Finite Group Databasebeta

← #11900892

Subgroups — #11900892

Order 1152.

2673 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×#5791C212yesmaximal, complemented
3#10595501C214yesmaximal, complemented
4#10595050C211yesmaximal, characteristic, complemented
5#10595033C214yesmaximal, complemented
6#10595032C211yesmaximal, characteristic, complemented
7#10594965C214yesmaximal, complemented
8#10594963C214yesmaximal, complemented
9#10594958C212yesmaximal, complemented
10#10594929C212yesmaximal, complemented
11C4×#3805C214yesmaximal, complemented
12#10594810C212yesmaximal, complemented
13#86018—32nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C2×C3×#235C2212yes—
17C2×#3805C2214yes—
18C2×C4×C3⋊Dic3C2212yes—
19C2×C4×C3⋊Dic3C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2212yes—
22C2×C4×C3⋊Dic3C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2212yes—
25C3×#953C2214yes—
26C3×#930C2214yes—
27C3×#929C2214yes—
28C3×C4×#67C2218yes—
29C3×#926C2212yes—
30C3×#924C2214yes—
31#63982C2214yes—
32#63982C2214yes—
33#63980C2214yes—
34#63980C2214yes—
35#67⋊Dic3C2218yes—
36#67⋊Dic3C2218yes—
37#63962C2218yes—
38#63957C2214yes—
39#63919C2212yescomplemented
40C4×#627C2214yescomplemented
41#63915C2214yescomplemented
42#63914C2211yescharacteristic, complemented
43#63902C2214yescomplemented
44C4×#625C2214yescomplemented
45#63898C2214yescomplemented
46#63878C2218yescomplemented
47C4×D3×Dic3C2214yescomplemented
48#63873C2211yescharacteristic, complemented
49#63872C2212yescomplemented
50#63870C2214yescomplemented
51#63863C2212yescomplemented
52#63862C2218yescomplemented
53#63855C2214yescomplemented
54#63843C2214yescomplemented
55#63838C2214yescomplemented
56C3×#525—32no—
57#5832—32no—
58Dic3×#41—32no—
59#5791D312yescomplemented
60C22×C4×Dic3—32no—
61C22×C4×Dic3—61no—
62#5649—38no—
63#5624—34no—
64#5622—34no—
65#5600—34no—
66#5596—34no—
67#5586—38no—
68#5538—38no—
69C4×#237—38no—
70#5522—32no—
71#5517—32no—
72C24×C32C2311yescharacteristic
73C22×C32×C4—24no—
74C22×C32×C4C2312yes—
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3—28no—
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2312yes—
82C22×C3⋊Dic3C2312yes—
83C22×C3⋊Dic3C2312yes—
84C22×C3⋊Dic3C2312yes—
85C2×C3×#67C2318yes—
86C2×C3×#67C2314yes—
87C3×#235—28no—
88C2×C3×D12C2312yes—
89C2×C3×C4×D3C2314yes—
90C2×C3×Dic6C2312yes—
91C2×#627C2314yes—
92C2×#625C2314yes—
93#3805—216no—
94C2×D3×Dic3C2318yes—
95C4×C3⋊Dic3C2312yes—
96C4×C3⋊Dic3C2312yes—
97C4×C3⋊Dic3C2311yescharacteristic
98C4×C3⋊Dic3C2312yes—
99C4×C3⋊Dic3C2311yescharacteristic
100C4×C3⋊Dic3C2312yes—
101C4×C3⋊Dic3C2311yescharacteristic
102C4×C3⋊Dic3C2311yescharacteristic
103C4×C3⋊Dic3C2312yes—
104C4×C3⋊Dic3C2312yes—
105C3×#217C2318yes—
106C3×#217C2314yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×C4⋊Dic3C2314yes—
109C3×Dic3⋊C4C2318yes—
110C3×C4×Dic3C2314yes—
111#3724C2314yes—
112#3724C2314yes—
113Dic3⋊Dic3C2318yes—
114Dic3⋊Dic3C2318yes—
115(C2×D3)⋊Dic3C2318yes—
116(C2×D3)⋊Dic3C2318yes—
117Dic32C2318yes—
118#3444—91noSylow
119C2×C3×#41—32no—
120C23×C3×C4—21no—
121C23×C3×C4C2×D312yes—
122C23×Dic3—34no—
123C23×Dic3—62no—
124C2×#237—38no—
125C2×#235C2×D312yes—
