Finite Group Databasebeta

← #75833

Subgroups — #75833

Order 384.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#892C211yesmaximal, characteristic, complemented
2C2×D3×C22⋊C4C211yesmaximal, characteristic
3C2×D3×C22⋊C4C211yesmaximal, characteristic
4C3×#388C211yesmaximal, characteristic, complemented
5#4989C211yesmaximal, characteristic, complemented
6#4955C211yesmaximal, characteristic
7#4951C211yesmaximal, characteristic, complemented
8#4945C211yesmaximal, characteristic, complemented
9#4944C211yesmaximal, characteristic, complemented
10C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#4668C211yesmaximal, characteristic, complemented
13#4667C211yesmaximal, characteristic, complemented
14#4666C211yesmaximal, characteristic, complemented
15#4664C211yesmaximal, characteristic, complemented
16#2342—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic, complemented
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C42C2211yescharacteristic, complemented
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic, complemented
39C2×Dic3⋊C4C2211yescharacteristic, complemented
40C2×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C4×Dic3C2211yescharacteristic, complemented
42C2×C4×Dic3C2211yescharacteristic, complemented
43C2×C4×Dic3C2211yescharacteristic, complemented
44#892—24no—
45D3×C22⋊C4—24no—
46D3×C22⋊C4C418yescomplemented
47C3×#95C2211yescharacteristic, complemented
48C3×#95C2211yescharacteristic, complemented
49C3⋊#95C2211yescharacteristic, complemented
50C3⋊#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C2×#117—31no—
56C22×C22⋊C4—31no—
57C22×C22⋊C4—31no—
58#388—31no—
59#388—31no—
60#388—31no—
61#388D311yescharacteristic, complemented
62#385—31no—
63#385—31no—
64#381—31no—
65#380—31no—
66#379—31no—
67C4×C22⋊C4—31no—
68C4×C22⋊C4—31no—
69C4×C22⋊C4—31no—
70C24×C3C2311yescharacteristic
71C23×D3—22no—
72C23×D3—22no—
73C23×D3—22no—
74C23×D3—22no—
75C23×D3—41no—
76C23×D3—41no—
77C23×D3C2×C414yes—
78C23×D3C2311yescharacteristic
79C23×D3C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C2×C4×D3—22no—
93C2×C4×D3—22no—
94C2×C4×D3—22no—
95C2×C4×D3—22no—
96C2×C4×D3—22no—
97C2×C4×D3—22no—
98C2×C4×D3—41no—
99C2×C4×D3—41no—
100C2×C4×D3—41no—
101C2×C4×D3—41no—
102C2×C4×D3C2×C414yescomplemented
103C2×C4×D3C2×C414yescomplemented
104C3×C4⋊C4—22no—
105C3×C22⋊C4—22no—
106C3×C22⋊C4—41no—
107C3×C22⋊C4C2×C414yescomplemented
108C3×C42—41no—
109#217—22no—
110#217—41no—
111#217C2×C414yescomplemented
112(C2×D3)⋊C4—22no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4—22no—
116(C2×D3)⋊C4—22no—
117(C2×D3)⋊C4C2×C414yes—
118(C2×D3)⋊C4C2×C414yes—
119(C2×D3)⋊C4D414yes—
120C4⋊Dic3—22no—
121Dic3⋊C4—41no—
122Dic3⋊C4—41no—
123C4×Dic3—22no—
124C4×Dic3—22no—
125C4×Dic3—41no—
126C25—31no—
127C23×C4—31no—
128C23×C4—31no—
129C23×C4—31no—
130C23×C4—31no—
131#117—64no—
132C2×C4⋊C4—31no—
133C2×C4⋊C4—31no—
134C2×C4⋊C4—31no—
135C2×C4⋊C4C2×D311yescharacteristic, complemented
136C2×C22⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4—38no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4—31no—
143C2×C22⋊C4—31no—
144C2×C22⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—64no—
