Finite Group Databasebeta

← #74021

Subgroups — #74021

Order 384.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
2C2×#894C211yesmaximal, characteristic, complemented
3C2×#882C211yesmaximal, characteristic
4C2×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#380C211yesmaximal, characteristic, complemented
6#5213C211yesmaximal, characteristic, complemented
7#4993C211yesmaximal, characteristic, complemented
8#4991C211yesmaximal, characteristic, complemented
9#4990C211yesmaximal, characteristic, complemented
10#4955C211yesmaximal, characteristic, complemented
11#4946C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4672C211yesmaximal, characteristic, complemented
14#4669C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2418—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C23×Dic3C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic, complemented
24C2×C3×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C4⋊C4C2211yescharacteristic, complemented
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×(C2×D3)⋊C4—24no—
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×Dic3⋊C4C2211yescharacteristic, complemented
44C2×Dic3⋊C4C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic3C2211yescharacteristic, complemented
47#894—24no—
48#882—24no—
49#67⋊C4—24no—
50C3×#95C2211yescharacteristic, complemented
51C3×#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C2×#123—31no—
57C2×#120—31no—
58C2×C4×D4—31no—
59C22×C22⋊C4—31no—
60#399—31no—
61#397—31no—
62#394—31no—
63#394—31no—
64#388—31no—
65#388—31no—
66#386—31no—
67#386—31no—
68#385—31no—
69#380D311yescharacteristic, complemented
70#379—31no—
71C24×C3C2311yescharacteristic
72C23×D3—22no—
73C23×D3—22no—
74C23×D3—22no—
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—41no—
78C23×D3—41no—
79C23×D3C2311yescharacteristic
80C23×D3C2311yescharacteristic
81C23×D3C2311yescharacteristic
82C22×C3×C4—22no—
83C22×C3×C4—22no—
84C22×C3×C4—41no—
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C2×#67—22no—
92C2×#67—22no—
93C2×#67D414yes—
94C22×Dic3—22no—
95C22×Dic3—22no—
96C22×Dic3—41no—
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C2×D12—22no—
103C2×D12—22no—
104C2×D12—22no—
105C2×D12—22no—
106C2×D12—41no—
107C2×D12—41no—
108C2×C4×D3—22no—
109C2×C4×D3—22no—
110C2×C4×D3—41no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—41no—
113C3×C22⋊C4—22no—
114C3×C22⋊C4—22no—
115#217—22no—
116(C2×D3)⋊C4—22no—
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—41no—
126(C2×D3)⋊C4—41no—
127(C2×D3)⋊C4—41no—
128(C2×D3)⋊C4D414yescomplemented
129Dic3⋊C4—22no—
130Dic3⋊C4—22no—
131Dic3⋊C4—41no—
132C4×Dic3—22no—
133C25—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C23×C4—31no—
138C23×C4—31no—
139C23×C4C2×D311yescharacteristic
140#123—64no—
141#120—64no—
142C4×D4—64no—
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4C2×D311yescharacteristic, complemented
147C2×C4⋊C4C2×D311yescharacteristic, complemented
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—31no—
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—31no—
158C2×C22⋊C4—31no—
159C2×C22⋊C4—31no—
160C2×C22⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4—64no—
163C2×C22⋊C4C2×D311yescharacteristic
164C2×C22⋊C4C2×D311yescharacteristic
165C2×C42—31no—
166#95—31no—
167#95—31no—
168#95—31no—
169#95—31no—
170#95C2×D311yescharacteristic, complemented
171#95C2×D311yescharacteristic, complemented
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3C2×D412yes—
177C23×C3#4112yes—
178C23×C3#4112yes—
179C23×C3C2411yescharacteristic
180C22×D3—28no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—21no—
185C22×D3—21no—
186C22×D3—21no—
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
191C22×D3—21no—
192C22×D3—21no—
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—44no—
200C22×D3—44no—
201C22×D3—44no—
202C22×D3—44no—
203C22×D3—44no—
204C22×D3—44no—
205C22×D3C2×D412yes—
206C22×D3C2×D412yes—
207C22×D3#4112yes—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—44no—
226C2×C3×C4C2×D412yes—
227#67—28no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—44no—
242C2×Dic3C2×D412yes—
243C2×Dic3C2×D412yes—
244D12—44no—
245D12—44no—
246C4×D3—44no—
247C24—31no—
248C24—31no—
249C24—31no—
250C24—62no—
251C24—62no—
252C24—62no—
253C24—62no—
254C24—62no—
255C24—121no—
256C24—121no—
257C24C22×D311yescharacteristic
258C2×D4—34no—
259C2×D4—62no—
