Finite Group Databasebeta

← #11866166

Subgroups — #11866166

Order 1152.

789 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 789 conjugacy classes of subgroups — too many to draw. Only its 166 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
1#10589907C211yesmaximal, characteristic, complemented
2C22×#3673C211yesmaximal, characteristic, complemented
3C2×#63470C211yesmaximal, characteristic, complemented
4#10589623C211yesmaximal, characteristic, complemented
5C9×#418C211yesmaximal, characteristic, complemented
6#10588803C211yesmaximal, characteristic, complemented
7#10588683C211yesmaximal, characteristic, complemented
8#10588467C214yesmaximal, complemented
9#10588466C214yesmaximal, complemented
10#78944—31nomaximal
11C22×D4×C9C2211yescharacteristic
12C2×#3697C2211yescharacteristic
13C22×D36C2211yescharacteristic
14C2×C9×M16C2211yescharacteristic
15C9×#117C2211yescharacteristic
16#63515—22no—
17#63502C2212yescomplemented
18#63500—22no—
19#63498C2212yescomplemented
20C2×#3673—24no—
21C2×#3673C2214yes—
22#63488C2211yescharacteristic
23C22×C9⋊C8C2211yescharacteristic
24#63470—24no—
25C2×D72C2212yescomplemented
26C2×#3664C2212yescomplemented
27#63455C2214yescomplemented
28C22⋊C4×D9—22no—
29C4×D36—22no—
30C9×#102C2214yescomplemented
31Dic9⋊C8C2214yescomplemented
32#63369C2212yescomplemented
33#63368C2212yescomplemented
34#5805—31no—
35C22×#213—31no—
36C2×#908—31no—
37#5521—31no—
38C3×#418D311yescharacteristic
39#5119—31no—
40#5002—31no—
41#4787—34no—
42#4786—34no—
43C24×C9—21no—
44C23×D9—21no—
45C2×D4×C9—22no—
46C2×D4×C9—21no—
47C2×D4×C9—22no—
48C2×D4×C9C2312yes—
49C22×C4×C9C2311yescharacteristic
50C2×#611—21no—
51C2×#611—24no—
52#3697—22no—
53#3697—22no—
54C2×D36—21no—
55C2×D36—22no—
56C2×D36D414yescomplemented
57C2×D36C2311yescharacteristic
58C2×D36C2312yes—
59C2×C4×D9—21no—
60C2×C4×D9—24no—
61C2×Dic18C2311yescharacteristic
62C9×M16—22no—
63C2×C8×C9C2312yes—
64C9×C4⋊C4C2312yes—
65C9×C22⋊C4—21no—
66C42×C9—21no—
67#3676—24no—
68#3676D412yes—
69#3673—28no—
70(C2×D9)⋊C4—24no—
71C4⋊Dic9D412yes—
72C4×Dic9C2312yes—
73C2×C9⋊C8—22no—
74C2×C9⋊C8C2312yes—
75D72—24no—
76#3664—24no—
77#3041—91noSylow
78C22×C3×D4C2×D311yescharacteristic
79C2×#235—31no—
80C22×D12—31no—
81C2×C3×M16C2×D311yescharacteristic
82C3×#117C2×D311yescharacteristic
83#953—62no—
84#940—32no—
85#938—62no—
86#936—32no—
87C2×#213—34no—
88C2×#213—64no—
89#926—31no—
90C22×C3⋊C8—31no—
91#908—64no—
92C2×D24—32no—
93C2×#204—32no—
94#893—34no—
95D3×C22⋊C4—62no—
96C4×D12—62no—
97C3×#102C2×D314yes—
98Dic3⋊C8—34no—
99#810—32no—
100#809—32no—
101C23×C9—22no—
102C23×C9—42no—
103C23×C9—82no—
104C23×C9C2×D411yescharacteristic
105C22×D9—22no—
106C22×D9—24no—
107C22×D9—21no—
108C22×D9—82no—
109D4×C9—22no—
