Finite Group Databasebeta

← C4×#63700 #11919687

Subgroups — C4×#63700 #11919687

Order 1152.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#63700C211yesmaximal, characteristic
2#520⋊C9C213yesmaximal, complemented
3C4×#41⋊C9C213yesmaximal, complemented
4C3×C4×H(5,𝔽2)C311yesmaximal, characteristic
5#63700C414yesdirect product factor
6C2×#41⋊C9C2213yes—
7C4×Q8×C9—41nomaximal
8C4×Q8⋊C9C2211yescharacteristic, complemented
9C4×Q8⋊C9C2213yescomplemented
10C2×C3×H(5,𝔽2)C2×C311yescharacteristic
11C3×#520—31no—
12C3×#520C2×C313yes—
13C3×#518—33no—
14C3×C4×#41—31no—
15C3×C4×#41C2×C313yes—
16C2×C3×C4×D4—33no—
17C2×Q8×C9—41no—
18#41⋊C9C2×C416yescomplemented
19C2×Q8⋊C9C2311yescharacteristic
20C9×C4⋊C4—43no—
21C42×C9—43no—
22C4×H(5,𝔽2)C911yescharacteristic, complemented, Sylow
23C3×H(5,𝔽2)—34no—
24C3×H(5,𝔽2)C3×C414yes—
25C2×C3×#41—31no—
26C2×C3×#41C22×C313yes—
27C22×C3×D4—33no—
28C23×C3×C4—32no—
29C3×C4×Q8—31no—
30C3×C4×Q8A411yescharacteristic
31C3×C4×Q8C22×C311yescharacteristic
32C3×C4×Q8C22×C313yes—
33C3×C4×D4—36no—
34C3×C4×D4—33no—
35C3×C4×D4—33no—
36C3×C4×D4—33no—
37C3×C4×D4—36no—
38C3×C4×D4—33no—
39C3×#117—33no—
40C3×#117—33no—
41C2×C3×C4⋊C4—33no—
42C2×C3×C22⋊C4—36no—
43C2×C3×C42—33no—
44Q8×C9—44no—
45C2×C4×C9—43no—
46C2×C4×C9—43no—
47C2×C4×C9—41no—
48Q8⋊C9C22×C411yescharacteristic, complemented
49C2×H(5,𝔽2)C2×C911yescharacteristic
50#520—31no—
51#520C2×C913yes—
52#518—33no—
53C4×#41—31no—
54C4×#41C2×C913yes—
55C2×C4×D4—33no—
56C24×C3—32no—
57C3×#41—34no—
58C3×#41—34no—
59C3×#41—36no—
60C3×#41C2×C3×C416yes—
61C2×C3×Q8C2×A411yescharacteristic
62C2×C3×Q8C23×C311yescharacteristic
63C2×C3×D4—33no—
64C2×C3×D4—312no—
65C2×C3×D4—312no—
66C2×C3×D4—33no—
67C22×C3×C4—33no—
68C22×C3×C4—36no—
69C22×C3×C4—33no—
70C22×C3×C4—33no—
71C22×C3×C4—124no—
72C3×C4⋊C4—33no—
73C3×C4⋊C4—31no—
74C3×C4⋊C4—33no—
75C3×C4⋊C4C2×A413yes—
76C3×C22⋊C4—36no—
77C3×C22⋊C4—36no—
78C3×C42—33no—
79C3×C42—33no—
80C3×C42—31no—
81C3×C42C2×A413yes—
82C22×C9—41no—
83C4×C9—46no—
84C4×C9—42no—
85C4×C9—83no—
86H(5,𝔽2)—34no—
87H(5,𝔽2)C4×C914yescomplemented
88C2×#41—31no—
89C2×#41C22×C913yes—
90C22×D4—33no—
91C23×C4—32no—
92C4×Q8—31no—
93C4×Q8C22⋊C911yescharacteristic
94C4×Q8C22×C911yescharacteristic
95C4×Q8C22×C913yes—
96C4×D4—36no—
97C4×D4—33no—
98C4×D4—33no—
99C4×D4—33no—
100C4×D4—36no—
101C4×D4—33no—
102#117—33no—
103#117—33no—
104C2×C4⋊C4—33no—
105C2×C22⋊C4—36no—
106C2×C42—33no—
107C23×C3—38no—
108C23×C3—33no—
109C23×C3—122no—
110C23×C3—122no—
111C3×Q8—31no—
112C3×Q8C4×A414yes—
