Finite Group Databasebeta

← #11900911

Subgroups — #11900911

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
1C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×C4×#235C212yesmaximal, complemented
3#10595050C211yesmaximal, characteristic, complemented
4#10595034C212yesmaximal, complemented
5#10595033C214yesmaximal, complemented
6#10595032C211yesmaximal, characteristic, complemented
7#10595016C214yesmaximal, complemented
8#10593980C214yesmaximal, complemented
9#10593972C212yesmaximal, complemented
10C4×#3798C214yesmaximal, complemented
11#10593882C212yesmaximal, complemented
12#10593875C214yesmaximal, complemented
13#85836—32nomaximal
14C22×C4×C3⋊D3C2212yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#235C2212yes—
17C2×#3798C2214yes—
18C2×C32×C42C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2212yes—
21C42×C3⋊D3C2212yes—
22C42×C3⋊D3C2212yes—
23C42×C3⋊D3C2212yes—
24C42×C3⋊D3C2212yes—
25C3×C4×#67C2218yes—
26C3×#926C2212yes—
27C3×C4×D12C2214yescomplemented
28C3×#872C2214yescomplemented
29C3×C42×D3C2214yescomplemented
30C3×C4×Dic6C2214yescomplemented
31#63982C2214yes—
32#63981C2214yes—
33#63980C2214yes—
34#63962C2214yes—
35#63919C2212yescomplemented
36C4×#627C2214yescomplemented
37C4×#627C2214yescomplemented
38#63916C2214yes—
39#63915C2214yescomplemented
40#63914C2211yescharacteristic, complemented
41#63912C2214yes—
42C4×#626C2218yes—
43C4×#626C2218yes—
44C4×#625C2214yescomplemented
45C4×#625C2214yescomplemented
46#63874C2214yes—
47#63873C2211yescharacteristic, complemented
48#63872C2212yescomplemented
49#63871C2214yes—
50#63870C2214yescomplemented
51#63865C2214yes—
52#63863C2212yescomplemented
53#63862C2218yescomplemented
54#63855C2218yescomplemented
55#63853C2218yes—
56C3×C4×#41—32no—
57#5832—32no—
58#5828—32no—
59#5580—34no—
60#5578—34no—
61#5557—34no—
62#5548—34no—
63#5547—38no—
64#5538—38no—
65#5528—38no—
66#5524—32no—
67#5517—32no—
68C4×#235—38no—
69C4×#235D312yescomplemented
70C2×C42×D3—32no—
71C2×C42×D3—61no—
72C23×C3⋊D3C2311yescharacteristic
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2312yes—
77C2×C4×C3⋊D3—24no—
78C2×C4×C3⋊D3—28no—
79C2×C4×C3⋊D3C2312yes—
80C2×C4×C3⋊D3C2312yes—
81C2×C4×C3⋊D3C2312yes—
82C2×C4×C3⋊D3C2312yes—
83C2×C4×C3⋊D3C2312yes—
84C2×C4×C3⋊D3C2312yes—
85C2×C3×#67C2314yes—
86C3×#235—28no—
87C2×C3×D12C2312yes—
88C2×C3×C4×D3C2318yes—
89C2×C3×C4×D3C2314yes—
90C2×C3×Dic6C2312yes—
91C2×#627C2314yes—
92C2×#626C2318yes—
93C2×#625C2314yes—
94#3798—216no—
95C32×C42C2312yes—
96C32×C42C2311yescharacteristic
97C32×C42C2311yescharacteristic
98C4×C3⋊Dic3C2312yes—
99C4×C3⋊Dic3C2312yes—
100C4×C3⋊Dic3C2311yescharacteristic
101C4×C3⋊Dic3C2312yes—
102C4×C3⋊Dic3C2311yescharacteristic
103C4×C3⋊Dic3C2312yes—
104C4×C3⋊Dic3C2312yes—
105C3×#217C2314yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×C4⋊Dic3C2314yes—
108C3×Dic3⋊C4C2318yes—
109C3×C4×Dic3C2314yes—
110C3×C4×Dic3C2318yes—
111#3724C2314yes—
112#3724C2314yes—
113Dic3⋊Dic3C2318yes—
114Dic3⋊Dic3C2318yes—
115#3722C2318yes—
116(C2×D3)⋊Dic3C2318yes—
117(C2×D3)⋊Dic3C2318yes—
118#3444—91noSylow
119C2×C3×#41—32no—
120C2×#235—38no—
