Finite Group Databasebeta

← #11904531

Subgroups — #11904531

Order 1152.

4608 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C22×#3830C211yesmaximal, characteristic, complemented
3C32×#535C211yesmaximal, characteristic, complemented
4#10596299C211yesmaximal, characteristic, complemented
5#10596276C211yesmaximal, characteristic, complemented
6#10596189C214yesmaximal, complemented
7#10596148C214yesmaximal, complemented
8#10596070C214yesmaximal, complemented
9#10596069C214yesmaximal, complemented
10#10596063C214yesmaximal, complemented
11#10596057C214yesmaximal, complemented
12#10595995C211yesmaximal, characteristic, complemented
13#10595987C211yesmaximal, characteristic, complemented
14#86315—34nomaximal
15C2×C32×#41C2211yescharacteristic
16C22×C32×D4C2211yescharacteristic
17C22×#638C2212yes—
18C23×C3⋊Dic3C2212yes—
19#64367—28no—
20C2×Q8×C3⋊D3C2212yescomplemented
21C2×#3830—28no—
22C2×#3830C2214yes—
23C2×#3830C2214yes—
24C2×#3830C2214yes—
25C2×#3830C2212yescomplemented
26C2×#3828C2211yescharacteristic
27C2×#3828C2212yescomplemented
28C22×C4×C3⋊D3C2211yescharacteristic
29C22×#634C2211yescharacteristic
30C22×#634C2212yescomplemented
31C32×#127C2212yescomplemented
32C32×#124C2212yescomplemented
33C32×#121C2214yescomplemented
34C32×#120C2214yes—
35C32×#117C2211yescharacteristic
36#64162C2214yes—
37#64155C2212yescomplemented
38#64149C2218yescomplemented
39#64149C2212yescomplemented
40#64148C2218yescomplemented
41#64148C2218yescomplemented
42#64147C2214yescomplemented
43#64147C2212yescomplemented
44#64146C2212yes—
45#64145C2212yescomplemented
46#64144C2212yes—
47D4×C3⋊Dic3C2218yescomplemented
48C4×#638C2214yescomplemented
49#64135C2211yescharacteristic
50#64106C2212yescomplemented
51#64104C2212yescomplemented
52#64096C2214yescomplemented
53#64095C2212yes—
54#64094C2218yescomplemented
55#64093C2218yescomplemented
56#64091C2212yes—
57#64090C2218yescomplemented
58#64087C2218yescomplemented
59#64086C2214yes—
60C4×C4⋊(C3⋊D3)C2214yescomplemented
61C4×#634C2214yescomplemented
62C2×#1010—34no—
63C22×#237—34no—
64C3×#535D314yescomplemented
65#5828—34no—
66#5805—34no—
67#5718—316no—
68#5677—316no—
69#5599—316no—
70#5598—316no—
71#5592—316no—
72#5586—316no—
73#5524—34no—
74#5516—34no—
75C24×C32C2312yes—
76C23×C3⋊D3C2311yescharacteristic
77C32×#41—24no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—24no—
80C2×C32×D4C2312yes—
81C2×C32×D4C2312yes—
82C2×C32×D4C2312yes—
83C2×C32×D4C2311yescharacteristic
84C2×C32×D4C2318yes—
85C22×C32×C4C2312yes—
86C22×C32×C4C2311yescharacteristic
87C2×#638—28no—
88C2×#638C2312yes—
89C2×#638C2318yes—
90C2×#638C2314yes—
91C2×#638C2318yes—
92C2×#638C2314yes—
