Finite Group Databasebeta

← #44509422

Subgroups — #44509422

Order 30848.

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

normal subgroups only

This group has 206 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
2#29508158C211yesmaximal, characteristic, complemented
3#29507989C211yesmaximal, characteristic, complemented
4#29507533C211yesmaximal, characteristic, complemented
5#29507525C211yesmaximal, characteristic, complemented
6#29507500C211yesmaximal, characteristic, complemented
7C2×Q32×C241C211yesmaximal, characteristic, complemented
8#21440690—21no—
9#21440674—22no—
10#21440673—21no—
11#21440673—21no—
12#21440665—21no—
13#21440664C2211yescharacteristic
14Q16×D241—21no—
15#21440648C2211yescharacteristic
16#21440588—21no—
17#21440585—21no—
18#21440582C2211yescharacteristic
19#21440578C2211yescharacteristic
20#21440561—21no—
21C2×Q16×C241C2211yescharacteristic
22C2×Q16×C241C2211yescharacteristic
23Q32×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#16838760—41no—
35#16838759—21no—
36#16838757—22no—
37#16838757—41no—
38D1928D411yescharacteristic
39#16838754—21no—
40#16838754D411yescharacteristic
41#16838753—21no—
42C8×D241—21no—
43#16838745—21no—
44C2×Q8×C241—21no—
45C2×Q8×C241—21no—
46Q16×C241—21no—
47Q16×C241—21no—
48Q16×C241—21no—
49Q16×C241D412yes—
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—
66Q8×C241—22no—
67Q8×C241—41no—
68Q8×C241—41no—
69Q8×C241—41no—
70C2×C4×C241—41no—
71C2×C4×C241—41no—
72C2×C4×C241C2×D411yescharacteristic
73C8×C241C2×D411yescharacteristic
74C8×C241C2×D411yescharacteristic
75C22×C241AGL(1,ℤ/8)11yescharacteristic
76C2×D241—21no—
77C2×D241—41no—
78C4×C241—42no—
79C4×C241—81no—
80C4×C241#12011yescharacteristic
81C4×C241C2×D811yescharacteristic
82Dic241—21no—
83Dic241—41no—
84C2×C241—21no—
85C2×C241#44711yescharacteristic
86D241—41no—
87D241—81no—
88C241#219511yescharacteristic, complemented, Sylow
89#2195—2411nomaximal, Sylow
90#578—2411no—
91#510—2411no—
92C2×Q32D24111yescharacteristic, complemented
93#473—2411no—
94#362—2411no—
95#359—2411no—
96#350—2411no—
972−1+4—4821no—
98#137—4821no—
99#137—4822no—
100#137—4821no—
101#135—4821no—
102#135—2411no—
103C2×Q16—4821no—
104C2×Q16C2×D24111yescharacteristic
105C2×Q16C2×D24111yescharacteristic
106#131—2411no—
107Q32—22no—
108Q32—4821no—
109SD32—4821no—
110M32—2411no—
111C2×C16C2×D24111yescharacteristic
112#108—2411no—
113#101—4821no—
114#41—9642no—
115#41—9641no—
116#41—4822no—
117#41—4821no—
118#41—2411no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—9641no—
122C2×Q8—4822no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—9641no—
127Q16—4822no—
128Q16—2411no—
129Q16C22⋊D24112yes—
130SD16—9641no—
131SD16—4822no—
132SD16—4821no—
133D8—2411no—
134M16—4821no—
135M16—4821no—
136M16—2411no—
137C2×C8—4821no—
138C2×C8C22×D24111yescharacteristic
139C16—21no—
140C16—4821no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—9642no—
146Q8—4821no—
147Q8—2411no—
148D4—9642no—
149D4—9641no—
150D4—4821no—
151D4—4821no—
152D4—2411no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—9642no—
156C2×C4—9642no—
157C2×C4—9641no—
158C2×C4—4821no—
159C2×C4D4×D24111yescharacteristic
160C8—9641no—
161C8—4821no—
162C8D4×D24111yescharacteristic
163C8C2×C22⋊D24111yescharacteristic
164C22—9641no—
165C22—4821no—
166C22#2144066611yescharacteristic
167C4—42no—
168C4—81no—
169C4—9641no—
170C4—4821no—
171C4#2144061011yescharacteristic
172C4D8×D24111yescharacteristic
173C2—21no—
174C2—19281no—
175C2—9641no—
176C2#2950784911yescharacteristic
subgroupG/H
centerC2#29507849
commutator, cosocleC2×C8×C241C23
FrattiniC2×C8C22×D241
FittingC2×Q32×C241C2
socleC2×C241#447
prime radical#29508530C2
hypercenterC2×Q32D241
hypocenterC241#2195
LCSG ▷ C2×C8×C241 ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #29508158C2semidirect
3. #29507989C2semidirect
4. #29507533C2semidirect
5. #29507525C2semidirect
6. #29507500C2semidirect
7. C2×Q32×C241C2semidirect
88. C241#2195semidirect
92. C2×Q32D241semidirect

Maximal subgroups

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

subgroupindex
#295085302
#295081582
#295079892
#295075332
#295075252
#295075002
C2×Q32×C2412
#2195241