Finite Group Databasebeta

← #25005886

Subgroups — #25005886

Order 11008.

440 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 87 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#19137303C211yesmaximal, characteristic
2#19132917C212yesmaximal, complemented
3#19132541C211yesmaximal, characteristic, complemented
4#19132526C212yesmaximal
5C43×#1325C211yesmaximal, characteristic, complemented
6C2×#13063313C411yescharacteristic
7C2×#13063290C2211yescharacteristic
8C2×#13063287C411yescharacteristic
9#14582949—22no—
10#14582804C411yescharacteristic
11#14582800C2211yescharacteristic
12#14582789—22no—
13#14582770—22no—
14#14582745C411yescharacteristic
15#14582625C2212yes—
16#14582624—22no—
17C43×#384C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C22×D172C2×C411yescharacteristic
21C22×C4×D43—21no—
22#13063313—22no—
23#13063313C814yescomplemented
24#13063290—42no—
25#13063287—42no—
26C2×Dic43⋊C4D412yes—
27C2×(C2×D43)⋊C4—22no—
28C2×(C2×D43)⋊C4—21no—
29C2×(C2×D43)⋊C4—22no—
30C2×C4×Dic43C2×C411yescharacteristic
31C2×C4×Dic43C2×C411yescharacteristic
32C2×C4×Dic43D412yes—
33Dic43⋊C8—42no—
34C22⋊(C43⋊C8)—22no—
35C8×Dic43—42no—
36C43⋊#95—21no—
37C43⋊#95—22no—
38C43⋊#95—21no—
39C2×C4⋊C4×C43—22no—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C42×C43C2×C411yescharacteristic
43C22⋊C8×C43—22no—
44C23×D43—21no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C22×C411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—21no—
50C22×Dic43C22⋊C412yes—
51C22×Dic43C22⋊C411yescharacteristic
52C22×Dic43C22⋊C411yescharacteristic
53C2×D172—21no—
54C2×D172—41no—
55C2×D172—41no—
56C2×D172C2×C812yes—
57C2×C4×D43—42no—
58C2×C4×D43—82no—
59C2×Dic86—41no—
60C2×Dic86—41no—
61C2×Dic86C2×C812yes—
62C2×Dic86M1612yes—
63C2×C8×C43—42no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—82no—
67C42×C43—21no—
68C42×C43C2×C812yes—
69(C2×D43)⋊C4—28no—
70(C2×D43)⋊C4—42no—
71(C2×D43)⋊C4—82no—
72Dic43⋊C4—42no—
73C4×Dic43—22no—
74C4×Dic43—22no—
75C4×Dic43—22no—
76C4×Dic43—41no—
77C2×C43⋊C8—42no—
78C23×C43C2×C22⋊C411yescharacteristic
79C22×D43—22no—
80C22×D43—42no—
81C22×D43—42no—
82C22×D43—41no—
83C22×D43—41no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—41no—
93C2×C4×C43C22×C811yescharacteristic
94C2×C4×C43C2×M1611yescharacteristic
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—41no—
99C2×Dic43—41no—
100C2×Dic43—41no—
101C2×Dic43—41no—
102C2×Dic43—41no—
103C2×Dic43C22⋊C814yes—
104C2×Dic43#9912yes—
105D172—42no—
106D172—42no—
107C4×D43—84no—
108Dic86—42no—
109Dic86—42no—
110C8×C43—82no—
111C43⋊C8—82no—
112#11480—431nomaximal, Sylow
113C22×C43—21no—
114C22×C43—21no—
115C22×C43C2×C22⋊C811yescharacteristic
116C22×C43C2×#9911yescharacteristic
117C22×C43#41311yescharacteristic
118C2×D43—44no—
119C2×D43—42no—
120C2×D43—82no—
121C2×D43—81no—
122C2×D43—81no—
123C4×C43—21no—
124C4×C43—21no—
125C4×C43—42no—
126C4×C43—42no—
127C4×C43—81no—
128Dic43—22no—
129Dic43—24no—
130Dic43—41no—
131Dic43—81no—
132#2326—431no—
133#1461—432no—
134#1325—431no—
