Finite Group Databasebeta

← #11868085

Subgroups — #11868085

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×#568C211yesmaximal, characteristic, complemented
2#10589925C211yesmaximal, characteristic, complemented
3C2×#63512C211yesmaximal, characteristic, complemented
4C2×#63470C211yesmaximal, characteristic, complemented
5#10588823C214yesmaximal, complemented
6#10588822C214yesmaximal, complemented
7#10588814C211yesmaximal, characteristic, complemented
8C2×#63383C211yesmaximal, characteristic, complemented
9#10588800C211yesmaximal, characteristic, complemented
10#83814—31nomaximal
11C2×C9×#41C2211yescharacteristic
12C2×#3697C2211yescharacteristic
13C22×D36C2211yescharacteristic
14C9×#131—22no—
15C9×#131C2214yescomplemented
16C2×C9×M16—22no—
17C2×C9×M16C2211yescharacteristic
18C2×C9×M16C2211yescharacteristic
19#63513—22no—
20#63512—22no—
21#63512C2214yes—
22#63512C2212yescomplemented
23#63511C2212yescomplemented
24#63505—21no—
25C2×#3675—21no—
26#63495—21no—
27C2×#3673—21no—
28C2×#3667C2211yescharacteristic
29C2×#3667C2211yescharacteristic
30#63470—22no—
31#63470—22no—
32C2×D72C2212yescomplemented
33C2×#3664C2212yescomplemented
34#63383C2214yescomplemented
35#63383C2212yescomplemented
36#63382C2212yescomplemented
37#63372C2214yescomplemented
38C3×#568D311yescharacteristic
39#5822—31no—
40C2×#949—31no—
41C2×#908—31no—
42#5142—34no—
43#5141—34no—
44#5132—31no—
45C2×#823—31no—
46#5125—31no—
47C23×D9—21no—
48C9×#41—21no—
49C9×#41—21no—
50C9×#41D412yes—
51C9×#41C2312yes—
52C2×Q8×C9D411yescharacteristic
53C2×D4×C9—21no—
54C2×D4×C9D411yescharacteristic
55C22×C4×C9—21no—
56C22×C4×C9C2311yescharacteristic
57C2×#611—21no—
58#3697—21no—
59#3697—21no—
60#3697—21no—
61#3697—21no—
62C2×D36—21no—
63C2×D36—21no—
64C2×D36—21no—
65C2×D36—21no—
66C2×D36—21no—
67C2×D36C2312yes—
68C2×D36C2311yescharacteristic
69C2×C4×D9—21no—
70C2×Dic18C2311yescharacteristic
71C9×M16—21no—
72C9×M16—24no—
73C9×M16D412yes—
74C9×M16D412yes—
75C9×M16C2312yes—
76C2×C8×C9—21no—
77C2×C8×C9—24no—
78C2×C8×C9C2312yes—
79#3675—24no—
80#3675—22no—
81#3674—22no—
82#3673—24no—
83#3673—22no—
84#3672—22no—
85#3667—21no—
86#3667—21no—
87#3667C2312yes—
88#3667C2312yes—
89C2×C9⋊C8—21no—
90C2×C9⋊C8—21no—
91D72—24no—
92#3664—24no—
93#3068—91noSylow
94C2×C3×#41C2×D311yescharacteristic
95C2×#235—31no—
96C22×D12—31no—
97C3×#131—22no—
98C3×#131C2×D314yes—
99C2×C3×M16—22no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C2×D311yescharacteristic
102#951—32no—
103#950—62no—
104#949—34no—
105#949—32no—
106#949—62no—
107#942—61no—
108C2×#215—61no—
109#932—61no—
110C2×#213—61no—
111C2×#208—31no—
112C2×#208—31no—
113#908—62no—
114#908—62no—
115C2×D24—32no—
116C2×#204—32no—
117#824—32no—
118#823—34no—
119#823—32no—
120#819—34no—
121C23×C9—21no—
122C23×C9#4111yescharacteristic
123C22×D9—21no—
124C22×D9—22no—
125C22×D9—41no—
126C22×D9—41no—
127C22×D9—82no—
128Q8×C9—21no—
129Q8×C9C2×D412yes—
130D4×C9—22no—
131D4×C9—22no—
132D4×C9—21no—
133D4×C9C2×D412yes—
134C2×C4×C9—21no—
135C2×C4×C9—22no—
136C2×C4×C9—22no—
137C2×C4×C9C2×D411yescharacteristic
138C2×C4×C9C2×D411yescharacteristic
139C2×C4×C9C2×D411yescharacteristic
