Finite Group Databasebeta

← #49120300

Subgroups — #49120300

Order 36224.

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

normal subgroups only

This group has 246 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#31827046C211yesmaximal, characteristic
2#31826784C212yesmaximal, complemented
3#31826404C211yesmaximal, characteristic, complemented
4#31826200C212yesmaximal, complemented
5#324×C283C211yesmaximal, characteristic, complemented
6C2×#17985392—21no—
7#22583590—22no—
8#22583585—22no—
9#22583584—21no—
10#22583584C2212yes—
11C2×C4⋊Dic283C2211yescharacteristic
12#22583542—22no—
13#22583532—22no—
14C283⋊#95—21no—
15C283⋊#95—21no—
16C283⋊#95C2211yescharacteristic
17C2×C4⋊C4×C283C2211yescharacteristic
18C22⋊C8×C283C2212yes—
19#17985392—42no—
20#17985392—42no—
21C2×Dic566—21no—
22C2×D1132—21no—
23C2×D1132—21no—
24C2×D1132D412yes—
25C2×C22⋊D283—22no—
26C22×Dic283—21no—
27C22×Dic283—21no—
28C2×C4×D283—22no—
29C4⋊Dic283—21no—
30C4⋊Dic283—22no—
31C4⋊Dic283D412yes—
32(C2×D283)⋊C4—22no—
33(C2×D283)⋊C4—22no—
34C22×C4×C283D411yescharacteristic
35C22×C4×C283D411yescharacteristic
36C22×C4×C283C2311yescharacteristic
37C2×C8×C283—22no—
38C4⋊C4×C283—22no—
39C22×D283—22no—
40Dic566—42no—
41D1132—42no—
42D1132—42no—
43D1132—81no—
44C22⋊D283—42no—
45C22⋊D283—42no—
46C2×Dic283—22no—
47C2×Dic283—41no—
48C2×Dic283—41no—
49C2×Dic283—42no—
50C2×Dic283—41no—
51C2×Dic283—41no—
52C4×D283—44no—
53C23×C283C2×D411yescharacteristic
54C2×C4×C283—21no—
55C2×C4×C283—21no—
56C2×C4×C283—21no—
57C2×C4×C283—41no—
58C2×C4×C283—41no—
59C2×C4×C283SD1612yes—
60C2×C4×C283C2×D412yes—
61C8×C283—42no—
62C22×C283—21no—
63C22×C283—21no—
64C22×C283#12011yescharacteristic
65C22×C283C2×SD1611yescharacteristic
66C22×C283AGL(1,ℤ/8)11yescharacteristic
67C2×D283—42no—
68C2×D283—42no—
69C2×D283—42no—
70C4×C283—22no—
71C4×C283—22no—
72C4×C283—41no—
73Dic283—42no—
74Dic283—81no—
75Dic283—81no—
76C2×C283—21no—
77C2×C283—21no—
78C2×C283#45011yescharacteristic
79C2×C283#45411yescharacteristic
80C2×C283#45811yescharacteristic
81D283—82no—
82C283#161611yescharacteristic, complemented, Sylow
83#1616—2831nomaximal, Sylow
84#537—2831no—
85#481—2832no—
86#400—2831no—
87#327—2832no—
88#324D28311yescharacteristic, complemented
89C2×#41—5661no—
90C22⋊Q8—5662no—
91#121—2832no—
92#121—5662no—
93#121—5661no—
94C2×C4⋊C4—2831no—
95C2×C4⋊C4C2×D28311yescharacteristic
96#106—5662no—
97#102—5662no—
98C22⋊C8C2×D28312yes—
99#95—2831no—
100#95—5661no—
101#95—5661no—
102#41—11322no—
103#41—11322no—
104C2×Q8—5661no—
105C2×D4—2832no—
106C2×D4—5661no—
107C2×D4—5661no—
108C2×D4—5662no—
109C22×C4—5662no—
110C22×C4—5661no—
111C22×C4—5661no—
112C22×C4D113211yescharacteristic
113C22×C4D113211yescharacteristic
114C22×C4C22×D28311yescharacteristic
115C2×C8—22no—
116C4⋊C4—22no—
117C4⋊C4—2832no—
118C4⋊C4—5661no—
119C4⋊C4—5662no—
120C22⋊C4—5662no—
121C22⋊C4—5662no—
122C23—5662no—
123C23C2×D113211yescharacteristic
124Q8—11322no—
125D4—11322no—
126D4—11322no—
127D4—11322no—
128D4—11322no—
129D4—22641no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—5662no—
136C2×C4—11324no—
137C2×C4—11321no—
138C2×C4—11321no—
139C2×C4—11322no—
140C2×C4—11321no—
141C2×C4—11321no—
142C2×C4#1798538112yes—
143C2×C4D4×D28312yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—11322no—
148C22—11322no—
149C22—11322no—
150C22#2258358011yescharacteristic
151C22C2×#1798538111yescharacteristic
152C22#2258363811yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—11322no—
157C4—22641no—
158C4—22641no—
159C2—21no—
160C2—21no—
161C2—22642no—
162C2#3182661811yescharacteristic
163C2#3182664011yescharacteristic
164C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#324×C283C2
socleC22×C283#120
prime radical#31827046C2
hypercenter#324D283
hypocenterC283#1616
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #31826784C2semidirect
3. #31826404C2semidirect
4. #31826200C2semidirect
5. #324×C283C2semidirect
82. C283#1616semidirect
88. #324D283semidirect

Maximal subgroups

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

subgroupindex
#318270462
#318267842
#318264042
#318262002
#324×C2832
#1616283