Finite Group Databasebeta

← #25001056

Subgroups — #25001056

Order 11008.

406 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#19139834C211yesmaximal, characteristic
2#19135351C211yesmaximal, characteristic
3#19134751C211yesmaximal, characteristic
4#19132479C211yesmaximal, characteristic
5#19132436C211yesmaximal, characteristic
6#19132434C211yesmaximal, characteristic
7C43×#1947C211yesmaximal, characteristic
8C2×#13063258—21no—
9C2×#13063256—22no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4×C43⋊C8C2211yescharacteristic
12#14582841—22no—
13#14582797—21no—
14#14582795—21no—
15#14582769C2211yescharacteristic
16#14582765—21no—
17#14582764—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582661—21no—
20C2×#107×C43—21no—
21C2×C4⋊C8×C43C2211yescharacteristic
22C43×#384C2211yescharacteristic
23C4×C4⋊C4×C43C2211yescharacteristic
24C43×#340—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43D411yescharacteristic
30C2×C4⋊Dic43D411yescharacteristic
31C2×C4⋊Dic43D412yes—
32C2×Dic43⋊C4—22no—
33C2×C4×Dic43—21no—
34#13063258—42no—
35#13063256—44no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)Q812yes—
38C4×C43⋊C8—21no—
39C4×C43⋊C8Q812yes—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C43⋊#95—22no—
43C43⋊#95—21no—
44C22×C8×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C42×C43—21no—
51C2×C42×C43C2311yescharacteristic
52#107×C43—42no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43Q812yes—
55#95×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—41no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—22no—
65C2×C8×C43—22no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C4⋊C4×C43—21no—
69C4⋊C4×C43—21no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43—42no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C42×C43—41no—
78C42×C43—41no—
79C42×C43C2×Q811yescharacteristic
80C42×C43C2×Q811yescharacteristic
81C42×C43C2×Q811yescharacteristic
82C42×C43#4111yescharacteristic
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—42no—
92Dic43⋊C4—82no—
93C4×Dic43—41no—
94C4×Dic43—41no—
95C2×C43⋊C8—22no—
96C2×C43⋊C8—22no—
97C2×C43⋊C8—22no—
98C2×C43⋊C8—22no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C23×C43#12011yescharacteristic
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—81no—
111C2×C4×C43—81no—
112C2×C4×C43—81no—
113C2×C4×C43C22⋊Q811yescharacteristic
114C2×C4×C43C22⋊Q811yescharacteristic
115C2×C4×C43C22⋊Q811yescharacteristic
116C2×C4×C43C4⋊Q811yescharacteristic
117C2×C4×C43C4⋊Q811yescharacteristic
118C2×C4×C43C4⋊Q811yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×C4×C43#13511yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×C4×C43#13511yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C43#13711yescharacteristic
126C2×C4×C43#13711yescharacteristic
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—41no—
134C2×Dic43—42no—
135C2×Dic43—41no—
136C8×C43—42no—
137C43⋊C8—24no—
138C43⋊C8—42no—
139#10577—431nomaximal, Sylow
140C22×C43#39511yescharacteristic
141C22×C43#44911yescharacteristic
142C22×C43#44911yescharacteristic
143C22×C43#45211yescharacteristic
144C22×C43#45211yescharacteristic
145C22×C43#45311yescharacteristic
146C22×C43#45611yescharacteristic
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—81no—
150C4×C43—81no—
151C4×C43—161no—
152C4×C43#47811yescharacteristic
153C4×C43#47811yescharacteristic
154C4×C43#47911yescharacteristic
155C4×C43#47911yescharacteristic
156C4×C43#49911yescharacteristic
157C4×C43#49911yescharacteristic
158C4×C43#50111yescharacteristic
159C4×C43#50111yescharacteristic
160Dic43—81no—
161Dic43—82no—
162Dic43—81no—
163#2571—431no—
164#1947—431no—
165#1947D4311yescharacteristic
166#1844—431no—
167#1296—431no—
168#1279—431no—
169#1279—431no—