149C2×C22⋊C4C2×D311yescharacteristic
150C2×C22⋊C4C2×D311yescharacteristic
151C2×C22⋊C4C2×D311yescharacteristic
152C2×C42—31no—
153C2×C42—31no—
154C2×C42—31no—
155C2×C42C2×D311yescharacteristic, complemented
156#95—31no—
157#95—31no—
158#95—31no—
159#95—31no—
160#95—31no—
161#95—31no—
162#95C2×D311yescharacteristic, complemented
163#95C2×D311yescharacteristic, complemented
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3C22×C412yes—
171C23×C3C2411yescharacteristic
172C22×D3—21no—
173C22×D3—21no—
174C22×D3—21no—
175C22×D3—21no—
176C22×D3—21no—
177C22×D3—21no—
178C22×D3—21no—
179C22×D3—21no—
180C22×D3—28no—
181C22×D3—28no—
182C22×D3—44no—
183C22×D3—44no—
184C22×D3—44no—
185C22×D3—44no—
186C22×D3—44no—
187C22×D3C22×C412yes—
188C22×D3C22×C412yes—
189C22×D3C2×D412yes—
190C22×D3#4112yes—
191C22×D3#4112yes—
192C22×D3#4112yes—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4C22×C412yes—
209C2×C3×C4C22×C412yes—
210C2×C3×C4C2×D412yes—
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—21no—
214C2×Dic3—21no—
215C2×Dic3—21no—
216C2×Dic3—21no—
217C2×Dic3—21no—
218C2×Dic3—21no—
219C2×Dic3—21no—
220C2×Dic3—21no—
221C2×Dic3—21no—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3C22×C412yes—
227C2×Dic3C22×C412yes—
228C2×Dic3C2×D412yes—
229C4×D3—28no—
230C4×D3—44no—
231C4×D3—44no—
232C4×D3—44no—
233C24—31no—
234C24—31no—
235C24—34no—
236C24—62no—
237C24—62no—
238C24—62no—
239C24—62no—
240C24—121no—
241C24—121no—
242C24C22×D311yescharacteristic
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—34no—
247C22×C4—34no—
248C22×C4—31no—
249C22×C4—31no—
250C22×C4—31no—
251C22×C4—62no—
252C22×C4—62no—
253C22×C4—62no—
254C22×C4—62no—
255C22×C4—62no—
256C22×C4—62no—
257C22×C4—121no—
258C22×C4—121no—
259C22×C4—121no—
260C22×C4—121no—
261C22×C4C22×D311yescharacteristic
262C22×C4C22×D311yescharacteristic
263C22×C4C22×D311yescharacteristic
264C22×C4C22×D311yescharacteristic
265C22×C4C22×D311yescharacteristic
266C22×C4C22×D311yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—62no—
269C4⋊C4—121no—
270C4⋊C4—121no—
271C22⋊C4—22no—
272C22⋊C4—34no—
273C22⋊C4—34no—
274C22⋊C4—34no—
275C22⋊C4—34no—
276C22⋊C4—41no—
277C22⋊C4—62no—
278C22⋊C4—62no—
279C22⋊C4—62no—
280C22⋊C4—62no—
281C22⋊C4—62no—
282C22⋊C4—62no—
283C22⋊C4—121no—
284C22⋊C4C4×D314yescomplemented
285C42—41no—
286C42—62no—
287C42—62no—
288C42—121no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3C23×C411yescharacteristic
297C22×C3C22×D411yescharacteristic
298C22×C3C2×#4111yescharacteristic
299C22×C3C2×#4111yescharacteristic
300C22×C3C2×#4111yescharacteristic
301C22×C3H(5,𝔽2)11yescharacteristic
302C22×C3H(5,𝔽2)11yescharacteristic
303C2×D3—22no—
304C2×D3—22no—
305C2×D3—22no—
306C2×D3—22no—
307C2×D3—22no—
308C2×D3—22no—
309C2×D3—22no—
310C2×D3—22no—
311C2×D3—22no—
312C2×D3—22no—
313C2×D3—22no—
314C2×D3—22no—
315C2×D3—416no—
316C2×D3#11714yescomplemented
317C2×D3C4×D414yes—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—22no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—41no—
324Dic3—22no—
325Dic3—22no—
326Dic3—22no—
327Dic3—41no—
328Dic3—41no—
329Dic3—41no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—32no—
337C23—32no—
