Finite Group Databasebeta

← #49121791

Subgroups — #49121791

Order 36224.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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#31827032C211yesmaximal, characteristic
2#31826940C211yesmaximal, characteristic, complemented
3#31826481C212yesmaximal, complemented
4#31826222C212yesmaximal, complemented
5C2×#100×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2211yescharacteristic
7#22583606C412yescomplemented
8#22583597C412yescomplemented
9#22583581—22no—
10#22583579—22no—
11D4×Dic283—24no—
12#22583569C2211yescharacteristic
13#22583569C2212yes—
14C2×C22⋊Dic283—22no—
15#22583536—24no—
16C22×D4×C283C2211yescharacteristic
17C2×M16×C283C2212yes—
18#100×C283—22no—
19#17985392—22no—
20#17985392—22no—
21C2×Dic566C2×C411yescharacteristic, complemented
22C2×D1132C2×C411yescharacteristic, complemented
23C2×C22⋊D283—24no—
24C2×C22⋊D283—21no—
25C22×Dic283—24no—
26C2×C4×D283—21no—
27C4⋊Dic283—22no—
28C4⋊Dic283—21no—
29C22⋊Dic283—24no—
30C22⋊Dic283—24no—
31C22⋊Dic283—22no—
32C22⋊Dic283—21no—
33C4×Dic283C2×C412yescomplemented
34C4×Dic283D414yescomplemented
35C24×C283D412yes—
36C2×D4×C283—22no—
37C2×D4×C283—22no—
38C2×D4×C283C2×C412yes—
39C2×D4×C283D412yes—
40C22×C4×C283C2311yescharacteristic
41M16×C283—22no—
42M16×C283—22no—
43C2×C8×C283—22no—
44C22×D283—21no—
45Dic566—22no—
46D1132—22no—
47C22⋊D283—41no—
48C22⋊D283—41no—
49C22⋊D283—84no—
50C2×Dic283—22no—
51C2×Dic283—21no—
52C2×Dic283—24no—
53C2×Dic283—84no—
54C4×D283—42no—
55C23×C283—22no—
56C23×C283—22no—
57C23×C283—82no—
58C23×C283C22⋊C414yes—
59C23×C283C2×D411yescharacteristic
60D4×C283—24no—
61D4×C283—24no—
62C2×C4×C283C22×C411yescharacteristic
63C2×C4×C283C2×D412yes—
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283#4112yes—
66C8×C283—42no—
67C22×C283—24no—
68C22×C283—41no—
69C22×C283—44no—
70C22×C283—44no—
71C22×C283—82no—
72C22×C283C2×C22⋊C411yescharacteristic
73C22×C283#12011yescharacteristic
74C22×C283#12311yescharacteristic
75C2×D283—42no—
76C2×D283—41no—
77C4×C283C4×D412yes—
78C4×C283#12112yes—
79Dic283—44no—
80Dic283—42no—
81Dic283—41no—
82C2×C283—21no—
83C2×C283—21no—
84C2×C283—21no—
85C2×C283—44no—
86C2×C283#38611yescharacteristic
87D283—81no—
88C283#191111yescharacteristic, complemented, Sylow
89#1911—2831nomaximal, Sylow
90#535—2831no—
91#518—2831no—
92#421—2832no—
93C2×#100D28311yescharacteristic, complemented
94H(3,ℤ/4)—2832no—
95C2×#41—2831no—
96C22×D4C2×D28311yescharacteristic
97C2×M16C2×D28312yes—
98#127—2832no—
99#124—2832no—
100#121—5662no—
101#120—5662no—
102C4×D4—5664no—
103#117—2832no—
104#117—2831no—
105C2×C22⋊C4—5662no—
106#104—5664no—
107#100—22no—
108C24D113212yes—
109#41—5662no—
110#41—5662no—
111C2×Q8—2831no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—2831no—
115C2×D4—5661no—
116C2×D4—5664no—
117C2×D4C4×D28312yes—
118C2×D4C22⋊D28312yes—
119C22×C4—5664no—
120C22×C4—5661no—
121C22×C4C22×D28311yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—5662no—
126C4⋊C4—5661no—
127C22⋊C4—5664no—
128C22⋊C4—5664no—
129C22⋊C4—5662no—
130C22⋊C4—5661no—
131C42—2832no—
132C42—2834no—
133C23—22no—
134C23—22no—
135C23—82no—
136C23—5661no—
137C23(C2×D283)⋊C414yes—
138C23C2×D113211yescharacteristic
139Q8—5662no—
140D4—24no—
141D4—24no—
142D4—5662no—
143D4—11321no—
144D4—11321no—
145D4—22644no—
146C2×C4—5662no—
147C2×C4—5661no—
148C2×C4—5664no—
149C2×C4—11322no—
150C2×C4—22644no—
151C2×C4C2×C4×D28311yescharacteristic
152C2×C4D4×D28312yes—
153C2×C4C2×C22⋊D28311yescharacteristic
154C2×C4#1798539112yes—
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—11322no—
162C22—11321no—
163C22C2×(C2×D283)⋊C411yescharacteristic
164C22#2258358011yescharacteristic
165C22#2258359411yescharacteristic
166C4—11324no—
167C4—11322no—
168C4—11321no—
169C4(C22⋊D283)⋊C412yes—
170C4#2258358212yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—22641no—
176C2#3182634211yescharacteristic
subgroupG/H
centerC2#31826342
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#100×C283C2
socleC2×C283#386
prime radical#31827032C2
cosocleC22×C4×C283C23
hypercenterC2×#100D283
hypocenterC283#1911
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #31826940C2semidirect
3. #31826481C2semidirect
4. #31826222C2semidirect
5. C2×#100×C283C2semidirect
7. #22583606C4semidirect
8. #22583597C4semidirect
21. C2×Dic566C2×C4semidirect
22. C2×D1132C2×C4semidirect
33. C4×Dic283C2×C4semidirect
34. C4×Dic283D4semidirect
88. C283#1911semidirect
93. C2×#100D283semidirect

Maximal subgroups

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

subgroupindex
#318270322
#318269402
#318264812
#318262222
C2×#100×C2832
#1911283