Finite Group Databasebeta

← #25006090

Subgroups — #25006090

Order 11008.

376 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 75 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#19137313C211yesmaximal, characteristic
2#19132937C212yesmaximal
3#19132538C212yesmaximal
4#19132529C211yesmaximal, characteristic
5C43×#1319C211yesmaximal, characteristic
6C2×#13063323C411yescharacteristic
7C2×Q8×Dic43C411yescharacteristic
8C2×#13063290C2211yescharacteristic
9#14582953—22no—
10#14582805C411yescharacteristic
11#14582786—22no—
12#14582781—22no—
13#14582764C2211yescharacteristic
14#14582745C411yescharacteristic
15#14582625C2212yes—
16#14582624—22no—
17C43×#391C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86C2×C411yescharacteristic
20#13063323—22no—
21#13063323—22no—
22Q8×Dic43—42no—
23#13063290—42no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×Dic43⋊C4—22no—
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—
34#13063235—42no—
35C43⋊#95—22no—
36C43⋊#95—21no—
37C43⋊#95—22no—
38C43⋊#95—21no—
39C22×Q8×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C42×C43C2×C411yescharacteristic
42C22⋊C8×C43—22no—
43#95×C43—22no—
44C2×Q8×C43—21no—
45C2×Q8×C43—41no—
46C2×Q8×C43—41no—
47C2×Q8×C43M1612yes—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43C22×C411yescharacteristic
51C22×C4×C43C2×D412yes—
52C22×Dic43—21no—
53C22×Dic43—21no—
54C22×Dic43C22⋊C412yes—
55C22×Dic43C22⋊C411yescharacteristic
56C22×Dic43C22⋊C411yescharacteristic
57C2×Dic86—21no—
58C2×Dic86—21no—
59C2×Dic86—41no—
60C2×Dic86—41no—
61C2×C8×C43—42no—
62C4⋊C4×C43—41no—
63C42×C43—41no—
64C4⋊Dic43—42no—
65C4⋊Dic43—41no—
66Dic43⋊C4—28no—
67Dic43⋊C4—42no—
68C4×Dic43—21no—
69C4×Dic43—22no—
70C4×Dic43—22no—
71C4×Dic43—22no—
72C4×Dic43—42no—
73C4×Dic43M1612yes—
74C2×C43⋊C8—42no—
75C23×C43C2×C22⋊C411yescharacteristic
76Q8×C43—42no—
77Q8×C43—42no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
84C2×C4×C43—42no—
85C2×C4×C43—41no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43C2×M1611yescharacteristic
89C2×C4×C43C2×M1611yescharacteristic
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—21no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—41no—
96C2×Dic43—41no—
97C2×Dic43—41no—
98C2×Dic43—41no—
99C2×Dic43—42no—
100C2×Dic43—41no—
101C2×Dic43#9912yes—
102Dic86—42no—
103Dic86—42no—
104C8×C43—82no—
105C43⋊C8—82no—
106#11536—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43#40711yescharacteristic
110C22×C43C2×#9911yescharacteristic
111C22×C43#41311yescharacteristic
112C4×C43—21no—
113C4×C43—21no—
114C4×C43—42no—
115C4×C43—42no—
116C4×C43—81no—
117Dic43—22no—
118Dic43—42no—
119Dic43—41no—
120Dic43—42no—
121Dic43—81no—
122#2327—431no—
123#1467—432no—
124#1324—432no—
125#1319—431no—
126#1319D4311yescharacteristic
127C2×C43—21no—
128C2×C43—21no—
129C2×C43#146511yescharacteristic
130C2×C43#212911yescharacteristic
131C2×C43#213311yescharacteristic
132C2×C4⋊Q8—431no—
133C2×C4×Q8—431no—
134C2×C4×Q8—431no—
135#432—862no—
136#391—431no—
137#391C2×D4311yescharacteristic
138#387—862no—
139#387—862no—
140#382—431no—
141#376—431no—
142#324—432no—
143#324—862no—
144#324C2×D4312yes—
145C43#1153611yescharacteristic, complemented, Sylow
146C22×Q8—431no—
147C22×Q8C4×D4311yescharacteristic
148C4⋊Q8—862no—
149C4⋊Q8—862no—
150C4×Q8—1722no—
151C4×Q8—1722no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—431no—
154C2×C4⋊C4—862no—
155C2×C4⋊C4—861no—
156C2×C4⋊C4C22×D4311yescharacteristic
157C2×C42—431no—
158C2×C42—431no—
159C2×C42—432no—
160C2×C42—861no—
161C2×C42C4×D4311yescharacteristic
162C4⋊C8—1722no—
163C22⋊C8—22no—
164C22⋊C8—862no—
165#97—1722no—
166#95—22no—
167#95—861no—
168#95—861no—
169#95—862no—
170#95—862no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—861no—
175C2×Q8—861no—
176C2×Q8—1721no—
177C2×Q8—1721no—
178C2×Q8#1062187212yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—431no—
182C22×C4—432no—
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—868no—
192C4⋊C4—1722no—
193C4⋊C4—1721no—
194C4⋊C4—1722no—
195C42—41no—
196C42—432no—
197C42—862no—
198C42—862no—
199C42—862no—
200C42—861no—
201C42—1722no—
202C23C22⋊C4×D4311yescharacteristic
203Q8—42no—
204Q8—42no—
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—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—432no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—861no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—1721no—
224C2×C4—1722no—
225C2×C4—1721no—
226C2×C4—1721no—
227C2×C4—1721no—
228C2×C4—1721no—
229C2×C4M16×D4311yescharacteristic
230C2×C4C2×#1062187211yescharacteristic
231C8—82no—
232C8—3442no—
233C22—21no—
234C22—21no—
235C22#1458286111yescharacteristic
236C22#99×D4311yescharacteristic
237C22#1458288011yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—862no—
244C4—3441no—
245C4—1722no—
246C4—1722no—
247C4—1721no—
248C2—21no—
249C2—21no—
250C2#1913293011yescharacteristic
251C2#1913626811yescharacteristic
252C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1319D43
hypocenterC43#11536
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
145. C43#11536semidirect

Maximal subgroups

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

subgroupindex
#191373132
#191329372
#191325382
#191325292
C43×#13192
#1153643