Finite Group Databasebeta

← #11896113

Subgroups — #11896113

Order 1152.

537 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#559C211yesmaximal, characteristic, complemented
2#10589681C211yesmaximal, characteristic, complemented
3#10588754C211yesmaximal, characteristic
4#10588751C211yesmaximal, characteristic, complemented
5#10588738C211yesmaximal, characteristic, complemented
6#10588738C211yesmaximal, characteristic, complemented
7#10588735C211yesmaximal, characteristic, complemented
8#10588734C211yesmaximal, characteristic, complemented
9#10588709C211yesmaximal, characteristic, complemented
10#10588704C211yesmaximal, characteristic, complemented
11#10588701C211yesmaximal, characteristic, complemented
12#10588697C211yesmaximal, characteristic, complemented
13C4×#3673C211yesmaximal, characteristic, complemented
14#10588692C211yesmaximal, characteristic, complemented
15#10588690C211yesmaximal, characteristic, complemented
16#83714—31nomaximal
17C9×#127C2211yescharacteristic
18C9×#124—21no—
19C9×#124C2211yescharacteristic
20C9×#124C2211yescharacteristic
21C9×#123—21no—
22C9×#123—21no—
23C4×Q8×C9C2211yescharacteristic
24C4×Q8×C9C2211yescharacteristic
25C4×D4×C9—21no—
26C4×D4×C9C2211yescharacteristic
27C4×D4×C9C2211yescharacteristic
28#63508—21no—
29C2×#3675C2211yescharacteristic
30C2×#3673C2211yescharacteristic
31C2×#3673C2211yescharacteristic
32#63458—21no—
33#63458—21no—
34C4⋊C4×D9—21no—
35C4×D36C2211yescharacteristic
36C4×D36C2211yescharacteristic
37C4×D36C2211yescharacteristic
38#63432C2211yescharacteristic
39#63432C2211yescharacteristic
40#63431C2211yescharacteristic
41#63395C2211yescharacteristic
42#63395C2211yescharacteristic
43#63395C2211yescharacteristic
44#63392C2211yescharacteristic
45#63392C2211yescharacteristic
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic
48#63392C2211yescharacteristic
49#63392C2211yescharacteristic
50#63369C2211yescharacteristic
51#63367C2211yescharacteristic
52#63366C2211yescharacteristic
53#63366C2211yescharacteristic
54C4⋊(C9⋊C8)C2211yescharacteristic
55C4⋊(C9⋊C8)C2211yescharacteristic
56C4⋊(C9⋊C8)C2211yescharacteristic
57#63362C2211yescharacteristic
58#63362C2211yescharacteristic
59C4×C9⋊C8C2211yescharacteristic
60C3×#559D311yescharacteristic
61#5579—31no—
62#5072—31no—
63#5071—31no—
64#5057—31no—
65#5057—31no—
66#5056—31no—
67#5055—31no—
68#5026—31no—
69#5024—31no—
70#5022—31no—
71#5014—31no—
72C4×#213—31no—
73#5009—31no—
74#5007—31no—
75C2×Q8×C9D411yescharacteristic
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9—21no—
78C2×D4×C9—21no—
79C2×D4×C9C2311yescharacteristic
80C2×D4×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C22×C4×C9—21no—
83C2×D36C2311yescharacteristic
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×Dic18—21no—
88C9×C4⋊C4—21no—
89C9×C4⋊C4D411yescharacteristic
90C9×C4⋊C4D411yescharacteristic
91C9×C4⋊C4D411yescharacteristic
92C9×C4⋊C4C2311yescharacteristic
93C9×C22⋊C4—21no—
94C9×C22⋊C4—21no—
95C9×C22⋊C4—21no—
96C9×C22⋊C4—21no—
97C9×C22⋊C4—21no—
98C9×C22⋊C4—21no—
99C42×C9—21no—
100C42×C9C2311yescharacteristic
101C42×C9C2311yescharacteristic
102C42×C9C2311yescharacteristic
103#3675—22no—
104#3673—22no—
105#3673—22no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109C4⋊Dic9—21no—
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117C2×C9⋊C8C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119C2×C9⋊C8C2311yescharacteristic
120C2×C9⋊C8C2311yescharacteristic
121#3370—91noSylow
122C3×#127C2×D311yescharacteristic
123C3×#124—21no—
124C3×#124C2×D311yescharacteristic
125C3×#124C2×D311yescharacteristic
