Finite Group Databasebeta

← #24989934

Subgroups — #24989934

Order 11008.

530 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#14582763C211yesmaximal, characteristic
2#19134661C212yesmaximal
3#19132438C211yesmaximal, characteristic
4#19132437C212yesmaximal
5C43×#1280C211yesmaximal, characteristic
6C22×Dic43⋊C4C412yes—
7C22×C4×Dic43C2211yescharacteristic
8C2×C22⋊(C43⋊C8)C2212yes—
9#14582763—22no—
10#14582763—22no—
11C2×C43⋊#95C412yes—
12C2×C43⋊#95C2211yescharacteristic
13#14582653—22no—
14#14582653—22no—
15C2×C22⋊C8×C43C2212yes—
16C2×#95×C43C2211yescharacteristic
17C23×Dic43C2×C411yescharacteristic
18C23×Dic43C2×C411yescharacteristic
19C23×Dic43C2×C412yes—
20C22×C43⋊C8—22no—
21C2×Dic43⋊C4—22no—
22C2×Dic43⋊C4—22no—
23C2×Dic43⋊C4—44no—
24C2×C4×Dic43—22no—
25C2×C4×Dic43—21no—
26C2×C4×Dic43—21no—
27C2×C4×Dic43D412yes—
28C2×C4×Dic43D412yes—
29C22⋊(C43⋊C8)—22no—
30C22⋊(C43⋊C8)—22no—
31C43⋊#95—22no—
32C43⋊#95—24no—
33C23×C4×C43C2×C412yes—
34C23×C4×C43C2311yescharacteristic
35C22×C8×C43—22no—
36C22⋊C8×C43—22no—
37C22⋊C8×C43—22no—
38#95×C43—22no—
39C24×C43C22×C411yescharacteristic
40C22×C4×C43—22no—
41C22×C4×C43—22no—
42C22×C4×C43—22no—
43C22×C4×C43—42no—
44C22×C4×C43—42no—
45C22×C4×C43—42no—
46C22×C4×C43C2×D412yes—
47C22×C4×C43#4112yes—
48C22×C4×C43#4111yescharacteristic
49C22×C4×C43#4111yescharacteristic
50C22×Dic43—22no—
51C22×Dic43—22no—
52C22×Dic43—22no—
53C22×Dic43—21no—
54C22×Dic43—21no—
55C22×Dic43—21no—
56C22×Dic43—21no—
57C22×Dic43—22no—
58C22×Dic43—22no—
59C22×Dic43—22no—
60C22×Dic43—22no—
61C22×Dic43—42no—
62C22×Dic43—42no—
63C22×Dic43C22⋊C412yes—
64C22×Dic43C22⋊C411yescharacteristic
65C22×Dic43C22⋊C411yescharacteristic
66C2×C8×C43—44no—
67C2×C8×C43—42no—
68Dic43⋊C4—44no—
69Dic43⋊C4—44no—
70C4×Dic43—22no—
71C4×Dic43—22no—
72C4×Dic43—22no—
73C4×Dic43—22no—
74C2×C43⋊C8—44no—
75C2×C43⋊C8—42no—
76C23×C43—22no—
77C23×C43—21no—
78C23×C43—21no—
79C23×C43C2×C22⋊C411yescharacteristic
80C23×C43#11711yescharacteristic
81C23×C43#11711yescharacteristic
82C23×C43#13112yes—
83C23×C43#13112yes—
84C2×C4×C43—24no—
85C2×C4×C43—42no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—82no—
92C2×C4×C43—82no—
93C2×C4×C43#12312yes—
94C2×C4×C43#12312yes—
95C2×Dic43—24no—
96C2×Dic43—24no—
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—24no—
103C2×Dic43—41no—
104C2×Dic43—42no—
105C2×Dic43—41no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—82no—
110C2×Dic43—82no—
111C2×Dic43#10012yes—
112C2×Dic43#10112yes—
113C8×C43—82no—
114C43⋊C8—82no—
115#8703—431nomaximal, Sylow
116C22×C43—21no—
117C22×C43—21no—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43#38111yescharacteristic
125C22×C43#40812yes—
126C22×C43#41012yes—
127C22×C43C2×#10011yescharacteristic
128C22×C43C2×#10111yescharacteristic
129C22×C43#43311yescharacteristic
130C22×C43#43312yes—
131C22×C43#43311yescharacteristic
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—82no—
135Dic43—22no—
136Dic43—22no—
137Dic43—42no—
138Dic43—82no—
139C2×#382—431no—
140#1817—432no—
141#1280—432no—
142#1280—431no—
143#1280D4311yescharacteristic
144C2×C43—21no—
145C2×C43—22no—
