Finite Group Databasebeta

← #25125360

Subgroups — #25125360

Order 11008.

1226 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582903C212yesmaximal
2C2×#14582801C211yesmaximal, characteristic
3#19136009C214yesmaximal, complemented
4#19135999C214yesmaximal, complemented
5#19134316C212yesmaximal, complemented
6#19134289C211yesmaximal, characteristic, complemented
7C43×#2285C211yesmaximal, characteristic, complemented
8C23×D172C2211yescharacteristic
9C22×#10621877C2212yes—
10C22×C4⋊Dic43C2211yescharacteristic
11C22×(C2×D43)⋊C4—22no—
12#14582903—28no—
13C2×#13063245C2218yes—
14#14582801—22no—
15#14582801C2212yes—
16#14582801C2212yes—
17#14582661C2218yescomplemented
18#14582654C2212yescomplemented
19#14582654C2212yescomplemented
20C2×#117×C43C2212yes—
21C22×C42×C43C2211yescharacteristic
22C43×#384C2212yescomplemented
23C43×#382C2212yescomplemented
24C43×#380—22no—
25C4×C4⋊C4×C43—22no—
26C24×D43—21no—
27C22×D172—24no—
28C22×D172—24no—
29C22×D172—21no—
30C22×D172—22no—
31C22×D172D414yes—
32C22×D172C2312yes—
33C23×Dic43—21no—
34C2×#10621877—24no—
35C2×#10621877—24no—
36C2×#10621877—24no—
37C22×C43⋊C8C2314yes—
38C2×C4⋊Dic43—24no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43C2312yes—
41C2×(C2×D43)⋊C4—24no—
42C2×(C2×D43)⋊C4—24no—
43C2×(C2×D43)⋊C4—48no—
44#13063245—216no—
45C23×C4×C43D412yes—
46C23×C4×C43C2311yescharacteristic
47#117×C43—24no—
48#117×C43—24no—
49C2×C4⋊C4×C43—22no—
50C2×C4⋊C4×C43—22no—
51C2×C4⋊C4×C43C2314yes—
52C2×C22⋊C4×C43—22no—
53C2×C42×C43—24no—
54C2×C42×C43—22no—
55C2×C42×C43D412yes—
56C2×C42×C43C2311yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#95×C43—24no—
59C24×C43C2×D411yescharacteristic
60C23×D43—24no—
61C23×D43—22no—
62C23×D43—44no—
63C23×D43—44no—
64C23×D43—42no—
65C23×D43—42no—
66C22×C4×C43—24no—
67C22×C4×C43—24no—
68C22×C4×C43—24no—
69C22×C4×C43—42no—
70C22×C4×C43C2×D412yes—
71C22×C4×C43C2×D412yes—
72C22×C4×C43C2×D412yes—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43#4112yes—
75C22×C4×C43#4114yes—
76C22×C4×C43#4114yes—
77C22×C4×C43C2411yescharacteristic
78C22×Dic43—22no—
79C22×Dic43—44no—
80C22×Dic43—42no—
81C2×D172—24no—
82C2×D172—22no—
83C2×D172—216no—
84C2×D172—24no—
85C2×D172—24no—
86C2×D172—42no—
87C2×D172—42no—
88C2×D172—48no—
89C2×D172C2×D414yes—
90C4⋊C4×C43—24no—
91C4⋊C4×C43—24no—
92C4⋊C4×C43—44no—
93C4⋊C4×C43—44no—
94C22⋊C4×C43—44no—
95C42×C43—24no—
96C42×C43—22no—
97C42×C43—22no—
98C42×C43—44no—
99(C2×D43)⋊C4—48no—
100(C2×D43)⋊C4—48no—
101C4⋊Dic43—24no—
102C4⋊Dic43—42no—
103#10621877—48no—
104C2×C43⋊C8—24no—
105C2×C43⋊C8—24no—
106C2×C43⋊C8—24no—
107C23×C43—22no—
108C23×C43—22no—
109C23×C43#12112yes—
110C23×C43#12312yes—
111C23×C43#12412yes—
112C23×C43C22×D411yescharacteristic
113C22×D43—24no—
114C22×D43—416no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—44no—
