Finite Group Databasebeta

← #44509401

Subgroups — #44509401

Order 30848.

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

normal subgroups only

This group has 220 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#29508518C211yesmaximal, characteristic, complemented
2#29508153C211yesmaximal, characteristic, complemented
3#29507984C211yesmaximal, characteristic, complemented
4#29507530C211yesmaximal, characteristic, complemented
5#29507525C211yesmaximal, characteristic, complemented
6#29507500C211yesmaximal, characteristic, complemented
7C2×D16×C241C211yesmaximal, characteristic, complemented
8#21440687—21no—
9#21440668—21no—
10#21440668—21no—
11#21440666—22no—
12#21440664C2211yescharacteristic
13#21440661—21no—
14D8×D241—21no—
15#21440648C2211yescharacteristic
16#21440586—21no—
17#21440583—21no—
18#21440582C2211yescharacteristic, complemented
19#21440578C2211yescharacteristic, complemented
20#21440559—21no—
21C2×D8×C241C2211yescharacteristic
22C2×D8×C241C2211yescharacteristic, complemented
23D16×C241—22no—
24C2×C16×C241C2211yescharacteristic, complemented
25#16838770—21no—
26#16838770D411yescharacteristic
27#16838769—22no—
28#16838769—41no—
29C2×C22⋊D241—42no—
30D4×D241—22no—
31D4×D241—41no—
32Dic964D411yescharacteristic
33#16838759—21no—
34#16838758—22no—
35#16838758—41no—
36D1928D411yescharacteristic
37#16838755—22no—
38#16838755—41no—
39#16838754—21no—
40#16838754D411yescharacteristic
41#16838753—21no—
42C8×D241—21no—
43#16838745—21no—
44C2×D4×C241—21no—
45C2×D4×C241—21no—
46D8×C241—21no—
47D8×C241—21no—
48D8×C241—21no—
49D8×C241D412yes—
50C2×C8×C241C2311yescharacteristic
51C16×C241—21no—
52C22×D241—42no—
53Dic482—21no—
54Dic482D811yescharacteristic
55D964—21no—
56D964D811yescharacteristic
57C22⋊D241—21no—
58C22⋊D241—42no—
59C22⋊D241—42no—
60C22⋊D241—41no—
61C2×Dic241—42no—
62C4×D241—21no—
63C4×D241—41no—
64#14515349—21no—
65#14515349—41no—
66C23×C241—41no—
67C23×C241—41no—
68D4×C241—22no—
69D4×C241—41no—
70D4×C241—41no—
71D4×C241—41no—
72C2×C4×C241C2×D411yescharacteristic
73C8×C241C2×D411yescharacteristic
74C8×C241C2×D411yescharacteristic
75C22×C241—42no—
76C22×C241—81no—
77C22×C241—161no—
78C22×C241—161no—
79C22×C241AGL(1,ℤ/8)11yescharacteristic
80C2×D241—21no—
81C2×D241—41no—
82C2×D241—162no—
83C4×C241#12011yescharacteristic
84C4×C241C2×D811yescharacteristic
85Dic241—21no—
86Dic241—41no—
87C2×C241—21no—
88C2×C241—82no—
89C2×C241—161no—
90C2×C241#44711yescharacteristic
91D241—41no—
92D241—81no—
93C241#219211yescharacteristic, complemented, Sylow
94#2192—2411nomaximal, Sylow
95#576—2411no—
96#509—2411no—
97C2×D16D24111yescharacteristic, complemented
98#472—2411no—
99#361—2411no—
100#359—2411no—
101#350—2411no—
102H(5,𝔽2)—4821no—
103AGL(1,ℤ/8)—4821no—
104AGL(1,ℤ/8)—4822no—
105AGL(1,ℤ/8)—4821no—
106#135—4821no—
107#135—2411no—
108C2×D8—4821no—
109C2×D8C2×D24111yescharacteristic
110C2×D8C2×D24111yescharacteristic, complemented
111#131—2411no—
112SD32—4821no—
113D16—22no—
114D16—4821no—
115M32—2411no—
116C2×C16C2×D24111yescharacteristic, complemented
117#108—2411no—
118#100—4821no—
119#41—9641no—
120#41—4822no—
121#41—4821no—
122#41—2411no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—9641no—
126C2×D4—9642no—
127C2×D4—4822no—
128Q16—2411no—
129SD16—9641no—
130SD16—4822no—
131SD16—4821no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—9641no—
136D8—4822no—
137D8—2411no—
138D8C22⋊D24112yes—
139M16—4821no—
140M16—4821no—
141M16—2411no—
142C2×C8—4821no—
143C2×C8C22×D24111yescharacteristic
144C16—21no—
145C16—4821no—
146C23—41no—
147C23—41no—
148C23—9642no—
149Q8—4821no—
150Q8—2411no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—9642no—
156D4—9641no—
157D4—9642no—
158D4—4821no—
159D4—4821no—
160D4—2411no—
161C2×C4—9642no—
162C2×C4—9641no—
163C2×C4—4821no—
164C2×C4D4×D24111yescharacteristic
165C8—9641no—
166C8—4821no—
167C8D4×D24111yescharacteristic
168C8C2×C22⋊D24111yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—38562no—
174C22—9641no—
175C22—4821no—
176C22#2144066611yescharacteristic
177C4—9641no—
178C4—4821no—
179C4#2144061011yescharacteristic
180C4D8×D24111yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—19281no—
185C2—9641no—
186C2#2950784911yescharacteristic
subgroupG/H
centerC2#29507849
commutator, cosocleC2×C8×C241C23
FrattiniC2×C8C22×D241
FittingC2×D16×C241C2
socleC2×C241#447
hypercenterC2×D16D241
hypocenterC241#2192
LCSG ▷ C2×C8×C241 ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #29508518C2semidirect
2. #29508153C2semidirect
3. #29507984C2semidirect
4. #29507530C2semidirect
5. #29507525C2semidirect
6. #29507500C2semidirect
7. C2×D16×C241C2semidirect
18. #21440582C22semidirect
19. #21440578C22semidirect
22. C2×D8×C241C22semidirect
24. C2×C16×C241C22semidirect
93. C241#2192semidirect
97. C2×D16D241semidirect
110. C2×D8C2×D241semidirect
116. C2×C16C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295085182
#295081532
#295079842
#295075302
#295075252
#295075002
C2×D16×C2412
#2192241