Finite Group Databasebeta

← #44506147

Subgroups — #44506147

Order 30848.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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
3#29507769C211yesmaximal, characteristic, complemented
4#29507464C211yesmaximal, characteristic, complemented
5#29507462C211yesmaximal, characteristic, complemented
6#29507461C211yesmaximal, characteristic, complemented
7#331×C241C211yesmaximal, characteristic, complemented
8C2×#16838769—21no—
9#21440642C2211yescharacteristic
10#21440629—21no—
11#21440613—21no—
12#21440613C412yes—
13D4×Dic241—21no—
14D4×Dic241C412yes—
15C42×D241C2211yescharacteristic
16C4⋊#14515349C2211yescharacteristic
17C4⋊#14515349C2211yescharacteristic
18#21440554—21no—
19#21440554—21no—
20#21440552—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—
35C4⋊Dic241—21no—
36C4⋊Dic241C2×C412yes—
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—41no—
50Dic482—41no—
51C22⋊D241—44no—
52C2×Dic241—22no—
53C2×Dic241—44no—
54C2×Dic241C22⋊C411yescharacteristic
55C2×Dic241C22⋊C411yescharacteristic
56C2×Dic241C22⋊C411yescharacteristic
57C4×D241—21no—
58C4×D241—21no—
59C4×D241—21no—
60C4×D241—21no—
61C4×D241—41no—
62#14515349—41no—
63#14515349—41no—
64C23×C241—22no—
65D4×C241—42no—
66D4×C241—41no—
67D4×C241—41no—
68D4×C241—41no—
69D4×C241—41no—
70C2×C4×C241C22×C411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C8×C241—41no—
74C8×C241—41no—
75C22×C241—42no—
76C22×C241—42no—
77C22×C241—42no—
78C22×C241C2×C22⋊C411yescharacteristic
79C2×D241—21no—
80C2×D241—21no—
81C2×D241—21no—
82C4×C241—21no—
83C4×C241#13511yescharacteristic
84C4×C241#13511yescharacteristic
85C4×C241AGL(1,ℤ/8)11yescharacteristic
86C4×C241AGL(1,ℤ/8)11yescharacteristic
87Dic241—21no—
88Dic241—21no—
89Dic241—21no—
90Dic241—42no—
91C2×C241—82no—
92C2×C241#41311yescharacteristic
93C2×C241#41611yescharacteristic
94C2×C241#41811yescharacteristic
95D241—41no—
96C241#155311yescharacteristic, complemented, Sylow
97#1553—2411nomaximal, Sylow
98#532—2411no—
99#432—2411no—
100#431—2411no—
101#332—2411no—
102#332—2411no—
103#331—2411no—
104#331D24111yescharacteristic, complemented
105C2×#41—4821no—
106C4⋊Q8—2411no—
107#127C2×D24111yescharacteristic
108#124—4821no—
109#121—4821no—
110#121—2412no—
111C4×D4—4821no—
112C4×D4—2412no—
113C2×C42—2411no—
114C4⋊C8—2411no—
115C4⋊C8—2411no—
116C4⋊C8C2×D24111yescharacteristic
117C4⋊C8C2×D24111yescharacteristic
118C22⋊C8—4821no—
119C22⋊C8—4821no—
120#97—4821no—
121C4×C8—4821no—
122#41—9642no—
123#41—9642no—
124C2×Q8—4821no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—4822no—
128C2×D4C4×D24112yes—
129C22×C4—4822no—
130C22×C4—2411no—
131C22×C4—2411no—
132C22×C4—2411no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—4821no—
136C2×C8—4821no—
137C4⋊C4—4821no—
138C4⋊C4—2412no—
139C22⋊C4—4822no—
140C22⋊C4—4822no—
141C42—2411no—
142C42—2411no—
143C42—2411no—
144C42C22×D24111yescharacteristic
145C23—22no—
146C23—2411no—
147Q8—9641no—
148Q8—9641no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—9644no—
155C2×C4—9641no—
156C2×C4—9644no—
157C2×C4—4822no—
158C2×C4—4821no—
159C2×C4—4821no—
160C2×C4—4821no—
161C2×C4—4821no—
162C2×C4—2411no—
163C2×C4—2411no—
164C2×C4—2411no—
165C2×C4C2×C4×D24111yescharacteristic
166C2×C4D4×D24111yescharacteristic
167C2×C4D4×D24111yescharacteristic
168C8—41no—
169C8—41no—
170C8—9641no—
171C8—9641no—
172C22—42no—
173C22—42no—
174C22—42no—
175C22—4821no—
176C22—4821no—
177C22—4821no—
178C22C22⋊C4×D24111yescharacteristic
179C4—21no—
180C4—9642no—
181C4—4821no—
182C4—4821no—
183C4—4821no—
184C4#2144066111yescharacteristic
185C4#2144066311yescharacteristic
186C4#2144066611yescharacteristic
187C4#2144066911yescharacteristic
188C2—82no—
189C2—9641no—
190C2#2950769811yescharacteristic
191C2#2950771011yescharacteristic
192C2#2950772011yescharacteristic
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#1553
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. #29507769C2semidirect
4. #29507464C2semidirect
5. #29507462C2semidirect
6. #29507461C2semidirect
7. #331×C241C2semidirect
96. C241#1553semidirect
104. #331D241semidirect

Maximal subgroups

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

subgroupindex
#295082652
#295077732
#295077692
#295074642
#295074622
#295074612
#331×C2412
#1553241