Finite Group Databasebeta

← #44506537

Subgroups — #44506537

Order 30848.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#29508372C211yesmaximal, characteristic, complemented
2#29508064C211yesmaximal, characteristic, complemented
3#29507913C211yesmaximal, characteristic, complemented
4#29507912C211yesmaximal, characteristic, complemented
5#29507464C211yesmaximal, characteristic, complemented
6#29507446C211yesmaximal, characteristic, complemented
7D4⋊C8×C241C211yesmaximal, characteristic, complemented
8C2×#16838770—21no—
9C2×D1928—21no—
10C2×#16838755—21no—
11#21440642C2211yescharacteristic
12#21440639C2211yescharacteristic
13#21440624—22no—
14#21440621—21no—
15#21440613—21no—
16C4×D964C2211yescharacteristic
17C4⋊C4×D241—21no—
18C4⋊#14515349C2211yescharacteristic
19#21440564—21no—
20#21440564—22no—
21#21440562—21no—
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25#16838770—42no—
26#16838770—42no—
27C2×Dic482—21no—
28C2×D964—21no—
29C2×D964—21no—
30C2×D964—21no—
31C2×D964D411yescharacteristic
32C2×C22⋊D241—22no—
33C2×C4×D241—22no—
34C2×C4×D241—21no—
35D1928—42no—
36#16838755—42no—
37C2×#14515349—21no—
38C4⋊Dic241—21no—
39C4⋊Dic241D411yescharacteristic
40C4⋊Dic241D412yes—
41#16838749—22no—
42C22⋊Dic241—22no—
43#16838747—21no—
44C2×D4×C241D411yescharacteristic
45C22×C4×C241—21no—
46C2×C8×C241—21no—
47C2×C8×C241—21no—
48C4⋊C4×C241D411yescharacteristic
49C22⋊C4×C241—21no—
50C42×C241C2311yescharacteristic
51C22×D241—21no—
52C22×D241—41no—
53Dic482—41no—
54Dic482—41no—
55D964—21no—
56D964—42no—
57D964—41no—
58D964—41no—
59D964—41no—
60D964—41no—
61D964D812yescomplemented
62C22⋊D241—44no—
63C2×Dic241—21no—
64C2×Dic241—22no—
65C4×D241—44no—
66C4×D241—41no—
67C4×D241—41no—
68#14515349—41no—
69C23×C241—21no—
70D4×C241—21no—
71D4×C241—21no—
72C2×C4×C241—21no—
73C2×C4×C241—41no—
74C2×C4×C241—41no—
75C2×C4×C241C2×D411yescharacteristic
76C2×C4×C241C2×D411yescharacteristic
77C2×C4×C241C2×D411yescharacteristic
78C8×C241—41no—
79C8×C241—41no—
80C22×C241—41no—
81C22×C241—41no—
82C22×C241—41no—
83C22×C241#12011yescharacteristic
84C2×D241—22no—
85C2×D241—41no—
86C2×D241—41no—
87C2×D241—81no—
88C2×D241—81no—
89C2×D241—81no—
90C4×C241—21no—
91C4×C241—41no—
92C4×C241C2×D811yescharacteristic
93C4×C241#13511yescharacteristic
94C4×C241AGL(1,ℤ/8)11yescharacteristic
95C4×C241AGL(1,ℤ/8)11yescharacteristic
96Dic241—42no—
97Dic241—41no—
98C2×C241—81no—
99C2×C241#44711yescharacteristic
100C2×C241#44911yescharacteristic
101C2×C241#45411yescharacteristic
102D241—42no—
103D241—161no—
104C241#162511yescharacteristic, complemented, Sylow
105#1625—2411nomaximal, Sylow
106#547—2411no—
107#486—2411no—
108#459—2411no—
109#459—2411no—
110#332—2411no—
111D4⋊C8—2411no—
112D4⋊C8D24111yescharacteristic, complemented
113C2×#41—4821no—
114C2×D8—4821no—
115C2×D8—4821no—
116C4⋊Q8—2411no—
117#127—2411no—
118#123—4822no—
119C22⋊Q8—4821no—
120#121—4821no—
121C4×D4—2411no—
122C4×D4C2×D24111yescharacteristic
123C2×C4⋊C4—4821no—
124C4⋊C8—2411no—
125C4⋊C8C2×D24111yescharacteristic
126#102—4821no—
127#102—4822no—
128#102—4821no—
129C4×C8C2×D24111yescharacteristic
130#41—9642no—
131#41—9642no—
132C2×Q8—4821no—
133C2×D4—4822no—
134C2×D4—4821no—
135C2×D4—4821no—
136C2×D4—4821no—
137C2×D4—2411no—
138C2×D4D96411yescharacteristic
139C22×C4—21no—
140C22×C4—4822no—
141C22×C4—4821no—
142D8—9642no—
143D8—9642no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—4821no—
147C4⋊C4—4822no—
148C4⋊C4—4821no—
149C4⋊C4—2411no—
150C4⋊C4—2412no—
151C4⋊C4D96411yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—4822no—
154C22⋊C4—4821no—
155C42C22×D24111yescharacteristic
156C23—21no—
157C23—9641no—
158C23—4821no—
159Q8—9641no—
160Q8—9641no—
161D4—21no—
162D4—21no—
163D4—9642no—
164D4—9644no—
165D4—9641no—
166D4—9641no—
167D4—9641no—
168D4—9641no—
169D4—4821no—
170D4—2412no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—9644no—
175C2×C4—9641no—
176C2×C4—9641no—
177C2×C4—4821no—
178C2×C4—4822no—
179C2×C4D4×D24111yescharacteristic
180C2×C4D4×D24111yescharacteristic
181C2×C4C2×D96411yescharacteristic
182C8—41no—
183C8—41no—
184C8—9641no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—19281no—
189C22—19281no—
190C22—19281no—
191C22—9641no—
192C22—9641no—
193C22—4822no—
194C22#2144061211yescharacteristic
195C4—21no—
196C4—41no—
197C4—9642no—
198C4—9641no—
199C4D8×D24111yescharacteristic
200C4#2144066411yescharacteristic
201C4#2144066911yescharacteristic
202C4#2144067011yescharacteristic
203C2—81no—
204C2—38561no—
205C2—9642no—
206C2#2950785211yescharacteristic
207C2#2950786411yescharacteristic
208C2#2950789111yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingD4⋊C8×C241C2
socleC22×C241#120
hypercenterD4⋊C8D241
hypocenterC241#1625
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #29508372C2semidirect
2. #29508064C2semidirect
3. #29507913C2semidirect
4. #29507912C2semidirect
5. #29507464C2semidirect
6. #29507446C2semidirect
7. D4⋊C8×C241C2semidirect
61. D964D8semidirect
104. C241#1625semidirect
112. D4⋊C8D241semidirect

Maximal subgroups

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

subgroupindex
#295083722
#295080642
#295079132
#295079122
#295074642
#295074462
D4⋊C8×C2412
#1625241