Finite Group Databasebeta

← #76454

Subgroups — #76454

Order 384.

900 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#937C211yesmaximal, characteristic, complemented
2C2×#894C211yesmaximal, characteristic, complemented
3C2×#884C211yesmaximal, characteristic, complemented
4C2×#883C211yesmaximal, characteristic, complemented
5C2×#882C211yesmaximal, characteristic, complemented
6C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#390C211yesmaximal, characteristic, complemented
8#5223C211yesmaximal, characteristic, complemented
9#4993C211yesmaximal, characteristic, complemented
10#4960C211yesmaximal, characteristic, complemented
11#4957C211yesmaximal, characteristic, complemented
12#4957C211yesmaximal, characteristic, complemented
13#4949C211yesmaximal, characteristic, complemented
14#4939C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
16#2539—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic, complemented
23C22×D12C2211yescharacteristic
24C22×D12C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C22×C4×D3C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic, complemented
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic, complemented
31C2×C3×C22⋊C4C2211yescharacteristic, complemented
32C2×C3×C42C2211yescharacteristic, complemented
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic, complemented
36#937—24no—
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic, complemented
47C2×Dic3⋊C4C2211yescharacteristic, complemented
48C2×Dic3⋊C4C2211yescharacteristic, complemented
49C2×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C4×Dic3C2211yescharacteristic, complemented
51#894—24no—
52#884—24no—
53#883—24no—
54#882—24no—
55D3×C22⋊C4—24no—
56C3⋊#95C2211yescharacteristic, complemented
57C3⋊#95C2211yescharacteristic, complemented
58C2×#123—31no—
59C2×#123—31no—
60C2×#121—31no—
61C2×#120—31no—
62C2×#120—31no—
63C22×C22⋊C4—31no—
64#399—31no—
65#399—31no—
66#392—31no—
67#392—31no—
68#390—31no—
69#390—31no—
70#390—31no—
71#390D311yescharacteristic, complemented
72C4×C22⋊C4—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—22no—
79C23×D3—22no—
80C23×D3—41no—
81C23×D3—41no—
82C23×D3C2311yescharacteristic
83C23×D3C2311yescharacteristic
84C23×D3C2311yescharacteristic
85C2×C3×D4—22no—
86C2×C3×D4—22no—
87C2×C3×D4—41no—
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C2×#67—22no—
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—22no—
98C2×#67—22no—
99C2×#67—22no—
100C2×#67—22no—
101C2×#67—41no—
102C2×#67—41no—
103C2×#67—41no—
104C2×#67—41no—
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C2×D12—22no—
111C2×D12—22no—
112C2×D12—22no—
113C2×D12—22no—
114C2×D12—22no—
115C2×D12—41no—
116C2×C4×D3—22no—
117C2×C4×D3—22no—
118C2×C4×D3—22no—
119C2×C4×D3—41no—
120C2×C4×D3—41no—
121C2×C4×D3D414yescomplemented
122C3×C4⋊C4—22no—
123C3×C22⋊C4—22no—
124C3×C22⋊C4—22no—
125C3×C22⋊C4—22no—
126C3×C22⋊C4—22no—
127C3×C42—41no—
128#217—22no—
129#217—22no—
130#217—22no—
131(C2×D3)⋊C4—22no—
132(C2×D3)⋊C4—22no—
133(C2×D3)⋊C4—22no—
134(C2×D3)⋊C4—22no—
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4D414yescomplemented
139(C2×D3)⋊C4D414yescomplemented
140C4⋊Dic3—22no—
141Dic3⋊C4—22no—
142Dic3⋊C4—22no—
143Dic3⋊C4—22no—
144C4×Dic3—41no—
145C25—31no—
146C22×D4—31no—
147C22×D4—31no—
148C22×D4—31no—
149C22×D4—31no—
150C22×D4—31no—
151C22×D4—31no—
152C22×D4C2×D311yescharacteristic
153C23×C4—31no—
154C23×C4—31no—
