Finite Group Databasebeta

← #44506709

Subgroups — #44506709

Order 30848.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#29508382C211yesmaximal, characteristic
2#29508113C211yesmaximal, characteristic, complemented
3#29508003C211yesmaximal, characteristic, complemented
4#29507923C211yesmaximal, characteristic
5#29507447C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic
7#332×C241C211yesmaximal, characteristic, complemented
8C2×Q8×D241—21no—
9C2×#16838759—21no—
10#21440642C2211yescharacteristic
11#21440641—21no—
12#21440620—22no—
13#21440618—21no—
14C4×Dic482C2211yescharacteristic
15C4×D964C2211yescharacteristic
16#21440604—21no—
17#21440574—21no—
18#21440573—22no—
19#21440567—21no—
20#21440567—21no—
21C4×#14515349C2211yescharacteristic
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25C2×Dic482—22no—
26C2×Dic482—21no—
27C2×Dic482D411yescharacteristic
28Q8×D241—42no—
29Q8×D241—42no—
30C2×D964D411yescharacteristic
31C2×C4×D241—22no—
32C2×C4×D241—21no—
33#16838759—42no—
34C2×#14515349—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241—21no—
37C4⋊Dic241D411yescharacteristic
38C4⋊Dic241D411yescharacteristic
39#16838749—22no—
40#16838749—21no—
41#16838747—22no—
42#16838747—21no—
43C4×Dic241—21no—
44C2×Q8×C241—21no—
45C2×C8×C241—21no—
46C2×C8×C241—21no—
47C4⋊C4×C241—21no—
48C4⋊C4×C241D412yes—
49C42×C241C2311yescharacteristic
50C22×D241—21no—
51Dic482—21no—
52Dic482—44no—
53Dic482—41no—
54Dic482—41no—
55Dic482SD1612yescomplemented
56D964—21no—
57D964SD1612yes—
58C2×Dic241—21no—
59C2×Dic241—21no—
60C2×Dic241—21no—
61C2×Dic241—41no—
62C4×D241—44no—
63C4×D241—41no—
64C4×D241—41no—
65#14515349—22no—
66Q8×C241—41no—
67Q8×C241—41no—
68C2×C4×C241—22no—
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C8×C241—41no—
73C8×C241—41no—
74C22×C241#12011yescharacteristic
75C2×D241—22no—
76C2×D241—41no—
77C2×D241—41no—
78C4×C241—21no—
79C4×C241—42no—
80C4×C241C2×SD1611yescharacteristic
81C4×C241C2×SD1611yescharacteristic
82C4×C241AGL(1,ℤ/8)11yescharacteristic
83C4×C241#13711yescharacteristic
84Dic241—22no—
85Dic241—41no—
86Dic241—41no—
87Dic241—81no—
88C2×C241#44811yescharacteristic
89C2×C241#45011yescharacteristic
90C2×C241#45611yescharacteristic
91D241—42no—
92C241#165111yescharacteristic, complemented, Sylow
93#1651—2411nomaximal, Sylow
94D4×Q8—2411no—
95#498—2411no—
96#475—2411no—
97#461—2411no—
98#332D24111yescharacteristic, complemented
99Q8⋊C8—2411no—
100D4⋊C8—2411no—
101C22×Q8—4821no—
102C2×SD16—4821no—
103C4⋊Q8—4821no—
104C4⋊Q8—2411no—
105C4⋊Q8C2×D24111yescharacteristic
106C22⋊Q8—4821no—
107C22⋊Q8—4822no—
108C4×Q8—2411no—
109C4×D4—4821no—
110C4×D4—2411no—
111#106—4821no—
112#106—4822no—
113C4⋊C8C2×D24111yescharacteristic
114C4⋊C8C2×D24111yescharacteristic
115#103—4821no—
116#103—4821no—
117C4×C8—2411no—
118C2×Q8—21no—
119C2×Q8—9642no—
120C2×Q8—9642no—
121C2×Q8—4822no—
122C2×Q8—4821no—
123C2×Q8—2411no—
124C2×D4—2411no—
125C22×C4—4822no—
126C22×C4—4821no—
127SD16—9642no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—4821no—
131C4⋊C4—21no—
132C4⋊C4—4822no—
133C4⋊C4—4821no—
134C4⋊C4—4821no—
135C4⋊C4—4821no—
136C4⋊C4—2411no—
137C4⋊C4—2411no—
138C4⋊C4D96412yes—
139C22⋊C4—4822no—
140C22⋊C4—4821no—
141C42—4821no—
142C42C22×D24111yescharacteristic
143C23—4821no—
144Q8—41no—
145Q8—41no—
146Q8—9644no—
147Q8—9641no—
148Q8—9641no—
149Q8—4821no—
150Q8—2412no—
151D4—4821no—
152D4—2412no—
153C2×C4—22no—
154C2×C4—9644no—
155C2×C4—9641no—
156C2×C4—9641no—
157C2×C4—9641no—
158C2×C4—4821no—
159C2×C4—4821no—
160C2×C4—4821no—
161C2×C4D4×D24111yescharacteristic
162C2×C4D4×D24111yescharacteristic
163C2×C4C2×D96411yescharacteristic
164C8—41no—
165C8—41no—
166C8—4822no—
167C22—9641no—
168C22—9641no—
169C22—4822no—
170C22#2144061211yescharacteristic
171C4—21no—
172C4—42no—
173C4—19281no—
174C4—9641no—
175C4—9641no—
176C4—4822no—
177C4SD16×D24111yescharacteristic
178C4SD16×D24111yescharacteristic
179C4#2144066611yescharacteristic
180C4#2144067411yescharacteristic
181C2—9642no—
182C2#2950785711yescharacteristic
183C2#2950786911yescharacteristic
184C2#2950790211yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#332×C241C2
socleC22×C241#120
prime radicalC2×D964D4
hypercenter#332D241
hypocenterC241#1651
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #29508113C2semidirect
3. #29508003C2semidirect
5. #29507447C2semidirect
7. #332×C241C2semidirect
55. Dic482SD16semidirect
92. C241#1651semidirect
98. #332D241semidirect

Maximal subgroups

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

subgroupindex
#295083822
#295081132
#295080032
#295079232
#295074472
#295074442
#332×C2412
#1651241