Finite Group Databasebeta

← #44508431

Subgroups — #44508431

Order 30848.

324 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 101 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#29507577C211yesmaximal, characteristic
2C4×C22⋊Dic241C211yesmaximal, characteristic
3#29507484C214yesmaximal
4C2×C22⋊Q8×C241C211yesmaximal, characteristic
5C2×C4⋊Dic241—21no—
6C2×C22⋊Dic241C2212yes—
7C2×C22⋊Dic241C2212yes—
8C2×C4×Dic241—21no—
9#21440549—21no—
10#21440549—21no—
11C22×Q8×C241C411yescharacteristic, complemented
12C23×C4×C241C2211yescharacteristic
13C22⋊Q8×C241—21no—
14C22⋊Q8×C241—21no—
15C22⋊Q8×C241—21no—
16C22⋊Q8×C241—21no—
17C2×C4⋊C4×C241C411yescharacteristic, complemented
18C2×C4⋊C4×C241C412yescomplemented
19C2×C22⋊C4×C241C2212yes—
20C22×Dic241—22no—
21C22×Dic241—22no—
22C4⋊Dic241—42no—
23C22⋊Dic241—22no—
24C22⋊Dic241—24no—
25C22⋊Dic241Q814yescomplemented
26C4×Dic241—42no—
27C24×C241C2311yescharacteristic
28C2×Q8×C241—21no—
29C2×Q8×C241—21no—
30C2×Q8×C241—42no—
31C22×C4×C241—42no—
32C22×C4×C241C2×C411yescharacteristic
33C22×C4×C241C2×C412yes—
34C22×C4×C241C2×C412yes—
35C22×C4×C241C2×C411yescharacteristic
36C22×C4×C241D411yescharacteristic
37C22×C4×C241D411yescharacteristic
38C22×C4×C241D411yescharacteristic
39C22×C4×C241D411yescharacteristic
40C4⋊C4×C241—21no—
41C4⋊C4×C241—21no—
42C4⋊C4×C241—22no—
43C4⋊C4×C241—22no—
44C22⋊C4×C241—22no—
45C22⋊C4×C241—22no—
46C2×Dic241—24no—
47C2×Dic241—42no—
48C2×Dic241—42no—
49C2×Dic241—42no—
50C2×Dic241—42no—
51C2×Dic241—42no—
52C23×C241—41no—
53C23×C241—41no—
54C23×C241C22×C411yescharacteristic
55C23×C241C2×D411yescharacteristic
56C23×C241C2×D411yescharacteristic
57C23×C241C2×Q812yes—
58C23×C241#4112yes—
59Q8×C241—42no—
60Q8×C241—42no—
61C2×C4×C241—22no—
62C2×C4×C241—22no—
63C2×C4×C241—22no—
64C2×C4×C241—22no—
65C2×C4×C241—22no—
66C2×C4×C241—41no—
67C2×C4×C241—41no—
68C2×C4×C241—41no—
69C2×C4×C241—42no—
70C2×C4×C241—42no—
71C2×C4×C241C22⋊C411yescharacteristic
72C2×C4×C241C22⋊C411yescharacteristic
73C2×C4×C241C22⋊C411yescharacteristic
74C2×C4×C241C22⋊C411yescharacteristic
75C22×C241—21no—
76C22×C241—21no—
77C22×C241—21no—
78C22×C241—21no—
79C22×C241—21no—
80C22×C241—21no—
81C22×C241—42no—
82C22×C241—42no—
83C22×C241C2×C22⋊C411yescharacteristic
84C22×C241C4×Q812yes—
85C22×C241C22⋊Q812yes—
86C22×C241#12411yescharacteristic
87C22×C241C4⋊Q811yescharacteristic
88C4×C241—21no—
89C4×C241—21no—
90C4×C241—21no—
91C4×C241—42no—
92C4×C241—42no—
93C4×C241#9912yes—
94Dic241—44no—
95Dic241—82no—
96C2×C241—22no—
97C2×C241—21no—
98C2×C241—22no—
99C2×C241—21no—
100C2×C241#39111yescharacteristic
101C2×C241C2×#9911yescharacteristic
102C2×C241#41011yescharacteristic
103C241#199611yescharacteristic, complemented, Sylow
104#1996—2411nomaximal, Sylow
105C2×C22⋊Q8D24111yescharacteristic
106#380—2411no—
107C4×C22⋊C4—2411no—
108#342—2414no—
109C22×Q8Dic24111yescharacteristic, complemented
110C23×C4C2×D24111yescharacteristic
111C22⋊Q8—21no—
112C22⋊Q8—21no—
113C22⋊Q8—21no—
114C22⋊Q8—21no—
115C2×C4⋊C4—4821no—
116C2×C4⋊C4Dic24111yescharacteristic, complemented
117C2×C4⋊C4Dic24112yescomplemented
118C2×C22⋊C4—2412no—
119C2×C22⋊C4—2412no—
120C2×C22⋊C4C2×D24112yes—
121C2×C42—4821no—
122#95—4821no—
123#95—4821no—
124C24C22×D24111yescharacteristic
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—42no—
128C22×C4—42no—
129C22×C4—4822no—
130C22×C4—4822no—
131C22×C4C2×Dic24111yescharacteristic
132C22×C4C2×Dic24112yes—
133C22×C4C2×Dic24112yes—
134C22×C4C2×Dic24111yescharacteristic
135C22×C4C22⋊D24111yescharacteristic
136C22×C4C22⋊D24111yescharacteristic
137C22×C4C22⋊D24111yescharacteristic
138C22×C4C22⋊D24111yescharacteristic
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—9642no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—4824no—
147C22⋊C4—4822no—
148C22⋊C4—2414no—
149C42—9642no—
150C23—41no—
151C23—41no—
152C23C22×Dic24111yescharacteristic
153C23C2×C22⋊D24111yescharacteristic
154C23C2×C22⋊D24111yescharacteristic
155C23Q8×D24112yes—
156C23#1683877112yes—
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—9642no—
170C2×C4—9642no—
171C2×C4—9642no—
172C2×C4—9642no—
173C2×C4—9642no—
174C2×C4—4824no—
175C2×C4C22⋊Dic24111yescharacteristic
176C2×C4C22⋊Dic24111yescharacteristic
177C2×C4C22⋊Dic24111yescharacteristic
178C2×C4C22⋊Dic24111yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×C22⋊Dic24111yescharacteristic
188C22Q8×Dic24112yes—
189C22#2144061812yes—
190C22#2144063111yescharacteristic
191C22#2144064011yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—42no—
196C4—42no—
197C4—19282no—
198C4—9644no—
199C4#2144055712yes—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2#2950762411yescharacteristic
205C2C2×#2144055711yescharacteristic
206C2#2950769111yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic241
commutatorC23×C241C22×C4
FrattiniC24C22×D241
FittingC2×C22⋊Q8×C241C2
socleC22×C241C2×C22⋊C4
prime radical, cosocleC24×C241C23
hypercenterC2×C22⋊Q8D241
hypocenterC241#1996
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
11. C22×Q8×C241C4semidirect
17. C2×C4⋊C4×C241C4semidirect
18. C2×C4⋊C4×C241C4semidirect
25. C22⋊Dic241Q8semidirect
103. C241#1996semidirect
109. C22×Q8Dic241semidirect
116. C2×C4⋊C4Dic241semidirect
117. C2×C4⋊C4Dic241semidirect

Maximal subgroups

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

subgroupindex
#295075772
C4×C22⋊Dic2412
#295074842
C2×C22⋊Q8×C2412
#1996241