Finite Group Databasebeta

← #11861136

Subgroups — #11861136

Order 1152.

687 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#568C211yesmaximal, characteristic, complemented
2#10589925C211yesmaximal, characteristic
3#10589847C211yesmaximal, characteristic, complemented
4C2×#63396C211yesmaximal, characteristic, complemented
5#10588825C214yesmaximal, complemented
6#10588824C214yesmaximal, complemented
7C2×#63384C211yesmaximal, characteristic, complemented
8M16×Dic9C211yesmaximal, characteristic, complemented
9#10588799C211yesmaximal, characteristic, complemented
10#83811—31nomaximal
11C2×C9×#41C2211yescharacteristic
12C2×#3697C2211yescharacteristic
13C9×#131—22no—
14C9×#131C2214yescomplemented
15C2×C9×M16—22no—
16C2×C9×M16C2211yescharacteristic
17C2×C9×M16C2211yescharacteristic
18#63513C2214yes—
19#63512C412yescomplemented
20#63511C412yescomplemented
21#63505C412yescomplemented
22#63495C412yescomplemented
23C2×C4×Dic9C2211yescharacteristic
24C2×#3667C2211yescharacteristic
25C2×#3667C2211yescharacteristic
26#63469—22no—
27M16×D9—22no—
28#63464C2214yescomplemented
29#63396C2212yescomplemented
30#63396C2212yescomplemented
31#63384C2212yescomplemented
32#63384C2212yescomplemented
33#63381C2214yescomplemented
34#63375C2212yescomplemented
35C8×Dic9C2212yescomplemented
36C3×#568D311yescharacteristic
37#5822—31no—
38#5745—31no—
39C2×#837—31no—
40#5145—34no—
41#5144—34no—
42C2×#825—31no—
43#5124—31no—
44Dic3×M16—31no—
45C9×#41—21no—
46C9×#41—21no—
47C9×#41C2×C412yes—
48C9×#41C2312yes—
49C2×Q8×C9C2×C411yescharacteristic
50C2×D4×C9—21no—
51C2×D4×C9C2×C411yescharacteristic
52C22×C4×C9—21no—
53C22×C4×C9C2311yescharacteristic
54C2×#611—21no—
55C22×Dic9—21no—
56#3697—21no—
57#3697—21no—
58#3697C2×C412yes—
59#3697C2312yes—
60C2×D36C2×C411yescharacteristic
61C2×C4×D9—21no—
62C2×Dic18C2×C411yescharacteristic
63C9×M16—21no—
64C9×M16—24no—
65C9×M16D412yes—
66C9×M16D412yes—
67C9×M16C2312yes—
68C2×C8×C9—21no—
69C2×C8×C9—24no—
70C2×C8×C9C2312yes—
71#3675C2×C414yescomplemented
72#3674C2×C414yescomplemented
73#3673C2×C414yescomplemented
74#3672C2×C414yescomplemented
75C4×Dic9—21no—
76C4×Dic9C2311yescharacteristic
77C4×Dic9C2311yescharacteristic
78#3667—21no—
79#3667C2×C412yes—
80#3667C2×C412yes—
81#3667C2312yes—
82C2×C9⋊C8—21no—
83C2×C9⋊C8C2312yes—
84#3663—24no—
85C8×D9—24no—
86#2956—91noSylow
87C2×C3×#41C2×D311yescharacteristic
88C2×#235—31no—
89C3×#131—22no—
90C3×#131C2×D314yes—
91C2×C3×M16—22no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94#951—32no—
95#950—34no—
96#949—32no—
97#942—32no—
98#932—32no—
99C2×C4×Dic3—31no—
100C2×#208—31no—
101C2×#208—31no—
102#907—62no—
103D3×M16—62no—
104#901—34no—
105#837—32no—
106#837—32no—
107#825—32no—
108#825—32no—
109#822—34no—
110#815—32no—
111C8×Dic3—32no—
112C23×C9—21no—
113C23×C9#4111yescharacteristic
114C22×D9—21no—
115Q8×C9—21no—
116Q8×C9C22×C412yes—
117D4×C9—22no—
118D4×C9—22no—
119D4×C9—21no—
120D4×C9C22×C412yes—
121C2×C4×C9—21no—
122C2×C4×C9—22no—
123C2×C4×C9—22no—
124C2×C4×C9C22×C411yescharacteristic
125C2×C4×C9C22×C411yescharacteristic
126C2×C4×C9C2×D411yescharacteristic
127C2×C4×C9C2×D411yescharacteristic
