Finite Group Databasebeta

← #44508513

Subgroups — #44508513

Order 30848.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#29508517C211yesmaximal, characteristic, complemented
2#29508229C212yesmaximal, complemented
3#29507735C212yesmaximal, complemented
4#29507680C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2212yes—
7C22×C4×D241C2211yescharacteristic
8#21440675—22no—
9#21440670—22no—
10#21440664—22no—
11C2×#16838754C2211yescharacteristic
12#21440626—22no—
13#21440622—22no—
14#21440617—22no—
15#21440612—22no—
16C4×D964—24no—
17#21440570—24no—
18#21440554—22no—
19C2×M16×C241C2211yescharacteristic
20#117×C241C2212yes—
21C23×D241D411yescharacteristic
22#16838770—22no—
23#16838770—22no—
24#16838770—22no—
25#16838770—22no—
26C2×Dic482D412yescomplemented
27C2×D964—24no—
28C2×D964D412yescomplemented
29C2×C22⋊D241—22no—
30C22×Dic241D411yescharacteristic
31C2×C4×D241—21no—
32C2×C4×D241—22no—
33C2×C4×D241—22no—
34C2×C4×D241—22no—
35C2×C4×D241—21no—
36Dic964—22no—
37#16838759—24no—
38D1928—22no—
39#16838754—22no—
40C2×#14515349—21no—
41C4⋊Dic241—24no—
42#16838747—24no—
43#16838747—24no—
44C22×C4×C241C2311yescharacteristic
45M16×C241—22no—
46C2×C8×C241D412yescomplemented
47C4⋊C4×C241—22no—
48C22⋊C4×C241—22no—
49C42×C241D414yescomplemented
50C22×D241—22no—
51C22×D241—21no—
52C22×D241—22no—
53C22×D241—42no—
54Dic482—22no—
55Dic482—22no—
56D964—22no—
57D964—22no—
58D964—48no—
59C22⋊D241—42no—
60C22⋊D241—42no—
61C2×Dic241—22no—
62C2×Dic241—22no—
63C2×Dic241—21no—
64C4×D241—41no—
65C4×D241—42no—
66C4×D241—42no—
67C4×D241—41no—
68C4×D241—42no—
69#14515349—41no—
70C23×C241C2×D411yescharacteristic
71C2×C4×C241—24no—
72C2×C4×C241C2×D412yes—
73C2×C4×C241C2×D411yescharacteristic
74C2×C4×C241C2×D412yes—
75C2×C4×C241#4111yescharacteristic
76C8×C241—22no—
77C22×C241—41no—
78C22×C241#12012yes—
79C22×C241#12111yescharacteristic
80C2×D241—24no—
81C2×D241—22no—
82C2×D241—42no—
83C2×D241—41no—
84C2×D241—41no—
85C2×D241—44no—
86C2×D241—42no—
87C4×C241—44no—
88C4×C241#12011yescharacteristic
89C4×C241#12112yes—
90C4×C241#12711yescharacteristic
91Dic241—41no—
92Dic241—42no—
93C2×C241—22no—
94C2×C241—21no—
95C2×C241#39211yescharacteristic
96D241—42no—
97D241—82no—
98C241#201011yescharacteristic, complemented, Sylow
99#2010—2411nomaximal, Sylow
100#575—2411no—
101#525—2412no—
102#421—2412no—
103#407—2411no—
104H(3,ℤ/4)D24111yescharacteristic, complemented
105C2×#41—2412no—
106C23×C4—2411no—
107#137—4822no—
108AGL(1,ℤ/8)—4822no—
109#135—4822no—
110C2×M16—2411no—
111C2×M16C2×D24111yescharacteristic
112#123—4822no—
113C22⋊Q8—4822no—
114#121—4822no—
115#120—4822no—
116C4×D4—4824no—
117#117C2×D24112yes—
118#104—4824no—
119C22⋊C8—4822no—
120C24—2411no—
121#41—4822no—
122#41—4822no—
123#41—4822no—
124#41—4822no—
125C2×Q8—2412no—
126C2×D4—4824no—
127C2×D4—4822no—
128C2×D4—2412no—
129C22×C4—4822no—
130C22×C4—4821no—
131C22×C4—4822no—
132C22×C4—4822no—
133C22×C4—4821no—
134C22×C4—2411no—
135C22×C4C22×D24111yescharacteristic
136Q16—4822no—
137SD16—4824no—
138D8—4822no—
139M16—22no—
140M16—4822no—
141C2×C8—4821no—
142C2×C8D96412yescomplemented
143C4⋊C4—22no—
144C4⋊C4—4824no—
145C22⋊C4—22no—
146C22⋊C4—4824no—
147C22⋊C4—4824no—
148C42D96414yescomplemented
149C23—9642no—
150C23—4822no—
151C23—4822no—
152C23—4821no—
153C23D4×D24111yescharacteristic
154Q8—4822no—
155Q8—4822no—
156D4—9648no—
157D4—9642no—
158D4—9642no—
159D4—4822no—
160D4—4822no—
161C2×C4—24no—
162C2×C4—9641no—
163C2×C4—9642no—
164C2×C4—9642no—
165C2×C4—9641no—
166C2×C4—9642no—
167C2×C4—4822no—
168C2×C4—4822no—
169C2×C4—4821no—
170C2×C4D4×D24112yes—
171C2×C4C2×D96411yescharacteristic
172C2×C4C2×D96412yes—
173C2×C4#1683877111yescharacteristic
174C8—22no—
175C8—9641no—
176C22—41no—
177C22—9644no—
178C22—9642no—
179C22—9641no—
180C22—9642no—
181C22—9641no—
182C22—4824no—
183C22—4822no—
184C22#2144061212yes—
185C22#2144061711yescharacteristic
186C4—44no—
187C4—9641no—
188C4—9642no—
189C4#2144061211yescharacteristic
190C4#2144061712yes—
191C4#2144063911yescharacteristic
192C2—22no—
193C2—21no—
194C2—19282no—
195C2—9642no—
196C2#2950762711yescharacteristic
subgroupG/H
centerC4#21440639
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
FittingH(3,ℤ/4)×C241C2
socleC2×C241#392
hypercenterH(3,ℤ/4)D241
hypocenterC241#2010
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #29508517C2semidirect
2. #29508229C2semidirect
3. #29507735C2semidirect
4. #29507680C2semidirect
5. H(3,ℤ/4)×C241C2semidirect
26. C2×Dic482D4semidirect
28. C2×D964D4semidirect
46. C2×C8×C241D4semidirect
49. C42×C241D4semidirect
98. C241#2010semidirect
104. H(3,ℤ/4)D241semidirect
142. C2×C8D964semidirect
148. C42D964semidirect

Maximal subgroups

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

subgroupindex
#295085172
#295082292
#295077352
#295076802
H(3,ℤ/4)×C2412
#2010241