146C2×C43—21no—
147C2×C43#146912yes—
148C2×C43#147012yes—
149C2×C43#181811yescharacteristic
150C2×C43#182011yescharacteristic
151C2×C43#182111yescharacteristic
152C22×C4⋊C4—432no—
153C22×C42—431no—
154C2×C22⋊C8—432no—
155C2×C22⋊C8C2×D4312yes—
156#382—862no—
157#382—862no—
158C2×#95—431no—
159C2×#95—432no—
160C2×#95C2×D4311yescharacteristic
161#336—862no—
162#336—862no—
163C43#870311yescharacteristic, complemented, Sylow
164C23×C4—431no—
165C23×C4—431no—
166C23×C4—432no—
167C23×C4C4×D4312yes—
168C23×C4C22×D4311yescharacteristic
169C22×C8—22no—
170C22×C8—862no—
171C2×C4⋊C4—862no—
172C2×C4⋊C4—862no—
173C2×C4⋊C4—1724no—
174C2×C42—432no—
175C2×C42—432no—
176C2×C42—862no—
177C2×C42—861no—
178C2×C42—861no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181C22⋊C8—862no—
182C22⋊C8—862no—
183#95—22no—
184#95—864no—
185#95—862no—
186C24C2×C4×D4311yescharacteristic
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—431no—
194C22×C4—431no—
195C22×C4—432no—
196C22×C4—862no—
197C22×C4—862no—
198C22×C4—861no—
199C22×C4—861no—
200C22×C4—861no—
201C22×C4—861no—
202C22×C4—862no—
203C22×C4—862no—
204C22×C4—862no—
205C22×C4—862no—
206C22×C4—862no—
207C22×C4—1722no—
208C22×C4—1722no—
209C22×C4#1062189812yes—
210C22×C4D4×D4312yes—
211C22×C4#1062190011yescharacteristic
212C22×C4#1062190211yescharacteristic
213C2×C8—44no—
214C2×C8—42no—
215C2×C8—1724no—
216C2×C8—1722no—
217C4⋊C4—1724no—
218C4⋊C4—1724no—
219C42—862no—
220C42—862no—
221C42—862no—
222C42—862no—
223C23—22no—
224C23—21no—
225C23—21no—
226C23C22⋊C4×D4311yescharacteristic
227C23#1306328211yescharacteristic
228C23#1306328311yescharacteristic
229C23#1306333112yes—
230C23#1306333312yes—
231C2×C4—24no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—432no—
241C2×C4—432no—
242C2×C4—864no—
243C2×C4—864no—
244C2×C4—861no—
245C2×C4—861no—
246C2×C4—861no—
247C2×C4—861no—
248C2×C4—864no—
249C2×C4—862no—
250C2×C4—3442no—
251C2×C4—3442no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4—1721no—
256C2×C4—1722no—
257C2×C4—1721no—
258C2×C4#1306330712yes—
259C2×C4#1306331012yes—
260C8—82no—
261C8—3442no—
262C22—22no—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22#1458276111yescharacteristic
271C22#1458286412yes—
272C22#1458287112yes—
273C22#100×D4311yescharacteristic
274C22#101×D4311yescharacteristic
275C22#1458295811yescharacteristic
276C22#1458295912yes—
277C22#1458296111yescharacteristic
278C4—22no—
279C4—22no—
280C4—82no—
281C4—862no—
282C4—862no—
283C4—3442no—
284C4—1722no—
285C2—21no—
286C2—22no—
287C2—21no—
288C2#1913294512yes—
289C2#1913294912yes—
290C2#1913466511yescharacteristic
291C2#1913467111yescharacteristic
292C2#1913467411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutator, prime radicalC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1280C2
socleC23×C43C2×C22⋊C4
cosocleC23×C4×C43C23
hypercenter#1280D43
hypocenterC43#8703
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
163. C43#8703semidirect

Maximal subgroups

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

subgroupindex
C2×#145827632
#191346612
#191324382
#191324372
C43×#12802
#870343