Finite Group Databasebeta

← #14739176

Subgroups — #14739176

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079559C211yesmaximal, characteristic, complemented
2#13078404C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic
4#13068032C212yesmaximal, complemented
5#13068025C212yesmaximal, complemented
6#13067964C212yesmaximal, complemented
7#13067957C212yesmaximal, complemented
8#13067387C211yesmaximal, characteristic, complemented
9#13067304C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#2988C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67002—21no—
14C2×#66927C2211yescharacteristic
15#10623001C2211yescharacteristic
16C8×Q8×C11C2212yescomplemented
17C8×D4×C11—22no—
18C8×D4×C11C2212yescomplemented
19C11×#431—21no—
20C11×#431C2211yescharacteristic
21C2×C11×C4⋊C8—21no—
22C2×C11×C4⋊C8C2211yescharacteristic
23#10622846—21no—
24#10622640—21no—
25#10622640C2212yes—
26#10622635—21no—
27#10622634C2211yescharacteristic, complemented
28#10622633C2211yescharacteristic, complemented
29#10622628—21no—
30#10622628C2212yes—
31#10622622—21no—
32#10622621C2211yescharacteristic, complemented
33#10622620C2211yescharacteristic, complemented
34#10622614—21no—
35#10622611—21no—
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622461—21no—
39#10622461—21no—
40#10622344—22no—
41#10622307C2212yes—
42#10622306C2212yes—
43#10622123C2212yes—
44#10622123C2212yes—
45#10622120C2212yescomplemented
46#10622119C2212yescomplemented
47#10622095C2212yescomplemented
48#10622095C2212yescomplemented
49C2×C11×#41D411yescharacteristic
50C22×D44—21no—
51C22×D44—21no—
52C22×D44—21no—
53C22×C8×C11—21no—
54C22×C8×C11—22no—
55C4×Q8×C11D411yescharacteristic
56C4×Q8×C11C2311yescharacteristic
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11D411yescharacteristic
60C4×D4×C11C2311yescharacteristic
61C11×#117—21no—
62C11×#117D411yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65#67002—44no—
66C2×#4325—22no—
67C2×#4323—22no—
68#66979—21no—
69#66977—21no—
70#66977—21no—
71C2×#4318—21no—
72C22×C11⋊C8—21no—
73C2×#4314—22no—
74C2×#4314—22no—
75#66927—21no—
76#66927—21no—
77#66927—21no—
78#66927C2312yes—
79#66923—21no—
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×C4⋊C8—22no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8D411yescharacteristic
87C11×C4⋊C8D411yescharacteristic
88C11×C4⋊C8C2312yes—
89C11×C22⋊C8—22no—
90C11×C22⋊C8D412yes—
91C4×C8×C11—22no—
92C4×C8×C11C2312yes—
93#66899—21no—
94#66899—21no—
95#66896—21no—
96#66896—21no—
97#66885—22no—
98#66885—22no—
99#66873—22no—
100#66873—22no—
101#66872—21no—
102#66872—21no—
103#66871—21no—
104#66871—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2312yes—
110#19409—111nomaximal, Sylow
111C23×D11—41no—
112C11×#41—22no—
113C11×#41SD1614yescomplemented
114C2×Q8×C11C2×D411yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11C2×D411yescharacteristic
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—41no—
127C2×D44—41no—
128C2×D44—41no—
129C2×D44—42no—
130C2×D44—42no—
131C2×D44—81no—
132C2×D44—81no—
133C2×D44—82no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×C8×C11—22no—
137C2×C8×C11—81no—
138C2×C8×C11—82no—
139C2×C8×C11C2×D412yes—
140C2×C8×C11C2×D412yes—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C4⋊C4C2×D411yescharacteristic
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C11×C22⋊C4—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155C22⋊Dic11—41no—
156#4325—44no—
