Finite Group Databasebeta

← #79869

Subgroups — #79869

Order 384.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5548C211yesmaximal, characteristic, complemented
2C4×D3×D4C211yesmaximal, characteristic, complemented
3C3×#442C211yesmaximal, characteristic, complemented
4#5156C211yesmaximal, characteristic, complemented
5#5150C211yesmaximal, characteristic, complemented
6#5014C211yesmaximal, characteristic, complemented
7#5014C211yesmaximal, characteristic, complemented
8#4870C211yesmaximal, characteristic, complemented
9#4863C211yesmaximal, characteristic, complemented
10#4786C211yesmaximal, characteristic, complemented
11#4777C211yesmaximal, characteristic, complemented
12#4773C211yesmaximal, characteristic, complemented
13#4761C211yesmaximal, characteristic, complemented
14#4711C211yesmaximal, characteristic, complemented
15#4705C211yesmaximal, characteristic, complemented
16#3109—31nomaximal, Sylow
17C2×D3×D4C2211yescharacteristic
18C2×#235—21no—
19C22×C4×D3—21no—
20C2×C3×D8C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22C3×C4×D4C2211yescharacteristic, complemented
23#940C2211yescharacteristic, complemented
24#938C2211yescharacteristic
25D4×Dic3C2211yescharacteristic
26C2×#213C2211yescharacteristic
27C2×#213C2211yescharacteristic
28C4×#67—21no—
29C4×#67—21no—
30C2×D24C2211yescharacteristic
31#895C2211yescharacteristic
32#893C2211yescharacteristic
33D3×C4⋊C4C2211yescharacteristic
34#888C2211yescharacteristic, complemented
35#885—21no—
36#884—21no—
37#67⋊C4—21no—
38D3×C22⋊C4—21no—
39C4×D12C2211yescharacteristic
40C4×D12C2211yescharacteristic, complemented
41C42×D3C2211yescharacteristic
42C3×#106C2211yescharacteristic, complemented
43C3×#102C2211yescharacteristic
44C3×#102C2211yescharacteristic, complemented
45C3×#97C2211yescharacteristic, complemented
46#832C2211yescharacteristic
47#832C2211yescharacteristic, complemented
48#821C2211yescharacteristic
49#821C2211yescharacteristic, complemented
50(C2×D3)⋊C8C2211yescharacteristic
51(C2×D3)⋊C8C2211yescharacteristic
52#817C2211yescharacteristic, complemented
53Dic3⋊C8C2211yescharacteristic, complemented
54Dic3⋊C8C2211yescharacteristic, complemented
55#809C2211yescharacteristic
56#809C2211yescharacteristic, complemented
57#808C2211yescharacteristic, complemented
58#808C2211yescharacteristic, complemented
59#803C2211yescharacteristic, complemented
60#532—31no—
61C2×C4×D4—31no—
62#481—31no—
63#481—31no—
64#476—31no—
65#476—31no—
66#459—31no—
67#459—31no—
68#447—31no—
69#447—31no—
70#442—31no—
71#442—31no—
72#442—31no—
73#442D311yescharacteristic, complemented
74#432—31no—
75C23×D3—21no—
76C2×C3×D4C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C2×#67—21no—
84C22×Dic3—21no—
85D3×D4—22no—
86D3×D4—22no—
87#235—44no—
88C2×D12—21no—
89C2×D12C2311yescharacteristic
90C2×D12C2311yescharacteristic
91C2×C4×D3—21no—
92C2×C4×D3—21no—
93C2×C4×D3—21no—
94C2×C4×D3—21no—
95C2×C4×D3—44no—
96C2×C4×D3D411yescharacteristic
97C2×C4×D3D411yescharacteristic
98C2×C4×D3C2311yescharacteristic
99C2×Dic6—21no—
100C3×D8—22no—
101C2×C3×C8C2311yescharacteristic
102C2×C3×C8C2311yescharacteristic
