Finite Group Databasebeta

← #11901803

Subgroups — #11901803

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×#64081C211yesmaximal, characteristic, complemented
2C3×C4×#235C212yesmaximal, complemented
3#10595050C211yesmaximal, characteristic, complemented
4#10595039C214yesmaximal, complemented
5#10595037C214yesmaximal, complemented
6#10595034C212yesmaximal, complemented
7#10595032C211yesmaximal, characteristic, complemented
8#10593984C212yesmaximal, complemented
9#10593973C218yesmaximal, complemented
10#10593883C212yesmaximal, complemented
11#10593876C214yesmaximal, complemented
12#85837—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C3×#235C2212yes—
15C2×C32×C42C2211yescharacteristic
16C2×#3752C2212yes—
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#64081C2212yes—
20#64081C2212yes—
21#64081C2214yes—
22C3×C4×#67C2218yes—
23C3×#926C2212yes—
24C3×C4×D12C2214yescomplemented
25C3×#872C2214yescomplemented
26C3×C42×D3C2214yescomplemented
27C3×C4×Dic6C2214yescomplemented
28#63982C2214yes—
29#63981C2214yes—
30#63980C2214yes—
31#63962C2214yes—
32#63919C2212yescomplemented
33C4×#627C2214yescomplemented
34#63916C2214yes—
35#63914C2211yescharacteristic, complemented
36#63906C2218yes—
37#63905C2218yescomplemented
38C4×#626C2218yes—
39C4×#625C2214yescomplemented
40#63873C2211yescharacteristic, complemented
41#63872C2212yescomplemented
42#63871C2214yes—
43#63868C2218yes—
44#63867C2218yescomplemented
45#63863C2212yescomplemented
46#63859C2218yescomplemented
47#63852C2218yes—
48#63851C2218yescomplemented
49#63850C2218yes—
50C3×C4×#41—32no—
51#5832—32no—
52#5828—32no—
53#5583—34no—
54#5582—34no—
55#5564—38no—
56#5562—34no—
57#5561—34no—
58#5560—38no—
59#5528—38no—
60#5524—32no—
61#5517—32no—
62#5479—38no—
63C4×#235D312yescomplemented
64C2×#872—32no—
65C2×#872—61no—
66C23×C3⋊D3C2311yescharacteristic
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C2×C4×C3⋊D3—24no—
72C2×C4×C3⋊D3C2312yes—
73C2×C4×C3⋊D3C2312yes—
74C2×C3×#67C2314yes—
75C3×#235—28no—
76C2×C3×D12C2312yes—
77C2×C3×C4×D3C2314yes—
78C2×C3×C4×D3C2318yes—
79C2×C3×Dic6C2312yes—
80C2×#627C2314yes—
81C2×#626C2318yes—
82C2×#625C2314yes—
83C32×C42C2312yes—
84C32×C42C2312yes—
85#3752C2314yes—
86#3752C2314yes—
87#3750C2314yes—
88#3750C2314yes—
89C4×C3⋊Dic3C2311yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C4×C3⋊Dic3C2312yes—
92C3×#217C2314yes—
93C3×(C2×D3)⋊C4C2318yes—
94C3×C4⋊Dic3C2314yes—
95C3×Dic3⋊C4C2318yes—
96C3×C4×Dic3C2314yes—
97C3×C4×Dic3C2318yes—
98#3724C2314yes—
99#3724C2314yes—
100Dic3⋊Dic3C2318yes—
101Dic3⋊Dic3C2318yes—
102#3722C2318yes—
103(C2×D3)⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yes—
105#3455—91noSylow
106C2×C3×#41—32no—
107C2×#235C2×D312yes—
108C22×C4×D3—32no—
109C22×C4×D3—61no—
