Finite Group Databasebeta

← #49122951

Subgroups — #49122951

Order 36224.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#31827033C211yesmaximal, characteristic
2#31826448C212yesmaximal, complemented
3#31826262C211yesmaximal, characteristic, complemented
4#31826261C212yesmaximal, complemented
5#355×C283C211yesmaximal, characteristic, complemented
6C2×#17985393C2211yescharacteristic
7C2×D4×D283C411yescharacteristic
8M16×D283—22no—
9#22583607C411yescharacteristic
10#22583606C411yescharacteristic
11#22583599C2211yescharacteristic
12#22583583—22no—
13#22583580—22no—
14#22583567C411yescharacteristic
15#22583529C2212yescomplemented
16#22583526—22no—
17#124×C283C2211yescharacteristic
18#101×C283C2212yescomplemented
19C23×D283—21no—
20#17985393—42no—
21C2×D1132—22no—
22C2×D1132C2×C411yescharacteristic
23C2×D1132C2×C411yescharacteristic
24C2×D1132D412yes—
25C2×C22⋊D283—22no—
26C2×C22⋊D283—21no—
27D4×D283—42no—
28C2×C4×D283C2×C411yescharacteristic
29C2×C4×D283D412yes—
30#17985376—22no—
31#17985375—42no—
32C8×D283—42no—
33Dic283⋊C4—21no—
34(C2×D283)⋊C4—21no—
35(C2×D283)⋊C4—22no—
36C4×Dic283C2×C411yescharacteristic
37C2×Q8×C283C2311yescharacteristic
38C2×D4×C283C2×C411yescharacteristic
39M16×C283—22no—
40C22⋊C4×C283—22no—
41C42×C283C2×C411yescharacteristic
42C22×D283—21no—
43C22×D283—42no—
44C22×D283—82no—
45C22×D283C22⋊C411yescharacteristic
46C22×D283C22⋊C412yes—
47D1132—41no—
48D1132—42no—
49D1132—41no—
50D1132—82no—
51C22⋊D283—42no—
52C22⋊D283—82no—
53C2×Dic283—21no—
54C2×Dic283C22⋊C411yescharacteristic
55C4×D283—22no—
56C4×D283—22no—
57C4×D283—22no—
58C283⋊C8—42no—
59C23×C283—21no—
60Q8×C283—41no—
61D4×C283—41no—
62C2×C4×C283—21no—
63C2×C4×C283C22×C411yescharacteristic
64C2×C4×C283C2×D412yes—
65C8×C283—42no—
66C22×C283—42no—
67C22×C283—41no—
68C22×C283C2×C22⋊C411yescharacteristic
69C2×D283—21no—
70C2×D283—22no—
71C2×D283—42no—
72C2×D283—41no—
73C2×D283—42no—
74C2×D283—41no—
75C2×D283—84no—
76C4×C283—22no—
77C4×C283—21no—
78C4×C283—41no—
79Dic283—41no—
80Dic283#9912yes—
81C2×C283—21no—
82C2×C283—81no—
83C2×C283C2×#9911yescharacteristic
84D283—42no—
85D283—41no—
86D283—81no—
87C283#213411yescharacteristic, complemented, Sylow
88#2134—2831nomaximal, Sylow
89#535—2831no—
90#413—2832no—
91#355—2831no—
92#355—2832no—
93#355D28311yescharacteristic, complemented
94C2×#41—2831no—
95C22×D4—2831no—
96C2×M16—5662no—
97#127—2831no—
98#127—2831no—
99#124—2831no—
100#124C2×D28311yescharacteristic
101#121—5662no—
102#120—5662no—
103#117—2831no—
104#101—2832no—
105#101C2×D28312yescomplemented
106#100—5662no—
107C24—5661no—
108#41—11322no—
109C2×Q8C22×D28311yescharacteristic
110C2×D4—2831no—
111C2×D4—2831no—
112C2×D4—2832no—
113C2×D4—5662no—
114C2×D4—5661no—
115C2×D4—5662no—
116C2×D4—11322no—
117C2×D4C4×D28311yescharacteristic
118C22×C4—2831no—
119C22×C4—2832no—
120M16—22no—
121M16—5662no—
122M16—11322no—
123C2×C8—11322no—
124C4⋊C4—5661no—
125C22⋊C4—22no—
126C22⋊C4—5661no—
127C22⋊C4—5662no—
128C42—2831no—
129C42C4×D28311yescharacteristic
130C23—21no—
131C23—2831no—
132C23—2832no—
133C23—5661no—
134C23—11322no—
135C23—22642no—
136Q8—41no—
137D4—41no—
138D4—11322no—
139D4—11321no—
140D4—11321no—
141D4—11322no—
142D4—22642no—
143D4—22642no—
144C2×C4—21no—
145C2×C4—2831no—
146C2×C4—5662no—
147C2×C4—5662no—
148C2×C4—5662no—
149C2×C4—5661no—
150C2×C4C2×C4×D28311yescharacteristic
151C2×C4D4×D28312yes—
152C8—42no—
153C8—11322no—
154C22—42no—
155C22—41no—
156C22—5661no—
157C22—5662no—
158C22—11322no—
159C22—11321no—
160C22—11322no—
161C22—11321no—
162C22—22644no—
163C22C22⋊C4×D28311yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—2832no—
168C4—11321no—
169C2—21no—
170C2—81no—
171C2—11321no—
172C2—11322no—
173C2—22641no—
174C2#99×D28311yescharacteristic
subgroupG/H
centerC2#99×D283
commutatorC2×C4×C283C22×C4
FrattiniC2×Q8C22×D283
Fitting#355×C283C2
socleC2×C283C2×#99
prime radical#31827033C2
cosocleC2×Q8×C283C23
hypercenter#355D283
hypocenterC283#2134
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #31826448C2semidirect
3. #31826262C2semidirect
4. #31826261C2semidirect
5. #355×C283C2semidirect
15. #22583529C22semidirect
18. #101×C283C22semidirect
87. C283#2134semidirect
93. #355D283semidirect
105. #101C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270332
#318264482
#318262622
#318262612
#355×C2832
#2134283