Finite Group Databasebeta

← #82609

Subgroups — #82609

Order 384.

932 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×C3×#120C211yesmaximal, characteristic, complemented
2C2×#953C211yesmaximal, characteristic, complemented
3C2×#953C211yesmaximal, characteristic, complemented
4C2×#940C211yesmaximal, characteristic, complemented
5C2×#938C211yesmaximal, characteristic, complemented
6C2×#884C211yesmaximal, characteristic, complemented
7#5223C211yesmaximal, characteristic, complemented
8#5223C211yesmaximal, characteristic, complemented
9#5223C211yesmaximal, characteristic, complemented
10#5222C211yesmaximal, characteristic, complemented
11#4961C211yesmaximal, characteristic, complemented
12#4960C211yesmaximal, characteristic, complemented
13#4956C211yesmaximal, characteristic, complemented
14#4951C211yesmaximal, characteristic, complemented
15#4945C211yesmaximal, characteristic, complemented
16#2669—31nomaximal, Sylow
17C25×C3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C22×C3×D4C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C22×#67C2211yescharacteristic
25C22×#67C2211yescharacteristic
26C22×#67C2211yescharacteristic
27C22×#67C2211yescharacteristic, complemented
28C22×#67C2211yescharacteristic, complemented
29C22×D12C2211yescharacteristic, complemented
30C22×C4×D3C2211yescharacteristic, complemented
31C3×#120—24no—
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic
35#953—24no—
36#953—24no—
37C2×#217C2211yescharacteristic
38C2×#217C2211yescharacteristic
39C2×#217C2211yescharacteristic
40C2×#217C2211yescharacteristic
41C2×#217C2211yescharacteristic
42C2×#217C2211yescharacteristic
43C2×#217C2211yescharacteristic, complemented
44C2×#217C2211yescharacteristic, complemented
45#940—24no—
46#938—24no—
47C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C4⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊C4C2211yescharacteristic, complemented
52C2×C4×Dic3C2211yescharacteristic, complemented
53#884—24no—
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C3⋊#95C2211yescharacteristic, complemented
57C3⋊#95C2211yescharacteristic, complemented
58C2×#127—31no—
59C2×#121—31no—
60C2×#121—31no—
61C2×#120—31no—
62C2×#120—31no—
63C2×#120D311yescharacteristic, complemented
64#394—31no—
65#394—31no—
66#392—31no—
67#392—31no—
68#392—31no—
69#392—31no—
70#388—31no—
71#388—31no—
72#386—31no—
73C24×C3—22no—
74C24×C3—22no—
75C24×C3—22no—
76C24×C3—41no—
77C24×C3—41no—
78C24×C3—41no—
79C24×C3—41no—
80C24×C3C2311yescharacteristic
81C24×C3C2311yescharacteristic
82C24×C3C2311yescharacteristic
83C24×C3C2311yescharacteristic
84C23×D3C2311yescharacteristic
85C23×D3C2311yescharacteristic
86C2×C3×D4—22no—
87C2×C3×D4—22no—
88C2×C3×D4—22no—
89C2×C3×D4—22no—
90C2×C3×D4—22no—
91C2×C3×D4—41no—
92C2×C3×D4—41no—
93C2×C3×D4—41no—
94C2×C3×D4—41no—
95C22×C3×C4C2311yescharacteristic
96C22×C3×C4C2311yescharacteristic
97C22×C3×C4C2311yescharacteristic
98C2×#67—22no—
99C2×#67—22no—
100C2×#67—22no—
101C2×#67—22no—
102C2×#67—22no—
103C2×#67—22no—
104C2×#67—22no—
105C2×#67—22no—
106C2×#67—22no—
107C2×#67—22no—
108C2×#67—22no—
109C2×#67—22no—
110C2×#67—41no—
111C2×#67—41no—
112C2×#67—41no—
113C2×#67—41no—
114C2×#67—41no—
115C2×#67—41no—
116C2×#67—41no—
117C2×#67—41no—
118C2×#67—41no—
119C2×#67—41no—
120C2×#67—41no—
121C2×#67D414yescomplemented
122C22×Dic3C2311yescharacteristic
123C22×Dic3C2311yescharacteristic
124C22×Dic3C2311yescharacteristic
125C22×Dic3C2311yescharacteristic
126C22×Dic3C2311yescharacteristic
127C22×Dic3C2311yescharacteristic
128C2×D12—22no—
129C2×D12—22no—
130C2×D12—41no—
131C2×C4×D3—22no—
