Finite Group Databasebeta

← #49093853

Subgroups — #49093853

Order 35968.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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#31824020C211yesmaximal, characteristic
2#31823520C211yesmaximal, characteristic
3#31823199C214yesmaximal
4#383×C281C211yesmaximal, characteristic
5#22582879C411yescharacteristic, complemented
6#22582879C411yescharacteristic, complemented
7#22582871—21no—
8#22582858—21no—
9#22582858C2212yes—
10C4×Dic562—21no—
11C4×Dic562C412yescomplemented
12#22582838—21no—
13C4⋊#14555886—21no—
14C22⋊#14555886C2212yes—
15#22582790—21no—
16C2×C42×C281C2211yescharacteristic
17#95×C281—21no—
18#95×C281—21no—
19#95×C281C2212yes—
20C2×Dic562—21no—
21C2×Dic562C2×C412yes—
22C2×#14555886—22no—
23C4⋊Dic281—21no—
24C4⋊Dic281—21no—
25C4⋊Dic281—21no—
26C4⋊Dic281C2×C412yes—
27#17985117—22no—
28#17985117—22no—
29C22⋊Dic281—22no—
30C4×Dic281—22no—
31C22×C4×C281—22no—
32C22×C4×C281D411yescharacteristic
33C22×C4×C281D411yescharacteristic
34C22×C4×C281C2311yescharacteristic
35C42×C281C2×C411yescharacteristic
36C42×C281C2×C411yescharacteristic
37C42×C281D411yescharacteristic
38C42×C281D411yescharacteristic
39Dic562—42no—
40Dic562—42no—
41C2×Dic281—22no—
42C2×Dic281—22no—
43#14555886—42no—
44C23×C281C2×D411yescharacteristic
45C2×C4×C281—22no—
46C2×C4×C281—41no—
47C2×C4×C281—41no—
48C2×C4×C281—42no—
49C2×C4×C281—42no—
50C2×C4×C281—42no—
51C2×C4×C281C22⋊C411yescharacteristic
52C2×C4×C281C22⋊C411yescharacteristic
53C2×C4×C281C22⋊C411yescharacteristic
54C2×C4×C281C22⋊C411yescharacteristic
55C2×C4×C281C22×C411yescharacteristic
56C2×C4×C281C2×D411yescharacteristic
57C22×C281—21no—
58C22×C281—21no—
59C22×C281C2×C22⋊C411yescharacteristic
60C22×C281#13712yes—
61C4×C281—21no—
62C4×C281—21no—
63C4×C281—21no—
64C4×C281—21no—
65C4×C281—21no—
66C4×C281—21no—
67C4×C281—82no—
68Dic281—42no—
69Dic281—42no—
70C2×C281—22no—
71C2×C281#41011yescharacteristic
72C2×C281#41911yescharacteristic
73C2×C281#42111yescharacteristic
74C281#151511yescharacteristic, complemented, Sylow
75#1515—2811nomaximal, Sylow
76#533—2811no—
77#432—2811no—
78#383D28111yescharacteristic
79#328—2814no—
80C4⋊Q8—2811no—
81C4⋊Q8—2811no—
82#125—5621no—
83C22⋊Q8—2812no—
84C22⋊Q8—5621no—
85C4×Q8—2812no—
86C4×Q8—5621no—
87#117—5621no—
88C2×C42C2×D28111yescharacteristic
89C4⋊C8—5621no—
90C22⋊C8—2812no—
91#97—5621no—
92#95—21no—
93#95—21no—
94#95C2×D28112yes—
95C2×Q8—2812no—
96C2×Q8—5621no—
97C22×C4—22no—
98C22×C4C22⋊D28111yescharacteristic
99C22×C4C22⋊D28111yescharacteristic
100C22×C4C22×D28111yescharacteristic
101C2×C8—5622no—
102C4⋊C4—2812no—
103C4⋊C4—5622no—
104C4⋊C4—5621no—
105C4⋊C4—5621no—
106C4⋊C4—5621no—
107C4⋊C4—5622no—
108C22⋊C4—5622no—
109C42—5622no—
110C42C4×D28111yescharacteristic
111C42C4×D28111yescharacteristic
112C42D112411yescharacteristic
113C42D112411yescharacteristic
114C23C2×C22⋊D28111yescharacteristic
115Q8—11242no—
116Q8—11242no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4—5622no—
124C2×C4—5622no—
125C2×C4#1798511511yescharacteristic
126C2×C4#1798511511yescharacteristic
127C2×C4#1798511511yescharacteristic
128C2×C4#1798511511yescharacteristic
129C2×C4C2×C4×D28111yescharacteristic
130C2×C4C2×D112411yescharacteristic
131C8—11242no—
132C22—21no—
133C22—21no—
134C22C2×#1798511511yescharacteristic
135C22#2258290912yes—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—82no—
143C4—11242no—
144C4—11242no—
145C2—22no—
146C2#3182343611yescharacteristic
147C2#3182347111yescharacteristic
148C2#3182348111yescharacteristic
subgroupG/H
centerC22C2×#17985115
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#383×C281C2
socleC22×C281C2×C22⋊C4
prime radicalC23×C281C2×D4
cosocleC22×C4×C281C23
hypercenter#383D281
hypocenterC281#1515
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
5. #22582879C4semidirect
6. #22582879C4semidirect
11. C4×Dic562C4semidirect
74. C281#1515semidirect

Maximal subgroups

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

subgroupindex
#318240202
#318235202
#318231992
#383×C2812
#1515281