Finite Group Databasebeta

← #25017417

Subgroups — #25017417

Order 11008.

216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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#19136910C211yesmaximal, characteristic, complemented
2#19136908C211yesmaximal, characteristic, complemented
3#19136843C211yesmaximal, characteristic, complemented
4#19136475C211yesmaximal, characteristic, complemented
5#19132792C211yesmaximal, characteristic, complemented
6#19132784C211yesmaximal, characteristic, complemented
7C43×#1419C211yesmaximal, characteristic, complemented
8#14583331C2211yescharacteristic
9C2×D688C2211yescharacteristic
10C2×#13063266—21no—
11#14583274—21no—
12#14583015—21no—
13#14582738—21no—
14#14582737—21no—
15D1376—21no—
16#14582734—21no—
17#14582733C2211yescharacteristic
18#14582705—21no—
19C16×Dic43C2211yescharacteristic
20C2×D16×C43C2211yescharacteristic
21C43×M64C2211yescharacteristic
22C43×#368C2211yescharacteristic
23#13063347—21no—
24C2×D344—21no—
25C2×#10621882—41no—
26#13063333—41no—
27#13063321—41no—
28Dic344D411yescharacteristic, complemented
29#13063270—21no—
30D688—21no—
31D688—21no—
32D688D411yescharacteristic, complemented
33#13063266—42no—
34C2×C43⋊C16D411yescharacteristic
35#13063251—41no—
36C8×Dic43D411yescharacteristic
37C43⋊C32—21no—
38C2×D8×C43—21no—
39D16×C43—21no—
40D16×C43—21no—
41C2×C16×C43C2311yescharacteristic
42#108×C43—21no—
43C32×C43—21no—
44C2×D4×C43—41no—
45C2×C22⋊D43—82no—
46#10621898—41no—
47C2×D172—41no—
48D8×C43—41no—
49D8×C43—41no—
50M16×C43—41no—
51C2×C8×C43C2×D411yescharacteristic
52#10621882—81no—
53#10621882—81no—
54C4×Dic43D811yescharacteristic
55C2×C43⋊C8D811yescharacteristic
56Dic172—21no—
57D344—21no—
58D344—41no—
59D344—41no—
60#10621873—41no—
61#10621872—81no—
62C8×D43—81no—
63C16×C43C2×D411yescharacteristic
64C16×C43#4111yescharacteristic
65C43⋊C16—21no—
66C23×C43—81no—
67C22×D43—81no—
68D4×C43—81no—
69D4×C43—81no—
70C2×C4×C43C2×D811yescharacteristic
71C22⋊D43—81no—
72C22⋊D43—164no—
73C2×Dic43—21no—
74D172—41no—
75D172—81no—
76D172—81no—
77C4×D43—81no—
78Dic86—41no—
79C8×C43—81no—
80C8×C43#12111yescharacteristic
81C8×C43AGL(1,ℤ/8)11yescharacteristic
82C43⋊C8D1611yescharacteristic
83C43⋊C8D1611yescharacteristic
84#13692—431nomaximal, Sylow
85C22×C43—162no—
86C22×C43—161no—
87C22×C43#50911yescharacteristic
88C2×D43—81no—
89C2×D43—162no—
90C2×D43—161no—
91C4×C43#45911yescharacteristic
92C4×C43C2×D1611yescharacteristic
93Dic43—22no—
94Dic43—81no—
95#2263—431no—
96#2263—431no—
97#2246—431no—
98#2178—431no—
99#1422—431no—
100#1419—431no—
101#1419D4311yescharacteristic, complemented
102C2×C43—21no—
103C2×C43—321no—
104C2×C43#220611yescharacteristic
105D43—161no—
106D43—321no—
107#508—431no—
108C2×D16—431no—
109C2×D16—861no—
110C2×D16C2×D4311yescharacteristic
111#493—861no—
112#443—861no—
113SD64—861no—
114SD64—861no—
115D32—861no—
116D32—861no—
117M64—431no—
118M64C2×D4311yescharacteristic
119#368C2×D4311yescharacteristic
120#359—861no—
121C4×C16—431no—
122C43#1369211yescharacteristic, complemented, Sylow
123#135—861no—
124C2×D8—21no—
125C2×D8—861no—
126C2×D8—1721no—
127#131—1721no—
128#127—1721no—
129Q32—431no—
130SD32—861no—
131D16—21no—
132D16—21no—
133D16—431no—
134D16—861no—
135D16—861no—
136D16—1722no—
137C2×C16—431no—
138C2×C16C22×D4311yescharacteristic
139#108—21no—
140#104—1721no—
141C4×C8—431no—
142C32—21no—
143C32—861no—
144#41—1721no—
145C2×D4—41no—
146C2×D4—3442no—
147C2×D4—1721no—
148Q16—861no—
149SD16—1721no—
150D8—41no—
151D8—41no—
152D8—861no—
153D8—3441no—
154D8—3441no—
155D8—1721no—
156D8—1721no—
157M16—41no—
158M16—3441no—
159C2×C8—431no—
160C2×C8—3441no—
161C2×C8D4×D4311yescharacteristic
162C42—431no—
163C16—861no—
164C16#1062189811yescharacteristic
165C16D4×D4311yescharacteristic
166C23—81no—
167C23—3441no—
168Q8—1721no—
169D4—81no—
170D4—81no—
171D4—3441no—
172D4—3441no—
173D4—3441no—
174D4—1721no—
175D4—6884no—
176C2×C4—861no—
177C2×C4—3441no—
178C2×C4D8×D4311yescharacteristic
179C8—81no—
180C8—431no—
181C8—431no—
182C8#1306329811yescharacteristic
183C8#1306335211yescharacteristic
184C22—162no—
185C22—161no—
186C22—3441no—
187C22—6882no—
188C22—6881no—
189C22#1458333611yescharacteristic
190C4—862no—
191C4—3441no—
192C4#1458309311yescharacteristic
193C4D16×D4311yescharacteristic
194C2—21no—
195C2—321no—
196C2—13761no—
197C2—6881no—
198C2#1913662911yescharacteristic
subgroupG/H
centerC2#19136629
commutator, cosocleC2×C16×C43C23
FrattiniC2×C16C22×D43
FittingC43×#1419C2
socleC2×C43#2206
hypercenter#1419D43
hypocenterC43#13692
LCSG ▷ C2×C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. #19136910C2semidirect
2. #19136908C2semidirect
3. #19136843C2semidirect
4. #19136475C2semidirect
5. #19132792C2semidirect
6. #19132784C2semidirect
7. C43×#1419C2semidirect
28. Dic344D4semidirect
32. D688D4semidirect
101. #1419D43semidirect
122. C43#13692semidirect

Maximal subgroups

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

subgroupindex
#191369102
#191369082
#191368432
#191364752
#191327922
#191327842
C43×#14192
#1369243