103C3×C4⋊C4C2311yescharacteristic
104C3×C4⋊C4C2311yescharacteristic
105C3×C22⋊C4—21no—
106C3×C22⋊C4—21no—
107C3×C42C2311yescharacteristic
108#217—21no—
109#217—21no—
110#213—22no—
111#213—22no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4—21no—
114(C2×D3)⋊C4—21no—
115(C2×D3)⋊C4—21no—
116C4⋊Dic3C2311yescharacteristic
117C4⋊Dic3C2311yescharacteristic
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120C4×Dic3D411yescharacteristic
121C4×Dic3D411yescharacteristic
122C4×Dic3C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125D24—22no—
126C2×#41—61no—
127C22×D4—31no—
128C23×C4—61no—
129C2×D8—31no—
130C2×D8—31no—
131C2×D8—31no—
132C2×D8C2×D311yescharacteristic
133C4⋊Q8—31no—
134#127—31no—
135#124—61no—
136#121—31no—
137#121—31no—
138#121—61no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—31no—
143C4×D4—61no—
144C4×D4—61no—
145C4×D4—61no—
146C4×D4C2×D311yescharacteristic
147C4×D4C2×D311yescharacteristic, complemented
148C2×C4⋊C4—31no—
149C2×C22⋊C4—61no—
150C2×C42—31no—
151#106—31no—
152#106—31no—
153#106—31no—
154#106C2×D311yescharacteristic, complemented
155C4⋊C8—31no—
156C4⋊C8—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163#102C2×D311yescharacteristic
164#102C2×D311yescharacteristic, complemented
165C22⋊C8—31no—
166C22⋊C8—31no—
167#97—31no—
168#97C2×D311yescharacteristic, complemented
169C23×C3—21no—
170C23×C3—21no—
171C22×D3—24no—
172C22×D3—21no—
173C22×D3—21no—
174C22×D3—42no—
175C22×D3—42no—
176C22×D3C2×D411yescharacteristic
177C3×D4—21no—
178C3×D4—21no—
179C3×D4—21no—
180C3×D4#4112yescomplemented
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2411yescharacteristic
188#67—24no—
189#67—42no—
190#67—42no—
191#67—42no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—42no—
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197C2×Dic3C2×D411yescharacteristic
198D12—21no—
199D12—21no—
200D12—21no—
201D12—42no—
202D12#4112yescomplemented
203C4×D3—22no—
204C4×D3—21no—
205C4×D3—21no—
206C4×D3—22no—
207C4×D3—42no—
208C4×D3—42no—
209C4×D3—42no—
210C4×D3—42no—
211Dic6—42no—
212C3×C8—21no—
213C3×C8—21no—
214C3⋊C8—21no—
215C3⋊C8—21no—
216C24—61no—
217#41—124no—
218C2×Q8—61no—
219C2×D4—31no—
220C2×D4—31no—
221C2×D4—61no—
222C2×D4—61no—
223C2×D4—61no—
224C2×D4—61no—
225C2×D4—62no—
226C2×D4—62no—
227C2×D4—61no—
228C2×D4C22×D311yescharacteristic
229C2×D4C22×D311yescharacteristic
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—31no—
233C22×C4—31no—
234C22×C4—31no—
235C22×C4—61no—
236C22×C4—61no—
237C22×C4—61no—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4—124no—
241D8—22no—
242D8—62no—
243D8—62no—
244D8—62no—
245C2×C8—31no—
246C2×C8—31no—
247C2×C8C22×D311yescharacteristic
248C2×C8C22×D311yescharacteristic
249C4⋊C4—31no—
250C4⋊C4—31no—
251C4⋊C4—61no—
252C4⋊C4—61no—
253C4⋊C4C22×D311yescharacteristic
254C4⋊C4C22×D311yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C22⋊C4—61no—
262C22⋊C4—61no—
263C42—31no—
264C42—31no—
265C42—31no—
266C42C22×D311yescharacteristic
267C22×C3—22no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3C22×D411yescharacteristic
274C2×D3—21no—
275C2×D3—21no—
276C2×D3—22no—
277C2×D3—48no—
