Finite Group Databasebeta

← #24989651

Subgroups — #24989651

Order 11008.

542 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134755C211yesmaximal, characteristic, complemented
2#19134595C212yesmaximal
3C2×#14582652C211yesmaximal, characteristic, complemented
4#19132479C212yesmaximal, complemented
5C2×C8×D4×C43C211yesmaximal, characteristic
6C2×#13063259—21no—
7C2×#13063259—21no—
8C2×C4⋊(C43⋊C8)C2212yes—
9C2×#13063246—22no—
10#14582769C2212yes—
11#14582661—22no—
12#14582652—22no—
13C23×C8×C43—21no—
14C2×C4×D4×C43C2211yescharacteristic
15C8×D4×C43—22no—
16C8×D4×C43C414yescomplemented
17C2×C4⋊C8×C43C2211yescharacteristic
18C2×C22⋊C8×C43—21no—
19C2×C4×C8×C43C2211yescharacteristic
20C22×C43⋊C8—22no—
21C2×C4⋊Dic43—22no—
22C2×C4⋊Dic43—22no—
23C2×C4⋊Dic43—22no—
24#13063259—42no—
25#13063259—42no—
26C4⋊(C43⋊C8)—22no—
27C4⋊(C43⋊C8)—22no—
28#13063246—44no—
29C22×D4×C43D411yescharacteristic
30C23×C4×C43—21no—
31C22×C8×C43—21no—
32C22×C8×C43—24no—
33C22×C8×C43—42no—
34C22×C8×C43—42no—
35C22×C8×C43D411yescharacteristic
36C22×C8×C43D411yescharacteristic
37C4×D4×C43—21no—
38C4×D4×C43—21no—
39C4×D4×C43C2×C412yes—
40C4×D4×C43Q812yes—
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C22⋊C4×C43—21no—
43C2×C42×C43C2311yescharacteristic
44C4⋊C8×C43—21no—
45C4⋊C8×C43C2×C412yes—
46C22⋊C8×C43—24no—
47C4×C8×C43C2×C412yes—
48C4×C8×C43D412yes—
49C24×C43—21no—
50C2×D4×C43—21no—
51C2×D4×C43—21no—
52C2×D4×C43—21no—
53C2×D4×C43C4⋊C412yes—
54C2×D4×C43D812yes—
55C2×D4×C43Q1612yes—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—21no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43#4111yescharacteristic
66C22×Dic43—42no—
67C2×C8×C43—21no—
68C2×C8×C43—21no—
69C2×C8×C43—22no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—48no—
73C2×C8×C43C22⋊C412yes—
74C2×C8×C43C22⋊C412yes—
75C2×C8×C43D812yes—
76C2×C8×C43SD1612yes—
77C4⋊C4×C43—21no—
78C4⋊C4×C43C4⋊C412yes—
79C22⋊C4×C43—22no—
80C22⋊C4×C43—22no—
81C42×C43C22×C411yescharacteristic
82C42×C43C2×D411yescharacteristic
83C42×C43C2×Q811yescharacteristic
84C42×C43#4111yescharacteristic
85C4⋊Dic43—42no—
86C4⋊Dic43—42no—
87C4⋊Dic43—42no—
88C4⋊Dic43—42no—
89C4⋊Dic43—82no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C2×C43⋊C8—42no—
93C23×C43—22no—
94C23×C43—22no—
95C23×C43—22no—
96C23×C43—41no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43#12111yescharacteristic
101D4×C43—22no—
102D4×C43—22no—
103D4×C43—22no—
104D4×C43#10714yescomplemented
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43C2×C22⋊C411yescharacteristic
115C2×C4×C43C2×C4⋊C411yescharacteristic
116C2×C4×C43#11711yescharacteristic
117C2×C4×C43#12111yescharacteristic
118C2×C4×C43C22⋊Q811yescharacteristic
119C2×C4×C43C22⋊Q811yescharacteristic
120C2×C4×C43C2×D811yescharacteristic
121C2×C4×C43C2×D811yescharacteristic
122C2×C4×C43C2×SD1611yescharacteristic
123C2×C4×C43C2×Q1611yescharacteristic
124C2×C4×C43#13511yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×Dic43—82no—
129C2×Dic43—82no—
130C2×Dic43—82no—
131C8×C43—22no—
132C8×C43—42no—
133C8×C43#10214yescomplemented
134C43⋊C8—82no—
135#8644—431nomaximal, Sylow
136C22×C43—24no—
137C22×C43—42no—
138C22×C43—42no—
139C22×C43—42no—
140C22×C43—42no—
141C22×C43—42no—
142C22×C43—42no—
143C22×C43#38011yescharacteristic
144C22×C43#45911yescharacteristic
145C22×C43#46111yescharacteristic
146C22×C43#46611yescharacteristic
147C22×C43#46711yescharacteristic
148C22×C43#47211yescharacteristic
149C22×C43#47311yescharacteristic
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—42no—
153C4×C43C2×#10211yescharacteristic
154C4×C43#41711yescharacteristic
155C4×C43C2×#10711yescharacteristic
156C4×C43#42711yescharacteristic
157C4×C43#46611yescharacteristic
158C4×C43#46711yescharacteristic
159C4×C43#47411yescharacteristic
160C4×C43#47611yescharacteristic
161Dic43—162no—
162C2×C8×D4D4311yescharacteristic
163#1845—431no—
164#1802—432no—
165C2×#335—431no—
166#1296—432no—
167C2×C43—44no—
168C2×C43#166711yescharacteristic
169C2×C43#166911yescharacteristic
170C2×C43#167311yescharacteristic
171C2×C43#167511yescharacteristic
172C2×C43#180211yescharacteristic
173C2×C43#180811yescharacteristic
174C2×C43#181611yescharacteristic
175C23×C8—21no—
176C2×C4×D4C2×D4311yescharacteristic