260C2×D4—62no—
261C2×D4—62no—
262C2×D4—62no—
263C2×D4—62no—
264C2×D4—62no—
265C2×D4—121no—
266C2×D4—121no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—41no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—62no—
279C22×C4—121no—
280C22×C4—121no—
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C22×C4C22×D311yescharacteristic
286C22×C4C22×D311yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—62no—
290C4⋊C4—62no—
291C4⋊C4—121no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—34no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22⋊C4—62no—
303C22⋊C4—62no—
304C22⋊C4—62no—
305C22⋊C4—121no—
306C22⋊C4—121no—
307C22⋊C4—121no—
308C42—62no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3#12314yescomplemented
316C22×C3C22×D411yescharacteristic
317C22×C3C22×D411yescharacteristic
318C22×C3C2×#4111yescharacteristic
319C22×C3C2×#4111yescharacteristic
320C22×C3C2×#4111yescharacteristic
321C22×C3H(5,𝔽2)11yescharacteristic
322C22×C3H(5,𝔽2)11yescharacteristic
323C2×D3—22no—
324C2×D3—22no—
325C2×D3—22no—
326C2×D3—22no—
327C2×D3—22no—
328C2×D3—22no—
329C2×D3—22no—
330C2×D3—22no—
331C2×D3—22no—
332C2×D3—416no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C3×C4—22no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—41no—
351Dic3—22no—
352Dic3—22no—
353Dic3—41no—
354Dic3—41no—
355Dic3—41no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—32no—
361C23—32no—
362C23—32no—
363C23—68no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—61no—
382C23—124no—
383C23—124no—
384C23—124no—
385C23—124no—
386C23—124no—
387C23—124no—
388C23#23512yes—
389C23D3×D412yes—
390C23#23912yes—
391C23C23×D311yescharacteristic
392D4—68no—
393D4—124no—
394D4—124no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—32no—
413C2×C4—32no—
414C2×C4—44no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—124no—
429C2×C4—124no—
430C2×C4D3×D412yes—
431C2×C3—24no—
432C2×C3C2×#12311yescharacteristic
433C2×C3#52511yescharacteristic
434C2×C3#53811yescharacteristic
435C2×C3D4211yescharacteristic
436C2×C3#54611yescharacteristic
437C2×C3#54611yescharacteristic
438C2×C3#55111yescharacteristic
439D3—42no—
440D3—42no—
441D3—42no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22—62no—
452C22—62no—
453C22—62no—
454C22—62no—
455C22—62no—
456C22—62no—
457C22—1216no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22—121no—
462C22—121no—
463C22—121no—
464C22—121no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22#89414yescomplemented
471C22C2×#23511yescharacteristic
472C22C2×D3×D411yescharacteristic
473C22C2×D3×D411yescharacteristic
474C22#100411yescharacteristic
475C22C2×#23911yescharacteristic
476C22D3×#4111yescharacteristic
477C22#100911yescharacteristic
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—62no—
485C4—62no—
486C4—121no—
487C4—121no—
488C4—121no—
489C3#241811yescharacteristic, complemented, Sylow
490C2—24no—
491C2—122no—
492C2—122no—
493C2—122no—
494C2#549011yescharacteristic
495C2C2×#89411yescharacteristic
496C2#552711yescharacteristic
497C2#560911yescharacteristic
498C2#561011yescharacteristic
499C2#562711yescharacteristic
500C2#564411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#380C2
prime radicalC2×#882C2
hypercenter#380D3
hypocenterC3#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C22×(C2×D3)⋊C4C2semidirect
2. C2×#894C2semidirect
4. C2×#67⋊C4C2semidirect
5. C3×#380C2semidirect
6. #5213C2semidirect
7. #4993C2semidirect
8. #4991C2semidirect
9. #4990C2semidirect
10. #4955C2semidirect
11. #4946C2semidirect
12. #4675C2semidirect
13. #4672C2semidirect
14. #4669C2semidirect
15. #4665C2semidirect
23. C22×C4×D3C22semidirect
24. C2×C3×C4⋊C4C22semidirect
25. C2×C3×C4⋊C4C22semidirect
40. C2×(C2×D3)⋊C4C22semidirect
41. C2×(C2×D3)⋊C4C22semidirect
42. C2×(C2×D3)⋊C4C22semidirect
43. C2×Dic3⋊C4C22semidirect
44. C2×Dic3⋊C4C22semidirect
45. C2×Dic3⋊C4C22semidirect
46. C2×C4×Dic3C22semidirect
50. C3×#95C22semidirect
51. C3×#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
69. #380D3semidirect
128. (C2×D3)⋊C4D4semidirect
146. C2×C4⋊C4C2×D3semidirect
147. C2×C4⋊C4C2×D3semidirect
170. #95C2×D3semidirect
171. #95C2×D3semidirect
315. C22×C3#123semidirect
470. C22#894semidirect
489. C3#2418semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D3)⋊C42
C2×#8942
C2×#8822
C2×#67⋊C42
C3×#3802
#52132
#49932
#49912
#49902
#49552
#49462
#46752
#46722
#46692
#46652
#24183