Finite Group Databasebeta

← #44509408

Subgroups — #44509408

Order 30848.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#29508530C211yesmaximal, characteristic, complemented
2#29508153C211yesmaximal, characteristic, complemented
3#29507984C211yesmaximal, characteristic, complemented
4#29507533C211yesmaximal, characteristic, complemented
5#29507525C211yesmaximal, characteristic, complemented
6#29507500C211yesmaximal, characteristic, complemented
7C2×SD32×C241C211yesmaximal, characteristic, complemented
8#21440690—21no—
9#21440674—22no—
10#21440673—21no—
11#21440668—21no—
12#21440665—21no—
13#21440664C2211yescharacteristic
14Q16×D241—21no—
15#21440648C2211yescharacteristic
16#21440586—21no—
17#21440583—21no—
18#21440582C2211yescharacteristic
19#21440578C2211yescharacteristic
20#21440559—21no—
21C2×Q16×C241C2211yescharacteristic
22C2×D8×C241C2211yescharacteristic
23SD32×C241—22no—
24C2×C16×C241C2211yescharacteristic
25#16838771—22no—
26#16838771—41no—
27#16838770—21no—
28#16838770—42no—
29#16838770D411yescharacteristic
30Q8×D241—22no—
31Q8×D241—41no—
32Dic964D411yescharacteristic
33#16838760—22no—
34#16838759—21no—
35#16838758—41no—
36#16838757—22no—
37D1928D411yescharacteristic
38#16838755—41no—
39#16838754—21no—
40#16838754D411yescharacteristic
41#16838753—21no—
42C8×D241—21no—
43#16838745—21no—
44C2×Q8×C241—21no—
45C2×D4×C241—21no—
46Q16×C241—21no—
47Q16×C241D412yes—
48D8×C241—21no—
49D8×C241—21no—
50C2×C8×C241C2311yescharacteristic
51C16×C241—21no—
52Dic482—21no—
53Dic482—42no—
54Dic482D811yescharacteristic
55D964—21no—
56D964—42no—
57D964D811yescharacteristic
58C22⋊D241—21no—
59C22⋊D241—41no—
60C4×D241—21no—
61C4×D241—42no—
62C4×D241—42no—
63C4×D241—41no—
64#14515349—21no—
65#14515349—41no—
66C23×C241—41no—
67Q8×C241—22no—
68Q8×C241—41no—
69D4×C241—41no—
70D4×C241—41no—
71C2×C4×C241—41no—
72C2×C4×C241C2×D411yescharacteristic
73C8×C241C2×D411yescharacteristic
74C8×C241C2×D411yescharacteristic
75C22×C241—81no—
76C22×C241—161no—
77C22×C241AGL(1,ℤ/8)11yescharacteristic
78C2×D241—21no—
79C2×D241—41no—
80C4×C241—42no—
81C4×C241#12011yescharacteristic
82C4×C241C2×D811yescharacteristic
83Dic241—21no—
84Dic241—41no—
85C2×C241—21no—
86C2×C241—161no—
87C2×C241#44711yescharacteristic
88D241—41no—
89D241—81no—
90C241#219311yescharacteristic, complemented, Sylow
91#2193—2411nomaximal, Sylow
92#578—2411no—
93#509—2411no—
94C2×SD32D24111yescharacteristic, complemented
95#472—2411no—
96#362—2411no—
97#359—2411no—
98#350—2411no—
992−1+4—4821no—
100#137—4822no—
101#137—4821no—
102AGL(1,ℤ/8)—4821no—
103#135—4821no—
104#135—2411no—
105C2×Q16—4821no—
106C2×Q16C2×D24111yescharacteristic
107C2×D8C2×D24111yescharacteristic
108#131—2411no—
109SD32—22no—
110SD32—4821no—
111D16—4821no—
112M32—2411no—
113C2×C16C2×D24111yescharacteristic
114#108—2411no—
115#100—4821no—
116#41—9642no—
117#41—9641no—
118#41—4822no—
119#41—4821no—
120#41—2411no—
121C2×Q8—21no—
122C2×Q8—9641no—
123C2×Q8—4822no—
124C2×D4—21no—
125Q16—21no—
126Q16—4822no—
127Q16—2411no—
128Q16C22⋊D24112yes—
129SD16—9641no—
130SD16—4822no—
131SD16—4821no—
132D8—21no—
133D8—21no—
134D8—9641no—
135D8—2411no—
136M16—4821no—
137M16—4821no—
138M16—2411no—
139C2×C8—4821no—
140C2×C8C22×D24111yescharacteristic
141C16—21no—
142C16—4821no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—9642no—
147Q8—4821no—
148Q8—2411no—
149D4—41no—
150D4—41no—
151D4—9642no—
152D4—9641no—
153D4—4821no—
154D4—4821no—
155D4—2411no—
156C2×C4—41no—
157C2×C4—9642no—
158C2×C4—9642no—
159C2×C4—9641no—
160C2×C4—4821no—
161C2×C4D4×D24111yescharacteristic
162C8—9641no—
163C8—4821no—
164C8D4×D24111yescharacteristic
165C8C2×C22⋊D24111yescharacteristic
166C22—81no—
167C22—161no—
168C22—9641no—
169C22—4821no—
170C22#2144066611yescharacteristic
171C4—42no—
172C4—9641no—
173C4—4821no—
174C4#2144061011yescharacteristic
175C4D8×D24111yescharacteristic
176C2—21no—
177C2—161no—
178C2—19281no—
179C2—9641no—
180C2#2950784911yescharacteristic
subgroupG/H
centerC2#29507849
commutator, cosocleC2×C8×C241C23
FrattiniC2×C8C22×D241
FittingC2×SD32×C241C2
socleC2×C241#447
hypercenterC2×SD32D241
hypocenterC241#2193
LCSG ▷ C2×C8×C241 ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #29508530C2semidirect
2. #29508153C2semidirect
3. #29507984C2semidirect
4. #29507533C2semidirect
5. #29507525C2semidirect
6. #29507500C2semidirect
7. C2×SD32×C241C2semidirect
90. C241#2193semidirect
94. C2×SD32D241semidirect

Maximal subgroups

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

subgroupindex
#295085302
#295081532
#295079842
#295075332
#295075252
#295075002
C2×SD32×C2412
#2193241