Finite Group Databasebeta

← #49120526

Subgroups — #49120526

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#31826863C211yesmaximal, characteristic, complemented
3#31826751C211yesmaximal, characteristic, complemented
4#31826670C211yesmaximal, characteristic
5#31826212C211yesmaximal, characteristic, complemented
6#31826197C211yesmaximal, characteristic, complemented
7D4⋊C8×C283C211yesmaximal, characteristic
8C22×Dic566—21no—
9C2×#17985380—21no—
10#22583610C2211yescharacteristic
11#22583610C2211yescharacteristic
12#22583609—21no—
13#22583589—21no—
14#22583587—22no—
15C4×Dic566C2211yescharacteristic
16D4×Dic283—21no—
17#22583542—21no—
18#22583542—22no—
19C4⋊(C283⋊C8)C2211yescharacteristic
20#22583535—21no—
21#22583533—21no—
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4×C8×C283C2211yescharacteristic
25C2×Dic566—22no—
26C2×Dic566—21no—
27C2×Dic566—21no—
28C2×Dic566—42no—
29C2×Dic566—42no—
30C2×Dic566D411yescharacteristic
31C22×Dic283—22no—
32#17985380—42no—
33C2×C283⋊C8—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283D411yescharacteristic
38C4⋊Dic283D412yes—
39Dic283⋊C4—22no—
40Dic283⋊C4—21no—
41C22⋊Dic283—22no—
42C4×Dic283—21no—
43C2×D4×C283D411yescharacteristic
44C22×C4×C283—21no—
45C2×C8×C283—21no—
46C2×C8×C283—21no—
47C4⋊C4×C283D411yescharacteristic
48C22⋊C4×C283—21no—
49C42×C283C2311yescharacteristic
50Dic566—21no—
51Dic566—44no—
52Dic566—41no—
53Dic566—41no—
54Dic566—41no—
55Dic566—41no—
56Dic566SD1612yescomplemented
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—22no—
60C2×Dic283—44no—
61C2×Dic283—41no—
62C283⋊C8—41no—
63C23×C283—21no—
64D4×C283—21no—
65D4×C283SD1612yes—
66C2×C4×C283—21no—
67C2×C4×C283—41no—
68C2×C4×C283—41no—
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C8×C283—22no—
73C8×C283—41no—
74C22×C283—22no—
75C22×C283—41no—
76C22×C283—41no—
77C22×C283#12011yescharacteristic
78C4×C283—21no—
79C4×C283—41no—
80C4×C283C2×SD1611yescharacteristic
81C4×C283C2×SD1611yescharacteristic
82C4×C283AGL(1,ℤ/8)11yescharacteristic
83C4×C283#13711yescharacteristic
84Dic283—22no—
85Dic283—42no—
86Dic283—41no—
87Dic283—81no—
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#461—2831no—
98#332—2831no—
99Q8⋊C8—2831no—
100D4⋊C8D28311yescharacteristic
101C22×Q8—5661no—
102C2×SD16—5661no—
103C4⋊Q8—2831no—
104C4⋊Q8—2831no—
105C4⋊Q8—5661no—
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—5661no—
116#103—5661no—
117C4×C8C2×D28311yescharacteristic
118C2×Q8—2831no—
119C2×Q8—5662no—
120C2×Q8—5661no—
121C2×Q8—5661no—
122C2×Q8—11322no—
123C2×Q8—11322no—
124C2×D4D113211yescharacteristic
125C22×C4—21no—
126C22×C4—5662no—
127SD16—11322no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5661no—
131C4⋊C4—2831no—
132C4⋊C4—2832no—
133C4⋊C4—5662no—
134C4⋊C4—5661no—
135C4⋊C4—5661no—
136C4⋊C4—5661no—
137C4⋊C4—5661no—
138C4⋊C4D113211yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5662no—
141C42—5661no—
142C42C22×D28311yescharacteristic
143C23—21no—
144Q8—2832no—
145Q8—5661no—
146Q8—11324no—
147Q8—11321no—
148Q8—11321no—
149Q8—11321no—
150Q8—11321no—
151D4—21no—
152D4#1798538112yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5661no—
157C2×C4—5661no—
158C2×C4—5662no—
159C2×C4—11324no—
160C2×C4—11321no—
161C2×C4D4×D28311yescharacteristic
162C2×C4D4×D28311yescharacteristic
163C2×C4C2×D113211yescharacteristic
164C8—22no—
165C8—41no—
166C8—11321no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2258358011yescharacteristic
171C4—21no—
172C4—41no—
173C4—5662no—
174C4—11322no—
175C4—11321no—
176C4—22641no—
177C4SD16×D28311yescharacteristic
178C4C2×#1798538111yescharacteristic
179C4#2258363411yescharacteristic
180C4#2258364311yescharacteristic
181C2—42no—
182C2#3182660611yescharacteristic
183C2#3182661711yescharacteristic
184C2#3182664911yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
FittingD4⋊C8×C283C2
socleC22×C283#120
prime radicalC2×D4×C283D4
hypercenterD4⋊C8D283
hypocenterC283#1651
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31826863C2semidirect
3. #31826751C2semidirect
5. #31826212C2semidirect
6. #31826197C2semidirect
56. 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
#318268632
#318267512
#318266702
#318262122
#318261972
D4⋊C8×C2832
#1651283