128C2×C4×C9#4111yescharacteristic
129C2×C4×C9C2411yescharacteristic
130#611—22no—
131#611—22no—
132C2×Dic9—21no—
133C2×Dic9—21no—
134C2×Dic9—21no—
135C2×Dic9—42no—
136D36—21no—
137D36C22×C412yes—
138C4×D9—22no—
139C4×D9—22no—
140Dic18—21no—
141Dic18C22×C412yes—
142C8×C9—22no—
143C8×C9C2×D414yes—
144C9⋊C8—22no—
145C9⋊C8C22×C414yes—
146#575—91no—
147#568—91no—
148#568D911yescharacteristic, complemented
149#444—94no—
150#443—94no—
151#430—91no—
152C2×#104—91no—
153C2×#104—91no—
154C4×M16—91no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41C4×D312yes—
158C3×#41C22×D312yes—
159C2×C3×Q8C4×D311yescharacteristic
160C2×C3×D4—21no—
161C2×C3×D4C4×D311yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—61no—
165C22×Dic3—61no—
166#235—32no—
167#235—32no—
168#235—61no—
169#235—61no—
170C2×D12—31no—
171C2×C4×D3—61no—
172C2×Dic6—31no—
173C3×M16—21no—
174C3×M16—24no—
175C3×M16#6712yes—
176C3×M16#6712yes—
177C3×M16C22×D312yes—
178C2×C3×C8—21no—
179C2×C3×C8—24no—
180C2×C3×C8C22×D312yes—
181#216—34no—
182#215—34no—
183#214—34no—
184#213—34no—
185C4×Dic3—31no—
186C4×Dic3—31no—
187C4×Dic3—61no—
188#208—32no—
189#208—32no—
190#208—32no—
191#208—61no—
192C2×C3⋊C8—32no—
193C2×C3⋊C8—61no—
194ΓL(1,𝔽25)—64no—
195D3×C8—64no—
196C22×C9—22no—
197C22×C9—41no—
198C22×C9—81no—
199C22×C9C4×D411yescharacteristic
200C22×C9C4×D411yescharacteristic
201C22×C9C2×#4111yescharacteristic
202C2×D9—22no—
203C2×D9—81no—
204C4×C9—22no—
205C4×C9C4×D411yescharacteristic
206C4×C9C4×D411yescharacteristic
207C4×C9C23×C411yescharacteristic
208C4×C9C22×D411yescharacteristic
209Dic9—22no—
210Dic9—22no—
211Dic9—41no—
212C2×#41—91no—
213C2×#41C2×D911yescharacteristic
214#137—92no—
215#137—92no—
216AGL(1,ℤ/8)—92no—
217AGL(1,ℤ/8)—92no—
218#135—94no—
219#131—22no—
220#131—94no—
221#131—182no—
222#131C2×D914yescomplemented
223C2×M16—22no—
224C2×M16—91no—
225C2×M16—91no—
226C2×M16—182no—
227C2×M16C2×D911yescharacteristic
228C2×M16C2×D911yescharacteristic
229C2×C42—91no—
230#108—94no—
231#104—92no—
232#104—92no—
233#104—92no—
234#104—92no—
235#97—92no—
236C4×C8—92no—
237C23×C3—21no—
238C23×C3#23511yescharacteristic
239C22×D3—61no—
240C3×Q8—21no—
241C3×Q8C2×C4×D312yes—
242C3×D4—22no—
243C3×D4—22no—
244C3×D4—21no—
245C3×D4C2×C4×D312yes—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4C2×C4×D311yescharacteristic
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4#23511yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254C2×C3×C4C23×D311yescharacteristic
255#67—62no—
256#67—62no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—122no—
261D12—32no—
262D12—61no—
263C4×D3—62no—
264C4×D3—62no—
265Dic6—32no—
266Dic6—61no—
267C3×C8—22no—
268C3×C8C2×#6714yes—
269C3⋊C8—34no—
270C3⋊C8—62no—
271C2×C9—21no—
272C2×C9—21no—
273C2×C9—21no—
274C2×C9—42no—
275C2×C9C2×C4×D411yescharacteristic
276D9—42no—
277#41—21no—
278#41—21no—
279#41—92no—
280#41—92no—
281#41—181no—
282#41—181no—
283#41C4×D912yes—
284#41C22×D912yes—
285C2×Q8—91no—
286C2×Q8C4×D911yescharacteristic
287C2×D4—21no—
288C2×D4—91no—
289C2×D4—181no—
290C2×D4C4×D911yescharacteristic
291C22×C4—21no—
292C22×C4—181no—
293C22×C4—181no—
294C22×C4C22×D911yescharacteristic
295Q16—94no—
