Finite Group Databasebeta

← #49094262

Subgroups — #49094262

Order 35968.

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

normal subgroups only

This group has 256 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#31824089C211yesmaximal, characteristic
2#31823621C212yesmaximal, complemented
3#31823375C211yesmaximal, characteristic
4#31823201C212yesmaximal, complemented
5#323×C281C211yesmaximal, characteristic
6C22×Dic562C2211yescharacteristic
7C2×Dic1124—22no—
8#22582858—21no—
9#22582858C2212yes—
10#22582856—22no—
11#22582856—22no—
12C2×C22⋊Dic281—21no—
13C2×C22⋊Dic281—21no—
14#22582804—22no—
15#22582786—21no—
16#22582786C2211yescharacteristic
17C2×C22⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C2×Dic562—21no—
20C2×Dic562—22no—
21C2×Dic562—42no—
22C2×Dic562D412yes—
23C22×Dic281—21no—
24C22×Dic281—21no—
25C22×Dic281—21no—
26C22×Dic281—21no—
27Dic1124—44no—
28C4⋊Dic281—21no—
29C4⋊Dic281D412yes—
30#17985117—22no—
31#17985117—22no—
32C22⋊Dic281—22no—
33C22⋊Dic281—22no—
34C22⋊Dic281—42no—
35C24×C281D411yescharacteristic
36C22×C4×C281D411yescharacteristic
37C22×C4×C281C2311yescharacteristic
38C2×C8×C281—22no—
39C22⋊C4×C281—22no—
40Dic562—24no—
41Dic562—42no—
42Dic562—42no—
43Dic562—81no—
44C2×Dic281—22no—
45C2×Dic281—22no—
46C2×Dic281—22no—
47C2×Dic281—41no—
48C2×Dic281—41no—
49C2×Dic281—41no—
50C2×Dic281—41no—
51C2×Dic281—41no—
52C2×Dic281—81no—
53C2×Dic281—81no—
54C23×C281—21no—
55C23×C281—21no—
56C23×C281—41no—
57C23×C281—41no—
58C23×C281Q1612yescomplemented
59C23×C281C2×D411yescharacteristic
60C2×C4×C281—21no—
61C2×C4×C281—41no—
62C2×C4×C281—41no—
63C2×C4×C281C2×D412yes—
64C8×C281—42no—
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—
77Dic281—42no—
78Dic281—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#543—2811no—
90#451—2812no—
91#393—2811no—
92#328—2812no—
93#323D28111yescharacteristic
94C22×Q8—2811no—
95C2×Q16—5622no—
96C22⋊Q8—2812no—
97C22⋊Q8—5622no—
98C22⋊Q8—5622no—
99C22⋊Q8—5621no—
100C2×C22⋊C4—5621no—
101C2×C22⋊C4—5621no—
102C2×C22⋊C4C2×D28111yescharacteristic
103#103—5622no—
104C22⋊C8C2×D28112yes—
105#95—2811no—
106#95—5621no—
107C24D112411yescharacteristic
108C2×Q8—2812no—
109C2×Q8—5621no—
110C2×Q8—5622no—
111C2×Q8—11242no—
112C22×C4—5621no—
113C22×C4—5621no—
114C22×C4—5621no—
115C22×C4—5621no—
116C22×C4D112411yescharacteristic
117C22×C4C22×D28111yescharacteristic
118Q16—11244no—
119C2×C8—22no—
120C4⋊C4—2812no—
121C4⋊C4—5622no—
122C4⋊C4—5621no—
123C4⋊C4—5622no—
124C22⋊C4—22no—
125C22⋊C4—5622no—
126C22⋊C4—5622no—
127C22⋊C4—11242no—
128C23—21no—
129C23—21no—
130C23—41no—
131C23—41no—
132C23Dic112412yescomplemented
133C23C2×D112411yescharacteristic
134Q8—5624no—
135Q8—11242no—
136Q8—11242no—
137Q8—22481no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—5622no—
142C2×C4—5622no—
143C2×C4—5622no—
144C2×C4—11241no—
145C2×C4—11241no—
146C2×C4—11241no—
147C2×C4—11241no—
148C2×C4—11241no—
149C2×C4—22481no—
150C2×C4—22481no—
151C2×C4D4×D28112yes—
152C8—42no—
153C22—21no—
154C22—21no—
155C22—22no—
156C22—42no—
157C22—41no—
158C22—41no—
159C22—81no—
160C22#2258284911yescharacteristic
161C22C2×Dic112411yescharacteristic
162C22#2258291211yescharacteristic
163C4—22no—
164C4—41no—
165C4—11242no—
166C4—11242no—
167C4—11242no—
168C4—22481no—
169C2—21no—
170C2—21no—
171C2—42no—
172C2#3182362111yescharacteristic
173C2#3182364311yescharacteristic
174C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#323×C281C2
socleC22×C281#120
prime radicalC24×C281D4
hypercenter#323D281
hypocenterC281#1602
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #31823621C2semidirect
4. #31823201C2semidirect
58. C23×C281Q16semidirect
87. C281#1602semidirect
132. C23Dic1124semidirect

Maximal subgroups

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

subgroupindex
#318240892
#318236212
#318233752
#318232012
#323×C2812
#1602281