Finite Group Databasebeta

← #11874466

Subgroups — #11874466

Order 1152.

984 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63473C214yesmaximal, complemented
2#10589818C211yesmaximal, characteristic, complemented
3D9×#127C211yesmaximal, characteristic, complemented
4C9×#493C211yesmaximal, characteristic, complemented
5#10588834C214yesmaximal, complemented
6#10588755C211yesmaximal, characteristic, complemented
7#10588753C211yesmaximal, characteristic, complemented
8#10588375C211yesmaximal, characteristic, complemented
9C4×#3663C211yesmaximal, characteristic, complemented
10#81783—31nomaximal
11C2×#3699C2212yes—
12C2×D4×D9—22no—
13C2×D4×D9C2212yes—
14C2×C9×D8C2214yescomplemented
15C9×#127C2211yescharacteristic
16C9×#127C2211yescharacteristic, complemented
17#63502—22no—
18#63502C2212yes—
19#63500—22no—
20#63498C2212yescomplemented
21D4×Dic9—22no—
22C2×#3673C2214yescomplemented
23C2×#3672C2214yescomplemented
24#63473—216no—
25C2×#3664C2214yescomplemented
26C2×#3663C2212yes—
27#63436C2211yescharacteristic
28C42×D9C2211yescharacteristic
29#63431C2211yescharacteristic, complemented
30C4×C8×C9C2211yescharacteristic, complemented
31#63375C2212yescomplemented
32C4×C9⋊C8C2211yescharacteristic, complemented
33C2×#911—34no—
34#5716—31no—
35D3×#127—31no—
36C3×#493D311yescharacteristic
37#5154—34no—
38#5076—31no—
39#5073—31no—
40#4693—31no—
41C4×ΓL(1,𝔽25)—31no—
42C23×D9—22no—
43C2×D4×C9—22no—
44C2×D4×C9—22no—
45C2×D4×C9C2312yes—
46C2×D4×C9C2312yes—
47C2×#611—22no—
48C2×#611—22no—
49C2×#611—24no—
50C22×Dic9—22no—
51#3699—28no—
52D4×D9—28no—
53D4×D9—48no—
54C2×D36—22no—
55C2×D36C2312yes—
56C2×C4×D9D412yes—
57C2×C4×D9C2311yescharacteristic
58C2×Dic18C2312yes—
59C9×D8—28no—
60C2×C8×C9C2312yes—
61C42×C9C2311yescharacteristic
62#3676—24no—
63#3673—28no—
64#3672—28no—
65C4⋊Dic9—22no—
66C4×Dic9D412yes—
67C4×Dic9C2311yescharacteristic
68C2×C9⋊C8C2312yes—
69#3664—28no—
70#3663D418yescomplemented
71#3151—91noSylow
72C2×#237—32no—
73C2×D3×D4—32no—
74C2×D3×D4—62no—
75C2×C3×D8C2×D314yes—
76C3×#127C2×D311yescharacteristic
77C3×#127C2×D311yescharacteristic
78#940—32no—
79#940—62no—
80#938—62no—
81#936—32no—
82D4×Dic3—62no—
83C2×#214—34no—
84C2×#213—34no—
85#911—616no—
86C2×#204—34no—
87C2×ΓL(1,𝔽25)—32no—
88#874—31no—
89C42×D3—31no—
90#869—31no—
91C3×C4×C8C2×D311yescharacteristic
92#815—32no—
93C4×C3⋊C8—31no—
94C23×C9—22no—
95C23×C9—22no—
96C22×D9—22no—
97C22×D9—48no—
98C22×D9—44no—
99C22×D9C2×D411yescharacteristic
100D4×C9—24no—
101D4×C9—24no—
102D4×C9—44no—
103D4×C9—44no—
104C2×C4×C9C2×D412yes—
