Finite Group Databasebeta

← #49130912

Subgroups — #49130912

Order 36224.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22583616C211yesmaximal, characteristic
2#31827039C212yesmaximal
3#31826720C214yesmaximal, complemented
4#31826703C214yesmaximal, complemented
5#31826503C211yesmaximal, characteristic, complemented
6#31826474C212yesmaximal, complemented
7C22×Q16×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9#22583616—24no—
10C2×#17985376C2211yescharacteristic
11C2×#17985375C2212yes—
12C2×C8×D283C2212yes—
13#22583608—22no—
14#22583599—22no—
15#22583593—24no—
16#22583586C2218yes—
17#22583569C2212yes—
18#22583544C2212yes—
19#22583542C2212yes—
20#22583534C2218yes—
21C22×Q8×C283C2212yes—
22C2×Q16×C283—24no—
23C2×Q16×C283C2212yes—
24C2×Q16×C283C2212yes—
25C22×C8×C283C2211yescharacteristic
26#17985392—22no—
27#17985392—22no—
28C2×Dic566D411yescharacteristic
29C2×D1132D411yescharacteristic
30C2×C22⋊D283D412yes—
31C2×C4×D283C2312yes—
32#17985376—22no—
33#17985375—24no—
34C2×C283⋊C8C2312yes—
35C8×D283—24no—
36C4⋊Dic283C2314yes—
37Dic283⋊C4—28no—
38C22⋊Dic283—22no—
39(C2×D283)⋊C4—28no—
40C4×Dic283—22no—
41C2×Q8×C283—22no—
42C2×Q8×C283—24no—
43C2×Q8×C283—24no—
44C2×Q8×C283C2314yes—
45C22×C4×C283—22no—
46C22×C4×C283C2311yescharacteristic
47Q16×C283—24no—
48Q16×C283—24no—
49C2×C8×C283D414yes—
50C2×C8×C283C2311yescharacteristic
51C2×C8×C283C2311yescharacteristic
52C22×D283C2×D412yes—
53Dic566—22no—
54D1132—22no—
55C22⋊D283—24no—
56C2×Dic283—24no—
57C2×Dic283C2×D412yes—
58C4×D283—22no—
59C4×D283—22no—
60C283⋊C8—22no—
61C23×C283C2×D411yescharacteristic
62Q8×C283—24no—
63Q8×C283—24no—
64Q8×C283—44no—
65C2×C4×C283—24no—
66C2×C4×C283—44no—
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D412yes—
69C2×C4×C283#4112yes—
70C2×C4×C283C2411yescharacteristic
71C8×C283C2×D412yes—
72C8×C283C2×D412yes—
73C22×C283—22no—
74C22×C283#12112yes—
75C22×C283C22×D411yescharacteristic
76C2×D283—22no—
77C2×D283—24no—
78C4×C283—44no—
79C4×C283#12112yes—
80C4×C283C22×D411yescharacteristic
81C4×C283C2×#4111yescharacteristic
82Dic283—22no—
83Dic283—44no—
84C2×C283—22no—
85C2×C283C2×#12111yescharacteristic
86C2×C283#57812yes—
87D283—42no—
88C283#305911yescharacteristic, complemented, Sylow
89#3059—2831nomaximal, Sylow
90C22×Q16D28311yescharacteristic, complemented
91C2×#131—2831no—
92#536—2832no—
93#470—2834no—
94#467—2834no—
95#427—2831no—
96#419—2832no—
97C2×#41—2831no—
98C22×Q8C2×D28312yes—
99C2×Q16—24no—
100C2×Q16C2×D28312yes—
101C2×Q16C2×D28312yes—
102#131—5664no—
103C2×M16—2831no—
104C2×M16—2832no—
105C22×C8—2832no—
106C22×C8C2×D28311yescharacteristic
107C4⋊Q8—5662no—
108#124—5662no—
109#123—5664no—
110C22⋊Q8—2838no—
111#117—2832no—
112#107—2832no—
113#106—2832no—
114#103—2838no—
115#41—5662no—
116#41—5662no—
117C2×Q8—22no—
118C2×Q8—24no—
119C2×Q8—24no—
120C2×Q8—2831no—
121C2×Q8C22×D28314yes—
122C2×D4—2832no—
123C2×D4—2831no—
124C22×C4—22no—
125C22×C4—2832no—
126C22×C4C22×D28311yescharacteristic
127Q16—24no—
128Q16—24no—
129M16—5662no—
130M16—5664no—
131C2×C8—2832no—
132C2×C8—5664no—
133C2×C8C22⋊D28314yes—
134C2×C8C22×D28311yescharacteristic
135C2×C8C22×D28311yescharacteristic
136C4⋊C4—2834no—
137C4⋊C4—5668no—
138C22⋊C4—5668no—
139C22⋊C4—5662no—
140C42—5662no—
141C23—2832no—
142C23D4×D28311yescharacteristic
143Q8—24no—
144Q8—24no—
145Q8—44no—
146Q8—5662no—
147D4—5664no—
148D4—5662no—
149C2×C4—24no—
150C2×C4—44no—
151C2×C4—2832no—
152C2×C4—5662no—
153C2×C4—5662no—
154C2×C4—5664no—
155C2×C4D4×D28311yescharacteristic
156C2×C4C2×C22⋊D28312yes—
157C2×C4#1798539112yes—
158C2×C4C23×D28311yescharacteristic
159C8—5662no—
160C8C2×C22⋊D28312yes—
161C8C2×C22⋊D28312yes—
162C22—22no—
163C22—5662no—
164C22—5664no—
165C22#2258358112yes—
166C22C2×D4×D28311yescharacteristic
167C4—44no—
168C4—5662no—
169C4—11324no—
170C4#2258358112yes—
171C4C22×C22⋊D28311yescharacteristic
172C4C2×#1798539111yescharacteristic
173C2—22no—
174C2—11322no—
175C2C2×#2258358111yescharacteristic
176C2#3182727812yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×Q16×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985392C22
hypercenterC22×Q16D283
hypocenterC283#3059
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
3. #31826720C2semidirect
4. #31826703C2semidirect
5. #31826503C2semidirect
6. #31826474C2semidirect
7. C22×Q16×C283C2semidirect
88. C283#3059semidirect
90. C22×Q16D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836162
#318270392
#318267202
#318267032
#318265032
#318264742
C22×Q16×C2832
#3059283