Finite Group Databasebeta

← #10596018

Subgroups — #10596018

Order 576.

990 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3828C211yesmaximal, characteristic, complemented
2C22×C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C4×D4C211yesmaximal, characteristic, complemented
4#64148C211yesmaximal, characteristic, complemented
5#64146C211yesmaximal, characteristic, complemented
6C4×#638C211yesmaximal, characteristic, complemented
7C4×#638C211yesmaximal, characteristic, complemented
8#64105C211yesmaximal, characteristic, complemented
9#64103C211yesmaximal, characteristic, complemented
10#64093C211yesmaximal, characteristic, complemented
11#64092C211yesmaximal, characteristic, complemented
12#64091C211yesmaximal, characteristic, complemented
13#64087C211yesmaximal, characteristic, complemented
14C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
15#64081C211yesmaximal, characteristic, complemented
16#5547—34nomaximal
17C23×C3⋊D3C2211yescharacteristic
18C2×C32×D4C2211yescharacteristic
19C22×C32×C4C2211yescharacteristic
20C22×C32×C4C2211yescharacteristic, complemented
21C2×#638C2211yescharacteristic
22C2×#638C2211yescharacteristic
23C2×#638C2211yescharacteristic
24C2×#638C2211yescharacteristic, complemented
25C22×C3⋊Dic3C2211yescharacteristic
26#3828—24no—
27C2×C4⋊(C3⋊D3)C2211yescharacteristic
28C2×C4⋊(C3⋊D3)C2211yescharacteristic
29C2×C4×C3⋊D3—24no—
30C2×C4×C3⋊D3C2211yescharacteristic
31C2×C4×C3⋊D3C2211yescharacteristic
32C2×C4×C3⋊D3C2211yescharacteristic
33C2×C4×C3⋊D3C2211yescharacteristic
34C2×C4×C3⋊D3C2211yescharacteristic, complemented
35C2×#634C2211yescharacteristic, complemented
36C32×C4⋊C4C2211yescharacteristic, complemented
37C32×C22⋊C4C2211yescharacteristic
38C32×C22⋊C4C2211yescharacteristic, complemented
39C32×C42C2211yescharacteristic, complemented
40#3757C2211yescharacteristic
41#3757C2211yescharacteristic, complemented
42#3752C2211yescharacteristic
43#3752C2211yescharacteristic
44#3752C2211yescharacteristic
45#3752C2211yescharacteristic
46#3752C2211yescharacteristic, complemented
47#3752C2211yescharacteristic, complemented
48C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#3750C2211yescharacteristic, complemented
50#3750C2211yescharacteristic, complemented
51#3750C2211yescharacteristic, complemented
52#3750C2211yescharacteristic, complemented
53C4×C3⋊Dic3C2211yescharacteristic, complemented
54C2×#235—34no—
55C22×C4×D3—34no—
56C3×C4×D4D314yescomplemented
57#939—34no—
58#937—34no—
59C4×#67—34no—
60C4×#67—34no—
61#896—34no—
62#894—34no—
63#884—34no—
64#883—34no—
65#882—34no—
66#878—34no—
67C4×D12—34no—
68#872—34no—
69C23×C32C2311yescharacteristic
70C23×C32C2311yescharacteristic
71C22×C3⋊D3—22no—
72C22×C3⋊D3—22no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3C2311yescharacteristic
75C22×C3⋊D3C2311yescharacteristic
76C22×C3⋊D3C2311yescharacteristic
77C32×D4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4C2311yescharacteristic
81C2×C32×C4C2311yescharacteristic
82C2×C32×C4C2311yescharacteristic
83C2×C32×C4C2311yescharacteristic
84C2×C32×C4C2311yescharacteristic
85#638—22no—
86#638—22no—
87#638—22no—
88#638—22no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊Dic3C2311yescharacteristic
95C4⋊(C3⋊D3)—22no—
96C4⋊(C3⋊D3)—22no—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—22no—