126C3×#123—34no—
127C3×C22⋊Q8—34no—
128C3×#121—34no—
129C3×#120—34no—
130C3×C4×D4—38no—
131C3×#117—32no—
132#953C2×D314yes—
133#947—32no—
134Q8×Dic3—34no—
135#944—32no—
136#940—32no—
137#939—38no—
138#939—38no—
139#936—32no—
140#935—38no—
141D4×Dic3—38no—
142D4×Dic3—38no—
143D4×Dic3—34no—
144#930C2×D314yes—
145#929C2×D314yes—
146C4×#67—38no—
147C4×#67C2×D318yes—
148#926—34no—
149#926C2×D312yes—
150#924C2×D314yes—
151C2×C4×Dic3—34no—
152C2×C4×Dic3—32no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—34no—
155C2×C4×Dic3—34no—
156C2×C4×Dic3—34no—
157C2×C4×Dic3—34no—
158C2×C4×Dic3—34no—
159C2×C4×Dic3—62no—
160C2×C4×Dic3—61no—
161C2×C4×Dic3—62no—
162C2×C4×Dic3—62no—
163C2×C4×Dic3—62no—
164C2×C4×Dic3—62no—
165C2×C4×Dic3—61no—
166#898—38no—
167#893—34no—
168#892—38no—
169#890—34no—
170#889—38no—
171#888—34no—
172#887—34no—
173#887—38no—
174#886—38no—
175#885—38no—
176#67⋊C4—38no—
177#67⋊C4—38no—
178#67⋊C4—38no—
179#879—38no—
180#878—38no—
181#878—38no—
182#877—38no—
183#877—38no—
184#872—34no—
185C42×D3—34no—
186C4×Dic6—38no—
187C23×C32—24no—
188C23×C32—22no—
189C23×C32C2411yescharacteristic
190C23×C32C2412yes—
191C22×C3×D3C2414yes—
192C2×C32×C4—22no—
193C2×C32×C4—24no—
194C2×C32×C4—24no—
195C2×C32×C4#4114yescomplemented
196C2×C32×C4C2412yes—
197C2×C32×C4C2411yescharacteristic
198C2×C32×C4C2411yescharacteristic
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3—24no—
201C2×C3⋊Dic3—24no—
202C2×C3⋊Dic3—24no—
203C2×C3⋊Dic3—24no—
204C2×C3⋊Dic3#4118yescomplemented
205C2×C3⋊Dic3C2412yes—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208C2×C3⋊Dic3C2412yes—
209C3×#67—216no—
210C3×#67—28no—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2418yes—
213C3×D12—24no—
214C3×C4×D3—28no—
215C3×Dic6—24no—
216#627—28no—
217#625—28no—
218D3×Dic3—216no—
219#533—91no—
220#533—92no—
221#532—92no—
222#532—91no—
223#529—94no—
224#529—94no—
225#529—94no—
226#525—32no—
227#525—94no—
228C4×#41—92no—
229C4×#41—94no—
230C22×C42—91no—
231C24×C3—21no—
232C24×C3C22×D312yes—
233C3×#41—68no—
234C2×C3×Q8—32no—
235C2×C3×D4—34no—
236C2×C3×D4—38no—
237C2×C3×D4—32no—
238C22×C3×C4—28no—
239C22×C3×C4—28no—
240C22×C3×C4—22no—
241C22×C3×C4—21no—
242C22×C3×C4—22no—
243C22×C3×C4—21no—
244C22×C3×C4—34no—
245C22×C3×C4C22×D314yes—
246C22×C3×C4C22×D314yes—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D312yes—
249C2×#67—38no—
250C2×#67C22×D314yes—
251C2×#67C22×D318yes—
252C22×Dic3—34no—
253C22×Dic3—34no—
254C22×Dic3—34no—
255C22×Dic3—34no—
256C22×Dic3—34no—
257C22×Dic3—34no—
258C22×Dic3—38no—
259C22×Dic3—62no—
260C22×Dic3—62no—
261C22×Dic3—62no—
262C22×Dic3—62no—
263C22×Dic3—62no—
264C22×Dic3—62no—
265C22×Dic3—616no—
266C22×Dic3—616no—
267#237—632no—
268#235—28no—
269C2×D12C22×D312yes—
270C2×C4×D3—38no—
271C2×C4×D3C22×D314yes—
272C2×Dic6—38no—
273C2×Dic6C22×D312yes—
274C3×C4⋊C4—34no—
275C3×C4⋊C4—38no—
276C3×C22⋊C4—38no—
277C3×C22⋊C4—34no—
278C3×C22⋊C4—38no—
279C3×C42—34no—
280#217—38no—
281#217—38no—
282#217C22×D318yes—
283#217C22×D314yes—
284(C2×D3)⋊C4—38no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4C22×D318yes—
287C4⋊Dic3—38no—
288C4⋊Dic3—38no—
289C4⋊Dic3C22×D314yes—
