Finite Group Databasebeta

← #49121796

Subgroups — #49121796

Order 36224.

314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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#31827039C211yesmaximal, characteristic
2#31826943C211yesmaximal, characteristic, complemented
3#31826481C212yesmaximal
4#31826222C212yesmaximal, complemented
5C2×#101×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2211yescharacteristic
7#22583608C412yescomplemented
8#22583599C412yescomplemented
9#22583593—22no—
10#22583586—22no—
11Q8×Dic283—24no—
12#22583569—22no—
13#22583569C2211yescharacteristic
14#22583569C2212yes—
15#22583536—24no—
16C22×Q8×C283C2211yescharacteristic
17C2×M16×C283C2212yes—
18#101×C283—22no—
19#17985392—22no—
20#17985392—22no—
21C2×Dic566C2×C411yescharacteristic
22C2×D1132C2×C411yescharacteristic
23C2×C22⋊D283—21no—
24C2×C4×D283—21no—
25C4⋊Dic283—24no—
26C4⋊Dic283—22no—
27C4⋊Dic283—21no—
28Dic283⋊C4—24no—
29C22⋊Dic283—22no—
30C22⋊Dic283—21no—
31(C2×D283)⋊C4—24no—
32C4×Dic283—24no—
33C4×Dic283C2×C412yes—
34C4×Dic283D414yes—
35C2×Q8×C283—22no—
36C2×Q8×C283—22no—
37C2×Q8×C283C2×C412yes—
38C2×Q8×C283D412yes—
39C22×C4×C283D412yes—
40C22×C4×C283C2311yescharacteristic
41M16×C283—22no—
42M16×C283—22no—
43C2×C8×C283—22no—
44C22×D283—21no—
45Dic566—22no—
46D1132—22no—
47C22⋊D283—41no—
48C22⋊D283—41no—
49C2×Dic283—22no—
50C2×Dic283—21no—
51C2×Dic283—24no—
52C4×D283—42no—
53C23×C283C2×D411yescharacteristic
54Q8×C283—24no—
55Q8×C283—24no—
56C2×C4×C283—22no—
57C2×C4×C283—22no—
58C2×C4×C283C22⋊C414yes—
59C2×C4×C283C22×C411yescharacteristic
60C2×C4×C283C2×D412yes—
61C2×C4×C283C2×D411yescharacteristic
62C2×C4×C283#4112yes—
63C8×C283—42no—
64C22×C283—41no—
65C22×C283C2×C22⋊C411yescharacteristic
66C22×C283#12011yescharacteristic
67C22×C283#12311yescharacteristic
68C2×D283—42no—
69C2×D283—41no—
70C4×C283—24no—
71C4×C283C4×D412yes—
72C4×C283#12112yes—
73Dic283—44no—
74Dic283—42no—
75Dic283—41no—
76C2×C283—21no—
77C2×C283—21no—
78C2×C283—21no—
79C2×C283#38611yescharacteristic
80D283—81no—
81C283#191211yescharacteristic, complemented, Sylow
82#1912—2831nomaximal, Sylow
83#536—2831no—
84#519—2831no—
85#421—2832no—
86C2×#101D28311yescharacteristic, complemented
87H(3,ℤ/4)—2832no—
88C2×#41—2831no—
89C22×Q8C2×D28311yescharacteristic
90C2×M16C2×D28312yes—
91C4⋊Q8—2832no—
92#124—2832no—
93#123—5662no—
94C22⋊Q8—5662no—
95C4×Q8—5664no—
96#117—2832no—
97#117—2831no—
98#117—5662no—
99#104—5664no—
100#101—22no—
101#41—5662no—
102#41—5662no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—2831no—
106C2×Q8C4×D28312yes—
107C2×Q8C22⋊D28312yes—
108C2×D4—2831no—
109C2×D4—5661no—
110C22×C4—5661no—
111C22×C4D113212yes—
112C22×C4C22×D28311yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—5664no—
117C4⋊C4—5664no—
118C4⋊C4—5662no—
119C4⋊C4—5661no—
120C22⋊C4—5662no—
121C22⋊C4—5661no—
122C22⋊C4—5664no—
123C42—2832no—
124C42—2834no—
125C42—5664no—
126C23—5661no—
127C23C2×D113211yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—5662no—
131D4—5662no—
132D4—11321no—
133D4—11321no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—5662no—
137C2×C4—5661no—
138C2×C4—5664no—
139C2×C4—11322no—
140C2×C4(C2×D283)⋊C414yes—
141C2×C4C2×C4×D28311yescharacteristic
142C2×C4D4×D28312yes—
143C2×C4C2×C22⋊D28311yescharacteristic
144C2×C4#1798539112yes—
145C8—42no—
146C22—41no—
147C22—11322no—
148C22—11321no—
149C22C2×(C2×D283)⋊C411yescharacteristic
150C22#2258358011yescharacteristic
151C22#2258359411yescharacteristic
152C4—24no—
153C4—11324no—
154C4—11322no—
155C4—11321no—
156C4(C22⋊D283)⋊C412yes—
157C4#2258358212yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—22641no—
162C2#3182634211yescharacteristic
subgroupG/H
centerC2#31826342
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#101×C283C2
socleC2×C283#386
prime radicalC2×#17985392C22
cosocleC22×C4×C283C23
hypercenterC2×#101D283
hypocenterC283#1912
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #31826943C2semidirect
4. #31826222C2semidirect
5. C2×#101×C283C2semidirect
7. #22583608C4semidirect
8. #22583599C4semidirect
81. C283#1912semidirect
86. C2×#101D283semidirect

Maximal subgroups

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

subgroupindex
#318270392
#318269432
#318264812
#318262222
C2×#101×C2832
#1912283