Finite Group Databasebeta

← #44509468

Subgroups — #44509468

Order 30848.

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

normal subgroups only

This group has 216 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#29508467C211yesmaximal, characteristic, complemented
2#29507902C212yesmaximal, complemented
3#29507889C211yesmaximal, characteristic
4#29507515C212yesmaximal, complemented
5#355×C241C211yesmaximal, characteristic, complemented
6#21440690C2211yescharacteristic
7#21440675—22no—
8#21440668—21no—
9#21440640C2212yes—
10#21440635—22no—
11#21440634—21no—
12#21440623—21no—
13#21440619—22no—
14#21440570—21no—
15#21440568—22no—
16#21440561C2211yescharacteristic
17#124×C241C2211yescharacteristic
18#101×C241C2212yes—
19#16838771—41no—
20#16838770—22no—
21#16838770—21no—
22C2×Dic482D412yes—
23Q8×D241—41no—
24C22×Dic241—21no—
25Dic964—42no—
26#16838759—42no—
27#16838758—41no—
28#16838755—41no—
29#16838754—21no—
30C4⋊Dic241—21no—
31C4⋊Dic241—21no—
32#16838749—22no—
33#16838749—22no—
34#16838749—22no—
35C22⋊Dic241—22no—
36C22⋊Dic241—21no—
37C4×Dic241D412yes—
38C2×Q8×C241C2311yescharacteristic
39C2×D4×C241D411yescharacteristic
40M16×C241—22no—
41C22⋊C4×C241—22no—
42C42×C241D411yescharacteristic
43Dic482—21no—
44Dic482—22no—
45Dic482—42no—
46D964—21no—
47D964—22no—
48C22⋊D241—41no—
49C2×Dic241—22no—
50C2×Dic241—22no—
51C2×Dic241—81no—
52C4×D241—42no—
53C4×D241—41no—
54#14515349—41no—
55C23×C241—21no—
56Q8×C241—41no—
57D4×C241—41no—
58C2×C4×C241—21no—
59C2×C4×C241C2×D412yes—
60C2×C4×C241C2×D411yescharacteristic
61C8×C241—42no—
62C22×C241—42no—
63C22×C241—41no—
64C22×C241#12011yescharacteristic
65C2×D241—41no—
66C4×C241—22no—
67C4×C241—21no—
68C4×C241—41no—
69Dic241—42no—
70Dic241—41no—
71Dic241—42no—
72C2×C241—21no—
73C2×C241—81no—
74C2×C241B(4,𝔽2)11yescharacteristic
75D241—81no—
76C241#220311yescharacteristic, complemented, Sylow
77#2203—2411nomaximal, Sylow
78#563—2411no—
79#456—2412no—
80#454—2411no—
81#356—2412no—
82#355D24111yescharacteristic, complemented
832−1+4—2411no—
84#137—4822no—
85AGL(1,ℤ/8)—4821no—
86C4⋊Q8—2412no—
87#126—4822no—
88#125—4821no—
89#124C2×D24111yescharacteristic
90#123—4821no—
91C22⋊Q8—4822no—
92#104—4822no—
93#104—4821no—
94#101—2411no—
95#101C2×D24112yes—
96#41—9641no—
97#41—4822no—
98#41—4821no—
99C2×Q8—9641no—
100C2×Q8—2412no—
101C2×Q8C22×D24111yescharacteristic
102C2×D4D96411yescharacteristic
103C22×C4—4821no—
104Q16—9642no—
105SD16—9642no—
106SD16—9641no—
107D8—9641no—
108M16—22no—
109M16—4821no—
110C4⋊C4—4822no—
111C4⋊C4—4821no—
112C4⋊C4—4821no—
113C4⋊C4—4822no—
114C4⋊C4—4822no—
115C22⋊C4—22no—
116C22⋊C4—4822no—
117C22⋊C4—4821no—
118C42—2412no—
119C42D96411yescharacteristic
120C23—21no—
121Q8—41no—
122Q8—9642no—
123Q8—4821no—
124Q8—4822no—
125D4—41no—
126D4—9641no—
127D4—4821no—
128D4—4822no—
129C2×C4—21no—
130C2×C4—19281no—
131C2×C4—9642no—
132C2×C4—9641no—
133C2×C4—4822no—
134C2×C4—4822no—
135C2×C4D4×D24112yes—
136C2×C4C2×D96411yescharacteristic
137C8—42no—
138C8—9641no—
139C22—42no—
140C22—41no—
141C22—9641no—
142C22#2144061211yescharacteristic
143C4—22no—
144C4—21no—
145C4—41no—
146C4—9642no—
147C4—9642no—
148C4—9641no—
149C2—21no—
150C2—81no—
151C2—19281no—
152C2#2950790511yescharacteristic
subgroupG/H
centerC2#29507905
commutator, cosocleC2×Q8×C241C23
FrattiniC2×Q8C22×D241
Fitting#355×C241C2
socleC2×C241B(4,𝔽2)
prime radical#29507889C2
hypercenter#355D241
hypocenterC241#2203
LCSG ▷ C2×Q8×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #29508467C2semidirect
2. #29507902C2semidirect
4. #29507515C2semidirect
5. #355×C241C2semidirect
76. C241#2203semidirect
82. #355D241semidirect

Maximal subgroups

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

subgroupindex
#295084672
#295079022
#295078892
#295075152
#355×C2412
#2203241