Finite Group Databasebeta

← #49130838

Subgroups — #49130838

Order 36224.

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

normal subgroups only

This group has 520 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
1C22×C8×D283C211yesmaximal, characteristic, complemented
2#31826972C212yesmaximal, complemented
3#31826703C212yesmaximal, complemented
4#31826698C212yesmaximal, complemented
5#31826691C214yesmaximal, complemented
6#31826503C211yesmaximal, characteristic, complemented
7#31826461C212yesmaximal, complemented
8C2×#135×C283C211yesmaximal, characteristic, complemented
9C22×C4×D283C2211yescharacteristic
10C22×C283⋊C8C2211yescharacteristic
11C2×C8×D283—24no—
12C2×C8×D283C2212yes—
13C2×C8×D283C2212yes—
14#22583591—22no—
15#22583586C2214yes—
16#22583581C2214yes—
17#22583578—22no—
18C4×C22⋊D283—24no—
19#22583569C2212yes—
20#22583544C2212yescomplemented
21#22583542C2212yescomplemented
22#22583534C2214yescomplemented
23#22583531C2214yescomplemented
24C2×#41×C283C2212yes—
25#135×C283—24no—
26C2×Q16×C283C2211yescharacteristic, complemented
27C2×SD16×C283C2212yescomplemented
28C2×D8×C283C2211yescharacteristic, complemented
29C22×C8×C283C2211yescharacteristic
30C23×D283D411yescharacteristic
31C2×C22⋊D283—24no—
32C22×Dic283D411yescharacteristic
33C2×C4×D283—22no—
34C2×C4×D283—22no—
35C2×C4×D283D412yes—
36C2×C4×D283C2312yes—
37C2×C283⋊C8—22no—
38C2×C283⋊C8C2312yes—
39C8×D283—24no—
40C8×D283—24no—
41C4⋊Dic283C2314yes—
42Dic283⋊C4—24no—
43C22⋊Dic283—24no—
44C22⋊Dic283—22no—
45(C2×D283)⋊C4—24no—
46C4×Dic283—22no—
47#41×C283—24no—
48#41×C283—24no—
49C2×Q8×C283C2312yes—
50C2×D4×C283—22no—
51C2×D4×C283C2312yes—
52C22×C4×C283—22no—
53C22×C4×C283C2311yescharacteristic
54Q16×C283—22no—
55SD16×C283—24no—
56D8×C283—22no—
57C2×C8×C283D414yescomplemented
58C2×C8×C283C2311yescharacteristic
59C2×C8×C283C2311yescharacteristic
60C22×D283—22no—
61C22×D283—24no—
62C22×D283C2×D412yes—
63C22⋊D283—48no—
64C2×Dic283—22no—
65C2×Dic283—24no—
66C2×Dic283C2×D412yes—
67C4×D283—24no—
68C4×D283—22no—
69C4×D283—22no—
70C283⋊C8—22no—
71C23×C283—22no—
72C23×C283C2×D411yescharacteristic
73Q8×C283—22no—
74Q8×C283—22no—
75D4×C283—22no—
76D4×C283—22no—
77D4×C283—44no—
78C2×C4×C283—22no—
79C2×C4×C283—44no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D412yes—
82C2×C4×C283#4112yes—
83C2×C4×C283C2411yescharacteristic
84C8×C283C2×D412yes—
85C8×C283C2×D412yes—
86C22×C283—22no—
87C22×C283—42no—
88C22×C283—44no—
89C22×C283#12112yes—
90C22×C283C22×D411yescharacteristic
91C2×D283—28no—
92C2×D283—22no—
93C2×D283—22no—
94C2×D283#13514yescomplemented
95C4×C283—42no—
96C4×C283#12112yes—
97C4×C283C22×D411yescharacteristic
98C4×C283C2×#4111yescharacteristic
99Dic283—22no—
100Dic283—44no—
101C2×C283—22no—
102C2×C283—82no—
103C2×C283C2×#12111yescharacteristic
104C2×C283C2×#13512yes—
105D283—24no—
106C283#305011yescharacteristic, complemented, Sylow
107#3050—2831nomaximal, Sylow
108C2×#135D28311yescharacteristic, complemented
109C23×C8—2831no—