110C3×C4×Q8—34no—
111C3×C4×D4—38no—
112C3×C4×D4—34no—
113C3×#117—32no—
114C3×#117—34no—
115C2×C3×C42—21no—
116C2×C3×C42—34no—
117C2×C3×C42C2×D312yes—
118#947—32no—
119#946—34no—
120#944—32no—
121#940—32no—
122#939—38no—
123#938—34no—
124#937—34no—
125#936—32no—
126#935—34no—
127#930—38no—
128#929—38no—
129#929—38no—
130C4×#67—38no—
131C4×#67—38no—
132C4×#67C2×D318yes—
133C2×(C2×D3)⋊C4—34no—
134C2×(C2×D3)⋊C4—62no—
135#926C2×D312yes—
136#924—38no—
137C2×Dic3⋊C4—34no—
138C2×Dic3⋊C4—62no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—61no—
141#898—38no—
142#897—34no—
143#896—38no—
144#895—34no—
145#894—38no—
146#890—34no—
147#889—38no—
148#888—34no—
149#886—34no—
150#885—38no—
151#884—38no—
152#883—38no—
153#882—34no—
154#879—38no—
155#878—38no—
156#876—38no—
157#876—38no—
158#875—38no—
159C4×D12—38no—
160C4×D12C2×D314yescomplemented
161#872—34no—
162#872—34no—
163#872—34no—
164#872—34no—
165#872—64no—
166#872—62no—
167#872—62no—
168#872C2×D314yescomplemented
169C42×D3C2×D314yescomplemented
170#870—38no—
171C4×Dic6—38no—
172C4×Dic6C2×D314yescomplemented
173C23×C32C2411yescharacteristic
174C22×C3⋊D3—22no—
175C22×C3⋊D3—42no—
176C22×C3⋊D3C2412yes—
177C22×C3×D3C2414yes—
178C2×C32×C4—42no—
179C2×C32×C4#4114yes—
180C2×C32×C4C2414yes—
181C2×C32×C4C2411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—42no—
185C2×C3⋊Dic3C2412yes—
186C2×C3⋊Dic3C2412yes—
187C2×C3⋊Dic3C2412yes—
188C4×C3⋊D3—24no—
189C4×C3⋊D3—24no—
190C3×#67—28no—
191C2×C3×Dic3C2414yes—
192C2×C3×Dic3C2418yes—
193C3×D12—24no—
194C3×C4×D3—28no—
195C3×C4×D3—48no—
196C3×Dic6—24no—
197#627—44no—
198#626—48no—
199#625—44no—
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—92no—
209C4×#41—32no—
210C2×#117—91no—
211C23×D3—32no—
212C23×D3—61no—
213C3×#41—68no—
214C2×C3×Q8—32no—
215C2×C3×D4—34no—
216C2×C3×D4—32no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—34no—
220C22×C3×C4—38no—
221C22×C3×C4C22×D314yes—
222C22×C3×C4C22×D312yes—
223C2×#67—38no—
224C2×#67—38no—
225C2×#67C22×D314yes—
226C22×Dic3—32no—
227C22×Dic3—34no—
228C22×Dic3—61no—
229C22×Dic3—62no—
230#235—28no—
231C2×D12—38no—
232C2×D12C22×D312yes—
233C2×C4×D3—34no—
234C2×C4×D3—34no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—68no—
238C2×C4×D3—68no—
239C2×C4×D3C22×D314yes—
240C2×C4×D3C22×D318yes—
241C2×Dic6—38no—
242C2×Dic6C22×D312yes—
243C3×C4⋊C4—34no—
244C3×C4⋊C4—38no—
245C3×C22⋊C4—34no—
246C3×C22⋊C4—38no—
247C3×C42—22no—
248C3×C42—22no—
249C3×C42—34no—
250C3×C42—38no—
251C3×C42C22×D314yes—
252C3×C42C22×D312yes—
253C3×C42C22×D312yes—
254#217—38no—
255#217—38no—
256#217C22×D314yes—
257(C2×D3)⋊C4—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—34no—
262(C2×D3)⋊C4—34no—
263(C2×D3)⋊C4—38no—
264(C2×D3)⋊C4—38no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4C22×D318yes—
