Finite Group Databasebeta

← #44505782

Subgroups — #44505782

Order 30848.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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×#21440604C211yesmaximal, characteristic
2#29507679C212yesmaximal, complemented
3#29507443C211yesmaximal, characteristic, complemented
4#29507440C212yesmaximal, complemented
5#324×C241C211yesmaximal, characteristic, complemented
6C22×D964C411yescharacteristic
7C22×C4×D241C411yescharacteristic
8C22×C4×D241C2211yescharacteristic
9C2×#16838753—22no—
10#21440604—22no—
11#21440604—22no—
12C2×#16838747C411yescharacteristic
13C2×#16838747C2211yescharacteristic
14C2×C4×Dic241C411yescharacteristic
15C22⋊#14515349C2212yes—
16#21440554—22no—
17C2×C4⋊C4×C241C2211yescharacteristic
18C22⋊C8×C241C2212yes—
19C23×D241C2×C411yescharacteristic
20C23×D241C2×C411yescharacteristic
21C2×D964—22no—
22C2×D964—22no—
23C2×D964—22no—
24C22×Dic241C2×C411yescharacteristic
25C22×Dic241C2×C411yescharacteristic
26C2×C4×D241—21no—
27C2×C4×D241—21no—
28C2×C4×D241—42no—
29C2×C4×D241—42no—
30C2×C4×D241D412yes—
31C2×C4×D241D412yes—
32#16838753—44no—
33C2×#14515349—22no—
34#16838747—22no—
35#16838747—22no—
36C4×Dic241—21no—
37C4×Dic241—21no—
38C22×C4×C241C2×C411yescharacteristic
39C22×C4×C241C2×C411yescharacteristic
40C22×C4×C241C2311yescharacteristic
41C2×C8×C241—22no—
42C4⋊C4×C241—22no—
43C22×D241—21no—
44C22×D241—21no—
45C22×D241—21no—
46C22×D241—21no—
47C22×D241—41no—
48C22×D241—41no—
49C22×D241—41no—
50C22×D241—41no—
51C22×D241C22⋊C412yes—
52C22×D241M1612yescomplemented
53D964—28no—
54C2×Dic241—22no—
55C2×Dic241—21no—
56C2×Dic241—41no—
57C2×Dic241C22⋊C411yescharacteristic
58C2×Dic241C22⋊C411yescharacteristic
59C4×D241—24no—
60C4×D241—42no—
61C4×D241—42no—
62C4×D241—42no—
63#14515349—42no—
64C23×C241C22×C411yescharacteristic
65C2×C4×C241—21no—
66C2×C4×C241—21no—
67C2×C4×C241—21no—
68C2×C4×C241—41no—
69C2×C4×C241—41no—
70C2×C4×C241M1612yescomplemented
71C2×C4×C241C2×D412yes—
72C8×C241—42no—
73C22×C241—21no—
74C22×C241—21no—
75C22×C241C2×C22⋊C411yescharacteristic
76C22×C241C2×M1611yescharacteristic
77C22×C241C2×M1611yescharacteristic
78C2×D241—22no—
79C2×D241—22no—
80C2×D241—22no—
81C2×D241—22no—
82C2×D241—42no—
83C2×D241—42no—
84C2×D241—42no—
85C2×D241—41no—
86C2×D241—41no—
87C2×D241—42no—
88C4×C241—22no—
89C4×C241—22no—
90C4×C241—41no—
91Dic241—21no—
92Dic241—41no—
93Dic241#9912yes—
94C2×C241—21no—
95C2×C241—21no—
96C2×C241#40711yescharacteristic
97C2×C241C2×#9911yescharacteristic
98C2×C241#41311yescharacteristic
99D241—42no—
100D241—42no—
101C241#146511yescharacteristic, complemented, Sylow
102#1465—2411nomaximal, Sylow
103C2×C4×D4—2411no—
104#407—2412no—
105#324—2411no—
106#324D24111yescharacteristic, complemented
107#323—2412no—
108C22×D4—2411no—
109C23×C4—2411no—
110C23×C4—2411no—
111C2×M16—4822no—
112C4×D4—4822no—
113C4×D4—4822no—
114C2×C4⋊C4C2×D24111yescharacteristic
115C2×C22⋊C4—2411no—
116C2×C22⋊C4—2411no—
117C2×C42—2411no—
118C22⋊C8—4822no—
119C22⋊C8—2412no—
120C22⋊C8C2×D24112yes—
121C24—2411no—
122C24—2411no—
123C2×D4—4822no—
124C2×D4—4822no—
125C2×D4—4822no—
126C22×C4—9642no—
127C22×C4—9642no—
128C22×C4—4821no—
129C22×C4—4821no—
130C22×C4—2411no—
131C22×C4—2412no—
132C22×C4—2411no—
133C22×C4—2412no—
134C22×C4C4×D24111yescharacteristic
135C22×C4C4×D24111yescharacteristic
136C22×C4C22×D24111yescharacteristic
137M16—9644no—
138C2×C8—22no—
139C2×C8—4822no—
140C4⋊C4—22no—
141C22⋊C4—4822no—
142C22⋊C4—4822no—
143C42—4821no—
144C42—4821no—
145C23—9641no—
146C23—9641no—
147C23—9641no—
148C23—9641no—
149C23—4821no—
150C23—4821no—
151C23—4821no—
152C23—4821no—
153C23—2412no—
154C23—2412no—
155C23C2×C4×D24111yescharacteristic
156D4—4828no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—9642no—
163C2×C4—9642no—
164C2×C4—9642no—
165C2×C4—9641no—
166C2×C4—4824no—
167C2×C4—4821no—
168C2×C4—4822no—
169C2×C4—2411no—
170C2×C4—2411no—
171C2×C4#1683875312yescomplemented
172C2×C4D4×D24112yes—
173C8—42no—
174C8—9642no—
175C22—21no—
176C22—21no—
177C22—9642no—
178C22—9642no—
179C22—9642no—
180C22—9642no—
181C22—9641no—
182C22—9641no—
183C22—4822no—
184C22—4822no—
185C22—4822no—
186C22—4822no—
187C22C22⋊C4×D24111yescharacteristic
188C22M16×D24111yescharacteristic
189C22C2×#1683875311yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—9641no—
194C4—4821no—
195C4—2412no—
196C2—21no—
197C2—21no—
198C2—9642no—
199C2—9642no—
200C2#2950767911yescharacteristic
201C2#99×D24111yescharacteristic
202C2#2950770011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC23×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#324×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC22×D964C4
cosocleC22×C4×C241C23
hypercenter#324D241
hypocenterC241#1465
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #29507679C2semidirect
3. #29507443C2semidirect
4. #29507440C2semidirect
5. #324×C241C2semidirect
52. C22×D241M16semidirect
70. C2×C4×C241M16semidirect
101. C241#1465semidirect
106. #324D241semidirect
171. C2×C4#16838753semidirect

Maximal subgroups

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

subgroupindex
C2×#214406042
#295076792
#295074432
#295074402
#324×C2412
#1465241