Finite Group Databasebeta

← #44506780

Subgroups — #44506780

Order 30848.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#29508471C211yesmaximal, characteristic
2#29508126C211yesmaximal, characteristic, complemented
3#29508087C211yesmaximal, characteristic, complemented
4#29508077C211yesmaximal, characteristic
5#29507458C211yesmaximal, characteristic, complemented
6#29507456C211yesmaximal, characteristic
7#330×C241C211yesmaximal, characteristic, complemented
8#21440642C2211yescharacteristic
9#21440641—21no—
10#21440637—21no—
11#21440637—21no—
12#21440634C2211yescharacteristic
13#21440630C2211yescharacteristic
14#21440627—21no—
15#21440622—21no—
16#21440620—21no—
17#21440576—21no—
18#21440574—21no—
19#21440567—21no—
20#21440565—21no—
21#21440565—21no—
22#21440564—21no—
23#21440553C2211yescharacteristic
24#125×C241C2211yescharacteristic
25#97×C241C2211yescharacteristic
26#97×C241C2211yescharacteristic
27C2×Dic482—21no—
28C2×Dic482—21no—
29C2×Dic482D411yescharacteristic
30C2×D964D411yescharacteristic
31C2×C4×D241—21no—
32C2×#14515349—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241D411yescharacteristic
37C4⋊Dic241D411yescharacteristic
38#16838749—21no—
39#16838749—21no—
40#16838749—21no—
41#16838747—21no—
42#16838747—21no—
43#16838747—21no—
44#16838747—21no—
45#16838747—21no—
46C4×Dic241—21no—
47C2×C8×C241—21no—
48C2×C8×C241—21no—
49C4⋊C4×C241—21no—
50C4⋊C4×C241—21no—
51C4⋊C4×C241D411yescharacteristic
52C4⋊C4×C241D411yescharacteristic
53C42×C241C2311yescharacteristic
54C22×D241—21no—
55Dic482—41no—
56Dic482—42no—
57Dic482—81no—
58D964—41no—
59C2×Dic241—21no—
60C2×Dic241—21no—
61C2×Dic241—21no—
62C2×Dic241—41no—
63C4×D241—81no—
64#14515349—41no—
65C2×C4×C241—21no—
66C2×C4×C241—21no—
67C2×C4×C241C2×D411yescharacteristic
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D411yescharacteristic
70C8×C241—22no—
71C8×C241—41no—
72C22×C241#12011yescharacteristic
73C2×D241—41no—
74C2×D241—41no—
75C2×D241—41no—
76C4×C241—21no—
77C4×C241—21no—
78C4×C241—21no—
79C4×C241—41no—
80C4×C241—41no—
81Dic241—41no—
82Dic241—41no—
83Dic241—41no—
84Dic241—81no—
85C2×C241#45411yescharacteristic
86C2×C241#45511yescharacteristic
87C2×C241#45611yescharacteristic
88D241—81no—
89C241#166411yescharacteristic, complemented, Sylow
90#1664—2411nomaximal, Sylow
91#563—2411no—
92#501—2411no—
93#491—2411no—
94#489—2411no—
95#330—2411no—
96#330D24111yescharacteristic, complemented
97#329—2411no—
98C4⋊Q8—4821no—
99C4⋊Q8—2411no—
100#126—4821no—
101#126—4821no—
102#125—2411no—
103#125C2×D24111yescharacteristic
104#124—2411no—
105#123—4821no—
106C22⋊Q8—4821no—
107C22⋊Q8—4821no—
108#107—4821no—
109#106—4821no—
110#103—4821no—
111#103—4821no—
112#103—4821no—
113#102—4821no—
114#97—2411no—
115#97C2×D24111yescharacteristic
116#97C2×D24111yescharacteristic
117C2×Q8—4821no—
118C2×Q8—4821no—
119C2×Q8—2411no—
120C2×D4—2411no—
121C22×C4—4821no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—4821no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—4821no—
128C4⋊C4—4821no—
129C4⋊C4—4821no—
130C4⋊C4—4821no—
131C4⋊C4—4821no—
132C4⋊C4—4821no—
133C4⋊C4—2411no—
134C4⋊C4—2411no—
135C4⋊C4D96411yescharacteristic
136C4⋊C4D96411yescharacteristic
137C22⋊C4—4821no—
138C22⋊C4—4821no—
139C22⋊C4—4821no—
140C22⋊C4—4821no—
141C22⋊C4—4821no—
142C42—4821no—
143C42C22×D24111yescharacteristic
144C23—4821no—
145Q8—19281no—
146Q8—9642no—
147Q8—9641no—
148D4—9641no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—19281no—
152C2×C4—9641no—
153C2×C4—4821no—
154C2×C4—4821no—
155C2×C4—4821no—
156C2×C4D4×D24111yescharacteristic
157C2×C4D4×D24111yescharacteristic
158C2×C4C2×D96411yescharacteristic
159C8—22no—
160C8—41no—
161C8—9641no—
162C22—9641no—
163C22—9641no—
164C22—9641no—
165C22#2144061211yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—19281no—
172C4—9641no—
173C4—9641no—
174C4—9641no—
175C2—19281no—
176C2#2950789211yescharacteristic
177C2#2950789611yescharacteristic
178C2#2950790111yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#330×C241C2
socleC22×C241#120
prime radicalC2×D964D4
hypercenter#330D241
hypocenterC241#1664
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #29508126C2semidirect
3. #29508087C2semidirect
5. #29507458C2semidirect
7. #330×C241C2semidirect
89. C241#1664semidirect
96. #330D241semidirect

Maximal subgroups

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

subgroupindex
#295084712
#295081262
#295080872
#295080772
#295074582
#295074562
#330×C2412
#1664241