268C4⋊Dic3—38no—
269C4⋊Dic3—38no—
270C4⋊Dic3C22×D314yes—
271Dic3⋊C4—34no—
272Dic3⋊C4—34no—
273Dic3⋊C4—34no—
274Dic3⋊C4—34no—
275Dic3⋊C4—38no—
276Dic3⋊C4—38no—
277Dic3⋊C4—38no—
278Dic3⋊C4—38no—
279Dic3⋊C4—64no—
280Dic3⋊C4—64no—
281Dic3⋊C4C22×D318yes—
282C4×Dic3—34no—
283C4×Dic3—32no—
284C4×Dic3—32no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—62no—
288C4×Dic3C22×D314yes—
289C4×Dic3C22×D318yes—
290C22×C32—22no—
291C22×C32C2×#4112yes—
292C22×C32C2511yescharacteristic
293C2×C3⋊D3—22no—
294C2×C3⋊D3—24no—
295C2×C3⋊D3—44no—
296C2×C3×D3—24no—
297C2×C3×D3—28no—
298C32×C4—24no—
299C32×C4C2×#4112yes—
300C32×C4C2×#4112yes—
301C3⋊Dic3—22no—
302C3⋊Dic3—22no—
303C3⋊Dic3—22no—
304C3×Dic3—24no—
305C3×Dic3—28no—
306C2×#41—32no—
307C23×C4—91no—
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—98no—
318#123—94no—
319#123—98no—
320C22⋊Q8—94no—
321C22⋊Q8—98no—
322C22⋊Q8—94no—
323#121—98no—
324#121—94no—
325#121—94no—
326#120—94no—
327C4×Q8—34no—
328C4×Q8—94no—
329C4×D4—38no—
330C4×D4—34no—
331C4×D4—98no—
332C4×D4—94no—
333#117—32no—
334#117—34no—
335#117—94no—
336#117—92no—
337#117—92no—
338C2×C4⋊C4—92no—
339C2×C22⋊C4—92no—
340C2×C42—34no—
341C2×C42—91no—
342C2×C42D3211yescharacteristic
343C23×C3—21no—
344C23×C3—34no—
345C23×C3C23×D312yes—
346C22×D3—34no—
347C22×D3—62no—
348C22×D3—64no—
349C22×D3—64no—
350C22×D3—124no—
351C22×D3—124no—
352C22×D3C23×D314yes—
353C3×Q8—64no—
354C3×D4—68no—
355C3×D4—64no—
356C2×C3×C4—21no—
357C2×C3×C4—24no—
358C2×C3×C4—21no—
359C2×C3×C4—24no—
360C2×C3×C4—34no—
361C2×C3×C4—38no—
362C2×C3×C4—44no—
363C2×C3×C4—44no—
364C2×C3×C4—68no—
365C2×C3×C4—128no—
366C2×C3×C4#23518yes—
367C2×C3×C4C23×D314yes—
368C2×C3×C4C23×D314yes—
369C2×C3×C4C23×D312yes—
370C2×C3×C4C23×D312yes—
371#67—28no—
372#67—128no—
373#67—128no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—34no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—124no—
383C2×Dic3—124no—
384C2×Dic3C23×D318yes—
385C2×Dic3C23×D314yes—
386D12—24no—
387D12—128no—
388C4×D3—28no—
389C4×D3—48no—
390C4×D3—68no—
391C4×D3—68no—
392C4×D3—68no—
393C4×D3—68no—
394Dic6—24no—
395Dic6—128no—
396C2×C32—22no—
397C2×C32C22×#4111yescharacteristic
398C2×C32#58512yes—
399C3⋊D3—42no—
400C3×D3—44no—
401C24—91no—
402#41—68no—
403C2×Q8—32no—
404C2×Q8—94no—
405C2×D4—34no—
406C2×D4—32no—
407C2×D4—98no—
408C2×D4—94no—
409C22×C4—34no—
410C22×C4—38no—
411C22×C4—91no—
412C22×C4—92no—
413C22×C4—92no—
414C22×C4—92no—
415C22×C4—184no—
416C22×C4C2×D3212yes—
417C22×C4C2×D3211yescharacteristic
418C4⋊C4—34no—
419C4⋊C4—38no—
420C4⋊C4—94no—
421C4⋊C4—98no—
422C4⋊C4—98no—
423C4⋊C4—94no—
424C4⋊C4—94no—
425C4⋊C4—94no—
426C22⋊C4—34no—
427C22⋊C4—38no—
428C22⋊C4—98no—
429C22⋊C4—98no—
430C22⋊C4—98no—
431C22⋊C4—94no—
432C22⋊C4—94no—