290Dic3⋊C4—38no—
291Dic3⋊C4—38no—
292Dic3⋊C4—38no—
293Dic3⋊C4—38no—
294Dic3⋊C4C22×D318yes—
295C4×Dic3—34no—
296C4×Dic3—32no—
297C4×Dic3—32no—
298C4×Dic3—34no—
299C4×Dic3—34no—
300C4×Dic3—34no—
301C4×Dic3—34no—
302C4×Dic3—34no—
303C4×Dic3—32no—
304C4×Dic3—32no—
305C4×Dic3—38no—
306C4×Dic3—38no—
307C4×Dic3—62no—
308C4×Dic3—62no—
309C4×Dic3—62no—
310C4×Dic3—61no—
311C4×Dic3—62no—
312C4×Dic3—62no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3—62no—
317C4×Dic3C22×D314yes—
318C22×C32—28no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—22no—
322C22×C32C2×#4112yes—
323C22×C32C2×#4114yes—
324C22×C32C2511yescharacteristic
325C2×C3×D3—28no—
326C2×C3×D3—24no—
327C32×C4—22no—
328C32×C4C2×#4112yes—
329C32×C4C2×#4112yes—
330C3⋊Dic3—22no—
331C3⋊Dic3—22no—
332C3⋊Dic3C2×#4114yes—
333C3⋊Dic3C2×#4114yes—
334C3×Dic3—28no—
335C3×Dic3—24no—
336C2×#41—32no—
337C2×#41—94no—
338C23×C4—92no—
339C23×C4D3211yescharacteristic
340C4⋊Q8—92no—
341C4⋊Q8—91no—
342#127—91no—
343#126—98no—
344#125—94no—
345#125—92no—
346#124—94no—
347#124—92no—
348#123—34no—
349#123—98no—
350C22⋊Q8—34no—
351C22⋊Q8—94no—
352C22⋊Q8—94no—
353#121—34no—
354#121—94no—
355#121—94no—
356#120—34no—
357C4×Q8—94no—
358C4×Q8—94no—
359C4×Q8—94no—
360C4×D4—38no—
361C4×D4—94no—
362C4×D4—98no—
363C4×D4—98no—
364C4×D4—94no—
365C4×D4—94no—
366#117—32no—
367#117—94no—
368#117—94no—
369#117—98no—
370C2×C42—94no—
371C2×C42—92no—
372C2×C42—91no—
373C2×C42—92no—
374C2×C42—92no—
375C2×C42—92no—
376C2×C42—92no—
377C2×C42—91no—
378C23×C3—28no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—28no—
382C23×C3—22no—
383C23×C3—21no—
384C23×C3—34no—
385C23×C3C23×D312yes—
386C23×C3C23×D314yes—
387C22×D3C23×D314yes—
388C3×Q8—64no—
389C3×D4—68no—
390C3×D4—616no—
391C3×D4—64no—
392C2×C3×C4—24no—
393C2×C3×C4—28no—
394C2×C3×C4—28no—
395C2×C3×C4—24no—
396C2×C3×C4—28no—
397C2×C3×C4—28no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—24no—
402C2×C3×C4—34no—
403C2×C3×C4—38no—
404C2×C3×C4—68no—
405C2×C3×C4#23718yescomplemented
406C2×C3×C4C23×D314yes—
407C2×C3×C4C23×D312yes—
408C2×C3×C4C23×D312yes—
409#67—28no—
410#67—216no—
411#67—616no—
412C2×Dic3—316no—
413C2×Dic3—34no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—34no—
417C2×Dic3—68no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—616no—
423C2×Dic3—68no—
424C2×Dic3—68no—
425C2×Dic3—68no—
426C2×Dic3—68no—
427C2×Dic3—68no—
428C2×Dic3—68no—
429C2×Dic3—68no—
430C2×Dic3—68no—
431C2×Dic3—68no—
432C2×Dic3—68no—
433C2×Dic3C23×D314yes—
434C2×Dic3C23×D318yes—
435D12—24no—
436C4×D3—28no—
437C4×D3—616no—
438Dic6—24no—
439Dic6—616no—
440C2×C32—22no—
441C2×C32—24no—
442C2×C32C22×#4111yescharacteristic
443C2×C32C22×#4112yes—
444C3×D3—44no—
445C24C2×D3211yescharacteristic
446#41—68no—
447#41—1816no—
448C2×Q8—32no—
449C2×Q8—94no—
450C2×D4—38no—
451C2×D4—34no—
452C2×D4—32no—
453C2×D4—94no—
454C22×C4—24no—
455C22×C4—34no—
456C22×C4—98no—
457C22×C4—92no—
458C22×C4—92no—
459C22×C4—92no—
460C22×C4—92no—
461C22×C4—92no—
462C22×C4—92no—
463C22×C4—188no—
464C22×C4C2×D3212yes—
465C22×C4C2×D3211yescharacteristic
466C22×C4C2×D3212yes—
467C22×C4C2×D3211yescharacteristic
468C4⋊C4—34no—
469C4⋊C4—38no—
