Finite Group Databasebeta

← #79592

Subgroups — #79592

Order 384.

454 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5557C211yesmaximal, characteristic, complemented
2C4×D3×D4C211yesmaximal, characteristic, complemented
3C3×C4×D8C211yesmaximal, characteristic, complemented
4#5156C211yesmaximal, characteristic
5#5153C211yesmaximal, characteristic, complemented
6C4×#214C211yesmaximal, characteristic, complemented
7C4×#213C211yesmaximal, characteristic, complemented
8#4891C211yesmaximal, characteristic, complemented
9#4884C211yesmaximal, characteristic, complemented
10#4787C211yesmaximal, characteristic, complemented
11#4777C211yesmaximal, characteristic, complemented
12#4776C211yesmaximal, characteristic, complemented
13#4763C211yesmaximal, characteristic, complemented
14C4×#204C211yesmaximal, characteristic, complemented
15#4685C211yesmaximal, characteristic, complemented
16#3105—31nomaximal, Sylow
17C2×D3×D4C2211yescharacteristic
18C22×C4×D3—21no—
19C2×C3×D8C2211yescharacteristic
20C3×C4×D4C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic, complemented
22#938C2211yescharacteristic
23#936C2211yescharacteristic, complemented
24D4×Dic3C2211yescharacteristic
25C2×#214C2211yescharacteristic
26C2×#213C2211yescharacteristic
27C4×#67—21no—
28C4×#67—21no—
29#926—21no—
30C2×#204C2211yescharacteristic
31#897C2211yescharacteristic
32#893C2211yescharacteristic
33D3×C4⋊C4C2211yescharacteristic
34#890C2211yescharacteristic, complemented
35#883—21no—
36#67⋊C4—21no—
37D3×C22⋊C4—21no—
38#879—21no—
39C4×D12C2211yescharacteristic
40C42×D3C2211yescharacteristic
41C4×Dic6C2211yescharacteristic, complemented
42C3×#107C2211yescharacteristic, complemented
43C3×#102C2211yescharacteristic
44C3×#102C2211yescharacteristic, complemented
45C3×C4×C8C2211yescharacteristic, complemented
46#832C2211yescharacteristic
47#832C2211yescharacteristic, complemented
48#821C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#817C2211yescharacteristic, complemented
52#816C2211yescharacteristic, complemented
53Dic3⋊C8C2211yescharacteristic, complemented
54Dic3⋊C8C2211yescharacteristic, complemented
55#810C2211yescharacteristic, complemented
56#809C2211yescharacteristic
57#808C2211yescharacteristic, complemented
58#807C2211yescharacteristic, complemented
59C4×C3⋊C8C2211yescharacteristic, complemented
60#529—31no—
61C2×C4×D4—31no—
62#484—31no—
63#481—31no—
64#478—31no—
65#478—31no—
66#463—31no—
67#463—31no—
68#450—31no—
69#447—31no—
70C4×SD16—31no—
71C4×SD16—31no—
72C4×D8—31no—
73C4×D8D311yescharacteristic, complemented
74#431—31no—
75C23×D3—21no—
76C2×C3×D4C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C2×#67—21no—
81C2×#67—21no—
82C22×Dic3—21no—
83D3×D4—22no—
84D3×D4—22no—
85C2×D12C2311yescharacteristic
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3—44no—
90C2×C4×D3D411yescharacteristic
91C2×C4×D3D411yescharacteristic
92C2×C4×D3C2311yescharacteristic
93C2×Dic6C2311yescharacteristic
94C3×D8—22no—
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100C3×C22⋊C4—21no—
101C3×C42C2311yescharacteristic
102#217—21no—
103#217—21no—
104#217—21no—
105#217—21no—
106#214—22no—
107#213—22no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118C4×Dic3—21no—
119C4×Dic3D411yescharacteristic
120C4×Dic3D411yescharacteristic
121C4×Dic3C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124#204—22no—
125C22×D4—31no—
126C23×C4—61no—
127C2×SD16—31no—
128C2×SD16—31no—
129C2×D8—31no—
130C2×D8C2×D311yescharacteristic
131#126—61no—
132#125—31no—
133#124—31no—
134#123—61no—
135C22⋊Q8—31no—
136#121—31no—
137C4×Q8—31no—
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—61no—
142C4×D4—61no—
143C4×D4—61no—
144C4×D4C2×D311yescharacteristic
145C4×D4C2×D311yescharacteristic, complemented
146#117—61no—
147C2×C4⋊C4—31no—
148C2×C22⋊C4—61no—
149C2×C42—31no—
150#107—31no—
151#107C2×D311yescharacteristic, complemented
152#106—31no—
153#106—31no—
154C4⋊C8—31no—
155C4⋊C8—31no—
156#103—31no—
157#103—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102C2×D311yescharacteristic
163#102C2×D311yescharacteristic, complemented
164C22⋊C8—31no—
165C22⋊C8—31no—
166C4×C8—31no—
167C4×C8C2×D311yescharacteristic, complemented
168C23×C3—21no—
169C23×C3—21no—
170C22×D3—24no—
171C22×D3—21no—
172C22×D3—42no—
173C22×D3—42no—
174C22×D3C2×D411yescharacteristic
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—21no—