93C22×C3⋊Dic3—28no—
94C22×C3⋊Dic3C2318yes—
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2314yes—
97C22×C3⋊Dic3C2312yes—
98Q8×C3⋊D3—28no—
99#3830—216no—
100#3830—216no—
101#3830—216no—
102#3830—28no—
103#3828—24no—
104#3828—28no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2314yes—
107C2×C4×C3⋊D3—24no—
108C2×C4×C3⋊D3C2312yes—
109C2×C4×C3⋊D3C2312yes—
110C2×C4×C3⋊D3C2314yes—
111C2×C4×C3⋊D3C2312yes—
112C2×#634—28no—
113C2×#634D418yescomplemented
114C2×#634C2314yes—
115C2×#634C2311yescharacteristic
116C2×#634C2312yes—
117C2×#634C2312yes—
118C32×C4⋊C4C2312yes—
119C32×C22⋊C4C2312yes—
120C32×C22⋊C4C2318yes—
121C32×C42C2312yes—
122#3757C2312yes—
123#3757C2318yes—
124#3757C2314yes—
125#3752C2314yes—
126#3752C2314yes—
127#3752C2314yes—
128C4⋊(C3⋊Dic3)C2312yes—
129C4⋊(C3⋊Dic3)C2314yes—
130#3750C2318yes—
131#3750C2314yes—
132C4×C3⋊Dic3C2318yes—
133C4×C3⋊Dic3C2312yes—
134#3487—91noSylow
135C2×C3×#41C2×D314yes—
136C22×C3×D4C2×D314yes—
137C22×#67—38no—
138C23×Dic3—38no—
139#1010—632no—
140C2×D3×Q8—38no—
141C2×#237—316no—
142C2×#237—316no—
143C2×#237—38no—
144C2×#237—316no—
145C2×#237—632no—
146C2×#235—34no—
147C2×#235—38no—
148C22×C4×D3—34no—
149C22×Dic6—34no—
150C22×Dic6—38no—
151C3×#127C2×D318yescomplemented
152C3×#124C2×D318yescomplemented
153C3×#121C2×D3116yescomplemented
154C3×#120C2×D3116yes—
155C3×#117C2×D314yes—
156#953—316no—
157#946—38no—
158#940—332no—
159#940—38no—
160#939—332no—
161#939—332no—
162#938—316no—
163#938—38no—
164#937—38no—
165#936—38no—
166#935—38no—
167D4×Dic3—332no—
168C4×#67—316no—
169#926—34no—
170#897—38no—
171#895—38no—
172#887—316no—
173#886—38no—
174#885—332no—
175#884—332no—
176#882—38no—
177#67⋊C4—332no—
178#878—332no—
179#877—316no—
180C4×D12—316no—
181C4×Dic6—316no—
182C23×C32—24no—
183C23×C32—44no—
184C23×C32C2414yes—
185C23×C32C2412yes—
186C23×C32C2411yescharacteristic
187C22×C3⋊D3—22no—
188C22×C3⋊D3—42no—
189C22×C3⋊D3C2412yes—
190C22×C3⋊D3C2412yes—
191C32×Q8—22no—
192C32×D4—24no—
193C32×D4—24no—
194C32×D4—24no—
195C32×D4—22no—
196C32×D4—48no—
197C2×C32×C4—24no—
198C2×C32×C4C2×D414yes—
199C2×C32×C4C2414yes—
200C2×C32×C4C2412yes—
201C2×C32×C4C2411yescharacteristic
202C2×C32×C4C2411yescharacteristic
203#638—24no—
204#638—28no—
205#638—216no—
206#638—48no—
207#638—44no—
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3—28no—
210C2×C3⋊Dic3—216no—
211C2×C3⋊Dic3C2×D418yes—
212C2×C3⋊Dic3C2414yes—
213C2×C3⋊Dic3C2412yes—
214C2×C3⋊Dic3C2412yes—
215C2×C3⋊Dic3C2414yes—
216C4⋊(C3⋊D3)—22no—
217C4⋊(C3⋊D3)—44no—
218C4×C3⋊D3—24no—
219C4×C3⋊D3—24no—
220C4×C3⋊D3—24no—
221C4×C3⋊D3—28no—
222#634—22no—
223#634—28no—
224#634C2×D418yes—
225#634C2×D418yes—
