Finite Group Databasebeta

← #24985006

Subgroups — #24985006

Order 11008.

468 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134663C211yesmaximal, characteristic
2C4×C22⋊(C43⋊C8)C211yesmaximal, characteristic
3#19132418C212yesmaximal, complemented
4#19132418C212yesmaximal, complemented
5C43×#2851C211yesmaximal, characteristic
6C2×C22⋊(C43⋊C8)—21no—
7C2×C22⋊(C43⋊C8)—21no—
8C2×C4×C43⋊C8—21no—
9#14582654—21no—
10#14582654C2212yes—
11#14582654C2212yes—
12C2×#125×C43C411yescharacteristic
13C22×C42×C43C2211yescharacteristic
14C43×#389C2211yescharacteristic
15C43×#389C2211yescharacteristic
16C43×#387—21no—
17C43×#387—21no—
18C43×#385—21no—
19C43×#385—21no—
20C43×#382C411yescharacteristic
21C43×#380C411yescharacteristic
22C43×#380C411yescharacteristic
23C22×C43⋊C8—22no—
24C22×C43⋊C8—22no—
25C22⋊(C43⋊C8)—24no—
26C22⋊(C43⋊C8)—42no—
27C4×C43⋊C8—42no—
28C23×C4×C43C2×C411yescharacteristic
29C23×C4×C43D411yescharacteristic
30C23×C4×C43D411yescharacteristic
31#125×C43—42no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43C2×C411yescharacteristic
37C2×C4⋊C4×C43C2×C411yescharacteristic
38C2×C4⋊C4×C43C2×C411yescharacteristic
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C22⋊C4×C43—21no—
41C2×C22⋊C4×C43—21no—
42C2×C42×C43—42no—
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43C2311yescharacteristic
47#95×C43—21no—
48#95×C43—21no—
49#95×C43—21no—
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53C24×C43C22⋊C411yescharacteristic
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C4⋊C4×C43—22no—
74C4⋊C4×C43—22no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43—42no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—42no—
83C42×C43—22no—
84C42×C43—22no—
85C42×C43—41no—
86C42×C43—41no—
87C2×C43⋊C8—24no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—42no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C2×C43⋊C8—42no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43#10412yes—
100C23×C43C2×C22⋊C411yescharacteristic
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—44no—
115C2×C4×C43—44no—
116C2×C4×C43—44no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43#9912yes—
130C2×C4×C43#10112yes—
131C2×C4×C43#13112yes—
132C2×C4×C43#13512yes—
133C2×C4×C43#13512yes—
134C43⋊C8—44no—
135C43⋊C8—82no—
136#7671—431nomaximal, Sylow
137C22×C43—22no—
138C22×C43—22no—
139C22×C43—22no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—41no—
144C22×C43#40811yescharacteristic
145C22×C43C2×#9911yescharacteristic
146C22×C43C2×#10111yescharacteristic
147C22×C43#41611yescharacteristic
148C22×C43#41611yescharacteristic
149C22×C43C2×#10411yescharacteristic
150C22×C43#42111yescharacteristic
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—22no—
155C4×C43—22no—
156C4×C43—41no—
157C4×C43—81no—
158C4×C43—81no—
159C4×C43—81no—
160C4×C43—81no—
161#2851D4311yescharacteristic
162#1817—431no—
163C4×C22⋊C8—431no—
164#1271—432no—
165#1271—432no—
166C2×C43—42no—
167C2×C43#147211yescharacteristic
168C2×C43#148211yescharacteristic
169C2×C43#149411yescharacteristic
170C2×C43#150111yescharacteristic
171C2×C43#151611yescharacteristic
172C2×C43#152811yescharacteristic
173C2×C43#154411yescharacteristic
174C2×#125Dic4311yescharacteristic
175C22×C42C2×D4311yescharacteristic
176C2×C22⋊C8—861no—
177C2×C22⋊C8—861no—
178C2×C4×C8—861no—
179#389C2×D4311yescharacteristic
180#389C2×D4311yescharacteristic
181#387—21no—
182#387—21no—
183#385—21no—
184#385—21no—
185#382Dic4311yescharacteristic
186#380Dic4311yescharacteristic
187#380Dic4311yescharacteristic
188#336—432no—
189#336—432no—
190#336—861no—
191C43#767111yescharacteristic, complemented, Sylow
192C23×C4C2×Dic4311yescharacteristic
193C23×C4C22⋊D4311yescharacteristic
194C23×C4C22⋊D4311yescharacteristic
195C22×C8—862no—
196C22×C8—862no—
197#125—42no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×Dic4311yescharacteristic
203C2×C4⋊C4C2×Dic4311yescharacteristic
204C2×C4⋊C4C2×Dic4311yescharacteristic
205C2×C4⋊C4C2×Dic4311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42—42no—
209C2×C42C2×Dic4311yescharacteristic
210C2×C42C22⋊D4311yescharacteristic
211C2×C42C22⋊D4311yescharacteristic
212C2×C42C22×D4311yescharacteristic
213C22⋊C8—864no—
214C22⋊C8—1722no—
215C4×C8—1722no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222C24C22⋊Dic4311yescharacteristic
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4C22⋊Dic4311yescharacteristic
237C22×C4C22⋊Dic4311yescharacteristic
238C22×C4C22⋊Dic4311yescharacteristic
239C22×C4C22×Dic4311yescharacteristic
240C22×C4C2×C22⋊D4311yescharacteristic
241C22×C4C2×C22⋊D4311yescharacteristic
242C2×C8—864no—
243C2×C8—1722no—
244C2×C8—1722no—
245C2×C8—1722no—
246C2×C8—1722no—
247C2×C8—1722no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C42—22no—
259C42—22no—
260C42—41no—
261C42—41no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#1306325212yes—
269C23C2×C22⋊Dic4311yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4#1306324012yes—
299C2×C4#1306324412yes—
300C2×C4#1306333212yes—
301C2×C4#1306334512yes—
302C2×C4#1306334512yes—
303C8—3442no—
304C8—1724no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22#1458286611yescharacteristic
313C22C2×#1306324011yescharacteristic
314C22C2×#1306324411yescharacteristic
315C22#1458289511yescharacteristic
316C22#1458289511yescharacteristic
317C22C2×#1306325211yescharacteristic
318C22#1458291611yescharacteristic
319C4—22no—
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—41no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—81no—
329C2—42no—
330C2#1913295911yescharacteristic
331C2#1913300311yescharacteristic
332C2#1913305511yescharacteristic
333C2#1913308611yescharacteristic
334C2#1913315111yescharacteristic
335C2#1913319711yescharacteristic
336C2#1913326011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2851C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#2851D43
hypocenterC43#7671
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. #19132418C2semidirect
4. #19132418C2semidirect
191. C43#7671semidirect

Maximal subgroups

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

subgroupindex
#191346632
C4×C22⋊(C43⋊C8)2
#191324182
C43×#28512
#767143