Finite Group Databasebeta

← #11868091

Subgroups — #11868091

Order 1152.

699 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#575C211yesmaximal, characteristic, complemented
2C2×#63512C211yesmaximal, characteristic, complemented
3C2×#63512C211yesmaximal, characteristic, complemented
4#10589921C211yesmaximal, characteristic, complemented
5#10588915C211yesmaximal, characteristic, complemented
6#10588884C214yesmaximal, complemented
7#10588880C214yesmaximal, complemented
8C2×#63383C211yesmaximal, characteristic, complemented
9#10588799C211yesmaximal, characteristic, complemented
10#84002—31nomaximal
11C2×C9×#41C2211yescharacteristic
12C2×C9×#41C2211yescharacteristic
13C22×D36C2211yescharacteristic
14C9×#137—21no—
15C9×#137C2212yescomplemented
16C9×AGL(1,ℤ/8)—21no—
17C9×AGL(1,ℤ/8)C2212yescomplemented
18C9×#135—22no—
19C2×C9×M16C2211yescharacteristic
20#63512—22no—
21#63512—22no—
22#63512—22no—
23#63512C2214yes—
24#63510—22no—
25#63510C2214yescomplemented
26C2×#3675—21no—
27C2×#3675C2212yescomplemented
28C2×#3673—21no—
29C2×#3673C2212yescomplemented
30C2×#3667—22no—
31C2×#3667C2211yescharacteristic
32C2×#3667C2211yescharacteristic
33C2×#3667C2211yescharacteristic
34#63394C2212yescomplemented
35#63391C2212yescomplemented
36#63383C2214yescomplemented
37#63381C2214yescomplemented
38C3×#575D311yescharacteristic
39C2×#949—31no—
40C2×#949—31no—
41#5819—31no—
42#5237—31no—
43#5203—34no—
44#5199—34no—
45C2×#823—31no—
46#5124—31no—
47C23×D9—21no—
48C9×#41—21no—
49C9×#41—21no—
50C9×#41—21no—
51C9×#41—21no—
52C9×#41—21no—
53C9×#41—21no—
54C9×#41D412yes—
55C9×#41C2312yes—
56C2×Q8×C9D411yescharacteristic
57C2×Q8×C9C2311yescharacteristic
58C2×D4×C9—21no—
59C2×D4×C9—21no—
60C2×D4×C9D411yescharacteristic
61C2×D4×C9C2311yescharacteristic
62C22×C4×C9—21no—
63C22×C4×C9—21no—
64C22×C4×C9C2311yescharacteristic
65C2×D36—21no—
66C2×D36—21no—
67C2×D36—21no—
68C2×D36—21no—
69C2×D36—21no—
70C2×D36C2312yes—
71C9×Q16—22no—
72C9×SD16—22no—
73C9×SD16—22no—
74C9×D8—22no—
75C9×M16—21no—
76C9×M16C2312yes—
77C2×C8×C9—21no—
78#3675—24no—
79#3675—24no—
80#3673—24no—
81#3673—24no—
82#3667—21no—
83#3667—21no—
84#3667—24no—
85#3667D412yes—
86#3667D412yes—
87#3667C2312yes—
88#3667C2312yes—
89C2×C9⋊C8—21no—
90C2×C9⋊C8—21no—
91C2×C9⋊C8—24no—
92C2×C9⋊C8C2312yes—
93#3068—91noSylow
94C2×C3×#41C2×D311yescharacteristic
95C2×C3×#41C2×D311yescharacteristic
96C22×D12—31no—
97C3×#137—21no—
98C3×#137C2×D312yes—
99C3×AGL(1,ℤ/8)—21no—
100C3×AGL(1,ℤ/8)C2×D312yes—
101C3×#135—22no—
102C2×C3×M16C2×D311yescharacteristic
103#949—34no—
104#949—62no—
105#949—62no—
106#949—62no—
107#948—34no—
108#948—62no—
109C2×#215—32no—
110C2×#215—61no—
111C2×#213—32no—
112C2×#213—61no—
113C2×#208—31no—
114C2×#208—31no—
115C2×#208—31no—
116C2×#208—62no—
117#836—32no—
118#833—32no—
119#823—34no—
120#822—34no—
121C23×C9—21no—
122C23×C9—21no—
123C23×C9#4111yescharacteristic
124C22×D9—22no—
125C22×D9—41no—
126C22×D9—41no—
127C22×D9—82no—
128Q8×C9—21no—
129Q8×C9—21no—
130Q8×C9—21no—
131Q8×C9C2×D412yes—
132D4×C9—22no—
133D4×C9—22no—
134D4×C9—21no—
135D4×C9—21no—
136D4×C9—21no—
137D4×C9—41no—
138D4×C9—41no—
139D4×C9C2×D412yes—
140C2×C4×C9—21no—
141C2×C4×C9—22no—
142C2×C4×C9—22no—
143C2×C4×C9—21no—
