Finite Group Databasebeta

← #25001081

Subgroups — #25001081

Order 11008.

426 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#19139631C211yesmaximal, characteristic
2#19135354C211yesmaximal, characteristic
3#19135354C211yesmaximal, characteristic
4#19134722C211yesmaximal, characteristic
5#19132434C211yesmaximal, characteristic
6#19132434C211yesmaximal, characteristic
7C43×#1296C211yesmaximal, characteristic
8C2×#13063316—21no—
9C2×#13063259—21no—
10C2×#13063259—21no—
11C2×C4×C43⋊C8C2211yescharacteristic
12#14582832—22no—
13#14582798—21no—
14#14582795—21no—
15#14582769C2211yescharacteristic
16#14582768—21no—
17C4×C4⋊Dic43C2211yescharacteristic
18C4×C4⋊Dic43C2211yescharacteristic
19#14582662—21no—
20#14582662—21no—
21#14582661—22no—
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C22×C43⋊C8—21no—
26#13063316—42no—
27#13063316—42no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×C4⋊Dic43D411yescharacteristic
34C2×C4⋊Dic43D411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—22no—
37C2×Dic43⋊C4—22no—
38C2×C4×Dic43—21no—
39C2×C4×Dic43—21no—
40#13063259—42no—
41#13063259—42no—
42C4×C43⋊C8—21no—
43C4×C43⋊C8Q812yes—
44C43⋊#95—22no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C22×C8×C43—21no—
48C22×C8×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43D412yes—
52C2×C42×C43C2311yescharacteristic
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43Q812yes—
56C4⋊C8×C43Q812yes—
57C22×C4×C43—22no—
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—41no—
66C2×C8×C43—22no—
67C2×C8×C43—22no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C4⋊C4×C43—42no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C42×C43C2×Q811yescharacteristic
78C42×C43C2×Q811yescharacteristic
79C42×C43C2×Q811yescharacteristic
80C42×C43#4111yescharacteristic
81C4⋊Dic43—21no—
82C4⋊Dic43—21no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—44no—
88C4⋊Dic43—42no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43D812yes—
94C4⋊Dic43Q1612yes—
95Dic43⋊C4—44no—
96Dic43⋊C4—82no—
97C4×Dic43—41no—
98C4×Dic43—41no—
99C4×Dic43—41no—
100C4×Dic43—41no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43#12011yescharacteristic
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43C22⋊Q811yescharacteristic
111C2×C4×C43C22⋊Q811yescharacteristic
112C2×C4×C43C22⋊Q811yescharacteristic
113C2×C4×C43C4⋊Q811yescharacteristic
114C2×C4×C43C4⋊Q811yescharacteristic
115C2×C4×C43C4⋊Q811yescharacteristic
116C2×C4×C43C2×D811yescharacteristic
117C2×C4×C43C2×Q1611yescharacteristic
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139C8×C43—42no—
140C8×C43—42no—
141C43⋊C8—42no—
142#10581—431nomaximal, Sylow
143C22×C43#39511yescharacteristic
144C22×C43#44711yescharacteristic
145C22×C43#44911yescharacteristic
146C22×C43#45111yescharacteristic
147C22×C43#45211yescharacteristic
148C22×C43#45411yescharacteristic
149C22×C43#45511yescharacteristic
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—82no—
153C4×C43#47411yescharacteristic
154C4×C43#47711yescharacteristic
155C4×C43#47811yescharacteristic
156C4×C43#47911yescharacteristic
157C4×C43#49911yescharacteristic
158C4×C43#50011yescharacteristic
159C4×C43#50111yescharacteristic
160C4×C43#50111yescharacteristic
161Dic43—42no—
162Dic43—42no—
163Dic43—81no—
164Dic43—81no—
165Dic43—161no—
166#2552—431no—
167#1947—431no—
168#1947—431no—
169#1834—431no—
170#1296D4311yescharacteristic
171#1279—431no—
172#1279—431no—
173C2×C43#162511yescharacteristic
174C2×C43#163611yescharacteristic
175C2×C43#164111yescharacteristic
176C2×C43#164411yescharacteristic