177C8×D4—22no—
178C8×D4Dic4314yescomplemented
179C2×#107—861no—
180C2×#107—861no—
181C2×C4⋊C8—432no—
182C2×C4⋊C8C2×D4311yescharacteristic
183C2×#102—862no—
184C2×C22⋊C8—21no—
185C2×C4×C8C2×D4311yescharacteristic
186#384—432no—
187#340—862no—
188#335—862no—
189C43#864411yescharacteristic, complemented, Sylow
190C22×D4D17211yescharacteristic
191C23×C4—21no—
192C22×C8—21no—
193C22×C8—24no—
194C22×C8—42no—
195C22×C8—42no—
196C22×C8—862no—
197C22×C8C22⋊D4311yescharacteristic
198C22×C8C22⋊D4311yescharacteristic
199C4×D4—21no—
200C4×D4—21no—
201C4×D4Dic8612yes—
202C4×D4C2×Dic4312yes—
203C2×C4⋊C4—862no—
204C2×C4⋊C4—862no—
205C2×C4⋊C4—862no—
206C2×C4⋊C4D17211yescharacteristic
207C2×C22⋊C4—21no—
208C2×C42C22×D4311yescharacteristic
209#107—1722no—
210#107—1722no—
211C4⋊C8—21no—
212C4⋊C8—862no—
213C4⋊C8—862no—
214C4⋊C8C2×Dic4312yes—
215#102—1724no—
216C22⋊C8—24no—
217C4×C8C2×Dic4312yes—
218C4×C8C22⋊D4312yes—
219C24—21no—
220C2×D4—21no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4D34412yes—
224C2×D4Dic17212yes—
225C2×D4C4⋊Dic4312yes—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—1722no—
234C22×C4C2×D17211yescharacteristic
235C22×C4#1062189811yescharacteristic
236C22×C4C2×C22⋊D4311yescharacteristic
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—48no—
243C2×C8—1722no—
244C2×C8—1722no—
245C2×C8—1722no—
246C2×C8#1062188212yes—
247C2×C8#1062188312yes—
248C2×C8C22⋊Dic4312yes—
249C2×C8C22⋊Dic4312yes—
250C4⋊C4—21no—
251C4⋊C4—3442no—
252C4⋊C4—1722no—
253C4⋊C4—1722no—
254C4⋊C4—1722no—
255C4⋊C4—1722no—
256C4⋊C4C4⋊Dic4312yes—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C42C2×Dic8611yescharacteristic
260C42#1062189811yescharacteristic
261C42C22×Dic4311yescharacteristic
262C42C2×C22⋊D4311yescharacteristic
263C23—22no—
264C23—22no—
265C23—22no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23#1306329911yescharacteristic
271D4—22no—
272D4—22no—
273D4—22no—
274D4#1306325914yescomplemented
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—3442no—
285C2×C4—3442no—
286C2×C4—3442no—
287C2×C4C2×C22⋊Dic4311yescharacteristic
288C2×C4C2×C4⋊Dic4311yescharacteristic
289C2×C4#1306328411yescharacteristic
290C2×C4#1306329911yescharacteristic
291C2×C4#1306330411yescharacteristic
292C2×C4#1306330411yescharacteristic
293C2×C4C2×#1062188211yescharacteristic
294C2×C4C2×D34411yescharacteristic
295C2×C4C2×#1062188311yescharacteristic
296C2×C4C2×Dic17211yescharacteristic
297C2×C4#1306334711yescharacteristic
298C2×C4#1306334711yescharacteristic
299C2×C4#1306335011yescharacteristic
300C2×C4#1306335511yescharacteristic
301C8—22no—
302C8—42no—
303C8—3442no—
304C8#1306324614yescomplemented
305C22—24no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—42no—
310C22—42no—
311C22—42no—
312C22#1458275911yescharacteristic
313C22#1458309411yescharacteristic
314C22#1458310411yescharacteristic
315C22#1458313511yescharacteristic
316C22#1458314011yescharacteristic
317C22#1458316911yescharacteristic
318C22#1458317411yescharacteristic
319C4—21no—
320C4—21no—
321C4—42no—
322C4—6882no—
323C4C2×#1306324611yescharacteristic
324C4#1458290011yescharacteristic
325C4C2×#1306325911yescharacteristic
326C4#1458293711yescharacteristic
327C4#1458313511yescharacteristic
328C4#1458314011yescharacteristic
329C4#1458317911yescharacteristic
330C4#1458318911yescharacteristic
331C2—44no—
332C2#1913395011yescharacteristic
333C2#1913396011yescharacteristic
334C2#1913398411yescharacteristic
335C2#1913399411yescharacteristic
336C2#1913459511yescharacteristic
337C2#1913462411yescharacteristic
338C2#1913465911yescharacteristic
subgroupG/H
centerC23#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C8×D4×C43C2
socleC23×C43#121
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenterC2×C8×D4D43
hypocenterC43#8644
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. #19134755C2semidirect
3. C2×#14582652C2semidirect
4. #19132479C2semidirect
16. C8×D4×C43C4semidirect
104. D4×C43#107semidirect
133. C8×C43#102semidirect
178. C8×D4Dic43semidirect
189. C43#8644semidirect
274. D4#13063259semidirect
304. C8#13063246semidirect

Maximal subgroups

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

subgroupindex
#191347552
#191345952
C2×#145826522
#191324792
C2×C8×D4×C432
#864443