121C2×#235C2×D312yes—
122C22×C4×D3—32no—
123C22×C4×D3—34no—
124C22×C4×D3—62no—
125C22×C4×D3—61no—
126C3×C4×Q8—34no—
127C3×C4×D4—38no—
128C3×C4×D4—34no—
129C3×#117—32no—
130C3×#117—34no—
131C2×C3×C42—21no—
132C2×C3×C42—34no—
133C2×C3×C42C2×D312yes—
134#947—32no—
135#946—34no—
136#944—32no—
137#940—32no—
138#939—38no—
139#938—34no—
140#937—34no—
141#936—32no—
142#935—34no—
143C4×#67—38no—
144C4×#67—38no—
145C4×#67—38no—
146C4×#67—38no—
147C4×#67C2×D318yes—
148#926—38no—
149#926C2×D312yes—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—34no—
152C2×C4×Dic3—62no—
153C2×C4×Dic3—61no—
154#898—38no—
155#897—34no—
156#896—38no—
157#895—34no—
158#894—38no—
159#890—34no—
160#889—38no—
161#888—34no—
162#886—34no—
163#885—38no—
164#884—38no—
165#883—38no—
166#882—34no—
167#879—38no—
168#878—38no—
169C4×D12—38no—
170C4×D12—38no—
171C4×D12C2×D314yescomplemented
172#872—38no—
173#872—38no—
174#872C2×D314yescomplemented
175C42×D3—34no—
176C42×D3—34no—
177C42×D3—34no—
178C42×D3—34no—
179C42×D3—62no—
180C42×D3—62no—
181C42×D3—62no—
182C42×D3—62no—
183C42×D3C2×D314yescomplemented
184C4×Dic6—38no—
185C4×Dic6—38no—
186C4×Dic6C2×D314yescomplemented
187C23×C32C2411yescharacteristic
188C22×C3⋊D3—22no—
189C22×C3⋊D3—24no—
190C22×C3⋊D3C2412yes—
191C22×C3×D3C2414yes—
192C2×C32×C4—24no—
193C2×C32×C4#4114yescomplemented
194C2×C32×C4C2412yes—
195C2×C32×C4C2411yescharacteristic
196C2×C32×C4C2412yes—
197C2×C32×C4C2411yescharacteristic
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3C2412yes—
201C2×C3⋊Dic3C2412yes—
202C2×C3⋊Dic3C2412yes—
203C4×C3⋊D3—24no—
204C4×C3⋊D3—24no—
205C4×C3⋊D3—24no—
206C4×C3⋊D3—24no—
207C4×C3⋊D3—24no—
208C4×C3⋊D3#4118yescomplemented
209C3×#67—28no—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2418yes—
212C3×D12—24no—
213C3×C4×D3—216no—
214C3×C4×D3—28no—
215C3×Dic6—24no—
216#627—28no—
217#626—216no—
218#625—28no—
219#533—91no—
220#533—92no—
221#532—92no—
222#532—91no—
223#529—94no—
224#529—94no—
225#529—94no—
226#525—92no—
227#525—94no—
228C4×#41—32no—
229C4×#41—94no—
230C22×C42—91no—
231C23×D3—32no—
232C23×D3—61no—
233C3×#41—68no—
234C2×C3×Q8—32no—
235C2×C3×D4—34no—
236C2×C3×D4—32no—
237C22×C3×C4—22no—
238C22×C3×C4—21no—
239C22×C3×C4—38no—
240C22×C3×C4—34no—
241C22×C3×C4C22×D314yes—
242C22×C3×C4C22×D312yes—
243C2×#67—38no—
244C2×#67—38no—
245C2×#67C22×D314yes—
246C22×Dic3—34no—
247C22×Dic3—32no—
248C22×Dic3—62no—
249C22×Dic3—61no—
250#235—28no—
251#235—632no—
252C2×D12—38no—
253C2×D12C22×D312yes—
254C2×C4×D3—34no—
255C2×C4×D3—34no—
256C2×C4×D3—34no—
257C2×C4×D3—34no—
258C2×C4×D3—34no—
259C2×C4×D3—34no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3—616no—
267C2×C4×D3—616no—
268C2×C4×D3—68no—
269C2×C4×D3—68no—
270C2×C4×D3C22×D318yes—
271C2×C4×D3C22×D314yes—
272C2×Dic6—38no—
273C2×Dic6C22×D312yes—
274C3×C4⋊C4—34no—
275C3×C4⋊C4—38no—
276C3×C22⋊C4—34no—
277C3×C22⋊C4—38no—
278C3×C42—21no—
279C3×C42—22no—
280C3×C42—21no—
281C3×C42—34no—
282C3×C42—38no—
283C3×C42C22×D314yes—
284C3×C42C22×D312yes—
285C3×C42C22×D312yes—
286#217—38no—
287#217—38no—
288#217C22×D314yes—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4C22×D318yes—
