Finite Group Databasebeta

← #44506598

Subgroups — #44506598

Order 30848.

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

normal subgroups only

This group has 234 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#29508371C211yesmaximal, characteristic
2#29508068C211yesmaximal, characteristic, complemented
3#29508008C211yesmaximal, characteristic, complemented
4#29508007C211yesmaximal, characteristic, complemented
5#29507462C211yesmaximal, characteristic, complemented
6#29507446C211yesmaximal, characteristic, complemented
7D4⋊C8×C241C211yesmaximal, characteristic, complemented
8C2×#16838769—21no—
9#21440642C2211yescharacteristic
10#21440642C2211yescharacteristic
11#21440626—22no—
12#21440622—21no—
13#21440616—21no—
14C4×D964C2211yescharacteristic
15C2×C4⋊Dic241—21no—
16#21440574—21no—
17#21440573—21no—
18C4⋊#14515349C2211yescharacteristic
19#21440567—22no—
20#21440564—21no—
21#21440563—21no—
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25#16838769—42no—
26#16838769—42no—
27C2×Dic482—21no—
28C2×Dic482—21no—
29C2×D964D411yescharacteristic
30C2×C22⋊D241—22no—
31C22×Dic241—22no—
32C2×C4×D241—21no—
33C2×#14515349—21no—
34C4⋊Dic241—22no—
35C4⋊Dic241—21no—
36C4⋊Dic241—21no—
37C4⋊Dic241—21no—
38C4⋊Dic241D412yes—
39C4⋊Dic241D411yescharacteristic
40#16838747—22no—
41#16838747—21no—
42C2×D4×C241D411yescharacteristic
43C22×C4×C241—21no—
44C2×C8×C241—21no—
45C2×C8×C241—21no—
46C4⋊C4×C241D411yescharacteristic
47C22⋊C4×C241—21no—
48C42×C241C2311yescharacteristic
49C22×D241—21no—
50Dic482—41no—
51Dic482—41no—
52Dic482—42no—
53D964—21no—
54D964—21no—
55C22⋊D241—44no—
56C2×Dic241—21no—
57C2×Dic241—22no—
58C2×Dic241—44no—
59C2×Dic241—41no—
60C4×D241—41no—
61C4×D241—41no—
62#14515349—41no—
63C23×C241—21no—
64D4×C241—21no—
65D4×C241SD1612yes—
66C2×C4×C241—21no—
67C2×C4×C241—41no—
68C2×C4×C241—41no—
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C8×C241—41no—
73C8×C241—41no—
74C22×C241—22no—
75C22×C241—41no—
76C22×C241—41no—
77C22×C241#12011yescharacteristic
78C2×D241—41no—
79C2×D241—41no—
80C2×D241—41no—
81C4×C241—21no—
82C4×C241—41no—
83C4×C241C2×SD1611yescharacteristic
84C4×C241#13511yescharacteristic
85C4×C241AGL(1,ℤ/8)11yescharacteristic
86C4×C241#13711yescharacteristic
87Dic241—41no—
88Dic241—42no—
89Dic241—81no—
90C2×C241—42no—
91C2×C241#45011yescharacteristic
92C2×C241#45211yescharacteristic
93C2×C241#45411yescharacteristic
94D241—81no—
95C241#163511yescharacteristic, complemented, Sylow
96#1635—2411nomaximal, Sylow
97#547—2411no—
98#487—2411no—
99#476—2411no—
100#476—2411no—
101#332—2411no—
102D4⋊C8—2411no—
103D4⋊C8D24111yescharacteristic, complemented
104C2×#41—4821no—
105C4⋊Q8—2411no—
106C4⋊Q8—2411no—
107#123—4822no—
108C22⋊Q8—4821no—
109#121—4821no—
110C4×D4—2411no—
111C4×D4C2×D24111yescharacteristic
112C2×C4⋊C4—4821no—
113#106—4821no—
114#106—4821no—
115C4⋊C8—2411no—
116C4⋊C8C2×D24111yescharacteristic
117#103—4822no—
118#102—4821no—
119#102—4821no—
120C4×C8C2×D24111yescharacteristic
121#41—9642no—
122#41—9642no—
123C2×Q8—4821no—
124C2×Q8—4821no—
125C2×D4—4822no—
126C2×D4—2411no—
127C2×D4D96411yescharacteristic
128C22×C4—21no—
129C22×C4—4822no—
130C22×C4—4821no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—4821no—
134C4⋊C4—4822no—
135C4⋊C4—4821no—
136C4⋊C4—4821no—
137C4⋊C4—4821no—
138C4⋊C4—2412no—
139C4⋊C4—2411no—
140C4⋊C4D96411yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—4822no—
143C22⋊C4—4821no—
144C42C22×D24111yescharacteristic
145C23—21no—
146C23—4821no—
147Q8—9642no—
148Q8—9641no—
149Q8—9641no—
150D4—21no—
151D4—9644no—
152D4—4821no—
153D4—4821no—
154D4#1683875912yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—9641no—
159C2×C4—9644no—
160C2×C4—9641no—
161C2×C4—9641no—
162C2×C4—4821no—
163C2×C4—4822no—
164C2×C4D4×D24111yescharacteristic
165C2×C4D4×D24111yescharacteristic
166C2×C4C2×D96411yescharacteristic
167C8—41no—
168C8—41no—
169C8—9641no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—9641no—
174C22—9641no—
175C22—9641no—
176C22#2144061211yescharacteristic
177C4—21no—
178C4—41no—
179C4—19281no—
180C4—9641no—
181C4—9642no—
182C4C2×#1683875911yescharacteristic
183C4#2144066111yescharacteristic
184C4#2144067011yescharacteristic
185C4#2144067111yescharacteristic
186C2—42no—
187C2—19281no—
188C2#2950787011yescharacteristic
189C2#2950788011yescharacteristic
190C2#2950789111yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingD4⋊C8×C241C2
socleC22×C241#120
prime radical#29508371C2
hypercenterD4⋊C8D241
hypocenterC241#1635
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
2. #29508068C2semidirect
3. #29508008C2semidirect
4. #29508007C2semidirect
5. #29507462C2semidirect
6. #29507446C2semidirect
7. D4⋊C8×C241C2semidirect
95. C241#1635semidirect
103. D4⋊C8D241semidirect

Maximal subgroups

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

subgroupindex
#295083712
#295080682
#295080082
#295080072
#295074622
#295074462
D4⋊C8×C2412
#1635241