126C3×#123—21no—
127C3×#123—21no—
128C3×C4×Q8C2×D311yescharacteristic
129C3×C4×Q8C2×D311yescharacteristic
130C3×C4×D4—21no—
131C3×C4×D4C2×D311yescharacteristic
132C3×C4×D4C2×D311yescharacteristic
133#946—61no—
134C2×#215—31no—
135C2×#213—31no—
136C2×#213—31no—
137#896—61no—
138#896—61no—
139D3×C4⋊C4—61no—
140C4×D12—31no—
141C4×D12—31no—
142C4×D12—31no—
143#870—31no—
144#870—31no—
145#869—31no—
146#835—31no—
147#835—31no—
148#835—31no—
149#832—31no—
150#832—31no—
151#832—31no—
152#832—31no—
153#832—31no—
154#832—31no—
155#809—31no—
156#808—31no—
157#807—31no—
158#807—31no—
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—31no—
162#803—31no—
163#803—31no—
164C4×C3⋊C8—31no—
165C23×C9—21no—
166C23×C9—21no—
167C22×D9—21no—
168Q8×C9—21no—
169Q8×C9—21no—
170Q8×C9—41no—
171D4×C9—21no—
172D4×C9—21no—
173D4×C9—21no—
174D4×C9—21no—
175D4×C9—42no—
176D4×C9—81no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—81no—
180C2×C4×C9—81no—
181C2×C4×C9C2×D411yescharacteristic
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2411yescharacteristic
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191D36—21no—
192D36#4112yes—
193C4×D9—42no—
194C4×D9—81no—
195C4×D9—81no—
196Dic18—81no—
197C9⋊C8—21no—
198C9⋊C8—21no—
199C9⋊C8—21no—
200C9⋊C8—21no—
201#559D911yescharacteristic, complemented
202#554—91no—
203#490—91no—
204#489—91no—
205#488—91no—
206#479—91no—
207#478—91no—
208#474—91no—
209#463—91no—
210#463—91no—
211#459—91no—
212#446—91no—
213#442—91no—
214#440—91no—
215C4×D8—91no—
216C2×C3×Q8#6711yescharacteristic
217C2×C3×Q8C22×D311yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4C22×D311yescharacteristic
221C2×C3×D4C22×D311yescharacteristic
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C2×D12—31no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×Dic6—61no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4#6711yescharacteristic
231C3×C4⋊C4#6711yescharacteristic
232C3×C4⋊C4#6711yescharacteristic
233C3×C4⋊C4C22×D311yescharacteristic
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C42—21no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#215—62no—
245#213—62no—
246#213—62no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—31no—
262C22×C9—41no—
263C22×C9—41no—
264C22×C9—41no—
265C22×C9—41no—
266C22×C9—41no—
267C22×C9—41no—
268C22×C9C22×D411yescharacteristic
269C2×D9—22no—
270C2×D9—41no—
271C2×D9—41no—
272C4×C9—21no—
273C4×C9—21no—
274C4×C9—21no—
275C4×C9—21no—
276C4×C9—21no—
277C4×C9—21no—
278C4×C9—41no—
279C4×C9—41no—
280C4×C9C2×#4111yescharacteristic
281C4×C92−1+411yescharacteristic
282Dic9—41no—
283Dic9—41no—
284Dic9—41no—
285C2×SD16—91no—
286C2×D8—91no—
287C2×D8—91no—
288C4⋊Q8—91no—
289#127C2×D911yescharacteristic
290#125—91no—
291#125—91no—
292#124—21no—
293#124C2×D911yescharacteristic
294#124C2×D911yescharacteristic
295#123—21no—
296#123—21no—
297C22⋊Q8—181no—
298C22⋊Q8—181no—
299C22⋊Q8—181no—
300C4×Q8C2×D911yescharacteristic
301C4×Q8C2×D911yescharacteristic
302C4×D4—21no—
303C4×D4—91no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4C2×D911yescharacteristic
307C4×D4C2×D911yescharacteristic
308C2×C4⋊C4—181no—
309#107—91no—
310#107—91no—
311#106—91no—
312C4⋊C8—91no—
313C4⋊C8—91no—
314C4⋊C8—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#102—91no—
319#102—91no—
320#102—91no—
321#102—91no—
322#102—91no—
323#102—91no—
324#102—91no—
325#97—91no—
326#97—91no—
327C4×C8—91no—
328C23×C3—21no—
329C23×C3—21no—
330C22×D3—61no—
331C3×Q8—21no—
332C3×Q8—21no—
333C3×Q8—41no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—42no—
