Finite Group Databasebeta

← #74878

Subgroups — #74878

Order 384.

1252 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D4C211yesmaximal, characteristic
2C2×C4×#67C211yesmaximal, characteristic, complemented
3C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#67⋊C4C211yesmaximal, characteristic, complemented
5C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#386C211yesmaximal, characteristic, complemented
7#5220C211yesmaximal, characteristic, complemented
8#4957C211yesmaximal, characteristic, complemented
9#4957C211yesmaximal, characteristic, complemented
10#4955C211yesmaximal, characteristic, complemented
11#4955C211yesmaximal, characteristic, complemented
12#4667C211yesmaximal, characteristic, complemented
13#4666C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16D4×C22⋊C4—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C24×D3C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C23×C3×C4C2211yescharacteristic, complemented
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C23×Dic3C2211yescharacteristic, complemented
24C2×D3×D4—24no—
25C2×D3×D4—24no—
26C2×D3×D4C418yescomplemented
27C22×D12C2211yescharacteristic
28C22×C4×D3C2211yescharacteristic
29C22×C4×D3C2211yescharacteristic, complemented
30C22×C4×D3C2211yescharacteristic, complemented
31C2×C3×C22⋊C4C2211yescharacteristic, complemented
32C2×C3×C22⋊C4C2211yescharacteristic, complemented
33C2×C3×C22⋊C4C2211yescharacteristic, complemented
34C2×#217C2211yescharacteristic, complemented
35C2×#217C2211yescharacteristic, complemented
36C2×#217C2211yescharacteristic, complemented
37C4×#67—24no—
38C2×(C2×D3)⋊C4—24no—
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×Dic3⋊C4C2211yescharacteristic, complemented
50C2×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C4×Dic3C2211yescharacteristic, complemented
52C2×C4×Dic3C2211yescharacteristic, complemented
53#67⋊C4—24no—
54D3×C22⋊C4—24no—
55C3×#95C2211yescharacteristic, complemented
56C3×#95C2211yescharacteristic, complemented
57C3⋊#95C2211yescharacteristic, complemented
58C3⋊#95C2211yescharacteristic, complemented
59C23×D4—31no—
60C2×C4×D4—31no—
61C2×C4×D4—31no—
62C22×C22⋊C4—31no—
63C22×C22⋊C4—31no—
64#390—31no—
65#390—31no—
66#386—31no—
67#386—31no—
68#386—31no—
69#386D311yescharacteristic, complemented
70#380—31no—
71#379—31no—
72#379—31no—
73C4×C22⋊C4—31no—
74C24×C3C2311yescharacteristic
75C24×C3C2311yescharacteristic
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—22no—
79C23×D3—22no—
80C23×D3—22no—
81C23×D3—22no—
82C23×D3—22no—
83C23×D3—22no—
84C23×D3—41no—
85C23×D3—41no—
86C23×D3—41no—
87C23×D3—41no—
88C23×D3C2×C414yescomplemented
89C23×D3C2×C414yescomplemented
90C23×D3C2311yescharacteristic
91C23×D3C2311yescharacteristic
92C23×D3C2311yescharacteristic
93C2×C3×D4—22no—
94C2×C3×D4—22no—
95C2×C3×D4C2×C414yescomplemented
96C22×C3×C4—22no—
97C22×C3×C4—22no—
98C22×C3×C4—41no—
99C22×C3×C4C2311yescharacteristic
100C22×C3×C4C2311yescharacteristic
101C22×C3×C4C2311yescharacteristic
102C22×C3×C4C2311yescharacteristic
103C22×C3×C4C2311yescharacteristic
104C2×#67—22no—
105C2×#67—22no—
106C2×#67C2×C414yes—
