Finite Group Databasebeta

← #49120504

Subgroups — #49120504

Order 36224.

194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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#31827190C211yesmaximal, characteristic
2#31826868C211yesmaximal, characteristic
3#31826751C211yesmaximal, characteristic
4#31826676C211yesmaximal, characteristic
5#31826195C211yesmaximal, characteristic
6#31826195C211yesmaximal, characteristic
7#332×C283C211yesmaximal, characteristic
8C2×Dic1132—21no—
9#22583610C2211yescharacteristic
10#22583608—21no—
11#22583601—21no—
12#22583600—22no—
13Q8×Dic283—21no—
14C4×Dic566C2211yescharacteristic
15C4×Dic566C2211yescharacteristic
16#22583575—21no—
17#22583543—22no—
18#22583542—21no—
19#22583535—21no—
20#22583535—21no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566—21no—
26C2×Dic566D411yescharacteristic
27C2×Dic566D411yescharacteristic
28Dic1132—42no—
29C2×C283⋊C8—21no—
30C4⋊Dic283—22no—
31C4⋊Dic283—21no—
32C4⋊Dic283—21no—
33C4⋊Dic283D411yescharacteristic
34C4⋊Dic283D411yescharacteristic
35Dic283⋊C4—22no—
36Dic283⋊C4—22no—
37Dic283⋊C4—21no—
38Dic283⋊C4—21no—
39C4×Dic283—22no—
40C4×Dic283—21no—
41C4×Dic283—21no—
42C2×Q8×C283—21no—
43C2×C8×C283—21no—
44C2×C8×C283—21no—
45C4⋊C4×C283—21no—
46C4⋊C4×C283D412yes—
47C42×C283C2311yescharacteristic
48Dic566—21no—
49Dic566—21no—
50Dic566—21no—
51Dic566—41no—
52Dic566—41no—
53Dic566Q1612yescomplemented
54C2×Dic283—21no—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C2×Dic283—21no—
58C2×Dic283—41no—
59C283⋊C8—22no—
60Q8×C283—41no—
61Q8×C283—41no—
62C2×C4×C283—22no—
63C2×C4×C283C2×D411yescharacteristic
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283C2×D411yescharacteristic
66C8×C283—41no—
67C8×C283—41no—
68C22×C283#12011yescharacteristic
69C4×C283—21no—
70C4×C283—42no—
71C4×C283C2×Q1611yescharacteristic
72C4×C283#13511yescharacteristic
73C4×C283AGL(1,ℤ/8)11yescharacteristic
74C4×C283#13711yescharacteristic
75Dic283—22no—
76Dic283—41no—
77Dic283—41no—
78Dic283—41no—
79Dic283—81no—
80C2×C283#44911yescharacteristic
81C2×C283#45111yescharacteristic
82C2×C283#45611yescharacteristic
83C283#164811yescharacteristic, complemented, Sylow
84#1648—2831nomaximal, Sylow
85#557—2831no—
86#500—2831no—
87#475—2831no—
88#462—2831no—
89#332D28311yescharacteristic
90Q8⋊C8—2831no—
91Q8⋊C8—2831no—
92C2×Q16—5661no—
93C4⋊Q8—2831no—
94C4⋊Q8—5661no—
95C4⋊Q8C2×D28311yescharacteristic
96#125—5661no—
97#125—5662no—
98C4×Q8—2831no—
99C4×Q8—2831no—
100C4×Q8—5661no—
101C4×Q8—5661no—
102#107—5662no—
103#106—5661no—
104C4⋊C8C2×D28311yescharacteristic
105C4⋊C8C2×D28311yescharacteristic
106#103—5661no—
107#103—5661no—
108C4×C8—2831no—
109C2×Q8—21no—
110C2×Q8—2831no—
111C2×Q8—2831no—
112C2×Q8—5661no—
113Q16—11322no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—5661no—
117C4⋊C4—21no—
118C4⋊C4—2831no—
119C4⋊C4—2831no—
120C4⋊C4—5662no—
121C4⋊C4—5662no—
122C4⋊C4—5662no—
123C4⋊C4—5661no—
124C4⋊C4—5661no—
125C4⋊C4—5661no—
126C4⋊C4—5661no—
127C4⋊C4D113212yes—
128C42—5662no—
129C42—5661no—
130C42—5661no—
131C42C22×D28311yescharacteristic
132Q8—41no—
133Q8—41no—
134Q8—2832no—
135Q8—5661no—
136Q8—5661no—
137Q8—5661no—
138Q8—11321no—
139Q8—11321no—
140C2×C4—22no—
141C2×C4—5661no—
142C2×C4—5661no—
143C2×C4—5661no—
144C2×C4—5661no—
145C2×C4—11321no—
146C2×C4D4×D28311yescharacteristic
147C2×C4D4×D28311yescharacteristic
148C2×C4C2×D113211yescharacteristic
149C8—41no—
150C8—41no—
151C8—5662no—
152C22#2258358011yescharacteristic
153C4—21no—
154C4—42no—
155C4—5662no—
156C4—11321no—
157C4—11321no—
158C4—11321no—
159C4—22641no—
160C4Q16×D28311yescharacteristic
161C4#2258363111yescharacteristic
162C4#2258363411yescharacteristic
163C4#2258363911yescharacteristic
164C2#3182661111yescharacteristic
165C2#3182662211yescharacteristic
166C2#3182665011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#332×C283C2
socle, prime radicalC22×C283#120
hypercenter#332D283
hypocenterC283#1648
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
53. Dic566Q16semidirect
83. C283#1648semidirect

Maximal subgroups

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

subgroupindex
#318271902
#318268682
#318267512
#318266762
#318261952
#332×C2832
#1648283