155#123—64no—
156#123—64no—
157#121—64no—
158#120—64no—
159#120—64no—
160C2×C4⋊C4—31no—
161C2×C4⋊C4—31no—
162C2×C4⋊C4—31no—
163C2×C4⋊C4—31no—
164C2×C4⋊C4C2×D311yescharacteristic, complemented
165C2×C22⋊C4—31no—
166C2×C22⋊C4—31no—
167C2×C22⋊C4—31no—
168C2×C22⋊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—64no—
178C2×C22⋊C4C2×D311yescharacteristic
179C2×C22⋊C4C2×D311yescharacteristic
180C2×C22⋊C4C2×D311yescharacteristic, complemented
181C2×C22⋊C4C2×D311yescharacteristic, complemented
182C2×C42—31no—
183C2×C42C2×D311yescharacteristic, complemented
184#95—31no—
185#95—31no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3#4112yes—
200C23×C3C2411yescharacteristic
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—28no—
206C22×D3—21no—
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—44no—
220C22×D3—44no—
221C22×D3—44no—
222C22×D3—44no—
223C22×D3—44no—
224C22×D3—44no—
225C22×D3C2×D412yes—
226C22×D3C2×D412yes—
227C22×D3C2×D412yes—
228C22×D3#4112yes—
229C3×D4—44no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4C2×D412yes—
243C2×C3×C4C2×D412yes—
244C2×C3×C4C2×D412yes—
245#67—44no—
246#67—44no—
247#67—44no—
248#67—44no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3C2×D412yes—
262C2×Dic3C2×D412yes—
263C2×Dic3C2×D412yes—
264D12—44no—
265D12—44no—
266C4×D3—44no—
267C4×D3—44no—
268C24—31no—
269C24—31no—
270C24—31no—
271C24—62no—
272C24—62no—
273C24—62no—
274C24—62no—
275C24—62no—
276C24—121no—
277C24—121no—
278C24C22×D311yescharacteristic
279C24C22×D311yescharacteristic
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—41no—
283C2×D4—62no—
284C2×D4—62no—
285C2×D4—62no—
286C2×D4—62no—
287C2×D4—62no—
288C2×D4—62no—
289C2×D4—62no—
290C2×D4—62no—
291C2×D4—62no—
292C2×D4—62no—
293C2×D4—62no—
294C2×D4—62no—
295C2×D4—62no—
296C2×D4—121no—
297C2×D4—121no—
298C2×D4—121no—
299C2×D4—121no—
300C2×D4—121no—
301C22×C4—31no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—34no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—62no—
308C22×C4—62no—
309C22×C4—62no—
310C22×C4—121no—
311C22×C4—121no—
312C22×C4C22×D311yescharacteristic
313C22×C4C22×D311yescharacteristic
314C22×C4C22×D311yescharacteristic
315C22×C4C22×D311yescharacteristic
316C22×C4C22×D311yescharacteristic
317C4⋊C4—22no—
318C4⋊C4—62no—
319C4⋊C4—62no—
320C4⋊C4—62no—
321C4⋊C4—62no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—34no—
327C22⋊C4—34no—
328C22⋊C4—62no—
329C22⋊C4—62no—
330C22⋊C4—62no—
331C22⋊C4—62no—
332C22⋊C4—62no—
333C22⋊C4—62no—
334C22⋊C4—62no—
335C22⋊C4—62no—
336C22⋊C4—62no—
337C22⋊C4—62no—
338C42—41no—
339C42—121no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3C22×D411yescharacteristic
355C22×C3C22×D411yescharacteristic
356C22×C3C22×D411yescharacteristic
357C22×C3C2×#4111yescharacteristic
358C22×C3C2×#4111yescharacteristic
359C22×C3H(5,𝔽2)11yescharacteristic
360C22×C3H(5,𝔽2)11yescharacteristic
361C2×D3—22no—
362C2×D3—22no—
363C2×D3—22no—
364C2×D3—22no—
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—22no—
368C2×D3—22no—
369C2×D3—22no—
370C2×D3—416no—
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—41no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—41no—
381C2×D3—41no—
382C2×D3#12714yes—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—41no—
387C3×C4—41no—
388Dic3—22no—
389Dic3—22no—
390Dic3—22no—
391Dic3—41no—
392Dic3—41no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—32no—
407C23—32no—