107C2×#67C2×C414yescomplemented
108C2×#67D414yes—
109C2×#67D414yes—
110C22×Dic3—22no—
111C22×Dic3—22no—
112C22×Dic3—41no—
113C22×Dic3C2311yescharacteristic
114C22×Dic3C2311yescharacteristic
115C22×Dic3C2311yescharacteristic
116C22×Dic3C2311yescharacteristic
117C22×Dic3C2311yescharacteristic
118D3×D4—232no—
119C2×D12—22no—
120C2×D12—22no—
121C2×D12C2×C414yescomplemented
122C2×C4×D3—22no—
123C2×C4×D3—22no—
124C2×C4×D3—22no—
125C2×C4×D3—22no—
126C2×C4×D3—22no—
127C2×C4×D3—22no—
128C2×C4×D3—41no—
129C2×C4×D3—41no—
130C2×C4×D3C2×C414yescomplemented
131C3×C22⋊C4—22no—
132C3×C22⋊C4—22no—
133C3×C22⋊C4—41no—
134#217—22no—
135#217—22no—
136#217—41no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4—22no—
139(C2×D3)⋊C4—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—41no—
145(C2×D3)⋊C4—41no—
146(C2×D3)⋊C4D414yescomplemented
147Dic3⋊C4—22no—
148Dic3⋊C4—22no—
149C4×Dic3—22no—
150C4×Dic3—22no—
151C25—31no—
152C25—31no—
153C22×D4—31no—
154C22×D4—31no—
155C22×D4—38no—
156C22×D4—31no—
157C22×D4—64no—
158C22×D4—64no—
159C22×D4C2×D311yescharacteristic
160C23×C4—31no—
161C23×C4—31no—
162C23×C4—31no—
163C23×C4—31no—
164C23×C4C2×D311yescharacteristic, complemented
165C4×D4—64no—
166C4×D4—64no—
167C2×C4⋊C4—31no—
168C2×C4⋊C4—31no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4—31no—
172C2×C22⋊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—64no—
183C2×C22⋊C4—64no—
184C2×C22⋊C4C2×D311yescharacteristic, complemented
185C2×C22⋊C4C2×D311yescharacteristic, complemented
186C2×C22⋊C4C2×D311yescharacteristic, complemented
187C2×C42—31no—
188C2×C42—31no—
189#95—31no—
190#95—31no—
191#95C2×D311yescharacteristic, complemented
192#95C2×D311yescharacteristic, complemented
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×C3C22×C412yes—
204C23×C3C22×C412yes—
205C23×C3C2×D412yes—
206C23×C3C2×D412yes—
207C23×C3C2411yescharacteristic
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—28no—
217C22×D3—21no—
218C22×D3—21no—
219C22×D3—21no—
220C22×D3—21no—
221C22×D3—21no—
222C22×D3—21no—
223C22×D3—28no—
224C22×D3—28no—
225C22×D3—28no—
226C22×D3—44no—
227C22×D3—44no—
228C22×D3—44no—
229C22×D3—44no—
230C22×D3—44no—
231C22×D3—44no—
232C22×D3—44no—
233C22×D3—44no—
234C22×D3—44no—
235C22×D3—44no—
236C22×D3C22×C412yes—
237C22×D3C22×C412yes—
238C22×D3C22×C412yes—
239C22×D3C2×D412yes—
240C22×D3C2×D412yes—
241C22×D3C2×D412yes—
242C22×D3#4112yes—
243C3×D4—28no—
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×C4—21no—
257C2×C3×C4—44no—
258C2×C3×C4C22×C412yes—
259C2×C3×C4C2×D412yescomplemented
260#67—28no—
261#67C22⋊C4116yescomplemented
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—44no—
274C2×Dic3C22×C412yes—
275C2×Dic3C2×D412yes—
276C2×Dic3C2×D412yes—
277C2×Dic3C2×D412yescomplemented
278D12—28no—
279C4×D3—28no—
280C4×D3—44no—
281C4×D3—44no—
282C24—31no—
283C24—31no—
284C24—31no—
285C24—34no—
286C24—34no—
287C24—62no—
288C24—62no—
289C24—62no—
290C24—62no—
291C24—62no—
292C24—62no—
293C24—62no—
294C24—62no—
295C24—121no—
296C24—121no—
297C24—121no—
298C24—121no—
299C24C22×D311yescharacteristic
300C24C22×D311yescharacteristic
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—34no—
