Finite Group Databasebeta

← #24996685

Subgroups — #24996685

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134357C211yesmaximal, characteristic
2#19132822C211yesmaximal, characteristic
3#19132473C214yesmaximal
4C43×#2857C211yesmaximal, characteristic
5C2×C22⋊(C43⋊C8)C2212yes—
6C2×#13063236—21no—
7C2×C43⋊#95—21no—
8C2×C43⋊#95—21no—
9C2×C43⋊#95C2212yes—
10#14582654—21no—
11C2×C4⋊Q8×C43C411yescharacteristic, complemented
12C2×C22⋊Q8×C43—21no—
13C22×C42×C43C2211yescharacteristic
14C43×#391—21no—
15C43×#389—21no—
16C43×#389C412yescomplemented
17C43×#384C411yescharacteristic, complemented
18C43×#380—21no—
19C43×#380C2212yes—
20C23×Dic43—22no—
21C22×C43⋊C8—22no—
22C22⋊(C43⋊C8)—22no—
23C22⋊(C43⋊C8)Q814yescomplemented
24#13063236—42no—
25C43⋊#95—24no—
26C43⋊#95—24no—
27C43⋊#95—42no—
28C22×Q8×C43—21no—
29C23×C4×C43D411yescharacteristic
30C23×C4×C43D411yescharacteristic
31C23×C4×C43C2311yescharacteristic
32C4⋊Q8×C43—42no—
33C22⋊Q8×C43—44no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43C2×C412yes—
39C2×C4⋊C4×C43C2×C412yes—
40C2×C22⋊C4×C43—22no—
41C2×C42×C43—42no—
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46#95×C43—22no—
47#95×C43—22no—
48C24×C43C2×D411yescharacteristic
49C2×Q8×C43—42no—
50C2×Q8×C43—42no—
51C2×Q8×C43—42no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×Q812yes—
69C22×C4×C43#4112yes—
70C22×Dic43—24no—
71C22×Dic43—42no—
72C22×Dic43—42no—
73C22×Dic43—42no—
74C22×Dic43—42no—
75C22×Dic43—42no—
76C22×Dic43—42no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43—44no—
81C4⋊C4×C43—42no—
82C4⋊C4×C43—42no—
83C22⋊C4×C43—44no—
84C42×C43—22no—
85C42×C43—22no—
86C42×C43—41no—
87C42×C43—41no—
88C2×C43⋊C8—24no—
89C2×C43⋊C8—42no—
90C2×C43⋊C8—42no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43C2×C22⋊C411yescharacteristic
96C23×C43#12411yescharacteristic
97C23×C43C4⋊Q811yescharacteristic
98C23×C43AGL(1,ℤ/8)12yes—
99C23×C43#13712yes—
100Q8×C43—84no—
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—21no—
115C2×C4×C43—42no—
116C2×C4×C43—42no—
117C2×C4×C43—44no—
118C2×C4×C43—44no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43#9912yes—
126C2×C4×C43#10412yes—
127C2×C4×C43C4×Q812yes—
128C2×C4×C43C22⋊Q812yes—
129C2×Dic43—44no—
130C2×Dic43—44no—
131C2×Dic43—44no—
132C2×Dic43—82no—
133C2×Dic43—82no—
134C2×Dic43—82no—
135C2×Dic43—82no—
136C43⋊C8—44no—
137#9889—431nomaximal, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—22no—
146C22×C43#39111yescharacteristic
147C22×C43C2×#9911yescharacteristic
148C22×C43#41011yescharacteristic
149C22×C43#41811yescharacteristic
150C22×C43#41911yescharacteristic
151C22×C43C2×#10411yescharacteristic
152C22×C43#42111yescharacteristic
153C22×C43#48912yes—
154C22×C43#50112yes—
155C4×C43—22no—
156C4×C43—22no—
157C4×C43—22no—
158C4×C43—22no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—82no—
162C4×C43—82no—
163Dic43—84no—
164#2857D4311yescharacteristic
165#1749—431no—
166#1434—431no—
167#1294—434no—
168C2×C43—22no—
169C2×C43—22no—
170C2×C43#150511yescharacteristic
171C2×C43#150811yescharacteristic
172C2×C43#151011yescharacteristic
173C2×C43#151511yescharacteristic
174C2×C43#198611yescharacteristic
175C2×C43#199311yescharacteristic
176C2×C43#199611yescharacteristic
177C2×C4⋊Q8Dic4311yescharacteristic, complemented
178C2×C22⋊Q8—21no—
179C22×C42C2×D4311yescharacteristic
180C2×C22⋊C8—432no—