110#525—2832no—
111#467—2832no—
112#466—2832no—
113#465—2834no—
114#427—2831no—
115#416—2832no—
116C2×#41C2×D28312yes—
117C23×C4—2831no—
118#135—24no—
119C2×Q16C2×D28311yescharacteristic, complemented
120C2×SD16C2×D28312yescomplemented
121C2×D8C2×D28311yescharacteristic, complemented
122C22×C8—2831no—
123C22×C8—2832no—
124C22×C8—2832no—
125C22×C8—5664no—
126C22×C8C2×D28311yescharacteristic
127#123—5662no—
128C22⋊Q8—2834no—
129#121—2834no—
130#120—5662no—
131C4×D4—5664no—
132#117—2832no—
133#107—2832no—
134#106—2832no—
135#103—2834no—
136#102—2834no—
137C24—2831no—
138#41—24no—
139#41—24no—
140C2×Q8C22×D28312yes—
141C2×D4—22no—
142C2×D4—5664no—
143C2×D4C22×D28312yes—
144C22×C4—22no—
145C22×C4—2831no—
146C22×C4—2832no—
147C22×C4—2832no—
148C22×C4—5662no—
149C22×C4—5662no—
150C22×C4C22×D28311yescharacteristic
151Q16—22no—
152SD16—24no—
153D8—22no—
154C2×C8—2832no—
155C2×C8—5662no—
156C2×C8—5664no—
157C2×C8—5664no—
158C2×C8C22⋊D28314yescomplemented
159C2×C8C22×D28311yescharacteristic
160C2×C8C22×D28311yescharacteristic
161C4⋊C4—2834no—
162C4⋊C4—5664no—
163C22⋊C4—5664no—
164C22⋊C4—5664no—
165C22⋊C4—5662no—
166C42—5662no—
167C23—22no—
168C23—2832no—
169C23—5664no—
170C23—5662no—
171C23D4×D28311yescharacteristic
172Q8—22no—
173Q8—22no—
174D4—22no—
175D4—22no—
176D4—44no—
177D4—11328no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—2832no—
181C2×C4—5662no—
182C2×C4—5664no—
183C2×C4—5662no—
184C2×C4—5662no—
185C2×C4—5664no—
186C2×C4D4×D28311yescharacteristic
187C2×C4C2×C22⋊D28312yes—
188C2×C4#1798539112yes—
189C2×C4C23×D28311yescharacteristic
190C8—5662no—
191C8C2×C22⋊D28312yes—
192C8C2×C22⋊D28312yes—
193C22—22no—
194C22—42no—
195C22—44no—
196C22—2834no—
197C22—5668no—
198C22—5662no—
199C22—5662no—
200C22#2258358112yes—
201C22C2×D4×D28311yescharacteristic
202C4—42no—
203C4—5662no—
204C4—11324no—
205C4#2258358112yes—
206C4C22×C22⋊D28311yescharacteristic
207C4C2×#1798539111yescharacteristic
208C2—22no—
209C2—82no—
210C2—5664no—
211C2C2×#2258358111yescharacteristic
212C2#135×D28312yes—
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#135×C283C2
socleC22×C283C22×D4
hypercenterC2×#135D283
hypocenterC283#3050
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×C8×D283C2semidirect
2. #31826972C2semidirect
3. #31826703C2semidirect
4. #31826698C2semidirect
5. #31826691C2semidirect
6. #31826503C2semidirect
7. #31826461C2semidirect
8. C2×#135×C283C2semidirect
20. #22583544C22semidirect
21. #22583542C22semidirect
22. #22583534C22semidirect
23. #22583531C22semidirect
26. C2×Q16×C283C22semidirect
27. C2×SD16×C283C22semidirect
28. C2×D8×C283C22semidirect
57. C2×C8×C283D4semidirect
94. C2×D283#135semidirect
106. C283#3050semidirect
108. C2×#135D283semidirect
119. C2×Q16C2×D283semidirect
120. C2×SD16C2×D283semidirect
121. C2×D8C2×D283semidirect
158. C2×C8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D2832
#318269722
#318267032
#318266982
#318266912
#318265032
#318264612
C2×#135×C2832
#3050283