157#4323—44no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164C4×Dic11—41no—
165#4318—42no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170#4314—82no—
171#4314—82no—
172#3208—111no—
173#3076—111no—
174#3038—111no—
175#2988D1111yescharacteristic, complemented
176#1678—112no—
177#1677—112no—
178#1666—112no—
179#1665—112no—
180#1570—111no—
181#1550—111no—
182C2×#331—111no—
183C23×C11—21no—
184C23×C11#12111yescharacteristic
185C22×D11—42no—
186C22×D11—82no—
187C22×D11—82no—
188C22×D11—82no—
189Q8×C11—21no—
190Q8×C11C2×SD1612yes—
191D4×C11—24no—
192D4×C11—21no—
193D4×C11C2×SD1612yes—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—81no—
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11C2×SD1612yes—
208C2×C4×C11#13512yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×Dic11—41no—
213C2×Dic11—41no—
214D44—42no—
215D44—42no—
216D44—42no—
217D44—42no—
218D44—82no—
219D44—82no—
220D44—82no—
221D44—82no—
222Dic22—41no—
223Dic22—41no—
224Dic22—81no—
225C8×C11—22no—
226C8×C11—22no—
227C8×C11—42no—
228C11⋊C8—42no—
229C11⋊C8—41no—
230C11⋊C8—41no—
231C2×AGL(1,ℤ/8)—221no—
232#533—111no—
233C2×#127—111no—
234C4×#41C2×D1111yescharacteristic
235#492—112no—
236#486—112no—
237#479—221no—
238#478—221no—
239#477—111no—
240#476—111no—
241#475—111no—
242#474—111no—
243#460—112no—
244#460—221no—
245#460—221no—
246#460—221no—
247#459—112no—
248#459—221no—
249#450—222no—
250C8×Q8C2×D1112yescomplemented
251C8×D4—22no—
252C8×D4C2×D1112yescomplemented
253#431—21no—
254#431C2×D1111yescharacteristic
255#427—221no—
256#423—111no—
257C2×C4⋊C8—21no—
258C2×C4⋊C8—111no—
259C2×C4⋊C8C2×D1111yescharacteristic
260#418—221no—
261#416—221no—
262#334—112no—
263#334—112no—
264#333—112no—
265#332—112no—
266#331—112no—
267#331—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—22no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11#46512yes—
274C22×C11C2×#12111yescharacteristic
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—82no—
278C2×D11—164no—
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11#46512yes—
286C4×C11C22×SD1611yescharacteristic
287C4×C11C2×#13511yescharacteristic
288C4×C11#57611yescharacteristic
289C4×C11#57711yescharacteristic
290Dic11—81no—
291Dic11—81no—
292C2×#41D4411yescharacteristic
293C22×D4—221no—
294C22×D4—221no—
295C22×D4—221no—
296AGL(1,ℤ/8)—444no—
297C2×SD16—222no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×D8—222no—
301C2×M16—221no—
302C22×C8—21no—
303C22×C8—22no—
304C22×C8—221no—
305C4⋊Q8—111no—
306C4⋊Q8—111no—
307#127—112no—
308#127—221no—
309#127—221no—
310#127—221no—
311#125—221no—
312C22⋊Q8—221no—
313C22⋊Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8D4411yescharacteristic
317C4×Q8C22×D1111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4D4411yescharacteristic
321C4×D4C22×D1111yescharacteristic
322#117—21no—
323#117—221no—
324#117D4411yescharacteristic
325C2×C42—21no—
326C2×C42C22×D1111yescharacteristic
327#107—221no—
328#107—221no—
329#106—221no—
330#106—221no—
331C4⋊C8—22no—
332C4⋊C8—21no—
333C4⋊C8—111no—
334C4⋊C8—111no—
335C4⋊C8—112no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8C22⋊D1111yescharacteristic
339C4⋊C8C22⋊D1111yescharacteristic
340C4⋊C8C22×D1112yes—
341#103—221no—
342#103—221no—
343#102—221no—
344#102—221no—
345#102—222no—
346#102—222no—
347#102—222no—
348#102—222no—
349C22⋊C8—22no—
350C22⋊C8C22⋊D1112yes—
351C4×C8—22no—
352C4×C8C22×D1112yes—
353C2×C11—22no—
354C2×C11—42no—
