Finite Group Databasebeta

← #75825

Subgroups — #75825

Order 384.

672 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊C4C211yesmaximal, characteristic
2C3×#388C211yesmaximal, characteristic, complemented
3#4990C211yesmaximal, characteristic, complemented
4#4987C211yesmaximal, characteristic, complemented
5#4955C211yesmaximal, characteristic
6#4955C211yesmaximal, characteristic
7#4951C211yesmaximal, characteristic, complemented
8#4945C211yesmaximal, characteristic, complemented
9#4944C211yesmaximal, characteristic, complemented
10#4940C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#4670C211yesmaximal, characteristic, complemented
13#4669C211yesmaximal, characteristic, complemented
14#4667C211yesmaximal, characteristic, complemented
15#4666C211yesmaximal, characteristic, complemented
16#2312—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic, complemented
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×C3×C42C2211yescharacteristic, complemented
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
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
44D3×C22⋊C4C418yescomplemented
45C3×#95C2211yescharacteristic, complemented
46C3×#95C2211yescharacteristic, complemented
47C3⋊#95C2211yescharacteristic, complemented
48C3⋊#95C2211yescharacteristic, complemented
49C3⋊#95C2211yescharacteristic, complemented
50C3⋊#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C22×C22⋊C4—31no—
54#388—31no—
55#388—31no—
56#388—31no—
57#388—31no—
58#388—31no—
59#388—31no—
60#388—31no—
61#388D311yescharacteristic, complemented
62#380—31no—
63#380—31no—
64#379—31no—
65#379—31no—
66C4×C22⋊C4—31no—
67C4×C22⋊C4—31no—
68C24×C3C2311yescharacteristic
69C23×D3—22no—
70C23×D3—22no—
71C23×D3—41no—
72C23×D3—41no—
73C23×D3—41no—
74C23×D3—41no—
75C23×D3C2×C414yes—
76C23×D3C2311yescharacteristic
77C23×D3C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C2×C4×D3—41no—
91C2×C4×D3—41no—
92C2×C4×D3—41no—
93C2×C4×D3—41no—
94C2×C4×D3C2×C414yes—
95C2×C4×D3C2×C414yes—
96C3×C4⋊C4—41no—
97C3×C22⋊C4—41no—
98C3×C22⋊C4—41no—
99C3×C22⋊C4C2×C414yes—
100C3×C42—41no—
101#217—41no—
102#217—41no—
103#217C2×C414yes—
104(C2×D3)⋊C4—22no—
105(C2×D3)⋊C4—22no—
106(C2×D3)⋊C4—22no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—41no—
109(C2×D3)⋊C4—41no—
110(C2×D3)⋊C4—41no—
111(C2×D3)⋊C4—41no—
112(C2×D3)⋊C4C2×C414yes—
113(C2×D3)⋊C4C2×C414yes—
114C4⋊Dic3—41no—
115Dic3⋊C4—41no—
116Dic3⋊C4—41no—
117C4×Dic3—41no—
118C4×Dic3—41no—
119C4×Dic3—41no—
120C25—31no—
121C23×C4—31no—
122C23×C4—31no—
123C2×C4⋊C4—31no—
124C2×C4⋊C4—31no—
125C2×C4⋊C4—31no—
126C2×C4⋊C4C2×D311yescharacteristic, complemented
127C2×C22⋊C4—31no—
128C2×C22⋊C4—31no—
129C2×C22⋊C4—31no—
130C2×C22⋊C4—38no—
131C2×C22⋊C4—31no—
132C2×C22⋊C4—31no—
133C2×C22⋊C4—31no—
134C2×C22⋊C4—31no—
135C2×C22⋊C4—31no—
136C2×C22⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4C2×D311yescharacteristic
142C2×C22⋊C4C2×D311yescharacteristic
143C2×C22⋊C4C2×D311yescharacteristic
144C2×C42—31no—
145C2×C42—31no—
146C2×C42—31no—
147C2×C42C2×D311yescharacteristic, complemented
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95C2×D311yescharacteristic, complemented
155#95C2×D311yescharacteristic, complemented
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3C22×C412yes—
163C23×C3C2411yescharacteristic
164C22×D3—21no—
165C22×D3—21no—
166C22×D3—21no—
167C22×D3—21no—
168C22×D3—21no—
169C22×D3—21no—
170C22×D3—21no—
171C22×D3—21no—
172C22×D3—21no—
173C22×D3—21no—
174C22×D3—28no—
175C22×D3—44no—
176C22×D3—44no—
177C22×D3—44no—
178C22×D3—44no—
179C22×D3—44no—
180C22×D3—44no—
181C22×D3C22×C412yes—
182C22×D3C22×C412yes—
183C22×D3#4112yes—
184C22×D3#4112yes—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
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×C4C22×C412yes—
202C2×C3×C4C22×C412yes—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—21no—
210C2×Dic3—21no—
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×Dic3C22×C412yes—
220C2×Dic3C22×C412yes—
221C4×D3—44no—
222C4×D3—44no—
223C24—31no—
224C24—31no—
225C24—34no—
226C24—62no—
227C24—62no—
228C24—121no—
229C24—121no—
230C24—121no—
231C24—121no—
232C24C22×D311yescharacteristic
233C22×C4—31no—
234C22×C4—31no—
235C22×C4—34no—
236C22×C4—34no—
