Finite Group Databasebeta

← C2×#10589802 #11910236

Subgroups — C2×#10589802 #11910236

Order 1152.

1728 conjugacy classes of subgroups; only the 550 normal subgroups are shown.

normal subgroups only

This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 550 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×C9×#125C211yesmaximal, characteristic, complemented
2#10589802C2116yesmaximal, direct product factor
3C2×#63458C214yesmaximal, complemented
4C2×#63457C214yesmaximal, complemented
5C2×#63456C214yesmaximal, complemented
6C2×#63437C212yesmaximal, complemented
7C2×#5700—31nomaximal
8C22×D36C2212yes—
9C22×D36C2214yes—
10C22×C4×D9C2214yes—
11C22×Dic18C2212yes—
12C9×#125C2218yescomplemented
13C2×C9×C4⋊C4C2212yes—
14C2×C9×C4⋊C4C2214yes—
15C2×C42×C9C2211yescharacteristic
16C2×(C2×D9)⋊C4C2214yes—
17C2×(C2×D9)⋊C4C2214yes—
18C2×(C2×D9)⋊C4C2214yes—
19C2×Dic9⋊C4C2214yes—
20#63458C22132yescomplemented
21#63457C22132yescomplemented
22#63456C22132yescomplemented
23#63437C22116yescomplemented
24C2×C3×#125D311yescharacteristic
25#5700—316no—
26C2×#896—34no—
27C2×#895—34no—
28C2×#894—34no—
29C2×#875—32no—
30C23×D9C2314yes—
31C22×C4×C9C2311yescharacteristic
32C22×C4×C9C2312yes—
33C22×C4×C9C2314yes—
34C22×Dic9C2314yes—
35C2×D36—44no—
36C2×D36—48no—
37C2×D36C2318yes—
38C2×D36C23116yes—
39C2×C4×D9—48no—
40C2×C4×D9C23116yes—
41C2×Dic18—44no—
42C2×Dic18C2318yes—
43C9×C4⋊C4C2318yes—
44C9×C4⋊C4C23116yes—
45C42×C9C2314yes—
46(C2×D9)⋊C4C23116yes—
47(C2×D9)⋊C4C23116yes—
48(C2×D9)⋊C4C23116yes—
49Dic9⋊C4C23116yes—
50C2×#562—91noSylow
51C22×D12—32no—
52C22×D12—34no—
53C22×C4×D3—34no—
54C22×Dic6—32no—
55C3×#125C2×D318yes—
56C2×C3×C4⋊C4C2×D312yes—
57C2×C3×C4⋊C4C2×D314yes—
58C2×C3×C42C2×D311yescharacteristic
59C2×(C2×D3)⋊C4—34no—
60C2×(C2×D3)⋊C4—34no—
61C2×(C2×D3)⋊C4—34no—
62C2×Dic3⋊C4—34no—
63#896—332no—
64#895—332no—
65#894—332no—
66#875—316no—
67C23×C9C2411yescharacteristic
68C22×D9—28no—
69C22×D9—28no—
70C22×D9—28no—
71C22×D9C2418yes—
72C2×C4×C9—24no—
73C2×C4×C9—28no—
74C2×C4×C9—22no—
75C2×C4×C9C2418yes—
76C2×C4×C9C2412yes—
77C2×C4×C9C2414yes—
78C2×Dic9—28no—
79C2×Dic9C2418yes—
80D36—48no—
81D36—416no—
82C4×D9—416no—
83Dic18—48no—
84#562—916no—
85C2×#125D911yescharacteristic, complemented
86C2×#124—92no—
87C2×#123—94no—
88C2×C22⋊Q8—94no—
89C2×#121—94no—
90C23×D3—34no—
91C22×C3×C4C22×D314yes—
92C22×C3×C4C22×D311yescharacteristic
93C22×C3×C4C22×D312yes—
94C22×Dic3—34no—
95C2×D12—38no—
96C2×D12—316no—
97C2×D12—124no—
98C2×D12—128no—
99C2×C4×D3—316no—
100C2×C4×D3—128no—
101C2×Dic6—38no—
102C2×Dic6—124no—
103C3×C4⋊C4C22×D318yes—
104C3×C4⋊C4C22×D3116yes—
105C3×C42C22×D314yes—
106(C2×D3)⋊C4—316no—
107(C2×D3)⋊C4—316no—
108(C2×D3)⋊C4—316no—
109Dic3⋊C4—316no—
110C22×C9H(5,𝔽2)14yes—
111C22×C92−1+412yes—
112C22×C9C2511yescharacteristic
113C2×D9—28no—
114C2×D9—28no—
115C2×D9—28no—
