Finite Group Databasebeta

← #76765

Subgroups — #76765

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×#938C211yesmaximal, characteristic, complemented
3C2×#937C211yesmaximal, characteristic, complemented
4C2×#937C211yesmaximal, characteristic, complemented
5C2×#884C211yesmaximal, characteristic, complemented
6C2×#882C211yesmaximal, characteristic, complemented
7C3×#392C211yesmaximal, characteristic, complemented
8#5223C211yesmaximal, characteristic, complemented
9#5223C211yesmaximal, characteristic, complemented
10#4961C211yesmaximal, characteristic, complemented
11#4960C211yesmaximal, characteristic, complemented
12#4959C211yesmaximal, characteristic, complemented
13#4944C211yesmaximal, characteristic, complemented
14#4670C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2669—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C22×C3×D4C2211yescharacteristic, complemented
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C22×#67C2211yescharacteristic
25C22×#67C2211yescharacteristic
26C22×#67C2211yescharacteristic, complemented
27C22×#67C2211yescharacteristic, complemented
28C22×D12C2211yescharacteristic
29C22×D12C2211yescharacteristic
30C22×C4×D3C2211yescharacteristic, complemented
31C2×C3×C22⋊C4C2211yescharacteristic
32C2×C3×C22⋊C4C2211yescharacteristic, complemented
33C2×C3×C22⋊C4C2211yescharacteristic, complemented
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36C2×#217C2211yescharacteristic, complemented
37C2×#217C2211yescharacteristic, complemented
38#940—24no—
39#938—24no—
40#937—24no—
41#937—24no—
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×(C2×D3)⋊C4C2211yescharacteristic
46C2×(C2×D3)⋊C4C2211yescharacteristic
47C2×(C2×D3)⋊C4C2211yescharacteristic
48C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C4⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C4×Dic3C2211yescharacteristic, complemented
52#884—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#394—31no—
66#392—31no—
67#392—31no—
68#392—31no—
69#392D311yescharacteristic, complemented
70#388—31no—
71#388—31no—
72#386—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C24×C3C2311yescharacteristic
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—22no—
79C23×D3—41no—
80C23×D3—41no—
81C23×D3—41no—
82C23×D3—41no—
83C23×D3C2311yescharacteristic
84C23×D3C2311yescharacteristic
85C23×D3C2311yescharacteristic
86C2×C3×D4—22no—
87C2×C3×D4—22no—
88C2×C3×D4—22no—
89C2×C3×D4—22no—
90C2×C3×D4—41no—
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
98C22×C3×C4C2311yescharacteristic
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—22no—
111C2×#67—22no—
112C2×#67—41no—
113C2×#67—41no—
114C2×#67—41no—
115C2×#67—41no—
116C2×#67—41no—
117C2×#67—41no—
118C2×#67—41no—
119C2×#67—41no—
120C22×Dic3C2311yescharacteristic
121C22×Dic3C2311yescharacteristic
122C22×Dic3C2311yescharacteristic
123C22×Dic3C2311yescharacteristic
124C22×Dic3C2311yescharacteristic
125C2×D12—22no—
126C2×D12—22no—
127C2×D12—41no—
128C2×D12—41no—
129C2×D12—41no—
130C2×D12D414yescomplemented
131C2×C4×D3—22no—
132C2×C4×D3—22no—
133C2×C4×D3—41no—
134C3×C22⋊C4—22no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—41no—
137#217—22no—
138#217—22no—
139#217—41no—
140#217D414yescomplemented
141(C2×D3)⋊C4—22no—
142(C2×D3)⋊C4—22no—
143(C2×D3)⋊C4—22no—
144(C2×D3)⋊C4—22no—
145(C2×D3)⋊C4—22no—
146(C2×D3)⋊C4—41no—
147(C2×D3)⋊C4D414yescomplemented
148C4⋊Dic3—22no—
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×D4C2×D311yescharacteristic
162C22×D4C2×D311yescharacteristic
163C22×D4C2×D311yescharacteristic, complemented
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⋊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, 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×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3C2×D412yes—
213C23×C3C2411yescharacteristic
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—
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×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4C2×D412yes—
256C2×C3×C4C2×D412yes—
257#67—44no—
