Finite Group Databasebeta

← #10594244

Subgroups — #10594244

Order 576.

569 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 569 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64091C211yesmaximal, characteristic, complemented
2C3×#883C212yesmaximal, complemented
3#63981C212yesmaximal, complemented
4#63979C211yesmaximal, characteristic, complemented
5#63975C211yesmaximal, characteristic, complemented
6#63910C212yesmaximal, complemented
7#63909C212yesmaximal, complemented
8#63906C212yesmaximal, complemented
9#63848C212yesmaximal, complemented
10#5666—32nomaximal
11C23×C3⋊D3C2211yescharacteristic
12C2×#638C2211yescharacteristic
13C2×C4⋊(C3⋊D3)C2212yes—
14C2×C3×#67C2212yes—
15C2×C3×C4×D3C2212yescomplemented
16C2×#626C2212yes—
17C2×#626C2212yes—
18C2×#626C2212yescomplemented
19C2×#625C2211yescharacteristic, complemented
20C2×#624C2211yescharacteristic, complemented
21C32×C22⋊C4C2211yescharacteristic
22#3752C2212yes—
23C3×#217C2212yes—
24C3×(C2×D3)⋊C4C2212yescomplemented
25C3×C4⋊Dic3C2212yescomplemented
26C3×Dic3⋊C4C2212yescomplemented
27Dic3⋊Dic3C2212yescomplemented
28#3722C2212yes—
29#3722C2212yes—
30#3722C2211yescharacteristic, complemented
31Dic32C2211yescharacteristic, complemented
32C3×#123—32no—
33#940—32no—
34#937—32no—
35#930—32no—
36#930—32no—
37#898—32no—
38#898—32no—
39#895—32no—
40#895—32no—
41#884—32no—
42#884—32no—
43#883—32no—
44#883D312yescomplemented
45#882—32no—
46#882—32no—
47#882—61no—
48C23×C32C2311yescharacteristic
49C22×C3⋊D3—42no—
50C22×C3⋊D3—41no—
51C22×C3⋊D3C2312yes—
52C22×C3⋊D3C2311yescharacteristic
53C22×C3×D3C2312yes—
54C2×C32×C4C2312yes—
55#638—41no—
56C2×C3⋊Dic3C2311yescharacteristic
57C4⋊(C3⋊D3)—42no—
58C3×#67—42no—
59C2×C3×Dic3C2312yes—
60C2×C3×Dic3C2312yes—
61C2×C3×Dic3C2312yes—
62C3×C4×D3—42no—
63#626—42no—
64#626—42no—
65#626—42no—
66#625—41no—
67#624—41no—
68#560—91noSylow
69C23×D3—32no—
70C23×D3—61no—
71C2×C3×D4—32no—
72C22×C3×C4—32no—
73C2×#67—32no—
74C2×#67—32no—
75C2×#67—32no—
76C2×#67—32no—
77C2×#67—32no—
78C2×#67—61no—
79C2×#67C2×D312yes—
80C2×D12—32no—
81C2×D12—32no—
82C2×D12—32no—
83C2×D12—32no—
84C2×D12—32no—
85C2×D12—62no—
86C2×C4×D3—32no—
87C2×C4×D3C2×D312yescomplemented
88C3×C4⋊C4—32no—
89C3×C4⋊C4—32no—
90C3×C22⋊C4—21no—
91C3×C22⋊C4—32no—
92C3×C22⋊C4—32no—
93C3×C22⋊C4C2×D312yes—
94#217C2×D312yes—
95(C2×D3)⋊C4—32no—
96(C2×D3)⋊C4—32no—
97(C2×D3)⋊C4—32no—
98(C2×D3)⋊C4—32no—
99(C2×D3)⋊C4—32no—
100(C2×D3)⋊C4—32no—
101(C2×D3)⋊C4—32no—
102(C2×D3)⋊C4—62no—
103(C2×D3)⋊C4C2×D312yescomplemented
104C4⋊Dic3—32no—
105C4⋊Dic3C2×D312yescomplemented
106Dic3⋊C4—32no—
107Dic3⋊C4C2×D312yescomplemented
108C4×Dic3—32no—
109C22×C32—21no—
110C22×C32—22no—
111C22×C32C2411yescharacteristic
112C2×C3⋊D3—22no—
113C2×C3⋊D3—21no—
114C2×C3⋊D3—22no—
115C2×C3⋊D3—22no—
116C2×C3⋊D3—22no—
117C2×C3⋊D3—44no—
118C2×C3×D3—22no—
119C2×C3×D3—22no—
120C2×C3×D3—22no—
121C32×C4—22no—
122C3⋊Dic3—21no—
123C3×Dic3—22no—
124C3×Dic3—22no—
125C3×Dic3—22no—
126#127—91no—
127#126—92no—
128#123—32no—
129#123—91no—
130#121—92no—
131#121—92no—
132#121—92no—
133#120—92no—
134#120—91no—
135C23×C3—21no—
136C23×C3—32no—
137C23×C3C22×D312yes—
138C22×D3—32no—
139C22×D3—32no—
140C22×D3—32no—
141C22×D3—62no—
142C22×D3—61no—
143C22×D3—122no—
144C22×D3—122no—
145C22×D3—122no—
146C22×D3—124no—
147C22×D3—122no—
148C22×D3C22×D312yes—
149C3×D4—122no—
