Finite Group Databasebeta

← #44506646

Subgroups — #44506646

Order 30848.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#29508387C211yesmaximal, characteristic
2#29508063C211yesmaximal, characteristic, complemented
3#29508003C211yesmaximal, characteristic, complemented
4#29507923C211yesmaximal, characteristic, complemented
5#29507447C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic, complemented
7#331×C241C211yesmaximal, characteristic, complemented
8C2×#16838769—21no—
9C2×#16838759—21no—
10#21440642C2211yescharacteristic
11#21440638—21no—
12#21440614—22no—
13#21440613—21no—
14C4×Dic482C2211yescharacteristic
15C4×D964C2211yescharacteristic
16D4×Dic241—21no—
17#21440574—21no—
18#21440567—21no—
19#21440567—21no—
20#21440563—22no—
21C4×#14515349C2211yescharacteristic
22#127×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25#16838769—42no—
26#16838769—42no—
27C2×Dic482—21no—
28C2×Dic482D411yescharacteristic
29C2×D964D411yescharacteristic
30C2×C22⋊D241—22no—
31C2×C22⋊D241—22no—
32C22×Dic241—22no—
33C2×C4×D241—21no—
34#16838759—42no—
35C2×#14515349—21no—
36C4⋊Dic241—21no—
37C4⋊Dic241—21no—
38C4⋊Dic241D411yescharacteristic
39C4⋊Dic241D411yescharacteristic
40#16838749—21no—
41C22⋊Dic241—22no—
42#16838747—21no—
43C4×Dic241—21no—
44C2×D4×C241—21no—
45C2×D4×C241—21no—
46C2×D4×C241D412yes—
47C2×C8×C241—21no—
48C2×C8×C241—21no—
49C42×C241C2311yescharacteristic
50C22×D241—21no—
51Dic482—21no—
52Dic482—41no—
53Dic482—41no—
54Dic482SD1612yescomplemented
55D964—21no—
56D964—21no—
57C22⋊D241—44no—
58C22⋊D241—82no—
59C2×Dic241—21no—
60C2×Dic241—21no—
61C2×Dic241—21no—
62C2×Dic241—44no—
63C2×Dic241—41no—
64C4×D241—41no—
65C4×D241—41no—
66#14515349—41no—
67C23×C241—22no—
68D4×C241—42no—
69D4×C241—41no—
70D4×C241—41no—
71D4×C241—41no—
72D4×C241—41no—
73C2×C4×C241C2×D411yescharacteristic
74C2×C4×C241C2×D411yescharacteristic
75C2×C4×C241C2×D411yescharacteristic
76C8×C241—41no—
77C8×C241—41no—
78C22×C241—42no—
79C22×C241—42no—
80C22×C241—42no—
81C22×C241#12011yescharacteristic
82C2×D241—41no—
83C2×D241—41no—
84C2×D241—41no—
85C4×C241—21no—
86C4×C241C2×SD1611yescharacteristic
87C4×C241#13511yescharacteristic
88C4×C241AGL(1,ℤ/8)11yescharacteristic
89C4×C241AGL(1,ℤ/8)11yescharacteristic
90Dic241—22no—
91Dic241—41no—
92Dic241—41no—
93Dic241—81no—
94C2×C241—82no—
95C2×C241#44911yescharacteristic
96C2×C241#45011yescharacteristic
97C2×C241#45511yescharacteristic
98D241—81no—
99C241#164211yescharacteristic, complemented, Sylow
100#1642—2411nomaximal, Sylow
101#550—2411no—
102#486—2411no—
103#475—2411no—
104#461—2411no—
105#331D24111yescharacteristic, complemented
106Q8⋊C8—2411no—
107D4⋊C8—2411no—
108C2×#41—4821no—
109C2×SD16—4821no—
110C4⋊Q8—2411no—
111#127—4821no—
112#127C2×D24111yescharacteristic
113#121—4822no—
114#121—4821no—
115C4×Q8—2411no—
116C4×D4—4821no—
117C4×D4—2411no—
118#106—4821no—
119C4⋊C8C2×D24111yescharacteristic
120C4⋊C8C2×D24111yescharacteristic
121#103—4821no—
122#103—4821no—
123#102—4822no—
124C4×C8—2411no—
125#41—9642no—
126#41—9642no—
127C2×Q8—4821no—
128C2×Q8—2411no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—4822no—
132C2×D4—4822no—
133C2×D4—2411no—
134C2×D4D96412yes—
135C22×C4—4822no—
136C22×C4—4821no—
137SD16—9642no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—4821no—
141C4⋊C4—4821no—
142C4⋊C4—4821no—
143C4⋊C4—4821no—
144C4⋊C4—2411no—
145C4⋊C4—2411no—
146C22⋊C4—4822no—
147C22⋊C4—4821no—
148C42—4821no—
149C42C22×D24111yescharacteristic
150C23—22no—
151C23—4821no—
152Q8—9641no—
153Q8—9641no—
154Q8—4821no—
155Q8—2412no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—19282no—
162D4—9644no—
163D4—4821no—
164D4—4821no—
165C2×C4—9641no—
166C2×C4—9644no—
167C2×C4—9641no—
168C2×C4—9641no—
169C2×C4—4821no—
170C2×C4—4821no—
171C2×C4—4821no—
172C2×C4D4×D24111yescharacteristic
173C2×C4D4×D24111yescharacteristic
174C2×C4C2×D96411yescharacteristic
175C8—41no—
176C8—41no—
177C8—9641no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—9641no—
182C22—9641no—
183C22—9641no—
184C22#2144061211yescharacteristic
185C4—21no—
186C4—19281no—
187C4—9641no—
188C4—9641no—
189C4—4822no—
190C4SD16×D24111yescharacteristic
191C4#2144066311yescharacteristic
192C4#2144066611yescharacteristic
193C4#2144066611yescharacteristic
194C2—82no—
195C2—19281no—
196C2#2950786311yescharacteristic
197C2#2950786911yescharacteristic
198C2#2950789711yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#331×C241C2
socleC22×C241#120
prime radical#29508387C2
hypercenter#331D241
hypocenterC241#1642
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #29508063C2semidirect
3. #29508003C2semidirect
4. #29507923C2semidirect
5. #29507447C2semidirect
6. #29507444C2semidirect
7. #331×C241C2semidirect
54. Dic482SD16semidirect
99. C241#1642semidirect
105. #331D241semidirect

Maximal subgroups

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

subgroupindex
#295083872
#295080632
#295080032
#295079232
#295074472
#295074442
#331×C2412
#1642241