278C2×D3—41no—
279C2×D3—41no—
280C2×D3—41no—
281C2×D3—41no—
282C2×D3—41no—
283C2×D3AGL(1,ℤ/8)12yes—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4C2×#4111yescharacteristic
289C3×C4C2×#4111yescharacteristic
290Dic3—21no—
291Dic3—21no—
292Dic3—41no—
293Dic3—41no—
294Dic3AGL(1,ℤ/8)12yes—
295C23—21no—
296C23—21no—
297C23—31no—
298C23—64no—
299C23—61no—
300C23—61no—
301C23—122no—
302C23—122no—
303Q8—122no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—32no—
308D4—64no—
309D4—61no—
310D4—61no—
311D4—61no—
312D4—122no—
313D4—122no—
314D4—122no—
315D4—122no—
316D4#23512yescomplemented
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—31no—
320C2×C4—31no—
321C2×C4—31no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—62no—
325C2×C4—62no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—122no—
331C2×C4—122no—
332C2×C4—122no—
333C2×C4—122no—
334C2×C4—122no—
335C2×C4D3×D411yescharacteristic
336C2×C4D3×D411yescharacteristic
337C2×C4C23×D311yescharacteristic
338C8—21no—
339C8—21no—
340C8—61no—
341C8—61no—
342C2×C3—42no—
343C2×C3—81no—
344C2×C3#52511yescharacteristic
345C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
346C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
347D3—22no—
348D3—42no—
349D3—81no—
350C22—22no—
351C22—32no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—61no—
358C22—61no—
359C22—62no—
360C22—128no—
361C22—121no—
362C22—121no—
363C22—121no—
364C22—121no—
365C22—121no—
366C22C2×D3×D411yescharacteristic
367C4—21no—
368C4—21no—
369C4—32no—
370C4—41no—
371C4—41no—
372C4—61no—
373C4—61no—
374C4—121no—
375C4—121no—
376C4C2×#23511yescharacteristic
377C4D3×#4111yescharacteristic
378C3#310911yescharacteristic, complemented, Sylow
379C2—42no—
380C2—62no—
381C2—81no—
382C2—122no—
383C2—241no—
384C2#554711yescharacteristic
385C2D3×AGL(1,ℤ/8)11yescharacteristic
386C2D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#442C2
socleC22×C3C22×D4
hypercenter#442D3
hypocenterC3#3109
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #5548C2semidirect
2. C4×D3×D4C2semidirect
3. C3×#442C2semidirect
4. #5156C2semidirect
5. #5150C2semidirect
6. #5014C2semidirect
7. #5014C2semidirect
8. #4870C2semidirect
9. #4863C2semidirect
10. #4786C2semidirect
11. #4777C2semidirect
12. #4773C2semidirect
13. #4761C2semidirect
14. #4711C2semidirect
15. #4705C2semidirect
22. C3×C4×D4C22semidirect
23. #940C22semidirect
34. #888C22semidirect
40. C4×D12C22semidirect
42. C3×#106C22semidirect
44. C3×#102C22semidirect
45. C3×#97C22semidirect
47. #832C22semidirect
49. #821C22semidirect
52. #817C22semidirect
53. Dic3⋊C8C22semidirect
54. Dic3⋊C8C22semidirect
56. #809C22semidirect
57. #808C22semidirect
58. #808C22semidirect
59. #803C22semidirect
73. #442D3semidirect
147. C4×D4C2×D3semidirect
154. #106C2×D3semidirect
164. #102C2×D3semidirect
168. #97C2×D3semidirect
180. C3×D4#41semidirect
202. D12#41semidirect
316. D4#235semidirect
378. C3#3109semidirect

Maximal subgroups

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

subgroupindex
#55482
C4×D3×D42
C3×#4422
#51562
#51502
#50142
#48702
#48632
#47862
#47772
#47732
#47612
#47112
#47052
#31093