178C3×D4#4112yes—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2411yescharacteristic
186#67—24no—
187#67—42no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—42no—
192C2×Dic3C2×D411yescharacteristic
193C2×Dic3C2×D411yescharacteristic
194C2×Dic3C2×D411yescharacteristic
195D12—21no—
196D12#4112yes—
197C4×D3—22no—
198C4×D3—22no—
199C4×D3—21no—
200C4×D3—21no—
201C4×D3—42no—
202C4×D3—42no—
203C4×D3—42no—
204Dic6—21no—
205Dic6—21no—
206C3×C8—21no—
207C3×C8—21no—
208C3⋊C8—21no—
209C3⋊C8—21no—
210C24—61no—
211C2×Q8—31no—
212C2×D4—31no—
213C2×D4—61no—
214C2×D4—62no—
215C2×D4—62no—
216C2×D4—61no—
217C2×D4C22×D311yescharacteristic
218C2×D4C22×D311yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—31no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—61no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—124no—
229SD16—62no—
230SD16—62no—
231D8—22no—
232D8—62no—
233C2×C8—31no—
234C2×C8—31no—
235C2×C8C22×D311yescharacteristic
236C2×C8C22×D311yescharacteristic
237C4⋊C4—31no—
238C4⋊C4—31no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4C22×D311yescharacteristic
245C4⋊C4C22×D311yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C42—31no—
256C42—31no—
257C42—31no—
258C42—61no—
259C42C22×D311yescharacteristic
260C22×C3—22no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3C22×D411yescharacteristic
267C2×D3—21no—
268C2×D3—21no—
269C2×D3—22no—
270C2×D3—48no—
271C2×D3—41no—
272C2×D3—41no—
273C2×D3#13512yes—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4AGL(1,ℤ/8)12yes—
278C3×C4C2×#4111yescharacteristic
279C3×C4C2×#4111yescharacteristic
280Dic3—21no—
281Dic3—21no—
282Dic3—21no—
283Dic3—41no—
284Dic3—41no—
285Dic3—41no—
286C23—21no—
287C23—21no—
288C23—31no—
289C23—64no—
290C23—61no—
291C23—122no—
292C23—122no—
293Q8—61no—
294Q8—61no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—32no—
299D4—64no—
300D4—61no—
301D4—122no—
302D4#23512yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—31no—
306C2×C4—31no—
307C2×C4—31no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—62no—
311C2×C4—62no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—122no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—122no—
321C2×C4D3×D411yescharacteristic
322C2×C4D3×D411yescharacteristic
323C2×C4C23×D311yescharacteristic
324C8—21no—
325C8—21no—
326C8—61no—
327C8—61no—
328C2×C3—42no—
329C2×C3—81no—
330C2×C3#52511yescharacteristic
331C2×C3C2×#13511yescharacteristic
332C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
333D3—22no—
334D3—42no—
335C22—22no—
336C22—32no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—61no—
343C22—61no—
344C22—62no—
345C22—128no—
346C22—121no—
347C22—121no—
348C22C2×D3×D411yescharacteristic
349C4—21no—
350C4—41no—
351C4—41no—
352C4—61no—
353C4—61no—
354C4—61no—
355C4—121no—
356C4—121no—
357C4—121no—
358C4#91112yes—
359C4C2×#23511yescharacteristic
360C4D3×#4111yescharacteristic
361C3#310511yescharacteristic, complemented, Sylow
362C2—42no—
363C2—62no—
364C2—81no—
365C2—122no—
366C2#554711yescharacteristic
367C2C2×#91111yescharacteristic
368C2D3×#13511yescharacteristic
subgroupG/H
centerC2×C4D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×D8C2
socleC22×C3C22×D4
prime radical#5156C2
hypercenterC4×D8D3
hypocenterC3#3105
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #5557C2semidirect
2. C4×D3×D4C2semidirect
3. C3×C4×D8C2semidirect
5. #5153C2semidirect
6. C4×#214C2semidirect
7. C4×#213C2semidirect
8. #4891C2semidirect
9. #4884C2semidirect
10. #4787C2semidirect
11. #4777C2semidirect
12. #4776C2semidirect
13. #4763C2semidirect
14. C4×#204C2semidirect
15. #4685C2semidirect
21. C3×C4×D4C22semidirect
23. #936C22semidirect
34. #890C22semidirect
41. C4×Dic6C22semidirect
42. C3×#107C22semidirect
44. C3×#102C22semidirect
45. C3×C4×C8C22semidirect
47. #832C22semidirect
51. #817C22semidirect
52. #816C22semidirect
53. Dic3⋊C8C22semidirect
54. Dic3⋊C8C22semidirect
55. #810C22semidirect
57. #808C22semidirect
58. #807C22semidirect
59. C4×C3⋊C8C22semidirect
73. C4×D8D3semidirect
145. C4×D4C2×D3semidirect
151. #107C2×D3semidirect
163. #102C2×D3semidirect
167. C4×C8C2×D3semidirect
361. C3#3105semidirect

Maximal subgroups

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

subgroupindex
#55572
C4×D3×D42
C3×C4×D82
#51562
#51532
C4×#2142
C4×#2132
#48912
#48842
#47872
#47772
#47762
#47632
C4×#2042
#46852
#31053