Finite Group Databasebeta

← #25001352

Subgroups — #25001352

Order 11008.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135389C211yesmaximal, characteristic
2#19134592C211yesmaximal, characteristic
3#19134592C211yesmaximal, characteristic
4#19132478C211yesmaximal, characteristic, complemented
5#19132478C211yesmaximal, characteristic, complemented
6#19132430C211yesmaximal, characteristic, complemented
7C43×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063245—21no—
13C2×#13063245—21no—
14C2×(C2×D43)⋊C8—21no—
15C2×(C2×D43)⋊C8—21no—
16#14582661—21no—
17#14582661—21no—
18C2×C4×C8×C43C2211yescharacteristic
19C43×#384C2211yescharacteristic
20C43×#384C2211yescharacteristic
21C43×#340—21no—
22C43×#340—21no—
23C22×D172D411yescharacteristic
24C22×C4×D43—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C22×C43⋊C8—21no—
28C4×D172—21no—
29C4×D172—21no—
30C4×D172—21no—
31C4×D172—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×(C2×D43)⋊C4—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40#13063245—42no—
41#13063245—42no—
42(C2×D43)⋊C8—42no—
43(C2×D43)⋊C8—42no—
44C22×C8×C43D411yescharacteristic
45C22×C8×C43D411yescharacteristic
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C42×C43C2311yescharacteristic
53C4×C8×C43—21no—
54C4×C8×C43—21no—
55C23×D43—21no—
56C22×C4×C43—41no—
57C22×C4×C43—41no—
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43#4111yescharacteristic
61C22×Dic43—21no—
62C2×D172—21no—
63C2×D172—21no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172SD1612yes—
68C2×C4×D43—41no—
69C2×C4×D43—41no—
70C2×C4×D43—41no—
71C2×C4×D43—41no—
72C2×C4×D43—41no—
73C2×C4×D43—41no—
74C2×C8×C43—21no—
75C2×C8×C43—21no—
76C2×C8×C43—21no—
77C2×C8×C43—21no—
78C2×C8×C43—21no—
79C2×C8×C43—21no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—81no—
89C4⋊C4×C43—81no—
90C42×C43#4111yescharacteristic
91C42×C43#4111yescharacteristic
92C42×C43#4111yescharacteristic
93C42×C43#4111yescharacteristic
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43#12111yescharacteristic
108C22×D43—22no—
109C22×D43—41no—
110C22×D43—41no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43—41no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43#12311yescharacteristic
124C2×C4×C43#12311yescharacteristic
125C2×C4×C43#12311yescharacteristic
126C2×C4×C43#12411yescharacteristic
127C2×C4×C43#12611yescharacteristic
128C2×C4×C43#12611yescharacteristic
129C2×C4×C43C2×SD1611yescharacteristic
130C2×C4×C43#13511yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43#13711yescharacteristic
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140D172—22no—
141D172—22no—
142D172—41no—
143D172—41no—
144C4×D43—81no—
145C4×D43—81no—
146C4×D43—81no—
147C4×D43—81no—
148C8×C43—41no—
149C8×C43—41no—
150C43⋊C8—81no—
151C43⋊C8—81no—
152C43⋊C8—81no—
153#10625—431nomaximal, Sylow
154C22×C43#39711yescharacteristic
155C22×C43#46311yescharacteristic
156C22×C43#46311yescharacteristic
157C22×C43#46511yescharacteristic
158C22×C43#46811yescharacteristic
159C22×C43#47211yescharacteristic
160C22×C43#47311yescharacteristic
161C2×D43—42no—
162C2×D43—42no—
163C2×D43—42no—
164C2×D43—81no—
165C2×D43—81no—
166C2×D43—81no—
167C2×D43—81no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—161no—
171C4×C43—161no—
172C4×C43#48111yescharacteristic
173C4×C43#48211yescharacteristic
174C4×C43#48211yescharacteristic
175C4×C43#48211yescharacteristic
176C4×C43#48311yescharacteristic
177C4×C43#48511yescharacteristic
178C4×C43#48811yescharacteristic
179C4×C43#49011yescharacteristic
180Dic43—81no—
181#1954—431no—
182#1834D4311yescharacteristic, complemented
183#1802—431no—
184#1802—431no—
185#1296—431no—
186#1296—431no—
187#1277—431no—
188C2×C43#167711yescharacteristic
189C2×C43#167911yescharacteristic
190C2×C43#169711yescharacteristic
191C2×C43#169911yescharacteristic
192C2×C43#207311yescharacteristic
193C2×C43#207711yescharacteristic
194C2×C43#207811yescharacteristic
195D43—82no—
196C2×C4×D4—431no—