339C3×D4—81no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—81no—
343C2×C3×C4—81no—
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354D12—32no—
355D12—61no—
356C4×D3—122no—
357C4×D3—241no—
358C4×D3—241no—
359Dic6—241no—
360C3⋊C8—61no—
361C3⋊C8—61no—
362C3⋊C8—61no—
363C3⋊C8—61no—
364C2×C9—81no—
365C2×C9—81no—
366C2×C9#54811yescharacteristic
367C2×C9#57511yescharacteristic
368C2×C9#57611yescharacteristic
369D9—42no—
370C2×Q8—181no—
371C2×Q8#61111yescharacteristic
372C2×Q8C22×D911yescharacteristic
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—91no—
376C2×D4C22×D911yescharacteristic
377C2×D4C22×D911yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—181no—
381C22×C4—181no—
382C22×C4—181no—
383SD16—182no—
384D8—182no—
385D8—182no—
386C2×C8—91no—
387C2×C8—91no—
388C2×C8—91no—
389C2×C8—91no—
390C4⋊C4—21no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4#61111yescharacteristic
400C4⋊C4#61111yescharacteristic
401C4⋊C4#61111yescharacteristic
402C4⋊C4C22×D911yescharacteristic
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—21no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—181no—
412C42—21no—
413C42C22×D911yescharacteristic
414C42C22×D911yescharacteristic
415C42C22×D911yescharacteristic
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3C22×#6711yescharacteristic
423C2×D3—62no—
424C2×D3—121no—
425C2×D3—121no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4D3×#4111yescharacteristic
435C3×C4#101011yescharacteristic
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439C9#337011yescharacteristic, complemented, Sylow
440C23—21no—
441C23—21no—
442C23—181no—
443Q8—21no—
444Q8—21no—
445Q8—41no—
446Q8—721no—
447D4—21no—
448D4—21no—
449D4—21no—
450D4—21no—
451D4—42no—
452D4—81no—
453D4—92no—
454D4—181no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—362no—
463C2×C4—721no—
464C2×C4—721no—
465C2×C4C2×#61111yescharacteristic
466C2×C4C2×#61111yescharacteristic
467C2×C4C2×#61111yescharacteristic
468C2×C4C2×#61111yescharacteristic
469C2×C4C2×#61111yescharacteristic
470C2×C4C2×#61111yescharacteristic
471C2×C4C23×D911yescharacteristic
472C8—181no—
473C8—181no—
474C8—181no—
475C8—181no—
476C2×C3—81no—
477C2×C3—81no—
478C2×C3#582211yescharacteristic
479C2×C3#583111yescharacteristic
480C2×C3#583511yescharacteristic
481D3—122no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—182no—
489C22—361no—
490C22—361no—
491C22C22×#61111yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—41no—
499C4—41no—
500C4—361no—
501C4—361no—
502C4—361no—
503C4#41×D911yescharacteristic
504C4#6371611yescharacteristic
505C3#8371411yescharacteristic
506C2—81no—
507C2—81no—
508C2—362no—
509C2#1058992511yescharacteristic
510C2#1058993311yescharacteristic
511C2#1058993711yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#559C2
socleC22×C3C22×#67
prime radical#10588754C2
hypercenter#559D9
hypocenterC9#3370
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. C9×#559C2semidirect
2. #10589681C2semidirect
4. #10588751C2semidirect
5. #10588738C2semidirect
6. #10588738C2semidirect
7. #10588735C2semidirect
8. #10588734C2semidirect
9. #10588709C2semidirect
10. #10588704C2semidirect
11. #10588701C2semidirect
12. #10588697C2semidirect
13. C4×#3673C2semidirect
14. #10588692C2semidirect
15. #10588690C2semidirect
201. #559D9semidirect
439. C9#3370semidirect

Maximal subgroups

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

subgroupindex
C9×#5592
#105896812
#105887542
#105887512
#105887382
#105887352
#105887342
#105887092
#105887042
#105887012
#105886972
C4×#36732
#105886922
#105886902
#837143