181C2×#97—861no—
182#391—21no—
183#389—21no—
184#389Dic4312yescomplemented
185#384Dic4311yescharacteristic, complemented
186#380—21no—
187#380C2×D4312yes—
188C2×#95—432no—
189C2×#95—861no—
190C2×#95—861no—
191#336—861no—
192C43#988911yescharacteristic, complemented, Sylow
193C22×Q8—21no—
194C23×C4—862no—
195C23×C4C22⋊D4311yescharacteristic
196C23×C4C22⋊D4311yescharacteristic
197C23×C4C22×D4311yescharacteristic
198C22×C8—862no—
199C4⋊Q8—42no—
200C22⋊Q8—44no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic4312yes—
206C2×C4⋊C4C2×Dic4312yes—
207C2×C22⋊C4—22no—
208C2×C42—42no—
209C2×C42C2×Dic4311yescharacteristic
210C2×C42C2×Dic4311yescharacteristic
211C2×C42C22⋊D4311yescharacteristic
212C2×C42C22⋊D4311yescharacteristic
213C22⋊C8—434no—
214C22⋊C8—862no—
215#97—1722no—
216#95—22no—
217#95—22no—
218#95—864no—
219#95—864no—
220#95—1722no—
221C24C2×C22⋊D4311yescharacteristic
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—42no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—864no—
236C22×C4—1722no—
237C22×C4—1722no—
238C22×C4—1722no—
239C22×C4—1722no—
240C22×C4—1722no—
241C22×C4—1722no—
242C22×C4C22⋊Dic4311yescharacteristic
243C22×C4C22⋊Dic4311yescharacteristic
244C22×C4C22⋊Dic4311yescharacteristic
245C22×C4C22⋊Dic4311yescharacteristic
246C22×C4Q8×D4312yes—
247C22×C4#1062190212yes—
248C22×C4C22×Dic4311yescharacteristic
249C22×C4C2×C22⋊D4311yescharacteristic
250C2×C8—864no—
251C2×C8—1722no—
252C2×C8—1722no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C22⋊C4—44no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42—41no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C2×C22⋊Dic4311yescharacteristic
269C23#1306331411yescharacteristic
270C23#1306332311yescharacteristic
271C23#1306335112yes—
272C23#1306335612yes—
273Q8—84no—
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—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—3442no—
299C2×C4—3442no—
300C2×C4—3442no—
301C2×C4—3442no—
302C2×C4—1724no—
303C2×C4—1724no—
304C2×C4—1724no—
305C2×C4#1306324012yes—
306C2×C4#1306325212yes—
307C2×C4Q8×Dic4312yes—
308C2×C4#1306330112yes—
309C8—1724no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22#1458280611yescharacteristic
319C22C2×#1306324011yescharacteristic
320C22#1458287311yescharacteristic
321C22#1458290411yescharacteristic
322C22#1458290811yescharacteristic
323C22C2×#1306325211yescharacteristic
324C22#1458291611yescharacteristic
325C22#1458326112yes—
326C22#1458330512yes—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—82no—
334C4—82no—
335C4—3444no—
336C2—22no—
337C2—22no—
338C2#1913310311yescharacteristic
339C2#1913311511yescharacteristic
340C2#1913312411yescharacteristic
341C2#1913314611yescharacteristic
342C2#1913554011yescharacteristic
343C2#1913556911yescharacteristic
344C2#1913558111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2857C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#2857D43
hypocenterC43#9889
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
11. C2×C4⋊Q8×C43C4semidirect
16. C43×#389C4semidirect
17. C43×#384C4semidirect
23. C22⋊(C43⋊C8)Q8semidirect
177. C2×C4⋊Q8Dic43semidirect
184. #389Dic43semidirect
185. #384Dic43semidirect
192. C43#9889semidirect

Maximal subgroups

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

subgroupindex
#191343572
#191328222
#191324732
C43×#28572
#988943