140C2×C4×C9C2×D411yescharacteristic
141C2×C4×C9#4111yescharacteristic
142C2×C4×C9C2411yescharacteristic
143#611—41no—
144#611—41no—
145C2×Dic9—21no—
146D36—22no—
147D36—21no—
148D36—22no—
149D36—21no—
150D36—41no—
151D36—41no—
152C4×D9—41no—
153C4×D9—41no—
154Dic18—21no—
155Dic18—21no—
156C8×C9—22no—
157C8×C9C2×D414yes—
158C9⋊C8—22no—
159C9⋊C8—22no—
160#575—91no—
161C2×AGL(1,ℤ/8)—91no—
162C2×AGL(1,ℤ/8)—91no—
163#568D911yescharacteristic, complemented
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×#41D1212yes—
173C3×#41C22×D312yes—
174C2×C3×Q8D1211yescharacteristic
175C2×C3×D4—21no—
176C2×C3×D4D1211yescharacteristic
177C22×C3×C4—21no—
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—61no—
180#235—61no—
181#235—61no—
182#235—61no—
183#235—61no—
184C2×D12—32no—
185C2×D12—31no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×C4×D3—61no—
192C2×Dic6—31no—
193C3×M16—21no—
194C3×M16—24no—
195C3×M16#6712yes—
196C3×M16#6712yes—
197C3×M16C22×D312yes—
198C2×C3×C8—21no—
199C2×C3×C8—24no—
200C2×C3×C8C22×D312yes—
201#216—62no—
202#215—64no—
203#215—62no—
204#214—62no—
205#213—64no—
206#213—62no—
207#208—32no—
208#208—32no—
209#208—61no—
210#208—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213D24—64no—
214#204—64no—
215C22×C9—22no—
216C22×C9—41no—
217C22×C9—81no—
218C22×C9#12111yescharacteristic
219C22×C9#12111yescharacteristic
220C22×C9C2×#4111yescharacteristic
221C2×D9—41no—
222C2×D9—42no—
223C2×D9—82no—
224C2×D9—82no—
225C2×D9—81no—
226C2×D9—82no—
227C4×C9—22no—
228C4×C9#12111yescharacteristic
229C4×C9#12111yescharacteristic
230C4×C9C22×D411yescharacteristic
231C4×C9C22×D411yescharacteristic
232Dic9—41no—
233C2×#41—91no—
234C2×#41C2×D911yescharacteristic
235C22×D4—91no—
236#137—92no—
237#137—181no—
238AGL(1,ℤ/8)—94no—
239AGL(1,ℤ/8)—92no—
240AGL(1,ℤ/8)—182no—
241AGL(1,ℤ/8)—181no—
242AGL(1,ℤ/8)—182no—
243AGL(1,ℤ/8)—182no—
244#135—182no—
245C2×SD16—92no—
246C2×SD16—181no—
247C2×D8—92no—
248C2×D8—181no—
249#131—22no—
250#131C2×D914yescomplemented
251C2×M16—22no—
252C2×M16—91no—
253C2×M16—91no—
254C2×M16C2×D911yescharacteristic
255C2×M16C2×D911yescharacteristic
256#108—94no—
257#101—92no—
258#100—94no—
259#100—92no—
260C23×C3—21no—
261C23×C3#23511yescharacteristic
262C22×D3—61no—
263C22×D3—62no—
264C22×D3—121no—
265C22×D3—121no—
266C22×D3—242no—
267C3×Q8—21no—
268C3×Q8C2×D1212yes—
269C3×D4—22no—
270C3×D4—22no—
271C3×D4—21no—
272C3×D4C2×D1212yes—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4C2×D1211yescharacteristic
277C2×C3×C4C2×D1211yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×C3×C4C23×D311yescharacteristic
282#67—121no—
283#67—121no—
284C2×Dic3—61no—
285D12—62no—
286D12—61no—
287D12—62no—
288D12—61no—
289D12—121no—
290D12—121no—
291C4×D3—121no—
292C4×D3—121no—
293Dic6—61no—
294Dic6—61no—
295C3×C8—22no—
296C3×C8C2×#6714yes—
297C3⋊C8—62no—
298C3⋊C8—62no—
299C2×C9—21no—
300C2×C9—21no—
301C2×C9—21no—
302C2×C9—42no—
303C2×C9C2×#12111yescharacteristic
304D9—81no—
305D9—82no—
306C24—181no—
307#41—21no—
308#41—21no—
309#41—181no—
310#41—181no—
311#41—181no—
312#41—181no—
313#41D3612yes—
314#41C22×D912yes—
315C2×Q8—91no—
316C2×Q8D3611yescharacteristic
317C2×D4—21no—
