Finite Group Databasebeta

← #49094276

Subgroups — #49094276

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#31823619C212yesmaximal
3#31823199C212yesmaximal
4#31823189C211yesmaximal, characteristic
5#395×C281C211yesmaximal, characteristic
6C2×#17985128—22no—
7#22582878—22no—
8#22582870—22no—
9#22582858—21no—
10#22582858C2212yes—
11#22582838—21no—
12#22582803—22no—
13C22⋊#14555886C2212yes—
14C22×Q8×C281C2211yescharacteristic
15C2×C4⋊C4×C281—21no—
16C2×C4⋊C4×C281C2211yescharacteristic
17#95×C281—21no—
18#95×C281C2211yescharacteristic
19C2×Dic562—21no—
20C2×Dic562D412yes—
21#17985128—44no—
22C2×#14555886—22no—
23C4⋊Dic281—21no—
24C4⋊Dic281—21no—
25C4⋊Dic281—21no—
26C4⋊Dic281D412yes—
27#17985117—22no—
28#17985117—22no—
29C22⋊Dic281—22no—
30C4×Dic281—22no—
31C2×Q8×C281—22no—
32C2×Q8×C281—42no—
33C22×C4×C281—21no—
34C22×C4×C281—21no—
35C22×C4×C281D411yescharacteristic
36C22×C4×C281D411yescharacteristic
37C22×C4×C281C2311yescharacteristic
38C4⋊C4×C281—22no—
39C4⋊C4×C281—42no—
40Dic562—42no—
41Dic562—81no—
42C2×Dic281—22no—
43C2×Dic281—22no—
44#14555886—42no—
45C23×C281C2×D411yescharacteristic
46Q8×C281—24no—
47Q8×C281—42no—
48C2×C4×C281—21no—
49C2×C4×C281—21no—
50C2×C4×C281—22no—
51C2×C4×C281—22no—
52C2×C4×C281—21no—
53C2×C4×C281—41no—
54C2×C4×C281—41no—
55C2×C4×C281—41no—
56C2×C4×C281—41no—
57C2×C4×C281—41no—
58C2×C4×C281—41no—
59C2×C4×C281Q1612yescomplemented
60C2×C4×C281C2×D412yes—
61C22×C281—21no—
62C22×C281—21no—
63C22×C281#12011yescharacteristic
64C22×C281C2×Q1611yescharacteristic
65C22×C281#13711yescharacteristic
66C4×C281—22no—
67C4×C281—22no—
68C4×C281—42no—
69C4×C281—42no—
70C4×C281—41no—
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#395D28111yescharacteristic
83#328—2812no—
84#324—2811no—
85C22×Q8C2×D28111yescharacteristic
86C2×Q16—5622no—
87C4⋊Q8—5622no—
88#125—5622no—
89C22⋊Q8—2812no—
90C22⋊Q8—5621no—
91#117—5621no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4C2×D28111yescharacteristic
94#103—5622no—
95C22⋊C8—2812no—
96#95—21no—
97#95C2×D28111yescharacteristic
98C2×Q8—22no—
99C2×Q8—42no—
100C2×Q8—2812no—
101C2×Q8—5621no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4C22⋊D28111yescharacteristic
105C22×C4C22⋊D28111yescharacteristic
106C22×C4C22×D28111yescharacteristic
107Q16—11244no—
108C2×C8—5622no—
109C4⋊C4—22no—
110C4⋊C4—42no—
111C4⋊C4—2812no—
112C4⋊C4—5622no—
113C4⋊C4—5621no—
114C4⋊C4—5621no—
115C4⋊C4—5621no—
116C4⋊C4—5622no—
117C22⋊C4—5622no—
118C42—5622no—
119C23C2×C22⋊D28111yescharacteristic
120Q8—24no—
121Q8—42no—
122Q8—11242no—
123Q8—22481no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—5622no—
136C2×C4—5622no—
137C2×C4#1798512812yescomplemented
138C2×C4D4×D28112yes—
139C8—11242no—
140C22—21no—
141C22—21no—
142C22#2258284711yescharacteristic
143C22C2×#1798512811yescharacteristic
144C22#2258290911yescharacteristic
145C4—22no—
146C4—22no—
147C4—42no—
148C4—42no—
149C4—41no—
150C4—11242no—
151C4—11242no—
152C2—21no—
153C2—21no—
154C2#3182361811yescharacteristic
155C2#3182364511yescharacteristic
156C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#395×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
hypercenter#395D281
hypocenterC281#1605
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
59. C2×C4×C281Q16semidirect
78. C281#1605semidirect
137. C2×C4#17985128semidirect

Maximal subgroups

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

subgroupindex
#318240942
#318236192
#318231992
#318231892
#395×C2812
#1605281