Finite Group Databasebeta

← #49122325

Subgroups — #49122325

Order 36224.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#31826972C212yesmaximal, complemented
2#31826482C212yesmaximal, complemented
3#31826428C211yesmaximal, characteristic, complemented
4#31826222C211yesmaximal, characteristic, complemented
5#575×C283C211yesmaximal, characteristic, complemented
6C22×C4×D283C2211yescharacteristic
7C2×#17985376C2211yescharacteristic
8#22583591—22no—
9#22583586—22no—
10#22583581—22no—
11#22583578—22no—
12C4×C22⋊D283—24no—
13#22583569C2212yes—
14#22583537—24no—
15(C2×D283)⋊C8—22no—
16C2×#41×C283C2212yes—
17#137×C283—22no—
18AGL(1,ℤ/8)×C283—22no—
19#135×C283—22no—
20C2×M16×C283C2211yescharacteristic
21C23×D283D411yescharacteristic
22C2×C22⋊D283—24no—
23C22×Dic283D411yescharacteristic
24C2×C4×D283—22no—
25C2×C4×D283—22no—
26C2×C4×D283—21no—
27C2×C4×D283—21no—
28#17985376—22no—
29C2×C283⋊C8—21no—
30C4⋊Dic283—22no—
31Dic283⋊C4—24no—
32C22⋊Dic283—24no—
33C22⋊Dic283—22no—
34(C2×D283)⋊C4—24no—
35C4×Dic283D414yescomplemented
36#41×C283—22no—
37#41×C283—22no—
38#41×C283—22no—
39#41×C283—22no—
40C2×Q8×C283D412yescomplemented
41C2×D4×C283—22no—
42C2×D4×C283D412yescomplemented
43C22×C4×C283—22no—
44C22×C4×C283C2311yescharacteristic
45Q16×C283—22no—
46SD16×C283—24no—
47D8×C283—22no—
48M16×C283—22no—
49C2×C8×C283D412yescomplemented
50C22×D283—22no—
51C22×D283—21no—
52C22×D283—42no—
53C22⋊D283—48no—
54C2×Dic283—24no—
55C2×Dic283—22no—
56C2×Dic283—21no—
57C4×D283—41no—
58C4×D283—42no—
59C4×D283—41no—
60C283⋊C8—41no—
61C23×C283—22no—
62C23×C283C2×D411yescharacteristic
63Q8×C283—22no—
64Q8×C283—22no—
65D4×C283—22no—
66D4×C283—22no—
67D4×C283—42no—
68D4×C283—42no—
69C2×C4×C283—22no—
70C2×C4×C283—42no—
71C2×C4×C283—42no—
72C2×C4×C283C2×D412yes—
73C2×C4×C283C2×D412yes—
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283#4111yescharacteristic
76C8×C283—22no—
77C22×C283—41no—
78C22×C283—44no—
79C22×C283—42no—
80C22×C283#12012yes—
81C22×C283#12111yescharacteristic
82C2×D283—24no—
83C2×D283—22no—
84C2×D283—42no—
85C2×D283—41no—
86C2×D283—41no—
87C4×C283—42no—
88C4×C283#12011yescharacteristic
89C4×C283#12112yes—
90C4×C283#12711yescharacteristic
91Dic283—44no—
92Dic283—41no—
93C2×C283—22no—
94C2×C283—21no—
95C2×C283—82no—
96C2×C283#39211yescharacteristic
97D283—42no—
98C283#201011yescharacteristic, complemented, Sylow
99#2010—2831nomaximal, Sylow
100#575D28311yescharacteristic, complemented
101#525—2832no—
102#421—2832no—
103#407—2831no—
104H(3,ℤ/4)—2831no—
105C2×#41C2×D28312yes—
106C23×C4—2831no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—2831no—
111C2×M16C2×D28311yescharacteristic
112#123—5662no—
113C22⋊Q8—5662no—
114#121—5662no—
115#120—5662no—
116C4×D4—5664no—
117#117—2832no—
118#104—5664no—
119C22⋊C8—5662no—
120C24—2831no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D28312yescomplemented
126C2×D4—22no—
127C2×D4—5664no—
128C2×D4C22⋊D28312yescomplemented
129C22×C4—22no—
130C22×C4—2831no—
131C22×C4—5662no—
132C22×C4—5661no—
133C22×C4—5662no—
134C22×C4—5661no—
135C22×C4C22×D28311yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—5662no—
141C2×C8—5661no—
142C2×C8C22⋊D28312yescomplemented
143C4⋊C4—5664no—
144C4⋊C4—5662no—
145C22⋊C4—5664no—
146C22⋊C4—5664no—
147C22⋊C4—5662no—
148C42—2834no—
149C23—22no—
150C23—5662no—
151C23—5661no—
152C23—11322no—
153C23D4×D28311yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—11328no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—5664no—
165C2×C4—5662no—
166C2×C4—5661no—
167C2×C4—11321no—
168C2×C4—11322no—
169C2×C4—11321no—
170C2×C4D4×D28312yes—
171C2×C4C2×C22⋊D28312yes—
172C2×C4C2×C22⋊D28311yescharacteristic
173C2×C4#1798539111yescharacteristic
174C8—22no—
175C8—11321no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—5664no—
180C22—5662no—
181C22—11322no—
182C22—11321no—
183C22—11321no—
184C22#2258357812yes—
185C22#2258358111yescharacteristic
186C4—42no—
187C4—11324no—
188C4—11321no—
189C4#2258357911yescharacteristic
190C4#2258358212yes—
191C4#2258360611yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—11322no—
196C2#3182637311yescharacteristic
subgroupG/H
centerC4#22583606
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#575×C283C2
socleC2×C283#392
hypercenter#575D283
hypocenterC283#2010
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #31826972C2semidirect
2. #31826482C2semidirect
3. #31826428C2semidirect
4. #31826222C2semidirect
5. #575×C283C2semidirect
35. C4×Dic283D4semidirect
40. C2×Q8×C283D4semidirect
42. C2×D4×C283D4semidirect
49. C2×C8×C283D4semidirect
98. C283#2010semidirect
100. #575D283semidirect
125. C2×Q8C22⋊D283semidirect
128. C2×D4C22⋊D283semidirect
142. C2×C8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318269722
#318264822
#318264282
#318262222
#575×C2832
#2010283