Finite Group Databasebeta

← #25016916

Subgroups — #25016916

Order 11008.

458 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 79 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#19136260C212yesmaximal, complemented
2#19132758C214yesmaximal, complemented
3C43×#3151C211yesmaximal, characteristic
4#14582873—22no—
5#14582694—22no—
6#14582692C2214yescomplemented
7C2×AGL(1,ℤ/8)×C43—22no—
8C43×#532C2211yescharacteristic
9C2×#127×C43C411yescharacteristic, complemented
10C43×#496—22no—
11C43×#493C2212yes—
12C43×#492C412yescomplemented
13C4×M16×C43C411yescharacteristic, complemented
14#13063284—42no—
15#13063240—24no—
16#13063240—42no—
17C2×#41×C43D412yes—
18C22×D4×C43—21no—
19C22×D4×C43—41no—
20AGL(1,ℤ/8)×C43—44no—
21AGL(1,ℤ/8)×C43—44no—
22C2×SD16×C43—24no—
23C2×D8×C43—24no—
24C2×M16×C43—21no—
25C4⋊Q8×C43C2×C411yescharacteristic
26#127×C43—21no—
27#127×C43—41no—
28#127×C43C2×C412yes—
29#127×C43C2311yescharacteristic
30#124×C43D412yes—
31#121×C43—41no—
32C4×D4×C43—41no—
33C2×C42×C43C2×C411yescharacteristic
34#97×C43—21no—
35C4×C8×C43C2×C412yes—
36C24×C43—41no—
37#41×C43—42no—
38#41×C43—42no—
39C2×Q8×C43C22⋊C412yes—
40C2×D4×C43—22no—
41C2×D4×C43—22no—
42C2×D4×C43—41no—
43C2×D4×C43—42no—
44C2×D4×C43—41no—
45C2×D4×C43—42no—
46C2×D4×C43—42no—
47C2×D4×C43—42no—
48C2×D4×C43—84no—
49C2×D4×C43C2×D412yes—
50C22×C4×C43—22no—
51C22×C4×C43—21no—
52C22×C4×C43C22⋊C411yescharacteristic
53SD16×C43—48no—
54D8×C43—48no—
55M16×C43—24no—
56C2×C8×C43—22no—
57C4⋊C4×C43—41no—
58C22⋊C4×C43—42no—
59C42×C43—21no—
60C42×C43C22⋊C411yescharacteristic
61C42×C43C22×C411yescharacteristic
62C22⋊Dic43—44no—
63C4⋊Dic43—82no—
64C4×Dic43—82no—
65C23×C43—22no—
66C23×C43—42no—
67C23×C43—81no—
68C23×C43—81no—
69C23×C43—84no—
70C23×C43#9911yescharacteristic
71Q8×C43—42no—
72D4×C43—42no—
73D4×C43—44no—
74D4×C43—82no—
75D4×C43—84no—
76D4×C43—82no—
77D4×C43—84no—
78D4×C43—82no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43#9911yescharacteristic
87C2×C4×C43C2×C22⋊C411yescharacteristic
88C2×Dic43—84no—
89C8×C43—24no—
90#13585—431nomaximal, Sylow
91C22×C43—21no—
92C22×C43—41no—
93C22×C43—42no—
94C22×C43—82no—
95C22×C43—84no—
96C22×C43—82no—
97C22×C43—162no—
98C22×C43—162no—
99C22×C43C2×#9911yescharacteristic
100C4×C43—22no—
101C4×C43—21no—
102C4×C43—41no—
103C4×C43—42no—
104C4×C43#35312yes—
105Dic43—164no—
106#3151D4311yescharacteristic
107#2126—432no—
108#1408—434no—
109C2×C43—21no—
110C2×C43—41no—
111C2×C43—82no—
112C2×C43—162no—
113C2×C43C2×#35311yescharacteristic
114C2×AGL(1,ℤ/8)—22no—
115#532C2×D4311yescharacteristic
116C2×#127Dic4311yescharacteristic, complemented
117#496—22no—
118#493C2×D4312yes—
119#492Dic4312yescomplemented
120#410—862no—
121C4×M16Dic4311yescharacteristic, complemented
122#354—862no—
123#353—434no—
124C43#1358511yescharacteristic, complemented, Sylow
125C2×#41C22⋊D4312yes—
126C22×D4—21no—
127C22×D4—41no—
128AGL(1,ℤ/8)—44no—
129AGL(1,ℤ/8)—44no—
130C2×SD16—24no—
131C2×D8—24no—
132C2×M16—21no—
133C4⋊Q8C2×Dic4311yescharacteristic
134#127—21no—
135#127—41no—
136#127C2×Dic4312yes—
137#127C22×D4311yescharacteristic
138#124C22⋊D4312yes—
139#121—41no—
140C4×D4—41no—
141#117—1722no—
142C2×C42C2×Dic4311yescharacteristic
143#99—864no—
144#99—1722no—
145#97—21no—
146C4×C8C2×Dic4312yes—
147C24—41no—
148#41—42no—
149#41—42no—
150C2×Q8C22⋊Dic4312yes—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—42no—
154C2×D4—42no—
155C2×D4—41no—
156C2×D4—42no—
157C2×D4—42no—
158C2×D4—41no—
159C2×D4—84no—
160C2×D4C2×C22⋊D4312yes—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4C22⋊Dic4311yescharacteristic
164SD16—48no—
165D8—48no—
166M16—24no—
167C2×C8—22no—
168C4⋊C4—41no—
169C4⋊C4—3442no—
170C22⋊C4—42no—
171C22⋊C4—1724no—
172C42—21no—
173C42—3442no—
174C42C22⋊Dic4311yescharacteristic
175C42C22×Dic4311yescharacteristic
176C23—22no—
177C23—42no—
178C23—81no—
179C23—81no—
180C23—84no—
181C23#1306324011yescharacteristic
182Q8—42no—
183D4—42no—
184D4—44no—
185D4—84no—
186D4—82no—
187D4—82no—
188D4—84no—
189D4—82no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—3444no—
198C2×C4#1306324011yescharacteristic
199C2×C4C2×C22⋊Dic4311yescharacteristic
200C8—24no—
201C22—21no—
202C22—41no—
203C22—42no—
204C22—82no—
205C22—84no—
206C22—82no—
207C22—162no—
208C22—162no—
209C22C2×#1306324011yescharacteristic
210C4—22no—
211C4—21no—
212C4—41no—
213C4—42no—
214C4—6884no—
215C4#1458269212yes—
216C2—21no—
217C2—41no—
218C2—82no—
219C2—162no—
220C2C2×#1458269211yescharacteristic
subgroupG/H
centerC2C2×#14582692
commutatorC42×C43C22×C4
Frattini#127C22×D43
Fitting, prime radicalC43×#3151C2
socleC2×C43C2×#353
cosocle#127×C43C23
hypercenter#3151D43
hypocenterC43#13585
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. #19136260C2semidirect
2. #19132758C2semidirect
6. #14582692C22semidirect
9. C2×#127×C43C4semidirect
12. C43×#492C4semidirect
13. C4×M16×C43C4semidirect
116. C2×#127Dic43semidirect
119. #492Dic43semidirect
121. C4×M16Dic43semidirect
124. C43#13585semidirect

Maximal subgroups

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

subgroupindex
#191362602
#191327582
C43×#31512
#1358543