Finite Group Databasebeta

← C2×#31826707 #49130836

Subgroups — C2×#31826707 #49130836

Order 36224.

512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×Dic1132C211yesmaximal, characteristic, complemented
2C22×C8×D283C211yesmaximal, characteristic
3C2×#22583590C212yesmaximal
4#31826707C218yesmaximal, direct product factor
5C2×#22583533C212yesmaximal, complemented
6C2×#107×C283C211yesmaximal, characteristic, complemented
7C22×Dic566C2212yes—
8C22×C4×D283C2211yescharacteristic
9C2×Dic1132—24no—
10C2×Dic1132C2214yescomplemented
11C22×C283⋊C8C2211yescharacteristic
12C2×C8×D283—24no—
13C2×C8×D283C2214yes—
14#22583590—24no—
15#22583590C2218yes—
16C2×C4⋊Dic283—22no—
17C2×(C2×D283)⋊C4—22no—
18#22583533C2218yescomplemented
19C22×C8×C283C2211yescharacteristic
20C2×C4⋊C4×C283C2212yes—
21#107×C283C2214yescomplemented
22C23×D283D411yescharacteristic
23C2×Dic566—22no—
24C2×Dic566—24no—
25C2×Dic566—24no—
26C2×Dic566C2314yes—
27C22×Dic283—22no—
28C22×Dic283D411yescharacteristic
29C2×C4×D283—22no—
30C2×C4×D283—22no—
31C2×C4×D283D412yes—
32C2×C4×D283C2312yes—
33Dic1132—28no—
34C2×C283⋊C8—22no—
35C2×C283⋊C8C2312yes—
36C8×D283—28no—
37C4⋊Dic283—28no—
38(C2×D283)⋊C4—28no—
39C22×C4×C283—22no—
40C22×C4×C283C2311yescharacteristic
41C2×C8×C283D414yes—
42C2×C8×C283C2312yes—
43C4⋊C4×C283—22no—
44C4⋊C4×C283C2314yes—
45C22×D283—22no—
46C22×D283—22no—
47C22×D283Q1614yescomplemented
48C22×D283C2×D412yes—
49Dic566—24no—
50Dic566—24no—
51Dic566—44no—
52C2×Dic283—22no—
53C2×Dic283—24no—
54C2×Dic283—44no—
55C2×Dic283C2×D412yes—
56C4×D283—24no—
57C4×D283—22no—
58C4×D283—22no—
59C283⋊C8—22no—
60C23×C283C2×D411yescharacteristic
61C2×C4×C283—24no—
62C2×C4×C283—44no—
63C2×C4×C283C2×D411yescharacteristic
64C2×C4×C283C2×D412yes—
65C2×C4×C283#4112yes—
66C2×C4×C283C2411yescharacteristic
67C8×C283C2×D414yes—
68C22×C283#12112yes—
69C22×C283C2×Q1612yes—
70C22×C283#13512yes—
71C22×C283C22×D411yescharacteristic
72C2×D283—22no—
73C2×D283—22no—
74C2×D283—28no—
75C2×D283C2×Q1614yescomplemented
76C4×C283—44no—
77C4×C283#12112yes—
78C4×C283C22×D411yescharacteristic
79C4×C283C2×#4111yescharacteristic
80Dic283—22no—
81Dic283—44no—
82C2×C283#46714yescomplemented
83C2×C283C2×#12111yescharacteristic
84C2×C283C22×Q1611yescharacteristic
85C2×C283C2×#13511yescharacteristic
86D283—24no—
87C283C2×#46711yescharacteristic, complemented, Sylow
88C2×#467—2831nomaximal, Sylow
89C22×Q16—2831no—
90C23×C8—2831no—
91C2×C22⋊Q8—2832no—
92#467—2838no—
93C2×#107D28311yescharacteristic, complemented
94C2×#103—2832no—
95C22×Q8—2832no—
96C23×C4—2831no—
97C2×Q16—2834no—
98C2×Q16—5664no—
99C22×C8—2831no—
100C22×C8—2834no—
101C22×C8—5664no—
102C22×C8C2×D28311yescharacteristic
103C22⋊Q8—2838no—
104C22⋊Q8—5664no—
105C2×C4⋊C4—5662no—
106C2×C4⋊C4C2×D28312yes—
107C2×C22⋊C4—5662no—
108#107C2×D28314yescomplemented
109#103—2838no—
110C24—2831no—
111C2×Q8—2834no—
112C2×Q8—5662no—
113C2×Q8—5664no—
114C2×Q8—5664no—
115C22×C4—22no—
116C22×C4—2831no—
117C22×C4—2832no—
118C22×C4—2832no—
119C22×C4—5662no—
120C22×C4—5662no—
121C22×C4—5662no—
122C22×C4C22×D28311yescharacteristic
123Q16—5668no—
124C2×C8—2832no—
125C2×C8—5662no—
126C2×C8—5668no—
127C2×C8D113214yes—
128C2×C8C22×D28312yes—
129C4⋊C4—22no—
130C4⋊C4—5668no—
131C4⋊C4C22×D28314yes—
132C22⋊C4—5668no—
133C23—2834no—
134C23—2832no—
135C23—5662no—
136C23—5662no—
137C23D4×D28311yescharacteristic
138Q8—5664no—
139Q8—5664no—
140Q8—11324no—
141C2×C4—24no—
142C2×C4—44no—
143C2×C4—2832no—
144C2×C4—5662no—
145C2×C4—5664no—
146C2×C4—5662no—
147C2×C4—5662no—
148C2×C4—5664no—
149C2×C4—11324no—
150C2×C4D4×D28311yescharacteristic
151C2×C4C2×D113212yes—
152C2×C4#1798539312yes—
153C2×C4C23×D28311yescharacteristic
154C8—5662no—
155C8C2×D113214yes—
156C22—2834no—
157C22—5662no—
158C22—5668no—
159C22—5662no—
160C22#2258358512yes—
161C22Q16×D28312yes—
162C22#2258362912yes—
163C22C2×D4×D28311yescharacteristic
164C4—44no—
165C4—5662no—
166C4—11324no—
167C4#2258358512yes—
168C4C22×D113211yescharacteristic
169C4C2×#1798539311yescharacteristic
170C2—5664no—
171C2#3182670714yesdirect product factor
172C2C2×#2258358511yescharacteristic
173C2C2×Q16×D28311yescharacteristic
174C2C2×#2258362911yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#107×C283C2
socleC23×C283C2×D4
prime radicalC23×D283D4
hypercenterC2×#107D283
hypocenterC283C2×#467
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×Dic1132C2semidirect
4. #31826707C2direct (N × H)
5. C2×#22583533C2semidirect
6. C2×#107×C283C2semidirect
10. C2×Dic1132C22semidirect
18. #22583533C22semidirect
21. #107×C283C22semidirect
47. C22×D283Q16semidirect
75. C2×D283C2×Q16semidirect
82. C2×C283#467semidirect
87. C283C2×#467semidirect
93. C2×#107D283semidirect
108. #107C2×D283semidirect
171. C2#31826707direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Dic11322
C22×C8×D2832
C2×#225835902
#318267072
C2×#225835332
C2×#107×C2832
C2×#467283