Finite Group Databasebeta

← #77128

Subgroups — #77128

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×#940C211yesmaximal, characteristic, complemented
2C2×#937C211yesmaximal, characteristic, complemented
3C2×#895C211yesmaximal, characteristic, complemented
4C2×#884C211yesmaximal, characteristic, complemented
5C2×#882C211yesmaximal, characteristic, complemented
6C2×#882C211yesmaximal, characteristic, complemented
7C3×#394C211yesmaximal, characteristic, complemented
8#4990C211yesmaximal, characteristic, complemented
9#4960C211yesmaximal, characteristic, complemented
10#4960C211yesmaximal, characteristic, complemented
11#4960C211yesmaximal, characteristic, complemented
12#4959C211yesmaximal, characteristic, complemented
13#4956C211yesmaximal, characteristic, complemented
14#4671C211yesmaximal, characteristic, complemented
15#4669C211yesmaximal, characteristic, complemented
16#2669—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic, complemented
24C22×#67C2211yescharacteristic, complemented
25C22×D12C2211yescharacteristic
26C22×D12C2211yescharacteristic
27C22×D12C2211yescharacteristic
28C22×D12C2211yescharacteristic
29C22×D12C2211yescharacteristic, complemented
30C22×C4×D3C2211yescharacteristic, complemented
31C2×C3×C4⋊C4C2211yescharacteristic, complemented
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic, complemented
35C2×C3×C22⋊C4C2211yescharacteristic, complemented
36C2×#217C2211yescharacteristic
37#940—24no—
38#937—24no—
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C4×Dic3C2211yescharacteristic, complemented
50#895—24no—
51#884—24no—
52#882—24no—
53#882—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×#120—31no—
64#394—31no—
65#394D311yescharacteristic, complemented
66#392—31no—
67#392—31no—
68#392—31no—
69#392—31no—
70#388—31no—
71#388—31no—
72#386—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—41no—
79C23×D3—41no—
80C23×D3—41no—
81C23×D3—41no—
82C23×D3C2311yescharacteristic
83C23×D3C2311yescharacteristic
84C23×D3C2311yescharacteristic
85C23×D3C2311yescharacteristic
86C2×C3×D4—22no—
87C2×C3×D4—22no—
88C2×C3×D4—41no—
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—22no—
98C2×#67—22no—
99C2×#67—22no—
100C2×#67—22no—
101C2×#67—22no—
102C2×#67—41no—
103C2×#67—41no—
104C2×#67—41no—
105C2×#67—41no—
106C2×#67—41no—
107C2×#67—41no—
108C2×#67—41no—
109C2×#67—41no—
110C2×#67—41no—
111C2×#67D414yescomplemented
112C22×Dic3C2311yescharacteristic
113C22×Dic3C2311yescharacteristic
114C22×Dic3C2311yescharacteristic
115C22×Dic3C2311yescharacteristic
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—22no—
119C2×D12—22no—
120C2×D12—22no—
121C2×D12—22no—
122C2×D12—22no—
123C2×D12—22no—
124C2×D12—22no—
125C2×D12—41no—
126C2×D12—41no—
127C2×D12—41no—
128C2×D12—41no—
129C2×D12—41no—
130C2×D12—41no—
131C2×C4×D3—22no—
132C2×C4×D3—22no—
133C2×C4×D3—41no—
134C3×C4⋊C4—22no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—22no—
138C3×C22⋊C4—41no—
139#217—22no—
140(C2×D3)⋊C4—22no—
141(C2×D3)⋊C4—22no—
142(C2×D3)⋊C4—22no—
143(C2×D3)⋊C4—22no—
144(C2×D3)⋊C4—22no—
145(C2×D3)⋊C4—41no—
146(C2×D3)⋊C4—41no—
147(C2×D3)⋊C4D414yescomplemented
148(C2×D3)⋊C4D414yescomplemented
149Dic3⋊C4—22no—
150C4×Dic3—22no—
151C25—31no—
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×D4—31no—
162C22×D4—31no—
163C22×D4C2×D311yescharacteristic
164C23×C4—31no—
165#127—64no—