338C23—32no—
339C23—32no—
340C23—32no—
341C23—32no—
342C23—68no—
343C23—68no—
344C23—61no—
345C23—61no—
346C23—61no—
347C23—61no—
348C23—61no—
349C23—61no—
350C23—61no—
351C23—61no—
352C23—124no—
353C23—124no—
354C23—124no—
355C23—124no—
356C23—124no—
357C23C2×C4×D312yes—
358C23C23×D311yescharacteristic
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—32no—
375C2×C4—32no—
376C2×C4—32no—
377C2×C4—68no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—124no—
394C2×C4—124no—
395C2×C4—124no—
396C2×C4C2×C4×D312yes—
397C2×C4C2×C4×D312yes—
398C2×C4D3×D412yes—
399C2×C3—42no—
400C2×C3C2×#11711yescharacteristic
401C2×C3C2×C4×D411yescharacteristic
402C2×C3#51811yescharacteristic
403C2×C3#54611yescharacteristic
404C2×C3#54611yescharacteristic
405C2×C3#55111yescharacteristic
406C2×C3#55111yescharacteristic
407D3—24no—
408D3—24no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—34no—
413C22—34no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—62no—
419C22—62no—
420C22—62no—
421C22—62no—
422C22—62no—
423C22—62no—
424C22—62no—
425C22—62no—
426C22—62no—
427C22—62no—
428C22—62no—
429C22—62no—
430C22—1216no—
431C22C22×C4×D311yescharacteristic
432C22C2×D3×D411yescharacteristic
433C22#100411yescharacteristic
434C22D3×#4111yescharacteristic
435C22D3×#4111yescharacteristic
436C22D3×#4111yescharacteristic
437C22#100911yescharacteristic
438C4—22no—
439C4—22no—
440C4—22no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4—62no—
445C4—62no—
446C4—62no—
447C4—121no—
448C4—121no—
449C4—121no—
450C3#234211yescharacteristic, complemented, Sylow
451C2—42no—
452C2—64no—
453C2—64no—
454C2D3×#11711yescharacteristic
455C2C4×D3×D411yescharacteristic
456C2#554511yescharacteristic
457C2#561011yescharacteristic
458C2#565911yescharacteristic
459C2#567611yescharacteristic
460C2#570511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#388C2
socle, cosocleC23×C3C24
prime radicalC24×D3C22
hypercenter#388D3
hypocenterC3#2342
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#892C2semidirect
4. C3×#388C2semidirect
5. #4989C2semidirect
7. #4951C2semidirect
8. #4945C2semidirect
9. #4944C2semidirect
10. C4×(C2×D3)⋊C4C2semidirect
11. C4×(C2×D3)⋊C4C2semidirect
12. #4668C2semidirect
13. #4667C2semidirect
14. #4666C2semidirect
15. #4664C2semidirect
22. C2×C3×C4⋊C4C22semidirect
26. C2×C3×C42C22semidirect
38. C2×C4⋊Dic3C22semidirect
39. C2×Dic3⋊C4C22semidirect
40. C2×Dic3⋊C4C22semidirect
41. C2×C4×Dic3C22semidirect
42. C2×C4×Dic3C22semidirect
43. C2×C4×Dic3C22semidirect
46. D3×C22⋊C4C4semidirect
47. C3×#95C22semidirect
48. C3×#95C22semidirect
49. C3⋊#95C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
61. #388D3semidirect
102. C2×C4×D3C2×C4semidirect
103. C2×C4×D3C2×C4semidirect
107. C3×C22⋊C4C2×C4semidirect
111. #217C2×C4semidirect
135. C2×C4⋊C4C2×D3semidirect
155. C2×C42C2×D3semidirect
162. #95C2×D3semidirect
163. #95C2×D3semidirect
284. C22⋊C4C4×D3semidirect
316. C2×D3#117semidirect
450. C3#2342semidirect

Maximal subgroups

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

subgroupindex
C2×#8922
C2×D3×C22⋊C42
C3×#3882
#49892
#49552
#49512
#49452
#49442
C4×(C2×D3)⋊C42
#46682
#46672
#46662
#46642
#23423