Finite Group Databasebeta

← #49094313

Subgroups — #49094313

Order 35968.

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

normal subgroups only

This group has 210 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#31823794C212yesmaximal
3#31823393C211yesmaximal, characteristic
4#31823201C212yesmaximal
5#324×C281C211yesmaximal, characteristic
6#22582878—22no—
7#22582870—22no—
8#22582858—21no—
9#22582858C2212yes—
10#22582838—21no—
11C2×C4⋊Dic281C2211yescharacteristic
12C2×#17985117—21no—
13#22582811—22no—
14#22582804—22no—
15#22582786—21no—
16#22582786C2211yescharacteristic
17C2×C4⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C2×Dic562—21no—
20C2×Dic562D412yes—
21C22×Dic281—21no—
22C22×Dic281—21no—
23C4⋊Dic281—21no—
24C4⋊Dic281—21no—
25C4⋊Dic281—21no—
26C4⋊Dic281—22no—
27C4⋊Dic281D412yes—
28#17985117—22no—
29#17985117—22no—
30#17985117—42no—
31C22⋊Dic281—22no—
32C4×Dic281—22no—
33C22×C4×C281D411yescharacteristic
34C22×C4×C281D411yescharacteristic
35C22×C4×C281C2311yescharacteristic
36C2×C8×C281—22no—
37C4⋊C4×C281—22no—
38Dic562—42no—
39Dic562—81no—
40C2×Dic281—22no—
41C2×Dic281—22no—
42C2×Dic281—22no—
43C2×Dic281—41no—
44C2×Dic281—41no—
45C2×Dic281—41no—
46C2×Dic281—41no—
47C2×Dic281—41no—
48C23×C281C2×D411yescharacteristic
49C2×C4×C281—21no—
50C2×C4×C281—21no—
51C2×C4×C281—21no—
52C2×C4×C281—41no—
53C2×C4×C281—41no—
54C2×C4×C281SD1612yes—
55C2×C4×C281C2×D412yes—
56C8×C281—42no—
57C22×C281—21no—
58C22×C281—21no—
59C22×C281#12011yescharacteristic
60C22×C281C2×SD1611yescharacteristic
61C22×C281#13711yescharacteristic
62C4×C281—22no—
63C4×C281—22no—
64C4×C281—41no—
65Dic281—42no—
66Dic281—42no—
67Dic281—42no—
68Dic281—81no—
69C2×C281—21no—
70C2×C281—21no—
71C2×C281#44811yescharacteristic
72C2×C281#45611yescharacteristic
73C2×C281#45811yescharacteristic
74C281#161111yescharacteristic, complemented, Sylow
75#1611—2811nomaximal, Sylow
76#544—2811no—
77#483—2812no—
78#398—2811no—
79#328—2812no—
80#324D28111yescharacteristic
81C4⋊Q8—5622no—
82#125—5622no—
83C22⋊Q8—2812no—
84C22⋊Q8—5621no—
85#117—5621no—
86C2×C4⋊C4—2811no—
87C2×C4⋊C4—5621no—
88C2×C4⋊C4C2×D28111yescharacteristic
89#106—5622no—
90#103—5622no—
91C22⋊C8C2×D28112yes—
92#95—2811no—
93#95—5621no—
94C2×Q8—2812no—
95C2×Q8—5621no—
96C22×C4—5621no—
97C22×C4—5621no—
98C22×C4D112411yescharacteristic
99C22×C4D112411yescharacteristic
100C22×C4C22×D28111yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—2812no—
104C4⋊C4—5622no—
105C4⋊C4—5621no—
106C4⋊C4—5621no—
107C4⋊C4—5621no—
108C4⋊C4—5622no—
109C4⋊C4—5622no—
110C4⋊C4—11242no—
111C22⋊C4—5622no—
112C42—5622no—
113C23C2×D112411yescharacteristic
114Q8—11242no—
115Q8—22481no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—5622no—
122C2×C4—5622no—
123C2×C4—5622no—
124C2×C4—11241no—
125C2×C4—11241no—
126C2×C4—11241no—
127C2×C4—11241no—
128C2×C4—11241no—
129C2×C4#1798512712yes—
130C2×C4D4×D28112yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#2258284911yescharacteristic
135C22C2×#1798512711yescharacteristic
136C22#2258291211yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—11242no—
141C4—11242no—
142C4—11242no—
143C4—22481no—
144C2—21no—
145C2—21no—
146C2#3182360411yescharacteristic
147C2#3182364811yescharacteristic
148C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
hypercenter#324D281
hypocenterC281#1611
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
74. C281#1611semidirect

Maximal subgroups

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

subgroupindex
#318240942
#318237942
#318233932
#318232012
#324×C2812
#1611281