Finite Group Databasebeta

← #25001580

Subgroups — #25001580

Order 11008.

372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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#19134770C211yesmaximal, characteristic, complemented
2#19133365C212yesmaximal, complemented
3#19133020C212yesmaximal
4#19132426C211yesmaximal, characteristic, complemented
5C43×#1955C211yesmaximal, characteristic
6#14582952C2212yes—
7C2×#13063261—22no—
8#14582923C2212yes—
9#14582649—24no—
10D4⋊(C43⋊C8)—24no—
11C2×C4×D4×C43C2211yescharacteristic
12C2×C4⋊C8×C43C2211yescharacteristic
13C2×C22⋊C8×C43—22no—
14C2×#97×C43C2211yescharacteristic
15C2×#10621877—22no—
16#13063261—44no—
17C4⋊(C43⋊C8)—22no—
18C4⋊(C43⋊C8)—22no—
19C4⋊(C43⋊C8)—22no—
20C22⋊(C43⋊C8)—22no—
21C4×C43⋊C8D414yes—
22C22×D4×C43Q811yescharacteristic
23C23×C4×C43—21no—
24C22×C8×C43—21no—
25C22×C8×C43D412yes—
26C4×D4×C43—22no—
27C4×D4×C43—22no—
28C2×C4⋊C4×C43Q811yescharacteristic
29C2×C22⋊C4×C43—21no—
30C2×C42×C43C2311yescharacteristic
31C4⋊C8×C43—22no—
32C22⋊C8×C43—44no—
33#97×C43—22no—
34C24×C43—21no—
35C2×D4×C43—22no—
36C2×D4×C43—42no—
37C22×C4×C43—21no—
38C22×C4×C43—41no—
39C22×C4×C43—41no—
40C22×C4×C43—42no—
41C22×C4×C43—42no—
42C22×C4×C43C2×D411yescharacteristic
43C22×C4×C43C2×Q811yescharacteristic
44C22×C4×C43#4111yescharacteristic
45C2×C8×C43—22no—
46C2×C8×C43—22no—
47C2×C8×C43—41no—
48C2×C8×C43—42no—
49C2×C8×C43SD1614yes—
50C4⋊C4×C43—22no—
51C22⋊C4×C43—42no—
52C42×C43C2×D412yes—
53C42×C43#4112yes—
54#10621877—44no—
55C2×C43⋊C8—24no—
56C2×C43⋊C8—42no—
57C23×C43—22no—
58C23×C43—41no—
59C23×C43—42no—
60C23×C43—41no—
61C23×C43—42no—
62C23×C43C22⋊Q811yescharacteristic
63D4×C43—24no—
64D4×C43—42no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43—42no—
69C2×C4×C43—82no—
70C2×C4×C43—81no—
71C2×C4×C43—81no—
72C2×C4×C43C22⋊Q812yes—
73C2×C4×C43#12311yescharacteristic
74C2×C4×C43#12312yes—
75C2×C4×C43#12711yescharacteristic
76C2×C4×C43C2×SD1612yes—
77C2×C4×C43AGL(1,ℤ/8)12yes—
78C8×C43—24no—
79C8×C43—81no—
80C43⋊C8—44no—
81C43⋊C8—82no—
82#10661—431nomaximal, Sylow
83C22×C43—21no—
84C22×C43—21no—
85C22×C43—44no—
86C22×C43—42no—
87C22×C43—82no—
88C22×C43—81no—
89C22×C43—81no—
90C22×C43#39911yescharacteristic
91C22×C43#47612yes—
92C4×C43—22no—
93C4×C43—22no—
94C4×C43—81no—
95C4×C43#48112yes—
96C4×C43#49211yescharacteristic
97C4×C43#49611yescharacteristic
98#1955D4311yescharacteristic
99#1849—431no—
100#1570—432no—
101#1486—432no—
102#1275—431no—
103C2×C43—22no—
104C2×C43—82no—
105C2×C43#209111yescharacteristic
106C2×C43#209411yescharacteristic
107C2×C43#209811yescharacteristic
108C2×C4×D4C2×D4311yescharacteristic
109#431—432no—
110C2×#108—862no—
111#423—432no—
112C2×C4⋊C8C2×D4311yescharacteristic
113C2×C22⋊C8—22no—
114C2×#97C2×D4311yescharacteristic
115#334—864no—
116D4⋊C8—864no—
117C43#1066111yescharacteristic, complemented, Sylow
118C22×D4Dic8611yescharacteristic
119C23×C4—21no—
120C2×M16—862no—
121C22×C8—21no—
122C22×C8C22⋊D4312yes—
123C4×D4—22no—
124C4×D4—22no—
125C2×C4⋊C4Dic8611yescharacteristic
126C2×C22⋊C4—21no—
127C2×C42C22×D4311yescharacteristic
128#108—1724no—
129C4⋊C8—22no—
130C4⋊C8—862no—
131C4⋊C8—862no—
132C4⋊C8—862no—
133C22⋊C8—44no—
134C22⋊C8—862no—
135#97—22no—
136C4×C8—434no—
137C24—21no—
138C2×D4—22no—
139C2×D4—42no—
140C22×C4—21no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4C2×Dic8611yescharacteristic
146C22×C4#1062189811yescharacteristic
147C22×C4C2×C22⋊D4311yescharacteristic
148M16—1724no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—42no—
153C2×C8—864no—
154C2×C8—1722no—
155C2×C8#1062188314yes—
156C4⋊C4—22no—
157C22⋊C4—42no—
158C42D4×D4312yes—
159C42#1062190012yes—
160C23—22no—
161C23—41no—
162C23—42no—
163C23—41no—
164C23—42no—
165C23#1306330411yescharacteristic
166D4—24no—
167D4—42no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—82no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4#1306330212yes—
176C2×C4#1306330611yescharacteristic
177C2×C4#1306330712yes—
178C2×C4#1306332111yescharacteristic
179C2×C4C2×#1062188312yes—
180C2×C4#1306335012yes—
181C8—24no—
182C8—81no—
183C8—3442no—
184C8—1724no—
185C22—21no—
186C22—21no—
187C22—44no—
188C22—42no—
189C22—82no—
190C22—81no—
191C22—81no—
192C22#1458283511yescharacteristic
193C22#1458318912yes—
194C4—22no—
195C4—22no—
196C4—81no—
197C4#1458321512yes—
198C4#1458327111yescharacteristic
199C4#1458328911yescharacteristic
200C2—22no—
201C2—82no—
202C2#1913611111yescharacteristic
203C2#1913612811yescharacteristic
204C2#1913614811yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1955C2
socleC22×C43#399
prime radicalC22×D4×C43Q8
hypercenter#1955D43
hypocenterC43#10661
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #19134770C2semidirect
2. #19133365C2semidirect
4. #19132426C2semidirect
117. C43#10661semidirect

Maximal subgroups

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

subgroupindex
#191347702
#191333652
#191330202
#191324262
C43×#19552
#1066143