Finite Group Databasebeta

← #25005890

Subgroups — #25005890

Order 11008.

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

normal subgroups only

This group has 460 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#19132912C212yesmaximal
3#19132541C211yesmaximal, characteristic, complemented
4#19132528C212yesmaximal, complemented
5C43×#1325C211yesmaximal, characteristic, complemented
6C2×#13063313C411yescharacteristic
7C2×#13063290C411yescharacteristic
8C2×#13063287C2211yescharacteristic
9C22⋊C8×D43—22no—
10#14582804C2211yescharacteristic
11#14582800C411yescharacteristic
12#14582789—22no—
13#14582770—22no—
14#14582745C411yescharacteristic
15#14582625C2212yes—
16#14582622—22no—
17C43×#384C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C22×D172C2×C411yescharacteristic
21C22×C4×D43D412yes—
22C2×C8×D43—42no—
23#13063313—22no—
24#13063313C814yescomplemented
25#13063290—42no—
26#13063287—42no—
27C2×Dic43⋊C4—21no—
28C2×(C2×D43)⋊C4—22no—
29C2×(C2×D43)⋊C4—22no—
30C2×(C2×D43)⋊C4D412yes—
31C2×C4×Dic43—21no—
32C2×C4×Dic43C2×C411yescharacteristic
33C2×C4×Dic43C2×C411yescharacteristic
34C22⋊(C43⋊C8)—22no—
35(C2×D43)⋊C8—42no—
36C43⋊#95—22no—
37C43⋊#95—21no—
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×D43C22⋊C412yes—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C22×C411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—21no—
50C22×Dic43—21no—
51C22×Dic43C22⋊C411yescharacteristic
52C22×Dic43C22⋊C411yescharacteristic
53C2×D172—41no—
54C2×D172—41no—
55C2×D172C2×C812yes—
56C2×D172M1612yes—
57C2×C4×D43—22no—
58C2×C4×D43—22no—
59C2×C4×D43—82no—
60C2×Dic86—21no—
61C2×Dic86—41no—
62C2×Dic86—41no—
63C2×Dic86C2×C812yescomplemented
64C2×C8×C43—42no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C4⋊C4×C43—82no—
68C42×C43—21no—
69C42×C43C2×C812yescomplemented
70(C2×D43)⋊C4—28no—
71(C2×D43)⋊C4—42no—
72(C2×D43)⋊C4—82no—
73Dic43⋊C4—42no—
74C4×Dic43—22no—
75C4×Dic43—42no—
76C4×Dic43—41no—
77C2×C43⋊C8—42no—
78C8×D43—84no—
79C23×C43C2×C22⋊C411yescharacteristic
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—42no—
83C22×D43—42no—
84C22×D43C22⋊C814yes—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—41no—
94C2×C4×C43C22×C811yescharacteristic
95C2×C4×C43C2×M1611yescharacteristic
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—41no—
99C2×Dic43—41no—
100C2×Dic43—41no—
101C2×Dic43—41no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43—41no—
105C2×Dic43#9912yes—
106D172—42no—
107D172—42no—
108C4×D43—44no—
109C4×D43—82no—
110Dic86—42no—
111Dic86—42no—
112C8×C43—82no—
113C43⋊C8—82no—
114#11481—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43C2×C22⋊C811yescharacteristic
118C22×C43C2×#9911yescharacteristic
119C22×C43#41311yescharacteristic
120C2×D43—24no—
121C2×D43—42no—
122C2×D43—42no—
123C2×D43—44no—
124C2×D43—82no—
125C4×C43—21no—
126C4×C43—21no—
127C4×C43—42no—
128C4×C43—42no—
129C4×C43—81no—
130Dic43—22no—
131Dic43—41no—
132Dic43—42no—
133Dic43—81no—
134#2326—431no—
135#1459—432no—
136#1325—431no—
137#1325D4311yescharacteristic, complemented
