Finite Group Databasebeta

← #49094260

Subgroups — #49094260

Order 35968.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#31823618C212yesmaximal, complemented
2#31823375C211yesmaximal, characteristic
3#31823200C212yesmaximal, complemented
4#31823187C211yesmaximal, characteristic
5#543×C281C211yesmaximal, characteristic
6C22×Dic562C2211yescharacteristic
7C2×#17985128—22no—
8C2×C22⋊Dic281—21no—
9#22582802—22no—
10C22⋊#14555886C2212yes—
11#22582786—21no—
12#22582786C2211yescharacteristic
13C22⋊Q8×C281—22no—
14C22⋊Q8×C281—21no—
15C22⋊Q8×C281—22no—
16C22⋊Q8×C281C2212yes—
17C2×C22⋊C4×C281—21no—
18C2×C22⋊C4×C281C2211yescharacteristic
19C2×Dic562—22no—
20C2×Dic562—42no—
21C22×Dic281—21no—
22C22×Dic281—21no—
23#17985128—44no—
24C2×#14555886—22no—
25C22⋊Dic281—42no—
26C24×C281D411yescharacteristic
27C2×Q8×C281—21no—
28C2×Q8×C281D412yes—
29C22×C4×C281—21no—
30C22×C4×C281—21no—
31C22×C4×C281D411yescharacteristic
32C22×C4×C281C2311yescharacteristic
33C4⋊C4×C281—21no—
34C4⋊C4×C281—22no—
35C4⋊C4×C281—22no—
36C4⋊C4×C281D412yes—
37C22⋊C4×C281—22no—
38C22⋊C4×C281—22no—
39C22⋊C4×C281—22no—
40Dic562—24no—
41Dic562—42no—
42C2×Dic281—22no—
43C2×Dic281—41no—
44C2×Dic281—41no—
45C2×Dic281—41no—
46C2×Dic281—41no—
47C2×Dic281—41no—
48#14555886—42no—
49C23×C281—21no—
50C23×C281—21no—
51C23×C281—41no—
52C23×C281—41no—
53C23×C281Q1612yescomplemented
54C23×C281C2×D411yescharacteristic
55Q8×C281—42no—
56Q8×C281—81no—
57C2×C4×C281—22no—
58C2×C4×C281—21no—
59C2×C4×C281—22no—
60C2×C4×C281—41no—
61C2×C4×C281—41no—
62C2×C4×C281—81no—
63C2×C4×C281—81no—
64C2×C4×C281C2×D412yes—
65C22×C281—21no—
66C22×C281—21no—
67C22×C281—22no—
68C22×C281—42no—
69C22×C281—41no—
70C22×C281—41no—
71C22×C281—81no—
72C22×C281#12011yescharacteristic
73C22×C281C2×Q1611yescharacteristic
74C22×C281#13711yescharacteristic
75C4×C281—22no—
76C4×C281—41no—
77C4×C281—42no—
78C4×C281—42no—
79Dic281—42no—
80Dic281—81no—
81C2×C281—21no—
82C2×C281—21no—
83C2×C281—42no—
84C2×C281#45111yescharacteristic
85C2×C281#45511yescharacteristic
86C2×C281B(4,𝔽2)11yescharacteristic
87C281#160211yescharacteristic, complemented, Sylow
88#1602—2811nomaximal, Sylow
89#543D28111yescharacteristic
90#451—2812no—
91#393—2811no—
92#328—2812no—
93#323—2811no—
94C22×Q8—2811no—
95C2×Q16—5622no—
96C22⋊Q8—22no—
97C22⋊Q8—21no—
98C22⋊Q8—22no—
99C22⋊Q8C2×D28112yes—
100C2×C22⋊C4—21no—
101C2×C22⋊C4—5621no—
102C2×C22⋊C4C2×D28111yescharacteristic
103#103—5622no—
104C22⋊C8—2812no—
105#95—2811no—
106#95—5621no—
107C24C22⋊D28111yescharacteristic
108C2×Q8—21no—
109C2×Q8—5622no—
110C2×Q8—11242no—
111C2×Q8C22⋊D28112yes—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—5621no—
115C22×C4—5621no—
116C22×C4C22⋊D28111yescharacteristic
117C22×C4C22×D28111yescharacteristic
118Q16—11244no—
119C2×C8—5622no—
120C4⋊C4—21no—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4C22⋊D28112yes—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C22⋊C4—11242no—
128C23—21no—
129C23—21no—
130C23—41no—
131C23—41no—
132C23#1798512812yescomplemented
133C23C2×C22⋊D28111yescharacteristic
134Q8—42no—
135Q8—81no—
136Q8—5624no—
137Q8—11242no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—81no—
144C2×C4—81no—
145C2×C4—5622no—
146C2×C4—11241no—
147C2×C4—11241no—
148C2×C4—11241no—
149C2×C4—11241no—
150C2×C4—11241no—
151C2×C4C2×C22⋊D28112yes—
152C8—11242no—
153C22—21no—
154C22—21no—
155C22—22no—
156C22—42no—
157C22—41no—
158C22—41no—
159C22—81no—
160C22#2258284811yescharacteristic
161C22C2×#1798512811yescharacteristic
162C22#2258291011yescharacteristic
163C4—22no—
164C4—41no—
165C4—42no—
166C4—42no—
167C4—11242no—
168C4—22481no—
169C2—21no—
170C2—21no—
171C2—42no—
172C2#3182361911yescharacteristic
173C2#3182364111yescharacteristic
174C2#3182365011yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#543×C281C2
socleC22×C281#120
prime radicalC24×C281D4
hypercenter#543D281
hypocenterC281#1602
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #31823618C2semidirect
3. #31823200C2semidirect
53. C23×C281Q16semidirect
87. C281#1602semidirect
132. C23#17985128semidirect

Maximal subgroups

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

subgroupindex
#318236182
#318233752
#318232002
#318231872
#543×C2812
#1602281