Finite Group Databasebeta

← #49122329

Subgroups — #49122329

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#31827265C211yesmaximal, characteristic, complemented
2#31826977C212yesmaximal, complemented
3#31826483C212yesmaximal, complemented
4#31826428C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2212yes—
7C22×C4×D283C2211yescharacteristic
8#22583643—22no—
9#22583638—22no—
10#22583632—22no—
11C2×#17985376C2211yescharacteristic
12#22583594—22no—
13#22583590—22no—
14#22583585—22no—
15#22583580—22no—
16C4×D1132—24no—
17#22583538—24no—
18(C2×D283)⋊C8—22no—
19C2×M16×C283C2211yescharacteristic
20#117×C283C2212yes—
21C23×D283D411yescharacteristic
22#17985392—22no—
23#17985392—22no—
24#17985392—22no—
25#17985392—22no—
26C2×Dic566D412yescomplemented
27C2×D1132—24no—
28C2×D1132D412yescomplemented
29C2×C22⋊D283—22no—
30C22×Dic283D411yescharacteristic
31C2×C4×D283—22no—
32C2×C4×D283—22no—
33C2×C4×D283—22no—
34C2×C4×D283—21no—
35C2×C4×D283—21no—
36Dic1132—22no—
37#17985381—24no—
38D2264—22no—
39#17985376—22no—
40C2×C283⋊C8—21no—
41C4⋊Dic283—24no—
42(C2×D283)⋊C4—24no—
43(C2×D283)⋊C4—24no—
44C22×C4×C283C2311yescharacteristic
45M16×C283—22no—
46C2×C8×C283D412yescomplemented
47C4⋊C4×C283—22no—
48C22⋊C4×C283—22no—
49C42×C283D414yescomplemented
50C22×D283—22no—
51C22×D283—21no—
52C22×D283—22no—
53C22×D283—42no—
54Dic566—22no—
55Dic566—22no—
56D1132—22no—
57D1132—22no—
58D1132—48no—
59C22⋊D283—42no—
60C22⋊D283—42no—
61C2×Dic283—22no—
62C2×Dic283—22no—
63C2×Dic283—21no—
64C4×D283—41no—
65C4×D283—42no—
66C4×D283—42no—
67C4×D283—41no—
68C4×D283—42no—
69C283⋊C8—41no—
70C23×C283C2×D411yescharacteristic
71C2×C4×C283—24no—
72C2×C4×C283C2×D412yes—
73C2×C4×C283C2×D411yescharacteristic
74C2×C4×C283C2×D412yes—
75C2×C4×C283#4111yescharacteristic
76C8×C283—22no—
77C22×C283—41no—
78C22×C283#12012yes—
79C22×C283#12111yescharacteristic
80C2×D283—24no—
81C2×D283—22no—
82C2×D283—42no—
83C2×D283—41no—
84C2×D283—41no—
85C2×D283—44no—
86C2×D283—42no—
87C4×C283—44no—
88C4×C283#12011yescharacteristic
89C4×C283#12112yes—
90C4×C283#12711yescharacteristic
91Dic283—41no—
92Dic283—42no—
93C2×C283—22no—
94C2×C283—21no—
95C2×C283#39211yescharacteristic
96D283—42no—
97D283—82no—
98C283#201011yescharacteristic, complemented, Sylow
99#2010—2831nomaximal, Sylow
100#575—2831no—
101#525—2832no—
102#421—2832no—
103#407—2831no—
104H(3,ℤ/4)D28311yescharacteristic, complemented
105C2×#41—2832no—
106C23×C4—2831no—
107#137—5662no—
108AGL(1,ℤ/8)—5662no—
109#135—5662no—
110C2×M16—2831no—
111C2×M16C2×D28311yescharacteristic
112#123—5662no—
113C22⋊Q8—5662no—
114#121—5662no—
115#120—5662no—
116C4×D4—5664no—
117#117C2×D28312yes—
118#104—5664no—
119C22⋊C8—5662no—
120C24—2831no—
121#41—5662no—
122#41—5662no—
123#41—5662no—
124#41—5662no—
125C2×Q8—2832no—
126C2×D4—2832no—
127C2×D4—5664no—
128C2×D4—5662no—
129C22×C4—2831no—
130C22×C4—5662no—
131C22×C4—5661no—
132C22×C4—5662no—
133C22×C4—5662no—
134C22×C4—5661no—
135C22×C4C22×D28311yescharacteristic
136Q16—5662no—
137SD16—5664no—
138D8—5662no—
139M16—22no—
140M16—5662no—
141C2×C8—5661no—
142C2×C8D113212yescomplemented
143C4⋊C4—22no—
144C4⋊C4—5664no—
145C22⋊C4—22no—
146C22⋊C4—5664no—
147C22⋊C4—5664no—
148C42D113214yescomplemented
149C23—5662no—
150C23—5661no—
151C23—5662no—
152C23—11322no—
153C23D4×D28311yescharacteristic
154Q8—5662no—
155Q8—5662no—
156D4—5662no—
157D4—5662no—
158D4—11328no—
159D4—11322no—
160D4—11322no—
161C2×C4—24no—
162C2×C4—5662no—
163C2×C4—5662no—
164C2×C4—5661no—
165C2×C4—11321no—
166C2×C4—11322no—
167C2×C4—11322no—
168C2×C4—11321no—
169C2×C4—11322no—
170C2×C4D4×D28312yes—
171C2×C4C2×D113211yescharacteristic
172C2×C4C2×D113212yes—
173C2×C4#1798539311yescharacteristic
174C8—22no—
175C8—11321no—
176C22—41no—
177C22—5664no—
178C22—5662no—
179C22—11322no—
180C22—11321no—
181C22—11324no—
182C22—11321no—
183C22—11322no—
184C22#2258358012yes—
185C22#2258358511yescharacteristic
186C4—44no—
187C4—11321no—
188C4—11322no—
189C4#2258358011yescharacteristic
190C4#2258358512yes—
191C4#2258360711yescharacteristic
192C2—22no—
193C2—21no—
194C2—11322no—
195C2—22642no—
196C2#3182637511yescharacteristic
subgroupG/H
centerC4#22583607
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingH(3,ℤ/4)×C283C2
socleC2×C283#392
hypercenterH(3,ℤ/4)D283
hypocenterC283#2010
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #31827265C2semidirect
2. #31826977C2semidirect
3. #31826483C2semidirect
4. #31826428C2semidirect
5. H(3,ℤ/4)×C283C2semidirect
26. C2×Dic566D4semidirect
28. C2×D1132D4semidirect
46. C2×C8×C283D4semidirect
49. C42×C283D4semidirect
98. C283#2010semidirect
104. H(3,ℤ/4)D283semidirect
142. C2×C8D1132semidirect
148. C42D1132semidirect

Maximal subgroups

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

subgroupindex
#318272652
#318269772
#318264832
#318264282
H(3,ℤ/4)×C2832
#2010283