Finite Group Databasebeta

← #44507901

Subgroups — #44507901

Order 30848.

378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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×#21440625C211yesmaximal, characteristic
2C2×#21440601C211yesmaximal, characteristic, complemented
3C2×#21440556C212yesmaximal
4#29507483C212yesmaximal, complemented
5#381×C241C211yesmaximal, characteristic, complemented
6C22×C22⋊D241C2211yescharacteristic
7#21440625—22no—
8#21440625—21no—
9#21440625—21no—
10#21440601—24no—
11C2×C4⋊Dic241—21no—
12C2×#16838749C412yescomplemented
13C2×C22⋊Dic241C2211yescharacteristic
14C2×C22⋊Dic241C2212yes—
15C2×#16838747C412yescomplemented
16C2×C4×Dic241—21no—
17#21440556—24no—
18C23×C4×C241C2211yescharacteristic
19C2×C22⋊C4×C241C2212yes—
20#95×C241—22no—
21C23×D241C2×C411yescharacteristic
22C2×C22⋊D241—22no—
23C2×C22⋊D241—21no—
24C2×C22⋊D241—21no—
25C2×C22⋊D241—22no—
26C22×Dic241—22no—
27C22×Dic241C2×C411yescharacteristic
28C22×Dic241C2×C412yes—
29C4⋊Dic241—24no—
30#16838749—22no—
31#16838749—22no—
32C22⋊Dic241—22no—
33C22⋊Dic241—21no—
34C22⋊Dic241—21no—
35C22⋊Dic241D414yes—
36#16838747—22no—
37#16838747—22no—
38C4×Dic241—24no—
39C24×C241C2311yescharacteristic
40C22×C4×C241—22no—
41C22×C4×C241—22no—
42C22×C4×C241—22no—
43C22×C4×C241C2×C412yes—
44C22×C4×C241D412yes—
45C22×C4×C241D411yescharacteristic
46C22×C4×C241D411yescharacteristic
47C22⋊C4×C241—22no—
48C22⋊C4×C241—22no—
49C22×D241—21no—
50C22×D241—22no—
51C22×D241—42no—
52C22⋊D241—41no—
53C22⋊D241—42no—
54C22⋊D241—41no—
55C2×Dic241—22no—
56C2×Dic241—21no—
57C2×Dic241—22no—
58C2×Dic241—24no—
59C2×Dic241—44no—
60C2×Dic241—42no—
61C23×C241—42no—
62C23×C241C22×C411yescharacteristic
63C23×C241C2×D412yes—
64C23×C241C2×D411yescharacteristic
65C23×C241C2×D411yescharacteristic
66C23×C241#4112yes—
67C2×C4×C241—24no—
68C2×C4×C241—21no—
69C2×C4×C241—21no—
70C2×C4×C241—24no—
71C2×C4×C241—21no—
72C2×C4×C241—21no—
73C2×C4×C241—44no—
74C2×C4×C241—42no—
75C2×C4×C241C22⋊C412yes—
76C2×C4×C241C22⋊C412yes—
77C22×C241—22no—
78C22×C241—22no—
79C22×C241—22no—
80C22×C241—42no—
81C22×C241—42no—
82C22×C241C2×C22⋊C411yescharacteristic
83C22×C241C4×D412yes—
84C22×C241#12011yescharacteristic
85C22×C241#12112yes—
86C22×C241#12311yescharacteristic
87C2×D241—41no—
88C2×D241—42no—
89C2×D241—82no—
90C4×C241—22no—
91C4×C241—22no—
92C4×C241—82no—
93Dic241—44no—
94Dic241—41no—
95Dic241—42no—
96C2×C241—21no—
97C2×C241—22no—
98C2×C241—22no—
99C2×C241—21no—
100C2×C241#38611yescharacteristic
101C2×C241#41012yes—
102D241—81no—
103C241#189911yescharacteristic, complemented, Sylow
104#1899—2411nomaximal, Sylow
105C2×#123—2411no—
106C2×#117—2411no—
107C2×#99—2412no—
108#381D24111yescharacteristic, complemented
109#342—2412no—
110C22×D4—2411no—
111C23×C4C2×D24111yescharacteristic
112#123—4822no—
113#123—4821no—
114#123—4821no—
115#117—4824no—
116C2×C4⋊C4—4821no—
117C2×C4⋊C4—2412no—
118C2×C22⋊C4—2411no—
119C2×C22⋊C4—2412no—
120C2×C22⋊C4—2412no—
121C2×C22⋊C4C2×D24112yes—
122C2×C42—4821no—
123#99—4824no—
124#95—22no—
125C24—2411no—
126C24C22×D24111yescharacteristic
127C2×D4—4822no—
128C2×D4—4821no—
129C2×D4—4821no—
130C2×D4—4822no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—4822no—
135C22×C4—2412no—
136C22×C4—2411no—
137C22×C4C4×D24112yes—
138C22×C4C22⋊D24112yes—
139C22×C4D96411yescharacteristic
140C22×C4D96411yescharacteristic
141C4⋊C4—4824no—
142C4⋊C4—4822no—
143C4⋊C4—4822no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—4822no—
147C22⋊C4—4821no—
148C22⋊C4—4821no—
149C22⋊C4—4822no—
150C22⋊C4—4822no—
151C22⋊C4—2414no—
152C42—4824no—
153C23—42no—
154C23—9642no—
155C23—4822no—
156C23—4821no—
157C23C2×C4×D24111yescharacteristic
158C23D4×D24112yes—
159C23C2×C22⋊D24111yescharacteristic
160C23C2×D96411yescharacteristic
161C23#1683876912yes—
162D4—9641no—
163D4—9642no—
164D4—9641no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—9644no—
174C2×C4—9642no—
175C2×C4—4822no—
176C2×C4—4821no—
177C2×C4—4822no—
178C2×C4—4824no—
179C2×C4#1683874712yes—
180C2×C4#1683874712yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—19282no—
187C22—9641no—
188C22—9642no—
189C22C2×#1683874711yescharacteristic
190C22#2144060212yes—
191C22#2144061211yescharacteristic
192C22#2144061412yes—
193C22#2144062611yescharacteristic
194C4—22no—
195C4—22no—
196C4—82no—
197C4—9644no—
198C4—9641no—
199C4—9642no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—19281no—
205C2#2950759411yescharacteristic
206C2#2950769012yes—
subgroupG/H
centerC22C2×#16838747
commutatorC23×C241C22×C4
FrattiniC24C22×D241
Fitting#381×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC22×C22⋊D241C22
cosocleC24×C241C23
hypercenter#381D241
hypocenterC241#1899
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#21440601C2semidirect
4. #29507483C2semidirect
5. #381×C241C2semidirect
12. C2×#16838749C4semidirect
15. C2×#16838747C4semidirect
103. C241#1899semidirect
108. #381D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406252
C2×#214406012
C2×#214405562
#295074832
#381×C2412
#1899241