Finite Group Databasebeta

← #49120490

Subgroups — #49120490

Order 36224.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#31827181C211yesmaximal, characteristic
2#31826815C211yesmaximal, characteristic, complemented
3#31826746C211yesmaximal, characteristic, complemented
4#31826671C211yesmaximal, characteristic, complemented
5#31826192C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#333×C283C211yesmaximal, characteristic, complemented
8C2×#17985381—21no—
9#22583610C2211yescharacteristic
10#22583599—22no—
11#22583585—21no—
12#22583585—21no—
13C4×D1132C2211yescharacteristic
14C4×D1132C2211yescharacteristic
15#22583568—21no—
16#22583568—21no—
17#22583544—21no—
18#22583535—21no—
19#22583534—22no—
20#22583532—21no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566—21no—
26C2×D1132—22no—
27C2×D1132D411yescharacteristic
28C2×D1132D411yescharacteristic
29C2×C4×D283—21no—
30C2×C4×D283—21no—
31#17985381—42no—
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283D411yescharacteristic
36C4⋊Dic283D411yescharacteristic
37(C2×D283)⋊C4—22no—
38(C2×D283)⋊C4—22no—
39(C2×D283)⋊C4—21no—
40(C2×D283)⋊C4—21no—
41C4×Dic283—22no—
42C2×Q8×C283D412yes—
43C2×C8×C283—21no—
44C2×C8×C283—21no—
45C4⋊C4×C283—21no—
46C4⋊C4×C283—21no—
47C42×C283C2311yescharacteristic
48C22×D283—21no—
49C22×D283—21no—
50Dic566—41no—
51Dic566—41no—
52D1132—21no—
53D1132—21no—
54D1132—21no—
55D1132—21no—
56D1132—82no—
57C2×Dic283—21no—
58C2×Dic283—21no—
59C2×Dic283—41no—
60C4×D283—41no—
61C4×D283—41no—
62C4×D283—41no—
63C4×D283—41no—
64C283⋊C8—41no—
65Q8×C283—42no—
66C2×C4×C283—22no—
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C8×C283—41no—
71C8×C283—41no—
72C22×C283#12011yescharacteristic
73C2×D283—41no—
74C2×D283—41no—
75C2×D283—41no—
76C2×D283—41no—
77C2×D283—41no—
78C2×D283—41no—
79C4×C283—21no—
80C4×C283—42no—
81C4×C283#13511yescharacteristic
82C4×C283#13511yescharacteristic
83C4×C283AGL(1,ℤ/8)11yescharacteristic
84C4×C283#13711yescharacteristic
85Dic283—41no—
86Dic283—41no—
87Dic283—81no—
88C2×C283#44911yescharacteristic
89C2×C283#45211yescharacteristic
90C2×C283#45511yescharacteristic
91D283—81no—
92D283—81no—
93C283#164611yescharacteristic, complemented, Sylow
94#1646—2831nomaximal, Sylow
95#555—2831no—
96#487—2831no—
97#474—2831no—
98#461—2831no—
99#333D28311yescharacteristic, complemented
100D4⋊C8—2831no—
101D4⋊C8—2831no—
102C2×SD16—5661no—
103C4⋊Q8—2831no—
104C4⋊Q8C2×D28311yescharacteristic
105#124—5662no—
106#121—5661no—
107#121—5661no—
108C4×D4—2831no—
109C4×D4—2831no—
110#117—5661no—
111#117—5661no—
112#107—5661no—
113C4⋊C8C2×D28311yescharacteristic
114C4⋊C8C2×D28311yescharacteristic
115#103—5661no—
116#103—5662no—
117#102—5661no—
118C4×C8—2831no—
119C2×Q8—5661no—
120C2×Q8D113212yes—
121C2×D4—2831no—
122C2×D4—2831no—
123C2×D4—5662no—
124C22×C4—5661no—
125C22×C4—5661no—
126SD16—11322no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—5661no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2831no—
133C4⋊C4—2831no—
134C4⋊C4—5661no—
135C4⋊C4—5661no—
136C22⋊C4—5662no—
137C22⋊C4—5662no—
138C22⋊C4—5661no—
139C22⋊C4—5661no—
140C42—5662no—
141C42C22×D28311yescharacteristic
142C23—5661no—
143C23—5661no—
144Q8—42no—
145Q8—11321no—
146Q8—11321no—
147D4—5661no—
148D4—5661no—
149D4—5661no—
150D4—5661no—
151D4—22642no—
152C2×C4—22no—
153C2×C4—5661no—
154C2×C4—5661no—
155C2×C4—11321no—
156C2×C4—11321no—
157C2×C4—11321no—
158C2×C4—11321no—
159C2×C4—11321no—
160C2×C4D4×D28311yescharacteristic
161C2×C4D4×D28311yescharacteristic
162C2×C4C2×D113211yescharacteristic
163C8—41no—
164C8—41no—
165C8—11321no—
166C22—11321no—
167C22—11321no—
168C22—11321no—
169C22—11321no—
170C22—11321no—
171C22—11321no—
172C22#2258358011yescharacteristic
173C4—21no—
174C4—42no—
175C4—11321no—
176C4—11321no—
177C4—22641no—
178C4#2258363111yescharacteristic
179C4#2258363311yescharacteristic
180C4#2258363711yescharacteristic
181C4#2258364211yescharacteristic
182C2—22641no—
183C2—22641no—
184C2#3182661311yescharacteristic
185C2#3182663011yescharacteristic
186C2#3182664511yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#333×C283C2
socleC22×C283#120
prime radical#31827181C2
hypercenter#333D283
hypocenterC283#1646
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31826815C2semidirect
3. #31826746C2semidirect
4. #31826671C2semidirect
5. #31826192C2semidirect
6. #31826192C2semidirect
7. #333×C283C2semidirect
93. C283#1646semidirect
99. #333D283semidirect

Maximal subgroups

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

subgroupindex
#318271812
#318268152
#318267462
#318266712
#318261922
#333×C2832
#1646283