Finite Group Databasebeta

← #44506137

Subgroups — #44506137

Order 30848.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#29508265C211yesmaximal, characteristic
2#29507773C211yesmaximal, characteristic, complemented
3C4⋊C8×D241C211yesmaximal, characteristic, complemented
4#29507465C211yesmaximal, characteristic, complemented
5#29507465C211yesmaximal, characteristic, complemented
6#29507461C211yesmaximal, characteristic, complemented
7#331×C241C211yesmaximal, characteristic, complemented
8C2×#16838769C412yes—
9C2×C8×D241—21no—
10#21440642C2211yescharacteristic
11#21440629C412yes—
12#21440613—21no—
13#21440613—21no—
14D4×Dic241—21no—
15D4×Dic241—21no—
16C42×D241C2211yescharacteristic
17C4⋊#14515349C2211yescharacteristic
18C4⋊#14515349C2211yescharacteristic
19#21440571—21no—
20#21440554—21no—
21#21440552—21no—
22#127×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25#16838769—44no—
26C2×Dic482C2×C412yes—
27C2×C22⋊D241—22no—
28C22×Dic241—22no—
29C2×C4×D241C2×C411yescharacteristic
30C2×C4×D241D411yescharacteristic
31C2×C4×D241D411yescharacteristic
32C2×#14515349—21no—
33C2×#14515349—21no—
34C8×D241—42no—
35C4⋊Dic241—21no—
36C4⋊Dic241—21no—
37C22⋊Dic241—22no—
38C22⋊Dic241—22no—
39C4×Dic241C2×C411yescharacteristic
40C4×Dic241D411yescharacteristic
41C4×Dic241D411yescharacteristic
42C2×D4×C241—21no—
43C2×D4×C241—21no—
44C2×D4×C241C2×C412yes—
45C2×C8×C241—21no—
46C2×C8×C241—21no—
47C42×C241C2311yescharacteristic
48C22×D241C22⋊C411yescharacteristic
49Dic482—42no—
50C22⋊D241—44no—
51C2×Dic241—22no—
52C2×Dic241—44no—
53C2×Dic241C22⋊C411yescharacteristic
54C2×Dic241C22⋊C411yescharacteristic
55C2×Dic241C22⋊C411yescharacteristic
56C4×D241—22no—
57C4×D241—21no—
58C4×D241—21no—
59C4×D241—21no—
60C4×D241—21no—
61#14515349—41no—
62#14515349—41no—
63C23×C241—22no—
64D4×C241—42no—
65D4×C241—41no—
66D4×C241—41no—
67D4×C241—41no—
68D4×C241—41no—
69C2×C4×C241C22×C411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C8×C241—41no—
73C8×C241—41no—
74C22×C241—42no—
75C22×C241—42no—
76C22×C241—42no—
77C22×C241C2×C22⋊C411yescharacteristic
78C2×D241—21no—
79C2×D241—21no—
80C2×D241#10012yes—
81C4×C241—21no—
82C4×C241#13511yescharacteristic
83C4×C241#13511yescharacteristic
84C4×C241AGL(1,ℤ/8)11yescharacteristic
85C4×C241#13711yescharacteristic
86Dic241—21no—
87Dic241—21no—
88Dic241—21no—
89Dic241—42no—
90C2×C241—82no—
91C2×C241C2×#10011yescharacteristic
92C2×C241#41611yescharacteristic
93C2×C241#41711yescharacteristic
94D241—22no—
95C241#155111yescharacteristic, complemented, Sylow
96#1551—2411nomaximal, Sylow
97#532—2411no—
98#432—2411no—
99C2×C4⋊C8—2411no—
100#333—2411no—
101#333—2411no—
102#331—2411no—
103#331D24111yescharacteristic, complemented
104C2×#41—2412no—
105C22×C8—4821no—
106C4⋊Q8—2411no—
107#127C2×D24111yescharacteristic
108#124—2412no—
109#121—4821no—
110#121—4821no—
111C4×D4—4821no—
112C4×D4—4821no—
113C2×C42—2411no—
114C4⋊C8—4821no—
115C4⋊C8—2411no—
116C4⋊C8—2411no—
117C4⋊C8C2×D24111yescharacteristic
118C4⋊C8C2×D24111yescharacteristic
119C22⋊C8—4821no—
120#97—4821no—
121#41—9644no—
122C2×Q8—2412no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—4822no—
126C2×D4C4×D24112yes—
127C22×C4—4822no—
128C22×C4—2411no—
129C22×C4—2411no—
130C22×C4—2411no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—9642no—
134C2×C8—4821no—
135C2×C8—4821no—
136C4⋊C4—4821no—
137C4⋊C4—4821no—
138C22⋊C4—4822no—
139C22⋊C4—4822no—
140C42—2411no—
141C42—2411no—
142C42—2411no—
143C42C22×D24111yescharacteristic
144C23—22no—
145C23—2411no—
146Q8—9642no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—9644no—
153C2×C4—9644no—
154C2×C4—4822no—
155C2×C4—4822no—
156C2×C4—4821no—
157C2×C4—4821no—
158C2×C4—4821no—
159C2×C4—4821no—
160C2×C4—2411no—
161C2×C4—2411no—
162C2×C4—2411no—
163C2×C4C2×C4×D24111yescharacteristic
164C2×C4D4×D24111yescharacteristic
165C2×C4D4×D24111yescharacteristic
166C8—41no—
167C8—41no—
168C8—9641no—
169C8—9641no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—4821no—
174C22—4821no—
175C22—2412no—
176C22C22⋊C4×D24111yescharacteristic
177C4—21no—
178C4—9642no—
179C4—4821no—
180C4—4821no—
181C4—4821no—
182C4#2144066111yescharacteristic
183C4#2144066311yescharacteristic
184C4#2144066611yescharacteristic
185C4#2144067111yescharacteristic
186C2—82no—
187C2—4822no—
188C2#100×D24111yescharacteristic
189C2#2950771011yescharacteristic
190C2#2950771511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC42C22×D241
Fitting#331×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508265C2
cosocleC42×C241C23
hypercenter#331D241
hypocenterC241#1551
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #29507773C2semidirect
3. C4⋊C8×D241C2semidirect
4. #29507465C2semidirect
5. #29507465C2semidirect
6. #29507461C2semidirect
7. #331×C241C2semidirect
95. C241#1551semidirect
103. #331D241semidirect

Maximal subgroups

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

subgroupindex
#295082652
#295077732
C4⋊C8×D2412
#295074652
#295074612
#331×C2412
#1551241