144C2×C4×C9—41no—
145C2×C4×C9—41no—
146C2×C4×C9C2×D411yescharacteristic
147C2×C4×C9C2×D411yescharacteristic
148C2×C4×C9C2×D411yescharacteristic
149C2×C4×C9C2×D411yescharacteristic
150C2×C4×C9#4111yescharacteristic
151C2×C4×C9C2411yescharacteristic
152D36—22no—
153D36—22no—
154D36—41no—
155D36—41no—
156C8×C9—22no—
157C9⋊C8—22no—
158C9⋊C8—22no—
159C9⋊C8C2×D414yes—
160#575D911yescharacteristic, complemented
161C2×AGL(1,ℤ/8)—91no—
162C2×AGL(1,ℤ/8)—91no—
163#568—91no—
164#472—94no—
165#471—94no—
166#430—91no—
167#413—91no—
168C2×#100—91no—
169C23×D3—61no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41#6712yes—
177C3×#41C22×D312yes—
178C2×C3×Q8#6711yescharacteristic
179C2×C3×Q8C22×D311yescharacteristic
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4#6711yescharacteristic
183C2×C3×D4C22×D311yescharacteristic
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4C22×D311yescharacteristic
187C2×D12—32no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C3×Q16—22no—
194C3×SD16—22no—
195C3×SD16—22no—
196C3×D8—22no—
197C3×M16—21no—
198C3×M16C22×D312yes—
199C2×C3×C8—21no—
200#215—64no—
201#215—64no—
202#213—64no—
203#213—64no—
204#208—32no—
205#208—32no—
206#208—32no—
207#208—32no—
208#208—64no—
209#208—61no—
210#208—61no—
211C2×C3⋊C8—32no—
212C2×C3⋊C8—64no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C22×C9—22no—
216C22×C9—41no—
217C22×C9—41no—
218C22×C9—81no—
219C22×C9—81no—
220C22×C9#12111yescharacteristic
221C22×C9#12111yescharacteristic
222C22×C9C2×#4111yescharacteristic
223C2×D9—42no—
224C2×D9—82no—
225C2×D9—82no—
226C2×D9—82no—
227C4×C9—22no—
228C4×C9—41no—
229C4×C9#12111yescharacteristic
230C4×C9#12111yescharacteristic
231C4×C9C22×D411yescharacteristic
232C4×C9C22×D411yescharacteristic
233C2×#41C2×D911yescharacteristic
234C2×#41C2×D911yescharacteristic
235C22×D4—91no—
236#137—21no—
237#137C2×D912yescomplemented
238AGL(1,ℤ/8)—21no—
239AGL(1,ℤ/8)—94no—
240AGL(1,ℤ/8)—182no—
241AGL(1,ℤ/8)—182no—
242AGL(1,ℤ/8)—182no—
243AGL(1,ℤ/8)C2×D912yescomplemented
244#135—22no—
245C2×SD16—92no—
246C2×SD16—181no—
247C2×D8—92no—
248C2×D8—181no—
249#131—94no—
250#131—182no—
251C2×M16—91no—
252C2×M16—91no—
253C2×M16—91no—
254C2×M16—182no—
255C2×M16C2×D911yescharacteristic
256#108—94no—
257#101—92no—
258#100—92no—
259#100—94no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3#23711yescharacteristic
263C22×D3—62no—
264C22×D3—121no—
265C22×D3—121no—
266C22×D3—242no—
267C3×Q8—21no—
268C3×Q8—21no—
269C3×Q8—21no—
270C3×Q8C2×#6712yes—
271C3×D4—22no—
272C3×D4—22no—
273C3×D4—21no—
274C3×D4—21no—
275C3×D4—21no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4C2×#6712yes—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×C3×C4C2×#6711yescharacteristic
290C2×C3×C4C23×D311yescharacteristic
291D12—62no—
292D12—62no—
293D12—121no—
294D12—121no—
295C3×C8—22no—
296C3⋊C8—34no—
297C3⋊C8—62no—
298C3⋊C8—62no—
299C2×C9—21no—
300C2×C9—21no—
301C2×C9—21no—
302C2×C9—42no—
303C2×C9—81no—
304C2×C9C2×#12111yescharacteristic
305D9—82no—
306C24—181no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—21no—
312#41—21no—
313#41#61112yes—
314#41C22×D912yes—
315C2×Q8#61111yescharacteristic
316C2×Q8C22×D911yescharacteristic
