Finite Group Databasebeta

← #49094279

Subgroups — #49094279

Order 35968.

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

normal subgroups only

This group has 238 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#31824094C211yesmaximal, characteristic
2#31823621C212yesmaximal
3#31823383C211yesmaximal, characteristic
4#31823201C212yesmaximal
5#324×C281C211yesmaximal, characteristic
6C22×Dic562C2211yescharacteristic
7C2×Dic1124—22no—
8#22582878—22no—
9#22582870—22no—
10#22582858—21no—
11#22582858C2212yes—
12#22582838—21no—
13C2×#17985117—21no—
14#22582804—22no—
15#22582786—21no—
16#22582786C2211yescharacteristic
17C2×C4⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C2×Dic562—21no—
20C2×Dic562—22no—
21C2×Dic562—42no—
22C2×Dic562D412yes—
23C22×Dic281—21no—
24C22×Dic281—21no—
25Dic1124—44no—
26C4⋊Dic281—21no—
27C4⋊Dic281—21no—
28C4⋊Dic281—21no—
29C4⋊Dic281D412yes—
30#17985117—22no—
31#17985117—22no—
32#17985117—42no—
33C22⋊Dic281—22no—
34C4×Dic281—22no—
35C22×C4×C281D411yescharacteristic
36C22×C4×C281D411yescharacteristic
37C22×C4×C281C2311yescharacteristic
38C2×C8×C281—22no—
39C4⋊C4×C281—22no—
40Dic562—24no—
41Dic562—42no—
42Dic562—42no—
43Dic562—81no—
44C2×Dic281—22no—
45C2×Dic281—22no—
46C2×Dic281—22no—
47C2×Dic281—22no—
48C2×Dic281—41no—
49C2×Dic281—41no—
50C2×Dic281—41no—
51C2×Dic281—41no—
52C23×C281C2×D411yescharacteristic
53C2×C4×C281—21no—
54C2×C4×C281—21no—
55C2×C4×C281—21no—
56C2×C4×C281—41no—
57C2×C4×C281—41no—
58C2×C4×C281Q1612yescomplemented
59C2×C4×C281C2×D412yes—
60C8×C281—42no—
61C22×C281—21no—
62C22×C281—21no—
63C22×C281#12011yescharacteristic
64C22×C281C2×Q1611yescharacteristic
65C22×C281#13711yescharacteristic
66C4×C281—22no—
67C4×C281—22no—
68C4×C281—41no—
69Dic281—42no—
70Dic281—42no—
71Dic281—42no—
72Dic281—42no—
73C2×C281—21no—
74C2×C281—21no—
75C2×C281#45111yescharacteristic
76C2×C281#45611yescharacteristic
77C2×C281B(4,𝔽2)11yescharacteristic
78C281#160511yescharacteristic, complemented, Sylow
79#1605—2811nomaximal, Sylow
80#544—2811no—
81#451—2812no—
82#395—2811no—
83#328—2812no—
84#324D28111yescharacteristic
85C22×Q8—2811no—
86C2×Q16—5622no—
87C4⋊Q8—5622no—
88#125—5622no—
89C22⋊Q8—2812no—
90C22⋊Q8—5621no—
91#117—5621no—
92C2×C4⋊C4—5621no—
93C2×C4⋊C4C2×D28111yescharacteristic
94#103—5622no—
95C22⋊C8C2×D28112yes—
96#95—2811no—
97#95—5621no—
98C2×Q8—2812no—
99C2×Q8—5621no—
100C2×Q8—5622no—
101C2×Q8—11242no—
102C22×C4—5621no—
103C22×C4—5621no—
104C22×C4D112411yescharacteristic
105C22×C4D112411yescharacteristic
106C22×C4C22×D28111yescharacteristic
107Q16—11244no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—2812no—
111C4⋊C4—5622no—
112C4⋊C4—5621no—
113C4⋊C4—5621no—
114C4⋊C4—5621no—
115C4⋊C4—5622no—
116C4⋊C4—11242no—
117C22⋊C4—5622no—
118C42—5622no—
119C23C2×D112411yescharacteristic
120Q8—5624no—
121Q8—11242no—
122Q8—11242no—
123Q8—22481no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—5622no—
130C2×C4—5622no—
131C2×C4—5622no—
132C2×C4—5622no—
133C2×C4—11241no—
134C2×C4—11241no—
135C2×C4—11241no—
136C2×C4—11241no—
137C2×C4Dic112412yescomplemented
138C2×C4D4×D28112yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#2258284911yescharacteristic
143C22C2×Dic112411yescharacteristic
144C22#2258291211yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—11242no—
149C4—11242no—
150C4—11242no—
151C4—11242no—
152C2—21no—
153C2—21no—
154C2#3182362111yescharacteristic
155C2#3182364811yescharacteristic
156C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
hypercenter#324D281
hypocenterC281#1605
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
58. C2×C4×C281Q16semidirect
78. C281#1605semidirect
137. C2×C4Dic1124semidirect

Maximal subgroups

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

subgroupindex
#318240942
#318236212
#318233832
#318232012
#324×C2812
#1605281