Finite Group Databasebeta

← #25000771

Subgroups — #25000771

Order 11008.

386 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 85 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#19134732C211yesmaximal, characteristic, complemented
2#19133330C212yesmaximal, complemented
3#19133046C212yesmaximal, complemented
4C43⋊#1309C211yesmaximal, characteristic, complemented
5C43×#3253C211yesmaximal, characteristic
6#14582923C2211yescharacteristic
7#14582923C2212yes—
8C2×C4×C43⋊C8C2211yescharacteristic
9#14582663—22no—
10#14582648—22no—
11#14582643—22no—
12D4⋊(C43⋊C8)—24no—
13C43×#532C2212yes—
14C43×#476—22no—
15C43×#469—22no—
16C43×#459—22no—
17C43×#423C2211yescharacteristic
18C2×#10621877—21no—
19C2×#10621877—22no—
20C22×C43⋊C8—21no—
21C4⋊(C43⋊C8)—22no—
22C4⋊(C43⋊C8)—22no—
23C4⋊(C43⋊C8)—22no—
24C4×C43⋊C8—21no—
25C4×C43⋊C8D412yes—
26C2×#41×C43—22no—
27C2×D8×C43—22no—
28C2×M16×C43D412yes—
29C4⋊Q8×C43D412yes—
30#127×C43D412yes—
31#124×C43—22no—
32#121×C43—22no—
33#121×C43—22no—
34C4×D4×C43—22no—
35C4×D4×C43—22no—
36C2×C42×C43C2311yescharacteristic
37#106×C43—22no—
38C4⋊C8×C43—22no—
39#102×C43—24no—
40#41×C43—82no—
41#41×C43—82no—
42C2×Q8×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—22no—
45C2×D4×C43—22no—
46C2×D4×C43—42no—
47C22×C4×C43—42no—
48C22×C4×C43C2×D411yescharacteristic
49C22×C4×C43#4112yes—
50D8×C43—82no—
51M16×C43—42no—
52C2×C8×C43—22no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43—22no—
55C22⋊C4×C43—42no—
56C22⋊C4×C43—42no—
57C42×C43C2×D411yescharacteristic
58C42×C43C2×D412yes—
59C42×C43#4111yescharacteristic
60#10621877—42no—
61#10621877—82no—
62C2×C43⋊C8—22no—
63C2×C43⋊C8—41no—
64C2×C43⋊C8—41no—
65C2×C43⋊C8—41no—
66C2×C43⋊C8—42no—
67C23×C43—42no—
68C23×C43#12411yescharacteristic
69Q8×C43—82no—
70D4×C43—42no—
71D4×C43—42no—
72D4×C43—42no—
73D4×C43—42no—
74D4×C43—82no—
75D4×C43—84no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—42no—
81C2×C4×C43—82no—
82C2×C4×C43—82no—
83C2×C4×C43#12011yescharacteristic
84C2×C4×C43#12111yescharacteristic
85C2×C4×C43#12112yes—
86C2×C4×C43#12312yes—
87C8×C43—42no—
88C43⋊C8—42no—
89C43⋊C8—81no—
90C43⋊C8—82no—
91#10531—431nomaximal, Sylow
92C22×C43—22no—
93C22×C43—21no—
94C22×C43—82no—
95C22×C43—82no—
96C22×C43—82no—
97C22×C43#39411yescharacteristic
98C4×C43—22no—
99C4×C43—21no—
100C4×C43—82no—
101C4×C43#45411yescharacteristic
102C4×C43#45511yescharacteristic
103C4×C43#47112yes—
104C4×C43#47212yes—
105#3253D4311yescharacteristic
106#1837—431no—
107#1560—432no—
108#1492—432no—
109#1309—431no—
110C2×C43—41no—
111C2×C43—162no—
112C2×C43#204011yescharacteristic
113C2×C43#205112yes—
114#532C2×D4312yes—
115#476—22no—
116#469—22no—
117#459—22no—
118#423—431no—
119#423—432no—
120#423C2×D4311yescharacteristic
121C2×C4×C8—431no—
122#341—862no—
123#333—862no—
124#331—862no—
125D4⋊C8—864no—
126C43#1053111yescharacteristic, complemented, Sylow
127C2×#41—22no—
128C2×D8—22no—
129C2×M16—862no—
130C2×M16—861no—
131C2×M16C22⋊D4312yes—
132C22×C8—861no—
133C4⋊Q8C22⋊D4312yes—
134#127C22⋊D4312yes—
135#124—22no—
136#121—22no—
137#121—22no—
138C4×D4—22no—
139C4×D4—22no—
140C2×C42C22×D4311yescharacteristic
141#106—22no—
142C4⋊C8—22no—
143C4⋊C8—862no—
144C4⋊C8—862no—
145C4⋊C8—862no—
146#102—24no—
147C4×C8—432no—
148C4×C8—861no—
149#41—82no—
150#41—82no—
151C2×Q8—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—42no—
156C22×C4—42no—
157C22×C4#1062190012yes—
158C22×C4C2×C22⋊D4311yescharacteristic
159D8—82no—
160M16—42no—
161M16—3442no—
162M16—1722no—
163C2×C8—22no—
164C2×C8—862no—
165C2×C8—1721no—
166C2×C8—1722no—
167C2×C8—1721no—
168C2×C8—1721no—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C42D4×D4311yescharacteristic
174C42#1062190011yescharacteristic
175C42C2×C22⋊D4312yes—
176C23—42no—
177C23#1306331211yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—42no—
182D4—42no—
183D4—82no—
184D4—84no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—82no—
191C2×C4—82no—
192C2×C4#1306329411yescharacteristic
193C2×C4#1306329611yescharacteristic
194C2×C4#1306329712yes—
195C2×C4#1306330612yes—
196C8—42no—
197C8—3441no—
198C8—3442no—
199C8—1722no—
200C22—21no—
201C22—22no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1458281311yescharacteristic
206C4—21no—
207C4—22no—
208C4—82no—
209C4#1458307211yescharacteristic
210C4#1458307711yescharacteristic
211C4#1458316012yes—
212C4#1458316712yes—
213C2—41no—
214C2—162no—
215C2#1913582111yescharacteristic
216C2#1913588412yes—
subgroupG/H
centerC22#14582813
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3253C2
socleC22×C43#394
hypercenter#3253D43
hypocenterC43#10531
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #19134732C2semidirect
2. #19133330C2semidirect
3. #19133046C2semidirect
4. C43⋊#1309C2semidirect
126. C43#10531semidirect

Maximal subgroups

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

subgroupindex
#191347322
#191333302
#191330462
C43⋊#13092
C43×#32532
#1053143