Finite Group Databasebeta

← #44506091

Subgroups — #44506091

Order 30848.

256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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#29507769C211yesmaximal, characteristic, complemented
3C4⋊C8×D241C211yesmaximal, characteristic, complemented
4#29507464C211yesmaximal, characteristic, complemented
5#29507462C211yesmaximal, characteristic, complemented
6#29507461C211yesmaximal, characteristic, complemented
7#331×C241C211yesmaximal, characteristic, complemented
8C2×#16838769—21no—
9C2×C8×D241—21no—
10#21440642C2211yescharacteristic
11#21440629—21no—
12#21440613—21no—
13#21440613C412yes—
14D4×Dic241—21no—
15D4×Dic241C412yes—
16C42×D241C2211yescharacteristic
17C4⋊#14515349C2211yescharacteristic
18C4⋊#14515349C2211yescharacteristic
19#21440571—21no—
20#21440554—21no—
21C8×Dic241—21no—
22#127×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25#16838769—42no—
26#16838769—42no—
27C2×Dic482—21no—
28C2×C22⋊D241—22no—
29C22×Dic241—22no—
30C2×C4×D241C2×C411yescharacteristic
31C2×C4×D241D411yescharacteristic
32C2×C4×D241D411yescharacteristic
33C2×#14515349—21no—
34C2×#14515349—21no—
35C8×D241—42no—
36C4⋊Dic241—21no—
37C4⋊Dic241C2×C412yes—
38C22⋊Dic241—22no—
39C22⋊Dic241—22no—
40C4×Dic241C2×C411yescharacteristic
41C4×Dic241D411yescharacteristic
42C4×Dic241D411yescharacteristic
43C2×D4×C241—21no—
44C2×D4×C241—21no—
45C2×D4×C241C2×C412yes—
46C2×C8×C241—21no—
47C2×C8×C241—21no—
48C42×C241C2311yescharacteristic
49C22×D241C22⋊C411yescharacteristic
50Dic482—41no—
51Dic482—41no—
52C22⋊D241—44no—
53C2×Dic241—22no—
54C2×Dic241—44no—
55C2×Dic241C22⋊C411yescharacteristic
56C2×Dic241C22⋊C411yescharacteristic
57C2×Dic241C22⋊C411yescharacteristic
58C4×D241—21no—
59C4×D241—21no—
60C4×D241—41no—
61C4×D241D812yes—
62C4×D241SD1612yes—
63#14515349—41no—
64#14515349—41no—
65C23×C241—22no—
66D4×C241—42no—
67D4×C241—41no—
68D4×C241—41no—
69D4×C241—41no—
70D4×C241—41no—
71C2×C4×C241C22×C411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C2×C4×C241C2×D411yescharacteristic
74C8×C241—41no—
75C8×C241—41no—
76C22×C241—42no—
77C22×C241—42no—
78C22×C241—42no—
79C22×C241C2×C22⋊C411yescharacteristic
80C2×D241—21no—
81C2×D241—21no—
82C2×D241#10212yes—
83C4×C241—21no—
84C4×C241C2×D811yescharacteristic
85C4×C241C2×SD1611yescharacteristic
86C4×C241#13511yescharacteristic
87C4×C241#13511yescharacteristic
88Dic241—21no—
89Dic241—21no—
90Dic241—42no—
91Dic241#10212yes—
92C2×C241—82no—
93C2×C241#41311yescharacteristic
94C2×C241C2×#10211yescharacteristic
95C2×C241#41611yescharacteristic
96D241—22no—
97C241#154011yescharacteristic, complemented, Sylow
98#1540—2411nomaximal, Sylow
99#532—2411no—
100#431—2411no—
101C2×C4⋊C8—2411no—
102#332—2411no—
103#332—2411no—
104#331—2411no—
105#331D24111yescharacteristic, complemented
106C2×#41—4821no—
107C22×C8—4821no—
108C4⋊Q8—2411no—
109#127C2×D24111yescharacteristic
110#124—4821no—
111#121—4821no—
112#121—2412no—
113C4×D4—4821no—
114C4×D4—2412no—
115C2×C42—2411no—
116C4⋊C8—4821no—
117C4⋊C8—2411no—
118C4⋊C8—2411no—
119C4⋊C8C2×D24111yescharacteristic
120C4⋊C8C2×D24111yescharacteristic
121C22⋊C8—4821no—
122C4×C8—4821no—
123#41—9642no—
124#41—9642no—
125C2×Q8—4821no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—4822no—
129C2×D4C4×D24112yes—
130C22×C4—4822no—
131C22×C4—2411no—
132C22×C4—2411no—
133C22×C4—2411no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—9642no—
137C2×C8—4821no—
138C2×C8—4821no—
139C4⋊C4—4821no—
140C4⋊C4—2412no—
141C22⋊C4—4822no—
142C22⋊C4—4822no—
143C42—2411no—
144C42—2411no—
145C42—2411no—
146C42C22×D24111yescharacteristic
147C23—22no—
148C23—2411no—
149Q8—9641no—
150Q8—9641no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—9644no—
157C2×C4—9641no—
158C2×C4—9644no—
159C2×C4—4822no—
160C2×C4—4821no—
161C2×C4—4821no—
162C2×C4—2411no—
163C2×C4—2411no—
164C2×C4—2411no—
165C2×C4—2412no—
166C2×C4—2412no—
167C2×C4C2×C4×D24111yescharacteristic
168C2×C4D4×D24111yescharacteristic
169C2×C4D4×D24111yescharacteristic
170C8—41no—
171C8—41no—
172C8—9641no—
173C8—9641no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—4821no—
178C22—4821no—
179C22—2412no—
180C22C22⋊C4×D24111yescharacteristic
181C4—21no—
182C4—9642no—
183C4—4821no—
184C4—4821no—
185C4—2412no—
186C4D8×D24111yescharacteristic
187C4SD16×D24111yescharacteristic
188C4#2144066111yescharacteristic
189C4#2144066311yescharacteristic
190C2—82no—
191C2—4822no—
192C2#2950769811yescharacteristic
193C2#102×D24111yescharacteristic
194C2#2950771011yescharacteristic
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#1540
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. #29507769C2semidirect
3. C4⋊C8×D241C2semidirect
4. #29507464C2semidirect
5. #29507462C2semidirect
6. #29507461C2semidirect
7. #331×C241C2semidirect
97. C241#1540semidirect
105. #331D241semidirect

Maximal subgroups

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

subgroupindex
#295082652
#295077692
C4⋊C8×D2412
#295074642
#295074622
#295074612
#331×C2412
#1540241