470C4⋊C4—94no—
471C4⋊C4—94no—
472C4⋊C4—98no—
473C4⋊C4—98no—
474C22⋊C4—34no—
475C22⋊C4—38no—
476C22⋊C4—38no—
477C22⋊C4—98no—
478C22⋊C4—98no—
479C42—34no—
480C42—98no—
481C42—92no—
482C42—92no—
483C42—92no—
484C42—92no—
485C42—91no—
486C42—92no—
487C42—91no—
488C42—91no—
489C42—91no—
490C42—92no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—216no—
495C22×C3—216no—
496C22×C3—24no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—64no—
503C22×C3—68no—
504C22×C3C2×#23714yes—
505C22×C3D3×#4118yes—
506C22×C3C24×D312yes—
507C2×D3—24no—
508C2×D3—28no—
509C3×C4—24no—
510C3×C4—24no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—64no—
514C3×C4—68no—
515C3×C4C2×#23714yes—
516C3×C4C2×#23714yes—
517Dic3—24no—
518Dic3—28no—
519Dic3—38no—
520Dic3—38no—
521Dic3—64no—
522Dic3—64no—
523Dic3—64no—
524Dic3—64no—
525Dic3—64no—
526Dic3—64no—
527C32#344411yescharacteristic, complemented, Sylow
528C23—24no—
529C23—22no—
530C23—34no—
531C23C22×D3212yes—
532C23C22×D3211yescharacteristic
533Q8—64no—
534Q8—188no—
535D4—616no—
536D4—68no—
537D4—64no—
538D4—188no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—38no—
543C2×C4—34no—
544C2×C4—68no—
545C2×C4—98no—
546C2×C4—92no—
547C2×C4—92no—
548C2×C4—92no—
549C2×C4—92no—
550C2×C4—1816no—
551C2×C4—184no—
552C2×C4—184no—
553C2×C4—184no—
554C2×C4—184no—
555C2×C4—184no—
556C2×C4#380514yescomplemented
557C2×C4C22×D3212yes—
558C2×C4C22×D3211yescharacteristic
559C2×C4C22×D3211yescharacteristic
560C2×C3—28no—
561C2×C3—24no—
562C2×C3—24no—
563C2×C3—28no—
564C2×C3—22no—
565C2×C3—21no—
566C2×C3—124no—
567C2×C3C22×#23712yes—
568C2×C3C2×D3×#4114yes—
569D3—44no—
570C22—28no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—68no—
575C22—64no—
576C22#6430614yes—
577C22C2×#380512yes—
578C22C23×D3211yescharacteristic
579C4—22no—
580C4—68no—
581C4—64no—
582C4—94no—
583C4—94no—
584C4—182no—
585C4—182no—
586C4C2×#380512yes—
587C4C2×#380512yes—
588C3—21no—
589C3#8601812yescomplemented
590C2—24no—
591C2—22no—
592C2—124no—
593C2C2×#6430612yes—
594C2C22×#380511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊Dic3C2semidirect
2. C3×#5791C2semidirect
3. #10595501C2semidirect
4. #10595050C2semidirect
5. #10595033C2semidirect
6. #10595032C2semidirect
7. #10594965C2semidirect
8. #10594963C2semidirect
9. #10594958C2semidirect
10. #10594929C2semidirect
11. C4×#3805C2semidirect
12. #10594810C2semidirect
39. #63919C22semidirect
40. C4×#627C22semidirect
41. #63915C22semidirect
42. #63914C22semidirect
43. #63902C22semidirect
44. C4×#625C22semidirect
45. #63898C22semidirect
46. #63878C22semidirect
47. C4×D3×Dic3C22semidirect
48. #63873C22semidirect
49. #63872C22semidirect
50. #63870C22semidirect
51. #63863C22semidirect
52. #63862C22semidirect
53. #63855C22semidirect
54. #63843C22semidirect
55. #63838C22semidirect
59. #5791D3semidirect
195. C2×C32×C4#41semidirect
204. C2×C3⋊Dic3#41semidirect
405. C2×C3×C4#237semidirect
527. C32#3444semidirect
556. C2×C4#3805semidirect
589. C3#86018semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C3×#57912
#105955012
#105950502
#105950332
#105950322
#105949652
#105949632
#105949582
#105949292
C4×#38052
#105948102
#860183