135#1325D4311yescharacteristic, complemented
136#1318—432no—
137C2×C43—21no—
138C2×C43—21no—
139C2×C43#145911yescharacteristic
140C2×C43#212811yescharacteristic
141C2×C43#213311yescharacteristic
142D43—82no—
143C2×#124—431no—
144C2×C4×Q8—431no—
145C2×C4×D4—431no—
146#431—862no—
147#391—431no—
148#390—431no—
149#388—862no—
150#385—862no—
151#384C2×D4311yescharacteristic
152#376—431no—
153#324—432no—
154#324—862no—
155#324C2×D4312yes—
156C43#1148011yescharacteristic, complemented, Sylow
157C22×Q8—431no—
158C22×D4—431no—
159C23×C4—861no—
160#124—434no—
161#124—862no—
162C4×Q8—1722no—
163C4×D4—1722no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—432no—
166C2×C4⋊C4C4×D4311yescharacteristic
167C2×C4⋊C4C22×D4311yescharacteristic
168C2×C22⋊C4—862no—
169C2×C22⋊C4—862no—
170C2×C22⋊C4—861no—
171C2×C42—431no—
172C2×C42—432no—
173C2×C42—431no—
174C2×C42C4×D4311yescharacteristic
175C4⋊C8—1722no—
176C22⋊C8—22no—
177C22⋊C8—862no—
178C4×C8—1722no—
179#95—861no—
180#95—861no—
181#95—862no—
182C24—861no—
183C2×Q8—432no—
184C2×Q8—432no—
185C2×Q8—1721no—
186C2×Q8—1721no—
187C2×D4—432no—
188C2×D4—861no—
189C2×D4—1721no—
190C2×D4—1721no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—432no—
194C22×C4—431no—
195C22×C4—431no—
196C22×C4—861no—
197C22×C4—3442no—
198C22×C4—1722no—
199C22×C4C2×C4×D4311yescharacteristic
200C22×C4D4×D4312yes—
201C2×C8—42no—
202C2×C8—1722no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—82no—
206C4⋊C4—1722no—
207C22⋊C4—868no—
208C22⋊C4—3442no—
209C22⋊C4—1722no—
210C42—21no—
211C42—862no—
212C42—862no—
213C42—862no—
214C42—1721no—
215C42C8×D4312yes—
216C23—862no—
217C23—1722no—
218C23—1722no—
219C23—1721no—
220C23—1721no—
221C23C22⋊C4×D4311yescharacteristic
222Q8—1722no—
223Q8—1722no—
224D4—1722no—
225D4—1722no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—434no—
236C2×C4—432no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—861no—
240C2×C4—3444no—
241C2×C4—1721no—
242C2×C4—1721no—
243C2×C4—1721no—
244C2×C4—1721no—
245C2×C4—1721no—
246C2×C4C2×C8×D4311yescharacteristic
247C2×C4M16×D4311yescharacteristic
248C8—82no—
249C8—3442no—
250C22—21no—
251C22—21no—
252C22—3442no—
253C22—3441no—
254C22—3441no—
255C22—1724no—
256C22—1722no—
257C22C22⋊C8×D4311yescharacteristic
258C22#99×D4311yescharacteristic
259C22#1458288211yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—42no—
264C4—81no—
265C4—862no—
266C4—864no—
267C4—3441no—
268C4—1721no—
269C2—21no—
270C2—21no—
271C2—3442no—
272C2#1913291211yescharacteristic
273C2#1913626511yescharacteristic
274C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1325C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1325D43
hypocenterC43#11480
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #19132917C2semidirect
3. #19132541C2semidirect
5. C43×#1325C2semidirect
23. #13063313C8semidirect
135. #1325D43semidirect
156. C43#11480semidirect

Maximal subgroups

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

subgroupindex
#191373032
#191329172
#191325412
#191325262
C43×#13252
#1148043