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—121no—
242C22×C4—121no—
243C22×C4—121no—
244C22×C4—121no—
245C22×C4C22×D311yescharacteristic
246C22×C4C22×D311yescharacteristic
247C22×C4C22×D311yescharacteristic
248C22×C4C22×D311yescharacteristic
249C22×C4C22×D311yescharacteristic
250C22×C4C22×D311yescharacteristic
251C4⋊C4—41no—
252C4⋊C4—121no—
253C4⋊C4—121no—
254C4⋊C4—121no—
255C22⋊C4—34no—
256C22⋊C4—34no—
257C22⋊C4—34no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—62no—
261C22⋊C4—62no—
262C22⋊C4—62no—
263C22⋊C4—62no—
264C22⋊C4—121no—
265C22⋊C4—121no—
266C22⋊C4—121no—
267C22⋊C4—121no—
268C22⋊C4—121no—
269C22⋊C4—121no—
270C22⋊C4C4×D314yes—
271C42—41no—
272C42—121no—
273C42—121no—
274C42—121no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3C23×C411yescharacteristic
283C22×C3C2×#4111yescharacteristic
284C22×C3C2×#4111yescharacteristic
285C22×C3H(5,𝔽2)11yescharacteristic
286C22×C3H(5,𝔽2)11yescharacteristic
287C22×C3H(5,𝔽2)11yescharacteristic
288C22×C3H(5,𝔽2)11yescharacteristic
289C2×D3—22no—
290C2×D3—22no—
291C2×D3—22no—
292C2×D3—22no—
293C2×D3—22no—
294C2×D3—22no—
295C2×D3—22no—
296C2×D3—22no—
297C2×D3—22no—
298C2×D3—416no—
299C2×D3—41no—
300C2×D3—41no—
301C2×D3—41no—
302C2×D3—41no—
303C2×D3#11714yes—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—41no—
310Dic3—22no—
311Dic3—22no—
312Dic3—41no—
313Dic3—41no—
314Dic3—41no—
315Dic3—41no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—32no—
323C23—32no—
324C23—32no—
325C23—32no—
326C23—68no—
327C23—61no—
328C23—61no—
329C23—61no—
330C23—61no—
331C23—61no—
332C23—61no—
333C23—61no—
334C23—61no—
335C23—61no—
336C23—61no—
337C23—124no—
338C23—124no—
339C23—124no—
340C23—124no—
341C23—124no—
342C23—124no—
343C23C2×C4×D312yes—
344C23C23×D311yescharacteristic
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—32no—
362C2×C4—32no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—124no—
380C2×C4—124no—
381C2×C4C2×C4×D312yes—
382C2×C4C2×C4×D312yes—
383C2×C3—42no—
384C2×C3C2×#11711yescharacteristic
385C2×C3#51811yescharacteristic
386C2×C3#51811yescharacteristic
387C2×C3#53811yescharacteristic
388C2×C3#53811yescharacteristic
389C2×C3#53811yescharacteristic
390C2×C3#53811yescharacteristic
391D3—24no—
392D3—42no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—34no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—62no—
402C22—62no—
403C22—62no—
404C22—62no—
405C22—62no—
406C22—62no—
407C22—62no—
408C22—62no—
409C22—62no—
410C22—1216no—
411C22—121no—
412C22—121no—
413C22—121no—
414C22—121no—
415C22C22×C4×D311yescharacteristic
416C22#100411yescharacteristic
417C22#100411yescharacteristic
418C22D3×#4111yescharacteristic
419C22D3×#4111yescharacteristic
420C22#100911yescharacteristic
421C22#100911yescharacteristic
422C4—22no—
423C4—22no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—62no—
429C4—62no—
430C4—121no—
431C4—121no—
432C4—121no—
433C4—121no—
434C3#231211yescharacteristic, complemented, Sylow
435C2—42no—
436C2—64no—
437C2—122no—
438C2D3×#11711yescharacteristic
439C2#554511yescharacteristic
440C2#554511yescharacteristic
441C2#561311yescharacteristic
442C2#565711yescharacteristic
443C2#567811yescharacteristic
444C2#570411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#388C2
socle, cosocleC23×C3C24
prime radicalC24×D3C22
hypercenter#388D3
hypocenterC3#2312
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C3×#388C2semidirect
3. #4990C2semidirect
4. #4987C2semidirect
7. #4951C2semidirect
8. #4945C2semidirect
9. #4944C2semidirect
10. #4940C2semidirect
11. C4×(C2×D3)⋊C4C2semidirect
12. #4670C2semidirect
13. #4669C2semidirect
14. #4667C2semidirect
15. #4666C2semidirect
20. C2×C3×C4⋊C4C22semidirect
24. 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
44. D3×C22⋊C4C4semidirect
45. C3×#95C22semidirect
46. C3×#95C22semidirect
47. C3⋊#95C22semidirect
48. C3⋊#95C22semidirect
49. C3⋊#95C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
61. #388D3semidirect
126. C2×C4⋊C4C2×D3semidirect
147. C2×C42C2×D3semidirect
154. #95C2×D3semidirect
155. #95C2×D3semidirect
434. C3#2312semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊C42
C3×#3882
#49902
#49872
#49552
#49512
#49452
#49442
#49402
C4×(C2×D3)⋊C42
#46702
#46692
#46672
#46662
#23123