Finite Group Databasebeta

← #49121798

Subgroups — #49121798

Order 36224.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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#31826483C212yesmaximal
3C2×#22583529C211yesmaximal, characteristic, complemented
4#31826221C212yesmaximal, complemented
5#519×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2211yescharacteristic
7C2×#17985376C2212yes—
8#22583608C412yescomplemented
9#22583599C412yescomplemented
10#22583593—22no—
11#22583586—22no—
12#22583569C2211yescharacteristic
13#22583538—24no—
14#22583529—22no—
15C22×Q8×C283C2211yescharacteristic
16C4×Q8×C283—24no—
17#117×C283—22no—
18#117×C283C2212yes—
19#17985392—22no—
20#17985392—22no—
21C2×Dic566C2×C411yescharacteristic
22C2×D1132C2×C411yescharacteristic
23C2×C22⋊D283—21no—
24C2×C4×D283—21no—
25#17985376—22no—
26#17985376—22no—
27C2×C283⋊C8—22no—
28C4⋊Dic283—21no—
29Dic283⋊C4—24no—
30C22⋊Dic283—21no—
31(C2×D283)⋊C4—24no—
32C4×Dic283C2×C412yes—
33C2×Q8×C283—22no—
34C2×Q8×C283—22no—
35C2×Q8×C283C2×C412yes—
36C2×Q8×C283D412yes—
37C22×C4×C283D412yes—
38C22×C4×C283C2311yescharacteristic
39C4⋊C4×C283—24no—
40C4⋊C4×C283—22no—
41C22⋊C4×C283—22no—
42C42×C283—24no—
43C42×C283D414yes—
44C22×D283—21no—
45Dic566—22no—
46D1132—22no—
47C22⋊D283—41no—
48C22⋊D283—41no—
49C2×Dic283—22no—
50C2×Dic283—21no—
51C4×D283—42no—
52C283⋊C8—42no—
53C23×C283C2×D411yescharacteristic
54Q8×C283—24no—
55Q8×C283—24no—
56C2×C4×C283—22no—
57C2×C4×C283—22no—
58C2×C4×C283—24no—
59C2×C4×C283C22⋊C414yes—
60C2×C4×C283C22×C411yescharacteristic
61C2×C4×C283C2×D412yes—
62C2×C4×C283C2×D411yescharacteristic
63C2×C4×C283#4112yes—
64C22×C283—41no—
65C22×C283C2×C22⋊C411yescharacteristic
66C22×C283#12011yescharacteristic
67C22×C283#12311yescharacteristic
68C2×D283—42no—
69C2×D283—41no—
70C4×C283—24no—
71C4×C283—44no—
72C4×C283C4×D412yes—
73C4×C283#12112yes—
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#519D28311yescharacteristic, complemented
85#421—2832no—
86C2×#101—2831no—
87H(3,ℤ/4)—2832no—
88C2×#41—2831no—
89C22×Q8C2×D28311yescharacteristic
90C2×M16—2832no—
91C4⋊Q8—2832no—
92#124—2832no—
93#123—5662no—
94C22⋊Q8—5662no—
95C4×Q8—24no—
96#117—22no—
97#117—2831no—
98#117C2×D28312yes—
99#104—5664no—
100#101—5662no—
101#41—5662no—
102#41—5662no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—2831no—
106C2×Q8C4×D28312yes—
107C2×Q8D113212yes—
108C2×D4—2831no—
109C2×D4—5661no—
110C22×C4—5661no—
111C22×C4C22⋊D28312yes—
112C22×C4C22×D28311yescharacteristic
113M16—5662no—
114M16—5662no—
115C2×C8—5662no—
116C4⋊C4—24no—
117C4⋊C4—22no—
118C4⋊C4—5664no—
119C4⋊C4—5661no—
120C22⋊C4—22no—
121C22⋊C4—5661no—
122C22⋊C4—5664no—
123C42—24no—
124C42—2832no—
125C42C22⋊D28314yes—
126C23—5661no—
127C23C2×C22⋊D28311yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—5662no—
131D4—5662no—
132D4—11321no—
133D4—11321no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—5662no—
138C2×C4—5661no—
139C2×C4—11322no—
140C2×C4(C2×D283)⋊C414yes—
141C2×C4C2×C4×D28311yescharacteristic
142C2×C4C2×C22⋊D28312yes—
143C2×C4C2×D113211yescharacteristic
144C2×C4#1798539212yes—
145C8—11322no—
146C22—41no—
147C22—11322no—
148C22—11321no—
149C22C2×(C2×D283)⋊C411yescharacteristic
150C22#2258357911yescharacteristic
151C22#2258359311yescharacteristic
152C4—24no—
153C4—44no—
154C4—11322no—
155C4—11321no—
156C4C4×C22⋊D28312yes—
157C4#2258358412yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—22641no—
162C2#3182634411yescharacteristic
subgroupG/H
centerC2#31826344
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#519×C283C2
socleC2×C283#386
prime radicalC2×#17985392C22
cosocleC22×C4×C283C23
hypercenter#519D283
hypocenterC283#1912
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. C2×#22583529C2semidirect
4. #31826221C2semidirect
5. #519×C283C2semidirect
8. #22583608C4semidirect
9. #22583599C4semidirect
81. C283#1912semidirect
84. #519D283semidirect

Maximal subgroups

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

subgroupindex
#318270392
#318264832
C2×#225835292
#318262212
#519×C2832
#1912283