221no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C2×SD16—22no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×SD16—222no—
301C2×SD16—222no—
302C2×SD16—444no—
303C2×SD16—444no—
304C2×D8—22no—
305C2×M16—221no—
306C22×C8—111no—
307C22×C8—111no—
308C22×C8—221no—
309C4⋊Q8—112no—
310C4⋊Q8—221no—
311C4⋊Q8—221no—
312C4⋊Q8—221no—
313#127—21no—
314#127—21no—
315#127—21no—
316#127C22×D1112yes—
317#126—21no—
318#125C22⋊D1111yescharacteristic
319#124C22⋊D1111yescharacteristic
320#123—21no—
321C22⋊Q8C22⋊D1111yescharacteristic
322#121C22⋊D1111yescharacteristic
323C4×Q8C22×D1111yescharacteristic
324C4×D4—21no—
325C4×D4C22×D1111yescharacteristic
326#117—21no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C42C22×D1111yescharacteristic
330#107—222no—
331#106—222no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—112no—
335C4⋊C8—221no—
336C4⋊C8—221no—
337C4⋊C8C22×D1112yes—
338#103—222no—
339#102—22no—
340#102—22no—
341#102—222no—
342C22⋊C8—21no—
343C22⋊C8—221no—
344C22⋊C8—221no—
345C22⋊C8—221no—
346C22⋊C8—221no—
347#97—21no—
348#97—221no—
349#97—221no—
350#97—221no—
351C4×C8—111no—
352C4×C8—111no—
353C4×C8—111no—
354C4×C8—111no—
355C4×C8—221no—
356C2×C11—22no—
357C2×C11—81no—
358C2×C11—162no—
359C2×C11#303811yescharacteristic
360C2×C11#305711yescharacteristic
361C2×C11C2×#47111yescharacteristic
362C24—41no—
363C2×Q8—222no—
364C2×Q8—442no—
365C2×Q8—442no—
366C2×Q8—441no—
367C2×Q8C2×C22⋊D1111yescharacteristic
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—82no—
378C2×D4—82no—
379C2×D4C2×C22⋊D1111yescharacteristic
380C22×C4—21no—
381C22×C4—441no—
382C22×C4D4×D1111yescharacteristic
383C22×C4#434111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385SD16—82no—
386SD16—444no—
387SD16—444no—
388SD16—444no—
389SD16—444no—
390D8—82no—
391M16—442no—
392C2×C8—22no—
393C2×C8—111no—
394C2×C8—111no—
395C2×C8—111no—
396C2×C8—111no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—222no—
402C2×C8—442no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4C2×C22⋊D1111yescharacteristic
412C4⋊C4C2×C22⋊D1111yescharacteristic
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C42—21no—
419C42D4×D1111yescharacteristic
420C42#434111yescharacteristic
421C42C2×C22⋊D1111yescharacteristic
422C42C23×D1111yescharacteristic
423C11#1935211yescharacteristic, complemented, Sylow
424C23—21no—
425C23—42no—
426C23—82no—
427C23—82no—
428C23—82no—
429C23#6699211yescharacteristic
430Q8—22no—
431Q8—442no—
432Q8—442no—
433Q8—882no—
434D4—22no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—82no—
441D4—82no—
442D4—82no—
443D4—82no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—442no—
454C2×C4—882no—
455C2×C4#6699211yescharacteristic
456C2×C4#6699211yescharacteristic
457C2×C4#6699211yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—42no—
462C8—112no—
463C8—112no—
464C8—221no—
465C8—221no—
466C8—441no—
467C8—441no—
468C8—442no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—164no—
478C22#1062281312yes—
479C22C2×#6699211yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—882no—
488C4D11×AGL(1,ℤ/8)11yescharacteristic
489C4D11×AGL(1,ℤ/8)11yescharacteristic
490C4#1062336712yes—
491C2—22no—
492C2—81no—
493C2—162no—
494C2#1307809411yescharacteristic
495C2#1307825211yescharacteristic
496C2C2×#1062281311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3217C2
socleC22×C11C2×#121
hypercenter#3217D11
hypocenterC11#19352
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3217

Complements

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

NH ≅ G/Ntype
1. #13079843C2semidirect
2. C2×#10622689C2semidirect
3. #13077592C2semidirect
4. #13068086C2semidirect
5. #13068079C2semidirect
6. #13067962C2semidirect
7. #13067955C2semidirect
8. #13067377C2semidirect
9. #13067332C2semidirect
10. #13067330C2semidirect
32. #10622637C22semidirect
33. Q8×C11⋊C8C22semidirect
34. #10622633C22semidirect
35. #10622625C22semidirect
38. D4×C11⋊C8C22semidirect
39. #10622620C22semidirect
47. #10622124C22semidirect
48. #10622124C22semidirect
49. #10622118C22semidirect
50. #10622117C22semidirect
423. C11#19352semidirect

Maximal subgroups

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

subgroupindex
#130798432
C2×#106226892
#130775922
#130680862
#130680792
#130679622
#130679552
#130673772
#130673322
#130673302
C11×#32172
#1935211