Finite Group Databasebeta

← #11889806

Subgroups — #11889806

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#547C211yesmaximal, characteristic
2#10589643C211yesmaximal, characteristic, complemented
3#10588918C211yesmaximal, characteristic, complemented
4#10588918C211yesmaximal, characteristic, complemented
5#10588917C211yesmaximal, characteristic, complemented
6#10588916C211yesmaximal, characteristic, complemented
7#10588763C211yesmaximal, characteristic, complemented
8#10588762C211yesmaximal, characteristic, complemented
9#10588728C211yesmaximal, characteristic, complemented
10#10588727C211yesmaximal, characteristic, complemented
11#10588725C211yesmaximal, characteristic, complemented
12#10588724C211yesmaximal, characteristic, complemented
13#10588694C211yesmaximal, characteristic, complemented
14#10588692C211yesmaximal, characteristic, complemented
15#10588688C211yesmaximal, characteristic, complemented
16#83513—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×C9×#41C2211yescharacteristic
19C9×C4⋊Q8C2211yescharacteristic
20C9×#123—21no—
21C9×#123—21no—
22C9×C22⋊Q8C2211yescharacteristic
23C9×C22⋊Q8C2211yescharacteristic
24C9×#121—21no—
25C4×D4×C9C2211yescharacteristic
26C4×D4×C9C2211yescharacteristic
27C2×C9×C4⋊C4—21no—
28C2×#3674C2211yescharacteristic
29C2×#3674C2211yescharacteristic
30#63497—21no—
31C2×#3672C2211yescharacteristic
32#63488C2211yescharacteristic
33C2×C4⋊Dic9C2211yescharacteristic
34#63486C2211yescharacteristic
35#63486C2211yescharacteristic
36C2×#3667C2211yescharacteristic
37C22×C9⋊C8C2211yescharacteristic
38#63451—21no—
39#63441—21no—
40#63439—21no—
41#63432C2211yescharacteristic
42C4×Dic18C2211yescharacteristic
43#63395C2211yescharacteristic
44#63395C2211yescharacteristic
45#63395C2211yescharacteristic
46#63395C2211yescharacteristic
47#63395C2211yescharacteristic
48#63395C2211yescharacteristic
49#63392C2211yescharacteristic
50#63392C2211yescharacteristic
51#63392C2211yescharacteristic
52#63389C2211yescharacteristic
53#63389C2211yescharacteristic
54#63368C2211yescharacteristic
55#63367C2211yescharacteristic
56#63366C2211yescharacteristic
57#63366C2211yescharacteristic
58C4⋊(C9⋊C8)C2211yescharacteristic
59#63362C2211yescharacteristic
60C3×#547D311yescharacteristic
61#5541—31no—
62#5239—31no—
63#5239—31no—
64#5233—31no—
65#5232—31no—
66#5090—31no—
67#5082—31no—
68#5052—31no—
69#5051—31no—
70#5045—31no—
71#5044—31no—
72#5018—31no—
73#5011—31no—
74#5009—31no—
75C9×#41—22no—
76C9×#41—22no—
77C9×#41—41no—
78C9×#41—41no—
79C2×Q8×C9C2311yescharacteristic
80C2×Q8×C9C2311yescharacteristic
81C2×D4×C9—21no—
82C2×D4×C9—21no—
83C2×D4×C9D411yescharacteristic
84C2×D4×C9C2311yescharacteristic
85C22×C4×C9—21no—
86C22×C4×C9—21no—
87C22×C4×C9—21no—
88C22×C4×C9C2311yescharacteristic
89C22×C4×C9C2311yescharacteristic
90C22×Dic9—21no—
91C2×Dic18C2311yescharacteristic
92C9×C4⋊C4—21no—
93C9×C4⋊C4—21no—
94C9×C4⋊C4—21no—
95C9×C4⋊C4—21no—
96C9×C4⋊C4D411yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C22⋊C4—21no—
99C9×C22⋊C4—21no—
100C9×C22⋊C4—21no—
101C9×C22⋊C4D411yescharacteristic
102C9×C22⋊C4D411yescharacteristic
103C42×C9C2311yescharacteristic
104#3676—21no—
105#3676—21no—
106#3676—21no—
107#3674—41no—
108#3674—41no—
109#3672—22no—
110C4⋊Dic9—21no—
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121#3667—41no—
122C2×C9⋊C8—41no—
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127#3315—91noSylow
128C2×C3×#41C2×D311yescharacteristic
129C2×C3×#41C2×D311yescharacteristic
130C3×C4⋊Q8C2×D311yescharacteristic