408C23—32no—
409C23—32no—
410C23—68no—
411C23—61no—
412C23—61no—
413C23—61no—
414C23—61no—
415C23—61no—
416C23—61no—
417C23—61no—
418C23—61no—
419C23—61no—
420C23—61no—
421C23—61no—
422C23—61no—
423C23—61no—
424C23—61no—
425C23—61no—
426C23—61no—
427C23—61no—
428C23—124no—
429C23—124no—
430C23—124no—
431C23—124no—
432C23—124no—
433C23—124no—
434C23#23512yes—
435C23C23×D311yescharacteristic
436D4—44no—
437D4—124no—
438D4—124no—
439D4—124no—
440D4—124no—
441D4—124no—
442D4—124no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—32no—
456C2×C4—32no—
457C2×C4—32no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—124no—
471C2×C4—124no—
472C2×C4D3×D412yes—
473C2×C4D3×D412yes—
474C2×C4D3×D412yes—
475C2×C3—42no—
476C2×C3—81no—
477C2×C3#52511yescharacteristic
478C2×C3C2×#12711yescharacteristic
479C2×C3#53411yescharacteristic
480C2×C3#54611yescharacteristic
481C2×C3#54611yescharacteristic
482C2×C3#54611yescharacteristic
483C2×C3#54611yescharacteristic
484D3—24no—
485D3—42no—
486D3—81no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—34no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—62no—
503C22—62no—
504C22—62no—
505C22—62no—
506C22—62no—
507C22—62no—
508C22—62no—
509C22—62no—
510C22—62no—
511C22—1216no—
512C22—121no—
513C22—121no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22—121no—
522C22—121no—
523C22C2×#23511yescharacteristic
524C22C2×D3×D411yescharacteristic
525C22C2×D3×D411yescharacteristic
526C22C2×D3×D411yescharacteristic
527C22#100411yescharacteristic
528C22D3×#4111yescharacteristic
529C22#100911yescharacteristic
530C4—22no—
531C4—22no—
532C4—22no—
533C4—41no—
534C4—41no—
535C4—62no—
536C4—62no—
537C4—62no—
538C4—121no—
539C4—121no—
540C3#253911yescharacteristic, complemented, Sylow
541C2—42no—
542C2—64no—
543C2—81no—
544C2—122no—
545C2—241no—
546C2#549011yescharacteristic
547C2#554711yescharacteristic
548C2#555011yescharacteristic
549C2#560511yescharacteristic
550C2#561011yescharacteristic
551C2#567611yescharacteristic
552C2D3×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#390C2
hypercenter#390D3
hypocenterC3#2539
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#937C2semidirect
2. C2×#894C2semidirect
3. C2×#884C2semidirect
4. C2×#883C2semidirect
5. C2×#882C2semidirect
6. C2×D3×C22⋊C4C2semidirect
7. C3×#390C2semidirect
8. #5223C2semidirect
9. #4993C2semidirect
10. #4960C2semidirect
11. #4957C2semidirect
12. #4957C2semidirect
13. #4949C2semidirect
14. #4939C2semidirect
15. C4×(C2×D3)⋊C4C2semidirect
22. C22×#67C22semidirect
27. C2×C3×C4⋊C4C22semidirect
30. C2×C3×C22⋊C4C22semidirect
31. C2×C3×C22⋊C4C22semidirect
32. C2×C3×C42C22semidirect
35. C2×#217C22semidirect
43. C2×(C2×D3)⋊C4C22semidirect
44. C2×(C2×D3)⋊C4C22semidirect
45. C2×(C2×D3)⋊C4C22semidirect
46. C2×C4⋊Dic3C22semidirect
47. C2×Dic3⋊C4C22semidirect
48. C2×Dic3⋊C4C22semidirect
49. C2×Dic3⋊C4C22semidirect
50. C2×C4×Dic3C22semidirect
56. C3⋊#95C22semidirect
57. C3⋊#95C22semidirect
71. #390D3semidirect
121. C2×C4×D3D4semidirect
138. (C2×D3)⋊C4D4semidirect
139. (C2×D3)⋊C4D4semidirect
164. C2×C4⋊C4C2×D3semidirect
180. C2×C22⋊C4C2×D3semidirect
181. C2×C22⋊C4C2×D3semidirect
183. C2×C42C2×D3semidirect
540. C3#2539semidirect

Maximal subgroups

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

subgroupindex
C2×#9372
C2×#8942
C2×#8842
C2×#8832
C2×#8822
C2×D3×C22⋊C42
C3×#3902
#52232
#49932
#49602
#49572
#49492
#49392
C4×(C2×D3)⋊C42
#25393