226C2×2−1+4—91no—
227C22×#41—91no—
228#550—94no—
229#550—94no—
230#548—94no—
231#548—94no—
232#535—91no—
233#535—94no—
234#535C3⋊D311yescharacteristic, complemented
235#525—91no—
236#525—94no—
237#525—91no—
238#519—91no—
239C24×C3C22×D318yes—
240C23×D3—34no—
241C3×#41—216no—
242C2×C3×Q8C22×D314yes—
243C2×C3×D4—216no—
244C2×C3×D4C22×D318yes—
245C2×C3×D4C22×D318yes—
246C2×C3×D4C22×D318yes—
247C2×C3×D4C22×D314yes—
248C2×C3×D4C22×D3132yes—
249C22×C3×C4C22×D318yes—
250C22×C3×C4C22×D314yes—
251C2×#67—38no—
252C2×#67—332no—
253C2×#67—316no—
254C2×#67—332no—
255C2×#67—316no—
256C2×#67—632no—
257C22×Dic3—38no—
258C22×Dic3—332no—
259C22×Dic3—34no—
260C22×Dic3—316no—
261C22×Dic3—632no—
262D3×Q8—632no—
263#237—664no—
264#237—664no—
265#237—632no—
266#237—664no—
267#235—632no—
268#235—616no—
269C2×D12—34no—
270C2×D12—316no—
271C2×C4×D3—38no—
272C2×C4×D3—38no—
273C2×C4×D3—316no—
274C2×C4×D3—38no—
275C2×C4×D3—616no—
276C2×Dic6—332no—
277C2×Dic6—38no—
278C2×Dic6—38no—
279C2×Dic6—316no—
280C2×Dic6—34no—
281C2×Dic6—632no—
282C3×C4⋊C4C22×D318yes—
283C3×C22⋊C4C22×D318yes—
284C3×C22⋊C4C22×D3132yes—
285C3×C42C22×D318yes—
286#217—38no—
287#217—332no—
288#217—316no—
289(C2×D3)⋊C4—316no—
290(C2×D3)⋊C4—316no—
291(C2×D3)⋊C4—316no—
292C4⋊Dic3—38no—
293C4⋊Dic3—316no—
294Dic3⋊C4—332no—
295Dic3⋊C4—316no—
296C4×Dic3—332no—
297C4×Dic3—38no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—24no—
301C22×C32—24no—
302C22×C32—28no—
303C22×C32—48no—
304C22×C32C22×D412yes—
305C22×C32C2511yescharacteristic
306C2×C3⋊D3—22no—
307C2×C3⋊D3—22no—
308C2×C3⋊D3—22no—
309C2×C3⋊D3—24no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—44no—
312C32×C4—22no—
313C32×C4—24no—
314C32×C4C22×D412yes—
315C32×C4C22×D412yes—
316C3⋊Dic3—22no—
317C3⋊Dic3—22no—
318C3⋊Dic3—24no—
319C3⋊Dic3C22×D418yes—
3202−1+4—188no—
321C2×#41—94no—
322C2×#41—94no—
323C2×#41—94no—
324C2×#41—92no—
325C2×#41—91no—
326C2×#41—92no—
327C2×#41—188no—
328C2×#41C2×C3⋊D311yescharacteristic
329C22×Q8—92no—
330C22×Q8—91no—
331C22×Q8—92no—
332C22×D4—92no—
333C22×D4C2×C3⋊D311yescharacteristic
334C23×C4—92no—
335C23×C4—91no—
336#127—98no—
337#127—92no—
338#127C2×C3⋊D312yescomplemented
339#124—92no—
340#124—98no—
341#124C2×C3⋊D312yescomplemented
342#123—92no—
343#123—92no—
344C22⋊Q8—92no—
345C22⋊Q8—92no—
346C22⋊Q8—98no—
347#121—92no—
348#121—98no—
349#121—94no—
350#121—98no—
351#121—92no—
352#121—98no—
353#121C2×C3⋊D314yescomplemented
354#120—94no—
355#120—92no—
356#120—92no—
357#120C2×C3⋊D314yes—
358C4×Q8—94no—
359C4×Q8—94no—
360C4×D4—98no—
361C4×D4—94no—
362C4×D4—98no—
363C4×D4—94no—
364#117—91no—
365#117—94no—
366#117C2×C3⋊D311yescharacteristic
367C23×C3—216no—
368C23×C3—416no—