150C2×C3×C4—22no—
151C2×C3×C4—32no—
152C2×C3×C4—32no—
153C2×C3×C4—32no—
154C2×C3×C4—122no—
155C2×C3×C4C22×D312yes—
156C2×C3×C4C22×D312yes—
157#67—42no—
158#67—122no—
159#67—122no—
160#67—122no—
161#67—122no—
162#67—122no—
163#67—122no—
164C2×Dic3—32no—
165C2×Dic3—61no—
166C2×Dic3C22×D312yes—
167C2×Dic3C22×D312yes—
168C2×Dic3C22×D312yes—
169D12—122no—
170D12—122no—
171D12—124no—
172D12—122no—
173D12—122no—
174D12—122no—
175C4×D3—42no—
176C4×D3—122no—
177C2×C32—41no—
178C2×C32H(5,𝔽2)12yes—
179C2×C32H(5,𝔽2)11yescharacteristic
180C3⋊D3—42no—
181C3⋊D3—41no—
182C3×D3—42no—
183C24—91no—
184C2×D4—32no—
185C2×D4—92no—
186C2×D4—92no—
187C2×D4—92no—
188C2×D4—91no—
189C2×D4—91no—
190C2×D4—92no—
191C22×C4—32no—
192C22×C4—91no—
193C4⋊C4—32no—
194C4⋊C4—32no—
195C4⋊C4—92no—
196C22⋊C4—32no—
197C22⋊C4—32no—
198C22⋊C4—92no—
199C22⋊C4—92no—
200C22⋊C4—91no—
201C22⋊C4—92no—
202C22⋊C4D3211yescharacteristic
203C42—91no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—21no—
209C22×C3—42no—
210C22×C3—62no—
211C22×C3—62no—
212C22×C3—62no—
213C22×C3C23×D312yes—
214C2×D3—22no—
215C2×D3—22no—
216C2×D3—22no—
217C2×D3—64no—
218C2×D3—62no—
219C2×D3—62no—
220C2×D3—62no—
221C2×D3—62no—
222C2×D3—62no—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—122no—
228C2×D3—122no—
229C2×D3—122no—
230C2×D3—121no—
231C2×D3—128no—
232C2×D3—128no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—42no—
236C3×C4—62no—
237C3×C4—62no—
238C3×C4—62no—
239Dic3—22no—
240Dic3—22no—
241Dic3—22no—
242Dic3—62no—
243Dic3—121no—
244C32#56011yescharacteristic, complemented, Sylow
245C23—32no—
246C23—92no—
247C23—91no—
248C23—361no—
249C23—362no—
250C23C2×D3211yescharacteristic
251D4—122no—
252D4—362no—
253D4—362no—
254D4—362no—
255D4—362no—
256D4—361no—
257D4—361no—
258C2×C4—32no—
259C2×C4—32no—
260C2×C4—32no—
261C2×C4—91no—
262C2×C4—122no—
263C2×C4—361no—
264C2×C4C2×D3212yes—
265C2×C3—21no—
266C2×C3—22no—
267C2×C3—42no—
268C2×C3—42no—
269C2×C3—122no—
270C2×C3#100412yes—
271C2×C3#100912yes—
272C2×C3#100912yes—
273D3—42no—
274D3—124no—
275D3—122no—
276D3—122no—
277D3—122no—
278D3—241no—
279C22—21no—
280C22—22no—
281C22—62no—
282C22—62no—
283C22—62no—
284C22—181no—
285C22—182no—
286C22—182no—
287C22—182no—
288C22—182no—
289C22—364no—
290C22C22×D3211yescharacteristic
291C4—22no—
292C4—62no—
293C4—62no—
294C4—62no—
295C4—181no—
296C3—21no—
297C3#566612yescomplemented
298C2—41no—
299C2—122no—
300C2—362no—
301C2—361no—
302C2#6430811yescharacteristic
303C2#6431412yes—
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #64091C2semidirect
2. C3×#883C2semidirect
3. #63981C2semidirect
4. #63979C2semidirect
5. #63975C2semidirect
6. #63910C2semidirect
7. #63909C2semidirect
8. #63906C2semidirect
9. #63848C2semidirect
15. C2×C3×C4×D3C22semidirect
18. C2×#626C22semidirect
19. C2×#625C22semidirect
20. C2×#624C22semidirect
24. C3×(C2×D3)⋊C4C22semidirect
25. C3×C4⋊Dic3C22semidirect
26. C3×Dic3⋊C4C22semidirect
27. Dic3⋊Dic3C22semidirect
30. #3722C22semidirect
31. Dic32C22semidirect
44. #883D3semidirect
87. C2×C4×D3C2×D3semidirect
103. (C2×D3)⋊C4C2×D3semidirect
105. C4⋊Dic3C2×D3semidirect
107. Dic3⋊C4C2×D3semidirect
244. C32#560semidirect
297. C3#5666semidirect

Maximal subgroups

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

subgroupindex
#640912
C3×#8832
#639812
#639792
#639752
#639102
#639092
#639062
#638482
#56663