Finite Group Databasebeta

← #49131719

Subgroups — #49131719

Order 36224.

552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#22583642C214yesmaximal, complemented
2#31827016C211yesmaximal, characteristic
3C4⋊Q8×D283C211yesmaximal, characteristic, complemented
4#31826858C214yesmaximal, complemented
5#31826844C211yesmaximal, characteristic, complemented
6#31826839C211yesmaximal, characteristic, complemented
7#31826838C211yesmaximal, characteristic, complemented
8C4×#17985375C211yesmaximal, characteristic, complemented
9#494×C283C211yesmaximal, characteristic, complemented
10C2×#17985393C2212yes—
11C2×Q8×D283C2212yes—
12#22583642—216no—
13C2×#17985382C2214yes—
14C2×#17985381C2214yes—
15C2×#17985379C2214yes—
16C2×#17985375C2212yes—
17#22583610C2211yescharacteristic
18#22583609—22no—
19#22583608C2212yes—
20#22583607C2211yescharacteristic
21#22583599C2212yes—
22#22583585—22no—
23#22583572—22no—
24C4⋊C4×D283—22no—
25C42×D283C2211yescharacteristic
26#22583520C2212yes—
27C4×C283⋊C8C2211yescharacteristic
28C2×Q16×C283C2214yes—
29C4⋊Q8×C283C2211yescharacteristic
30C4⋊Q8×C283C2211yescharacteristic
31C4×C8×C283C2211yescharacteristic
32#17985393—28no—
33C2×Dic566—22no—
34C2×Dic566C2312yes—
35Q8×D283—28no—
36C2×D1132—22no—
37C2×D1132—22no—
38C2×D1132C2312yes—
39C2×C4×D283—22no—
40C2×C4×D283—22no—
41C2×C4×D283D412yes—
42C2×C4×D283C2311yescharacteristic
43#17985382—28no—
44#17985381—28no—
45#17985379—28no—
46#17985375D418yescomplemented
47C2×C283⋊C8C2312yes—
48C4⋊Dic283—22no—
49Dic283⋊C4—24no—
50(C2×D283)⋊C4—24no—
51C4×Dic283D412yes—
52C4×Dic283C2311yescharacteristic
53C2×Q8×C283C2312yes—
54C2×Q8×C283C2312yes—
55Q16×C283—28no—
56C2×C8×C283C2312yes—
57C4⋊C4×C283—22no—
58C4⋊C4×C283—22no—
59C42×C283C2311yescharacteristic
60C22×D283—22no—
61C22×D283C2×D411yescharacteristic
62Dic566—24no—
63Dic566—44no—
64D1132—24no—
65D1132—44no—
66D1132—44no—
67C2×Dic283—22no—
68C2×Dic283C2×D412yes—
69C2×Dic283C2×D411yescharacteristic
70C4×D283—24no—
71C4×D283—44no—
72C4×D283—44no—
73C4×D283C2×D414yes—
74C283⋊C8C2×D414yes—
75Q8×C283—24no—
76Q8×C283—24no—
77C2×C4×C283—22no—
78C2×C4×C283—22no—
79C2×C4×C283C2×D412yes—
80C2×C4×C283C2411yescharacteristic
81C8×C283C2×D414yes—
82C22×C283C22×D411yescharacteristic
83C2×D283—22no—
84C2×D283—42no—
85C2×D283—44no—
86C2×D283#12712yes—
87C4×C283—42no—
88C4×C283—42no—
89C4×C283#13714yescomplemented
90C4×C283C22×D412yes—
91Dic283—22no—
92Dic283—42no—
93Dic283#12712yes—
94C2×C283C2×#12711yescharacteristic
95C2×C283C2×#13712yes—
96D283—22no—
97D283—82no—
98C283#315211yescharacteristic, complemented, Sylow
99#3152—2831nomaximal, Sylow
100C2×#137—2834no—
101#532—2831no—
102C2×C4⋊Q8—2831no—
103#497—2834no—
104#494—2831no—
105#494D28311yescharacteristic, complemented
106#492—2831no—
107#492—2831no—
108C4×M16—2831no—
109C2×#41—2832no—
110C22×Q8—2832no—
111#137—56616no—
112C2×Q16—2834no—
113C2×Q16C2×D28314yes—
114C2×SD16—2834no—
115C2×SD16—2834no—
116C2×M16—2832no—
117C4⋊Q8—2832no—
118C4⋊Q8—2831no—
119C4⋊Q8—5662no—
120C4⋊Q8C2×D28311yescharacteristic
121C4⋊Q8C2×D28311yescharacteristic
122#127—2831no—
123#124—2832no—
124#121—5662no—
125C4×D4—5662no—
126C2×C4⋊C4—5662no—
127C2×C42—2831no—
128#97—2832no—
129C4×C8—2831no—
130C4×C8C2×D28311yescharacteristic
131#41—5668no—
132C2×Q8—2832no—
133C2×Q8—5662no—
134C2×Q8—5668no—
135C2×Q8C22×D28312yes—
136C2×Q8C22×D28312yes—
137C2×D4—2832no—
138C2×D4—5662no—
139C2×D4—5662no—
140C22×C4—2831no—
141C22×C4—2832no—
142C22×C4—5662no—
143C22×C4—5662no—
144Q16—28no—
145Q16—5668no—
146SD16—5668no—
147SD16—5668no—
148M16—2838no—
149C2×C8—2832no—
150C2×C8C22×D28312yes—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—5664no—
154C4⋊C4—5662no—
155C22⋊C4—5664no—
156C42—2832no—
157C42—2831no—
158C42C22×D28311yescharacteristic
159C23—2831no—
160C23—5662no—
161Q8—24no—
162Q8—24no—
163Q8—5664no—
164Q8—11324no—
165D4—5664no—
166D4—11324no—
167D4—11324no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—2831no—
171C2×C4—2834no—
172C2×C4—2832no—
173C2×C4—5664no—
174C2×C4—5662no—
175C2×C4—11324no—
176C2×C4—11324no—
177C2×C4D4×D28312yes—
178C2×C4C23×D28311yescharacteristic
179C8—2834no—
180C8D4×D28314yes—
181C22—2832no—
182C22—5662no—
183C22—11322no—
184C22—11324no—
185C22C2×D4×D28311yescharacteristic
186C4—42no—
187C4—42no—
188C4—2832no—
189C4—5662no—
190C4—11322no—
191C4#2258364214yescomplemented
192C4C2×D4×D28312yes—
193C2—5662no—
194C2—22642no—
195C2#127×D28311yescharacteristic
196C2C2×#2258364212yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#494×C283C2
socleC22×C283C22×D4
prime radical#31827016C2
hypercenter#494D283
hypocenterC283#3152
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. C2×#22583642C2semidirect
3. C4⋊Q8×D283C2semidirect
4. #31826858C2semidirect
5. #31826844C2semidirect
6. #31826839C2semidirect
7. #31826838C2semidirect
8. C4×#17985375C2semidirect
9. #494×C283C2semidirect
46. #17985375D4semidirect
89. C4×C283#137semidirect
98. C283#3152semidirect
105. #494D283semidirect
191. C4#22583642semidirect

Maximal subgroups

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

subgroupindex
C2×#225836422
#318270162
C4⋊Q8×D2832
#318268582
#318268442
#318268392
#318268382
C4×#179853752
#494×C2832
#3152283