Finite Group Databasebeta

← #1496×C263 #46778465

Subgroups — #1496×C263 #46778465

Order 33664.

246 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 92 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#532×C263C211yesmaximal, characteristic
2#432×C263C211yesmaximal, characteristic, complemented
3#431×C263C211yesmaximal, characteristic, complemented
4D4⋊C8×C263C214yesmaximal, complemented
5C2×#41×C263—21no—
6C4⋊Q8×C263C411yescharacteristic
7#127×C263C411yescharacteristic
8#124×C263—21no—
9#121×C263—21no—
10#121×C263C412yes—
11C4×D4×C263—21no—
12C4×D4×C263C2212yes—
13C2×C42×C263C2211yescharacteristic
14C4⋊C8×C263—21no—
15C4⋊C8×C263C2212yes—
16C22⋊C8×C263—21no—
17C22⋊C8×C263—21no—
18#97×C263—21no—
19C4×C8×C263C2212yes—
20#41×C263—44no—
21C2×Q8×C263—21no—
22C2×D4×C263—22no—
23C2×D4×C263—21no—
24C2×D4×C263—21no—
25C2×D4×C263C2×C412yes—
26C22×C4×C263—22no—
27C22×C4×C263C2×C411yescharacteristic
28C22×C4×C263D411yescharacteristic
29C22×C4×C263D411yescharacteristic
30C2×C8×C263—22no—
31C2×C8×C263—22no—
32C4⋊C4×C263—21no—
33C4⋊C4×C263C2×C412yes—
34C22⋊C4×C263—22no—
35C22⋊C4×C263—22no—
36C42×C263C2×C411yescharacteristic
37C42×C263D411yescharacteristic
38C42×C263D411yescharacteristic
39C42×C263C2311yescharacteristic
40C23×C263—22no—
41C23×C263C22⋊C411yescharacteristic
42Q8×C263—42no—
43D4×C263—24no—
44D4×C263—42no—
45D4×C263—42no—
46D4×C263—44no—
47C2×C4×C263—22no—
48C2×C4×C263—22no—
49C2×C4×C263—22no—
50C2×C4×C263—41no—
51C2×C4×C263—44no—
52C2×C4×C263C22⋊C411yescharacteristic
53C2×C4×C263C22⋊C411yescharacteristic
54C2×C4×C263C22⋊C411yescharacteristic
55C2×C4×C263C22×C411yescharacteristic
56C2×C4×C263C2×D411yescharacteristic
57C2×C4×C263C2×D411yescharacteristic
58C8×C263—42no—
59C8×C263—42no—
60C22×C263—21no—
61C22×C263—21no—
62C22×C263—21no—
63C22×C263—42no—
64C22×C263—42no—
65C22×C263—42no—
66C22×C263C2×C22⋊C411yescharacteristic
67C4×C263—21no—
68C4×C263—21no—
69C4×C263—21no—
70C4×C263—21no—
71C4×C263—42no—
72C4×C263#13112yes—
73C4×C263AGL(1,ℤ/8)12yes—
74C2×C263—41no—
75C2×C263—82no—
76C2×C263#40811yescharacteristic
77C2×C263#41811yescharacteristic
78C2×C263#42111yescharacteristic
79C263#149611yescharacteristic, direct product factor, Sylow
80#1496C26311yesmaximal, characteristic, direct product factor, Sylow
81#532C2×C26311yescharacteristic
82#432C2×C26311yescharacteristic, complemented
83#431C2×C26311yescharacteristic, complemented
84D4⋊C8C2×C26314yescomplemented
85C2×#41—21no—
86C4⋊Q8C4×C26311yescharacteristic
87#127C4×C26311yescharacteristic
88#124—21no—
89#121—21no—
90#121C4×C26312yes—
91C4×D4—21no—
92C4×D4C22×C26312yes—
93C2×C42C22×C26311yescharacteristic
94C4⋊C8—21no—
95C4⋊C8C22×C26312yes—
96C22⋊C8—21no—
97C22⋊C8—21no—
98#97—21no—
99C4×C8C22×C26312yes—
100#41—44no—
101C2×Q8—21no—
102C2×D4—22no—
103C2×D4—21no—
104C2×D4—21no—
105C2×D4C2×C4×C26312yes—
106C22×C4—22no—
107C22×C4C2×C4×C26311yescharacteristic
108C22×C4D4×C26311yescharacteristic
109C22×C4D4×C26311yescharacteristic
110C2×C8—22no—
111C2×C8—22no—
112C4⋊C4—21no—
113C4⋊C4C2×C4×C26312yes—
114C22⋊C4—22no—
115C22⋊C4—22no—
116C42C2×C4×C26311yescharacteristic
117C42D4×C26311yescharacteristic
118C42D4×C26311yescharacteristic
119C42C23×C26311yescharacteristic
120C23—22no—
121C23C22⋊C4×C26311yescharacteristic
122Q8—42no—
123D4—24no—
124D4—42no—
125D4—42no—
126D4—44no—
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—41no—
131C2×C4—44no—
132C2×C4C22⋊C4×C26311yescharacteristic
133C2×C4C22⋊C4×C26311yescharacteristic
134C2×C4C22⋊C4×C26311yescharacteristic
135C2×C4C22×C4×C26311yescharacteristic
136C2×C4C2×D4×C26311yescharacteristic
137C2×C4C2×D4×C26311yescharacteristic
138C8—42no—
139C8—42no—
140C22—21no—
141C22—21no—
142C22—21no—
143C22—42no—
144C22—42no—
145C22—42no—
146C22C2×C22⋊C4×C26311yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—21no—
151C4—42no—
152C4#131×C26312yes—
153C4AGL(1,ℤ/8)×C26312yes—
154C2—41no—
155C2—82no—
156C2#408×C26311yescharacteristic
157C2#418×C26311yescharacteristic
158C2#421×C26311yescharacteristic
subgroupG/H
centerC2×C4×C263C2×D4
commutatorC2×C4C22×C4×C263
Frattini, cosocleC42C23×C263
socleC22×C263C2×C22⋊C4
prime radical#532×C263C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C263 ◁ C2×C42×C263 ◁ G

Complements

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

NH ≅ G/Ntype
2. #432×C263C2semidirect
3. #431×C263C2semidirect
4. D4⋊C8×C263C2semidirect
79. C263#1496direct (N × H)
80. #1496C263direct (N × H)
82. #432C2×C263semidirect
83. #431C2×C263semidirect
84. D4⋊C8C2×C263semidirect

Maximal subgroups

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

subgroupindex
#532×C2632
#432×C2632
#431×C2632
D4⋊C8×C2632
#1496263