Finite Group Databasebeta

← #25007246

Subgroups — #25007246

Order 11008.

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

normal subgroups only

This group has 378 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#19139807C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic
3#19132623C214yesmaximal
4C43×#1467C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6C2×#13063244—21no—
7C4×#10621877—21no—
8#14582838C412yes—
9#14582838C2212yes—
10#14582806—21no—
11#14582805—21no—
12#14582805—21no—
13#14582764—21no—
14C4×C4⋊Dic43C411yescharacteristic
15#14582668C2212yes—
16C2×C4×Q8×C43C2211yescharacteristic
17C43×#432—21no—
18C43×#324—21no—
19C43×#324C2212yes—
20C22×Dic86—21no—
21C2×#10621877—22no—
22#13063325—41no—
23#13063325—41no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2×C412yes—
27C2×C4×Dic43—21no—
28#13063244—24no—
29#13063236—41no—
30C4×C43⋊C8—41no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95C2×C412yes—
36C22×Q8×C43D411yescharacteristic
37C4×Q8×C43—41no—
38C4×Q8×C43—41no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43D411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C4⋊C8×C43—41no—
46C22⋊C8×C43—22no—
47#97×C43—41no—
48C2×Q8×C43—22no—
49C2×Q8×C43—22no—
50C2×Q8×C43—41no—
51C22×C4×C43C22⋊C411yescharacteristic
52C22×C4×C43C22⋊C411yescharacteristic
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×Dic43—22no—
59C22×Dic43—22no—
60C2×Dic86—44no—
61C2×Dic86—41no—
62C2×Dic86—41no—
63C2×C8×C43—42no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C42×C43—21no—
68C42×C43—21no—
69C42×C43—21no—
70C42×C43—21no—
71C42×C43—21no—
72C42×C43—21no—
73C4⋊Dic43—42no—
74C4⋊Dic43—42no—
75C4⋊Dic43—42no—
76C4×Dic43—42no—
77#10621877—24no—
78#10621877—42no—
79C2×C43⋊C8—42no—
80C23×C43C2×C22⋊C411yescharacteristic
81Q8×C43—44no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43#9911yescharacteristic
97C2×C4×C43#9911yescharacteristic
98C2×C4×C43#10412yes—
99C2×C4×C43#13712yes—
100C2×Dic43—42no—
101C2×Dic43—44no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105Dic86—82no—
106Dic86—82no—
107C8×C43—82no—
108C43⋊C8—44no—
109#11794—431nomaximal, Sylow
110C22×C43—21no—
111C22×C43—21no—
112C22×C43C2×#9911yescharacteristic
113C22×C43#41911yescharacteristic
114C22×C43C2×#10411yescharacteristic
115C4×C43—21no—
116C4×C43—22no—
117C4×C43—22no—
118C4×C43—41no—
119C4×C43—41no—
120C4×C43—41no—
121C4×C43—41no—
122C4×C43#35512yes—
123Dic43—82no—
124Dic43—82no—
125#2568—431no—
126C4×#101—431no—
127#1467D4311yescharacteristic
128#1353—434no—
129C2×C43—21no—
130C2×C43—21no—
131C2×C43#150811yescharacteristic
132C2×C43#212311yescharacteristic
133C2×C43C2×#35511yescharacteristic
134C2×C4⋊Q8—431no—
135C2×C4×Q8C2×D4311yescharacteristic
136#432—21no—
137C2×#101—861no—
138C4×M16—861no—
139#400—432no—
140#400—432no—
141#391—861no—
142#391—861no—
143#391—861no—
144#382—861no—
145C4×C4⋊C4—431no—
146#343—432no—
147#324—21no—
148#324C2×D4312yes—
149C43#1179411yescharacteristic, complemented, Sylow
150C22×Q8—861no—
151C22×Q8D17211yescharacteristic
152C2×M16—862no—
153C4⋊Q8—1721no—
154C4⋊Q8—1721no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—861no—
159C2×C4⋊C4—861no—
160C2×C4⋊C4C4×D4311yescharacteristic
161C2×C4⋊C4C22⋊D4311yescharacteristic
162C2×C4⋊C4C22×D4311yescharacteristic
163C2×C42—861no—
164C2×C42C4×D4311yescharacteristic
165C2×C42D17211yescharacteristic
166C2×C42C22⋊D4311yescharacteristic
167C4⋊C8—41no—
168#101—864no—
169C22⋊C8—22no—
170#97—41no—
171#97—1721no—
172C4×C8—1721no—
173#95—432no—
174#95—862no—
175#95—862no—
176#95—862no—
177#95—862no—
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—1724no—
182C2×Q8—1721no—
183C2×Q8—1721no—
184C22×C4—862no—
185C22×C4—862no—
186C22×C4(C2×D43)⋊C411yescharacteristic
187C22×C4(C2×D43)⋊C411yescharacteristic
188C22×C4(C2×D43)⋊C411yescharacteristic
189C22×C4(C2×D43)⋊C411yescharacteristic
190C22×C4C2×C4×D4311yescharacteristic
191C22×C4C2×D17211yescharacteristic
192C22×C4C2×C22⋊D4311yescharacteristic
193M16—864no—
194M16—1722no—
195C2×C8—42no—
196C2×C8—1722no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—1722no—
201C4⋊C4—1722no—
202C4⋊C4—1722no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—1722no—
210C23C2×(C2×D43)⋊C411yescharacteristic
211Q8—44no—
212Q8—3442no—
213Q8—3442no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—1722no—
229C2×C4—1724no—
230C2×C4—1722no—
231C2×C4—1722no—
232C2×C4—1722no—
233C2×C4#1306323911yescharacteristic
234C2×C4#1306323911yescharacteristic
235C2×C4#1306325112yes—
236C2×C4#1306335812yes—
237C8—82no—
238C8—1724no—
239C22—21no—
240C22—21no—
241C22C2×#1306323911yescharacteristic
242C22#1458290911yescharacteristic
243C22C2×#1306325111yescharacteristic
244C4—21no—
245C4—22no—
246C4—22no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—3442no—
252C4—3442no—
253C4#1458269512yes—
254C2—21no—
255C2—21no—
256C2#1913311611yescharacteristic
257C2#1913624811yescharacteristic
258C2C2×#1458269511yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1467C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1467D43
hypocenterC43#11794
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
149. C43#11794semidirect

Maximal subgroups

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

subgroupindex
#191398072
C4×#130632442
#191326232
C43×#14672
#1179443