Finite Group Databasebeta

← #19135639

Subgroups — #19135639

Order 5504.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#13063353C212yesmaximal, complemented
2#14583480C211yesmaximal, characteristic, complemented
3C2×#13063251C212yesmaximal, complemented
4#14582800C211yesmaximal, characteristic, complemented
5C43×#343C211yesmaximal, characteristic, complemented
6C2×#10621898C2212yes—
7C22×D172C2211yescharacteristic
8#13063353—24no—
9#13063353—24no—
10C2×#10621873—22no—
11C2×D344—22no—
12#13063305—22no—
13#13063300—22no—
14#13063299—22no—
15C2×(C2×D43)⋊C4—22no—
16C2×C4×Dic43C2211yescharacteristic
17#13063251—24no—
18C2×M16×C43C2212yes—
19C2×C4⋊C4×C43C2211yescharacteristic
20C23×D43—21no—
21C22×C4×C43D412yes—
22C22×C4×C43C2311yescharacteristic
23C2×C22⋊D43—22no—
24C22×Dic43—21no—
25#10621898—22no—
26#10621898—22no—
27#10621898—22no—
28#10621898—22no—
29C2×D172—21no—
30C2×D172—22no—
31C2×D172—22no—
32C2×D172—22no—
33C2×D172D412yes—
34C2×D172D412yescomplemented
35C2×C4×D43—22no—
36C2×Dic86D412yes—
37M16×C43—22no—
38M16×C43D414yescomplemented
39C2×C8×C43—22no—
40C4⋊C4×C43—22no—
41(C2×D43)⋊C4—24no—
42(C2×D43)⋊C4—44no—
43C4⋊Dic43—22no—
44C4×Dic43—22no—
45D344—28no—
46#10621873—28no—
47C23×C43C2×D411yescharacteristic
48C22×D43—22no—
49C22×D43—22no—
50C22×D43—42no—
51C22×D43—42no—
52C22×D43—41no—
53C22×D43—41no—
54C2×C4×C43—22no—
55C2×C4×C43—42no—
56C2×C4×C43C2×D412yes—
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×D412yes—
59C2×C4×C43#4111yescharacteristic
60C22⋊D43—42no—
61C22⋊D43—42no—
62C2×Dic43—22no—
63C2×Dic43—22no—
64C2×Dic43—41no—
65C2×Dic43—41no—
66D172—24no—
67D172—22no—
68D172—22no—
69D172—42no—
70D172—82no—
71C4×D43—42no—
72C4×D43—42no—
73Dic86—22no—
74Dic86—22no—
75C8×C43—24no—
76C22×C43—21no—
77C22×C43—21no—
78C22×C43#12011yescharacteristic
79C22×C43#12111yescharacteristic
80C22×C43#12711yescharacteristic
81C2×D43—44no—
82C2×D43—42no—
83C2×D43—42no—
84C2×D43—42no—
85C2×D43—42no—
86C2×D43—82no—
87C2×D43—81no—
88C2×D43—81no—
89C4×C43—42no—
90C4×C43#12012yes—
91C4×C43#12112yes—
92Dic43—42no—
93Dic43—42no—
94#2006—431nomaximal, Sylow
95C2×C43—21no—
96C2×C43—21no—
97C2×C43#39211yescharacteristic
98C2×C43#45311yescharacteristic
99C2×C43#45411yescharacteristic
100D43—82no—
101D43—82no—
102C2×AGL(1,ℤ/8)—432no—
103#537—431no—
104C2×#104—432no—
105#390—431no—
106#343D4311yescharacteristic, complemented
107C43#200611yescharacteristic, complemented, Sylow
108C2×#41—432no—
109C22×D4—431no—
110AGL(1,ℤ/8)—864no—
111AGL(1,ℤ/8)—864no—
112C2×SD16—862no—
113C2×D8—862no—
114C2×M16C2×D4312yes—
115C22⋊Q8—862no—
116#121—862no—
117#121—862no—
118C2×C4⋊C4C2×D4311yescharacteristic
119C2×C22⋊C4—862no—
120C2×C42—431no—
121#104—864no—
122C24—861no—
123#41—862no—
124#41—862no—
125#41—862no—
126#41—862no—
127C2×Q8—432no—
128C2×D4—432no—
129C2×D4—432no—
130C2×D4—862no—
131C2×D4—862no—
132C2×D4—862no—
133C2×D4—862no—
134C2×D4—861no—
135C22×C4—861no—
136C22×C4—862no—
137C22×C4D17212yes—
138C22×C4C22×D4311yescharacteristic
139SD16—868no—
140D8—868no—
141M16—22no—
142M16D17214yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—862no—
146C22⋊C4—864no—
147C22⋊C4—1724no—
148C42—862no—
149C23—862no—
150C23—862no—
151C23—1722no—
152C23—1722no—
153C23—1721no—
154C23—1721no—
155C23C2×D17211yescharacteristic
156Q8—862no—
157Q8—862no—
158D4—862no—
159D4—864no—
160D4—862no—
161D4—3442no—
162D4—1722no—
163D4—1722no—
164D4—1722no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—862no—
168C2×C4—862no—
169C2×C4—1721no—
170C2×C4—1721no—
171C2×C4—1722no—
172C2×C4—1722no—
173C2×C4C2×D17212yes—
174C2×C4D4×D4311yescharacteristic
175C2×C4D4×D4312yes—
176C2×C4#1062190211yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—3442no—
181C22—3441no—
182C22—3441no—
183C22—1724no—
184C22—1722no—
185C22—1722no—
186C22—1722no—
187C22—1722no—
188C22#1306329511yescharacteristic
189C22#1306330011yescharacteristic
190C22#1306332211yescharacteristic
191C4—42no—
192C4—1722no—
193C4—1722no—
194C4#1306329512yes—
195C4#1306330012yes—
196C2—21no—
197C2—21no—
198C2—3442no—
199C2—3442no—
200C2#1458280911yescharacteristic
201C2#1458306911yescharacteristic
202C2#1458307411yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#343C2
socleC22×C43#120
hypercenter#343D43
hypocenterC43#2006
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#13063353C2semidirect
2. #14583480C2semidirect
3. C2×#13063251C2semidirect
4. #14582800C2semidirect
5. C43×#343C2semidirect
34. C2×D172D4semidirect
38. M16×C43D4semidirect
106. #343D43semidirect
107. C43#2006semidirect
142. M16D172semidirect