Finite Group Databasebeta

← #49120485

Subgroups — #49120485

Order 36224.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic566C211yesmaximal, characteristic
2#31826816C211yesmaximal, characteristic
3#31826750C211yesmaximal, characteristic
4#31826676C211yesmaximal, characteristic
5#31826213C211yesmaximal, characteristic
6#31826197C211yesmaximal, characteristic
7Q8⋊C8×C283C211yesmaximal, characteristic
8C2×Dic1132—21no—
9#22583610—21no—
10#22583610C2211yescharacteristic
11#22583610C2211yescharacteristic
12#22583609—22no—
13#22583609—21no—
14Q8×Dic283—21no—
15C4×Dic566—21no—
16C4×Dic566C2211yescharacteristic
17#22583541—21no—
18C4⋊(C283⋊C8)C2211yescharacteristic
19#22583535—22no—
20#22583535—21no—
21#22583534—21no—
22C4×Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4×C8×C283C2211yescharacteristic
25C2×Dic566—22no—
26C2×Dic566—21no—
27C2×Dic566D411yescharacteristic
28C2×Dic566D412yes—
29Dic1132—42no—
30C2×C283⋊C8—21no—
31C4⋊Dic283—22no—
32C4⋊Dic283—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283D411yescharacteristic
37Dic283⋊C4—22no—
38Dic283⋊C4—21no—
39C4×Dic283—22no—
40C4×Dic283—21no—
41C2×Q8×C283D411yescharacteristic
42C2×C8×C283—21no—
43C2×C8×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283D411yescharacteristic
46C42×C283—21no—
47C42×C283C2311yescharacteristic
48Dic566—21no—
49Dic566—42no—
50Dic566—41no—
51Dic566—41no—
52Dic566—82no—
53Dic566SD1612yes—
54C2×Dic283—21no—
55C2×Dic283—22no—
56C2×Dic283—21no—
57C2×Dic283—41no—
58C283⋊C8—41no—
59Q8×C283—21no—
60Q8×C283Q1612yescomplemented
61C2×C4×C283—21no—
62C2×C4×C283—21no—
63C2×C4×C283C2×D411yescharacteristic
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283C2×D411yescharacteristic
66C8×C283—41no—
67C8×C283—41no—
68C22×C283#12011yescharacteristic
69C4×C283—22no—
70C4×C283—21no—
71C4×C283—41no—
72C4×C283C2×SD1611yescharacteristic
73C4×C283C2×Q1611yescharacteristic
74C4×C283#13711yescharacteristic
75C4×C283#13711yescharacteristic
76Dic283—22no—
77Dic283—42no—
78Dic283—41no—
79Dic283—81no—
80C2×C283#44811yescharacteristic
81C2×C283#45111yescharacteristic
82C2×C283#45511yescharacteristic
83C283#164511yescharacteristic, complemented, Sylow
84#1645—2831nomaximal, Sylow
85Q82—2831no—
86#487—2831no—
87#475—2831no—
88#462—2831no—
89#333—2831no—
90Q8⋊C8—2831no—
91Q8⋊C8D28311yescharacteristic
92C2×Q16—5661no—
93C4⋊Q8—2831no—
94C4⋊Q8—2831no—
95C4⋊Q8—5661no—
96C4⋊Q8—5662no—
97C4⋊Q8—5661no—
98C4×Q8—2831no—
99C4×Q8—5661no—
100C4×Q8—5661no—
101C4×Q8C2×D28311yescharacteristic
102#106—5661no—
103C4⋊C8—2831no—
104C4⋊C8C2×D28311yescharacteristic
105#103—5661no—
106#103—5662no—
107#103—5661no—
108C4×C8C2×D28311yescharacteristic
109C2×Q8—2831no—
110C2×Q8—2832no—
111C2×Q8—5662no—
112C2×Q8—5661no—
113C2×Q8D113211yescharacteristic
114Q16—11322no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—5661no—
118C4⋊C4—21no—
119C4⋊C4—2831no—
120C4⋊C4—5662no—
121C4⋊C4—5662no—
122C4⋊C4—5661no—
123C4⋊C4—5661no—
124C4⋊C4—5661no—
125C4⋊C4—5661no—
126C4⋊C4—5661no—
127C4⋊C4D113211yescharacteristic
128C42—21no—
129C42—5662no—
130C42—5661no—
131C42C22×D28311yescharacteristic
132Q8—21no—
133Q8—2832no—
134Q8—5661no—
135Q8—11322no—
136Q8—11321no—
137Q8—11321no—
138Q8—22642no—
139Q8Dic113212yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—5661no—
143C2×C4—5661no—
144C2×C4—5662no—
145C2×C4—11321no—
146C2×C4D4×D28311yescharacteristic
147C2×C4D4×D28311yescharacteristic
148C2×C4C2×D113211yescharacteristic
149C8—41no—
150C8—41no—
151C8—11321no—
152C22#2258358011yescharacteristic
153C4—22no—
154C4—21no—
155C4—41no—
156C4—5662no—
157C4—11322no—
158C4—11321no—
159C4—22641no—
160C4SD16×D28311yescharacteristic
161C4C2×Dic113211yescharacteristic
162C4#2258364211yescharacteristic
163C4#2258364311yescharacteristic
164C2#3182660511yescharacteristic
165C2#3182662311yescharacteristic
166C2#3182664411yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
FittingQ8⋊C8×C283C2
socle, prime radicalC22×C283#120
hypercenterQ8⋊C8D283
hypocenterC283#1645
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
60. Q8×C283Q16semidirect
83. C283#1645semidirect
139. Q8Dic1132semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic5662
#318268162
#318267502
#318266762
#318262132
#318261972
Q8⋊C8×C2832
#1645283