Finite Group Databasebeta

← #25007655

Subgroups — #25007655

Order 11008.

408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 107 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#19134591C211yesmaximal, characteristic
2#19132919C211yesmaximal, characteristic
3#19132601C214yesmaximal
4C43×#2546C211yesmaximal, characteristic
5#14582952—21no—
6#14582923—21no—
7C2×#13063244—21no—
8#14582668C2212yes—
9#14582625—21no—
10#14582625C2212yes—
11C2×C4⋊Q8×C43—21no—
12C2×C4⋊Q8×C43C411yescharacteristic
13C2×C4×Q8×C43C2211yescharacteristic
14C43×#398C412yes—
15C43×#398C2212yes—
16C43×#391—21no—
17C43×#389—21no—
18C43×#389—21no—
19C4×C4⋊C4×C43C411yescharacteristic
20C2×#10621877—22no—
21C4⋊(C43⋊C8)—41no—
22C4⋊(C43⋊C8)—41no—
23C4⋊(C43⋊C8)—41no—
24#13063244—42no—
25C22⋊(C43⋊C8)—22no—
26C4×C43⋊C8—41no—
27C22×Q8×C43—21no—
28C22×Q8×C43D411yescharacteristic
29C4⋊Q8×C43—41no—
30C4⋊Q8×C43—41no—
31C4⋊Q8×C43—42no—
32C4⋊Q8×C43—42no—
33C4×Q8×C43—41no—
34C4×Q8×C43—41no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—22no—
39C2×C4⋊C4×C43C2×C412yes—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C42×C43—21no—
44C2×C42×C43C2×C411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47#95×C43—22no—
48#95×C43—22no—
49#95×C43C2×C412yes—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43—42no—
53C2×Q8×C43—42no—
54C2×Q8×C43—42no—
55C2×Q8×C43D812yes—
56C2×Q8×C43SD1612yes—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C4⋊C4×C43—24no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—42no—
71C4⋊C4×C43—41no—
72C4⋊C4×C43—41no—
73C4⋊C4×C43—44no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—42no—
76C42×C43—21no—
77C42×C43—21no—
78C42×C43—21no—
79C42×C43—21no—
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—42no—
83#10621877—42no—
84#10621877—42no—
85C2×C43⋊C8—42no—
86C2×C43⋊C8—42no—
87C23×C43C2×C22⋊C411yescharacteristic
88Q8×C43—42no—
89Q8×C43—42no—
90Q8×C43—84no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—24no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43#9911yescharacteristic
111C2×C4×C43#9911yescharacteristic
112C2×C4×C43#10212yes—
113C2×C4×C43#10212yes—
114C2×C4×C43C2×D811yescharacteristic
115C2×C4×C43C2×SD1611yescharacteristic
116C43⋊C8—82no—
117C43⋊C8—82no—
118#11883—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43C2×#9911yescharacteristic
122C22×C43C2×#10211yescharacteristic
123C22×C43#42111yescharacteristic
124C4×C43—21no—
125C4×C43—21no—
126C4×C43—22no—
127C4×C43—22no—
128C4×C43—21no—
129C4×C43—44no—
130C4×C43—41no—
131C4×C43—41no—
132C4×C43—41no—
133C4×C43—82no—
134C4×C43#35612yes—
135#2546D4311yescharacteristic
136#1801—431no—
137#1461—431no—
138#1346—434no—
139C2×C43—21no—
140C2×C43—21no—
141C2×C43#151911yescharacteristic
142C2×C43#212311yescharacteristic
143C2×C43C2×#35611yescharacteristic
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8Dic4311yescharacteristic
146C2×C4×Q8C2×D4311yescharacteristic
147#431—861no—
148#423—861no—
149C2×#101—861no—
150#398Dic4312yes—
151#398C2×D4312yes—
152#391—21no—
153#389—21no—
154#389—21no—
155C4×C4⋊C4Dic4311yescharacteristic
156#343—432no—
157#324—432no—
158#324—861no—
159C43#1188311yescharacteristic, complemented, Sylow
160C22×Q8—21no—
161C22×Q8C22⋊D4311yescharacteristic
162C2×M16—862no—
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165C4⋊Q8—42no—
166C4⋊Q8—42no—
167C4×Q8—41no—
168C4×Q8—41no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4C2×Dic4312yes—
174C2×C4⋊C4C2×Dic4311yescharacteristic
175C2×C4⋊C4C22⋊D4311yescharacteristic
176C2×C4⋊C4C22×D4311yescharacteristic
177C2×C42—21no—
178C2×C42C2×Dic4311yescharacteristic
179C2×C42C22⋊D4311yescharacteristic
180C2×C42C22⋊D4311yescharacteristic
181C4⋊C8—1721no—
182C4⋊C8—1721no—
183C4⋊C8—1721no—
184#101—1722no—
185C22⋊C8—862no—
186C4×C8—1721no—
187#95—22no—
188#95—22no—
189#95C2×Dic4312yes—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8#1062188212yes—
196C2×Q8#1062188312yes—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4C22⋊Dic4311yescharacteristic
200C22×C4C22⋊Dic4311yescharacteristic
201C22×C4C22⋊Dic4311yescharacteristic
202C22×C4C22⋊Dic4311yescharacteristic
203C22×C4C22×Dic4311yescharacteristic
204C22×C4C2×C22⋊D4311yescharacteristic
205C22×C4C2×C22⋊D4311yescharacteristic
206M16—1722no—
207M16—1722no—
208C2×C8—1722no—
209C2×C8—1722no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—44no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C23C2×C22⋊Dic4311yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4#1306324011yescharacteristic
251C2×C4#1306324011yescharacteristic
252C2×C4#1306324612yes—
253C2×C4#1306324612yes—
254C2×C4C2×#1062188211yescharacteristic
255C2×C4C2×#1062188311yescharacteristic
256C8—3442no—
257C8—3442no—
258C22—21no—
259C22—21no—
260C22C2×#1306324011yescharacteristic
261C22C2×#1306324611yescharacteristic
262C22#1458291611yescharacteristic
263C4—21no—
264C4—21no—
265C4—22no—
266C4—22no—
267C4—21no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4#1458269812yes—
274C2—21no—
275C2—21no—
276C2#1913316311yescharacteristic
277C2#1913624911yescharacteristic
278C2C2×#1458269811yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2546C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2546D43
hypocenterC43#11883
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
159. C43#11883semidirect

Maximal subgroups

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

subgroupindex
#191345912
#191329192
#191326012
C43×#25462
#1188343