Finite Group Databasebeta

← #25016936

Subgroups — #25016936

Order 11008.

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

normal subgroups only

This group has 450 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#19136280C212yesmaximal, complemented
2#19132762C214yesmaximal, complemented
3C43×#3151C211yesmaximal, characteristic
4#14582883—22no—
5#14582698C2214yescomplemented
6#14582696—22no—
7C2×AGL(1,ℤ/8)×C43—22no—
8C43×#532C2211yescharacteristic
9C2×#127×C43C411yescharacteristic
10C43×#496—22no—
11C43×#493C412yes—
12C43×#492C2212yes—
13C4×M16×C43C411yescharacteristic
14C2×#10621877—42no—
15#13063244—24no—
16#13063242—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×C43C2311yescharacteristic
26#127×C43—21no—
27#127×C43—41no—
28#127×C43C2×C412yes—
29#127×C43C2×C411yescharacteristic
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×C43C2×D412yes—
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×C43C22⋊C412yes—
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
62#10621877—44no—
63#10621877—82no—
64C2×C43⋊C8—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—22no—
82C2×C4×C43—21no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43#9911yescharacteristic
87C2×C4×C43C2×C22⋊C411yescharacteristic
88C8×C43—24no—
89C43⋊C8—84no—
90#13591—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—
105#3151D4311yescharacteristic
106#2132—432no—
107#1410—434no—
108C2×C43—21no—
109C2×C43—41no—
110C2×C43—82no—
111C2×C43—162no—
112C2×C43C2×#35311yescharacteristic
113C2×AGL(1,ℤ/8)—22no—
114#532C2×D4311yescharacteristic
115C2×#127Dic4311yescharacteristic
116#496—22no—
117#493Dic4312yes—
118#492C2×D4312yes—
119#413—862no—
120C4×M16Dic4311yescharacteristic
121#356—434no—
122#355—862no—
123C43#1359111yescharacteristic, complemented, Sylow
124C2×#41C22⋊D4312yes—
125C22×D4—21no—
126C22×D4—41no—
127AGL(1,ℤ/8)—44no—
128AGL(1,ℤ/8)—44no—
129C2×SD16—24no—
130C2×D8—24no—
131C2×M16—21no—
132C2×M16—1722no—
133C4⋊Q8C22×D4311yescharacteristic
134#127—21no—
135#127—41no—
136#127C2×Dic4312yes—
137#127C2×Dic4311yescharacteristic
138#124C22⋊D4312yes—
139#121—41no—
140C4×D4—41no—
141C2×C42C2×Dic4311yescharacteristic
142#101—864no—
143#100—1722no—
144#97—21no—
145C4×C8C2×Dic4312yes—
146C24—41no—
147#41—42no—
148#41—42no—
149C2×Q8C2×C22⋊D4312yes—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4—42no—
153C2×D4—42no—
154C2×D4—41no—
155C2×D4—42no—
156C2×D4—42no—
157C2×D4—41no—
158C2×D4—84no—
159C2×D4C22⋊Dic4312yes—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4C22⋊Dic4311yescharacteristic
163SD16—48no—
164D8—48no—
165M16—24no—
166M16—3442no—
167M16—1724no—
168C2×C8—22no—
169C2×C8—3442no—
170C4⋊C4—41no—
171C22⋊C4—42no—
172C42—21no—
173C42C22⋊Dic4311yescharacteristic
174C42C22×Dic4311yescharacteristic
175C23—22no—
176C23—42no—
177C23—81no—
178C23—81no—
179C23—84no—
180C23#1306324011yescharacteristic
181Q8—42no—
182D4—42no—
183D4—44no—
184D4—84no—
185D4—82no—
186D4—82no—
187D4—84no—
188D4—82no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4#1306324011yescharacteristic
197C2×C4C2×C22⋊Dic4311yescharacteristic
198C8—24no—
199C8—3444no—
200C22—21no—
201C22—41no—
202C22—42no—
203C22—82no—
204C22—84no—
205C22—82no—
206C22—162no—
207C22—162no—
208C22C2×#1306324011yescharacteristic
209C4—22no—
210C4—21no—
211C4—41no—
212C4—42no—
213C4#1458269212yes—
214C2—21no—
215C2—41no—
216C2—82no—
217C2—162no—
218C2C2×#1458269211yescharacteristic
subgroupG/H
centerC2C2×#14582692
commutatorC42×C43C22×C4
FrattiniC4⋊Q8C22×D43
Fitting, prime radicalC43×#3151C2
socleC2×C43C2×#353
cosocleC4⋊Q8×C43C23
hypercenter#3151D43
hypocenterC43#13591
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. #19136280C2semidirect
2. #19132762C2semidirect
5. #14582698C22semidirect
123. C43#13591semidirect

Maximal subgroups

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

subgroupindex
#191362802
#191327622
C43×#31512
#1359143