132C2×C4×D3—22no—
133C2×C4×D3—41no—
134C3×C22⋊C4—22no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4D414yescomplemented
137#217—22no—
138#217—22no—
139#217—22no—
140#217—22no—
141#217—22no—
142#217—22no—
143#217—41no—
144#217D414yescomplemented
145(C2×D3)⋊C4—22no—
146(C2×D3)⋊C4—41no—
147(C2×D3)⋊C4—41no—
148C4⋊Dic3—22no—
149Dic3⋊C4—22no—
150C4×Dic3—22no—
151C25C2×D311yescharacteristic
152C22×D4—31no—
153C22×D4—31no—
154C22×D4—31no—
155C22×D4—31no—
156C22×D4—31no—
157C22×D4—31no—
158C22×D4—31no—
159C22×D4—31no—
160C22×D4—31no—
161C22×D4C2×D311yescharacteristic
162C22×D4C2×D311yescharacteristic
163C22×D4C2×D311yescharacteristic
164C23×C4—31no—
165#127—64no—
166#121—64no—
167#121—64no—
168#120—24no—
169#120—64no—
170#120—64no—
171C2×C4⋊C4—31no—
172C2×C4⋊C4—31no—
173C2×C22⋊C4—31no—
174C2×C22⋊C4—31no—
175C2×C22⋊C4—31no—
176C2×C22⋊C4—31no—
177C2×C22⋊C4—31no—
178C2×C22⋊C4—31no—
179C2×C22⋊C4—31no—
180C2×C22⋊C4—31no—
181C2×C22⋊C4—31no—
182C2×C22⋊C4—31no—
183C2×C22⋊C4—31no—
184C2×C22⋊C4C2×D311yescharacteristic
185C2×C22⋊C4C2×D311yescharacteristic
186C2×C22⋊C4C2×D311yescharacteristic
187C2×C42—31no—
188#95—31no—
189#95—31no—
190#95—31no—
191#95—31no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—21no—
215C23×C3—21no—
216C23×C3—21no—
217C23×C3—44no—
218C23×C3—44no—
219C23×C3—44no—
220C23×C3—44no—
221C23×C3—44no—
222C23×C3—44no—
223C23×C3—44no—
224C23×C3C2×D412yes—
225C23×C3C2×D412yes—
226C23×C3C2×D412yes—
227C23×C3C2411yescharacteristic
228C22×D3—21no—
229C22×D3—21no—
230C22×D3—21no—
231C22×D3—21no—
232C22×D3—21no—
233C22×D3—21no—
234C22×D3—21no—
235C22×D3—21no—
236C22×D3—21no—
237C22×D3—21no—
238C22×D3—21no—
239C22×D3—21no—
240C22×D3—21no—
241C22×D3C2×D412yes—
242C3×D4—44no—
243C3×D4—44no—
244C3×D4—44no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4C2×D412yes—
253C2×C3×C4C2×D412yes—
254#67—44no—
255#67—44no—
256#67—44no—
257#67—44no—
258#67—44no—
259#67—44no—
260#67—44no—
261#67—44no—
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3C2×D412yes—
278C2×Dic3C2×D412yes—
279C2×Dic3C2×D412yes—
280D12—44no—
281C4×D3—44no—
282C24—22no—
283C24—22no—
284C24—22no—
285C24—31no—
286C24—31no—
287C24—41no—
288C24—41no—
289C24—41no—
290C24—41no—
291C24C22×D311yescharacteristic
292C24C22×D311yescharacteristic
293C24C22×D311yescharacteristic
294C24C22×D311yescharacteristic
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—34no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—62no—
306C2×D4—62no—
307C2×D4—62no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4—62no—
311C2×D4—62no—
312C2×D4—62no—
313C2×D4—62no—
314C2×D4—62no—
315C2×D4—62no—
316C2×D4—62no—
317C2×D4—62no—
318C2×D4—62no—
319C2×D4—121no—
320C2×D4—121no—
321C2×D4—121no—
322C2×D4—121no—
323C2×D4—121no—
324C2×D4—121no—
325C2×D4—121no—
326C2×D4—121no—
327C2×D4—121no—
328C2×D4—121no—
329C2×D4—121no—
330C2×D4—121no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—62no—
338C22×C4—62no—
339C22×C4—121no—
340C22×C4C22×D311yescharacteristic
341C22×C4C22×D311yescharacteristic
342C22×C4C22×D311yescharacteristic
343C4⋊C4—62no—
344C4⋊C4—62no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—34no—
348C22⋊C4—62no—
349C22⋊C4—62no—
350C22⋊C4—62no—
351C22⋊C4—62no—
352C22⋊C4—62no—
353C22⋊C4—62no—
354C22⋊C4—62no—
355C22⋊C4—121no—
356C22⋊C4—121no—
357C22⋊C4—121no—
358C22⋊C4#6714yescomplemented
359C42—62no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—416no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3C22×D411yescharacteristic
390C22×C3C22×D411yescharacteristic
391C22×C3C22×D411yescharacteristic
392C22×C3H(5,𝔽2)11yescharacteristic
