Finite Group Databasebeta

← #44509415

Subgroups — #44509415

Order 30848.

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

normal subgroups only

This group has 216 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
2#29508158C211yesmaximal, characteristic, complemented
3#29507989C211yesmaximal, characteristic, complemented
4#29507530C211yesmaximal, characteristic, complemented
5#29507525C211yesmaximal, characteristic, complemented
6#29507500C211yesmaximal, characteristic, complemented
7C2×SD32×C241C211yesmaximal, characteristic, complemented
8#21440687—21no—
9#21440673—21no—
10#21440668—21no—
11#21440666—22no—
12#21440664C2211yescharacteristic
13#21440661—21no—
14D8×D241—21no—
15#21440648C2211yescharacteristic
16#21440588—21no—
17#21440585—21no—
18#21440582C2211yescharacteristic, complemented
19#21440578C2211yescharacteristic, complemented
20#21440561—21no—
21C2×Q16×C241C2211yescharacteristic, complemented
22C2×D8×C241C2211yescharacteristic
23SD32×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#16838760—41no—
34#16838759—21no—
35#16838758—22no—
36#16838757—41no—
37D1928D411yescharacteristic
38#16838755—22no—
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×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—
67Q8×C241—41no—
68Q8×C241—41no—
69D4×C241—22no—
70D4×C241—41no—
71C2×C4×C241—41no—
72C2×C4×C241C2×D411yescharacteristic
73C8×C241C2×D411yescharacteristic
74C8×C241C2×D411yescharacteristic
75C22×C241—42no—
76C22×C241—161no—
77C22×C241AGL(1,ℤ/8)11yescharacteristic
78C2×D241—21no—
79C2×D241—41no—
80C2×D241—162no—
81C4×C241—81no—
82C4×C241#12011yescharacteristic
83C4×C241C2×D811yescharacteristic
84Dic241—21no—
85Dic241—41no—
86C2×C241—21no—
87C2×C241—82no—
88C2×C241#44711yescharacteristic
89D241—41no—
90D241—81no—
91C241#219411yescharacteristic, complemented, Sylow
92#2194—2411nomaximal, Sylow
93#576—2411no—
94#510—2411no—
95C2×SD32D24111yescharacteristic, complemented
96#473—2411no—
97#361—2411no—
98#359—2411no—
99#350—2411no—
100H(5,𝔽2)—4821no—
101#137—4821no—
102AGL(1,ℤ/8)—4822no—
103AGL(1,ℤ/8)—4821no—
104#135—4821no—
105#135—2411no—
106C2×Q16C2×D24111yescharacteristic, complemented
107C2×D8—4821no—
108C2×D8C2×D24111yescharacteristic
109#131—2411no—
110Q32—4821no—
111SD32—22no—
112SD32—4821no—
113M32—2411no—
114C2×C16C2×D24111yescharacteristic, complemented
115#108—2411no—
116#101—4821no—
117#41—9641no—
118#41—4822no—
119#41—4821no—
120#41—2411no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—9641no—
124C2×D4—9642no—
125C2×D4—4822no—
126Q16—21no—
127Q16—21no—
128Q16—9641no—
129Q16—2411no—
130SD16—9641no—
131SD16—4822no—
132SD16—4821no—
133D8—21no—
134D8—4822no—
135D8—2411no—
136D8C22⋊D24112yes—
137M16—4821no—
138M16—4821no—
139M16—2411no—
140C2×C8—4821no—
141C2×C8C22×D24111yescharacteristic
142C16—21no—
143C16—4821no—
144C23—41no—
145C23—9642no—
146Q8—41no—
147Q8—41no—
148Q8—4821no—
149Q8—2411no—
150D4—22no—
151D4—41no—
152D4—9642no—
153D4—9641no—
154D4—9642no—
155D4—4821no—
156D4—4821no—
157D4—2411no—
158C2×C4—41no—
159C2×C4—9642no—
160C2×C4—9641no—
161C2×C4—4821no—
162C2×C4D4×D24111yescharacteristic
163C8—9641no—
164C8—4821no—
165C8D4×D24111yescharacteristic
166C8C2×C22⋊D24111yescharacteristic
167C22—42no—
168C22—161no—
169C22—38562no—
170C22—9641no—
171C22—4821no—
172C22#2144066611yescharacteristic
173C4—81no—
174C4—9641no—
175C4—4821no—
176C4#2144061011yescharacteristic
177C4D8×D24111yescharacteristic
178C2—21no—
179C2—82no—
180C2—19281no—
181C2—9641no—
182C2#2950784911yescharacteristic
subgroupG/H
centerC2#29507849
commutator, cosocleC2×C8×C241C23
FrattiniC2×C8C22×D241
FittingC2×SD32×C241C2
socleC2×C241#447
prime radical#29508518C2
hypercenterC2×SD32D241
hypocenterC241#2194
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
2. #29508158C2semidirect
3. #29507989C2semidirect
4. #29507530C2semidirect
5. #29507525C2semidirect
6. #29507500C2semidirect
7. C2×SD32×C241C2semidirect
18. #21440582C22semidirect
19. #21440578C22semidirect
21. C2×Q16×C241C22semidirect
24. C2×C16×C241C22semidirect
91. C241#2194semidirect
95. C2×SD32D241semidirect
106. C2×Q16C2×D241semidirect
114. C2×C16C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295085182
#295081582
#295079892
#295075302
#295075252
#295075002
C2×SD32×C2412
#2194241