138#1319—432no—
139C2×C43—21no—
140C2×C43—21no—
141C2×C43#145911yescharacteristic
142C2×C43#212711yescharacteristic
143C2×C43#213511yescharacteristic
144D43—44no—
145C2×#124—431no—
146C2×C4×Q8—431no—
147C2×C4×D4—431no—
148C2×C22⋊C8—862no—
149#391—431no—
150#390—431no—
151#388—862no—
152#385—862no—
153#384C2×D4311yescharacteristic
154#376—431no—
155#324—432no—
156#324C2×D4312yes—
157#323—862no—
158C43#1148111yescharacteristic, complemented, Sylow
159C22×Q8—431no—
160C22×D4—431no—
161C23×C4—432no—
162C22×C8—1722no—
163#124—434no—
164#124—862no—
165C4×Q8—1722no—
166C4×D4—1722no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—861no—
169C2×C4⋊C4C4×D4311yescharacteristic
170C2×C4⋊C4C22×D4311yescharacteristic
171C2×C22⋊C4—432no—
172C2×C22⋊C4—862no—
173C2×C22⋊C4—862no—
174C2×C42—431no—
175C2×C42—431no—
176C2×C42—861no—
177C2×C42C4×D4311yescharacteristic
178C22⋊C8—22no—
179C22⋊C8—862no—
180C22⋊C8—1722no—
181#95—861no—
182#95—861no—
183#95—862no—
184C24—432no—
185C2×Q8—432no—
186C2×Q8—861no—
187C2×Q8—1721no—
188C2×Q8—1721no—
189C2×D4—432no—
190C2×D4—432no—
191C2×D4—1721no—
192C2×D4—1721no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—431no—
196C22×C4—431no—
197C22×C4—862no—
198C22×C4—862no—
199C22×C4—861no—
200C22×C4—861no—
201C22×C4—3442no—
202C22×C4C2×C4×D4311yescharacteristic
203C22×C4D4×D4312yes—
204C2×C8—42no—
205C2×C8—3444no—
206C2×C8—1722no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—82no—
210C4⋊C4—1722no—
211C22⋊C4—868no—
212C22⋊C4—3442no—
213C22⋊C4—1722no—
214C42—21no—
215C42—862no—
216C42—1721no—
217C42—1722no—
218C42C8×D4312yescomplemented
219C23—434no—
220C23—862no—
221C23—862no—
222C23—1722no—
223C23—1722no—
224C23C22⋊C4×D4311yescharacteristic
225Q8—1722no—
226Q8—1722no—
227D4—1722no—
228D4—1722no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—432no—
239C2×C4—862no—
240C2×C4—861no—
241C2×C4—3442no—
242C2×C4—1724no—
243C2×C4—1721no—
244C2×C4—1721no—
245C2×C4—1721no—
246C2×C4—1721no—
247C2×C4—1721no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4C2×C8×D4311yescharacteristic
251C2×C4M16×D4311yescharacteristic
252C8—82no—
253C8—3442no—
254C22—21no—
255C22—21no—
256C22—864no—
257C22—3442no—
258C22—1724no—
259C22—1722no—
260C22—1722no—
261C22C22⋊C8×D4311yescharacteristic
262C22#99×D4311yescharacteristic
263C22#1458288211yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—42no—
268C4—81no—
269C4—862no—
270C4—3441no—
271C4—1721no—
272C4—1722no—
273C2—21no—
274C2—21no—
275C2—1724no—
276C2#1913291211yescharacteristic
277C2#1913626111yescharacteristic
278C2#1913628811yescharacteristic
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#11481
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
3. #19132541C2semidirect
4. #19132528C2semidirect
5. C43×#1325C2semidirect
24. #13063313C8semidirect
63. C2×Dic86C2×C8semidirect
69. C42×C43C2×C8semidirect
137. #1325D43semidirect
158. C43#11481semidirect
218. C42C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191373032
#191329122
#191325412
#191325282
C43×#13252
#1148143