Finite Group Databasebeta

← C4×#22575422 #46813387

Subgroups — C4×#22575422 #46813387

Order 34432.

1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 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×#22575422C211yesmaximal, characteristic
2C2×C4×C22⋊D269C213yesmaximal, complemented
3#31770484C213yesmaximal, complemented
4#31770478C213yesmaximal, complemented
5#31770461C211yesmaximal, characteristic, complemented
6C4×C22⋊Dic269C213yesmaximal, complemented
7C24×C4×C269C211yesmaximal, characteristic, complemented
8C22×C22⋊D269C2213yes—
9C22×C4×D269C2211yescharacteristic, complemented
10#22575422C418yesdirect product factor
11C4×C22⋊D269—212no—
12C2×#16864381C2213yescomplemented
13C2×C22⋊Dic269C2213yes—
14C2×C22⋊Dic269C2213yes—
15C2×C22⋊Dic269C2213yes—
16C2×#16864379C2213yescomplemented
17C2×C4×Dic269C2213yescomplemented
18#22575360C2216yescomplemented
19C25×C269C2211yescharacteristic
20C23×C4×C269—212no—
21C23×C4×C269C2213yes—
22C23×C4×C269C2213yes—
23C23×D269C2311yescharacteristic
24C2×C22⋊D269—26no—
25C2×C22⋊D269—26no—
26C2×C22⋊D269C2×C4112yescomplemented
27C22×Dic269C2313yes—
28C22×Dic269C2311yescharacteristic
29C22×Dic269C2313yes—
30C2×C4×D269—26no—
31#16864381—26no—
32C22⋊Dic269—26no—
33C22⋊Dic269—26no—
34C22⋊Dic269C2×C4112yescomplemented
35#16864379—26no—
36C4×Dic269—26no—
37C24×C269—26no—
38C24×C269—26no—
39C24×C269C2×C414yescomplemented
40C24×C269C2313yes—
41C22×C4×C269—232no—
42C22×C4×C269—26no—
43C22×C4×C269—212no—
44C22×C4×C269—212no—
45C22×C4×C269D4112yescomplemented
46C22×C4×C269C2313yes—
47C22×C4×C269C2311yescharacteristic
48C22×D269—23no—
49C22×D269—23no—
50C22×D269C22×C412yescomplemented
51C22⋊D269—224no—
52C2×Dic269—23no—
53C2×Dic269—23no—
54C2×Dic269—23no—
55C2×Dic269—23no—
56C2×Dic269—26no—
57C2×Dic269C22×C416yescomplemented
58C4×D269—44no—
59C23×C269—28no—
60C23×C269—224no—
61C23×C269—224no—
62C23×C269—26no—
63C23×C269—26no—
64C23×C269C22×C416yes—
65C23×C269C2×D416yes—
66C23×C269#4116yes—
67C23×C269C2411yescharacteristic
68C2×C4×C269—224no—
69C2×C4×C269—26no—
70C2×C4×C269—224no—
71C2×C4×C269C2×D416yes—
72C2×C4×C269C2×D416yes—
73C22×C269—232no—
74C22×C269—212no—
75C22×C269—26no—
76C22×C269—26no—
77C22×C269—212no—
78C22×C269C4×D4112yescomplemented
79C22×C269C23×C411yescharacteristic
80C22×C269C22×D413yes—
81C22×C269C2×#4113yes—
82C2×D269—26no—
83C2×D269—41no—
84C2×D269—43no—
85C4×C269—26no—
86C4×C269#12014yescomplemented
87Dic269—26no—
88Dic269—41no—
89Dic269—43no—
90C2×C269—212no—
91C2×C269C2×C4×D413yes—
92C2×C269C2×#12011yescharacteristic
93C2×C269#52513yes—
94D269—42no—
95C269C4×#12011yescharacteristic, complemented, Sylow
96C4×#120—2691nomaximal, Sylow
97C24×C4D26911yescharacteristic, complemented
98C2×#120—2691no—
99C2×C4×D4—2693no—
100#386—2693no—
101#385—2693no—
102#379—2691no—
103C4×C22⋊C4—2693no—
