Finite Group Databasebeta

← #49131192

Subgroups — #49131192

Order 36224.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#31826976C211yesmaximal, characteristic
2#31826806C214yesmaximal, complemented
3#31826789C214yesmaximal, complemented
4#31826505C212yesmaximal, complemented
5#31826464C212yesmaximal, complemented
6#31826429C211yesmaximal, characteristic, complemented
7C2×#117×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C2×#17985376C2212yes—
10#22583593—21no—
11#22583589C2212yes—
12#22583584C2212yes—
13#22583579—21no—
14C4×C22⋊D283—22no—
15#22583569C2211yescharacteristic
16#22583543C2214yescomplemented
17#22583541C2214yescomplemented
18#22583533C2214yescomplemented
19#22583530C2214yescomplemented
20C22⋊(C283⋊C8)C2214yes—
21C23×C4×C283C2211yescharacteristic
22#117×C283—22no—
23#117×C283C2214yes—
24C2×C4⋊C4×C283C2212yes—
25C2×C22⋊C4×C283—21no—
26C2×C42×C283—21no—
27#17985392—24no—
28C2×Dic566C2311yescharacteristic
29C2×D1132C2311yescharacteristic
30C2×C22⋊D283—22no—
31C2×C22⋊D283—21no—
32C2×C4×D283—21no—
33#17985376—24no—
34C2×C283⋊C8C2314yes—
35C4⋊Dic283C2312yes—
36Dic283⋊C4—22no—
37C22⋊Dic283—21no—
38C22⋊Dic283—22no—
39(C2×D283)⋊C4—22no—
40C4×Dic283—21no—
41C24×C283D411yescharacteristic
42C22×C4×C283—24no—
43C22×C4×C283—22no—
44C22×C4×C283D412yes—
45C22×C4×C283D411yescharacteristic
46C22×C4×C283C2312yes—
47C22×C4×C283C2311yescharacteristic
48C4⋊C4×C283—22no—
49C4⋊C4×C283C2314yes—
50C22⋊C4×C283—24no—
51C42×C283—24no—
52C22×D283—21no—
53Dic566—22no—
54D1132—22no—
55C22⋊D283—44no—
56C22⋊D283—42no—
57C2×Dic283—22no—
58C2×Dic283—21no—
59C4×D283—42no—
60C283⋊C8—24no—
61C23×C283—22no—
62C23×C283—42no—
63C23×C283C2×D412yes—
64C23×C283C2×D411yescharacteristic
65C2×C4×C283—22no—
66C2×C4×C283—24no—
67C2×C4×C283—24no—
68C2×C4×C283—24no—
69C2×C4×C283—44no—
70C2×C4×C283C2×D412yes—
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283#4114yes—
73C2×C4×C283C2411yescharacteristic
74C22×C283—22no—
75C22×C283—22no—
76C22×C283—22no—
77C22×C283—22no—
78C22×C283—44no—
79C22×C283#12312yes—
80C22×C283C22×D411yescharacteristic
81C2×D283—41no—
82C2×D283—42no—
83C4×C283—22no—
84C4×C283—44no—
85C4×C283#12312yes—
86C4×C283C2×#4112yes—
87Dic283—41no—
88Dic283—42no—
89C2×C283—22no—
90C2×C283—42no—
91C2×C283C2×#12311yescharacteristic
92C2×C283#57512yes—
93D283—81no—
94C283#309311yescharacteristic, complemented, Sylow
95#3093—2831nomaximal, Sylow
96#525—2831no—
97C2×#117D28311yescharacteristic, complemented
98#485—2834no—
99#482—2834no—
100#428—2832no—
101#417—2832no—
102#407—2831no—
103C2×#41—2831no—
104C23×C4C2×D28311yescharacteristic
105C2×M16—2832no—
106#123—5661no—
107C22⋊Q8—2832no—
108#121—2832no—
109#120—5661no—
110C4×D4—5662no—
111#117—22no—
112#117—2831no—
113#117C2×D28314yes—
114C2×C4⋊C4C2×D28312yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—2834no—
118#106—2834no—
119#103—2834no—
120#102—2834no—
121C22⋊C8—2834no—
122C24C22⋊D28311yescharacteristic
123#41—5664no—
124C2×Q8—2831no—
125C2×D4—2831no—
126C2×D4—5662no—
127C2×D4—5661no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—5661no—
131C22×C4C22⋊D28311yescharacteristic
132C22×C4C22⋊D28312yes—
133C22×C4C22×D28312yes—
134C22×C4C22×D28311yescharacteristic
135M16—5664no—
136C2×C8—2834no—
137C4⋊C4—22no—
138C4⋊C4—2832no—
139C4⋊C4—5662no—
140C4⋊C4C22×D28314yes—
141C22⋊C4—24no—
142C22⋊C4—5661no—
143C22⋊C4—5662no—
144C22⋊C4—5662no—
145C42—24no—
146C42—5661no—
147C23—22no—
148C23—42no—
149C23—5661no—
150C23C2×C22⋊D28312yes—
151C23C2×C22⋊D28311yescharacteristic
152Q8—5662no—
153D4—5662no—
154D4—11324no—
155D4—11322no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—5662no—
162C2×C4—5661no—
163C2×C4—11322no—
164C2×C4C2×C22⋊D28312yes—
165C2×C4C2×C22⋊D28311yescharacteristic
166C2×C4#1798539214yes—
167C2×C4C23×D28311yescharacteristic
168C8—5664no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—11321no—
175C22—11322no—
176C22#2258359312yes—
177C22C22×C22⋊D28311yescharacteristic
178C4—22no—
179C4—44no—
180C4—11321no—
181C4—11322no—
182C4#2258359312yes—
183C4C2×#1798539212yes—
184C2—22no—
185C2—42no—
186C2—22641no—
187C2C2×#2258359311yescharacteristic
188C2#3182726312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#117×C283C2
socleC22×C283C22×D4
prime radical#31826976C2
hypercenterC2×#117D283
hypocenterC283#3093
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #31826806C2semidirect
3. #31826789C2semidirect
4. #31826505C2semidirect
5. #31826464C2semidirect
6. #31826429C2semidirect
7. C2×#117×C283C2semidirect
16. #22583543C22semidirect
17. #22583541C22semidirect
18. #22583533C22semidirect
19. #22583530C22semidirect
94. C283#3093semidirect
97. C2×#117D283semidirect

Maximal subgroups

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

subgroupindex
#318269762
#318268062
#318267892
#318265052
#318264642
#318264292
C2×#117×C2832
#3093283