Finite Group Databasebeta

← #49097334

Subgroups — #49097334

Order 35968.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#31824193C211yesmaximal, characteristic, complemented
2#31823648C212yesmaximal
3#31823645C211yesmaximal, characteristic
4#31823261C212yesmaximal, complemented
5#356×C281C211yesmaximal, characteristic, complemented
6#22582927C2211yescharacteristic
7#22582912—22no—
8#22582910—21no—
9#22582878—22no—
10#22582877—21no—
11#22582877C2212yes—
12C4×Dic562—21no—
13#22582844—22no—
14#22582807—21no—
15#22582805—22no—
16#22582798C2211yescharacteristic
17C4⋊Q8×C281C2211yescharacteristic
18#101×C281C2212yes—
19#17985139—41no—
20#17985138—22no—
21#17985138—21no—
22C2×Dic562—21no—
23C2×Dic562—21no—
24C2×Dic562D412yes—
25Q8×D281—41no—
26Dic1124—42no—
27#17985128—41no—
28#17985127—42no—
29#17985125—41no—
30#17985122—21no—
31C4⋊Dic281—21no—
32#17985117—22no—
33#17985117—22no—
34#17985117—22no—
35C4×Dic281—21no—
36C4×Dic281—22no—
37C4×Dic281D412yes—
38C2×Q8×C281D411yescharacteristic
39C2×Q8×C281C2311yescharacteristic
40M16×C281—22no—
41C4⋊C4×C281—22no—
42C42×C281D411yescharacteristic
43Dic562—24no—
44Dic562—21no—
45Dic562—22no—
46Dic562—42no—
47Dic562—81no—
48D1124—21no—
49D1124—22no—
50C22⋊D281—41no—
51C2×Dic281—22no—
52C2×Dic281—22no—
53C4×D281—42no—
54C4×D281—41no—
55#14555886—41no—
56Q8×C281—41no—
57Q8×C281—41no—
58C2×C4×C281—21no—
59C2×C4×C281—21no—
60C2×C4×C281C2×D412yes—
61C2×C4×C281C2×D411yescharacteristic
62C8×C281—42no—
63C22×C281#12011yescharacteristic
64C2×D281—41no—
65C4×C281—22no—
66C4×C281—22no—
67C4×C281—21no—
68C4×C281—41no—
69Dic281—24no—
70Dic281—41no—
71Dic281—42no—
72C2×C281—21no—
73C2×C281B(4,𝔽2)11yescharacteristic
74D281—81no—
75C281#220511yescharacteristic, complemented, Sylow
76#2205—2811nomaximal, Sylow
77Q82—2811no—
78#456—2811no—
79#456—2812no—
80#356—2812no—
81#356D28111yescharacteristic, complemented
822−1+4—2811no—
83#137—5622no—
84#137—5621no—
85C4⋊Q8—2812no—
86C4⋊Q8—5622no—
87C4⋊Q8—5621no—
88C4⋊Q8C2×D28111yescharacteristic
89C4×Q8—5622no—
90C4×Q8—5621no—
91#104—5622no—
92#104—5621no—
93#101—2811no—
94#101C2×D28112yes—
95#41—5622no—
96#41—5621no—
97#41—11241no—
98C2×Q8—2812no—
99C2×Q8—5621no—
100C2×Q8—5621no—
101C2×Q8—11241no—
102C2×Q8D112411yescharacteristic
103C2×Q8C22×D28111yescharacteristic
104Q16—11242no—
105Q16—11241no—
106SD16—11242no—
107SD16—11241no—
108M16—22no—
109M16—5621no—
110C4⋊C4—22no—
111C4⋊C4—5622no—
112C4⋊C4—5621no—
113C4⋊C4—5622no—
114C4⋊C4—5622no—
115C42—2812no—
116C42—5622no—
117C42—5621no—
118C42D112411yescharacteristic
119Q8—41no—
120Q8—41no—
121Q8—5624no—
122Q8—5622no—
123Q8—5621no—
124Q8—11242no—
125Q8—22481no—
126D4—5622no—
127D4—5621no—
128D4—11241no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—5622no—
132C2×C4—5622no—
133C2×C4—11242no—
134C2×C4—11241no—
135C2×C4D4×D28112yes—
136C2×C4C2×D112411yescharacteristic
137C8—42no—
138C8—11241no—
139C22—11241no—
140C22#2258284911yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—5624no—
146C4—11242no—
147C4—11241no—
148C2—21no—
149C2—22481no—
150C2#3182365111yescharacteristic
subgroupG/H
centerC2#31823651
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting#356×C281C2
socleC2×C281B(4,𝔽2)
prime radical#22582927C22
hypercenter#356D281
hypocenterC281#2205
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #31824193C2semidirect
4. #31823261C2semidirect
5. #356×C281C2semidirect
75. C281#2205semidirect
81. #356D281semidirect

Maximal subgroups

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

subgroupindex
#318241932
#318236482
#318236452
#318232612
#356×C2812
#2205281