Finite Group Databasebeta

← #49095034

Subgroups — #49095034

Order 35968.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#22582835C212yesmaximal
2C2×#22582835C211yesmaximal, characteristic
3#31823230C211yesmaximal, characteristic
4#31823229C212yesmaximal
5#342×C281C211yesmaximal, characteristic
6C23×Dic281C2211yescharacteristic
7#22582835—24no—
8#22582835—22no—
9#22582835—22no—
10#22582835C418yescomplemented
11C2×#17985117—22no—
12C2×#17985117C412yescomplemented
13C2×C22⋊Dic281C2211yescharacteristic
14C2×C22⋊Dic281C2212yes—
15C2×C4×Dic281—22no—
16C2×C4×Dic281C412yescomplemented
17C2×C22⋊C4×C281C2211yescharacteristic
18C2×C22⋊C4×C281C2212yes—
19C22×Dic281—22no—
20C22×Dic281C2×C412yes—
21C22×Dic281C2×C411yescharacteristic
22C22×Dic281C2×C411yescharacteristic
23C22×Dic281C2×C414yes—
24C22×Dic281D412yes—
25C22×Dic281D412yes—
26C22×Dic281D412yes—
27C22×Dic281Q812yes—
28#17985117—28no—
29#17985117—24no—
30C22⋊Dic281—22no—
31C22⋊Dic281—22no—
32C22⋊Dic281C2×C414yes—
33C4×Dic281—28no—
34C4×Dic281—22no—
35C4×Dic281—22no—
36C24×C281C2311yescharacteristic
37C22×C4×C281—22no—
38C22×C4×C281C2×C412yes—
39C22⋊C4×C281—22no—
40C22⋊C4×C281—22no—
41C22⋊C4×C281C2×C414yes—
42C2×Dic281—22no—
43C2×Dic281—24no—
44C2×Dic281—44no—
45C2×Dic281—42no—
46C2×Dic281C4212yes—
47C2×Dic281C4212yes—
48C2×Dic281C22⋊C414yes—
49C2×Dic281C22⋊C411yescharacteristic
50C2×Dic281C22⋊C411yescharacteristic
51C2×Dic281C22⋊C414yes—
52C2×Dic281C22⋊C412yes—
53C2×Dic281C4⋊C412yes—
54C2×Dic281C4⋊C412yes—
55C2×Dic281C4⋊C414yes—
56C2×Dic281C4⋊C414yes—
57C23×C281—42no—
58C23×C281C22×C411yescharacteristic
59C23×C281C22×C412yes—
60C23×C281C2×D412yes—
61C23×C281C2×D411yescharacteristic
62C23×C281C2×Q811yescharacteristic
63C2×C4×C281—22no—
64C2×C4×C281—24no—
65C2×C4×C281—44no—
66C2×C4×C281—42no—
67C22×C281—22no—
68C22×C281—24no—
69C22×C281—42no—
70C22×C281—41no—
71C22×C281—41no—
72C22×C281C2×C4211yescharacteristic
73C22×C281C2×C22⋊C412yes—
74C22×C281C2×C22⋊C411yescharacteristic
75C22×C281C2×C4⋊C411yescharacteristic
76C22×C281C2×C4⋊C412yes—
77C4×C281—44no—
78C4×C281—42no—
79Dic281—44no—
80Dic281—42no—
81Dic281#9512yes—
82Dic281#9514yes—
83Dic281#9512yes—
84C2×C281—22no—
85C2×C281—21no—
86C2×C281—21no—
87C2×C281—22no—
88C2×C281C2×#9511yescharacteristic
89C2×C281#41012yes—
90C281#174011yescharacteristic, complemented, Sylow
91#1740—2811nomaximal, Sylow
92C2×#117—2811no—
93C2×#117—2812no—
94#342—2812no—
95#342—2811no—
96#342D28111yescharacteristic
97C23×C4—2811no—
98#117—2818no—
99#117—5622no—
100#117—5622no—
101#117—5624no—
102C2×C4⋊C4—2812no—
103C2×C4⋊C4—5622no—
104C2×C22⋊C4—2812no—
105C2×C22⋊C4—2811no—
106C2×C22⋊C4C2×D28111yescharacteristic
107C2×C22⋊C4C2×D28112yes—
108C2×C42—2812no—
109C2×C42—5622no—
110C24C22×D28111yescharacteristic
111C22×C4—22no—
112C22×C4—2811no—
113C22×C4—2811no—
114C22×C4—2814no—
115C22×C4—2812no—
116C22×C4—2812no—
117C22×C4—2812no—
118C22×C4—2812no—
119C22×C4—2812no—
120C22×C4—5622no—
121C22×C4C4×D28112yes—
122C4⋊C4—5624no—
123C4⋊C4—5628no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—2814no—
127C22⋊C4—5622no—
128C22⋊C4—5622no—
129C22⋊C4C4×D28114yes—
130C42—5622no—
131C42—5622no—
132C42—5628no—
133C23—42no—
134C23C2×C4×D28111yescharacteristic
135C23C2×C4×D28112yes—
136C23D4×D28112yes—
137C23D4×D28111yescharacteristic
138C23Q8×D28111yescharacteristic
139C2×C4—24no—
140C2×C4—22no—
141C2×C4—44no—
142C2×C4—42no—
143C2×C4—2812no—
144C2×C4—2812no—
145C2×C4—2814no—
146C2×C4—2814no—
147C2×C4—2811no—
148C2×C4—2811no—
149C2×C4—2812no—
150C2×C4—2812no—
151C2×C4—2812no—
152C2×C4—2814no—
153C2×C4—2814no—
154C2×C4—5624no—
155C2×C4—5622no—
156C2×C4—11244no—
157C2×C4—11242no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22C42×D28111yescharacteristic
164C22C22⋊C4×D28112yes—
165C22C22⋊C4×D28111yescharacteristic
166C22C4⋊C4×D28111yescharacteristic
167C22C4⋊C4×D28112yes—
168C4—44no—
169C4—42no—
170C4—2812no—
171C4—2814no—
172C4—2812no—
173C4—11244no—
174C4—11242no—
175C2—22no—
176C2—21no—
177C2—21no—
178C2—22no—
179C2#95×D28111yescharacteristic
180C2#3182343512yes—
subgroupG/H
centerC22C22⋊C4×D281
commutatorC22×C281C2×C42
FrattiniC24C22×D281
Fitting#342×C281C2
socleC22×C281C2×C22⋊C4
prime radical, cosocleC24×C281C23
hypercenter#342D281
hypocenterC281#1740
LCSG ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
10. #22582835C4semidirect
12. C2×#17985117C4semidirect
16. C2×C4×Dic281C4semidirect
90. C281#1740semidirect

Maximal subgroups

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

subgroupindex
C2×#225828352
#318232302
#318232292
#342×C2812
#1740281