294C4⋊Dic3—38no—
295C4⋊Dic3—38no—
296C4⋊Dic3C22×D314yes—
297Dic3⋊C4—38no—
298Dic3⋊C4—38no—
299Dic3⋊C4—38no—
300Dic3⋊C4—38no—
301Dic3⋊C4C22×D318yes—
302C4×Dic3—34no—
303C4×Dic3—34no—
304C4×Dic3—34no—
305C4×Dic3—34no—
306C4×Dic3—34no—
307C4×Dic3—32no—
308C4×Dic3—32no—
309C4×Dic3—62no—
310C4×Dic3—62no—
311C4×Dic3—62no—
312C4×Dic3—61no—
313C4×Dic3—62no—
314C4×Dic3—62no—
315C4×Dic3—61no—
316C4×Dic3C22×D314yes—
317C4×Dic3C22×D318yes—
318C22×C32—22no—
319C22×C32C2×#4112yes—
320C22×C32C2511yescharacteristic
321C2×C3⋊D3—28no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3C2×#4114yes—
325C2×C3×D3—28no—
326C2×C3×D3—24no—
327C32×C4—22no—
328C32×C4C2×#4112yes—
329C32×C4C2×#4112yes—
330C32×C4C2×#4114yes—
331C3⋊Dic3—22no—
332C3⋊Dic3—22no—
333C3⋊Dic3C2×#4114yes—
334C3×Dic3—28no—
335C3×Dic3—24no—
336C2×#41—32no—
337C2×#41—94no—
338C23×C4—92no—
339C23×C4—91no—
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—98no—
349#123—94no—
350C22⋊Q8—94no—
351C22⋊Q8—94no—
352C22⋊Q8—94no—
353#121—94no—
354#121—94no—
355#121—94no—
356#120—94no—
357C4×Q8—34no—
358C4×Q8—94no—
359C4×Q8—94no—
360C4×D4—38no—
361C4×D4—34no—
362C4×D4—98no—
363C4×D4—98no—
364C4×D4—94no—
365C4×D4—94no—
366#117—32no—
367#117—34no—
368#117—94no—
369#117—98no—
370C2×C42—34no—
371C2×C42—92no—
372C2×C42—91no—
373C2×C42—92no—
374C2×C42—92no—
375C2×C42—92no—
376C2×C42—92no—
377C2×C42D3211yescharacteristic
378C23×C3—21no—
379C23×C3—34no—
380C23×C3C23×D312yes—
381C22×D3—34no—
382C22×D3—62no—
383C22×D3—68no—
384C22×D3—68no—
385C22×D3—64no—
386C22×D3—64no—
387C22×D3C23×D314yes—
388C3×Q8—64no—
389C3×D4—68no—
390C3×D4—64no—
391C2×C3×C4—28no—
392C2×C3×C4—28no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—24no—
398C2×C3×C4—34no—
399C2×C3×C4—38no—
400C2×C3×C4—68no—
401C2×C3×C4—616no—
402C2×C3×C4#23518yescomplemented
403C2×C3×C4C23×D314yes—
404C2×C3×C4C23×D312yes—
405C2×C3×C4C23×D312yes—
406C2×C3×C4C23×D314yes—
407#67—28no—
408#67—616no—
409#67—616no—
410C2×Dic3—34no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—68no—
417C2×Dic3—68no—
418C2×Dic3—64no—
419C2×Dic3—64no—
420C2×Dic3C23×D318yes—
421C2×Dic3C23×D314yes—
422D12—24no—
423D12—616no—
424C4×D3—28no—
425C4×D3—216no—
426C4×D3—316no—
427C4×D3—68no—
428C4×D3—68no—
429C4×D3—68no—
430C4×D3—68no—
431C4×D3—68no—
432C4×D3—68no—
433C4×D3—68no—
434C4×D3—68no—
435C4×D3—68no—
436C4×D3—68no—
437C4×D3—68no—
438Dic6—24no—
439Dic6—616no—
440C2×C32—22no—
441C2×C32C22×#4111yescharacteristic
442C2×C32C22×#4112yes—
443C3⋊D3—24no—
444C3×D3—44no—
445C24—91no—
446#41—68no—
447#41—1816no—
448C2×Q8—32no—
449C2×Q8—94no—
450C2×D4—34no—
451C2×D4—32no—
452C2×D4—98no—
453C2×D4—94no—
454C22×C4—34no—
455C22×C4—38no—
456C22×C4—92no—
457C22×C4—92no—
458C22×C4—91no—
459C22×C4—92no—
460C22×C4—92no—
461C22×C4—92no—
462C22×C4—92no—
463C22×C4—92no—
464C22×C4—188no—
465C22×C4—184no—
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—98no—
477C22⋊C4—98no—
478C22⋊C4—98no—
479C42—34no—
480C42—38no—
481C42—92no—
482C42—92no—
483C42—92no—
484C42—92no—
485C42—91no—
486C42—92no—
487C42—91no—
488C42C2×D3211yescharacteristic