131C3×#123—21no—
132C3×#123—21no—
133C3×C22⋊Q8C2×D311yescharacteristic
134C3×C22⋊Q8C2×D311yescharacteristic
135C3×#121—21no—
136C3×C4×D4C2×D311yescharacteristic
137C3×C4×D4C2×D311yescharacteristic
138C2×C3×C4⋊C4—21no—
139C2×#216—31no—
140C2×#216—31no—
141#935—61no—
142C2×#214—31no—
143#926—31no—
144C2×C4⋊Dic3—31no—
145#924—31no—
146#924—31no—
147C2×#208—31no—
148C22×C3⋊C8—31no—
149#889—61no—
150#879—61no—
151#877—61no—
152#870—31no—
153C4×Dic6—31no—
154#835—31no—
155#835—31no—
156#835—31no—
157#835—31no—
158#835—31no—
159#835—31no—
160#832—31no—
161#832—31no—
162#832—31no—
163#830—31no—
164#830—31no—
165#810—31no—
166#808—31no—
167#807—31no—
168#807—31no—
169C4⋊(C3⋊C8)—31no—
170#803—31no—
171C23×C9—21no—
172C23×C9C2×D411yescharacteristic
173C23×C9C2×D411yescharacteristic
174Q8×C9—21no—
175Q8×C9—21no—
176Q8×C9—21no—
177Q8×C9—21no—
178D4×C9—21no—
179D4×C9—41no—
180D4×C9—42no—
181D4×C9—42no—
182D4×C9#4112yes—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9—42no—
191C2×C4×C9—42no—
192C2×C4×C9—42no—
193C2×C4×C9C2×D411yescharacteristic
194C2×C4×C9C2×D411yescharacteristic
195C2×C4×C9C2×D411yescharacteristic
196C2×C4×C9C2×D411yescharacteristic
197C2×C4×C9C2411yescharacteristic
198C2×Dic9—21no—
199C2×Dic9—21no—
200C2×Dic9—21no—
201C2×Dic9—21no—
202C2×Dic9—42no—
203Dic18—21no—
204Dic18—21no—
205C9⋊C8—21no—
206C9⋊C8—21no—
207C9⋊C8—21no—
208C9⋊C8—21no—
209#552—91no—
210#547D911yescharacteristic
211#491—91no—
212#485—91no—
213#484—91no—
214#478—91no—
215#470—91no—
216#467—91no—
217#462—91no—
218#452—91no—
219#452—91no—
220#440—91no—
221#435—91no—
222#417—91no—
223#416—91no—
224C3×#41—22no—
225C3×#41—22no—
226C3×#41—41no—
227C3×#41—41no—
228C2×C3×Q8C22×D311yescharacteristic
229C2×C3×Q8C22×D311yescharacteristic
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4#6711yescharacteristic
233C2×C3×D4C22×D311yescharacteristic
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×Dic3—61no—
240C2×Dic6—31no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4#6711yescharacteristic
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C22⋊C4—21no—
248C3×C22⋊C4—21no—
249C3×C22⋊C4—21no—
250C3×C22⋊C4#6711yescharacteristic
251C3×C22⋊C4#6711yescharacteristic
252C3×C42C22×D311yescharacteristic
253#217—61no—
254#217—61no—
255#217—61no—
256#216—121no—
257#216—121no—
258#214—62no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270#208—121no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—121no—
276C22×C9—21no—
277C22×C9—21no—
278C22×C9—22no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9—21no—
283C22×C9—41no—
284C22×C9—41no—
285C22×C9C22×D411yescharacteristic
286C4×C9—21no—
287C4×C9—21no—
288C4×C9—21no—
289C4×C9—21no—
290C4×C9—41no—
291C4×C9—41no—
292C4×C9—41no—
293C4×C9C2×#4111yescharacteristic
294C4×C9H(5,𝔽2)11yescharacteristic
295Dic9—41no—
296Dic9—41no—
297Dic9—41no—
298Dic9—41no—
299C2×#41C2×D911yescharacteristic
300C2×#41C2×D911yescharacteristic
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C2×M16—91no—
305C22×C8—91no—
306C4⋊Q8C2×D911yescharacteristic
307#126—181no—
308#125—91no—
309#125—181no—
310#123—21no—
311#123—21no—
312#123—181no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8C2×D911yescharacteristic
316C22⋊Q8C2×D911yescharacteristic
317#121—21no—
318C4×Q8—91no—
319C4×D4C2×D911yescharacteristic
320C4×D4C2×D911yescharacteristic
321#117—91no—
322#117—181no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—91no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341#97—91no—
342C23×C3—21no—