433C42—38no—
434C42—34no—
435C42—91no—
436C42—91no—
437C42—92no—
438C42C2×D3212yes—
439C42C2×D3212yes—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—64no—
445C22×C3—68no—
446C22×C3C2×#23514yes—
447C22×C3C24×D312yes—
448C2×D3—24no—
449C2×D3—28no—
450C2×D3—64no—
451C2×D3—64no—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—124no—
455C2×D3—128no—
456C2×D3—128no—
457C3×C4—24no—
458C3×C4—24no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—44no—
462C3×C4—64no—
463C3×C4—68no—
464C3×C4C2×#23514yes—
465C3×C4C2×#23514yes—
466Dic3—24no—
467Dic3—28no—
468Dic3—64no—
469Dic3—64no—
470Dic3—64no—
471Dic3—64no—
472Dic3—122no—
473Dic3—122no—
474C32#345511yescharacteristic, complemented, Sylow
475C23—34no—
476C23—92no—
477C23—182no—
478C23—362no—
479C23C22×D3211yescharacteristic
480Q8—64no—
481Q8—364no—
482D4—68no—
483D4—64no—
484D4—368no—
485D4—364no—
486C2×C4—38no—
487C2×C4—34no—
488C2×C4—42no—
489C2×C4—68no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—128no—
494C2×C4—182no—
495C2×C4—184no—
496C2×C4—184no—
497C2×C4—362no—
498C2×C4#379814yes—
499C2×C4C22×D3214yes—
500C2×C4C22×D3211yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C2×C3—24no—
503C2×C3—24no—
504C2×C3—21no—
505C2×C3—22no—
506C2×C3—124no—
507C2×C3C22×#23512yes—
508C2×C3#596414yes—
509D3—44no—
510D3—124no—
511D3—124no—
512C22—22no—
513C22—64no—
514C22—68no—
515C22—182no—
516C22—184no—
517C22—364no—
518C22C2×#379812yes—
519C22C23×D3211yescharacteristic
520C4—24no—
521C4—64no—
522C4—68no—
523C4—182no—
524C4—182no—
525C4—182no—
526C4C2×#379812yes—
527C4C2×#379812yes—
528C3—21no—
529C3#8583712yescomplemented
530C2—22no—
531C2—124no—
532C2—362no—
533C2C22×#379811yescharacteristic
534C2#1059666912yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64081C2semidirect
2. C3×C4×#235C2semidirect
3. #10595050C2semidirect
4. #10595039C2semidirect
5. #10595037C2semidirect
6. #10595034C2semidirect
7. #10595032C2semidirect
8. #10593984C2semidirect
9. #10593973C2semidirect
10. #10593883C2semidirect
11. #10593876C2semidirect
24. C3×C4×D12C22semidirect
25. C3×#872C22semidirect
26. C3×C42×D3C22semidirect
27. C3×C4×Dic6C22semidirect
32. #63919C22semidirect
33. C4×#627C22semidirect
35. #63914C22semidirect
37. #63905C22semidirect
39. C4×#625C22semidirect
40. #63873C22semidirect
41. #63872C22semidirect
44. #63867C22semidirect
45. #63863C22semidirect
46. #63859C22semidirect
48. #63851C22semidirect
63. C4×#235D3semidirect
160. C4×D12C2×D3semidirect
168. #872C2×D3semidirect
169. C42×D3C2×D3semidirect
172. C4×Dic6C2×D3semidirect
474. C32#3455semidirect
529. C3#85837semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×C4×#2352
#105950502
#105950392
#105950372
#105950342
#105950322
#105939842
#105939732
#105938832
#105938762
#858373