166#121—64no—
167#121—64no—
168#120—64no—
169#120—64no—
170#120—64no—
171C2×C4⋊C4—31no—
172C2×C4⋊C4C2×D311yescharacteristic, complemented
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⋊C4C2×D311yescharacteristic
184C2×C22⋊C4C2×D311yescharacteristic
185C2×C22⋊C4C2×D311yescharacteristic, complemented
186C2×C22⋊C4C2×D311yescharacteristic, complemented
187C2×C42—31no—
188#95—31no—
189#95—31no—
190#95—31no—
191#95C2×D311yescharacteristic, complemented
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×C3C2×D412yes—
206C23×C3C2411yescharacteristic
207C22×D3—21no—
208C22×D3—21no—
209C22×D3—21no—
210C22×D3—21no—
211C22×D3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—21no—
216C22×D3—21no—
217C22×D3—21no—
218C22×D3—21no—
219C22×D3—21no—
220C22×D3—21no—
221C22×D3—21no—
222C22×D3—21no—
223C22×D3—21no—
224C22×D3—21no—
225C22×D3—21no—
226C22×D3—21no—
227C22×D3—21no—
228C22×D3—21no—
229C22×D3—21no—
230C22×D3—21no—
231C22×D3—21no—
232C22×D3—44no—
233C22×D3—44no—
234C22×D3—44no—
235C22×D3—44no—
236C22×D3—44no—
237C22×D3—44no—
238C22×D3—44no—
239C22×D3C2×D412yes—
240C22×D3C2×D412yes—
241C22×D3C2×D412yes—
242C3×D4—44no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
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×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4C2×D412yes—
257C2×C3×C4C2×D412yes—
258#67—44no—
259#67—44no—
260#67—44no—
261#67—44no—
262#67—44no—
263#67—44no—
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×Dic3C2×D412yes—
274C2×Dic3C2×D412yes—
275C2×Dic3C2×D412yes—
276D12—44no—
277D12—44no—
278D12—44no—
279D12—44no—
280D12—44no—
281C4×D3—44no—
282C24—31no—
283C24—31no—
284C24—31no—
285C24—31no—
286C24—62no—
287C24—62no—
288C24—62no—
289C24—121no—
290C24—121no—
291C24—121no—
292C24—121no—
293C24C22×D311yescharacteristic
294C24C22×D311yescharacteristic
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—34no—
298C2×D4—41no—
299C2×D4—62no—
300C2×D4—62no—
301C2×D4—62no—
302C2×D4—62no—
303C2×D4—62no—
304C2×D4—62no—
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—121no—
317C2×D4—121no—
318C2×D4—121no—
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—62no—
336C22×C4—62no—
337C22×C4—121no—
338C22×C4C22×D311yescharacteristic
339C22×C4C22×D311yescharacteristic
340C22×C4C22×D311yescharacteristic
341C22×C4C22×D311yescharacteristic
342C22×C4C22×D311yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—62no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—34no—
349C22⋊C4—34no—
350C22⋊C4—41no—
351C22⋊C4—62no—
352C22⋊C4—62no—
353C22⋊C4—62no—
354C22⋊C4—62no—
355C22⋊C4—62no—
356C22⋊C4—62no—
357C22⋊C4—121no—
358C22⋊C4—121no—
359C42—62no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3C22×D411yescharacteristic
375C22×C3C22×D411yescharacteristic
376C22×C3C22×D411yescharacteristic
377C22×C3H(5,𝔽2)11yescharacteristic
378C22×C3H(5,𝔽2)11yescharacteristic
379C22×C3H(5,𝔽2)11yescharacteristic
380C22×C3H(5,𝔽2)11yescharacteristic
381C2×D3—22no—
382C2×D3—22no—
383C2×D3—22no—
384C2×D3—22no—
385C2×D3—22no—
386C2×D3—22no—
387C2×D3—22no—
388C2×D3—22no—
389C2×D3—22no—
390C2×D3—416no—
391C2×D3—41no—
392C2×D3—41no—
393C2×D3—41no—
394C2×D3—41no—
395C2×D3—41no—
396C2×D3—41no—
397C2×D3—41no—
398C2×D3—41no—
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—
413C3×C4—41no—
414C3×C4—41no—
415Dic3—22no—
416Dic3—22no—
417Dic3—22no—
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—32no—