197C2×C4⋊C8—431no—
198C2×C4⋊C8—431no—
199C2×C4⋊C8—431no—
200C2×#102—861no—
201C2×#102—861no—
202C2×C22⋊C8—861no—
203C2×C22⋊C8—861no—
204C2×C4×C8C2×D4311yescharacteristic
205#384C2×D4311yescharacteristic
206#384C2×D4311yescharacteristic
207#340—21no—
208#340—21no—
209#340—861no—
210#340—861no—
211C43#1062511yescharacteristic, complemented, Sylow
212C22×D4—431no—
213C23×C4—861no—
214C22×C8—861no—
215C22×C8—861no—
216C22×C8—861no—
217C22×C8C22⋊D4311yescharacteristic
218C22×C8C22⋊D4311yescharacteristic
219C4×D4—861no—
220C4×D4—861no—
221C4×D4—861no—
222C4×D4—861no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—431no—
230C2×C22⋊C4—861no—
231C2×C42C22×D4311yescharacteristic
232C4⋊C8—861no—
233C4⋊C8—861no—
234C4⋊C8—861no—
235C4⋊C8—861no—
236C4⋊C8—861no—
237C4⋊C8—861no—
238#102—1722no—
239#102—1722no—
240C22⋊C8—1722no—
241C22⋊C8—1722no—
242C4×C8—21no—
243C4×C8—21no—
244C24—861no—
245C2×D4—432no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4—861no—
250C2×D4—861no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—861no—
254C22×C4—1721no—
255C22×C4—1721no—
256C22×C4—1721no—
257C22×C4—1721no—
258C22×C4—1721no—
259C22×C4—1721no—
260C22×C4D4×D4311yescharacteristic
261C22×C4#1062190011yescharacteristic
262C22×C4C2×C22⋊D4311yescharacteristic
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—1721no—
270C2×C8—1721no—
271C2×C8—1721no—
272C2×C8—1721no—
273C2×C8—1721no—
274C2×C8—1721no—
275C2×C8—1721no—
276C2×C8—1721no—
277C2×C8—1721no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C42#1062189811yescharacteristic
293C42#1062189811yescharacteristic
294C42#1062190211yescharacteristic
295C42#1062190211yescharacteristic
296C23—862no—
297C23—1721no—
298C23—1721no—
299C23—1721no—
300C23—1721no—
301C23—1721no—
302C23—1721no—
303C23#1306329611yescharacteristic
304D4—862no—
305D4—862no—
306D4—1721no—
307D4—1721no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4#1306330811yescharacteristic
324C2×C4#1306331011yescharacteristic
325C2×C4#1306331011yescharacteristic
326C2×C4#1306331411yescharacteristic
327C2×C4#1306332011yescharacteristic
328C2×C4#1306332011yescharacteristic
329C2×C4SD16×D4311yescharacteristic
330C2×C4#1306334511yescharacteristic
331C2×C4#1306334511yescharacteristic
332C2×C4#1306334611yescharacteristic
333C2×C4#1306335011yescharacteristic
334C2×C4#1306335011yescharacteristic
335C2×C4#1306335211yescharacteristic
336C2×C4#1306335411yescharacteristic
337C8—41no—
338C8—41no—
339C8—3441no—
340C8—3441no—
341C8—3441no—
342C22—3441no—
343C22—3441no—
344C22—3441no—
345C22—3441no—
346C22—1722no—
347C22—1722no—
348C22—1722no—
349C22#1458282511yescharacteristic
350C22#1458311111yescharacteristic
351C22#1458311111yescharacteristic
352C22#1458312511yescharacteristic
353C22#1458314211yescharacteristic
354C22#1458316611yescharacteristic
355C22#1458317111yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—161no—
360C4—3441no—
361C4#1458321911yescharacteristic
362C4#1458322311yescharacteristic
363C4#1458322311yescharacteristic
364C4#1458322511yescharacteristic
365C4#1458323111yescharacteristic
366C4#1458324311yescharacteristic
367C4#1458325611yescharacteristic
368C4#1458326511yescharacteristic
369C2—3442no—
370C2#1913400111yescharacteristic
371C2#1913401511yescharacteristic
372C2#1913412511yescharacteristic
373C2#1913413911yescharacteristic
374C2#1913600911yescharacteristic
375C2#1913602911yescharacteristic
376C2#1913603611yescharacteristic
subgroupG/H
centerC23#13063296
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1834C2
socleC23×C43#121
prime radicalC22×D172D4
hypercenter#1834D43
hypocenterC43#10625
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #19132478C2semidirect
5. #19132478C2semidirect
6. #19132430C2semidirect
7. C43×#1834C2semidirect
182. #1834D43semidirect
211. C43#10625semidirect

Maximal subgroups

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

subgroupindex
#191353892
#191345922
#191324782
#191324302
C43×#18342
#1062543