Finite Group Databasebeta

← #44506387

Subgroups — #44506387

Order 30848.

266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508348C211yesmaximal, characteristic, complemented
2#29507870C212yesmaximal
3#29507634C211yesmaximal, characteristic
4#29507455C212yesmaximal, complemented
5#324×C241C211yesmaximal, characteristic, complemented
6C22×D964C2211yescharacteristic
7C2×#16838759—22no—
8#21440641—22no—
9#21440633—22no—
10#21440621—21no—
11#21440621C2212yes—
12#21440601—21no—
13C2×#16838747—21no—
14C2×#16838747—21no—
15#21440564—22no—
16#21440549C2211yescharacteristic
17C2×C4⋊C4×C241C2211yescharacteristic
18C22⋊C8×C241C2212yes—
19C23×D241—21no—
20C2×Dic482—21no—
21C2×Dic482D412yes—
22C2×D964—22no—
23C2×D964—42no—
24C22×Dic241—21no—
25#16838759—44no—
26C4⋊Dic241—21no—
27C4⋊Dic241—21no—
28C4⋊Dic241—21no—
29C4⋊Dic241D412yes—
30#16838749—22no—
31#16838749—22no—
32C22⋊Dic241—22no—
33#16838747—42no—
34#16838747—42no—
35C4×Dic241—22no—
36C22×C4×C241D411yescharacteristic
37C22×C4×C241D411yescharacteristic
38C22×C4×C241C2311yescharacteristic
39C2×C8×C241—22no—
40C4⋊C4×C241—22no—
41C22×D241—22no—
42C22×D241—41no—
43C22×D241—41no—
44C22×D241—41no—
45C22×D241—41no—
46C22×D241—41no—
47C22×D241—41no—
48Dic482—42no—
49Dic482—81no—
50D964—24no—
51D964—42no—
52C2×Dic241—22no—
53C2×Dic241—22no—
54C2×Dic241—41no—
55C2×Dic241—41no—
56C2×Dic241—41no—
57C23×C241C2×D411yescharacteristic
58C2×C4×C241—21no—
59C2×C4×C241—21no—
60C2×C4×C241—21no—
61C2×C4×C241—41no—
62C2×C4×C241—41no—
63C2×C4×C241SD1612yescomplemented
64C2×C4×C241C2×D412yes—
65C8×C241—42no—
66C22×C241—21no—
67C22×C241—21no—
68C22×C241#12011yescharacteristic
69C22×C241C2×SD1611yescharacteristic
70C22×C241#13711yescharacteristic
71C2×D241—42no—
72C2×D241—42no—
73C2×D241—42no—
74C2×D241—81no—
75C2×D241—81no—
76C2×D241—81no—
77C2×D241—81no—
78C4×C241—22no—
79C4×C241—22no—
80C4×C241—41no—
81Dic241—42no—
82Dic241—42no—
83Dic241—81no—
84C2×C241—21no—
85C2×C241—21no—
86C2×C241#44811yescharacteristic
87C2×C241#45411yescharacteristic
88C2×C241B(4,𝔽2)11yescharacteristic
89D241—82no—
90C241#159911yescharacteristic, complemented, Sylow
91#1599—2411nomaximal, Sylow
92#544—2411no—
93#450—2412no—
94#394—2411no—
95#328—2412no—
96#324D24111yescharacteristic, complemented
97C22×D4—2411no—
98C2×SD16—4822no—
99C4⋊Q8—4822no—
100#125—4822no—
101C22⋊Q8—4821no—
102C22⋊Q8—2412no—
103#117—4821no—
104C2×C4⋊C4C2×D24111yescharacteristic
105C2×C22⋊C4—4821no—
106C2×C22⋊C4—4821no—
107#102—4822no—
108C22⋊C8C2×D24112yes—
109#95—2411no—
110C24—4821no—
111C2×Q8—4821no—
112C2×Q8—2412no—
113C2×D4—9642no—
114C2×D4—4822no—
115C22×C4—4821no—
116C22×C4D96411yescharacteristic
117C22×C4D96411yescharacteristic
118C22×C4C22×D24111yescharacteristic
119SD16—9644no—
120C2×C8—22no—
121C4⋊C4—22no—
122C4⋊C4—4822no—
123C4⋊C4—4821no—
124C4⋊C4—4821no—
125C4⋊C4—4821no—
126C4⋊C4—4822no—
127C4⋊C4—2412no—
128C22⋊C4—9642no—
129C22⋊C4—9642no—
130C22⋊C4—4822no—
131C42—4822no—
132C23—9641no—
133C23—9641no—
134C23—9641no—
135C23—9641no—
136C23—9641no—
137C23—9641no—
138C23—4822no—
139C23C2×D96411yescharacteristic
140Q8—19281no—
141Q8—9642no—
142D4—9642no—
143D4—4824no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—9641no—
150C2×C4—9641no—
151C2×C4—9641no—
152C2×C4—4822no—
153C2×C4—4822no—
154C2×C4#1683875912yescomplemented
155C2×C4D4×D24112yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—19281no—
160C22—19281no—
161C22—19281no—
162C22—19281no—
163C22—9642no—
164C22—9642no—
165C22—9642no—
166C22#2144061211yescharacteristic
167C22C2×#1683875911yescharacteristic
168C22#2144067511yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—19281no—
173C4—9642no—
174C4—9642no—
175C2—21no—
176C2—21no—
177C2—19282no—
178C2#2950785811yescharacteristic
179C2#2950789211yescharacteristic
180C2#2950790511yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#324×C241C2
socleC22×C241#120
prime radicalC22×D964C22
hypercenter#324D241
hypocenterC241#1599
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #29508348C2semidirect
4. #29507455C2semidirect
5. #324×C241C2semidirect
63. C2×C4×C241SD16semidirect
90. C241#1599semidirect
96. #324D241semidirect
154. C2×C4#16838759semidirect

Maximal subgroups

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

subgroupindex
#295083482
#295078702
#295076342
#295074552
#324×C2412
#1599241