118C22×D43—44no—
119C22×D43—48no—
120C22×D43—88no—
121C22×D43—84no—
122C22×D43—84no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—48no—
129C2×C4×C43—44no—
130C2×C4×C43—44no—
131C2×C4×C43—44no—
132C2×C4×C43#12112yes—
133C2×C4×C43#12312yes—
134C2×C4×C43#12318yes—
135C2×C4×C43#12412yes—
136C2×C4×C43#12618yes—
137C2×C4×C43AGL(1,ℤ/8)14yes—
138C2×C4×C43C22×D411yescharacteristic
139C2×C4×C43C2×#4111yescharacteristic
140C2×C4×C43C2×#4112yes—
141C2×C4×C43C2×#4112yes—
142C2×Dic43—42no—
143C2×Dic43—44no—
144C2×Dic43—84no—
145D172—28no—
146D172—44no—
147D172—48no—
148C43⋊C8—44no—
149#23628—431nomaximal, Sylow
150C22×C43—24no—
151C22×C43—22no—
152C22×C43—22no—
153C22×C43—24no—
154C22×C43#39714yes—
155C22×C43C2×#12111yescharacteristic
156C22×C43C2×#12311yescharacteristic
157C22×C43C2×#12411yescharacteristic
158C22×C43C2×AGL(1,ℤ/8)12yes—
159C22×C43#57512yes—
160C2×D43—44no—
161C2×D43—48no—
162C2×D43—816no—
163C2×D43—84no—
164C2×D43—82no—
165C2×D43—82no—
166C4×C43—24no—
167C4×C43—42no—
168C4×C43—84no—
169C4×C43#39714yes—
170C4×C43C2×#12312yes—
171C4×C43C2×#12612yes—
172Dic43—82no—
173C2×#418—432no—
174C2×#390—431no—
175#2285D4311yescharacteristic, complemented
176#2073—434no—
177#2071—434no—
178#1736—432no—
179#1728—431no—
180C2×C43—24no—
181C2×C43C2×#39711yescharacteristic
182C2×C43#303612yes—
183C2×C43#309412yes—
184C2×C43#313811yescharacteristic
185C2×C43#314011yescharacteristic
186D43—84no—
187C23×D4—431no—
188C22×M16—432no—
189C2×#117C2×D4312yes—
190C22×C4⋊C4—431no—
191C22×C22⋊C4—862no—
192C22×C42C2×D4311yescharacteristic
193#418—868no—
194C2×#102—438no—
195#390—432no—
196#390—432no—
197#390—862no—
198#384C2×D4312yescomplemented
199#382C2×D4312yescomplemented
200#380—22no—
201C4×C4⋊C4—22no—
202#340—438no—
203#336—432no—
204#336—432no—
205C43#2362811yescharacteristic, complemented, Sylow
206C25—861no—
207C22×D4—434no—
208C22×D4—432no—
209C22×D4—864no—
210C22×D4—862no—
211C22×D4—864no—
212C22×D4—861no—
213C23×C4—861no—
214C23×C4C22⋊D4312yes—
215C23×C4C22×D4311yescharacteristic
216C2×M16—864no—
217C2×M16—864no—
218C2×M16—864no—
219C22×C8—434no—
220#117—24no—
221#117—24no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—432no—
225C2×C4⋊C4—864no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4C22×D4314yes—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—864no—
230C2×C22⋊C4—864no—
231C2×C22⋊C4—1728no—
232C2×C42—24no—
233C2×C42—22no—
234C2×C42C22⋊D4312yes—
235C2×C42C22×D4311yescharacteristic
236C2×C42C22×D4311yescharacteristic
237#102—8616no—
238#95—24no—
239C24—864no—
240C24—862no—
241C24—1724no—
242C24—1724no—
243C24—1722no—
244C24—1722no—
245C24C2×C22⋊D4311yescharacteristic
246C2×D4—434no—
247C2×D4—864no—
248C2×D4—8616no—
249C2×D4—862no—
250C2×D4—864no—