110D4×C9—22no—
111D4×C9—42no—
112C2×C4×C9—22no—
113C2×C4×C9C2×D411yescharacteristic
114C2×C4×C9C2×D412yes—
115C2×C4×C9#4112yes—
116C2×C4×C9C2411yescharacteristic
117#611—42no—
118#611—84no—
119C2×Dic9—21no—
120C2×Dic9C2×D414yes—
121D36—24no—
122D36—21no—
123D36—22no—
124D36—21no—
125D36C2×D414yes—
126C4×D9—42no—
127C4×D9—84no—
128Dic18—21no—
129Dic18—21no—
130C8×C9—22no—
131C9⋊C8—22no—
132C2×AGL(1,ℤ/8)—91no—
133C22×D8—91no—
134#535—91no—
135#518—91no—
136#463—94no—
137#459—94no—
138#424—91no—
139#418D911yescharacteristic, complemented
140#416—91no—
141C24×C3—21no—
142C23×D3—61no—
143C2×C3×D4—22no—
144C2×C3×D4—22no—
145C2×C3×D4—21no—
146C2×C3×D4C22×D312yes—
147C22×C3×C4C22×D311yescharacteristic
148C2×#67—64no—
149C2×#67—61no—
150#235—62no—
151#235—62no—
152C2×D12—34no—
153C2×D12—32no—
154C2×D12—31no—
155C2×D12—62no—
156C2×D12—61no—
157C2×C4×D3—61no—
158C2×C4×D3—64no—
159C2×Dic6—31no—
160C3×M16—22no—
161C2×C3×C8C22×D312yes—
162C3×C4⋊C4C22×D312yes—
163C3×C22⋊C4—21no—
164C3×C42—21no—
165#217—32no—
166#217—64no—
167#213—68no—
168(C2×D3)⋊C4—64no—
169C4⋊Dic3—32no—
170C4×Dic3—32no—
171C2×C3⋊C8—32no—
172C2×C3⋊C8—62no—
173D24—64no—
174#204—64no—
175C22×C9—22no—
176C22×C9—42no—
177C22×C9—44no—
178C22×C9—84no—
179C22×C9#12112yes—
180C22×C9C22×D411yescharacteristic
181C2×D9—24no—
182C2×D9—44no—
183C2×D9—41no—
184C2×D9—42no—
185C2×D9—84no—
186C4×C9—42no—
187C4×C9#12112yes—
188C4×C9C22×D411yescharacteristic
189C4×C9C2×#4111yescharacteristic
190Dic9—24no—
191Dic9—41no—
192C2×#41—91no—
193C22×D4—91no—
194C22×D4C2×D911yescharacteristic
195AGL(1,ℤ/8)—184no—
196C2×SD16—92no—
197C2×D8—94no—
198C2×D8—92no—
199C2×D8—184no—
200C2×M16C2×D911yescharacteristic
201C22×C8—91no—
202#127—92no—
203#124—92no—
204#121—182no—
205#120—182no—
206C4×D4—94no—
207C4×D4—182no—
208#117—91no—
209#117C2×D911yescharacteristic
210C2×C22⋊C4—182no—
211C4⋊C8—94no—
212#103—92no—
213#102—92no—
214#102C2×D914yescomplemented
215C23×C3—22no—
216C23×C3—42no—
217C23×C3—82no—
218C23×C3D3×D411yescharacteristic
219C22×D3—62no—
220C22×D3—64no—
221C22×D3—61no—
222C22×D3—242no—
223C3×D4—22no—
224C3×D4—22no—
225C3×D4—42no—
226C2×C3×C4—22no—
227C2×C3×C4#23512yes—
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D412yes—
230C2×C3×C4C23×D311yescharacteristic
231#67—122no—
232#67—244no—
233C2×Dic3—34no—
234C2×Dic3—61no—
235D12—34no—
236D12—64no—
237D12—62no—
238D12—61no—
239D12—61no—
240C4×D3—122no—
241C4×D3—244no—
242Dic6—61no—
243Dic6—61no—
244C3×C8—22no—
245C3⋊C8—62no—
246C2×C9—22no—
247C2×C9—82no—
248C2×C9C2×#12111yescharacteristic
249C2×C9#57612yes—
250D9—44no—
251D9—81no—
252C24—21no—
253C24—181no—
254#41—182no—
255#41—182no—
256C2×Q8—91no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—94no—
261C2×D4—92no—
262C2×D4—91no—
