Finite Group Databasebeta

← #11896267

Subgroups — #11896267

Order 1152.

516 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#559C211yesmaximal, characteristic
2#10589669C211yesmaximal, characteristic, complemented
3#10588752C211yesmaximal, characteristic
4#10588751C211yesmaximal, characteristic
5#10588736C211yesmaximal, characteristic, complemented
6#10588736C211yesmaximal, characteristic, complemented
7#10588735C211yesmaximal, characteristic, complemented
8#10588734C211yesmaximal, characteristic, complemented
9#10588706C211yesmaximal, characteristic, complemented
10#10588704C211yesmaximal, characteristic, complemented
11#10588701C211yesmaximal, characteristic, complemented
12#10588694C211yesmaximal, characteristic, complemented
13C4×#3672C211yesmaximal, characteristic, complemented
14#10588692C211yesmaximal, characteristic, complemented
15#10588691C211yesmaximal, characteristic, complemented
16#83718—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#63506—21no—
29C2×#3674C2211yescharacteristic
30C2×#3672C2211yescharacteristic
31C2×#3672C2211yescharacteristic
32#63451—21no—
33#63451—21no—
34#63449—21no—
35#63432C2211yescharacteristic
36#63432C2211yescharacteristic
37#63431C2211yescharacteristic
38C4×Dic18C2211yescharacteristic
39C4×Dic18C2211yescharacteristic
40C4×Dic18C2211yescharacteristic
41#63395C2211yescharacteristic
42#63395C2211yescharacteristic
43#63395C2211yescharacteristic
44#63392C2211yescharacteristic
45#63392C2211yescharacteristic
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic
48#63392C2211yescharacteristic
49#63392C2211yescharacteristic
50#63368C2211yescharacteristic
51#63367C2211yescharacteristic
52#63367C2211yescharacteristic
53#63366C2211yescharacteristic
54C4⋊(C9⋊C8)C2211yescharacteristic
55C4⋊(C9⋊C8)C2211yescharacteristic
56C4⋊(C9⋊C8)C2211yescharacteristic
57#63362C2211yescharacteristic
58#63362C2211yescharacteristic
59C4×C9⋊C8C2211yescharacteristic
60C3×#559D311yescharacteristic
61#5567—31no—
62#5075—31no—
63#5071—31no—
64#5056—31no—
65#5055—31no—
66#5054—31no—
67#5054—31no—
68#5030—31no—
69#5024—31no—
70#5022—31no—
71#5018—31no—
72C4×#214—31no—
73#5009—31no—
74#5008—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×Dic18—21no—
84C2×Dic18C2311yescharacteristic
85C9×C4⋊C4—21no—
86C9×C4⋊C4D411yescharacteristic
87C9×C4⋊C4D411yescharacteristic
88C9×C4⋊C4D411yescharacteristic
89C9×C4⋊C4C2311yescharacteristic
90C9×C22⋊C4—21no—
91C9×C22⋊C4—21no—
92C9×C22⋊C4—21no—
93C9×C22⋊C4—21no—
94C9×C22⋊C4—21no—
95C9×C22⋊C4—21no—
96C42×C9—21no—
97C42×C9C2311yescharacteristic
98C42×C9C2311yescharacteristic
99C42×C9C2311yescharacteristic
100#3674—22no—
101#3672—22no—
102#3672—22no—
103C4⋊Dic9—21no—
104C4⋊Dic9C2311yescharacteristic
105C4⋊Dic9C2311yescharacteristic
106C4⋊Dic9C2311yescharacteristic
107Dic9⋊C4—21no—
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114C4×Dic9—21no—
115C4×Dic9—21no—
116C4×Dic9—21no—
117C2×C9⋊C8C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119C2×C9⋊C8C2311yescharacteristic
120C2×C9⋊C8C2311yescharacteristic
121#3371—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#944—61no—
134C2×#216—31no—
135C2×#214—31no—
136C2×#214—31no—
137#889—61no—
138#889—61no—
139#887—61no—
140#870—31no—
141#870—31no—
142#869—31no—
143C4×Dic6—31no—
144C4×Dic6—31no—
145C4×Dic6—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#810—31no—
156#808—31no—
157#808—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—
167Q8×C9—21no—
168Q8×C9—21no—
169Q8×C9—41no—
170D4×C9—21no—
171D4×C9—21no—
172D4×C9—21no—
173D4×C9—21no—
174D4×C9—42no—
175D4×C9—81no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—81no—
179C2×C4×C9—81no—
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2×D411yescharacteristic
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2411yescharacteristic
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191Dic18—21no—
192Dic18—42no—
193Dic18#4112yes—
194C9⋊C8—21no—
195C9⋊C8—21no—
196C9⋊C8—21no—
197C9⋊C8—21no—
198#559D911yescharacteristic
199#557—91no—
200#490—91no—
201#489—91no—
202#488—91no—
203#479—91no—
204#478—91no—
205#476—91no—
206#464—91no—
207#464—91no—
208#460—91no—
209#446—91no—
210#441—91no—
211#440—91no—
212C4×SD16—91no—
213C2×C3×Q8#6711yescharacteristic
214C2×C3×Q8C22×D311yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4C22×D311yescharacteristic
218C2×C3×D4C22×D311yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4#6711yescharacteristic
225C3×C4⋊C4#6711yescharacteristic
226C3×C4⋊C4#6711yescharacteristic
227C3×C4⋊C4C22×D311yescharacteristic
228C3×C22⋊C4—21no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C42—21no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#216—62no—
239#214—62no—