99C4×C3⋊D3—22no—
100C4×C3⋊D3—22no—
101C4×C3⋊D3D414yescomplemented
102#634—22no—
103#525—91noSylow
104C23×D3—34no—
105C2×C3×D4C2×D314yes—
106C22×C3×C4C2×D314yes—
107C22×C3×C4C2×D314yescomplemented
108C2×#67—34no—
109C2×#67—34no—
110C2×#67—34no—
111C2×#67—34no—
112C22×Dic3—34no—
113#235—616no—
114C2×D12—34no—
115C2×D12—34no—
116C2×C4×D3—34no—
117C2×C4×D3—34no—
118C2×C4×D3—34no—
119C2×C4×D3—34no—
120C2×C4×D3—34no—
121C2×C4×D3—616no—
122C2×Dic6—34no—
123C3×C4⋊C4C2×D314yescomplemented
124C3×C22⋊C4C2×D314yes—
125C3×C22⋊C4C2×D314yescomplemented
126C3×C42C2×D314yescomplemented
127#217—34no—
128#217—34no—
129(C2×D3)⋊C4—34no—
130(C2×D3)⋊C4—34no—
131(C2×D3)⋊C4—34no—
132(C2×D3)⋊C4—34no—
133(C2×D3)⋊C4—34no—
134(C2×D3)⋊C4—34no—
135C4⋊Dic3—34no—
136Dic3⋊C4—34no—
137Dic3⋊C4—34no—
138Dic3⋊C4—34no—
139Dic3⋊C4—34no—
140C4×Dic3—34no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32#4112yescomplemented
147C22×C32C2411yescharacteristic
148C2×C3⋊D3—28no—
149C2×C3⋊D3—21no—
150C2×C3⋊D3—21no—
151C2×C3⋊D3—21no—
152C2×C3⋊D3—21no—
153C2×C3⋊D3—21no—
154C2×C3⋊D3—21no—
155C2×C3⋊D3—21no—
156C2×C3⋊D3C2×D412yes—
157C2×C3⋊D3#4112yescomplemented
158C32×C4—21no—
159C32×C4—21no—
160C32×C4—21no—
161C32×C4—21no—
162C32×C4C2×D412yes—
163C3⋊Dic3—21no—
164C3⋊Dic3—21no—
165C3⋊Dic3—21no—
166C3⋊Dic3—21no—
167C3⋊Dic3C2×D412yes—
168C2×#41—91no—
169C23×C4—91no—
170#123—91no—
171#123—91no—
172C22⋊Q8—91no—
173C22⋊Q8—91no—
174#121—91no—
175#121—91no—
176#120—91no—
177#120—91no—
178C4×D4—91no—
179C4×D4—91no—
180C4×D4—91no—
181C4×D4C3⋊D311yescharacteristic, complemented
182#117—91no—
183C23×C3C22×D314yes—
184C23×C3C22×D314yes—
185C22×D3—34no—
186C22×D3—34no—
187C22×D3—34no—
188C22×D3—68no—
189C22×D3—68no—
190C22×D3—68no—
191C3×D4—28no—
192C2×C3×C4—28no—
193C2×C3×C4—28no—
194C2×C3×C4C22×D314yes—
195C2×C3×C4C22×D314yes—
196C2×C3×C4C22×D314yes—
197C2×C3×C4C22×D314yes—
198C2×C3×C4C22×D314yes—
199#67—68no—
200#67—68no—
201#67—68no—
202#67—68no—
203C2×Dic3—34no—
204C2×Dic3—34no—
205C2×Dic3—34no—
206C2×Dic3—34no—
207C2×Dic3—34no—
208C2×Dic3—68no—
209D12—68no—
210D12—68no—
211C4×D3—316no—
212C4×D3—68no—
213C4×D3—68no—
214C4×D3—68no—
215C4×D3—68no—
216Dic6—68no—
217C2×C32—22no—
218C2×C32—41no—
219C2×C32C22×D411yescharacteristic
220C2×C32C2×#4111yescharacteristic
221C2×C32C2×#4111yescharacteristic
222C3⋊D3—22no—
223C3⋊D3—22no—
224C3⋊D3—41no—
225C24—91no—
226#41—184no—
227C2×Q8—91no—
228C2×D4—91no—
229C2×D4—91no—
230C2×D4—91no—
231C2×D4—91no—
232C2×D4—91no—
233C2×D4—91no—
234C2×D4C2×C3⋊D311yescharacteristic
235C22×C4—91no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—184no—
242C22×C4C2×C3⋊D311yescharacteristic
243C22×C4C2×C3⋊D311yescharacteristic, complemented
244C4⋊C4—91no—
245C4⋊C4—91no—
246C4⋊C4—91no—
247C4⋊C4—91no—
248C4⋊C4—91no—
249C4⋊C4C2×C3⋊D311yescharacteristic, complemented
250C22⋊C4—91no—
251C22⋊C4—91no—
252C22⋊C4—91no—
253C22⋊C4—91no—
254C22⋊C4—91no—
255C22⋊C4—91no—
256C22⋊C4—91no—
257C22⋊C4—91no—
258C22⋊C4C2×C3⋊D311yescharacteristic
259C22⋊C4C2×C3⋊D311yescharacteristic, complemented
260C42—91no—
261C42C2×C3⋊D311yescharacteristic, complemented
262C22×C3—24no—
263C22×C3—24no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—24no—
267C22×C3#23518yescomplemented
268C22×C3C23×D314yes—
269C2×D3—38no—
