Finite Group Databasebeta

← #49097301

Subgroups — #49097301

Order 35968.

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

normal subgroups only

This group has 246 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#31824199C211yesmaximal, characteristic, complemented
2#31823654C212yesmaximal, complemented
3#31823630C211yesmaximal, characteristic
4#31823252C212yesmaximal, complemented
5#353×C281C211yesmaximal, characteristic, complemented
6#22582924C2211yescharacteristic
7#22582905—21no—
8#22582866—22no—
9#22582863—22no—
10#22582860—21no—
11#22582860C2212yes—
12C4×Dic562—21no—
13D4×Dic281—22no—
14#22582807—21no—
15#22582796C2211yescharacteristic
16#22582793—22no—
17#127×C281C2211yescharacteristic
18#99×C281C2212yes—
19#17985138—21no—
20#17985137—41no—
21C2×Dic562—21no—
22C2×C22⋊D281—22no—
23D4×D281—41no—
24C22×Dic281—21no—
25C22×Dic281D412yes—
26#17985126—41no—
27#17985123—41no—
28#17985122—21no—
29C4⋊Dic281—21no—
30C4⋊Dic281—42no—
31#17985117—22no—
32C22⋊Dic281—22no—
33C22⋊Dic281—21no—
34C22⋊Dic281—22no—
35C22⋊Dic281D412yes—
36#17985115—42no—
37C4×Dic281—22no—
38C2×D4×C281—22no—
39C2×D4×C281D411yescharacteristic
40C2×D4×C281C2311yescharacteristic
41C22⋊C4×C281—22no—
42C42×C281D411yescharacteristic
43C22×D281—22no—
44Dic562—21no—
45Dic562—42no—
46D1124—21no—
47C22⋊D281—42no—
48C22⋊D281—41no—
49C2×Dic281—22no—
50C2×Dic281—22no—
51C2×Dic281—22no—
52C2×Dic281—42no—
53C2×Dic281—81no—
54C4×D281—41no—
55#14555886—41no—
56C23×C281—21no—
57C23×C281C2×D412yes—
58D4×C281—41no—
59D4×C281—41no—
60D4×C281—44no—
61C2×C4×C281—21no—
62C2×C4×C281—42no—
63C2×C4×C281C2×D411yescharacteristic
64C22×C281—22no—
65C22×C281—42no—
66C22×C281—42no—
67C22×C281—41no—
68C22×C281#12011yescharacteristic
69C2×D281—41no—
70C2×D281—82no—
71C4×C281—22no—
72C4×C281—21no—
73C4×C281—82no—
74Dic281—42no—
75Dic281—41no—
76Dic281—42no—
77C2×C281—21no—
78C2×C281—42no—
79C2×C281—81no—
80C2×C281B(4,𝔽2)11yescharacteristic
81D281—81no—
82C281#219811yescharacteristic, complemented, Sylow
83#2198—2811nomaximal, Sylow
84#559—2811no—
85#458—2812no—
86#453—2811no—
87#353D28111yescharacteristic, complemented
88#352—2812no—
89H(5,𝔽2)—2811no—
90AGL(1,ℤ/8)—5621no—
91#127C2×D28111yescharacteristic
92#124—5622no—
93#123—2812no—
94#123—5622no—
95#123—5621no—
96C4×Q8—5621no—
97C4×D4—5622no—
98#104—5621no—
99#100—2811no—
100#99—5622no—
101#99C2×D28112yes—
102#41—5621no—
103#41—11241no—
104C2×Q8—5621no—
105C2×D4—22no—
106C2×D4—5622no—
107C2×D4—11241no—
108C2×D4D112411yescharacteristic
109C2×D4C22×D28111yescharacteristic
110C22×C4—2812no—
111C22×C4—5621no—
112SD16—11241no—
113D8—11241no—
114M16—5621no—
115C4⋊C4—5621no—
116C4⋊C4—5622no—
117C4⋊C4—11242no—
118C22⋊C4—22no—
119C22⋊C4—2812no—
120C22⋊C4—5622no—
121C22⋊C4—5621no—
122C22⋊C4—5622no—
123C22⋊C4—11242no—
124C42—5622no—
125C42D112411yescharacteristic
126C23—21no—
127C23—5622no—
128C23D4×D28112yes—
129Q8—5621no—
130Q8—11242no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—5621no—
135D4—11242no—
136D4—11241no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—5622no—
140C2×C4—5622no—
141C2×C4—5622no—
142C2×C4—11241no—
143C2×C4—11242no—
144C2×C4—22481no—
145C2×C4C2×D112411yescharacteristic
146C8—11241no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—11241no—
152C22—22482no—
153C22#2258284911yescharacteristic
154C4—22no—
155C4—21no—
156C4—82no—
157C4—11242no—
158C4—11241no—
159C4—11242no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—22481no—
164C2#3182365111yescharacteristic
subgroupG/H
centerC2#31823651
commutator, cosocleC2×D4×C281C23
FrattiniC2×D4C22×D281
Fitting#353×C281C2
socleC2×C281B(4,𝔽2)
prime radical#31823630C2
hypercenter#353D281
hypocenterC281#2198
LCSG ▷ C2×D4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
1. #31824199C2semidirect
2. #31823654C2semidirect
4. #31823252C2semidirect
5. #353×C281C2semidirect
82. C281#2198semidirect
87. #353D281semidirect

Maximal subgroups

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

subgroupindex
#318241992
#318236542
#318236302
#318232522
#353×C2812
#2198281