170C2×C43#162411yescharacteristic
171C2×C43#163011yescharacteristic
172C2×C43#165211yescharacteristic
173C2×C43#165211yescharacteristic
174C2×C43#205911yescharacteristic
175C2×C43#205911yescharacteristic
176C2×C43#206011yescharacteristic
177C2×#107—21no—
178C2×#107—861no—
179C2×#106—862no—
180C2×C4⋊C8—431no—
181C2×C4⋊C8C2×D4311yescharacteristic
182C2×C4×C8—431no—
183#400—862no—
184#389—861no—
185#389—861no—
186#384—431no—
187#384C2×D4311yescharacteristic
188#382—861no—
189#382—861no—
190C4×C4⋊C4—431no—
191C4×C4⋊C4C2×D4311yescharacteristic
192#340—21no—
193#340—861no—
194C43#1057711yescharacteristic, complemented, Sylow
195C22×C8—21no—
196C22×C8—861no—
197C22×C8—861no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—431no—
203C2×C4⋊C4—432no—
204C2×C4⋊C4—862no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4C22⋊D4311yescharacteristic
208C2×C4⋊C4C22⋊D4311yescharacteristic
209C2×C42—21no—
210C2×C42—861no—
211C2×C42C22×D4311yescharacteristic
212#107—42no—
213#107—1722no—
214#106—1724no—
215C4⋊C8—21no—
216C4⋊C8—432no—
217C4⋊C8—861no—
218C4⋊C8Dic8612yes—
219C4×C8—432no—
220C4×C8—861no—
221#95—21no—
222#95—862no—
223#95—862no—
224#95—862no—
225#95—861no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—862no—
232C22×C4D4×D4311yescharacteristic
233C22×C4D4×D4311yescharacteristic
234C22×C4C2×C22⋊D4311yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—862no—
239C2×C8—862no—
240C2×C8—862no—
241C2×C8—862no—
242C2×C8—1721no—
243C2×C8—1721no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—3442no—
258C4⋊C4—1722no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C42—41no—
264C42—41no—
265C42—1721no—
266C42—1721no—
267C42C2×Dic8611yescharacteristic
268C42#1062189811yescharacteristic
269C42Q8×D4311yescharacteristic
270C42Q8×D4311yescharacteristic
271C23#1306329311yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1722no—
287C2×C4—1721no—
288C2×C4—1722no—
289C2×C4—1721no—
290C2×C4—1722no—
291C2×C4—1721no—
292C2×C4#1306330311yescharacteristic
293C2×C4#1306330311yescharacteristic
294C2×C4#1306330411yescharacteristic
295C2×C4#1306332311yescharacteristic
296C2×C4#1306332411yescharacteristic
297C2×C4#1306332411yescharacteristic
298C2×C4#1306334411yescharacteristic
299C2×C4#1306334511yescharacteristic
300C2×C4#1306334511yescharacteristic
301C2×C4#1306334811yescharacteristic
302C2×C4#1306334911yescharacteristic
303C2×C4#1306335111yescharacteristic
304C2×C4#1306335611yescharacteristic
305C2×C4#1306335711yescharacteristic
306C8—42no—
307C8—864no—
308C8—1722no—
309C22#1458281911yescharacteristic
310C22#1458304111yescharacteristic
311C22#1458304211yescharacteristic
312C22#1458305911yescharacteristic
313C22#1458306011yescharacteristic
314C22#1458306511yescharacteristic
315C22#1458308011yescharacteristic
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—161no—
321C4—3442no—
322C4—3441no—
323C4—3441no—
324C4#1458319911yescharacteristic
325C4#1458320211yescharacteristic
326C4#1458320511yescharacteristic
327C4#1458320611yescharacteristic
328C4#1458329811yescharacteristic
329C4#1458330011yescharacteristic
330C4#1458330511yescharacteristic
331C4#1458330711yescharacteristic
332C2#1913367711yescharacteristic
333C2#1913371511yescharacteristic
334C2#1913386311yescharacteristic
335C2#1913386411yescharacteristic
336C2#1913593111yescharacteristic
337C2#1913593311yescharacteristic
338C2#1913593811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1947C2
socle, prime radicalC23×C43#120
hypercenter#1947D43
hypocenterC43#10577
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
194. C43#10577semidirect

Maximal subgroups

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

subgroupindex
#191398342
#191353512
#191347512
#191324792
#191324362
#191324342
C43×#19472
#1057743