270C2×D3—38no—
271C2×D3—632no—
272C2×D3—64no—
273C2×D3—64no—
274C2×D3—64no—
275C2×D3—64no—
276C2×D3—64no—
277C2×D3—64no—
278C2×D3—64no—
279C3×C4—24no—
280C3×C4—24no—
281C3×C4—24no—
282C3×C4—24no—
283C3×C4D3×D418yes—
284Dic3—38no—
285Dic3—64no—
286Dic3—64no—
287Dic3—64no—
288Dic3—64no—
289C32#52511yescharacteristic, complemented, Sylow
290C23—91no—
291C23—91no—
292C23—91no—
293C23—182no—
294C23—182no—
295C23—182no—
296C23C22×C3⋊D311yescharacteristic
297C23C22×C3⋊D311yescharacteristic
298Q8—182no—
299D4—22no—
300D4—182no—
301D4—182no—
302D4—182no—
303D4—182no—
304D4—182no—
305D4—182no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—91no—
309C2×C4—94no—
310C2×C4—91no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—182no—
319C2×C4C22×C3⋊D311yescharacteristic
320C2×C4C22×C3⋊D311yescharacteristic
321C2×C4C22×C3⋊D311yescharacteristic
322C2×C4C22×C3⋊D311yescharacteristic
323C2×C4C22×C3⋊D311yescharacteristic
324C2×C3—28no—
325C2×C3—44no—
326C2×C3C2×#23514yes—
327C2×C3C2×D3×D414yes—
328C2×C3D3×#4114yes—
329D3—68no—
330D3—68no—
331D3—124no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—92no—
338C22—92no—
339C22—188no—
340C22—181no—
341C22—181no—
342C22—181no—
343C22—181no—
344C22—181no—
345C22—181no—
346C22—181no—
347C22#382812yescomplemented
348C22C23×C3⋊D311yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—92no—
354C4—181no—
355C4—181no—
356C4—181no—
357C4—181no—
358C4D4×C3⋊D312yes—
359C3#554714yescomplemented
360C2—22no—
361C2—41no—
362C2—182no—
363C2—182no—
364C2—361no—
365C2C2×#382811yescharacteristic
366C2C2×D4×C3⋊D311yescharacteristic
367C2#41×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C4C22×C3⋊D3
commutator, socle, cosocleC22×C32C24
FrattiniC22C23×C3⋊D3
FittingC32×C4×D4C2
hypercenterC4×D4C3⋊D3
hypocenterC32#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#3828C2semidirect
2. C22×C4×C3⋊D3C2semidirect
3. C32×C4×D4C2semidirect
4. #64148C2semidirect
5. #64146C2semidirect
6. C4×#638C2semidirect
7. C4×#638C2semidirect
8. #64105C2semidirect
9. #64103C2semidirect
10. #64093C2semidirect
11. #64092C2semidirect
12. #64091C2semidirect
13. #64087C2semidirect
14. C4×C4⋊(C3⋊D3)C2semidirect
15. #64081C2semidirect
20. C22×C32×C4C22semidirect
24. C2×#638C22semidirect
34. C2×C4×C3⋊D3C22semidirect
35. C2×#634C22semidirect
36. C32×C4⋊C4C22semidirect
38. C32×C22⋊C4C22semidirect
39. C32×C42C22semidirect
41. #3757C22semidirect
46. #3752C22semidirect
47. #3752C22semidirect
48. C4⋊(C3⋊Dic3)C22semidirect
49. #3750C22semidirect
50. #3750C22semidirect
51. #3750C22semidirect
52. #3750C22semidirect
53. C4×C3⋊Dic3C22semidirect
56. C3×C4×D4D3semidirect
101. C4×C3⋊D3D4semidirect
107. C22×C3×C4C2×D3semidirect
123. C3×C4⋊C4C2×D3semidirect
125. C3×C22⋊C4C2×D3semidirect
126. C3×C42C2×D3semidirect
146. C22×C32#41semidirect
157. C2×C3⋊D3#41semidirect
181. C4×D4C3⋊D3semidirect
243. C22×C4C2×C3⋊D3semidirect
249. C4⋊C4C2×C3⋊D3semidirect
259. C22⋊C4C2×C3⋊D3semidirect
261. C42C2×C3⋊D3semidirect
267. C22×C3#235semidirect
289. C32#525semidirect
347. C22#3828semidirect
359. C3#5547semidirect

Maximal subgroups

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

subgroupindex
C2×#38282
C22×C4×C3⋊D32
C32×C4×D42
#641482
#641462
C4×#6382
#641052
#641032
#640932
#640922
#640912
#640872
C4×C4⋊(C3⋊D3)2
#640812
#55473