Finite Group Databasebeta

← #10589826

Subgroups — #10589826

Order 576.

405 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 405 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#3701C211yesmaximal, characteristic
2C2×Q8×D9C211yesmaximal, characteristic, complemented
3C9×C4⋊Q8C211yesmaximal, characteristic, complemented
4#63509C211yesmaximal, characteristic, complemented
5#63506C211yesmaximal, characteristic, complemented
6#63458C214yesmaximal, complemented
7#63456C214yesmaximal, complemented
8#63437C211yesmaximal, characteristic, complemented
9#63434C211yesmaximal, characteristic, complemented
10#5724—31nomaximal
11C2×Q8×C9C2211yescharacteristic
12C2×Q8×C9C2211yescharacteristic
13#3701—24no—
14Q8×D9—24no—
15C2×D36C2211yescharacteristic
16C2×D36C2212yes—
17C2×C4×D9C2212yes—
18C2×C4×D9C2212yes—
19C2×C4×D9C2211yescharacteristic
20C2×Dic18C2211yescharacteristic
21C2×Dic18C2212yes—
22C9×C4⋊C4C2214yes—
23C42×C9C2211yescharacteristic
24(C2×D9)⋊C4C2214yes—
25(C2×D9)⋊C4C2212yes—
26(C2×D9)⋊C4C2214yes—
27Dic9⋊C4C2214yes—
28Dic9⋊C4C2212yes—
29C4×Dic9C2211yescharacteristic
30C2×#239—31no—
31C2×D3×Q8—31no—
32C3×C4⋊Q8D311yescharacteristic
33#947—31no—
34#944—31no—
35#896—34no—
36#894—34no—
37#875—31no—
38#872—31no—
39C22×D9C2312yes—
40C22×D9C2311yescharacteristic
41Q8×C9—22no—
42Q8×C9—22no—
43C2×C4×C9C2312yes—
44C2×C4×C9C2312yes—
45C2×C4×C9C2312yes—
46C2×C4×C9C2311yescharacteristic
47C2×Dic9C2312yes—
48C2×Dic9C2312yes—
49C2×Dic9C2311yescharacteristic
50D36—24no—
51D36—22no—
52C4×D9—24no—
53C4×D9—24no—
54C4×D9D414yes—
55Dic18—22no—
56Dic18—24no—
57#536—91noSylow
58C2×C3×Q8C2×D311yescharacteristic
59C2×C3×Q8C2×D311yescharacteristic
60#239—64no—
61D3×Q8—64no—
62C2×D12—31no—
63C2×D12—32no—
64C2×C4×D3—31no—
65C2×C4×D3—32no—
66C2×C4×D3—32no—
67C2×Dic6—31no—
68C2×Dic6—32no—
69C3×C4⋊C4C2×D314yes—
70C3×C42C2×D311yescharacteristic
71(C2×D3)⋊C4—32no—
72(C2×D3)⋊C4—34no—
73(C2×D3)⋊C4—34no—
74Dic3⋊C4—32no—
75Dic3⋊C4—34no—
76C4×Dic3—31no—
77C22×C9C2411yescharacteristic
78C2×D9—22no—
79C2×D9—22no—
80C2×D9—24no—
81C2×D9C2×D412yes—
82C4×C9—22no—
83C4×C9—22no—
84C4×C9—22no—
85C4×C9C2×D412yes—
86Dic9—22no—
87Dic9—22no—
88Dic9C2×D412yes—
89C2×#41—91no—
90C22×Q8—91no—
91C4⋊Q8—91no—
92C4⋊Q8D911yescharacteristic, complemented
93#124—91no—
94#124—91no—
95#123—94no—
96C22⋊Q8—94no—
97#117—91no—
98C22×D3—31no—
99C22×D3—32no—
100C3×Q8—22no—
101C3×Q8—22no—
102C2×C3×C4C22×D312yes—
103C2×C3×C4C22×D312yes—
104C2×C3×C4C22×D312yes—
105C2×C3×C4C22×D311yescharacteristic
106C2×Dic3—31no—
107C2×Dic3—32no—
108C2×Dic3—32no—
109D12—64no—
110D12—62no—
111C4×D3—34no—
112C4×D3—64no—
113C4×D3—64no—
114Dic6—64no—
115Dic6—62no—
116C2×C9C22×D411yescharacteristic
117C2×C92−1+412yes—
118D9—22no—
119D9—42no—
120#41—184no—
121C2×Q8—92no—
122C2×Q8—91no—
123C2×Q8—184no—
124C2×Q8C2×D911yescharacteristic
125C2×Q8C2×D911yescharacteristic
126C2×D4—92no—
127C2×D4—91no—
128C22×C4—91no—
129C22×C4—92no—
130C22×C4—92no—
131C4⋊C4—92no—
132C4⋊C4—94no—
133C4⋊C4C2×D914yes—
134C22⋊C4—92no—
135C22⋊C4—94no—
136C22⋊C4—94no—
137C42—91no—
138C42C2×D911yescharacteristic
139C22×C3C23×D311yescharacteristic
140C2×D3—32no—
141C2×D3—62no—
142C2×D3—62no—
143C2×D3—64no—
144C3×C4—22no—
145C3×C4—22no—
146C3×C4—22no—
147C3×C4D3×D412yes—
148Dic3—32no—
149Dic3—62no—
150Dic3—62no—
151C9#53611yescharacteristic, complemented, Sylow
152C23—91no—
153C23—92no—
154Q8—22no—
155Q8—22no—
156Q8—184no—
157Q8—182no—
158D4—184no—
159D4—182no—
160C2×C4—91no—
161C2×C4—94no—
162C2×C4—92no—
163C2×C4—92no—
164C2×C4—184no—
165C2×C4—184no—
166C2×C4C22×D912yes—
167C2×C4C22×D912yes—
168C2×C4C22×D912yes—
169C2×C4C22×D911yescharacteristic
170C2×C3C2×D3×D411yescharacteristic
171C2×C3#100712yes—
172D3—62no—
173D3—122no—
174C22—92no—
175C22—182no—
176C22—182no—
177C22—184no—
178C22C23×D911yescharacteristic
179C4—22no—
180C4—22no—
181C4—22no—
182C4—92no—
183C4—182no—
184C4—182no—
185C4D4×D912yes—
186C3#572411yescharacteristic
187C2—182no—
188C2—362no—
189C2C2×D4×D911yescharacteristic
190C2#6371312yes—
subgroupG/H
centerC22C23×D9
commutator, cosocleC22×C9C24
Frattini, socleC22×C3C23×D3
FittingC9×C4⋊Q8C2
prime radicalC2×#3701C2
hypercenterC4⋊Q8D9
hypocenterC9#536
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×D9C2semidirect
3. C9×C4⋊Q8C2semidirect
4. #63509C2semidirect
5. #63506C2semidirect
6. #63458C2semidirect
7. #63456C2semidirect
8. #63437C2semidirect
9. #63434C2semidirect
92. C4⋊Q8D9semidirect
151. C9#536semidirect

Maximal subgroups

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

subgroupindex
C2×#37012
C2×Q8×D92
C9×C4⋊Q82
#635092
#635062
#634582
#634562
#634372
#634342
#57243