240#214—62no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247Dic3⋊C4—61no—
248Dic3⋊C4—61no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C22×C9—41no—
260C22×C9—41no—
261C22×C9—41no—
262C22×C9—41no—
263C22×C9—41no—
264C22×C9—41no—
265C22×C9C22×D411yescharacteristic
266C4×C9—21no—
267C4×C9—21no—
268C4×C9—21no—
269C4×C9—21no—
270C4×C9—21no—
271C4×C9—21no—
272C4×C9—41no—
273C4×C9—41no—
274C4×C9C2×#4111yescharacteristic
275C4×C92−1+411yescharacteristic
276Dic9—22no—
277Dic9—41no—
278Dic9—41no—
279Dic9—41no—
280C2×Q16—91no—
281C2×SD16—91no—
282C2×SD16—91no—
283C4⋊Q8—91no—
284C4⋊Q8—181no—
285#127C2×D911yescharacteristic
286#125—91no—
287#125—91no—
288#125—181no—
289#125—181no—
290#124—21no—
291#124C2×D911yescharacteristic
292#124C2×D911yescharacteristic
293#123—21no—
294#123—21no—
295C4×Q8—91no—
296C4×Q8—91no—
297C4×Q8—91no—
298C4×Q8—181no—
299C4×Q8C2×D911yescharacteristic
300C4×Q8C2×D911yescharacteristic
301C4×D4—21no—
302C4×D4C2×D911yescharacteristic
303C4×D4C2×D911yescharacteristic
304#107—91no—
305#106—91no—
306#106—91no—
307C4⋊C8—91no—
308C4⋊C8—91no—
309C4⋊C8—91no—
310#103—91no—
311#103—91no—
312#103—91no—
313#103—91no—
314#102—91no—
315#102—91no—
316#102—91no—
317#102—91no—
318#102—91no—
319#102—91no—
320#97—91no—
321#97—91no—
322C4×C8—91no—
323C23×C3—21no—
324C23×C3—21no—
325C3×Q8—21no—
326C3×Q8—21no—
327C3×Q8—41no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—42no—
333C3×D4—81no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—81no—
337C2×C3×C4—81no—
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349Dic6—32no—
350Dic6—61no—
351Dic6—122no—
352C3⋊C8—61no—
353C3⋊C8—61no—
354C3⋊C8—61no—
355C3⋊C8—61no—
356C2×C9—81no—
357C2×C9—81no—
358C2×C9#54811yescharacteristic
359C2×C9#57511yescharacteristic
360C2×C9#57711yescharacteristic
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8#61111yescharacteristic
364C2×Q8C22×D911yescharacteristic
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C22×D911yescharacteristic
368C2×D4C22×D911yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371Q16—182no—
372SD16—182no—
373SD16—182no—
374C2×C8—91no—
375C2×C8—91no—
376C2×C8—91no—
377C2×C8—91no—
378C4⋊C4—21no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4#61111yescharacteristic
391C4⋊C4#61111yescharacteristic
392C4⋊C4#61111yescharacteristic
393C4⋊C4C22×D911yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C42—21no—
401C42—181no—
402C42—181no—
403C42—181no—
404C42C22×D911yescharacteristic
405C42C22×D911yescharacteristic
406C42C22×D911yescharacteristic
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3C22×#6711yescharacteristic
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—41no—
421C3×C4—41no—
422C3×C4D3×#4111yescharacteristic
423C3×C4#101011yescharacteristic
424Dic3—62no—
425Dic3—121no—
426Dic3—121no—
427Dic3—121no—
428C9#337111yescharacteristic, complemented, Sylow
429C23—21no—
430C23—21no—
431Q8—21no—
432Q8—21no—
433Q8—41no—
434Q8—92no—
435Q8—181no—
436Q8—362no—
437D4—21no—
438D4—21no—
439D4—21no—
440D4—21no—
441D4—42no—
442D4—81no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—181no—
451C2×C4C2×#61111yescharacteristic
452C2×C4C2×#61111yescharacteristic
453C2×C4C2×#61111yescharacteristic
454C2×C4C2×#61111yescharacteristic
455C2×C4C2×#61111yescharacteristic
456C2×C4C2×#61111yescharacteristic
457C2×C4C23×D911yescharacteristic
458C8—181no—
459C8—181no—
460C8—181no—
461C8—181no—
462C2×C3—81no—
463C2×C3—81no—
464C2×C3#582211yescharacteristic
465C2×C3#583111yescharacteristic
466C2×C3#583611yescharacteristic
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22C22×#61111yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—41no—
481C4—41no—
482C4—182no—
483C4—361no—
484C4—361no—
485C4—361no—
486C4#41×D911yescharacteristic
487C4#6371611yescharacteristic
488C3#8371811yescharacteristic
489C2—81no—
490C2—81no—
491C2#1058992511yescharacteristic
492C2#1058993311yescharacteristic
493C2#1058993811yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#559C2
socleC22×C3C22×#67
prime radicalC3×#127C2×D3
hypercenter#559D9
hypocenterC9#3371
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
2. #10589669C2semidirect
5. #10588736C2semidirect
6. #10588736C2semidirect
7. #10588735C2semidirect
8. #10588734C2semidirect
9. #10588706C2semidirect
10. #10588704C2semidirect
11. #10588701C2semidirect
12. #10588694C2semidirect
13. C4×#3672C2semidirect
14. #10588692C2semidirect
15. #10588691C2semidirect
428. C9#3371semidirect

Maximal subgroups

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

subgroupindex
C9×#5592
#105896692
#105887522
#105887512
#105887362
#105887352
#105887342
#105887062
#105887042
#105887012
#105886942
C4×#36722
#105886922
#105886912
#837183