Finite Group Databasebeta

← #49120332

Subgroups — #49120332

Order 36224.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#31827175C211yesmaximal, characteristic, complemented
2#31826837C211yesmaximal, characteristic, complemented
3#31826657C211yesmaximal, characteristic
4#31826213C211yesmaximal, characteristic, complemented
5Q8⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#460×C283C211yesmaximal, characteristic, complemented
8C2×#17985380—22no—
9C2×#17985377—21no—
10#22583610C2211yescharacteristic
11#22583602—21no—
12#22583588—22no—
13#22583586—21no—
14C4×D1132—21no—
15C4×D1132C2211yescharacteristic
16C4⋊C4×D283—21no—
17C4⋊(C283⋊C8)C2211yescharacteristic
18#22583531—21no—
19C4×C283⋊C8C2211yescharacteristic
20C2×SD16×C283—21no—
21#127×C283C2211yescharacteristic
22C4×Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25C2×Dic566D412yes—
26C2×D1132D411yescharacteristic
27C2×C4×D283—22no—
28C2×C4×D283—21no—
29#17985380—44no—
30#17985377—42no—
31C2×C283⋊C8—21no—
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283D411yescharacteristic
36Dic283⋊C4—22no—
37Dic283⋊C4—22no—
38(C2×D283)⋊C4—22no—
39(C2×D283)⋊C4—21no—
40C2×Q8×C283D411yescharacteristic
41C2×D4×C283—21no—
42C2×D4×C283—21no—
43C2×D4×C283—21no—
44SD16×C283—42no—
45C2×C8×C283—21no—
46C4⋊C4×C283—21no—
47C4⋊C4×C283D411yescharacteristic
48C42×C283—21no—
49C42×C283C2311yescharacteristic
50C22×D283—21no—
51Dic566—42no—
52D1132—21no—
53D1132SD1612yescomplemented
54C2×Dic283—21no—
55C2×Dic283—22no—
56C4×D283—41no—
57C4×D283—41no—
58C4×D283—82no—
59C283⋊C8—22no—
60C283⋊C8—41no—
61C23×C283—41no—
62Q8×C283—21no—
63Q8×C283—21no—
64D4×C283—42no—
65D4×C283—41no—
66D4×C283—41no—
67D4×C283—41no—
68D4×C283—41no—
69C2×C4×C283—21no—
70C2×C4×C283—21no—
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C2×C4×C283C2×D411yescharacteristic
74C8×C283—41no—
75C22×C283—81no—
76C22×C283—81no—
77C22×C283—81no—
78C22×C283#12011yescharacteristic
79C2×D283—22no—
80C2×D283—41no—
81C2×D283—41no—
82C4×C283—21no—
83C4×C283—41no—
84C4×C283—41no—
85C4×C283C2×SD1611yescharacteristic
86C4×C283#13511yescharacteristic
87C4×C283AGL(1,ℤ/8)11yescharacteristic
88C4×C283#13711yescharacteristic
89Dic283—41no—
90Dic283—42no—
91C2×C283—161no—
92C2×C283#44811yescharacteristic
93C2×C283#44911yescharacteristic
94C2×C283#45311yescharacteristic
95D283—42no—
96C283#162211yescharacteristic, complemented, Sylow
97#1622—2831nomaximal, Sylow
98#554—2831no—
99#492—2831no—
100#460D28311yescharacteristic, complemented
101#459—2831no—
102#333—2831no—
103Q8⋊C8—2831no—
104D4⋊C8—2831no—
105C2×SD16—21no—
106C2×SD16—5662no—
107C2×D8—5661no—
108C4⋊Q8—2831no—
109#127C2×D28311yescharacteristic
110#125—5661no—
111C22⋊Q8—5662no—
112C22⋊Q8—5661no—
113C4×Q8C2×D28311yescharacteristic
114C4×D4—2831no—
115C4×D4—5661no—
116C2×C4⋊C4—5661no—
117C4⋊C8—2831no—
118C4⋊C8C2×D28311yescharacteristic
119#102—21no—
120#102—5661no—
121C4×C8—2831no—
122C2×Q8—2832no—
123C2×Q8C22⋊D28311yescharacteristic
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2831no—
128C22×C4—5662no—
129C22×C4—5661no—
130SD16—42no—
131SD16—11324no—
132D8—11322no—
133C2×C8—21no—
134C2×C8—5661no—
135C2×C8—5661no—
136C4⋊C4—21no—
137C4⋊C4—2831no—
138C4⋊C4—5662no—
139C4⋊C4—5662no—
140C4⋊C4—5661no—
141C4⋊C4—5661no—
142C4⋊C4C22⋊D28311yescharacteristic
143C22⋊C4—5662no—
144C22⋊C4—5661no—
145C42—21no—
146C42C22×D28311yescharacteristic
147C23—41no—
148C23—5661no—
149Q8—21no—
150Q8—21no—
151Q8—11322no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2832no—
158D4—5661no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—5661no—
162C2×C4—5662no—
163C2×C4—11321no—
164C2×C4—11321no—
165C2×C4—22642no—
166C2×C4D4×D28311yescharacteristic
167C2×C4D4×D28311yescharacteristic
168C2×C4C2×C22⋊D28311yescharacteristic
169C8—41no—
170C8—5662no—
171C8—11321no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—5662no—
176C22—11321no—
177C22—11321no—
178C22#2258357811yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—11321no—
183C4—11322no—
184C4SD16×D28311yescharacteristic
185C4#2258363011yescharacteristic
186C4#2258363611yescharacteristic
187C4#2258363911yescharacteristic
188C2—161no—
189C2—11322no—
190C2#3182660211yescharacteristic
191C2#3182660811yescharacteristic
192C2#3182663111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#460×C283C2
socleC22×C283#120
prime radical#31826657C2
hypercenter#460D283
hypocenterC283#1622
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #31827175C2semidirect
2. #31826837C2semidirect
4. #31826213C2semidirect
5. Q8⋊(C283⋊C8)C2semidirect
6. #31826192C2semidirect
7. #460×C283C2semidirect
53. D1132SD16semidirect
96. C283#1622semidirect
100. #460D283semidirect

Maximal subgroups

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

subgroupindex
#318271752
#318268372
#318266572
#318262132
Q8⋊(C283⋊C8)2
#318261922
#460×C2832
#1622283