Finite Group Databasebeta

← #11901805

Subgroups — #11901805

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C3×#5791C212yesmaximal, complemented
3#10595508C214yesmaximal, complemented
4#10595050C211yesmaximal, characteristic, complemented
5#10595041C212yesmaximal, complemented
6#10595032C211yesmaximal, characteristic, complemented
7#10594994C214yesmaximal, complemented
8#10594984C214yesmaximal, complemented
9#10594958C212yesmaximal, complemented
10#10594934C218yesmaximal, complemented
11#10594826C212yesmaximal, complemented
12#86019—32nomaximal
13C23×C32×C4C2211yescharacteristic
14C2×C3×#235C2212yes—
15C2×#3757C2212yes—
16#64135C2212yes—
17#64135C2214yes—
18#64135C2212yes—
19C2×C4⋊(C3⋊Dic3)C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C3×#953C2214yes—
23C3×#930C2214yes—
24C3×#929C2214yes—
25C3×C4×#67C2218yes—
26C3×#926C2212yes—
27C3×#924C2214yes—
28#63982C2214yes—
29#63980C2214yes—
30#67⋊Dic3C2218yes—
31#63970C2218yes—
32#63969C2218yes—
33#63959C2218yes—
34#63956C2218yes—
35#63919C2212yescomplemented
36C4×#627C2214yescomplemented
37#63914C2211yescharacteristic, complemented
38C4×#625C2214yescomplemented
39#63898C2214yescomplemented
40#63893C2218yescomplemented
41#63891C2218yescomplemented
42C4×D3×Dic3C2214yescomplemented
43#63873C2211yescharacteristic, complemented
44#63872C2212yescomplemented
45#63863C2212yescomplemented
46#63861C2218yescomplemented
47#63855C2214yescomplemented
48#63845C2218yescomplemented
49#63843C2214yescomplemented
50C3×#525—32no—
51#5832—32no—
52Dic3×#41—32no—
53#5791D312yescomplemented
54C2×#926—32no—
55C2×#926—61no—
56#5665—38no—
57#5643—34no—
58#5625—34no—
59#5619—34no—
60#5603—34no—
61#5593—38no—
62#5557—38no—
63#5538—38no—
64#5522—32no—
65#5517—32no—
66C24×C32C2311yescharacteristic
67C22×C32×C4—24no—
68C22×C32×C4C2312yes—
69C22×C32×C4C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C3⋊Dic3C2312yes—
73C22×C3⋊Dic3C2312yes—
74C2×C3×#67C2314yes—
75C2×C3×#67C2318yes—
76C3×#235—28no—
77C2×C3×D12C2312yes—
78C2×C3×C4×D3C2314yes—
79C2×C3×Dic6C2312yes—
80C2×#627C2314yes—
81C2×#625C2314yes—
82C2×D3×Dic3C2318yes—
83#3757C2314yes—
84#3757C2314yes—
85C4⋊(C3⋊Dic3)C2314yes—
86C4⋊(C3⋊Dic3)C2314yes—
87C4×C3⋊Dic3C2312yes—
88C4×C3⋊Dic3C2312yes—
89C4×C3⋊Dic3C2311yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C4×C3⋊Dic3C2312yes—
92C3×#217C2318yes—
93C3×#217C2314yes—
94C3×(C2×D3)⋊C4C2318yes—
95C3×C4⋊Dic3C2314yes—
96C3×Dic3⋊C4C2318yes—
97C3×C4×Dic3C2314yes—
98#3724C2314yes—
99#3724C2314yes—
100Dic3⋊Dic3C2318yes—
101Dic3⋊Dic3C2318yes—
102(C2×D3)⋊Dic3C2318yes—
103(C2×D3)⋊Dic3C2318yes—
104Dic32C2318yes—
105#3455—91noSylow
106C2×C3×#41—32no—
107C23×C3×C4—21no—
108C23×C3×C4C2×D312yes—
109C2×#235C2×D312yes—
110C3×#123—34no—
111C3×C22⋊Q8—34no—