343C23×C3C2×#6711yescharacteristic
344C23×C3C2×#6711yescharacteristic
345C3×Q8—21no—
346C3×Q8—21no—
347C3×Q8—21no—
348C3×Q8—21no—
349C3×D4—21no—
350C3×D4—41no—
351C3×D4—42no—
352C3×D4—42no—
353C3×D4#23712yes—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—122no—
374Dic6—61no—
375Dic6—61no—
376C3⋊C8—61no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C2×C9—41no—
381C2×C9—41no—
382C2×C9—42no—
383C2×C9#54611yescharacteristic
384C2×C9#57511yescharacteristic
385C2×C9#57811yescharacteristic
386#41—22no—
387#41—22no—
388#41—41no—
389#41—41no—
390C2×Q8—91no—
391C2×Q8C22×D911yescharacteristic
392C2×Q8C22×D911yescharacteristic
393C2×D4—21no—
394C2×D4—21no—
395C2×D4#61111yescharacteristic
396C2×D4C22×D911yescharacteristic
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—181no—
401C22×C4C22×D911yescharacteristic
402C22×C4C22×D911yescharacteristic
403Q16—361no—
404Q16—361no—
405SD16—182no—
406M16—361no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—361no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—91no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4#61111yescharacteristic
426C4⋊C4C22×D911yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4#61111yescharacteristic
434C22⋊C4#61111yescharacteristic
435C42—181no—
436C42—181no—
437C42C22×D911yescharacteristic
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3C22×#6711yescharacteristic
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4C2×#23711yescharacteristic
456C3×C4#100411yescharacteristic
457Dic3—121no—
458Dic3—121no—
459Dic3—121no—
460Dic3—121no—
461C9#331511yescharacteristic, complemented, Sylow
462C23—21no—
463C23C2×#61111yescharacteristic
464C23C2×#61111yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—21no—
468Q8—21no—
469Q8—181no—
470Q8—181no—
471D4—21no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4#369912yes—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—362no—
491C2×C4C2×#61111yescharacteristic
492C2×C4C2×#61111yescharacteristic
493C2×C4C2×#61111yescharacteristic
494C2×C4C2×#61111yescharacteristic
495C2×C4C23×D911yescharacteristic
496C8—181no—
497C8—181no—
498C8—181no—
499C8—181no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—42no—
503C2×C3#580611yescharacteristic
504C2×C3#582211yescharacteristic
505C2×C3#583811yescharacteristic
506C22—21no—
507C22—21no—
508C22—22no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—41no—
514C22—41no—
515C22C22×#61111yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4C2×#369911yescharacteristic
528C4#6371011yescharacteristic
529C3#8351311yescharacteristic
530C2—41no—
531C2—41no—
532C2—42no—
533C2#1058990811yescharacteristic
534C2#1058992511yescharacteristic
535C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#547C2
socleC22×C3C22×#67
prime radicalC3×#547D3
hypercenter#547D9
hypocenterC9#3315
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #10589643C2semidirect
3. #10588918C2semidirect
4. #10588918C2semidirect
5. #10588917C2semidirect
6. #10588916C2semidirect
7. #10588763C2semidirect
8. #10588762C2semidirect
9. #10588728C2semidirect
10. #10588727C2semidirect
11. #10588725C2semidirect
12. #10588724C2semidirect
13. #10588694C2semidirect
14. #10588692C2semidirect
15. #10588688C2semidirect
461. C9#3315semidirect

Maximal subgroups

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

subgroupindex
C9×#5472
#105896432
#105889182
#105889172
#105889162
#105887632
#105887622
#105887282
#105887272
#105887252
#105887242
#105886942
#105886922
#105886882
#835133