177C2×C43#205711yescharacteristic
178C2×C43#205911yescharacteristic
179C2×C43#206111yescharacteristic
180C2×#125—861no—
181C2×#107—861no—
182C2×#107—861no—
183C2×C4⋊C8C2×D4311yescharacteristic
184C2×C4⋊C8C2×D4311yescharacteristic
185C2×C4×C8—431no—
186#398—862no—
187#389—861no—
188#389—861no—
189#384—431no—
190#384—861no—
191#384C2×D4311yescharacteristic
192C4×C4⋊C4—431no—
193C4×C4⋊C4—431no—
194#340—861no—
195#340—861no—
196#340—862no—
197C43#1058111yescharacteristic, complemented, Sylow
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—861no—
201#125—1722no—
202#125—1722no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—862no—
210C2×C4⋊C4—862no—
211C2×C4⋊C4—862no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4D17212yes—
216C2×C42—861no—
217C2×C42—861no—
218C2×C42C22×D4311yescharacteristic
219#107—1722no—
220#107—1722no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8Dic8612yes—
224C4⋊C8Dic8612yes—
225C4×C8—432no—
226C4×C8—861no—
227#95—862no—
228#95—861no—
229#95—861no—
230C22×C4—22no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—1721no—
236C22×C4C2×D17211yescharacteristic
237C22×C4D4×D4311yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—862no—
246C2×C8—1721no—
247C2×C8—1721no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—432no—
254C4⋊C4—432no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—3442no—
262C4⋊C4—1722no—
263C4⋊C4—1724no—
264C4⋊C4—1724no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C42—1721no—
270C42—1721no—
271C42—1721no—
272C42—1721no—
273C42C2×Dic8611yescharacteristic
274C42C2×Dic8611yescharacteristic
275C42#1062190011yescharacteristic
276C42Q8×D4311yescharacteristic
277C23#1306329511yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—862no—
284C2×C4—862no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4#1306330211yescharacteristic
299C2×C4#1306330211yescharacteristic
300C2×C4#1306330511yescharacteristic
301C2×C4#1306332411yescharacteristic
302C2×C4#1306332411yescharacteristic
303C2×C4#1306332511yescharacteristic
304C2×C4D8×D4311yescharacteristic
305C2×C4Q16×D4311yescharacteristic
306C2×C4#1306334411yescharacteristic
307C2×C4#1306334811yescharacteristic
308C2×C4#1306335211yescharacteristic
309C2×C4#1306335211yescharacteristic
310C2×C4#1306335411yescharacteristic
311C2×C4#1306335411yescharacteristic
312C8—42no—
313C8—42no—
314C8—1722no—
315C22#1458282011yescharacteristic
316C22#1458303411yescharacteristic
317C22#1458304711yescharacteristic
318C22#1458305611yescharacteristic
319C22#1458306211yescharacteristic
320C22#1458307411yescharacteristic
321C22#1458307911yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—3441no—
326C4—3441no—
327C4—1722no—
328C4—1722no—
329C4—6881no—
330C4#1458317711yescharacteristic
331C4#1458319211yescharacteristic
332C4#1458319711yescharacteristic
333C4#1458320811yescharacteristic
334C4#1458330011yescharacteristic
335C4#1458330311yescharacteristic
336C4#1458330611yescharacteristic
337C4#1458330611yescharacteristic
338C2#1913368511yescharacteristic
339C2#1913375411yescharacteristic
340C2#1913378911yescharacteristic
341C2#1913381011yescharacteristic
342C2#1913592211yescharacteristic
343C2#1913593611yescharacteristic
344C2#1913594611yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1296C2
socle, prime radicalC23×C43#120
hypercenter#1296D43
hypocenterC43#10581
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
197. C43#10581semidirect

Maximal subgroups

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

subgroupindex
#191396312
#191353542
#191347222
#191324342
C43×#12962
#1058143