Finite Group Databasebeta

← #49120429

Subgroups — #49120429

Order 36224.

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

normal subgroups only

This group has 228 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#31826816C211yesmaximal, characteristic, complemented
3#31826761C211yesmaximal, characteristic, complemented
4#31826755C211yesmaximal, characteristic
5#31826212C211yesmaximal, characteristic, complemented
6#31826197C211yesmaximal, characteristic, complemented
7D4⋊C8×C283C211yesmaximal, characteristic
8C22×Dic566—21no—
9#22583610C2211yescharacteristic
10#22583610C2211yescharacteristic
11#22583609—21no—
12#22583589—21no—
13#22583587—22no—
14C4×Dic566C2211yescharacteristic
15D4×Dic283—21no—
16#22583544—21no—
17#22583541—21no—
18C4⋊(C283⋊C8)C2211yescharacteristic
19#22583535—21no—
20#22583535—22no—
21#22583531—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—
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283D411yescharacteristic
37C4⋊Dic283D412yes—
38Dic283⋊C4—22no—
39Dic283⋊C4—21no—
40C22⋊Dic283—22no—
41C4×Dic283—21no—
42C2×D4×C283D411yescharacteristic
43C22×C4×C283—21no—
44C2×C8×C283—21no—
45C2×C8×C283—21no—
46C4⋊C4×C283D411yescharacteristic
47C22⋊C4×C283—21no—
48C42×C283C2311yescharacteristic
49Dic566—21no—
50Dic566—44no—
51Dic566—41no—
52Dic566—41no—
53Dic566—42no—
54Dic566SD1612yes—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C2×Dic283—22no—
58C2×Dic283—44no—
59C2×Dic283—41no—
60C283⋊C8—41no—
61C23×C283—21no—
62D4×C283—21no—
63D4×C283Q1612yes—
64C2×C4×C283—21no—
65C2×C4×C283—41no—
66C2×C4×C283—41no—
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C8×C283—41no—
71C8×C283—41no—
72C22×C283—22no—
73C22×C283—41no—
74C22×C283—41no—
75C22×C283#12011yescharacteristic
76C4×C283—21no—
77C4×C283—41no—
78C4×C283C2×SD1611yescharacteristic
79C4×C283C2×Q1611yescharacteristic
80C4×C283AGL(1,ℤ/8)11yescharacteristic
81C4×C283#13711yescharacteristic
82Dic283—22no—
83Dic283—42no—
84Dic283—41no—
85Dic283—81no—
86C2×C283—42no—
87C2×C283#45011yescharacteristic
88C2×C283#45111yescharacteristic
89C2×C283#45411yescharacteristic
90C283#163711yescharacteristic, complemented, Sylow
91#1637—2831nomaximal, Sylow
92D4×Q8—2831no—
93#487—2831no—
94#477—2831no—
95#476—2831no—
96#332—2831no—
97Q8⋊C8—2831no—
98D4⋊C8D28311yescharacteristic
99C22×Q8—5661no—
100C4⋊Q8—2831no—
101C4⋊Q8—2831no—
102C4⋊Q8—5661no—
103C22⋊Q8—5662no—
104C22⋊Q8—5661no—
105C4×Q8—2831no—
106C4×D4—5661no—
107C4×D4C2×D28311yescharacteristic
108#107—5661no—
109#106—5661no—
110C4⋊C8—2831no—
111C4⋊C8C2×D28311yescharacteristic
112#103—5662no—
113#103—5661no—
114#102—5661no—
115C4×C8C2×D28311yescharacteristic
116C2×Q8—2831no—
117C2×Q8—5662no—
118C2×Q8—5661no—
119C2×Q8—5661no—
120C2×Q8—11322no—
121C2×Q8—11322no—
122C2×D4D113211yescharacteristic
123C22×C4—21no—
124C22×C4—5662no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5661no—
128C4⋊C4—2832no—
129C4⋊C4—2831no—
130C4⋊C4—5662no—
131C4⋊C4—5661no—
132C4⋊C4—5661no—
133C4⋊C4—5661no—
134C4⋊C4—5661no—
135C4⋊C4D113211yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5662no—
138C42—5661no—
139C42C22×D28311yescharacteristic
140C23—21no—
141Q8—2832no—
142Q8—5661no—
143Q8—11322no—
144Q8—11324no—
145Q8—11321no—
146Q8—11321no—
147D4—21no—
148D4Dic113212yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5661no—
153C2×C4—5661no—
154C2×C4—5662no—
155C2×C4—11324no—
156C2×C4—11321no—
157C2×C4D4×D28311yescharacteristic
158C2×C4D4×D28311yescharacteristic
159C2×C4C2×D113211yescharacteristic
160C8—41no—
161C8—41no—
162C8—11321no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2258358011yescharacteristic
167C4—21no—
168C4—41no—
169C4—5662no—
170C4—11322no—
171C4—11321no—
172C4—22641no—
173C4SD16×D28311yescharacteristic
174C4C2×Dic113211yescharacteristic
175C4#2258363411yescharacteristic
176C4#2258364311yescharacteristic
177C2—42no—
178C2#3182661711yescharacteristic
179C2#3182662311yescharacteristic
180C2#3182663911yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
FittingD4⋊C8×C283C2
socleC22×C283#120
prime radicalC2×D4×C283D4
hypercenterD4⋊C8D283
hypocenterC283#1637
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. #31826816C2semidirect
3. #31826761C2semidirect
5. #31826212C2semidirect
6. #31826197C2semidirect
90. C283#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5662
#318268162
#318267612
#318267552
#318262122
#318261972
D4⋊C8×C2832
#1637283