Finite Group Databasebeta

← #49120420

Subgroups — #49120420

Order 36224.

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

normal subgroups only

This group has 188 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#31826817C211yesmaximal, characteristic
3#31826761C211yesmaximal, characteristic
4#31826761C211yesmaximal, characteristic
5#31826195C211yesmaximal, characteristic
6#31826195C211yesmaximal, characteristic
7#332×C283C211yesmaximal, characteristic
8#22583610C2211yescharacteristic
9#22583608—21no—
10#22583601—21no—
11#22583600—22no—
12Q8×Dic283—21no—
13C4×Dic566C2211yescharacteristic
14C4×Dic566C2211yescharacteristic
15#22583575—21no—
16#22583544—21no—
17#22583544—21no—
18#22583535—21no—
19#22583535—21no—
20#22583533—22no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566—21no—
26C2×Dic566D411yescharacteristic
27C2×Dic566D411yescharacteristic
28C2×C283⋊C8—21no—
29C4⋊Dic283—22no—
30C4⋊Dic283—21no—
31C4⋊Dic283—21no—
32C4⋊Dic283D411yescharacteristic
33C4⋊Dic283D411yescharacteristic
34Dic283⋊C4—22no—
35Dic283⋊C4—22no—
36Dic283⋊C4—21no—
37Dic283⋊C4—21no—
38C4×Dic283—22no—
39C4×Dic283—21no—
40C4×Dic283—21no—
41C2×Q8×C283—21no—
42C2×C8×C283—21no—
43C2×C8×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283D412yes—
46C42×C283C2311yescharacteristic
47Dic566—21no—
48Dic566—21no—
49Dic566—21no—
50Dic566—42no—
51Dic566Q1612yes—
52C2×Dic283—21no—
53C2×Dic283—21no—
54C2×Dic283—21no—
55C2×Dic283—21no—
56C2×Dic283—41no—
57C283⋊C8—41no—
58Q8×C283—41no—
59Q8×C283—41no—
60C2×C4×C283—22no—
61C2×C4×C283C2×D411yescharacteristic
62C2×C4×C283C2×D411yescharacteristic
63C2×C4×C283C2×D411yescharacteristic
64C8×C283—41no—
65C8×C283—41no—
66C22×C283#12011yescharacteristic
67C4×C283—21no—
68C4×C283—42no—
69C4×C283C2×Q1611yescharacteristic
70C4×C283#13511yescharacteristic
71C4×C283#13711yescharacteristic
72C4×C283#13711yescharacteristic
73Dic283—22no—
74Dic283—41no—
75Dic283—41no—
76Dic283—41no—
77Dic283—81no—
78C2×C283#45111yescharacteristic
79C2×C283#45211yescharacteristic
80C2×C283#45411yescharacteristic
81C283#163611yescharacteristic, complemented, Sylow
82#1636—2831nomaximal, Sylow
83#557—2831no—
84#487—2831no—
85#477—2831no—
86#477—2831no—
87#332D28311yescharacteristic
88Q8⋊C8—2831no—
89Q8⋊C8—2831no—
90C4⋊Q8—2831no—
91C4⋊Q8—5661no—
92C4⋊Q8C2×D28311yescharacteristic
93#125—5661no—
94#125—5662no—
95C4×Q8—2831no—
96C4×Q8—2831no—
97C4×Q8—5661no—
98C4×Q8—5661no—
99#107—5661no—
100#107—5661no—
101C4⋊C8C2×D28311yescharacteristic
102C4⋊C8C2×D28311yescharacteristic
103#103—5661no—
104#103—5661no—
105#103—5662no—
106C4×C8—2831no—
107C2×Q8—21no—
108C2×Q8—2831no—
109C2×Q8—2831no—
110C2×Q8—5661no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—5661no—
114C4⋊C4—21no—
115C4⋊C4—2831no—
116C4⋊C4—2831no—
117C4⋊C4—5662no—
118C4⋊C4—5662no—
119C4⋊C4—5662no—
120C4⋊C4—5661no—
121C4⋊C4—5661no—
122C4⋊C4—5661no—
123C4⋊C4—5661no—
124C4⋊C4D113212yes—
125C42—5662no—
126C42—5661no—
127C42—5661no—
128C42C22×D28311yescharacteristic
129Q8—41no—
130Q8—41no—
131Q8—2832no—
132Q8—5661no—
133Q8—5661no—
134Q8—5661no—
135Q8—11322no—
136C2×C4—22no—
137C2×C4—5661no—
138C2×C4—5661no—
139C2×C4—5661no—
140C2×C4—5661no—
141C2×C4—11321no—
142C2×C4D4×D28311yescharacteristic
143C2×C4D4×D28311yescharacteristic
144C2×C4C2×D113211yescharacteristic
145C8—41no—
146C8—41no—
147C8—11321no—
148C22#2258358011yescharacteristic
149C4—21no—
150C4—42no—
151C4—5662no—
152C4—11321no—
153C4—11321no—
154C4—11321no—
155C4—22641no—
156C4Q16×D28311yescharacteristic
157C4#2258362911yescharacteristic
158C4#2258363911yescharacteristic
159C4#2258363911yescharacteristic
160C2#3182662211yescharacteristic
161C2#3182662811yescharacteristic
162C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#332×C283C2
socle, prime radicalC22×C283#120
hypercenter#332D283
hypocenterC283#1636
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
81. C283#1636semidirect

Maximal subgroups

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

subgroupindex
#318271902
#318268172
#318267612
#318261952
#332×C2832
#1636283