433C23—32no—
434C23—32no—
435C23—61no—
436C23—61no—
437C23—61no—
438C23—61no—
439C23—61no—
440C23—61no—
441C23—61no—
442C23—61no—
443C23—61no—
444C23—61no—
445C23—61no—
446C23—61no—
447C23—61no—
448C23—61no—
449C23—61no—
450C23—61no—
451C23—61no—
452C23—61no—
453C23—61no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23—61no—
458C23—61no—
459C23—61no—
460C23—124no—
461C23—124no—
462C23—124no—
463C23—124no—
464C23—124no—
465C23—124no—
466C23—124no—
467C23D3×D412yes—
468C23C23×D311yescharacteristic
469D4—44no—
470D4—124no—
471D4—124no—
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—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—32no—
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×C4D3×D412yes—
508C2×C4D3×D412yes—
509C2×C3—42no—
510C2×C3—81no—
511C2×C3#53411yescharacteristic
512C2×C3#53511yescharacteristic
513C2×C3#53511yescharacteristic
514C2×C3D4211yescharacteristic
515C2×C3D4211yescharacteristic
516C2×C3D4211yescharacteristic
517C2×C3#56011yescharacteristic
518D3—42no—
519D3—42no—
520D3—42no—
521D3—81no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—62no—
537C22—62no—
538C22—62no—
539C22—62no—
540C22—62no—
541C22—62no—
542C22—62no—
543C22—62no—
544C22—62no—
545C22—1216no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22—121no—
550C22—121no—
551C22—121no—
552C22—121no—
553C22—121no—
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
567C22C2×D3×D411yescharacteristic
568C22#100411yescharacteristic
569C22#100911yescharacteristic
570C22#100911yescharacteristic
571C22#100911yescharacteristic
572C4—22no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—62no—
578C4—62no—
579C4—62no—
580C4—121no—
581C3#266911yescharacteristic, complemented, Sylow
582C2—42no—
583C2—81no—
584C2—122no—
585C2—122no—
586C2—122no—
587C2—241no—
588C2#559011yescharacteristic
589C2#560711yescharacteristic
590C2#560911yescharacteristic
591C2#560911yescharacteristic
592C2#565311yescharacteristic
593C2#566611yescharacteristic
594C2#567411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#394C2
hypercenter#394D3
hypocenterC3#2669
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#940C2semidirect
2. C2×#937C2semidirect
3. C2×#895C2semidirect
4. C2×#884C2semidirect
5. C2×#882C2semidirect
6. C2×#882C2semidirect
7. C3×#394C2semidirect
8. #4990C2semidirect
9. #4960C2semidirect
10. #4960C2semidirect
11. #4960C2semidirect
12. #4959C2semidirect
13. #4956C2semidirect
14. #4671C2semidirect
15. #4669C2semidirect
23. C22×#67C22semidirect
24. C22×#67C22semidirect
29. C22×D12C22semidirect
30. C22×C4×D3C22semidirect
31. C2×C3×C4⋊C4C22semidirect
34. C2×C3×C22⋊C4C22semidirect
35. C2×C3×C22⋊C4C22semidirect
45. C2×(C2×D3)⋊C4C22semidirect
46. C2×(C2×D3)⋊C4C22semidirect
47. C2×(C2×D3)⋊C4C22semidirect
48. C2×Dic3⋊C4C22semidirect
49. C2×C4×Dic3C22semidirect
54. C3×#95C22semidirect
55. C3⋊#95C22semidirect
56. C3⋊#95C22semidirect
57. C3⋊#95C22semidirect
65. #394D3semidirect
111. C2×#67D4semidirect
147. (C2×D3)⋊C4D4semidirect
148. (C2×D3)⋊C4D4semidirect
172. C2×C4⋊C4C2×D3semidirect
185. C2×C22⋊C4C2×D3semidirect
186. C2×C22⋊C4C2×D3semidirect
191. #95C2×D3semidirect
581. C3#2669semidirect

Maximal subgroups

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

subgroupindex
C2×#9402
C2×#9372
C2×#8952
C2×#8842
C2×#8822
C3×#3942
#49902
#49602
#49592
#49562
#46712
#46692
#26693