112C3×#121—34no—
113C3×#120—34no—
114C3×C4×D4—38no—
115C3×#117—32no—
116#953C2×D314yes—
117C2×#217—34no—
118C2×#217—62no—
119#947—32no—
120Q8×Dic3—34no—
121#944—32no—
122#940—32no—
123#939—38no—
124#939—38no—
125#938—38no—
126#936—32no—
127#936—38no—
128#935—38no—
129D4×Dic3—38no—
130D4×Dic3—34no—
131#930C2×D314yes—
132#929C2×D314yes—
133C4×#67—38no—
134C4×#67C2×D318yes—
135#926—34no—
136#926—34no—
137#926—34no—
138#926—34no—
139#926—34no—
140#926—64no—
141#926—62no—
142#926—62no—
143#926C2×D312yes—
144C2×C4⋊Dic3—34no—
145C2×C4⋊Dic3—62no—
146#924C2×D314yes—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—34no—
150C2×C4×Dic3—61no—
151C2×C4×Dic3—61no—
152#898—38no—
153#897—38no—
154#893—34no—
155#890—34no—
156#890—38no—
157#889—38no—
158#888—34no—
159#887—34no—
160#886—38no—
161#885—38no—
162#883—38no—
163#883—38no—
164#67⋊C4—38no—
165#879—38no—
166#879—38no—
167#879—38no—
168#878—38no—
169#878—38no—
170#872—34no—
171C42×D3—34no—
172C4×Dic6—38no—
173C23×C32—22no—
174C23×C32—42no—
175C23×C32C2412yes—
176C23×C32C2411yescharacteristic
177C22×C3×D3C2414yes—
178C2×C32×C4—22no—
179C2×C32×C4—24no—
180C2×C32×C4—24no—
181C2×C32×C4#4114yes—
182C2×C32×C4C2412yes—
183C2×C32×C4C2411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—42no—
186C2×C3⋊Dic3—42no—
187C2×C3⋊Dic3C2414yes—
188C2×C3⋊Dic3C2412yes—
189C2×C3⋊Dic3C2412yes—
190C3×#67—28no—
191C3×#67—48no—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2418yes—
194C3×D12—24no—
195C3×C4×D3—28no—
196C3×Dic6—24no—
197#627—44no—
198#625—44no—
199D3×Dic3—48no—
200#542—94no—
201#541—92no—
202#540—92no—
203#539—94no—
204#538—94no—
205#533—91no—
206#532—91no—
207#529—98no—
208#525—32no—
209C4×#41—92no—
210C2×#117—91no—
211C24×C3—21no—
212C24×C3C22×D312yes—
213C3×#41—68no—
214C2×C3×Q8—32no—
215C2×C3×D4—34no—
216C2×C3×D4—38no—
217C2×C3×D4—32no—
218C22×C3×C4—28no—
219C22×C3×C4—28no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—34no—
225C22×C3×C4C22×D314yes—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D314yes—
228C22×C3×C4C22×D312yes—
229C2×#67—38no—
230C2×#67C22×D314yes—
231C2×#67C22×D318yes—
232C22×Dic3—34no—
233C22×Dic3—34no—
234C22×Dic3—38no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237#235—28no—
238C2×D12C22×D312yes—
239C2×C4×D3—38no—
240C2×C4×D3C22×D314yes—
241C2×Dic6—38no—
242C2×Dic6C22×D312yes—
243C3×C4⋊C4—34no—
244C3×C4⋊C4—38no—
245C3×C22⋊C4—34no—
246C3×C22⋊C4—38no—
247C3×C22⋊C4—38no—
248C3×C42—34no—
249#217—34no—
250#217—34no—
251#217—34no—
252#217—34no—
253#217—38no—
254#217—38no—
255#217—64no—
256#217—64no—
257#217C22×D314yes—
258#217C22×D318yes—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4—38no—
261(C2×D3)⋊C4C22×D318yes—
262C4⋊Dic3—34no—
