Finite Group Databasebeta

← #49121799

Subgroups — #49121799

Order 36224.

314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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#31826943C211yesmaximal, characteristic, complemented
2#31826482C212yesmaximal
3C2×#22583529C211yesmaximal, characteristic, complemented
4#31826221C212yesmaximal, complemented
5#536×C283C211yesmaximal, characteristic
6C2×#17985376C2212yes—
7Q8×Dic283—24no—
8#22583569—22no—
9#22583569C2212yes—
10#22583537—24no—
11#22583529—22no—
12C2×#41×C283C2211yescharacteristic
13C22×Q8×C283C2211yescharacteristic
14C4⋊Q8×C283C412yescomplemented
15#124×C283C412yescomplemented
16#123×C283—22no—
17C22⋊Q8×C283—22no—
18#117×C283C2211yescharacteristic
19#17985376—22no—
20#17985376—22no—
21C2×C283⋊C8—22no—
22C4⋊Dic283—24no—
23C4⋊Dic283—22no—
24C22⋊Dic283—22no—
25C4×Dic283—24no—
26C4×Dic283D414yes—
27#41×C283—22no—
28#41×C283—22no—
29C2×Q8×C283—22no—
30C2×Q8×C283—22no—
31C2×Q8×C283C2×C411yescharacteristic
32C2×Q8×C283C2×C412yes—
33C2×Q8×C283D412yes—
34C2×D4×C283—21no—
35C2×D4×C283C2×C411yescharacteristic
36C22×C4×C283—21no—
37C22×C4×C283D412yes—
38C22×C4×C283C2311yescharacteristic
39C4⋊C4×C283—24no—
40C4⋊C4×C283—21no—
41C22⋊C4×C283—21no—
42C22⋊C4×C283—24no—
43C42×C283C2×C412yes—
44C2×Dic283—24no—
45C283⋊C8—42no—
46C23×C283—21no—
47C23×C283C2×D411yescharacteristic
48Q8×C283—24no—
49Q8×C283—24no—
50Q8×C283—22no—
51D4×C283—22no—
52D4×C283—41no—
53D4×C283—41no—
54C2×C4×C283—22no—
55C2×C4×C283—22no—
56C2×C4×C283—22no—
57C2×C4×C283—21no—
58C2×C4×C283—42no—
59C2×C4×C283C22⋊C414yes—
60C2×C4×C283C22×C411yescharacteristic
61C2×C4×C283C2×D412yes—
62C2×C4×C283C2×D411yescharacteristic
63C2×C4×C283#4112yes—
64C22×C283—41no—
65C22×C283—42no—
66C22×C283—41no—
67C22×C283C2×C22⋊C411yescharacteristic
68C22×C283#12011yescharacteristic
69C22×C283#12311yescharacteristic
70C4×C283—24no—
71C4×C283—42no—
72C4×C283—41no—
73C4×C283C4×D412yes—
74C4×C283#12112yes—
75Dic283—44no—
76C2×C283—21no—
77C2×C283—21no—
78C2×C283—21no—
79C2×C283—81no—
80C2×C283#38611yescharacteristic
81C283#191211yescharacteristic, complemented, Sylow
82#1912—2831nomaximal, Sylow
83#536D28311yescharacteristic
84#519—2831no—
85#421—2832no—
86C2×#101—2831no—
87H(3,ℤ/4)—2832no—
88C2×#41C2×D28311yescharacteristic
89C22×Q8C2×D28311yescharacteristic
90C2×M16—2832no—
91C4⋊Q8Dic28312yescomplemented
92#124Dic28312yescomplemented
93#123—22no—
94C22⋊Q8—22no—
95C4×Q8—5664no—
96#117—2832no—
97#117—5662no—
98#117C2×D28311yescharacteristic
99#104—5664no—
100#101—5662no—
101#41—22no—
102#41—22no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic28311yescharacteristic
106C2×Q8C2×Dic28312yes—
107C2×Q8C22⋊D28312yes—
108C2×D4—21no—
109C2×D4C2×Dic28311yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D28312yes—
112C22×C4C22×D28311yescharacteristic
113M16—5662no—
114M16—5662no—
115C2×C8—5662no—
116C4⋊C4—24no—
117C4⋊C4—21no—
118C4⋊C4—5664no—
119C4⋊C4—5662no—
120C22⋊C4—21no—
121C22⋊C4—24no—
122C22⋊C4—5662no—
123C42—2834no—
124C42—5664no—
125C42C2×Dic28312yes—
126C23—21no—
127C23C2×C22⋊D28311yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—22no—
131D4—22no—
132D4—41no—
133D4—41no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—5664no—
140C2×C4C22⋊Dic28314yes—
141C2×C4C22×Dic28311yescharacteristic
142C2×C4D4×D28312yes—
143C2×C4C2×C22⋊D28311yescharacteristic
144C2×C4#1798539112yes—
145C8—11322no—
146C22—41no—
147C22—42no—
148C22—41no—
149C22C2×C22⋊Dic28311yescharacteristic
150C22#2258357811yescharacteristic
151C22#2258359111yescharacteristic
152C4—24no—
153C4—42no—
154C4—41no—
155C4—11324no—
156C4D4×Dic28312yes—
157C4#2258358212yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—81no—
162C2#3182634511yescharacteristic
subgroupG/H
centerC2#31826345
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#536×C283C2
socleC2×C283#386
prime radicalC2×#41×C283C22
cosocleC22×C4×C283C23
hypercenter#536D283
hypocenterC283#1912
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #31826943C2semidirect
3. C2×#22583529C2semidirect
4. #31826221C2semidirect
14. C4⋊Q8×C283C4semidirect
15. #124×C283C4semidirect
81. C283#1912semidirect
91. C4⋊Q8Dic283semidirect
92. #124Dic283semidirect

Maximal subgroups

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

subgroupindex
#318269432
#318264822
C2×#225835292
#318262212
#536×C2832
#1912283