Finite Group Databasebeta

← #44506549

Subgroups — #44506549

Order 30848.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#29508382C211yesmaximal, characteristic, complemented
2#29508065C211yesmaximal, characteristic, complemented
3#29507918C211yesmaximal, characteristic, complemented
4#29507913C211yesmaximal, characteristic
5#29507447C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic, complemented
7#332×C241C211yesmaximal, characteristic, complemented
8C2×Q8×D241—21no—
9C2×#16838759—21no—
10C2×D1928—21no—
11#21440641—21no—
12#21440639C2211yescharacteristic
13#21440620—22no—
14#21440618—21no—
15C4×Dic482C2211yescharacteristic
16C4×D964C2211yescharacteristic
17#21440604—21no—
18#21440564—21no—
19#21440564—21no—
20#21440562—22no—
21C4×#14515349C2211yescharacteristic
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25C2×Dic482—22no—
26C2×Dic482D411yescharacteristic
27Q8×D241—42no—
28Q8×D241—42no—
29C2×D964—21no—
30C2×D964—21no—
31C2×D964—21no—
32C2×D964D411yescharacteristic
33C2×C4×D241—22no—
34C2×C4×D241—21no—
35#16838759—42no—
36D1928—42no—
37C2×#14515349—21no—
38C4⋊Dic241D411yescharacteristic
39C4⋊Dic241D411yescharacteristic
40#16838749—22no—
41#16838749—21no—
42#16838747—22no—
43#16838747—21no—
44C4×Dic241—21no—
45C2×Q8×C241—21no—
46C2×C8×C241—21no—
47C2×C8×C241—21no—
48C4⋊C4×C241—21no—
49C4⋊C4×C241D412yes—
50C42×C241C2311yescharacteristic
51C22×D241—21no—
52C22×D241—41no—
53Dic482—21no—
54Dic482—44no—
55Dic482D812yescomplemented
56D964—21no—
57D964—42no—
58D964—41no—
59D964—41no—
60D964—41no—
61D964—41no—
62D964SD1612yescomplemented
63C2×Dic241—21no—
64C2×Dic241—21no—
65C2×Dic241—21no—
66C4×D241—44no—
67C4×D241—41no—
68C4×D241—41no—
69#14515349—41no—
70Q8×C241—41no—
71Q8×C241—41no—
72C2×C4×C241—22no—
73C2×C4×C241C2×D411yescharacteristic
74C2×C4×C241C2×D411yescharacteristic
75C2×C4×C241C2×D411yescharacteristic
76C8×C241—41no—
77C8×C241—41no—
78C22×C241#12011yescharacteristic
79C2×D241—22no—
80C2×D241—41no—
81C2×D241—41no—
82C2×D241—81no—
83C2×D241—81no—
84C2×D241—81no—
85C4×C241—21no—
86C4×C241—42no—
87C4×C241C2×D811yescharacteristic
88C4×C241C2×SD1611yescharacteristic
89C4×C241AGL(1,ℤ/8)11yescharacteristic
90C4×C241#13711yescharacteristic
91Dic241—22no—
92Dic241—41no—
93Dic241—41no—
94C2×C241#44711yescharacteristic
95C2×C241#44811yescharacteristic
96C2×C241#45411yescharacteristic
97D241—42no—
98D241—161no—
99C241#162711yescharacteristic, complemented, Sylow
100#1627—2411nomaximal, Sylow
101D4×Q8—2411no—
102#486—2411no—
103#460—2411no—
104#459—2411no—
105#332D24111yescharacteristic, complemented
106Q8⋊C8—2411no—
107D4⋊C8—2411no—
108C22×Q8—4821no—
109C2×SD16—4821no—
110C2×D8—4821no—
111C4⋊Q8—4821no—
112C4⋊Q8C2×D24111yescharacteristic
113#127—2411no—
114C22⋊Q8—4821no—
115C22⋊Q8—4822no—
116C4×Q8—2411no—
117C4×D4—4821no—
118C4×D4—2411no—
119C4⋊C8C2×D24111yescharacteristic
120C4⋊C8C2×D24111yescharacteristic
121#102—4821no—
122#102—4821no—
123#102—4822no—
124C4×C8—2411no—
125C2×Q8—21no—
126C2×Q8—9642no—
127C2×Q8—9642no—
128C2×Q8—4822no—
129C2×Q8—2411no—
130C2×D4—4821no—
131C2×D4—4821no—
132C2×D4—4821no—
133C2×D4—2411no—
134C22×C4—4822no—
135C22×C4—4821no—
136SD16—9642no—
137D8—9642no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—4821no—
141C4⋊C4—21no—
142C4⋊C4—4822no—
143C4⋊C4—4821no—
144C4⋊C4—2411no—
145C4⋊C4—2411no—
146C4⋊C4D96412yes—
147C22⋊C4—4822no—
148C22⋊C4—4821no—
149C42—4821no—
150C42C22×D24111yescharacteristic
151C23—9641no—
152C23—4821no—
153Q8—41no—
154Q8—41no—
155Q8—9644no—
156Q8—4821no—
157Q8—2412no—
158D4—9642no—
159D4—9641no—
160D4—9641no—
161D4—9641no—
162D4—9641no—
163D4—4821no—
164D4—2412no—
165C2×C4—22no—
166C2×C4—9644no—
167C2×C4—9641no—
168C2×C4—9641no—
169C2×C4—4821no—
170C2×C4—4821no—
171C2×C4—4821no—
172C2×C4D4×D24111yescharacteristic
173C2×C4D4×D24111yescharacteristic
174C2×C4C2×D96411yescharacteristic
175C8—41no—
176C8—41no—
177C8—9641no—
178C22—19281no—
179C22—19281no—
180C22—19281no—
181C22—9641no—
182C22—9641no—
183C22—4822no—
184C22#2144061211yescharacteristic
185C4—21no—
186C4—42no—
187C4—9641no—
188C4—9641no—
189C4—4822no—
190C4D8×D24111yescharacteristic
191C4SD16×D24111yescharacteristic
192C4#2144066911yescharacteristic
193C4#2144067411yescharacteristic
194C2—38561no—
195C2—9642no—
196C2#2950785211yescharacteristic
197C2#2950785711yescharacteristic
198C2#2950789211yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#332×C241C2
socleC22×C241#120
prime radical#29507913C2
hypercenter#332D241
hypocenterC241#1627
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #29508382C2semidirect
2. #29508065C2semidirect
3. #29507918C2semidirect
5. #29507447C2semidirect
6. #29507444C2semidirect
7. #332×C241C2semidirect
55. Dic482D8semidirect
62. D964SD16semidirect
99. C241#1627semidirect
105. #332D241semidirect

Maximal subgroups

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

subgroupindex
#295083822
#295080652
#295079182
#295079132
#295074472
#295074442
#332×C2412
#1627241