296SD16—94no—
297SD16—94no—
298D8—94no—
299M16—21no—
300M16—24no—
301M16—92no—
302M16—92no—
303M16—92no—
304M16—181no—
305M16—184no—
306M16#61112yes—
307M16#61112yes—
308M16C22×D912yes—
309C2×C8—21no—
310C2×C8—24no—
311C2×C8—92no—
312C2×C8—181no—
313C2×C8—184no—
314C2×C8C22×D912yes—
315C42—91no—
316C42—91no—
317C42—181no—
318C22×C3—22no—
319C22×C3—41no—
320C22×C3—81no—
321C22×C3C4×#6711yescharacteristic
322C22×C3C4×#6711yescharacteristic
323C22×C3C2×#23511yescharacteristic
324C2×D3—62no—
325C2×D3—241no—
326C3×C4—22no—
327C3×C4C4×#6711yescharacteristic
328C3×C4C4×#6711yescharacteristic
329C3×C4C22×C4×D311yescharacteristic
330C3×C4C22×#6711yescharacteristic
331Dic3—62no—
332Dic3—62no—
333Dic3—121no—
334C9#295611yescharacteristic, complemented, Sylow
335C23—21no—
336C23—181no—
337C23#369711yescharacteristic
338Q8—21no—
339Q8—92no—
340Q8—181no—
341Q8C2×C4×D912yes—
342D4—22no—
343D4—22no—
344D4—21no—
345D4—92no—
346D4—182no—
347D4—182no—
348D4—181no—
349D4C2×C4×D912yes—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—181no—
358C2×C4—362no—
359C2×C4C2×C4×D911yescharacteristic
360C2×C4C2×C4×D911yescharacteristic
361C2×C4#369711yescharacteristic
362C2×C4C2×#61111yescharacteristic
363C2×C4C2×#61111yescharacteristic
364C2×C4C23×D911yescharacteristic
365C8—22no—
366C8—94no—
367C8—182no—
368C8C2×#61114yes—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—42no—
373C2×C3C2×C4×#6711yescharacteristic
374D3—122no—
375C22—22no—
376C22—41no—
377C22—81no—
378C22—182no—
379C22—721no—
380C22C4×#61111yescharacteristic
381C22C4×#61111yescharacteristic
382C22C2×#369711yescharacteristic
383C4—22no—
384C4—182no—
385C4—182no—
386C4—361no—
387C4C4×#61111yescharacteristic
388C4C4×#61111yescharacteristic
389C4C22×C4×D911yescharacteristic
390C4C22×#61111yescharacteristic
391C3#8381111yescharacteristic
392C2—21no—
393C2—21no—
394C2—21no—
395C2—42no—
396C2—362no—
397C2C2×C4×#61111yescharacteristic
subgroupG/H
centerC4C22×#611
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#568C2
socleC2×C3C2×C4×#67
prime radical#10589925C2
cosocleC2×C4×C9C24
hypercenter#568D9
hypocenterC9#2956
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C2×M16 ◁ #568

Complements

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

NH ≅ G/Ntype
1. C9×#568C2semidirect
3. #10589847C2semidirect
4. C2×#63396C2semidirect
5. #10588825C2semidirect
6. #10588824C2semidirect
7. C2×#63384C2semidirect
8. M16×Dic9C2semidirect
9. #10588799C2semidirect
14. C9×#131C22semidirect
19. #63512C4semidirect
20. #63511C4semidirect
21. #63505C4semidirect
22. #63495C4semidirect
28. #63464C22semidirect
29. #63396C22semidirect
30. #63396C22semidirect
31. #63384C22semidirect
32. #63384C22semidirect
33. #63381C22semidirect
34. #63375C22semidirect
35. C8×Dic9C22semidirect
71. #3675C2×C4semidirect
72. #3674C2×C4semidirect
73. #3673C2×C4semidirect
74. #3672C2×C4semidirect
148. #568D9semidirect
222. #131C2×D9semidirect
334. C9#2956semidirect

Maximal subgroups

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

subgroupindex
C9×#5682
#105899252
#105898472
C2×#633962
#105888252
#105888242
C2×#633842
M16×Dic92
#105887992
#838113