Finite Group Databasebeta

← #25126408

Subgroups — #25126408

Order 11008.

1314 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582942C212yesmaximal, complemented
2C2×#14582903C212yesmaximal
3C2×#14582801C211yesmaximal, characteristic
4#19136129C212yesmaximal, complemented
5#19136124C212yesmaximal, complemented
6#19136119C214yesmaximal, complemented
7#19134289C211yesmaximal, characteristic, complemented
8C43×#2285C211yesmaximal, characteristic, complemented
9C23×D172C2211yescharacteristic
10C22×#10621877C2212yes—
11C22×C4⋊Dic43C2211yescharacteristic
12C22×(C2×D43)⋊C4—22no—
13#14582942—28no—
14C2×#13063258C2214yescomplemented
15C2×#13063256C2214yescomplemented
16#14582903—28no—
17C2×#13063245C2214yes—
18C2×#13063245C2214yes—
19#14582801—22no—
20#14582801C2212yes—
21#14582801C2212yes—
22#14582654C2212yescomplemented
23#14582654C2212yescomplemented
24C2×#117×C43C2212yes—
25C22×C42×C43C2211yescharacteristic
26C43×#384C2211yescharacteristic, complemented
27C43×#384C2211yescharacteristic, complemented
28C43×#382C2212yescomplemented
29C43×#380—22no—
30C4×C4⋊C4×C43—22no—
31C24×D43—21no—
32C22×D172—24no—
33C22×D172—24no—
34C22×D172—21no—
35C22×D172—22no—
36C22×D172Q814yes—
37C22×D172C2312yes—
38C23×Dic43—21no—
39C2×#10621877—24no—
40C2×#10621877—24no—
41C2×#10621877D418yes—
42C22×C43⋊C8C2314yes—
43C2×C4⋊Dic43—24no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43C2312yes—
46C2×(C2×D43)⋊C4—24no—
47C2×(C2×D43)⋊C4—24no—
48C2×(C2×D43)⋊C4—48no—
49#13063258—28no—
50#13063256—28no—
51#13063245—28no—
52#13063245—28no—
53C23×C4×C43D412yes—
54C23×C4×C43C2311yescharacteristic
55#117×C43—24no—
56#117×C43—24no—
57C2×C4⋊C4×C43—22no—
58C2×C4⋊C4×C43—22no—
59C2×C4⋊C4×C43C2312yes—
60C2×C4⋊C4×C43C2312yes—
61C2×C22⋊C4×C43—22no—
62C2×C42×C43—24no—
63C2×C42×C43—22no—
64C2×C42×C43D412yes—
65C2×C42×C43C2311yescharacteristic
66C2×C42×C43C2311yescharacteristic
67#95×C43—24no—
68C24×C43C2×D411yescharacteristic
69C23×D43—24no—
70C23×D43—22no—
71C23×D43—44no—
72C23×D43—44no—
73C23×D43—42no—
74C23×D43—42no—
75C22×C4×C43—24no—
76C22×C4×C43—24no—
77C22×C4×C43—22no—
78C22×C4×C43—22no—
79C22×C4×C43—42no—
80C22×C4×C43C2×D414yes—
81C22×C4×C43C2×D412yes—
82C22×C4×C43C2×D412yes—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×Q812yes—
85C22×C4×C43#4112yes—
86C22×C4×C43#4114yes—
87C22×C4×C43C2411yescharacteristic
88C22×Dic43—22no—
89C22×Dic43—44no—
90C22×Dic43—42no—
91C2×D172—24no—
92C2×D172—22no—
93C2×D172—216no—
94C2×D172—24no—
95C2×D172—24no—
96C2×D172—42no—
97C2×D172—48no—
98C2×D172—42no—
99C2×D172C2×Q814yes—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—44no—
105C4⋊C4×C43—44no—
106C22⋊C4×C43—44no—
107C42×C43—24no—
108C42×C43—22no—
109C42×C43—22no—
110C42×C43—44no—
111(C2×D43)⋊C4—48no—
112(C2×D43)⋊C4—48no—
113C4⋊Dic43—24no—
114C4⋊Dic43—42no—
115#10621877—216no—
116C2×C43⋊C8—24no—
117C2×C43⋊C8—24no—
118C2×C43⋊C8C2×D418yes—
119C23×C43—22no—
120C23×C43—22no—
121C23×C43C22⋊Q812yes—
122C23×C43#12312yes—
123C23×C43#12712yes—
124C23×C43C22×D411yescharacteristic