105C2×C4×C9C2411yescharacteristic
106#611—48no—
107#611—44no—
108#611—44no—
109C2×Dic9—22no—
110C2×Dic9—44no—
111C2×Dic9C2×D412yes—
112C2×Dic9C2×D411yescharacteristic
113D36—24no—
114D36—44no—
115C4×D9—24no—
116C4×D9C2×D414yes—
117Dic18—24no—
118C8×C9C2×D414yescomplemented
119C9⋊C8C2×D414yescomplemented
120C2×AGL(1,ℤ/8)—94no—
121#532—91no—
122C2×#127—91no—
123#496—94no—
124#493—91no—
125#493D911yescharacteristic, complemented
126#492—91no—
127#492—91no—
128C4×M16—91no—
129C23×D3—62no—
130C2×C3×D4—22no—
131C2×C3×D4—22no—
132C2×C3×D4C22×D312yes—
133C2×C3×D4C22×D312yes—
134C2×#67—64no—
135C2×#67—62no—
136C2×#67—62no—
137C22×Dic3—62no—
138#237—68no—
139D3×D4—68no—
140D3×D4—128no—
141C2×D12—32no—
142C2×D12—62no—
143C2×C4×D3—31no—
144C2×C4×D3—32no—
145C2×Dic6—32no—
146C3×D8—28no—
147C2×C3×C8C22×D312yes—
148C3×C42C22×D311yescharacteristic
149#217—64no—
150#214—68no—
151#213—68no—
152C4⋊Dic3—62no—
153C4×Dic3—32no—
154C4×Dic3—31no—
155C2×C3⋊C8—32no—
156#204—68no—
157ΓL(1,𝔽25)—38no—
158C22×C9—42no—
159C22×C9—42no—
160C22×C9—44no—
161C22×C9—44no—
162C22×C9C22×D411yescharacteristic
163C2×D9—22no—
164C2×D9—42no—
165C2×D9—44no—
166C2×D9—88no—
167C2×D9#12712yes—
168C4×C9AGL(1,ℤ/8)14yescomplemented
169C4×C9C22×D412yes—
170Dic9—22no—
171Dic9—42no—
172Dic9#12712yes—
173C2×#41—92no—
174C22×D4—92no—
175C22×D4—182no—
176AGL(1,ℤ/8)—1816no—
177C2×SD16—94no—
178C2×SD16—94no—
179C2×D8—94no—
180C2×D8C2×D914yescomplemented
181C2×M16—92no—
182C4⋊Q8—91no—
183#127—92no—
184#127—91no—
185#127—182no—
186#127C2×D911yescharacteristic
187#127C2×D911yescharacteristic, complemented
188#124—92no—
189#121—182no—
190C4×D4—182no—
191C2×C42—91no—
192#97—92no—
193C4×C8—91no—
194C4×C8C2×D911yescharacteristic, complemented
195C23×C3—22no—
196C23×C3—22no—
197C22×D3—31no—
198C22×D3—62no—
199C22×D3—124no—
200C22×D3—128no—
201C3×D4—24no—
202C3×D4—24no—
203C3×D4—44no—
204C3×D4—44no—
205C2×C3×C4D3×D412yes—
206C2×C3×C4C23×D311yescharacteristic
207#67—124no—
208#67—128no—
209#67—124no—
210C2×Dic3—31no—
211C2×Dic3—32no—
212C2×Dic3—62no—
213C2×Dic3—124no—
214D12—64no—
215D12—124no—
216C4×D3—34no—
217C4×D3—64no—
218Dic6—64no—
219C3×C8D3×D414yes—
220C3⋊C8—34no—
221C2×C9—82no—
222C2×C9—82no—
223C2×C9C2×#12711yescharacteristic
224C2×C9C2×AGL(1,ℤ/8)12yes—
225D9—22no—
226D9—82no—
227C24—182no—
228#41—188no—
229C2×Q8—92no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—92no—
233C2×D4—188no—
234C2×D4—184no—
235C2×D4—182no—
236C2×D4—182no—
237C2×D4—182no—
238C2×D4—368no—
239C2×D4C22×D912yes—
240C2×D4C22×D912yes—
241C22×C4—91no—