263C2×D4—184no—
264C2×D4—181no—
265C2×D4—182no—
266C2×D4—181no—
267C2×D4C22×D912yes—
268C22×C4—184no—
269C22×C4—181no—
270C22×C4C22×D911yescharacteristic
271SD16—184no—
272D8—184no—
273D8—188no—
274M16—22no—
275C2×C8—92no—
276C2×C8—182no—
277C2×C8C22×D912yes—
278C4⋊C4—92no—
279C4⋊C4C22×D912yes—
280C22⋊C4—21no—
281C22⋊C4—92no—
282C22⋊C4—184no—
283C22⋊C4—184no—
284C42—21no—
285C42—92no—
286C22×C3—22no—
287C22×C3—42no—
288C22×C3—44no—
289C22×C3—84no—
290C22×C3#88412yes—
291C22×C3C2×D3×D411yescharacteristic
292C2×D3—64no—
293C2×D3—124no—
294C2×D3—121no—
295C2×D3—122no—
296C2×D3—244no—
297C3×C4—42no—
298C3×C4#88412yes—
299C3×C4C2×#23511yescharacteristic
300C3×C4C2×D3×D411yescharacteristic
301Dic3—64no—
302Dic3—121no—
303C9#304111yescharacteristic, complemented, Sylow
304C23—22no—
305C23—42no—
306C23—82no—
307C23—182no—
308C23—184no—
309C23—181no—
310C23—722no—
311C23D4×D911yescharacteristic
312Q8—181no—
313Q8—181no—
314D4—22no—
315D4—22no—
316D4—42no—
317D4—94no—
318D4—184no—
319D4—182no—
320D4—181no—
321D4—181no—
322D4—362no—
323D4—724no—
324C2×C4—22no—
325C2×C4—94no—
326C2×C4—181no—
327C2×C4—362no—
328C2×C4—724no—
329C2×C4#369712yes—
330C2×C4D4×D911yescharacteristic
331C2×C4D4×D912yes—
332C2×C4C23×D911yescharacteristic
333C8—22no—
334C8—182no—
335C2×C3—22no—
336C2×C3—82no—
337C2×C3C2×#88411yescharacteristic
338C2×C3#577412yes—
339D3—124no—
340D3—241no—
341C22—22no—
342C22—42no—
343C22—44no—
344C22—84no—
345C22—184no—
346C22—364no—
347C22—361no—
348C22—362no—
349C22—724no—
350C22#6344612yes—
351C22C2×D4×D911yescharacteristic
352C4—42no—
353C4—184no—
354C4—361no—
355C4#6344612yes—
356C4C2×#369711yescharacteristic
357C4C2×D4×D911yescharacteristic
358C3#7894411yescharacteristic
359C2—22no—
360C2—82no—
361C2—364no—
362C2—721no—
363C2C2×#6344611yescharacteristic
364C2#1058987612yes—
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#418C2
socleC22×C3C2×D3×D4
hypercenter#418D9
hypocenterC9#3041
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #10589907C2semidirect
2. C22×#3673C2semidirect
3. C2×#63470C2semidirect
4. #10589623C2semidirect
5. C9×#418C2semidirect
6. #10588803C2semidirect
7. #10588683C2semidirect
8. #10588467C2semidirect
9. #10588466C2semidirect
17. #63502C22semidirect
19. #63498C22semidirect
25. C2×D72C22semidirect
26. C2×#3664C22semidirect
27. #63455C22semidirect
30. C9×#102C22semidirect
31. Dic9⋊C8C22semidirect
32. #63369C22semidirect
33. #63368C22semidirect
56. C2×D36D4semidirect
139. #418D9semidirect
214. #102C2×D9semidirect
303. C9#3041semidirect

Maximal subgroups

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

subgroupindex
#105899072
C22×#36732
C2×#634702
#105896232
C9×#4182
#105888032
#105886832
#105884672
#105884662
#789443