369C23×C3C23×D3116yes—
370C23×C3C23×D318yes—
371C23×C3C23×D314yes—
372C22×D3—38no—
373C22×D3—38no—
374C22×D3—68no—
375C22×D3—128no—
376C3×Q8—28no—
377C3×D4—216no—
378C3×D4—216no—
379C3×D4—216no—
380C3×D4—28no—
381C3×D4—432no—
382C2×C3×C4—216no—
383C2×C3×C4D3×D4116yes—
384C2×C3×C4C23×D3116yes—
385C2×C3×C4C23×D318yes—
386C2×C3×C4C23×D314yes—
387C2×C3×C4C23×D314yes—
388#67—632no—
389#67—664no—
390#67—616no—
391#67—1232no—
392#67—1216no—
393C2×Dic3—332no—
394C2×Dic3—316no—
395C2×Dic3—316no—
396C2×Dic3—38no—
397C2×Dic3—38no—
398C2×Dic3—632no—
399C2×Dic3—664no—
400C2×Dic3—68no—
401D12—68no—
402D12—1216no—
403C4×D3—632no—
404C4×D3—616no—
405C4×D3—616no—
406C4×D3—616no—
407Dic6—332no—
408Dic6—332no—
409Dic6—632no—
410Dic6—68no—
411C2×C32—22no—
412C2×C32—42no—
413C2×C32—44no—
414C2×C32C23×D411yescharacteristic
415C2×C32#58512yes—
416C3⋊D3—42no—
417C3⋊D3—42no—
418C24—91no—
419C24C22×C3⋊D312yes—
420#41—24no—
421#41—188no—
422#41—1816no—
423#41—1816no—
424#41—1816no—
425#41—188no—
426#41—184no—
427C2×Q8—92no—
428C2×Q8—92no—
429C2×Q8—94no—
430C2×Q8—91no—
431C2×Q8—98no—
432C2×Q8—188no—
433C2×Q8—188no—
434C2×Q8C22×C3⋊D311yescharacteristic
435C2×D4—24no—
436C2×D4—92no—
437C2×D4—98no—
438C2×D4—94no—
439C2×D4—94no—
440C2×D4—98no—
441C2×D4—91no—
442C2×D4—94no—
443C2×D4—188no—
444C2×D4C22×C3⋊D312yes—
445C2×D4C22×C3⋊D312yes—
446C2×D4C22×C3⋊D311yescharacteristic
447C2×D4C22×C3⋊D312yes—
448C2×D4C22×C3⋊D318yes—
449C22×C4—92no—
450C22×C4—94no—
451C22×C4—98no—
452C22×C4—91no—
453C22×C4—94no—
454C22×C4—92no—
455C22×C4—92no—
456C22×C4—92no—
457C22×C4—188no—
458C22×C4—184no—
459C22×C4C22×C3⋊D312yes—
460C22×C4C22×C3⋊D311yescharacteristic
461C4⋊C4—98no—
462C4⋊C4—92no—
463C4⋊C4—94no—
464C4⋊C4—94no—
465C4⋊C4C22×C3⋊D312yes—
466C22⋊C4—92no—
467C22⋊C4—94no—
468C22⋊C4—98no—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4—94no—
472C22⋊C4C22×C3⋊D312yes—
473C22⋊C4C22×C3⋊D318yes—
474C42—98no—
475C42—92no—
476C42C22×C3⋊D312yes—
477C22×C3—28no—
478C22×C3—28no—
479C22×C3—216no—
480C22×C3—216no—
481C22×C3—232no—
482C22×C3—432no—
483C22×C3C2×D3×D418yes—
484C22×C3C24×D314yes—
485C2×D3—68no—
486C2×D3—68no—
487C2×D3—68no—
488C2×D3—616no—
489C2×D3—68no—
490C2×D3—1216no—
491C3×C4—28no—
492C3×C4—216no—
493C3×C4C2×D3×D418yes—
494C3×C4C2×D3×D418yes—
495Dic3—332no—
496Dic3—68no—
497Dic3—68no—
498Dic3—616no—
499C32#348711yescharacteristic, complemented, Sylow
500C23—24no—
501C23—44no—
502C23—92no—
503C23—92no—
504C23—182no—
505C23—362no—
506C23C23×C3⋊D314yes—
507C23C23×C3⋊D312yes—
508C23C23×C3⋊D311yescharacteristic
509Q8—22no—
510Q8—98no—
511Q8—98no—
512Q8—188no—
513Q8—182no—
514D4—24no—
515D4—24no—
516D4—24no—
517D4—22no—