304C2×D4—34no—
305C2×D4—34no—
306C2×D4—34no—
307C2×D4—34no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4—62no—
311C2×D4—62no—
312C2×D4—632no—
313C2×D4C4×D314yescomplemented
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—34no—
319C22×C4—31no—
320C22×C4—31no—
321C22×C4—31no—
322C22×C4—41no—
323C22×C4—62no—
324C22×C4—62no—
325C22×C4—62no—
326C22×C4—62no—
327C22×C4—62no—
328C22×C4—62no—
329C22×C4—62no—
330C22×C4—62no—
331C22×C4—121no—
332C22×C4—121no—
333C22×C4—121no—
334C22×C4C22×D311yescharacteristic
335C22×C4C22×D311yescharacteristic
336C22×C4C22×D311yescharacteristic
337C22×C4C22×D311yescharacteristic
338C22×C4C22×D311yescharacteristic
339C4⋊C4—62no—
340C4⋊C4—62no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—34no—
344C22⋊C4—41no—
345C22⋊C4—62no—
346C22⋊C4—62no—
347C22⋊C4—62no—
348C22⋊C4—62no—
349C22⋊C4—62no—
350C22⋊C4—62no—
351C22⋊C4—62no—
352C22⋊C4—62no—
353C22⋊C4—62no—
354C22⋊C4—121no—
355C22⋊C4—121no—
356C22⋊C4—121no—
357C42—62no—
358C42—62no—
359C22×C3—22no—
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—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3C2×C22⋊C414yescomplemented
373C22×C3C23×C411yescharacteristic
374C22×C3C22×D411yescharacteristic
375C22×C3C22×D411yescharacteristic
376C22×C3C22×D411yescharacteristic
377C22×C3C2×#4111yescharacteristic
378C22×C3H(5,𝔽2)11yescharacteristic
379C22×C3H(5,𝔽2)11yescharacteristic
380C2×D3—22no—
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—22no—
391C2×D3—22no—
392C2×D3—22no—
393C2×D3—22no—
394C2×D3—22no—
395C2×D3—416no—
396C2×D3—416no—
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C2×D3—41no—
401C2×D3C2×C22⋊C414yescomplemented
402C2×D3C4×D414yescomplemented
403C3×C4—22no—
404C3×C4—22no—
405C3×C4—41no—
406C3×C4—41no—
407C3×C4—41no—
408Dic3—22no—
409Dic3—41no—
410Dic3—41no—
411Dic3—41no—
412Dic3C2×C22⋊C414yescomplemented
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—32no—
424C23—32no—
425C23—32no—
426C23—32no—
427C23—32no—
428C23—32no—
429C23—32no—
430C23—68no—
431C23—68no—
432C23—68no—
433C23—61no—
434C23—61no—
435C23—61no—
436C23—61no—
437C23—61no—
438C23—61no—
439C23—61no—
440C23—61no—
441C23—68no—
442C23—61no—
443C23—61no—
444C23—61no—
445C23—61no—
446C23—61no—
447C23—61no—
448C23—124no—
449C23—124no—
450C23—124no—
451C23—124no—
452C23—124no—
453C23—124no—
454C23—124no—
455C23—124no—
456C23—124no—
457C23—124no—
458C23C2×C4×D312yes—
459C23C2×C4×D312yes—
460C23D3×D412yes—
461C23D3×D412yes—
462C23C23×D311yescharacteristic
463D4—28no—
464D4—316no—
465D4—68no—
466D4—68no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—44no—
485C2×C4—68no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—124no—
498C2×C4—124no—
499C2×C4—124no—
500C2×C4C2×C4×D312yes—
501C2×C4D3×D412yescomplemented
502C2×C3—24no—
503C2×C3—42no—
504C2×C3C22×C22⋊C411yescharacteristic
505C2×C3C2×C4×D411yescharacteristic
506C2×C3#51811yescharacteristic
507C2×C3D4211yescharacteristic
508C2×C3D4211yescharacteristic
509C2×C3#54611yescharacteristic
510C2×C3#54611yescharacteristic
511D3—24no—
512D3—24no—
513D3—42no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—34no—