489C42C2×D3212yes—
490C42C2×D3211yescharacteristic
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3—64no—
496C22×C3—68no—
497C22×C3C2×#23514yes—
498C22×C3C24×D312yes—
499C2×D3—24no—
500C2×D3—28no—
501C2×D3—38no—
502C2×D3—64no—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—616no—
506C2×D3—616no—
507C2×D3—64no—
508C2×D3—64no—
509C3×C4—24no—
510C3×C4—24no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—24no—
514C3×C4—64no—
515C3×C4—68no—
516C3×C4C2×#23514yes—
517C3×C4C2×#23514yes—
518C3×C4D3×#4118yes—
519Dic3—24no—
520Dic3—28no—
521Dic3—38no—
522Dic3—64no—
523Dic3—64no—
524Dic3—64no—
525Dic3—64no—
526Dic3—64no—
527C32#344411yescharacteristic, complemented, Sylow
528C23—34no—
529C23—92no—
530C23—184no—
531C23—182no—
532C23C22×D3211yescharacteristic
533Q8—64no—
534Q8—188no—
535D4—68no—
536D4—64no—
537D4—1816no—
538D4—188no—
539C2×C4—24no—
540C2×C4—38no—
541C2×C4—34no—
542C2×C4—68no—
543C2×C4—616no—
544C2×C4—92no—
545C2×C4—98no—
546C2×C4—92no—
547C2×C4—92no—
548C2×C4—184no—
549C2×C4—184no—
550C2×C4—184no—
551C2×C4—182no—
552C2×C4—184no—
553C2×C4—184no—
554C2×C4—184no—
555C2×C4#379814yescomplemented
556C2×C4C22×D3212yes—
557C2×C4C22×D3211yescharacteristic
558C2×C4C22×D3211yescharacteristic
559C2×C4C22×D3212yes—
560C2×C3—24no—
561C2×C3—24no—
562C2×C3—21no—
563C2×C3—22no—
564C2×C3—124no—
565C2×C3C22×#23512yes—
566C2×C3C2×D3×#4114yes—
567D3—44no—
568D3—68no—
569D3—68no—
570C22—22no—
571C22—64no—
572C22—68no—
573C22—94no—
574C22—188no—
575C22—182no—
576C22—182no—
577C22C2×#379812yes—
578C22C23×D3211yescharacteristic
579C4—22no—
580C4—64no—
581C4—68no—
582C4—94no—
583C4—182no—
584C4—182no—
585C4C2×#379812yes—
586C4C2×#379812yes—
587C4#6430614yes—
588C3—21no—
589C3#8583612yescomplemented
590C2—22no—
591C2—124no—
592C2—184no—
593C2C22×#379811yescharacteristic
594C2C2×#6430612yes—
subgroupG/H
centerC42C2×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C42×C3⋊D3C2semidirect
2. C3×C4×#235C2semidirect
3. #10595050C2semidirect
4. #10595034C2semidirect
5. #10595033C2semidirect
6. #10595032C2semidirect
7. #10595016C2semidirect
8. #10593980C2semidirect
9. #10593972C2semidirect
10. C4×#3798C2semidirect
11. #10593882C2semidirect
12. #10593875C2semidirect
27. C3×C4×D12C22semidirect
28. C3×#872C22semidirect
29. C3×C42×D3C22semidirect
30. C3×C4×Dic6C22semidirect
35. #63919C22semidirect
36. C4×#627C22semidirect
37. C4×#627C22semidirect
39. #63915C22semidirect
40. #63914C22semidirect
44. C4×#625C22semidirect
45. C4×#625C22semidirect
47. #63873C22semidirect
48. #63872C22semidirect
50. #63870C22semidirect
52. #63863C22semidirect
53. #63862C22semidirect
54. #63855C22semidirect
69. C4×#235D3semidirect
171. C4×D12C2×D3semidirect
174. #872C2×D3semidirect
183. C42×D3C2×D3semidirect
186. C4×Dic6C2×D3semidirect
193. C2×C32×C4#41semidirect
208. C4×C3⋊D3#41semidirect
402. C2×C3×C4#235semidirect
527. C32#3444semidirect
555. C2×C4#3798semidirect
589. C3#85836semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C3×C4×#2352
#105950502
#105950342
#105950332
#105950322
#105950162
#105939802
#105939722
C4×#37982
#105938822
#105938752
#858363