113C3×Q8C22×C3×C411yescharacteristic
114C3×D4—36no—
115C3×D4—36no—
116C3×D4—312no—
117C2×C3×C4—31no—
118C2×C3×C4—36no—
119C2×C3×C4—36no—
120C2×C3×C4—31no—
121C2×C3×C4—33no—
122C2×C3×C4—66no—
123C2×C3×C4—123no—
124C2×C3×C4—126no—
125C2×C3×C4C22×A413yes—
126C2×C3×C4C22×A413yes—
127C2×C3×C4C22×A411yescharacteristic
128C2×C9—41no—
129C2×C9—41no—
130C2×C9—41no—
131C24—32no—
132#41—34no—
133#41—34no—
134#41—36no—
135#41C2×C4×C916yes—
136C2×Q8C2×C22⋊C911yescharacteristic
137C2×Q8C23×C911yescharacteristic
138C2×D4—33no—
139C2×D4—312no—
140C2×D4—312no—
141C2×D4—33no—
142C22×C4—33no—
143C22×C4—36no—
144C22×C4—33no—
145C22×C4—33no—
146C22×C4—124no—
147C4⋊C4—33no—
148C4⋊C4—31no—
149C4⋊C4—33no—
150C4⋊C4C2×C22⋊C913yes—
151C22⋊C4—36no—
152C22⋊C4—36no—
153C42—31no—
154C42—33no—
155C42—33no—
156C42C2×C22⋊C913yes—
157C22×C3—36no—
158C22×C3—63no—
159C22×C3—63no—
160C22×C3—128no—
161C22×C3C23×A411yescharacteristic
162C3×C4—23no—
163C3×C4—31no—
164C3×C4—31no—
165C3×C4—63no—
166C3×C4—61no—
167C3×C4C2×C4×A416yes—
168C3×C4#99412yes—
169C9—41noSylow
170C23—38no—
171C23—33no—
172C23—122no—
173C23—122no—
174Q8—31no—
175Q8C4×C22⋊C914yes—
176Q8C22×C4×C911yescharacteristic
177D4—36no—
178D4—36no—
179D4—312no—
180C2×C4—31no—
181C2×C4—36no—
182C2×C4—36no—
183C2×C4—31no—
184C2×C4—33no—
185C2×C4—66no—
186C2×C4—123no—
187C2×C4—126no—
188C2×C4C22×C22⋊C913yes—
189C2×C4C22×C22⋊C913yes—
190C2×C4C22×C22⋊C911yescharacteristic
191C2×C3—66no—
192C2×C3C22×C4×A411yescharacteristic
193C2×C3C2×#99411yescharacteristic
194C2×C3#594511yescharacteristic
195C22—36no—
196C22—63no—
197C22—63no—
198C22—128no—
199C22C23×C22⋊C911yescharacteristic
200C4—23no—
201C4—31no—
202C4—31no—
203C4—63no—
204C4—61no—
205C4C2×C4×C22⋊C916yes—
206C4#6370012yesdirect product factor
207C3C4×#99411yescharacteristic
208C2—66no—
209C2C22×C4×C22⋊C911yescharacteristic
210C2C2×#6370011yescharacteristic
211C2#1059312011yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutator, hypocenterQ8C22×C4×C9
Frattini, socleC22×C3C23×A4
FittingC3×C4×H(5,𝔽2)C3
prime radicalC2×C3×H(5,𝔽2)C2×C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×C4×Q8A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #520⋊C9C2semidirect
3. C4×#41⋊C9C2semidirect
5. #63700C4direct (N × H)
8. C4×Q8⋊C9C22semidirect
9. C4×Q8⋊C9C22semidirect
18. #41⋊C9C2×C4semidirect
22. C4×H(5,𝔽2)C9semidirect
48. Q8⋊C9C22×C4semidirect
87. H(5,𝔽2)C4×C9semidirect
206. C4#63700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#637002
#520⋊C92
C4×#41⋊C92
C3×C4×H(5,𝔽2)3
C4×Q8×C94