Finite Group Databasebeta

← C2×#10596171 #11910237

Subgroups — C2×#10596171 #11910237

Order 1152.

3456 conjugacy classes of subgroups; only the 793 normal subgroups are shown.

normal subgroups only

This group has 3456 conjugacy classes of subgroups — too many to draw. Only its 793 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×C32×#125C211yesmaximal, characteristic, complemented
2#10596171C2116yesmaximal, direct product factor
3C2×#64105C214yesmaximal, complemented
4C2×#64104C214yesmaximal, complemented
5C2×#64103C214yesmaximal, complemented
6C2×#64084C212yesmaximal, complemented
7C2×#5700—34nomaximal
8C22×C4⋊(C3⋊D3)C2212yes—
9C22×C4⋊(C3⋊D3)C2214yes—
10C22×C4×C3⋊D3C2214yes—
11C22×#634C2212yes—
12C32×#125C2218yescomplemented
13C2×C32×C4⋊C4C2212yes—
14C2×C32×C4⋊C4C2214yes—
15C2×C32×C42C2211yescharacteristic
16C2×#3752C2214yes—
17C2×#3752C2214yes—
18C2×#3752C2214yes—
19C2×#3750C2214yes—
20#64105C22132yescomplemented
21#64104C22132yescomplemented
22#64103C22132yescomplemented
23#64084C22116yescomplemented
24C2×C3×#125D314yescomplemented
25#5700—364no—
26C2×#896—316no—
27C2×#895—316no—
28C2×#894—316no—
29C2×#875—38no—
30C23×C3⋊D3C2314yes—
31C22×C32×C4C2312yes—
32C22×C32×C4C2314yes—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3C2314yes—
35C2×C4⋊(C3⋊D3)—44no—
36C2×C4⋊(C3⋊D3)—48no—
37C2×C4⋊(C3⋊D3)C2318yes—
38C2×C4⋊(C3⋊D3)C23116yes—
39C2×C4×C3⋊D3—48no—
40C2×C4×C3⋊D3C23116yes—
41C2×#634—44no—
42C2×#634C2318yes—
43C32×C4⋊C4C2318yes—
44C32×C4⋊C4C23116yes—
45C32×C42C2314yes—
46#3752C23116yes—
47#3752C23116yes—
48#3752C23116yes—
49#3750C23116yes—
50C2×#562—91noSylow
51C22×D12—38no—
52C22×D12—316no—
53C22×C4×D3—316no—
54C22×Dic6—38no—
55C3×#125C2×D3132yescomplemented
56C2×C3×C4⋊C4C2×D318yes—
57C2×C3×C4⋊C4C2×D3116yes—
58C2×C3×C42C2×D314yes—
59C2×(C2×D3)⋊C4—316no—
60C2×(C2×D3)⋊C4—316no—
61C2×(C2×D3)⋊C4—316no—
62C2×Dic3⋊C4—316no—
63#896—3128no—
64#895—3128no—
65#894—3128no—
66#875—364no—
67C23×C32C2411yescharacteristic
68C22×C3⋊D3—28no—
69C22×C3⋊D3—28no—
70C22×C3⋊D3—28no—
71C22×C3⋊D3C2418yes—
72C2×C32×C4—24no—
73C2×C32×C4—28no—
74C2×C32×C4—22no—
75C2×C32×C4C2418yes—
76C2×C32×C4C2412yes—
77C2×C32×C4C2414yes—
78C2×C3⋊Dic3—28no—
79C2×C3⋊Dic3C2418yes—
80C4⋊(C3⋊D3)—48no—
81C4⋊(C3⋊D3)—416no—
82C4×C3⋊D3—416no—
83#634—48no—
84#562—916no—
85C2×#125C3⋊D311yescharacteristic, complemented
86C2×#124—92no—
87C2×#123—94no—
88C2×C22⋊Q8—94no—
89C2×#121—94no—
90C23×D3—316no—
91C22×C3×C4C22×D3116yes—
92C22×C3×C4C22×D314yes—
93C22×C3×C4C22×D318yes—
94C22×Dic3—316no—
95C2×D12—332no—
96C2×D12—364no—
97C2×D12—1216no—
98C2×D12—1232no—
99C2×C4×D3—364no—
100C2×C4×D3—1232no—
101C2×Dic6—332no—
102C2×Dic6—1216no—
103C3×C4⋊C4C22×D3132yes—
104C3×C4⋊C4C22×D3164yes—
105C3×C42C22×D3116yes—
106(C2×D3)⋊C4—364no—
107(C2×D3)⋊C4—364no—
108(C2×D3)⋊C4—364no—
109Dic3⋊C4—364no—
110C22×C32H(5,𝔽2)14yes—
111C22×C322−1+412yes—
