Finite Group Databasebeta

← #25005894

Subgroups — #25005894

Order 11008.

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

normal subgroups only

This group has 392 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#19137312C211yesmaximal, characteristic
2#19132917C212yesmaximal
3#19132539C211yesmaximal, characteristic
4#19132528C212yesmaximal
5C43×#1324C211yesmaximal, characteristic
6C2×#13063325C411yescharacteristic
7C2×#13063290C411yescharacteristic
8C2×#13063290C2211yescharacteristic
9#14582949—22no—
10#14582804C411yescharacteristic
11#14582804C2211yescharacteristic
12#14582782—22no—
13#14582782—22no—
14#14582745C411yescharacteristic
15#14582625C2212yes—
16#14582624—22no—
17C43×#382C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C22×Dic86C2×C411yescharacteristic
21#13063325—22no—
22#13063325C814yescomplemented
23#13063290—42no—
24#13063290—42no—
25C2×C4⋊Dic43—22no—
26C2×Dic43⋊C4—21no—
27C2×Dic43⋊C4D412yes—
28C2×C4×Dic43—21no—
29C2×C4×Dic43C2×C411yescharacteristic
30C2×C4×Dic43C2×C411yescharacteristic
31C2×C4×Dic43D412yes—
32Dic43⋊C8—42no—
33C22⋊(C43⋊C8)—22no—
34C8×Dic43—42no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C42×C43C2×C411yescharacteristic
42C22⋊C8×C43—22no—
43#95×C43—22no—
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43C22×C411yescharacteristic
47C22×C4×C43C2×D412yes—
48C22×Dic43—21no—
49C22×Dic43—21no—
50C22×Dic43C22⋊C412yes—
51C22×Dic43C22⋊C411yescharacteristic
52C22×Dic43C22⋊C411yescharacteristic
53C2×Dic86—21no—
54C2×Dic86—41no—
55C2×Dic86—41no—
56C2×Dic86—41no—
57C2×Dic86—41no—
58C2×Dic86C2×C812yes—
59C2×Dic86C2×C812yes—
60C2×Dic86M1612yes—
61C2×C8×C43—42no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—41no—
64C42×C43—21no—
65C42×C43C2×C812yes—
66C4⋊Dic43—28no—
67Dic43⋊C4—42no—
68Dic43⋊C4—42no—
69C4×Dic43—22no—
70C4×Dic43—22no—
71C4×Dic43—22no—
72C4×Dic43—42no—
73C4×Dic43—41no—
74C2×C43⋊C8—42no—
75C23×C43C2×C22⋊C411yescharacteristic
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—41no—
81C2×C4×C43—41no—
82C2×C4×C43—42no—
83C2×C4×C43—42no—
84C2×C4×C43—41no—
85C2×C4×C43C22×C811yescharacteristic
86C2×C4×C43C2×M1611yescharacteristic
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—21no—
91C2×Dic43—41no—
92C2×Dic43—41no—
93C2×Dic43—41no—
94C2×Dic43—41no—
95C2×Dic43—41no—
96C2×Dic43—41no—
97C2×Dic43—41no—
98C2×Dic43C22⋊C814yes—
99C2×Dic43#9912yes—
100Dic86—42no—
101Dic86—42no—
102Dic86—42no—
103Dic86—42no—
104C8×C43—82no—
105C43⋊C8—82no—
106#11482—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43C2×C22⋊C811yescharacteristic
110C22×C43C2×#9911yescharacteristic
111C22×C43#41311yescharacteristic
112C4×C43—21no—
113C4×C43—21no—
114C4×C43—42no—
115C4×C43—42no—
116C4×C43—81no—
117Dic43—22no—
118Dic43—24no—
119Dic43—41no—
120Dic43—42no—
121Dic43—81no—
122#2327—431no—
123#1461—432no—
124#1324—431no—
125#1324D4311yescharacteristic
126#1319—432no—
127C2×C43—21no—
128C2×C43—21no—
129C2×C43#145911yescharacteristic
130C2×C43#212911yescharacteristic
131C2×C43#213311yescharacteristic
132C2×C4⋊Q8—431no—
133C2×C4×Q8—431no—
134C2×C4×Q8—431no—
135#431—862no—
136#391—431no—
137#391—431no—
138#387—862no—
139#387—862no—
140#382C2×D4311yescharacteristic
141#376—431no—
142#324—432no—
143#324—862no—
144#324C2×D4312yes—
145C43#1148211yescharacteristic, complemented, Sylow
146C22×Q8—431no—
147C22×Q8—431no—
148C4⋊Q8—434no—
149C4⋊Q8—862no—
150C4×Q8—1722no—
151C4×Q8—1722no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—862no—
154C2×C4⋊C4—861no—
155C2×C4⋊C4C4×D4311yescharacteristic
156C2×C4⋊C4C22×D4311yescharacteristic
157C2×C42—431no—
158C2×C42—432no—
159C2×C42—431no—
160C2×C42—861no—
161C2×C42C4×D4311yescharacteristic
162C4⋊C8—1722no—
163C22⋊C8—22no—
164C22⋊C8—862no—
165C4×C8—1722no—
166#95—22no—
167#95—861no—
168#95—861no—
169#95—862no—
170#95—862no—
171C2×Q8—432no—
172C2×Q8—432no—
173C2×Q8—432no—
174C2×Q8—861no—
175C2×Q8—1721no—
176C2×Q8—1721no—
177C2×Q8—1721no—
178C2×Q8—1721no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—432no—
182C22×C4—431no—
183C22×C4—431no—
184C22×C4—861no—
185C22×C4—861no—
186C22×C4C2×C4×D4311yescharacteristic
187C22×C4D4×D4312yes—
188C2×C8—42no—
189C2×C8—1722no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—868no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C42—21no—
196C42—862no—
197C42—862no—
198C42—862no—
199C42—1721no—
200C42—1722no—
201C42C8×D4312yes—
202C23C22⋊C4×D4311yescharacteristic
203Q8—1722no—
204Q8—1722no—
205Q8—1722no—
206Q8—1722no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—434no—
217C2×C4—432no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—861no—
222C2×C4—1721no—
223C2×C4—1721no—
224C2×C4—1721no—
225C2×C4—1721no—
226C2×C4—1721no—
227C2×C4—1721no—
228C2×C4—1721no—
229C2×C4C2×C8×D4311yescharacteristic
230C2×C4M16×D4311yescharacteristic
231C8—82no—
232C8—3442no—
233C22—21no—
234C22—21no—
235C22C22⋊C8×D4311yescharacteristic
236C22#99×D4311yescharacteristic
237C22#1458288211yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—862no—
244C4—864no—
245C4—3441no—
246C4—1721no—
247C4—1722no—
248C2—21no—
249C2—21no—
250C2#1913291211yescharacteristic
251C2#1913626811yescharacteristic
252C2#1913628111yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1324D43
hypocenterC43#11482
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
22. #13063325C8semidirect
145. C43#11482semidirect

Maximal subgroups

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

subgroupindex
#191373122
#191329172
#191325392
#191325282
C43×#13242
#1148243