Finite Group Databasebeta

← #44508576

Subgroups — #44508576

Order 30848.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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#29508279C211yesmaximal, characteristic
2C2×#21440625C212yesmaximal, complemented
3C2×#21440556C212yesmaximal, complemented
4#29507484C211yesmaximal, characteristic, complemented
5#381×C241C211yesmaximal, characteristic, complemented
6C22×C22⋊D241C2212yes—
7#21440626—22no—
8#21440625—24no—
9#21440625—24no—
10#21440616—22no—
11#21440612—22no—
12C2×#16838749—22no—
13C2×C22⋊Dic241C2212yes—
14C2×#16838747—22no—
15#21440556—24no—
16C23×C4×C241C2211yescharacteristic
17C2×C22⋊C4×C241C2211yescharacteristic
18C2×C22⋊C4×C241C2211yescharacteristic
19#95×C241—22no—
20C23×D241D412yes—
21C2×D964—22no—
22C2×C22⋊D241—22no—
23C2×C22⋊D241—22no—
24C2×C22⋊D241—22no—
25C2×C22⋊D241—22no—
26C2×C22⋊D241—22no—
27C2×C22⋊D241—22no—
28C22×Dic241—22no—
29C22×Dic241D412yes—
30C4⋊Dic241—22no—
31#16838749—28no—
32C22⋊Dic241—22no—
33C22⋊Dic241D414yescomplemented
34#16838747—28no—
35#16838747—24no—
36C24×C241C2311yescharacteristic
37C22×C4×C241—22no—
38C22×C4×C241—22no—
39C22×C4×C241—21no—
40C22×C4×C241—21no—
41C22×C4×C241—21no—
42C22×C4×C241D412yes—
43C22×C4×C241D412yescomplemented
44C22⋊C4×C241—22no—
45C22⋊C4×C241—22no—
46C22×D241—22no—
47C22×D241—22no—
48C22×D241—22no—
49C22×D241—44no—
50D964—82no—
51C22⋊D241—42no—
52C22⋊D241—42no—
53C22⋊D241—42no—
54C22⋊D241—42no—
55C2×Dic241—24no—
56C2×Dic241—22no—
57C2×Dic241—22no—
58C2×Dic241—22no—
59C2×Dic241—44no—
60C23×C241—42no—
61C23×C241C2×D412yes—
62C23×C241C2×D412yes—
63C23×C241C2×D411yescharacteristic
64C23×C241C2×D411yescharacteristic
65C23×C241#4111yescharacteristic
66C2×C4×C241—22no—
67C2×C4×C241—24no—
68C2×C4×C241—22no—
69C2×C4×C241—41no—
70C2×C4×C241—42no—
71C2×C4×C241—41no—
72C2×C4×C241—42no—
73C2×C4×C241—42no—
74C2×C4×C241—41no—
75C22×C241—22no—
76C22×C241—24no—
77C22×C241—42no—
78C22×C241—41no—
79C22×C241—41no—
80C22×C241#12011yescharacteristic
81C22×C241#12012yes—
82C22×C241#12112yes—
83C22×C241#12111yescharacteristic
84C22×C241#12711yescharacteristic
85C2×D241—44no—
86C2×D241—42no—
87C2×D241—44no—
88C2×D241—82no—
89C4×C241—42no—
90C4×C241—42no—
91C4×C241—81no—
92Dic241—44no—
93Dic241—42no—
94C2×C241—22no—
95C2×C241—21no—
96C2×C241—22no—
97C2×C241—21no—
98C2×C241#39211yescharacteristic
99C2×C241#45812yes—
100D241—82no—
101C241#202211yescharacteristic, complemented, Sylow
102#2022—2411nomaximal, Sylow
103#534—2411no—
104C2×#123—2412no—
105C2×#99—2412no—
106#381D24111yescharacteristic, complemented
107#342—2411no—
108C22×D4—2412no—
109C23×C4C2×D24111yescharacteristic
110#123—4822no—
111#123—4824no—
112#123—4824no—
113#121—4822no—
114#120—4822no—
115C2×C4⋊C4—4822no—
116C2×C22⋊C4—4822no—
117C2×C22⋊C4—2412no—
118C2×C22⋊C4C2×D24111yescharacteristic
119C2×C22⋊C4C2×D24111yescharacteristic
120#99—4824no—
121#95—22no—
122C24—2412no—
123C24C22×D24111yescharacteristic
124C2×D4—4822no—
125C2×D4—4822no—
126C2×D4—4822no—
127C2×D4—4822no—
128C2×D4—4822no—
129C2×D4—4822no—
130C2×D4—4822no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—4822no—
137C22×C4—2412no—
138C22×C4C22⋊D24112yes—
139C22×C4D96412yescomplemented
140C4⋊C4—4828no—
141C4⋊C4—4822no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—4828no—
145C22⋊C4—4824no—
146C22⋊C4—4822no—
147C22⋊C4—2414no—
148C23—42no—
149C23—9644no—
150C23—4822no—
151C23—4822no—
152C23—4822no—
153C23D4×D24112yes—
154C23D4×D24112yes—
155C23C2×C22⋊D24111yescharacteristic
156C23C2×D96411yescharacteristic
157C23#1683877011yescharacteristic
158D4—19282no—
159D4—9642no—
160D4—9642no—
161D4—9642no—
162D4—9642no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—9644no—
173C2×C4—4822no—
174C2×C4—4824no—
175C2×C4—4822no—
176C2×C4—4822no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—19282no—
183C22—9644no—
184C22—9642no—
185C22—9644no—
186C22#2144061011yescharacteristic
187C22#2144061212yes—
188C22#2144061512yes—
189C22#2144061611yescharacteristic
190C22#2144063811yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—9644no—
195C4—9642no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—19282no—
201C2#2950762611yescharacteristic
202C2#2950790612yes—
subgroupG/H
centerC22#21440610
commutator, cosocleC24×C241C23
FrattiniC24C22×D241
Fitting#381×C241C2
socleC22×C241#120
prime radical#29508279C2
hypercenter#381D241
hypocenterC241#2022
LCSG ▷ C24×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#21440625C2semidirect
3. C2×#21440556C2semidirect
4. #29507484C2semidirect
5. #381×C241C2semidirect
33. C22⋊Dic241D4semidirect
43. C22×C4×C241D4semidirect
101. C241#2022semidirect
106. #381D241semidirect
139. C22×C4D964semidirect

Maximal subgroups

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

subgroupindex
#295082792
C2×#214406252
C2×#214405562
#295074842
#381×C2412
#2022241