Finite Group Databasebeta

← #49120522

Subgroups — #49120522

Order 36224.

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

normal subgroups only

This group has 234 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
1D4×Dic566C211yesmaximal, characteristic
2#31826861C211yesmaximal, characteristic, complemented
3#31826747C211yesmaximal, characteristic, complemented
4#31826210C211yesmaximal, characteristic, complemented
5#31826195C211yesmaximal, characteristic, complemented
6D4⋊(C283⋊C8)C211yesmaximal, characteristic
7#461×C283C211yesmaximal, characteristic
8C22×Dic566—21no—
9#22583610C2211yescharacteristic
10#22583609—21no—
11#22583589—21no—
12#22583587—22no—
13C4×Dic566C2211yescharacteristic
14D4×Dic283—21no—
15#22583541—21no—
16#22583541—22no—
17C4⋊(C283⋊C8)C2211yescharacteristic
18#22583533—21no—
19C4×C283⋊C8C2211yescharacteristic
20C2×SD16×C283—21no—
21C4⋊Q8×C283C2211yescharacteristic
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24#103×C283—21no—
25C2×Dic566—22no—
26C2×Dic566—21no—
27C2×Dic566—42no—
28C2×Dic566—42no—
29C2×Dic566D411yescharacteristic
30C22×Dic283—22no—
31C2×C283⋊C8—21no—
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283D411yescharacteristic
35C4⋊Dic283D412yes—
36Dic283⋊C4—22no—
37Dic283⋊C4—21no—
38C22⋊Dic283—22no—
39C4×Dic283—21no—
40C2×Q8×C283—21no—
41C2×D4×C283D411yescharacteristic
42C22×C4×C283—21no—
43SD16×C283—42no—
44C2×C8×C283—21no—
45C4⋊C4×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283D411yescharacteristic
48C22⋊C4×C283—21no—
49C42×C283C2311yescharacteristic
50Dic566—21no—
51Dic566—44no—
52Dic566—41no—
53Dic566—41no—
54Dic566SD1612yescomplemented
55C2×Dic283—21no—
56C2×Dic283—21no—
57C2×Dic283—22no—
58C2×Dic283—44no—
59C283⋊C8—22no—
60C283⋊C8—41no—
61C23×C283—21no—
62Q8×C283—41no—
63Q8×C283—41no—
64D4×C283—21no—
65D4×C283SD1612yes—
66C2×C4×C283—21no—
67C2×C4×C283—41no—
68C2×C4×C283—41no—
69C2×C4×C283—41no—
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C8×C283—41no—
74C22×C283—22no—
75C22×C283—41no—
76C22×C283—41no—
77C22×C283#12011yescharacteristic
78C4×C283—21no—
79C4×C283—41no—
80C4×C283—81no—
81C4×C283C2×SD1611yescharacteristic
82C4×C283C2×SD1611yescharacteristic
83C4×C283AGL(1,ℤ/8)11yescharacteristic
84C4×C283#13711yescharacteristic
85Dic283—22no—
86Dic283—42no—
87Dic283—41no—
88C2×C283—42no—
89C2×C283#44811yescharacteristic
90C2×C283#45011yescharacteristic
91C2×C283#45611yescharacteristic
92C283#165111yescharacteristic, complemented, Sylow
93#1651—2831nomaximal, Sylow
94D4×Q8—2831no—
95#498—2831no—
96#475—2831no—
97#461D28311yescharacteristic
98#332—2831no—
99Q8⋊C8—2831no—
100D4⋊C8—2831no—
101C22×Q8—5661no—
102C2×SD16—21no—
103C4⋊Q8—2831no—
104C4⋊Q8—5661no—
105C4⋊Q8C2×D28311yescharacteristic
106C22⋊Q8—5662no—
107C22⋊Q8—5661no—
108C4×Q8—2831no—
109C4×D4—5661no—
110C4×D4C2×D28311yescharacteristic
111#106—5661no—
112#106—5662no—
113C4⋊C8—2831no—
114C4⋊C8C2×D28311yescharacteristic
115#103—21no—
116#103—5661no—
117C4×C8—2831no—
118C2×Q8—21no—
119C2×Q8—2831no—
120C2×Q8—5662no—
121C2×Q8—5661no—
122C2×Q8—11322no—
123C2×Q8—11322no—
124C2×D4C22⋊D28311yescharacteristic
125C22×C4—21no—
126C22×C4—5662no—
127SD16—42no—
128C2×C8—21no—
129C2×C8—5661no—
130C2×C8—5661no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—2831no—
134C4⋊C4—2832no—
135C4⋊C4—5662no—
136C4⋊C4—5661no—
137C4⋊C4—5661no—
138C4⋊C4C22⋊D28311yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5662no—
141C42—5661no—
142C42C22×D28311yescharacteristic
143C23—21no—
144Q8—41no—
145Q8—41no—
146Q8—2832no—
147Q8—5661no—
148Q8—11324no—
149Q8—11321no—
150Q8—11321no—
151D4—21no—
152D4#1798538012yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—5661no—
158C2×C4—5661no—
159C2×C4—5662no—
160C2×C4—11324no—
161C2×C4D4×D28311yescharacteristic
162C2×C4D4×D28311yescharacteristic
163C2×C4C2×C22⋊D28311yescharacteristic
164C8—41no—
165C8—5662no—
166C8—11321no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2258357811yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—5662no—
175C4—11322no—
176C4—11321no—
177C4SD16×D28311yescharacteristic
178C4C2×#1798538011yescharacteristic
179C4#2258363711yescharacteristic
180C4#2258364011yescharacteristic
181C2—42no—
182C2#3182660311yescharacteristic
183C2#3182661411yescharacteristic
184C2#3182664611yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#461×C283C2
socleC22×C283#120
prime radicalC2×D4×C283D4
hypercenter#461D283
hypocenterC283#1651
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #31826861C2semidirect
3. #31826747C2semidirect
4. #31826210C2semidirect
5. #31826195C2semidirect
54. Dic566SD16semidirect
92. C283#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5662
#318268612
#318267472
#318262102
#318261952
D4⋊(C283⋊C8)2
#461×C2832
#1651283