518D4—48no—
519D4—1816no—
520D4—188no—
521D4—184no—
522D4—182no—
523D4—364no—
524D4—364no—
525D4—368no—
526C2×C4—24no—
527C2×C4—98no—
528C2×C4—94no—
529C2×C4—94no—
530C2×C4—92no—
531C2×C4—92no—
532C2×C4—188no—
533C2×C4—1816no—
534C2×C4—188no—
535C2×C4—182no—
536C2×C4—184no—
537C2×C4—184no—
538C2×C4—184no—
539C2×C4D4×C3⋊D314yes—
540C2×C4C23×C3⋊D314yes—
541C2×C4C23×C3⋊D312yes—
542C2×C4C23×C3⋊D311yescharacteristic
543C2×C4C23×C3⋊D311yescharacteristic
544C2×C3—28no—
545C2×C3—416no—
546C2×C3—48no—
547C2×C3C22×D3×D414yes—
548C2×C3#596618yes—
549D3—128no—
550D3—128no—
551C22—22no—
552C22—22no—
553C22—24no—
554C22—24no—
555C22—28no—
556C22—48no—
557C22—182no—
558C22—182no—
559C22—184no—
560C22—182no—
561C22—182no—
562C22—364no—
563C22C2×D4×C3⋊D312yes—
564C22C24×C3⋊D311yescharacteristic
565C4—22no—
566C4—24no—
567C4—98no—
568C4—182no—
569C4—182no—
570C4—184no—
571C4C2×D4×C3⋊D312yes—
572C4C2×D4×C3⋊D312yes—
573C3#8631514yescomplemented
574C2—22no—
575C2—44no—
576C2—42no—
577C2—362no—
578C2—362no—
579C2C22×D4×C3⋊D311yescharacteristic
580C2#1059675812yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#535C2
hypercenter#535C3⋊D3
hypocenterC32#3487
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C22×#3830C2semidirect
3. C32×#535C2semidirect
4. #10596299C2semidirect
5. #10596276C2semidirect
6. #10596189C2semidirect
7. #10596148C2semidirect
8. #10596070C2semidirect
9. #10596069C2semidirect
10. #10596063C2semidirect
11. #10596057C2semidirect
12. #10595995C2semidirect
13. #10595987C2semidirect
20. C2×Q8×C3⋊D3C22semidirect
25. C2×#3830C22semidirect
27. C2×#3828C22semidirect
30. C22×#634C22semidirect
31. C32×#127C22semidirect
32. C32×#124C22semidirect
33. C32×#121C22semidirect
37. #64155C22semidirect
38. #64149C22semidirect
39. #64149C22semidirect
40. #64148C22semidirect
41. #64148C22semidirect
42. #64147C22semidirect
43. #64147C22semidirect
45. #64145C22semidirect
47. D4×C3⋊Dic3C22semidirect
48. C4×#638C22semidirect
50. #64106C22semidirect
51. #64104C22semidirect
52. #64096C22semidirect
54. #64094C22semidirect
55. #64093C22semidirect
57. #64090C22semidirect
58. #64087C22semidirect
60. C4×C4⋊(C3⋊D3)C22semidirect
61. C4×#634C22semidirect
64. C3×#535D3semidirect
113. C2×#634D4semidirect
151. C3×#127C2×D3semidirect
152. C3×#124C2×D3semidirect
153. C3×#121C2×D3semidirect
234. #535C3⋊D3semidirect
338. #127C2×C3⋊D3semidirect
341. #124C2×C3⋊D3semidirect
353. #121C2×C3⋊D3semidirect
499. C32#3487semidirect
573. C3#86315semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C22×#38302
C32×#5352
#105962992
#105962762
#105961892
#105961482
#105960702
#105960692
#105960632
#105960572
#105959952
#105959872
#863153