125C22×D43—24no—
126C22×D43—416no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—44no—
130C22×D43—44no—
131C22×D43—48no—
132C22×D43—88no—
133C22×D43—84no—
134C22×D43—84no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—48no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—44no—
144C2×C4×C43—44no—
145C2×C4×C43C22⋊Q812yes—
146C2×C4×C43C22⋊Q818yes—
147C2×C4×C43#12312yes—
148C2×C4×C43#12318yes—
149C2×C4×C43#12712yes—
150C2×C4×C43AGL(1,ℤ/8)14yes—
151C2×C4×C43C22×D412yes—
152C2×C4×C43C22×Q811yescharacteristic
153C2×C4×C43C2×#4112yes—
154C2×C4×C43C2×#4111yescharacteristic
155C2×Dic43—42no—
156C2×Dic43—44no—
157C2×Dic43—84no—
158D172—28no—
159D172—44no—
160D172—48no—
161C43⋊C8—28no—
162#23731—431nomaximal, Sylow
163C22×C43—24no—
164C22×C43—24no—
165C22×C43—22no—
166C22×C43—22no—
167C22×C43#39914yes—
168C22×C43C2×C22⋊Q811yescharacteristic
169C22×C43C2×#12311yescharacteristic
170C22×C43C2×#12711yescharacteristic
171C22×C43C2×AGL(1,ℤ/8)12yes—
172C22×C43#57512yes—
173C2×D43—48no—
174C2×D43—44no—
175C2×D43—816no—
176C2×D43—84no—
177C2×D43—82no—
178C2×D43—82no—
179C4×C43—24no—
180C4×C43—42no—
181C4×C43—82no—
182C4×C43—82no—
183C4×C43#39914yes—
184C4×C43C2×C22⋊Q812yes—
185C4×C43C2×#12312yes—
186Dic43—82no—
187C2×#428—432no—
188C2×#418—432no—
189C2×#390—431no—
190#2285D4311yescharacteristic, complemented
191#2094—432no—
192#2093—432no—
193#2092—434no—
194#1728—431no—
195C2×C43—24no—
196C2×C43C2×#39911yescharacteristic
197C2×C43#307712yes—
198C2×C43#309412yes—
199C2×C43#315111yescharacteristic
200C2×C43#315311yescharacteristic
201D43—84no—
202C23×D4—431no—
203C22×M16—432no—
204C2×#117C2×D4312yes—
205C22×C4⋊C4—431no—
206C22×C22⋊C4—862no—
207C22×C42C2×D4311yescharacteristic
208#428—868no—
209C2×#107—434no—
210C2×#106—434no—
211#418—868no—
212C2×#102—434no—
213C2×#102—434no—
214#390—432no—
215#390—432no—
216#390—862no—
217#384C2×D4311yescharacteristic, complemented
218#384C2×D4311yescharacteristic, complemented
219#382C2×D4312yescomplemented
220#380—22no—
221C4×C4⋊C4—22no—
222#336—432no—
223#336—432no—
224C43#2373111yescharacteristic, complemented, Sylow
225C25—861no—
226C22×D4—434no—
227C22×D4—432no—
228C22×D4—864no—
229C22×D4—864no—
230C22×D4—862no—
231C22×D4—861no—
232C23×C4—861no—
233C23×C4C22⋊D4312yes—
234C23×C4C22×D4311yescharacteristic
235C2×M16—438no—
236C2×M16—864no—
237C2×M16—864no—
238C22×C8—434no—
239#117—24no—
240#117—24no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—432no—
244C2×C4⋊C4—864no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4C22×D4312yes—
247C2×C4⋊C4C22×D4312yes—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—864no—
250C2×C22⋊C4—864no—
251C2×C22⋊C4—1728no—
252C2×C42—24no—
253C2×C42—22no—
254C2×C42C22⋊D4312yes—
255C2×C42C22×D4311yescharacteristic
256C2×C42C22×D4311yescharacteristic
257#107—868no—
258#106—868no—
259#102—868no—
260#102—868no—
261#95—24no—
262C24—864no—
263C24—862no—
264C24—1724no—
265C24—1724no—
266C24—1722no—
267C24—1722no—
268C24C2×C22⋊D4311yescharacteristic
269C2×D4—434no—