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—92no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C2×D4#61111yescharacteristic
326C2×D4C22×D911yescharacteristic
327C22×C4—21no—
328C22×C4—21no—
329C22×C4C22×D911yescharacteristic
330Q16—22no—
331SD16—22no—
332SD16—22no—
333SD16—184no—
334SD16—184no—
335D8—22no—
336D8—184no—
337D8—184no—
338M16—21no—
339M16—92no—
340M16—92no—
341M16—92no—
342M16—92no—
343M16—184no—
344M16—181no—
345M16—181no—
346M16C22×D912yes—
347C2×C8—21no—
348C2×C8—92no—
349C2×C8—184no—
350C2×C8—181no—
351C2×C8—181no—
352C22×C3—22no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3#93911yescharacteristic
358C22×C3#93911yescharacteristic
359C22×C3C2×#23711yescharacteristic
360C2×D3—122no—
361C2×D3—242no—
362C2×D3—242no—
363C2×D3—242no—
364C3×C4—22no—
365C3×C4—41no—
366C3×C4#93911yescharacteristic
367C3×C4#93911yescharacteristic
368C3×C4C2×D3×D411yescharacteristic
369C3×C4C22×#6711yescharacteristic
370C9#306811yescharacteristic, complemented, Sylow
371C23—21no—
372C23—21no—
373C23—182no—
374C23—361no—
375C23—361no—
376C23—722no—
377C23#369911yescharacteristic
378Q8—21no—
379Q8—21no—
380Q8—21no—
381Q8C2×#61112yes—
382D4—22no—
383D4—22no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—41no—
388D4—41no—
389D4—182no—
390D4—182no—
391D4—361no—
392D4—361no—
393D4C2×#61112yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4D4×D911yescharacteristic
401C2×C4D4×D911yescharacteristic
402C2×C4#369911yescharacteristic
403C2×C4C2×#61111yescharacteristic
404C2×C4C2×#61111yescharacteristic
405C2×C4C23×D911yescharacteristic
406C8—22no—
407C8—94no—
408C8—182no—
409C8—182no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—42no—
414C2×C3—81no—
415C2×C3C2×#93911yescharacteristic
416D3—242no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—81no—
422C22—362no—
423C22—722no—
424C22—722no—
425C22—722no—
426C22#6350111yescharacteristic
427C22#6350111yescharacteristic
428C22C2×#369911yescharacteristic
429C4—22no—
430C4—41no—
431C4#6350111yescharacteristic
432C4#6350111yescharacteristic
433C4C2×D4×D911yescharacteristic
434C4C22×#61111yescharacteristic
435C3#8400211yescharacteristic
436C2—21no—
437C2—21no—
438C2—21no—
439C2—42no—
440C2—81no—
441C2—722no—
442C2C2×#6350111yescharacteristic
subgroupG/H
centerC2C2×#63501
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#575C2
socleC2×C3C2×#939
hypercenter#575D9
hypocenterC9#3068
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C9×#575C2semidirect
2. C2×#63512C2semidirect
3. C2×#63512C2semidirect
4. #10589921C2semidirect
5. #10588915C2semidirect
6. #10588884C2semidirect
7. #10588880C2semidirect
8. C2×#63383C2semidirect
9. #10588799C2semidirect
15. C9×#137C22semidirect
17. C9×AGL(1,ℤ/8)C22semidirect
25. #63510C22semidirect
27. C2×#3675C22semidirect
29. C2×#3673C22semidirect
34. #63394C22semidirect
35. #63391C22semidirect
36. #63383C22semidirect
37. #63381C22semidirect
160. #575D9semidirect
237. #137C2×D9semidirect
243. AGL(1,ℤ/8)C2×D9semidirect
370. C9#3068semidirect

Maximal subgroups

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

subgroupindex
C9×#5752
C2×#635122
#105899212
#105889152
#105888842
#105888802
C2×#633832
#105887992
#840023