Finite Group Databasebeta

← #25009938

Subgroups — #25009938

Order 11008.

342 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 55 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#19145460C211yesmaximal, characteristic
2#19136809C212yesmaximal, complemented
3#19132579C212yesmaximal, complemented
4#19132533C211yesmaximal, characteristic, complemented
5C43×#2098C211yesmaximal, characteristic, complemented
6#14583463—21no—
7#14583224—22no—
8#14583152C2212yes—
9#14583135—21no—
10#14583035—22no—
11#14582723—22no—
12#14582711—22no—
13#14582681C2212yescomplemented
14C43×#430C2211yescharacteristic, complemented
15C43×#424—21no—
16C43×#421—21no—
17C43×#408C2211yescharacteristic
18C43×H(3,ℤ/4)C2211yescharacteristic, complemented
19C22×D172—21no—
20C2×D344—21no—
21C2×D344D412yes—
22#13063321—41no—
23#13063314—41no—
24#13063299—22no—
25#13063299—22no—
26#13063293—41no—
27#13063293—41no—
28#13063284—21no—
29#13063265—22no—
30#13063259—21no—
31#13063257D412yes—
32#13063247—22no—
33#13063247—22no—
34C2×#41×C43D411yescharacteristic
35C2×M16×C43—21no—
36C2×M16×C43C2311yescharacteristic
37C22×C8×C43D411yescharacteristic
38#117×C43—21no—
39#108×C43—22no—
40C4⋊C8×C43—42no—
41#104×C43—42no—
42C22⋊C8×C43—22no—
43C23×D43—41no—
44#41×C43—41no—
45#41×C43—41no—
46C2×Q8×C43SD1611yescharacteristic
47C2×D4×C43—21no—
48C2×D4×C43SD1611yescharacteristic
49C22×C4×C43—21no—
50C22×C4×C43C2×D411yescharacteristic
51C2×C22⋊D43—42no—
52C2×C22⋊D43—42no—
53C2×D172—22no—
54C2×D172—41no—
55C2×D172—81no—
56C2×D172—81no—
57M16×C43—41no—
58M16×C43—41no—
59M16×C43—41no—
60C2×C8×C43—21no—
61C2×C8×C43—41no—
62C2×C8×C43—41no—
63C2×C8×C43C2×D412yes—
64C4⋊C4×C43—41no—
65C22⋊C4×C43—41no—
66C42×C43—22no—
67C22⋊Dic43—41no—
68(C2×D43)⋊C4—42no—
69(C2×D43)⋊C4—42no—
70C4⋊Dic43—22no—
71C4×Dic43—41no—
72D344—42no—
73D344—81no—
74C43⋊C16—42no—
75C23×C43—21no—
76C23×C43AGL(1,ℤ/8)11yescharacteristic
77C22×D43—42no—
78C22×D43—82no—
79C22×D43—162no—
80Q8×C43—41no—
81D4×C43—41no—
82D4×C43—81no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43#12011yescharacteristic
90C2×C4×C43C2×SD1611yescharacteristic
91C22⋊D43—162no—
92C22⋊D43—162no—
93C2×Dic43—42no—
94D172—42no—
95D172—42no—
96D172—82no—
97C8×C43—22no—
98C8×C43—41no—
99C8×C43—81no—
100#12301—431nomaximal, Sylow
101C22×C43—21no—
102C22×C43—41no—
103C22×C43—42no—
104C22×C43—41no—
105C22×C43#45011yescharacteristic
106C2×D43—82no—
107C2×D43—82no—
108C2×D43—82no—
109C2×D43—164no—
110C4×C43—21no—
111C4×C43—41no—
112C4×C43—82no—
113C4×C43#45311yescharacteristic
114C4×C43#45811yescharacteristic
115Dic43—82no—
116#3199—431no—
117#2238—432no—
118#2098D4311yescharacteristic, complemented
119#1339—432no—
120#1321—431no—
121C2×C43—21no—
122C2×C43—41no—
123C2×C43—81no—
124C2×C43#161311yescharacteristic
125D43—162no—
126#535—861no—
127#482—862no—
128#469—432no—
129#466—861no—
130#447—862no—
131#430C2×D4311yescharacteristic, complemented
132#424—21no—
133#421—21no—
134#408C2×D4311yescharacteristic
135#365—862no—
136#361—862no—
137#349—432no—
138H(3,ℤ/4)C2×D4311yescharacteristic, complemented
139C43#1230111yescharacteristic, complemented, Sylow
140C2×#41C22⋊D4311yescharacteristic
141C22×D4—861no—
142C2×D8—432no—
143C2×D8—861no—
144C2×M16—21no—
145C2×M16C22×D4311yescharacteristic
146C22×C8C22⋊D4311yescharacteristic
147#127—1721no—
148#124—1721no—
149#121—862no—
150#121—862no—
151#120—1721no—
152#120—1721no—
153#117—21no—
154#117—861no—
155M32—862no—
156#108—22no—
157#107—861no—
158#106—432no—
159C4⋊C8—42no—
160#104—42no—
161#102—862no—
162#102—862no—
163C22⋊C8—22no—
164C24—1721no—
165#41—41no—
166#41—41no—
167C2×Q8#1062188411yescharacteristic
168C2×D4—21no—
169C2×D4—862no—
170C2×D4—3441no—
171C2×D4—3441no—
172C2×D4—1721no—
173C2×D4—1722no—
174C2×D4—1722no—
175C2×D4#1062188411yescharacteristic
176C22×C4—21no—
177C22×C4C2×C22⋊D4311yescharacteristic
178D8—3441no—
179D8—1722no—
180M16—41no—
181M16—41no—
182M16—41no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8D4×D4312yes—
187C4⋊C4—41no—
188C4⋊C4—862no—
189C22⋊C4—41no—
190C22⋊C4—1722no—
191C22⋊C4—1721no—
192C22⋊C4—1722no—
193C42—22no—
194C42—1721no—
195C16—1722no—
196C23—21no—
197C23—3442no—
198C23—1722no—
199C23—6882no—
200C23#1306335011yescharacteristic
201Q8—41no—
202D4—41no—
203D4—81no—
204D4—3442no—
205D4—1722no—
206D4—1722no—
207D4—6882no—
208D4—6882no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—1722no—
216C2×C4#1306329311yescharacteristic
217C2×C4C2×#1062188411yescharacteristic
218C8—22no—
219C8—41no—
220C8—81no—
221C22—21no—
222C22—41no—
223C22—42no—
224C22—41no—
225C22—3442no—
226C22—3442no—
227C22—3442no—
228C22—6884no—
229C22#1458304911yescharacteristic
230C4—21no—
231C4—41no—
232C4—82no—
233C4—3442no—
234C4#1458306611yescharacteristic
235C4#1458308811yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—6882no—
240C2#1913361411yescharacteristic
subgroupG/H
centerC2#19133614
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#2098C2
socleC2×C43#1613
prime radical#19145460C2
hypercenter#2098D43
hypocenterC43#12301
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2098

Complements

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

NH ≅ G/Ntype
2. #19136809C2semidirect
3. #19132579C2semidirect
4. #19132533C2semidirect
5. C43×#2098C2semidirect
13. #14582681C22semidirect
14. C43×#430C22semidirect
18. C43×H(3,ℤ/4)C22semidirect
118. #2098D43semidirect
131. #430C2×D43semidirect
138. H(3,ℤ/4)C2×D43semidirect
139. C43#12301semidirect

Maximal subgroups

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

subgroupindex
#191454602
#191368092
#191325792
#191325332
C43×#20982
#1230143