Finite Group Databasebeta

← #25014041

Subgroups — #25014041

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583316C211yesmaximal, characteristic, complemented
2C2×#14582712C211yesmaximal, characteristic, complemented
3C2×#14582700C211yesmaximal, characteristic, complemented
4#19134659C211yesmaximal, characteristic, complemented
5#19132705C211yesmaximal, characteristic, complemented
6#19132688C211yesmaximal, characteristic, complemented
7C2×C43×#472C211yesmaximal, characteristic
8#14583316—22no—
9#14583316—22no—
10C2×#13063265—21no—
11C2×#13063265C2211yescharacteristic
12C22×C43⋊C16—21no—
13C22×C43⋊C16C2211yescharacteristic
14C2×#13063261C2211yescharacteristic
15C2×#13063259C2211yescharacteristic
16#14582900—21no—
17#14582712—22no—
18#14582700—21no—
19#14582700—21no—
20#14582667—21no—
21C2×AGL(1,ℤ/8)×C43—21no—
22C22×D8×C43C2211yescharacteristic
23C2×#131×C43C2211yescharacteristic
24C43×#472—22no—
25C43×#472C414yescomplemented
26C2×#108×C43C2211yescharacteristic
27C2×#100×C43—21no—
28C2×#10621877—21no—
29C2×C4⋊Dic43—21no—
30#13063265—24no—
31#13063265—21no—
32#13063265D412yes—
33C2×C43⋊C16—24no—
34C2×C43⋊C16—21no—
35C2×C43⋊C16—21no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16D411yescharacteristic
38C2×C43⋊C16D411yescharacteristic
39#13063261—21no—
40#13063261—21no—
41#13063259—21no—
42#13063259—21no—
43#13063249—41no—
44#13063246—41no—
45C2×#41×C43D411yescharacteristic
46C22×D4×C43—21no—
47AGL(1,ℤ/8)×C43—24no—
48AGL(1,ℤ/8)×C43—42no—
49C2×SD16×C43—41no—
50C2×D8×C43—21no—
51C2×D8×C43—21no—
52C2×D8×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43—41no—
56C2×D8×C43C2×C412yes—
57#131×C43—21no—
58#131×C43—21no—
59#131×C43C2×C412yes—
60#131×C43D412yes—
61C2×M16×C43—21no—
62C2×M16×C43—21no—
63C2×M16×C43D411yescharacteristic
64C22×C8×C43—21no—
65C22×C8×C43C2311yescharacteristic
66#108×C43—21no—
67#108×C43C2×C412yes—
68#100×C43—24no—
69C24×C43—41no—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43C22⋊C412yes—
73#41×C43SD1612yes—
74C2×Q8×C43D811yescharacteristic
75C2×D4×C43—21no—
76C2×D4×C43—22no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43D811yescharacteristic
83C22×C4×C43—21no—
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—41no—
86SD16×C43—44no—
87D8×C43—22no—
88D8×C43—22no—
89D8×C43—44no—
90D8×C43—41no—
91D8×C43—41no—
92M16×C43—21no—
93M16×C43—22no—
94M16×C43—22no—
95M16×C43—22no—
96M16×C43—41no—
97M16×C43C22⋊C412yes—
98C2×C8×C43—21no—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43—41no—
102C2×C8×C43C22×C411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43#4111yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110#10621877—41no—
111#10621877—41no—
112C2×C43⋊C8—41no—
113C43⋊C16—21no—
114C43⋊C16—22no—
115C43⋊C16—21no—
116C23×C43—21no—
117C23×C43—42no—
118C23×C43—81no—
119C23×C43—81no—
120C23×C43—161no—
121C23×C43—161no—
122C23×C43#13511yescharacteristic
123Q8×C43—21no—
124Q8×C43#10212yes—
125D4×C43—22no—
126D4×C43—22no—
127D4×C43—21no—
128D4×C43—42no—
129D4×C43—42no—
130D4×C43—81no—
131D4×C43—81no—
132D4×C43#10212yes—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43C2×D811yescharacteristic
140C2×C4×C43C2×SD1611yescharacteristic
141C2×C4×C43#13511yescharacteristic
142C2×Dic43—81no—
143C2×Dic43—161no—
144C8×C43—22no—
145C8×C43—42no—
146C8×C43C4×D411yescharacteristic
147C8×C43C4×D411yescharacteristic
148C8×C43#12011yescharacteristic
149C8×C43#12311yescharacteristic
150C43⋊C8—81no—
151#13073—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—22no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—82no—
158C22×C43—162no—
159C22×C43—162no—
160C22×C43—161no—
161C22×C43—161no—
162C22×C43#41611yescharacteristic
163C22×C43#46511yescharacteristic
164C22×C43#46611yescharacteristic
165C4×C43—22no—
166C4×C43#38611yescharacteristic
167C4×C43C2×#10211yescharacteristic
168C4×C43#46511yescharacteristic
169C4×C43#46611yescharacteristic
170Dic43—161no—
171C2×#504—431no—
172C2×#472D4311yescharacteristic
173C2×#361—431no—
174C2×#357—431no—
175#1816—431no—
176#1387—431no—
177#1381—431no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43—42no—