112C22×C32C2511yescharacteristic
113C2×C3⋊D3—28no—
114C2×C3⋊D3—28no—
115C2×C3⋊D3—28no—
116C2×C3⋊D3—416no—
117C32×C4—24no—
118C32×C4—28no—
119C32×C4—22no—
120C3⋊Dic3—28no—
121C22×Q8—92no—
122C22×D4—94no—
123C22×D4—92no—
124C23×C4—94no—
125#125C2×C3⋊D318yescomplemented
126#124—916no—
127#123—932no—
128C22⋊Q8—932no—
129#121—932no—
130C2×C4⋊C4—94no—
131C2×C4⋊C4C2×C3⋊D314yes—
132C2×C4⋊C4C2×C3⋊D312yes—
133C2×C22⋊C4—94no—
134C2×C22⋊C4—94no—
135C2×C22⋊C4—94no—
136C2×C42C2×C3⋊D311yescharacteristic
137C23×C3C23×D314yes—
138C22×D3—332no—
139C22×D3—632no—
140C22×D3—632no—
141C22×D3—632no—
142C2×C3×C4—28no—
143C2×C3×C4—216no—
144C2×C3×C4—232no—
145C2×C3×C4C23×D3132yes—
146C2×C3×C4C23×D318yes—
147C2×C3×C4C23×D3116yes—
148C2×Dic3—332no—
149C2×Dic3—632no—
150D12—1232no—
151D12—1264no—
152C4×D3—1264no—
153Dic6—1232no—
154C2×C32#56214yescomplemented
155C2×C32C2×H(5,𝔽2)12yes—
156C2×C32C2×2−1+411yescharacteristic
157C3⋊D3—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×C3⋊D311yescharacteristic
169C22×C4C22×C3⋊D312yes—
170C22×C4C22×C3⋊D314yes—
171C4⋊C4—916no—
172C4⋊C4C22×C3⋊D3116yes—
173C4⋊C4C22×C3⋊D318yes—
174C22⋊C4—916no—
175C22⋊C4—916no—
176C22⋊C4—916no—
177C42C22×C3⋊D314yes—
178C22×C3#100718yes—
179C22×C3#1009116yes—
180C22×C3C24×D314yes—
181C2×D3—632no—
182C2×D3—632no—
183C2×D3—632no—
184C2×D3—1264no—
185C3×C4—28no—
186C3×C4—216no—
187C3×C4—232no—
188Dic3—632no—
189C32C2×#56211yescharacteristic, complemented, Sylow
190C23—98no—
191C23—188no—
192C23—188no—
193C23—188no—
194C23C23×C3⋊D311yescharacteristic
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×C3⋊D312yes—
205C2×C4C23×C3⋊D314yes—
206C2×C4C23×C3⋊D318yes—
207C2×C3#5700116yescomplemented
208C2×C3C2×#100714yes—
209C2×C3C2×#100918yes—
210D3—1232no—
211C22—188no—
212C22—188no—
213C22—188no—
214C22—3616no—
215C22#6436412yes—
216C22#6436614yes—
217C22C24×C3⋊D311yescharacteristic
218C4—22no—
219C4—28no—
220C4—24no—
221C4—188no—
222C3C2×#570014yescomplemented
223C2—368no—
224C2#1059617114yesdirect product factor
225C2C2×#6436411yescharacteristic
226C2C2×#6436612yes—
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#125C2
socleC23×C32C24
hypercenterC2×#125C3⋊D3
hypocenterC32C2×#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C32×#125C2semidirect
2. #10596171C2direct (N × H)
3. C2×#64105C2semidirect
4. C2×#64104C2semidirect
5. C2×#64103C2semidirect
6. C2×#64084C2semidirect
12. C32×#125C22semidirect
20. #64105C22semidirect
21. #64104C22semidirect
22. #64103C22semidirect
23. #64084C22semidirect
24. C2×C3×#125D3semidirect
55. C3×#125C2×D3semidirect
85. C2×#125C3⋊D3semidirect
125. #125C2×C3⋊D3semidirect
154. C2×C32#562semidirect
189. C32C2×#562semidirect
207. C2×C3#5700semidirect
222. C3C2×#5700semidirect
224. C2#10596171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1252
#105961712
C2×#641052
C2×#641042
C2×#641032
C2×#640842
C2×#57003