263C4⋊Dic3—34no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—38no—
267C4⋊Dic3—38no—
268C4⋊Dic3—64no—
269C4⋊Dic3—64no—
270C4⋊Dic3C22×D314yes—
271Dic3⋊C4—38no—
272Dic3⋊C4—38no—
273Dic3⋊C4—38no—
274Dic3⋊C4—38no—
275Dic3⋊C4C22×D318yes—
276C4×Dic3—34no—
277C4×Dic3—32no—
278C4×Dic3—32no—
279C4×Dic3—34no—
280C4×Dic3—32no—
281C4×Dic3—32no—
282C4×Dic3—38no—
283C4×Dic3—38no—
284C4×Dic3—62no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3C22×D314yes—
290C22×C32—22no—
291C22×C32—22no—
292C22×C32—24no—
293C22×C32—44no—
294C22×C32C2×#4112yes—
295C22×C32C2511yescharacteristic
296C2×C3×D3—24no—
297C2×C3×D3—28no—
298C32×C4—22no—
299C32×C4C2×#4112yes—
300C32×C4C2×#4112yes—
301C3⋊Dic3—24no—
302C3⋊Dic3—22no—
303C3⋊Dic3—22no—
304C3×Dic3—24no—
305C3×Dic3—28no—
306C2×#41—32no—
307C23×C4D3211yescharacteristic
308C4⋊Q8—92no—
309C4⋊Q8—91no—
310#127—91no—
311#126—98no—
312#126—98no—
313#125—98no—
314#125—92no—
315#124—98no—
316#124—92no—
317#123—34no—
318#123—98no—
319#123—98no—
320C22⋊Q8—34no—
321C22⋊Q8—94no—
322C22⋊Q8—98no—
323#121—34no—
324#121—98no—
325#121—94no—
326#120—34no—
327C4×Q8—94no—
328C4×Q8—94no—
329C4×D4—38no—
330C4×D4—98no—
331C4×D4—94no—
332C4×D4—94no—
333#117—32no—
334#117—94no—
335#117—94no—
336#117—92no—
337#117—92no—
338C2×C4⋊C4—92no—
339C2×C22⋊C4—92no—
340C2×C42—94no—
341C2×C42—91no—
342C2×C42—91no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—21no—
346C23×C3—22no—
347C23×C3—34no—
348C23×C3—44no—
349C23×C3—44no—
350C23×C3C23×D314yes—
351C23×C3C23×D312yes—
352C22×D3C23×D314yes—
353C3×Q8—64no—
354C3×D4—68no—
355C3×D4—64no—
356C3×D4—128no—
357C2×C3×C4—24no—
358C2×C3×C4—28no—
359C2×C3×C4—28no—
360C2×C3×C4—24no—
361C2×C3×C4—28no—
362C2×C3×C4—28no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—24no—
367C2×C3×C4—34no—
368C2×C3×C4—38no—
369C2×C3×C4—68no—
370C2×C3×C4#23718yes—
371C2×C3×C4C23×D314yes—
372C2×C3×C4C23×D312yes—
373C2×C3×C4C23×D312yes—
374#67—28no—
375#67—48no—
376#67—128no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—128no—
385C2×Dic3—124no—
386C2×Dic3—124no—
387C2×Dic3—124no—
388C2×Dic3—124no—
389C2×Dic3C23×D314yes—
390C2×Dic3C23×D318yes—
391D12—24no—
392C4×D3—28no—
393C4×D3—128no—
394Dic6—24no—
395Dic6—128no—
396C2×C32—22no—
397C2×C32—42no—
398C2×C32C22×#4111yescharacteristic
399C2×C32#58512yes—
400C3×D3—44no—
401C24C2×D3211yescharacteristic
402#41—68no—
403C2×Q8—32no—
404C2×Q8—94no—
405C2×D4—34no—
406C2×D4—38no—
407C2×D4—32no—
408C2×D4—94no—
409C22×C4—24no—
410C22×C4—34no—
411C22×C4—98no—
412C22×C4—92no—
413C22×C4—92no—
414C22×C4C2×D3211yescharacteristic
415C22×C4C2×D3212yes—
416C22×C4C2×D3212yes—
417C22×C4C2×D3211yescharacteristic
418C4⋊C4—34no—
419C4⋊C4—38no—
420C4⋊C4—98no—
421C4⋊C4—94no—
422C4⋊C4—98no—
423C4⋊C4—94no—
424C4⋊C4—94no—
425C4⋊C4—94no—