104C25C2×D26911yescharacteristic
105C22×D4—2693no—
106C23×C4—212no—
107C23×C4—2691no—
108C23×C4C2×D26913yes—
109C23×C4C2×D26913yes—
110#120—2698no—
111C4×D4—53812no—
112C2×C4⋊C4—2693no—
113C2×C22⋊C4—2693no—
114C2×C22⋊C4—2693no—
115C2×C22⋊C4—2693no—
116C2×C22⋊C4—2693no—
117C2×C42—2693no—
118#95—2696no—
119C24—26no—
120C24—26no—
121C24—2691no—
122C24C4×D26914yescomplemented
123C24C22×D26913yes—
124C2×D4—26912no—
125C2×D4—5386no—
126C2×D4—5386no—
127C22×C4—232no—
128C22×C4—26no—
129C22×C4—212no—
130C22×C4—212no—
131C22×C4—2693no—
132C22×C4—2693no—
133C22×C4—2691no—
134C22×C4—5386no—
135C22×C4C22⋊D269112yescomplemented
136C22×C4C22×D26913yes—
137C22×C4C22×D26911yescharacteristic
138C4⋊C4—5386no—
139C22⋊C4—26912no—
140C22⋊C4—5386no—
141C22⋊C4—5386no—
142C22⋊C4—5386no—
143C42—5386no—
144C23—28no—
145C23—224no—
146C23—224no—
147C23—26no—
148C23—26no—
149C23—2692no—
150C23—5383no—
151C23—5383no—
152C23C2×C4×D26916yes—
153C23C2×C22⋊D26916yes—
154C23#1686440216yes—
155C23C23×D26911yescharacteristic
156D4—53824no—
157C2×C4—224no—
158C2×C4—26no—
159C2×C4—224no—
160C2×C4—2696no—
161C2×C4—5383no—
162C2×C4—5383no—
163C2×C4—5383no—
164C2×C4—5383no—
165C2×C4—5386no—
166C2×C4—10764no—
167C2×C4C2×C22⋊D26916yes—
168C2×C4C2×C22⋊D26916yes—
169C22—232no—
170C22—212no—
171C22—26no—
172C22—26no—
173C22—212no—
174C22—5386no—
175C22—10761no—
176C22—10763no—
177C22C4×C22⋊D269112yescomplemented
178C22C22×C4×D26911yescharacteristic
179C22C22×C22⋊D26913yes—
180C22C2×#1686440213yes—
181C4—26no—
182C4—5386no—
183C4—10761no—
184C4—10763no—
185C4#2257542214yesdirect product factor
186C2—212no—
187C2—10762no—
188C2C2×C4×C22⋊D26913yes—
189C2C2×#2257542211yescharacteristic
190C2#3177111613yes—
subgroupG/H
centerC22×C4C22×D269
commutatorC22×C269C23×C4
FrattiniC23C23×D269
FittingC24×C4×C269C2
socle, cosocleC23×C269C24
prime radicalC2×#22575422C2
hypercenterC24×C4D269
hypocenterC269C4×#120
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D269C2semidirect
3. #31770484C2semidirect
4. #31770478C2semidirect
5. #31770461C2semidirect
6. C4×C22⋊Dic269C2semidirect
7. C24×C4×C269C2semidirect
9. C22×C4×D269C22semidirect
10. #22575422C4direct (N × H)
12. C2×#16864381C22semidirect
16. C2×#16864379C22semidirect
17. C2×C4×Dic269C22semidirect
18. #22575360C22semidirect
26. C2×C22⋊D269C2×C4semidirect
34. C22⋊Dic269C2×C4semidirect
39. C24×C269C2×C4semidirect
45. C22×C4×C269D4semidirect
50. C22×D269C22×C4semidirect
57. C2×Dic269C22×C4semidirect
78. C22×C269C4×D4semidirect
86. C4×C269#120semidirect
95. C269C4×#120semidirect
97. C24×C4D269semidirect
122. C24C4×D269semidirect
135. C22×C4C22⋊D269semidirect
177. C22C4×C22⋊D269semidirect
185. C4#22575422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225754222
C2×C4×C22⋊D2692
#317704842
#317704782
#317704612
C4×C22⋊Dic2692
C24×C4×C2692
C4×#120269