355C2×C11#304511yescharacteristic
356C2×C11C2×#46511yescharacteristic
357C2×C11#306811yescharacteristic
358D11—162no—
359C24—441no—
360#41—22no—
361#41#431414yescomplemented
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8C2×D4411yescharacteristic
365C2×D4—21no—
366C2×D4—222no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—442no—
370C2×D4—442no—
371C2×D4—441no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—881no—
375C2×D4—881no—
376C2×D4—882no—
377C2×D4C2×D4411yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4C2×D4411yescharacteristic
382C22×C4#433911yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384SD16—444no—
385SD16—882no—
386SD16—882no—
387D8—444no—
388M16—442no—
389C2×C8—22no—
390C2×C8—82no—
391C2×C8—81no—
392C2×C8—222no—
393C2×C8—221no—
394C2×C8—221no—
395C2×C8—442no—
396C2×C8C2×C22⋊D1112yes—
397C2×C8C2×C22⋊D1112yes—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4C2×D4411yescharacteristic
407C4⋊C4C2×D4411yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—441no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—441no—
416C42C2×D4411yescharacteristic
417C42#433911yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1940911yescharacteristic, complemented, Sylow
421C23—21no—
422C23—442no—
423C23—882no—
424C23—882no—
425C23—882no—
426C23#6698311yescharacteristic
427Q8—21no—
428Q8—441no—
429Q8—441no—
430Q8—881no—
431Q8C2×#431412yes—
432D4—24no—
433D4—21no—
434D4—442no—
435D4—442no—
436D4—442no—
437D4—442no—
438D4—882no—
439D4—882no—
440D4—882no—
441D4—882no—
442D4C2×#431412yes—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4C2×#431412yes—
456C2×C4#6695712yes—
457C2×C4#6698311yescharacteristic
458C2×C4#6698311yescharacteristic
459C2×C4#6698311yescharacteristic
460C2×C4C22×D4411yescharacteristic
461C2×C4C2×#433911yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—22no—
464C8—22no—
465C8—42no—
466C8—442no—
467C8—441no—
468C8—441no—
469C22—21no—
470C22—21no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22—1764no—
478C22#1062272712yes—
479C22C2×#6698311yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—881no—
487C4—881no—
488C4#1062272712yes—
489C4C22×#431411yescharacteristic
490C4C2×#6695711yescharacteristic
491C4#1062336611yescharacteristic
492C4#1062336811yescharacteristic
493C2—22no—
494C2—42no—
495C2—1762no—
496C2#1307815511yescharacteristic
497C2C2×#1062272711yescharacteristic
498C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
prime radical#13078096C2
hypercenter#2988D11
hypocenterC11#19409
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079559C2semidirect
2. #13078404C2semidirect
4. #13068032C2semidirect
5. #13068025C2semidirect
6. #13067964C2semidirect
7. #13067957C2semidirect
8. #13067387C2semidirect
9. #13067304C2semidirect
10. C2×#10622123C2semidirect
11. C11×#2988C2semidirect
16. C8×Q8×C11C22semidirect
18. C8×D4×C11C22semidirect
27. #10622634C22semidirect
28. #10622633C22semidirect
32. #10622621C22semidirect
33. #10622620C22semidirect
45. #10622120C22semidirect
46. #10622119C22semidirect
47. #10622095C22semidirect
48. #10622095C22semidirect
113. C11×#41SD16semidirect
175. #2988D11semidirect
250. C8×Q8C2×D11semidirect
252. C8×D4C2×D11semidirect
361. #41#4314semidirect
420. C11#19409semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130784042
#130780962
#130680322
#130680252
#130679642
#130679572
#130673872
#130673042
C2×#106221232
C11×#29882
#1940911