251C2×D4—864no—
252C2×D4—1722no—
253C2×D4—1722no—
254C2×D4—1728no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—862no—
260C22×C4—1724no—
261C22×C4—1722no—
262C22×C4#1062189814yes—
263C22×C4D4×D4312yes—
264C22×C4#1062190012yes—
265C22×C4#1062190214yes—
266C22×C4C2×C22⋊D4312yes—
267C22×C4C2×C22⋊D4312yes—
268C22×C4C2×C22⋊D4311yescharacteristic
269C22×C4C23×D4311yescharacteristic
270M16—1728no—
271C2×C8—864no—
272C2×C8—864no—
273C2×C8—864no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—44no—
277C4⋊C4—44no—
278C4⋊C4—864no—
279C4⋊C4—1722no—
280C22⋊C4—44no—
281C22⋊C4—1728no—
282C22⋊C4—1728no—
283C42—24no—
284C42—22no—
285C42—22no—
286C42—44no—
287C23—22no—
288C23—22no—
289C23—864no—
290C23—3444no—
291C23—3444no—
292C23—3448no—
293C23—17216no—
294C23—1728no—
295C23—1722no—
296C23—1722no—
297C23—1724no—
298C23—1724no—
299C23#1306329612yes—
300C23#1306330812yes—
301C23#1306331412yes—
302C23C22×C22⋊D4311yescharacteristic
303D4—868no—
304D4—1728no—
305D4—1724no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—48no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—3444no—
316C2×C4—1722no—
317C2×C4—1724no—
318C2×C4#1306329612yes—
319C2×C4#1306330812yes—
320C2×C4#1306331018yes—
321C2×C4#1306331412yes—
322C2×C4#1306332018yes—
323C2×C4#1306335014yes—
324C2×C4C2×D4×D4311yescharacteristic
325C2×C4C2×#1062190011yescharacteristic
326C2×C4C2×#1062189812yes—
327C2×C4C2×#1062190212yes—
328C8—1724no—
329C22—22no—
330C22—22no—
331C22—24no—
332C22—24no—
333C22—34416no—
334C22—3442no—
335C22—3442no—
336C22—3444no—
337C22—1724no—
338C22—1728no—
339C22#1458282514yes—
340C22C2×#1306329611yescharacteristic
341C22C2×#1306330811yescharacteristic
342C22C2×#1306331411yescharacteristic
343C22C2×#1306335012yes—
344C22#1458369712yes—
345C4—24no—
346C4—42no—
347C4—84no—
348C4—3442no—
349C4#1458282514yes—
350C4C2×#1306331012yes—
351C4C2×#1306332012yes—
352C2—24no—
353C2—3444no—
354C2C2×#1458282511yescharacteristic
355C2#1914405512yes—
356C2#1914453512yes—
357C2#1914497111yescharacteristic
358C2#1914498411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2285C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#2285D43
hypocenterC43#23628
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
3. #19136009C2semidirect
4. #19135999C2semidirect
5. #19134316C2semidirect
6. #19134289C2semidirect
7. C43×#2285C2semidirect
17. #14582661C22semidirect
18. #14582654C22semidirect
19. #14582654C22semidirect
22. C43×#384C22semidirect
23. C43×#382C22semidirect
175. #2285D43semidirect
198. #384C2×D43semidirect
199. #382C2×D43semidirect
205. C43#23628semidirect

Maximal subgroups

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

subgroupindex
C2×#145829032
C2×#145828012
#191360092
#191359992
#191343162
#191342892
C43×#22852
#2362843