524C22—34no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—62no—
530C22—62no—
531C22—62no—
532C22—62no—
533C22—62no—
534C22—62no—
535C22—62no—
536C22—62no—
537C22—62no—
538C22—62no—
539C22—62no—
540C22—62no—
541C22—62no—
542C22—62no—
543C22—62no—
544C22—1216no—
545C22—1216no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22—121no—
550C22D3×C22⋊C414yescomplemented
551C22C22×C4×D311yescharacteristic
552C22C2×D3×D411yescharacteristic
553C22C2×D3×D411yescharacteristic
554C22C2×D3×D411yescharacteristic
555C22#100411yescharacteristic
556C22D3×#4111yescharacteristic
557C22#100911yescharacteristic
558C4—22no—
559C4—22no—
560C4—34no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—62no—
565C4—121no—
566C4—121no—
567C4—121no—
568C3D4×C22⋊C411yescharacteristic, complemented, Sylow
569C2—24no—
570C2—42no—
571C2—64no—
572C2—64no—
573C2—122no—
574C2C2×D3×C22⋊C411yescharacteristic
575C2C4×D3×D411yescharacteristic
576C2#554511yescharacteristic
577C2#559011yescharacteristic
578C2#560911yescharacteristic
579C2#561011yescharacteristic
580C2#565411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#386C2
socle, cosocleC23×C3C24
prime radicalC22×D3×D4C2
hypercenter#386D3
hypocenterC3D4×C22⋊C4
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#67C2semidirect
3. C22×(C2×D3)⋊C4C2semidirect
4. C2×#67⋊C4C2semidirect
5. C2×D3×C22⋊C4C2semidirect
6. C3×#386C2semidirect
7. #5220C2semidirect
8. #4957C2semidirect
9. #4957C2semidirect
10. #4955C2semidirect
11. #4955C2semidirect
12. #4667C2semidirect
13. #4666C2semidirect
14. #4665C2semidirect
15. #4665C2semidirect
20. C23×C3×C4C22semidirect
23. C23×Dic3C22semidirect
26. C2×D3×D4C4semidirect
29. C22×C4×D3C22semidirect
30. C22×C4×D3C22semidirect
31. C2×C3×C22⋊C4C22semidirect
32. C2×C3×C22⋊C4C22semidirect
33. C2×C3×C22⋊C4C22semidirect
34. C2×#217C22semidirect
35. C2×#217C22semidirect
36. C2×#217C22semidirect
43. C2×(C2×D3)⋊C4C22semidirect
44. C2×(C2×D3)⋊C4C22semidirect
45. C2×(C2×D3)⋊C4C22semidirect
46. C2×(C2×D3)⋊C4C22semidirect
47. C2×(C2×D3)⋊C4C22semidirect
48. C2×(C2×D3)⋊C4C22semidirect
49. C2×Dic3⋊C4C22semidirect
50. C2×Dic3⋊C4C22semidirect
51. C2×C4×Dic3C22semidirect
52. C2×C4×Dic3C22semidirect
55. C3×#95C22semidirect
56. C3×#95C22semidirect
57. C3⋊#95C22semidirect
58. C3⋊#95C22semidirect
69. #386D3semidirect
88. C23×D3C2×C4semidirect
89. C23×D3C2×C4semidirect
95. C2×C3×D4C2×C4semidirect
107. C2×#67C2×C4semidirect
121. C2×D12C2×C4semidirect
130. C2×C4×D3C2×C4semidirect
146. (C2×D3)⋊C4D4semidirect
164. C23×C4C2×D3semidirect
184. C2×C22⋊C4C2×D3semidirect
185. C2×C22⋊C4C2×D3semidirect
186. C2×C22⋊C4C2×D3semidirect
191. #95C2×D3semidirect
192. #95C2×D3semidirect
259. C2×C3×C4C2×D4semidirect
261. #67C22⋊C4semidirect
277. C2×Dic3C2×D4semidirect
313. C2×D4C4×D3semidirect
372. C22×C3C2×C22⋊C4semidirect
401. C2×D3C2×C22⋊C4semidirect
402. C2×D3C4×D4semidirect
412. Dic3C2×C22⋊C4semidirect
501. C2×C4D3×D4semidirect
550. C22D3×C22⋊C4semidirect
568. C3D4×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D42
C2×C4×#672
C22×(C2×D3)⋊C42
C2×#67⋊C42
C2×D3×C22⋊C42
C3×#3862
#52202
#49572
#49552
#46672
#46662
#46652
D4×C22⋊C43