Finite Group Databasebeta

← #49094935

Subgroups — #49094935

Order 35968.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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#31823859C211yesmaximal, characteristic
2#31823859C211yesmaximal, characteristic
3#31823842C211yesmaximal, characteristic
4#31823814C211yesmaximal, characteristic
5#31823813C211yesmaximal, characteristic
6#31823185C211yesmaximal, characteristic
7#498×C281C211yesmaximal, characteristic
8C2×#17985128—22no—
9#22582879C2211yescharacteristic
10#22582879C2211yescharacteristic
11#22582810—22no—
12#22582810—22no—
13#22582804—22no—
14#22582803—22no—
15C4×#14555886C2211yescharacteristic
16C4×#14555886C2211yescharacteristic
17C4⋊Q8×C281C2211yescharacteristic
18C4⋊Q8×C281C2211yescharacteristic
19#106×C281—22no—
20C4×C8×C281C2211yescharacteristic
21C2×Dic562—21no—
22C2×Dic562—21no—
23#17985128—44no—
24C2×#14555886D412yes—
25C2×#14555886D412yes—
26C4⋊Dic281—21no—
27C4⋊Dic281—21no—
28C4⋊Dic281—21no—
29C4⋊Dic281—21no—
30C2×Q8×C281—21no—
31C2×Q8×C281—21no—
32C2×C8×C281D412yes—
33C4⋊C4×C281—21no—
34C4⋊C4×C281—21no—
35C4⋊C4×C281—21no—
36C4⋊C4×C281—21no—
37C42×C281C2311yescharacteristic
38Dic562—42no—
39Dic562—42no—
40C2×Dic281—41no—
41C2×Dic281—41no—
42#14555886—22no—
43#14555886SD1614yes—
44Q8×C281—42no—
45Q8×C281—42no—
46C2×C4×C281—41no—
47C2×C4×C281—41no—
48C2×C4×C281C2×D411yescharacteristic
49C2×C4×C281C2×D411yescharacteristic
50C2×C4×C281C2×D411yescharacteristic
51C8×C281—22no—
52C22×C281#12711yescharacteristic
53C4×C281—81no—
54C4×C281—81no—
55C4×C281C2×SD1612yes—
56C4×C281#13712yes—
57C4×C281#13712yes—
58Dic281—81no—
59Dic281—81no—
60C2×C281#49211yescharacteristic
61C2×C281#49711yescharacteristic
62C2×C281#49711yescharacteristic
63C281#171611yescharacteristic, complemented, Sylow
64#1716—2811nomaximal, Sylow
65#498—2811no—
66#498—2811no—
67#498D28111yescharacteristic
68#494—2811no—
69#487—2811no—
70#487—2811no—
71#322—2811no—
72C2×Q16—5622no—
73C4⋊Q8—2811no—
74C4⋊Q8—2811no—
75C4⋊Q8C2×D28111yescharacteristic
76C4⋊Q8C2×D28111yescharacteristic
77#106—22no—
78#106—5622no—
79#106—5622no—
80#103—5622no—
81#103—5622no—
82C4×C8—2811no—
83C4×C8—2811no—
84C4×C8C2×D28111yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—5621no—
88C2×Q8—5621no—
89Q16—11244no—
90C2×C8—2812no—
91C2×C8—2812no—
92C2×C8C22⋊D28112yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—5621no—
98C4⋊C4—5621no—
99C4⋊C4—5621no—
100C4⋊C4—5621no—
101C42C22×D28111yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—11242no—
105Q8—11242no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—11241no—
109C2×C4—11241no—
110C2×C4D4×D28111yescharacteristic
111C2×C4D4×D28111yescharacteristic
112C2×C4C2×C22⋊D28111yescharacteristic
113C8—22no—
114C8—2814no—
115C8—5622no—
116C22#2258287511yescharacteristic
117C4—81no—
118C4—81no—
119C4—22481no—
120C4—22481no—
121C4SD16×D28112yes—
122C4#2258290812yes—
123C4#2258291012yes—
124C2#3182383411yescharacteristic
125C2#3182385411yescharacteristic
126C2#3182385511yescharacteristic
subgroupG/H
centerC22#22582875
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#498×C281C2
socle, prime radicalC22×C281#127
hypercenter#498D281
hypocenterC281#1716
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
63. C281#1716semidirect

Maximal subgroups

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

subgroupindex
#318238592
#318238422
#318238142
#318238132
#318231852
#498×C2812
#1716281