426C22⋊C4—34no—
427C22⋊C4—38no—
428C22⋊C4—38no—
429C22⋊C4—98no—
430C22⋊C4—98no—
431C22⋊C4—94no—
432C22⋊C4—94no—
433C42—34no—
434C42—98no—
435C42—92no—
436C42—91no—
437C42—91no—
438C42—92no—
439C42—92no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3—24no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—22no—
447C22×C3—21no—
448C22×C3—44no—
449C22×C3—48no—
450C22×C3—48no—
451C22×C3—64no—
452C22×C3—68no—
453C22×C3C2×#23714yes—
454C22×C3C24×D312yes—
455C2×D3—24no—
456C2×D3—28no—
457C3×C4—24no—
458C3×C4—24no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—64no—
462C3×C4—68no—
463C3×C4C2×#23714yes—
464C3×C4C2×#23714yes—
465Dic3—24no—
466Dic3—28no—
467Dic3—64no—
468Dic3—64no—
469Dic3—64no—
470Dic3—64no—
471Dic3—124no—
472Dic3—122no—
473Dic3—122no—
474C32#345511yescharacteristic, complemented, Sylow
475C23—22no—
476C23—34no—
477C23—42no—
478C23C22×D3212yes—
479C23C22×D3211yescharacteristic
480Q8—64no—
481Q8—364no—
482D4—68no—
483D4—64no—
484D4—128no—
485D4—364no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—38no—
490C2×C4—34no—
491C2×C4—68no—
492C2×C4—94no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—368no—
496C2×C4—362no—
497C2×C4—362no—
498C2×C4#380514yes—
499C2×C4C22×D3212yes—
500C2×C4C22×D3211yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C2×C3—24no—
503C2×C3—24no—
504C2×C3—22no—
505C2×C3—21no—
506C2×C3—44no—
507C2×C3—44no—
508C2×C3—124no—
509C2×C3C22×#23712yes—
510C2×C3#596414yes—
511D3—44no—
512C22—22no—
513C22—24no—
514C22—22no—
515C22—44no—
516C22—68no—
517C22—64no—
518C22C2×#380512yes—
519C22C23×D3211yescharacteristic
520C4—22no—
521C4—68no—
522C4—64no—
523C4—184no—
524C4—182no—
525C4—182no—
526C4C2×#380512yes—
527C4C2×#380512yes—
528C3—21no—
529C3#8601912yescomplemented
530C2—22no—
531C2—42no—
532C2—124no—
533C2#1059666912yes—
534C2C22×#380511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
2. C3×#5791C2semidirect
3. #10595508C2semidirect
4. #10595050C2semidirect
5. #10595041C2semidirect
6. #10595032C2semidirect
7. #10594994C2semidirect
8. #10594984C2semidirect
9. #10594958C2semidirect
10. #10594934C2semidirect
11. #10594826C2semidirect
35. #63919C22semidirect
36. C4×#627C22semidirect
37. #63914C22semidirect
38. C4×#625C22semidirect
39. #63898C22semidirect
40. #63893C22semidirect
41. #63891C22semidirect
42. C4×D3×Dic3C22semidirect
43. #63873C22semidirect
44. #63872C22semidirect
45. #63863C22semidirect
46. #63861C22semidirect
47. #63855C22semidirect
48. #63845C22semidirect
49. #63843C22semidirect
53. #5791D3semidirect
474. C32#3455semidirect
529. C3#86019semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C3×#57912
#105955082
#105950502
#105950412
#105950322
#105949942
#105949842
#105949582
#105949342
#105948262
#860193