181C2×C43—162no—
182C2×C43#189311yescharacteristic
183C2×C43#222111yescharacteristic
184C2×C43#222311yescharacteristic
185C2×AGL(1,ℤ/8)—21no—
186C22×D8C2×D4311yescharacteristic
187C2×#131C2×D4311yescharacteristic
188#504—862no—
189#504—862no—
190C2×M32—431no—
191C2×M32—861no—
192C22×C16—431no—
193C22×C16—861no—
194#472—22no—
195#472Dic4314yescomplemented
196C2×#108—431no—
197C2×#108C2×D4311yescharacteristic
198C2×#107—431no—
199#417—861no—
200C2×#100—21no—
201#361—862no—
202#357—861no—
203#357—861no—
204#343—861no—
205C43#1307311yescharacteristic, complemented, Sylow
206C2×#41C22⋊D4311yescharacteristic
207C22×D4—21no—
208AGL(1,ℤ/8)—24no—
209AGL(1,ℤ/8)—42no—
210C2×SD16—41no—
211C2×D8—21no—
212C2×D8—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—41no—
217C2×D8C2×Dic4312yes—
218#131—21no—
219#131—21no—
220#131C2×Dic4312yes—
221#131C22⋊D4312yes—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—861no—
225C2×M16C22⋊D4311yescharacteristic
226C22×C8—21no—
227C22×C8C22×D4311yescharacteristic
228C2×C4⋊C4—861no—
229M32—432no—
230M32—864no—
231M32—861no—
232C2×C16—431no—
233C2×C16—431no—
234C2×C16—864no—
235C2×C16—861no—
236C2×C16—861no—
237C2×C16—861no—
238#108—21no—
239#108—861no—
240#108—861no—
241#108C2×Dic4312yes—
242#107—861no—
243#107—861no—
244#103—1721no—
245#102—1721no—
246#100—24no—
247C24—41no—
248#41—21no—
249#41—21no—
250#41#1062188312yes—
251#41C22⋊Dic4312yes—
252C2×Q8#1062188211yescharacteristic
253C2×D4—21no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4#1062188211yescharacteristic
261C22×C4—21no—
262C22×C4—1721no—
263C22×C4C2×C22⋊D4311yescharacteristic
264SD16—44no—
265D8—22no—
266D8—22no—
267D8—44no—
268D8—41no—
269D8—41no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—22no—
274M16—41no—
275M16—1721no—
276M16—1721no—
277M16C22⋊Dic4312yes—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—1721no—
283C2×C8D4×D4311yescharacteristic
284C2×C8D4×D4311yescharacteristic
285C2×C8#1062190011yescharacteristic
286C2×C8#1062190011yescharacteristic
287C2×C8C22×Dic4311yescharacteristic
288C2×C8C2×C22⋊D4311yescharacteristic
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C16—861no—
292C16—861no—
293C16—862no—
294C23—21no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23—161no—
299C23—161no—
300C23#1306334511yescharacteristic
301Q8—21no—
302Q8#1306324612yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—42no—
307D4—42no—
308D4—81no—
309D4—81no—
310D4#1306324612yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—3441no—
315C2×C4—6881no—
316C2×C4C2×C22⋊Dic4311yescharacteristic
317C2×C4#1306329711yescharacteristic
318C2×C4#1306329711yescharacteristic
319C2×C4C2×#1062188211yescharacteristic
320C2×C4C2×#1062188311yescharacteristic
321C2×C4#1306334511yescharacteristic
322C8—22no—
323C8—42no—
324C8—3441no—
325C8D4×Dic4311yescharacteristic
326C8D4×Dic4311yescharacteristic
327C8#1306329311yescharacteristic
328C8#1306330611yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—82no—
335C22—162no—
336C22—162no—
337C22—161no—
338C22—161no—
339C22#1458289511yescharacteristic
340C22#1458312611yescharacteristic
341C22#1458313311yescharacteristic
342C4—22no—
343C4—6881no—
344C4#1458277911yescharacteristic
345C4C2×#1306324611yescharacteristic
346C4#1458312611yescharacteristic
347C4#1458313311yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—162no—
352C2#1913502411yescharacteristic
353C2#1913671311yescharacteristic
354C2#1913672311yescharacteristic
subgroupG/H
centerC22#14583133
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC2×C43×#472C2
socleC22×C43#466
cosocleC22×C8×C43C23
hypercenterC2×#472D43
hypocenterC43#13073
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C2×#14583316C2semidirect
2. C2×#14582712C2semidirect
3. C2×#14582700C2semidirect
4. #19134659C2semidirect
5. #19132705C2semidirect
6. #19132688C2semidirect
25. C43×#472C4semidirect
195. #472Dic43semidirect
205. C43#13073semidirect

Maximal subgroups

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

subgroupindex
C2×#145833162
C2×#145827122
C2×#145827002
#191346592
#191327052
#191326882
C2×C43×#4722
#1307343