Finite Group Databasebeta

← #44507518

Subgroups — #44507518

Order 30848.

504 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C22⋊C4×D241C211yesmaximal, characteristic
2#29507572C212yesmaximal
3#29507484C211yesmaximal, characteristic, complemented
4#29507483C212yesmaximal, complemented
5#342×C241C211yesmaximal, characteristic, complemented
6C24×D241C2211yescharacteristic
7C22×C4×D241C412yescomplemented
8C2×C22⋊Dic241C2212yes—
9C2×C22⋊Dic241C2211yescharacteristic
10C2×#16838747—24no—
11C2×#16838747C412yescomplemented
12C22⋊C4×D241—24no—
13C2×C22⋊C4×C241C2212yes—
14C2×C22⋊C4×C241C2211yescharacteristic
15C23×D241—21no—
16C23×D241—22no—
17C23×D241—21no—
18C23×D241—44no—
19C23×D241C2×C411yescharacteristic
20C23×D241C2×C411yescharacteristic
21C23×D241D414yes—
22C22×Dic241—22no—
23C22×Dic241C2×C412yes—
24C2×C4×D241—22no—
25C2×C4×D241—22no—
26C2×C4×D241—44no—
27C22⋊Dic241—22no—
28C22⋊Dic241—22no—
29C22⋊Dic241—22no—
30#16838747—24no—
31#16838747—48no—
32C24×C241C2311yescharacteristic
33C22×C4×C241—22no—
34C22×C4×C241C2×C412yes—
35C22⋊C4×C241—22no—
36C22⋊C4×C241—22no—
37C22⋊C4×C241—22no—
38C22×D241—21no—
39C22×D241—21no—
40C22×D241—24no—
41C22×D241—21no—
42C22×D241—21no—
43C22×D241—24no—
44C22×D241—24no—
45C22×D241—28no—
46C22×D241—42no—
47C22×D241—44no—
48C22×D241—44no—
49C22×D241—48no—
50C22×D241—44no—
51C22×D241C22⋊C412yes—
52C22×D241C22⋊C412yes—
53C2×Dic241—22no—
54C2×Dic241—42no—
55C2×Dic241—44no—
56C2×Dic241—42no—
57C4×D241—44no—
58C4×D241—44no—
59C23×C241—42no—
60C23×C241C22×C411yescharacteristic
61C23×C241C2×D412yes—
62C23×C241#4111yescharacteristic
63C23×C241#4112yes—
64C23×C241#4111yescharacteristic
65C2×C4×C241—22no—
66C2×C4×C241—42no—
67C2×C4×C241—44no—
68C2×C4×C241—42no—
69C22×C241—22no—
70C22×C241—24no—
71C22×C241—41no—
72C22×C241—42no—
73C22×C241—41no—
74C22×C241C2×C22⋊C411yescharacteristic
75C22×C241#11711yescharacteristic
76C22×C241#11711yescharacteristic
77C22×C241#12312yes—
78C22×C241#12312yes—
79C2×D241—24no—
80C2×D241—24no—
81C2×D241—22no—
82C2×D241—22no—
83C2×D241—22no—
84C2×D241—24no—
85C2×D241—48no—
86C2×D241—48no—
87C2×D241—42no—
88C2×D241—42no—
89C2×D241#9914yes—
90C4×C241—42no—
91C4×C241—82no—
92Dic241—42no—
93Dic241—82no—
94C2×C241—22no—
95C2×C241—22no—
96C2×C241—21no—
97C2×C241—21no—
98C2×C241#38111yescharacteristic
99C2×C241C2×#9912yes—
100D241—24no—
101D241—42no—
102C241#181911yescharacteristic, complemented, Sylow
103#1819—2411nomaximal, Sylow
104C22×C22⋊C4—2411no—
105#379—2412no—
106#342—2412no—
107#342—2411no—
108#342D24111yescharacteristic, complemented
109C25—2411no—
110C23×C4—2412no—
111C2×C22⋊C4—4824no—
112C2×C22⋊C4—4824no—
113C2×C22⋊C4—2412no—
114C2×C22⋊C4—2411no—
115C2×C22⋊C4—2412no—
116C2×C22⋊C4C2×D24112yes—
117C2×C22⋊C4C2×D24111yescharacteristic
118C24—9644no—
119C24—4821no—
120C24—4822no—
121C24—4821no—
122C24—2411no—
123C24—2414no—
124C24—2411no—
125C24C22×D24111yescharacteristic
126C22×C4—22no—
127C22×C4—9644no—
128C22×C4—4822no—
129C22×C4—4822no—
130C22×C4—4822no—
131C22×C4—2412no—
132C22×C4C4×D24112yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—9648no—
137C22⋊C4—4824no—
138C22⋊C4—4822no—
139C22⋊C4—4822no—
140C22⋊C4—4822no—
141C23—42no—
142C23—9642no—
143C23—9644no—
144C23—9644no—
145C23—9648no—
146C23—9644no—
147C23—4828no—
148C23—4824no—
149C23—4821no—
150C23—4821no—
151C23—4824no—
152C23—4824no—
153C23—4821no—
154C23—4821no—
155C23—2412no—
156C23—2412no—
157C23C2×C4×D24111yescharacteristic
158C23D4×D24112yes—
159C23#1683876911yescharacteristic
160C23#1683877012yes—
161C23#1683877111yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—9644no—
167C2×C4—9644no—
168C2×C4—9644no—
169C2×C4—9642no—
170C2×C4—9642no—
171C2×C4—4822no—
172C22—22no—
173C22—24no—
174C22—41no—
175C22—42no—
176C22—41no—
177C22—9642no—
178C22—9642no—
179C22—9648no—
180C22—9648no—
181C22—4824no—
182C22—4824no—
183C22—4824no—
184C22—4822no—
185C22—4822no—
186C22—4822no—
187C22—2414no—
188C22C22⋊C4×D24111yescharacteristic
189C22#2144059911yescharacteristic
190C22#2144060011yescharacteristic
191C22#2144062412yes—
192C22#2144062712yes—
193C4—42no—
194C4—82no—
195C4—19282no—
196C4—9642no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—9642no—
202C2—4824no—
203C2#2950757911yescharacteristic
204C2#99×D24112yes—
subgroupG/H
centerC22C22⋊C4×D241
commutatorC23×C241C22×C4
FrattiniC24C22×D241
Fitting#342×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC24×D241C22
cosocleC24×C241C23
hypercenter#342D241
hypocenterC241#1819
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #29507484C2semidirect
4. #29507483C2semidirect
5. #342×C241C2semidirect
7. C22×C4×D241C4semidirect
11. C2×#16838747C4semidirect
102. C241#1819semidirect
108. #342D241semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D2412
#295075722
#295074842
#295074832
#342×C2412
#1819241