270C2×D4—864no—
271C2×D4—8616no—
272C2×D4—864no—
273C2×D4—864no—
274C2×D4—862no—
275C2×D4—1722no—
276C2×D4—1728no—
277C2×D4—1722no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—862no—
284C22×C4—1724no—
285C22×C4—1722no—
286C22×C4#1062189814yes—
287C22×C4D4×D4314yes—
288C22×C4Q8×D4312yes—
289C22×C4#1062190212yes—
290C22×C4C2×C22⋊D4312yes—
291C22×C4C2×C22⋊D4312yes—
292C22×C4C2×C22⋊D4311yescharacteristic
293C22×C4C23×D4311yescharacteristic
294M16—8616no—
295C2×C8—438no—
296C2×C8—864no—
297C2×C8—864no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—44no—
303C4⋊C4—44no—
304C4⋊C4—864no—
305C4⋊C4—1722no—
306C22⋊C4—44no—
307C22⋊C4—1728no—
308C22⋊C4—1728no—
309C42—24no—
310C42—22no—
311C42—22no—
312C42—44no—
313C23—22no—
314C23—22no—
315C23—864no—
316C23—3448no—
317C23—3444no—
318C23—3444no—
319C23—17216no—
320C23—1728no—
321C23—1722no—
322C23—1724no—
323C23—1722no—
324C23—1724no—
325C23#1306330112yes—
326C23#1306330812yes—
327C23#1306332112yes—
328C23C22×C22⋊D4311yescharacteristic
329D4—868no—
330D4—1728no—
331D4—1724no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—48no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—44no—
342C2×C4—3444no—
343C2×C4—1724no—
344C2×C4—1722no—
345C2×C4#1306330112yes—
346C2×C4#1306330318yes—
347C2×C4#1306330812yes—
348C2×C4#1306331018yes—
349C2×C4#1306332112yes—
350C2×C4#1306335014yes—
351C2×C4C2×D4×D4312yes—
352C2×C4C2×Q8×D4311yescharacteristic
353C2×C4C2×#1062189812yes—
354C2×C4C2×#1062190211yescharacteristic
355C8—868no—
356C22—24no—
357C22—22no—
358C22—22no—
359C22—24no—
360C22—34416no—
361C22—3444no—
362C22—3442no—
363C22—3442no—
364C22—1724no—
365C22—1728no—
366C22#1458283414yes—
367C22C2×#1306330111yescharacteristic
368C22C2×#1306330811yescharacteristic
369C22C2×#1306332111yescharacteristic
370C22C2×#1306335012yes—
371C22#1458369712yes—
372C4—24no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4—3442no—
377C4#1458283414yes—
378C4C2×#1306330312yes—
379C4C2×#1306331012yes—
380C2—24no—
381C2—3444no—
382C2C2×#1458283411yescharacteristic
383C2#1914438812yes—
384C2#1914453512yes—
385C2#1914504811yescharacteristic
386C2#1914506311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2285C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#2285D43
hypocenterC43#23731
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
1. C2×#14582942C2semidirect
4. #19136129C2semidirect
5. #19136124C2semidirect
6. #19136119C2semidirect
7. #19134289C2semidirect
8. C43×#2285C2semidirect
14. C2×#13063258C22semidirect
15. C2×#13063256C22semidirect
22. #14582654C22semidirect
23. #14582654C22semidirect
26. C43×#384C22semidirect
27. C43×#384C22semidirect
28. C43×#382C22semidirect
190. #2285D43semidirect
217. #384C2×D43semidirect
218. #384C2×D43semidirect
219. #382C2×D43semidirect
224. C43#23731semidirect

Maximal subgroups

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

subgroupindex
C2×#145829422
C2×#145829032
C2×#145828012
#191361292
#191361242
#191361192
#191342892
C43×#22852
#2373143