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×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3C2×D412yes—
277C2×Dic3C2×D412yes—
278C2×Dic3C2×D412yes—
279D12—44no—
280D12—44no—
281C4×D3—44no—
282C24—31no—
283C24—31no—
284C24—31no—
285C24—62no—
286C24—62no—
287C24—62no—
288C24—121no—
289C24—121no—
290C24—121no—
291C24—121no—
292C24C22×D311yescharacteristic
293C24C22×D311yescharacteristic
294C24C22×D311yescharacteristic
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—34no—
300C2×D4—41no—
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—62no—
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—62no—
337C22×C4—62no—
338C22×C4—121no—
339C22×C4C22×D311yescharacteristic
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—34no—
349C22⋊C4—41no—
350C22⋊C4—62no—
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×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3C22×D411yescharacteristic
382C22×C3C22×D411yescharacteristic
383C22×C3C22×D411yescharacteristic
384C22×C3H(5,𝔽2)11yescharacteristic
385C22×C3H(5,𝔽2)11yescharacteristic
386C22×C3H(5,𝔽2)11yescharacteristic
387C22×C3H(5,𝔽2)11yescharacteristic
388C2×D3—22no—
389C2×D3—22no—
390C2×D3—22no—
391C2×D3—22no—
392C2×D3—22no—
393C2×D3—22no—
394C2×D3—22no—
395C2×D3—22no—
396C2×D3—22no—
397C2×D3—416no—
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—
414Dic3—22no—
415Dic3—22no—
416Dic3—22no—
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—32no—
440C23—32no—
441C23—32no—
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—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—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—32no—
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×C4D3×D412yes—
508C2×C4D3×D412yes—
509C2×C3—42no—
510C2×C3—81no—
511C2×C3—81no—
512C2×C3#53411yescharacteristic
513C2×C3#53511yescharacteristic
514C2×C3#53511yescharacteristic
515C2×C3D4211yescharacteristic
516C2×C3D4211yescharacteristic
517C2×C3D4211yescharacteristic
518C2×C3#56011yescharacteristic
519D3—42no—
520D3—42no—
521D3—42no—
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—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—62no—
544C22—62no—
545C22—62no—
546C22—62no—
547C22—62no—
548C22—62no—
549C22—62no—
550C22—62no—
551C22—62no—
552C22—1216no—
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#100411yescharacteristic
570C22#100411yescharacteristic
571C22#100911yescharacteristic
572C4—22no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—62no—
577C4—62no—
578C4—62no—
579C4—121no—
580C4—121no—
581C3#266911yescharacteristic, complemented, Sylow
582C2—42no—
583C2—81no—
584C2—81no—
585C2—122no—
586C2—122no—
587C2—122no—
588C2#558911yescharacteristic
589C2#559011yescharacteristic
590C2#559211yescharacteristic
591C2#560711yescharacteristic
592C2#560911yescharacteristic
593C2#562011yescharacteristic
594C2#571711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#392C2
hypercenter#392D3
hypocenterC3#2669
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#940C2semidirect
2. C2×#938C2semidirect
3. C2×#937C2semidirect
4. C2×#937C2semidirect
5. C2×#884C2semidirect
6. C2×#882C2semidirect
7. C3×#392C2semidirect
8. #5223C2semidirect
9. #5223C2semidirect
10. #4961C2semidirect
11. #4960C2semidirect
12. #4959C2semidirect
13. #4944C2semidirect
14. #4670C2semidirect
15. #4665C2semidirect
20. C22×C3×D4C22semidirect
26. C22×#67C22semidirect
27. C22×#67C22semidirect
30. C22×C4×D3C22semidirect
32. C2×C3×C22⋊C4C22semidirect
33. C2×C3×C22⋊C4C22semidirect
36. C2×#217C22semidirect
37. C2×#217C22semidirect
48. C2×(C2×D3)⋊C4C22semidirect
49. C2×C4⋊Dic3C22semidirect
50. C2×Dic3⋊C4C22semidirect
51. C2×C4×Dic3C22semidirect
54. C3×#95C22semidirect
55. C3⋊#95C22semidirect
56. C3⋊#95C22semidirect
57. C3⋊#95C22semidirect
69. #392D3semidirect
130. C2×D12D4semidirect
140. #217D4semidirect
147. (C2×D3)⋊C4D4semidirect
163. C22×D4C2×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×#9382
C2×#9372
C2×#8842
C2×#8822
C3×#3922
#52232
#49612
#49602
#49592
#49442
#46702
#46652
#26693