242C22×C4—92no—
243C22×C4—182no—
244SD16—188no—
245SD16—188no—
246D8—28no—
247D8—188no—
248M16—98no—
249C2×C8—92no—
250C2×C8C22×D912yes—
251C4⋊C4—182no—
252C22⋊C4—184no—
253C42—92no—
254C42—91no—
255C42C22×D911yescharacteristic
256C22×C3—42no—
257C22×C3—42no—
258C22×C3—44no—
259C22×C3—44no—
260C22×C3C2×D3×D411yescharacteristic
261C2×D3—32no—
262C2×D3—62no—
263C2×D3—122no—
264C2×D3—124no—
265C2×D3—248no—
266C3×C4#91114yes—
267C3×C4C2×D3×D412yes—
268Dic3—32no—
269Dic3—62no—
270Dic3—122no—
271C9#315111yescharacteristic, complemented, Sylow
272C23—22no—
273C23—22no—
274C23—91no—
275C23—182no—
276C23—364no—
277C23—368no—
278Q8—184no—
279D4—24no—
280D4—24no—
281D4—44no—
282D4—44no—
283D4—184no—
284D4—364no—
285D4—368no—
286D4—364no—
287D4—364no—
288C2×C4—91no—
289C2×C4—94no—
290C2×C4—92no—
291C2×C4—184no—
292C2×C4—182no—
293C2×C4—364no—
294C2×C4D4×D912yes—
295C2×C4C23×D911yescharacteristic
296C8—94no—
297C8D4×D914yescomplemented
298C2×C3—82no—
299C2×C3—82no—
300C2×C3D3×#12711yescharacteristic
301C2×C3C2×#91112yes—
302D3—62no—
303D3—242no—
304C22—42no—
305C22—42no—
306C22—44no—
307C22—44no—
308C22—92no—
309C22—182no—
310C22—362no—
311C22—364no—
312C22—728no—
313C22C2×D4×D911yescharacteristic
314C4—92no—
315C4—182no—
316C4—362no—
317C4#6347314yescomplemented
318C4C2×D4×D912yes—
319C3#8178311yescharacteristic
320C2—82no—
321C2—82no—
322C2—182no—
323C2—722no—
324C2D9×#12711yescharacteristic
325C2C2×#6347312yes—
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#493C2
socleC22×C3C2×D3×D4
hypercenter#493D9
hypocenterC9#3151
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C2×#63473C2semidirect
2. #10589818C2semidirect
3. D9×#127C2semidirect
4. C9×#493C2semidirect
5. #10588834C2semidirect
6. #10588755C2semidirect
7. #10588753C2semidirect
8. #10588375C2semidirect
9. C4×#3663C2semidirect
14. C2×C9×D8C22semidirect
16. C9×#127C22semidirect
20. #63498C22semidirect
22. C2×#3673C22semidirect
23. C2×#3672C22semidirect
25. C2×#3664C22semidirect
29. #63431C22semidirect
30. C4×C8×C9C22semidirect
31. #63375C22semidirect
32. C4×C9⋊C8C22semidirect
70. #3663D4semidirect
118. C8×C9C2×D4semidirect
119. C9⋊C8C2×D4semidirect
125. #493D9semidirect
168. C4×C9AGL(1,ℤ/8)semidirect
180. C2×D8C2×D9semidirect
187. #127C2×D9semidirect
194. C4×C8C2×D9semidirect
271. C9#3151semidirect
297. C8D4×D9semidirect
317. C4#63473semidirect

Maximal subgroups

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

subgroupindex
C2×#634732
#105898182
D9×#1272
C9×#4932
#105888342
#105887552
#105887532
#105883752
C4×#36632
#817833