318C2×D4—91no—
319C2×D4—92no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C2×D4—181no—
326C2×D4D3611yescharacteristic
327C22×C4—21no—
328C22×C4—181no—
329C22×C4C22×D911yescharacteristic
330Q16—182no—
331SD16—184no—
332SD16—182no—
333SD16—182no—
334SD16—184no—
335D8—184no—
336D8—182no—
337D8—184no—
338M16—21no—
339M16—24no—
340M16—92no—
341M16—92no—
342M16—181no—
343M16—181no—
344M16#61112yes—
345M16#61112yes—
346M16C22×D912yes—
347C2×C8—21no—
348C2×C8—24no—
349C2×C8—181no—
350C2×C8—181no—
351C2×C8C22×D912yes—
352C22×C3—22no—
353C22×C3—41no—
354C22×C3—81no—
355C22×C3#93011yescharacteristic
356C22×C3#93011yescharacteristic
357C22×C3C2×#23511yescharacteristic
358C2×D3—121no—
359C2×D3—122no—
360C2×D3—242no—
361C2×D3—242no—
362C2×D3—242no—
363C2×D3—241no—
364C3×C4—22no—
365C3×C4#93011yescharacteristic
366C3×C4#93011yescharacteristic
367C3×C4C22×D1211yescharacteristic
368C3×C4C22×#6711yescharacteristic
369Dic3—121no—
370C9#306811yescharacteristic, complemented, Sylow
371C23—21no—
372C23—181no—
373C23—182no—
374C23—361no—
375C23—361no—
376C23—722no—
377C23#369711yescharacteristic
378Q8—21no—
379Q8—181no—
380Q8—181no—
381Q8C2×D3612yes—
382D4—22no—
383D4—22no—
384D4—21no—
385D4—182no—
386D4—181no—
387D4—181no—
388D4—182no—
389D4—361no—
390D4—361no—
391D4—361no—
392D4—361no—
393D4C2×D3612yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—181no—
398C2×C4—361no—
399C2×C4—361no—
400C2×C4C2×D3611yescharacteristic
401C2×C4C2×D3611yescharacteristic
402C2×C4#369711yescharacteristic
403C2×C4C2×#61111yescharacteristic
404C2×C4C2×#61111yescharacteristic
405C2×C4C23×D911yescharacteristic
406C8—22no—
407C8—182no—
408C8—182no—
409C8C2×#61114yes—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—42no—
414C2×C3C2×#93011yescharacteristic
415D3—242no—
416D3—241no—
417C22—22no—
418C22—41no—
419C22—81no—
420C22—361no—
421C22—362no—
422C22—722no—
423C22—721no—
424C22—722no—
425C22—722no—
426C22#6349211yescharacteristic
427C22#6349211yescharacteristic
428C22C2×#369711yescharacteristic
429C4—22no—
430C4—361no—
431C4#6349211yescharacteristic
432C4#6349211yescharacteristic
433C4C22×D3611yescharacteristic
434C4C22×#61111yescharacteristic
435C3#8381411yescharacteristic
436C2—21no—
437C2—21no—
438C2—21no—
439C2—42no—
440C2—722no—
441C2—721no—
442C2C2×#6349211yescharacteristic
subgroupG/H
centerC2C2×#63492
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#568C2
socleC2×C3C2×#930
hypercenter#568D9
hypocenterC9#3068
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
1. C9×#568C2semidirect
2. #10589925C2semidirect
3. C2×#63512C2semidirect
4. C2×#63470C2semidirect
5. #10588823C2semidirect
6. #10588822C2semidirect
7. #10588814C2semidirect
8. C2×#63383C2semidirect
9. #10588800C2semidirect
15. C9×#131C22semidirect
22. #63512C22semidirect
23. #63511C22semidirect
32. C2×D72C22semidirect
33. C2×#3664C22semidirect
34. #63383C22semidirect
35. #63383C22semidirect
36. #63382C22semidirect
37. #63372C22semidirect
163. #568D9semidirect
250. #131C2×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×#5682
#105899252
C2×#635122
C2×#634702
#105888232
#105888222
#105888142
C2×#633832
#105888002
#838143