Finite Group Databasebeta

← #49120405

Subgroups — #49120405

Order 36224.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#31827180C211yesmaximal, characteristic
2#31826844C211yesmaximal, characteristic, complemented
3#31826752C211yesmaximal, characteristic, complemented
4#31826213C211yesmaximal, characteristic, complemented
5D4⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#476×C283C211yesmaximal, characteristic, complemented
8C2×#17985382—22no—
9#22583610C2211yescharacteristic
10#22583596—22no—
11#22583584—21no—
12#22583581—21no—
13C4×D1132C2211yescharacteristic
14#22583569—21no—
15#22583568—21no—
16#22583541—21no—
17C4⋊(C283⋊C8)C2211yescharacteristic
18#22583530—21no—
19C4×C283⋊C8C2211yescharacteristic
20C4⋊Q8×C283C2211yescharacteristic
21C4×D4×C283C2211yescharacteristic
22#106×C283—21no—
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25C2×Dic566D412yes—
26C2×D1132D411yescharacteristic
27C2×C22⋊D283—22no—
28C2×C4×D283—21no—
29#17985382—44no—
30C2×C283⋊C8—21no—
31C2×C283⋊C8—21no—
32C4⋊Dic283—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283D411yescharacteristic
35C22⋊Dic283—22no—
36(C2×D283)⋊C4—22no—
37(C2×D283)⋊C4—21no—
38C4×Dic283—22no—
39C2×Q8×C283—21no—
40C2×D4×C283D411yescharacteristic
41C22×C4×C283—21no—
42C2×C8×C283—21no—
43C4⋊C4×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283D411yescharacteristic
46C22⋊C4×C283—21no—
47C42×C283C2311yescharacteristic
48C22×D283—21no—
49Dic566—42no—
50D1132—21no—
51D1132—21no—
52C22⋊D283—82no—
53C2×Dic283—21no—
54C2×Dic283—22no—
55C4×D283—41no—
56C4×D283—41no—
57C283⋊C8—22no—
58C283⋊C8—41no—
59C23×C283—21no—
60Q8×C283—42no—
61D4×C283—21no—
62D4×C283—21no—
63C2×C4×C283—21no—
64C2×C4×C283—41no—
65C2×C4×C283—41no—
66C2×C4×C283—41no—
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C8×C283—41no—
71C22×C283—41no—
72C22×C283—41no—
73C22×C283—41no—
74C22×C283#12011yescharacteristic
75C2×D283—41no—
76C2×D283—41no—
77C2×D283—41no—
78C4×C283—21no—
79C4×C283—41no—
80C4×C283—81no—
81C4×C283#13511yescharacteristic
82C4×C283#13511yescharacteristic
83C4×C283#13711yescharacteristic
84C4×C283#13711yescharacteristic
85Dic283—41no—
86Dic283—42no—
87C2×C283—81no—
88C2×C283#45211yescharacteristic
89C2×C283#45211yescharacteristic
90C2×C283#45311yescharacteristic
91D283—81no—
92C283#163411yescharacteristic, complemented, Sylow
93#1634—2831nomaximal, Sylow
94#555—2831no—
95#494—2831no—
96#476—2831no—
97#476D28311yescharacteristic, complemented
98#333—2831no—
99D4⋊C8—2831no—
100D4⋊C8—2831no—
101C2×Q16—5662no—
102C4⋊Q8—2831no—
103C4⋊Q8C2×D28311yescharacteristic
104#124—5662no—
105#121—5661no—
106#121—5661no—
107C4×D4—2831no—
108C4×D4C2×D28311yescharacteristic
109#117—5661no—
110#117—5661no—
111#106—21no—
112#106—5661no—
113C4⋊C8—2831no—
114C4⋊C8C2×D28311yescharacteristic
115#102—21no—
116#102—5661no—
117C4×C8—2831no—
118C2×Q8—21no—
119C2×Q8—2832no—
120C2×D4—2831no—
121C2×D4—5662no—
122C2×D4C22⋊D28311yescharacteristic
123C22×C4—21no—
124C22×C4—5661no—
125Q16—11324no—
126C2×C8—21no—
127C2×C8—5661no—
128C2×C8—5661no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2831no—
132C4⋊C4—5661no—
133C4⋊C4—5661no—
134C4⋊C4C22⋊D28311yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—5662no—
137C22⋊C4—5662no—
138C22⋊C4—5661no—
139C42—5662no—
140C42C22×D28311yescharacteristic
141C23—21no—
142C23—5661no—
143Q8—42no—
144Q8—11322no—
145D4—21no—
146D4—21no—
147D4—5661no—
148D4—5661no—
149D4—22642no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—5661no—
155C2×C4—5662no—
156C2×C4—11321no—
157C2×C4—11321no—
158C2×C4D4×D28311yescharacteristic
159C2×C4D4×D28311yescharacteristic
160C2×C4C2×C22⋊D28311yescharacteristic
161C8—41no—
162C8—5662no—
163C8—11321no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—11321no—
168C22—11321no—
169C22—11321no—
170C22#2258357811yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—11321no—
175C4—11322no—
176C4#2258363011yescharacteristic
177C4#2258363111yescharacteristic
178C4#2258363911yescharacteristic
179C4#2258364111yescharacteristic
180C2—81no—
181C2—22641no—
182C2#3182662411yescharacteristic
183C2#3182662511yescharacteristic
184C2#3182663111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#476×C283C2
socleC22×C283#120
prime radical#31827180C2
hypercenter#476D283
hypocenterC283#1634
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31826844C2semidirect
3. #31826752C2semidirect
4. #31826213C2semidirect
5. D4⋊(C283⋊C8)C2semidirect
6. #31826192C2semidirect
7. #476×C283C2semidirect
92. C283#1634semidirect
97. #476D283semidirect

Maximal subgroups

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

subgroupindex
#318271802
#318268442
#318267522
#318262132
D4⋊(C283⋊C8)2
#318261922
#476×C2832
#1634283