393C22×C3H(5,𝔽2)11yescharacteristic
394C22×C3H(5,𝔽2)11yescharacteristic
395C22×C3H(5,𝔽2)11yescharacteristic
396C2×D3—22no—
397C2×D3—22no—
398C2×D3—22no—
399C2×D3—41no—
400C2×D3—41no—
401C2×D3—41no—
402C2×D3—41no—
403C2×D3—41no—
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—41no—
408C2×D3—41no—
409C2×D3—41no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—41no—
413Dic3—22no—
414Dic3—22no—
415Dic3—22no—
416Dic3—41no—
417Dic3—41no—
418Dic3—41no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—32no—
445C23—44no—
446C23—44no—
447C23—44no—
448C23—44no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23—61no—
453C23—61no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23—61no—
458C23—61no—
459C23—61no—
460C23—61no—
461C23—61no—
462C23—61no—
463C23—61no—
464C23—61no—
465C23D3×D412yes—
466C23D3×D412yes—
467C23C2×#6712yes—
468C23C23×D311yescharacteristic
469D4—44no—
470D4—44no—
471D4—44no—
472D4—124no—
473D4—124no—
474D4—124no—
475D4—124no—
476D4—124no—
477D4—124no—
478D4—124no—
479D4—124no—
480D4—124no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—124no—
507C2×C4C2×#6712yes—
508C2×C4C2×#6712yes—
509C2×C3—42no—
510C2×C3—42no—
511C2×C3—42no—
512C2×C3—81no—
513C2×C3#53411yescharacteristic
514C2×C3#53511yescharacteristic
515C2×C3#53511yescharacteristic
516C2×C3D4211yescharacteristic
517C2×C3D4211yescharacteristic
518C2×C3D4211yescharacteristic
519C2×C3#56011yescharacteristic
520D3—42no—
521D3—81no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—416no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—62no—
552C22—62no—
553C22—62no—
554C22—121no—
555C22—121no—
556C22—121no—
557C22—121no—
558C22—121no—
559C22—121no—
560C22—121no—
561C22—121no—
562C22—121no—
563C22—121no—
564C22—121no—
565C22C2×D3×D411yescharacteristic
566C22C2×D3×D411yescharacteristic
567C22#100411yescharacteristic
568C22#100411yescharacteristic
569C22#100411yescharacteristic
570C22#100411yescharacteristic
571C22C22×#6711yescharacteristic
572C4—22no—
573C4—22no—
574C4—41no—
575C4—62no—
576C4—62no—
577C4—62no—
578C4—121no—
579C4—121no—
580C4—121no—
581C3#266911yescharacteristic, complemented, Sylow
582C2—42no—
583C2—42no—
584C2—42no—
585C2—81no—
586C2—122no—
587C2—241no—
588C2#558911yescharacteristic
589C2#559011yescharacteristic
590C2#559211yescharacteristic
591C2#559511yescharacteristic
592C2D4×#6711yescharacteristic
593C2D4×#6711yescharacteristic
594C2#580511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#120C2
hypercenterC2×#120D3
hypocenterC3#2669
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C3×#120C2semidirect
2. C2×#953C2semidirect
3. C2×#953C2semidirect
4. C2×#940C2semidirect
5. C2×#938C2semidirect
6. C2×#884C2semidirect
7. #5223C2semidirect
8. #5223C2semidirect
9. #5223C2semidirect
10. #5222C2semidirect
11. #4961C2semidirect
12. #4960C2semidirect
13. #4956C2semidirect
14. #4951C2semidirect
15. #4945C2semidirect
27. C22×#67C22semidirect
28. C22×#67C22semidirect
29. C22×D12C22semidirect
30. C22×C4×D3C22semidirect
43. C2×#217C22semidirect
44. C2×#217C22semidirect
47. C2×(C2×D3)⋊C4C22semidirect
48. C2×(C2×D3)⋊C4C22semidirect
49. C2×(C2×D3)⋊C4C22semidirect
50. C2×C4⋊Dic3C22semidirect
51. C2×Dic3⋊C4C22semidirect
52. C2×C4×Dic3C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
56. C3⋊#95C22semidirect
57. C3⋊#95C22semidirect
63. C2×#120D3semidirect
121. C2×#67D4semidirect
136. C3×C22⋊C4D4semidirect
144. #217D4semidirect
358. C22⋊C4#67semidirect
581. C3#2669semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1202
C2×#9532
C2×#9402
C2×#9382
C2×#8842
#52232
#52222
#49612
#49602
#49562
#49512
#49452
#26693