116C2×D9—416no—
117C4×C9—24no—
118C4×C9—28no—
119C4×C9—22no—
120Dic9—28no—
121C22×Q8—92no—
122C22×D4—94no—
123C22×D4—92no—
124C23×C4—94no—
125#125C2×D918yescomplemented
126#124—916no—
127#123—932no—
128C22⋊Q8—932no—
129#121—932no—
130C2×C4⋊C4—94no—
131C2×C4⋊C4C2×D914yes—
132C2×C4⋊C4C2×D912yes—
133C2×C22⋊C4—94no—
134C2×C22⋊C4—94no—
135C2×C22⋊C4—94no—
136C2×C42C2×D911yescharacteristic
137C23×C3C23×D311yescharacteristic
138C22×D3—38no—
139C22×D3—68no—
140C22×D3—68no—
141C22×D3—68no—
142C2×C3×C4—22no—
143C2×C3×C4—24no—
144C2×C3×C4—28no—
145C2×C3×C4C23×D318yes—
146C2×C3×C4C23×D312yes—
147C2×C3×C4C23×D314yes—
148C2×Dic3—38no—
149C2×Dic3—68no—
150D12—128no—
151D12—1216no—
152C4×D3—1216no—
153Dic6—128no—
154C2×C9#56214yescomplemented
155C2×C9C2×H(5,𝔽2)12yes—
156C2×C9C2×2−1+411yescharacteristic
157D9—48no—
158C24—94no—
159C2×Q8—98no—
160C2×Q8—364no—
161C2×D4—916no—
162C2×D4—98no—
163C2×D4—368no—
164C2×D4—364no—
165C22×C4—94no—
166C22×C4—916no—
167C22×C4—368no—
168C22×C4C22×D911yescharacteristic
169C22×C4C22×D912yes—
170C22×C4C22×D914yes—
171C4⋊C4—916no—
172C4⋊C4C22×D9116yes—
173C4⋊C4C22×D918yes—
174C22⋊C4—916no—
175C22⋊C4—916no—
176C22⋊C4—916no—
177C42C22×D914yes—
178C22×C3#100712yes—
179C22×C3#100914yes—
180C22×C3C24×D311yescharacteristic
181C2×D3—68no—
182C2×D3—68no—
183C2×D3—68no—
184C2×D3—1216no—
185C3×C4—22no—
186C3×C4—24no—
187C3×C4—28no—
188Dic3—68no—
189C9C2×#56211yescharacteristic, complemented, Sylow
190C23—98no—
191C23—188no—
192C23—188no—
193C23—188no—
194C23C23×D911yescharacteristic
195Q8—368no—
196D4—3616no—
197D4—368no—
198C2×C4—22no—
199C2×C4—28no—
200C2×C4—24no—
201C2×C4—98no—
202C2×C4—188no—
203C2×C4—3616no—
204C2×C4C23×D912yes—
205C2×C4C23×D914yes—
206C2×C4C23×D918yes—
207C2×C3#570014yes—
208C2×C3C2×#100711yescharacteristic
209C2×C3C2×#100912yes—
210D3—128no—
211C22—188no—
212C22—188no—
213C22—188no—
214C22—3616no—
215C22#6371312yes—
216C22#6371514yes—
217C22C24×D911yescharacteristic
218C4—22no—
219C4—28no—
220C4—24no—
221C4—188no—
222C3C2×#570011yescharacteristic
223C2—368no—
224C2#1058980214yesdirect product factor
225C2C2×#6371311yescharacteristic
226C2C2×#6371512yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#125C2
socleC23×C3C23×D3
hypercenterC2×#125D9
hypocenterC9C2×#562
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C9×#125C2semidirect
2. #10589802C2direct (N × H)
3. C2×#63458C2semidirect
4. C2×#63457C2semidirect
5. C2×#63456C2semidirect
6. C2×#63437C2semidirect
12. C9×#125C22semidirect
20. #63458C22semidirect
21. #63457C22semidirect
22. #63456C22semidirect
23. #63437C22semidirect
85. C2×#125D9semidirect
125. #125C2×D9semidirect
154. C2×C9#562semidirect
189. C9C2×#562semidirect
224. C2#10589802direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1252
#105898022
C2×#634582
C2×#634572
C2×#634562
C2×#634372
C2×#57003