Finite Group Databasebeta

← #49120460

Subgroups — #49120460

Order 36224.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#31827137C211yesmaximal, characteristic
2#31826813C211yesmaximal, characteristic, complemented
3#31826667C211yesmaximal, characteristic, complemented
4#31826208C211yesmaximal, characteristic, complemented
5Q8⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#475×C283C211yesmaximal, characteristic, complemented
8C2×#17985393—21no—
9C2×#17985379—21no—
10#22583607—21no—
11#22583607C2211yescharacteristic
12#22583585—22no—
13#22583585—21no—
14C4×D1132—21no—
15C4×D1132C2211yescharacteristic
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583534—21no—
18#22583530—22no—
19C4×C283⋊C8C2211yescharacteristic
20C4⋊Q8×C283C2211yescharacteristic
21C4×Q8×C283C2211yescharacteristic
22#106×C283—21no—
23C4⋊C8×C283C2211yescharacteristic
24#103×C283—21no—
25#17985393—42no—
26#17985393—42no—
27C2×D1132—22no—
28C2×D1132—22no—
29C2×D1132—21no—
30C2×D1132—21no—
31C2×D1132D411yescharacteristic
32C2×D1132D412yes—
33C2×C4×D283—22no—
34C2×C4×D283—21no—
35#17985379—42no—
36C2×C283⋊C8—21no—
37C2×C283⋊C8—21no—
38C4⋊Dic283D411yescharacteristic
39(C2×D283)⋊C4—22no—
40(C2×D283)⋊C4—21no—
41C2×Q8×C283—21no—
42C2×Q8×C283D411yescharacteristic
43C2×C8×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283D411yescharacteristic
48C42×C283—21no—
49C42×C283C2311yescharacteristic
50C22×D283—21no—
51C22×D283—22no—
52D1132—21no—
53D1132—21no—
54D1132—42no—
55D1132—44no—
56D1132—41no—
57D1132—41no—
58D1132—41no—
59D1132—41no—
60D1132—82no—
61C2×Dic283—21no—
62C4×D283—44no—
63C4×D283—41no—
64C4×D283—41no—
65C283⋊C8—41no—
66C283⋊C8—41no—
67Q8×C283—21no—
68Q8×C283—41no—
69Q8×C283—41no—
70Q8×C283SD1612yescomplemented
71C2×C4×C283—21no—
72C2×C4×C283—21no—
73C2×C4×C283—41no—
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×D411yescharacteristic
77C8×C283—41no—
78C22×C283#12011yescharacteristic
79C2×D283—41no—
80C2×D283—42no—
81C2×D283—42no—
82C2×D283—41no—
83C2×D283—42no—
84C2×D283—41no—
85C4×C283—22no—
86C4×C283—21no—
87C4×C283—41no—
88C4×C283—81no—
89C4×C283C2×SD1611yescharacteristic
90C4×C283#13511yescharacteristic
91C4×C283AGL(1,ℤ/8)11yescharacteristic
92C4×C283AGL(1,ℤ/8)11yescharacteristic
93Dic283—41no—
94C2×C283#44911yescharacteristic
95C2×C283#45011yescharacteristic
96C2×C283#45511yescharacteristic
97D283—81no—
98D283—82no—
99C283#164211yescharacteristic, complemented, Sylow
100#1642—2831nomaximal, Sylow
101#550—2831no—
102#486—2831no—
103#475D28311yescharacteristic, complemented
104#461—2831no—
105#331—2831no—
106Q8⋊C8—2831no—
107D4⋊C8—2831no—
108C2×#41—5661no—
109C2×SD16—5661no—
110C4⋊Q8C2×D28311yescharacteristic
111#127—2831no—
112#127—5661no—
113#121—5662no—
114#121—5661no—
115C4×Q8C2×D28311yescharacteristic
116C4×D4—2831no—
117C4×D4—5661no—
118#106—21no—
119C4⋊C8—2831no—
120C4⋊C8C2×D28311yescharacteristic
121#103—21no—
122#103—5661no—
123#102—5662no—
124C4×C8—2831no—
125#41—11322no—
126#41—11322no—
127C2×Q8—21no—
128C2×Q8C22⋊D28311yescharacteristic
129C2×D4—2831no—
130C2×D4—2832no—
131C2×D4—5662no—
132C2×D4—5662no—
133C2×D4—5661no—
134C2×D4—5661no—
135C22×C4—5662no—
136C22×C4—5661no—
137SD16—11322no—
138C2×C8—21no—
139C2×C8—5661no—
140C2×C8—5661no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—2831no—
145C4⋊C4C22⋊D28311yescharacteristic
146C22⋊C4—5662no—
147C22⋊C4—5661no—
148C42—21no—
149C42C22×D28311yescharacteristic
150C23—5661no—
151C23—5662no—
152Q8—21no—
153Q8—41no—
154Q8—41no—
155Q8#1798537912yescomplemented
156D4—5661no—
157D4—5661no—
158D4—11322no—
159D4—11324no—
160D4—11321no—
161D4—11321no—
162D4—11321no—
163D4—11321no—
164D4—22642no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—5661no—
169C2×C4—11324no—
170C2×C4—11321no—
171C2×C4—11321no—
172C2×C4D4×D28311yescharacteristic
173C2×C4D4×D28311yescharacteristic
174C2×C4C2×C22⋊D28311yescharacteristic
175C8—41no—
176C8—11321no—
177C8—11321no—
178C22—11321no—
179C22—11322no—
180C22—11322no—
181C22—11321no—
182C22—11322no—
183C22—11321no—
184C22#2258357811yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—81no—
189C4—11321no—
190C4C2×#1798537911yescharacteristic
191C4#2258363111yescharacteristic
192C4#2258363511yescharacteristic
193C4#2258363711yescharacteristic
194C2—22641no—
195C2—22642no—
196C2#3182660911yescharacteristic
197C2#3182661511yescharacteristic
198C2#3182664111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#475×C283C2
socleC22×C283#120
prime radical#31827137C2
hypercenter#475D283
hypocenterC283#1642
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #31826813C2semidirect
3. #31826667C2semidirect
4. #31826208C2semidirect
5. Q8⋊(C283⋊C8)C2semidirect
6. #31826192C2semidirect
7. #475×C283C2semidirect
70. Q8×C283SD16semidirect
99. C283#1642semidirect
103. #475D283semidirect
155. Q8#17985379semidirect

Maximal subgroups

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

subgroupindex
#318271372
#318268132
#318266672
#318262082
Q8⋊(C283⋊C8)2
#318261922
#475×C2832
#1642283