Finite Group Databasebeta

← #44506067

Subgroups — #44506067

Order 30848.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D241C211yesmaximal, characteristic
2#29507772C212yesmaximal, complemented
3#29507457C211yesmaximal, characteristic, complemented
4#29507456C212yesmaximal, complemented
5#329×C241C211yesmaximal, characteristic, complemented
6C2×Q8×D241C411yescharacteristic
7C2×D4×D241C411yescharacteristic
8#21440631C411yescharacteristic
9#21440630C2211yescharacteristic
10#21440629C411yescharacteristic
11#21440628—22no—
12C22⋊C4×D241—22no—
13C42×D241C2211yescharacteristic
14#21440571—22no—
15#21440554—22no—
16#21440553C2212yescomplemented
17#124×C241C2211yescharacteristic
18#97×C241C2212yescomplemented
19C23×D241—21no—
20C2×Dic482—21no—
21C2×Dic482C2×C411yescharacteristic
22Q8×D241—42no—
23C2×D964C2×C411yescharacteristic
24C2×C22⋊D241—21no—
25D4×D241—42no—
26C2×C4×D241—21no—
27C2×C4×D241C2×C411yescharacteristic
28C2×C4×D241D412yes—
29C2×#14515349—22no—
30C22⋊Dic241—22no—
31#16838747—22no—
32#16838747—22no—
33C4×Dic241C2×C411yescharacteristic
34C4×Dic241D412yes—
35C2×Q8×C241C2×C411yescharacteristic
36C2×D4×C241C2×C411yescharacteristic
37C2×C8×C241—22no—
38C22⋊C4×C241—22no—
39C42×C241C2311yescharacteristic
40C22×D241—21no—
41C22×D241—44no—
42C22×D241—42no—
43C22×D241C22⋊C411yescharacteristic
44Dic482—42no—
45Dic482—41no—
46D964—41no—
47C22⋊D241—42no—
48C2×Dic241—21no—
49C2×Dic241C22⋊C412yes—
50C2×Dic241C22⋊C411yescharacteristic
51C4×D241—22no—
52C4×D241—42no—
53C4×D241—42no—
54#14515349—42no—
55C23×C241—21no—
56Q8×C241—41no—
57D4×C241—41no—
58C2×C4×C241—21no—
59C2×C4×C241C22×C411yescharacteristic
60C2×C4×C241C2×D412yes—
61C8×C241—42no—
62C22×C241—41no—
63C22×C241—42no—
64C22×C241C2×C22⋊C411yescharacteristic
65C2×D241—22no—
66C2×D241—41no—
67C2×D241—42no—
68C2×D241—84no—
69C2×D241#10012yes—
70C4×C241—21no—
71C4×C241—22no—
72C4×C241—41no—
73Dic241—21no—
74Dic241—22no—
75Dic241—41no—
76C2×C241—81no—
77C2×C241C2×#10011yescharacteristic
78C2×C241#42112yes—
79D241—22no—
80D241—81no—
81C241#153311yescharacteristic, complemented, Sylow
82#1533—2411nomaximal, Sylow
83C2×#124—2411no—
84#432—2412no—
85#329—2411no—
86#329—2412no—
87#329D24111yescharacteristic, complemented
88C22×Q8—2411no—
89C22×D4—2411no—
90#124—4822no—
91#124—2411no—
92#124—2411no—
93#124—2411no—
94#124C2×D24111yescharacteristic
95C2×C22⋊C4—4822no—
96C2×C42—2411no—
97C4⋊C8—4822no—
98C22⋊C8—4822no—
99#97—2412no—
100#97C2×D24112yescomplemented
101C24—4821no—
102C2×Q8—9642no—
103C2×Q8—4821no—
104C2×Q8—2411no—
105C2×Q8C4×D24111yescharacteristic
106C2×D4—9642no—
107C2×D4—4821no—
108C2×D4—2411no—
109C2×D4C4×D24111yescharacteristic
110C22×C4—4821no—
111C22×C4—2412no—
112C22×C4—2411no—
113C2×C8—22no—
114C2×C8—4822no—
115C22⋊C4—22no—
116C22⋊C4—4822no—
117C22⋊C4—4822no—
118C22⋊C4—4822no—
119C42—2411no—
120C42—2412no—
121C42C22×D24111yescharacteristic
122C23—21no—
123C23—9644no—
124C23—9642no—
125C23—4821no—
126C23—2411no—
127Q8—41no—
128Q8—9641no—
129Q8—9642no—
130D4—41no—
131D4—9641no—
132D4—9642no—
133C2×C4—21no—
134C2×C4—9642no—
135C2×C4—9642no—
136C2×C4—4822no—
137C2×C4—4821no—
138C2×C4—2412no—
139C2×C4—2411no—
140C2×C4C2×C4×D24111yescharacteristic
141C2×C4D4×D24112yes—
142C8—42no—
143C8—9642no—
144C22—41no—
145C22—42no—
146C22—19284no—
147C22—9641no—
148C22—9642no—
149C22—4822no—
150C22—2412no—
151C22C22⋊C4×D24111yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—9641no—
156C4—4821no—
157C4—4822no—
158C2—81no—
159C2—19281no—
160C2—4822no—
161C2#100×D24111yescharacteristic
162C2#2950773212yes—
subgroupG/H
centerC22C22⋊C4×D241
commutatorC2×C4×C241C22×C4
FrattiniC42C22×D241
Fitting#329×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC2×D4×D241C4
cosocleC42×C241C23
hypercenter#329D241
hypocenterC241#1533
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #29507772C2semidirect
3. #29507457C2semidirect
4. #29507456C2semidirect
5. #329×C241C2semidirect
16. #21440553C22semidirect
18. #97×C241C22semidirect
81. C241#1533semidirect
87. #329D241semidirect
100. #97C2×D241semidirect

Maximal subgroups

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

subgroupindex
#124×D2412
#295077722
#295074572
#295074562
#329×C2412
#1533241