Finite Group Databasebeta

← #25005991

Subgroups — #25005991

Order 11008.

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

normal subgroups only

This group has 510 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#19132929C212yesmaximal
2#19132529C214yesmaximal, complemented
3C43×#2310C211yesmaximal, characteristic
4#14582956—22no—
5#14582625C2214yes—
6#14582623—22no—
7C23×Q8×C43C411yescharacteristic
8C2×#117×C43C411yescharacteristic
9C2×#117×C43C2211yescharacteristic
10C43×#391—22no—
11C43×#391C412yes—
12C43×#391C2212yes—
13C43×#381—22no—
14C4⋊(C43⋊C8)—42no—
15C22⋊(C43⋊C8)—24no—
16#13063236—42no—
17C22×Q8×C43—24no—
18C22×Q8×C43—21no—
19C22×Q8×C43—42no—
20C22×Q8×C43—42no—
21C22×Q8×C43C2×C412yes—
22C23×C4×C43—21no—
23C23×C4×C43C2×C411yescharacteristic
24#117×C43—42no—
25#117×C43—42no—
26C2×C4⋊C4×C43—21no—
27C2×C4⋊C4×C43C2×C411yescharacteristic
28C2×C4⋊C4×C43C2311yescharacteristic
29C2×C22⋊C4×C43—21no—
30C2×C22⋊C4×C43D412yes—
31C2×C42×C43C2×C412yes—
32C2×C42×C43D412yes—
33#95×C43—24no—
34#95×C43—24no—
35C24×C43C22⋊C411yescharacteristic
36C2×Q8×C43—24no—
37C2×Q8×C43—22no—
38C2×Q8×C43—416no—
39C2×Q8×C43—42no—
40C2×Q8×C43—42no—
41C2×Q8×C43—42no—
42C2×Q8×C43—42no—
43C2×Q8×C43M1614yes—
44C22×C4×C43—22no—
45C22×C4×C43—22no—
46C22×C4×C43—24no—
47C22×C4×C43—22no—
48C22×C4×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43—42no—
51C22×C4×C43—42no—
52C22×C4×C43C22⋊C412yes—
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22×C411yescharacteristic
55C22×C4×C43C2×D412yes—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C4⋊C4×C43—42no—
59C22⋊C4×C43—42no—
60C22⋊C4×C43—42no—
61C42×C43—22no—
62C42×C43—22no—
63C42×C43—42no—
64C2×C43⋊C8—44no—
65C23×C43—21no—
66C23×C43—21no—
67C23×C43—41no—
68C23×C43—41no—
69C23×C43#10012yes—
70C23×C43C2×C22⋊C411yescharacteristic
71Q8×C43—44no—
72Q8×C43—48no—
73Q8×C43—44no—
74C2×C4×C43—28no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—24no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—48no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43#9912yes—
91C2×C4×C43C2×M1612yes—
92C43⋊C8—84no—
93#11510—431nomaximal, Sylow
94C22×C43—21no—
95C22×C43—21no—
96C22×C43—22no—
97C22×C43—42no—
98C22×C43—42no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43#40711yescharacteristic
102C22×C43C2×#9911yescharacteristic
103C22×C43C2×#10011yescharacteristic
104C4×C43—22no—
105C4×C43—22no—
106C4×C43—42no—
107C4×C43—42no—
108C4×C43—44no—
109C4×C43—82no—
110#2310D4311yescharacteristic
111#1464—432no—
112#1319—434no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—42no—
116C2×C43#146211yescharacteristic
117C2×C43#212911yescharacteristic
118C2×C43#213511yescharacteristic
119C23×Q8Dic4311yescharacteristic
120C2×#117Dic4311yescharacteristic
121C2×#117C2×D4311yescharacteristic
122#432—862no—
123#391—22no—
124#391Dic4312yes—
125#391C2×D4312yes—
126#381—22no—
127#324—434no—
128#323—862no—
129C43#1151011yescharacteristic, complemented, Sylow
130C22×Q8—24no—
131C22×Q8—21no—
132C22×Q8—42no—
133C22×Q8—42no—
134C22×Q8C2×Dic4312yes—
135C23×C4—21no—
136C23×C4C2×Dic4311yescharacteristic
137#117—42no—
138#117—42no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4C2×Dic4311yescharacteristic
141C2×C4⋊C4C22×D4311yescharacteristic
142C2×C22⋊C4—21no—
143C2×C22⋊C4C22⋊D4312yes—
144C2×C42C2×Dic4312yes—
145C2×C42C22⋊D4312yes—
146C4⋊C8—1722no—
147C22⋊C8—864no—
148#97—1722no—
149#95—24no—
150#95—24no—
151C24C22⋊Dic4311yescharacteristic
152C2×Q8—24no—
153C2×Q8—22no—
154C2×Q8—416no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8#1062187714yes—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4C22⋊Dic4312yes—
169C22×C4C22⋊Dic4311yescharacteristic
170C22×C4C22×Dic4311yescharacteristic
171C22×C4C2×C22⋊D4312yes—
172C2×C8—1724no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C22⋊C4—42no—
177C22⋊C4—42no—
178C42—22no—
179C42—22no—
180C42—42no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23#1306324212yes—
186C23C2×C22⋊Dic4311yescharacteristic
187Q8—44no—
188Q8—48no—
189Q8—44no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—48no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4#1306324012yes—
207C2×C4C2×#1062187712yes—
208C8—3444no—
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22#1458286311yescharacteristic
217C22C2×#1306324011yescharacteristic
218C22C2×#1306324211yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—44no—
224C4—82no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2#1913292211yescharacteristic
229C2#1913627011yescharacteristic
230C2#1913629011yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2310C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2310D43
hypocenterC43#11510
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. #19132529C2semidirect
129. C43#11510semidirect

Maximal subgroups

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

subgroupindex
#191329292
#191325292
C43×#23102
#1151043