Finite Group Databasebeta

← #11872408

Subgroups — #11872408

Order 1152.

558 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#520C211yesmaximal, characteristic
2#10589620C211yesmaximal, characteristic, complemented
3#10588918C211yesmaximal, characteristic
4#10588918C211yesmaximal, characteristic
5#10588707C211yesmaximal, characteristic, complemented
6#10588706C211yesmaximal, characteristic, complemented
7C4×#3674C211yesmaximal, characteristic, complemented
8#10588704C211yesmaximal, characteristic, complemented
9#10588695C211yesmaximal, characteristic, complemented
10#10588694C211yesmaximal, characteristic, complemented
11C4×#3672C211yesmaximal, characteristic, complemented
12#10588692C211yesmaximal, characteristic, complemented
13#10588678C211yesmaximal, characteristic, complemented
14#10588647C211yesmaximal, characteristic, complemented
15#10588646C211yesmaximal, characteristic, complemented
16#82575—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C4×Q8×C9C2211yescharacteristic
19C4×Q8×C9C2211yescharacteristic
20C4×D4×C9—21no—
21C4×D4×C9—21no—
22C4×D4×C9C2211yescharacteristic
23C4×D4×C9C2211yescharacteristic
24C9×#117—21no—
25C9×#117C2211yescharacteristic
26C2×C9×C4⋊C4—21no—
27C2×C9×C4⋊C4C2211yescharacteristic
28C2×#3674C2211yescharacteristic
29C2×#3674C2211yescharacteristic
30C2×#3672C2211yescharacteristic
31C2×#3672C2211yescharacteristic
32#63486C2211yescharacteristic
33#63486C2211yescharacteristic
34#63451—21no—
35#63451—21no—
36#63441—21no—
37#63441—21no—
38#63432C2211yescharacteristic
39#63431C2211yescharacteristic
40C4×Dic18C2211yescharacteristic
41C4×Dic18C2211yescharacteristic
42#63395C2211yescharacteristic
43#63395C2211yescharacteristic
44#63392C2211yescharacteristic
45#63392C2211yescharacteristic
46#63389C2211yescharacteristic
47#63389C2211yescharacteristic
48#63368C2211yescharacteristic
49#63368C2211yescharacteristic
50#63368C2211yescharacteristic
51#63368C2211yescharacteristic
52#63367C2211yescharacteristic
53#63367C2211yescharacteristic
54#63366C2211yescharacteristic
55#63366C2211yescharacteristic
56C4⋊(C9⋊C8)C2211yescharacteristic
57C4⋊(C9⋊C8)C2211yescharacteristic
58#63362C2211yescharacteristic
59C4×C9⋊C8C2211yescharacteristic
60C3×#520D311yescharacteristic
61#5518—31no—
62#5239—31no—
63#5239—31no—
64#5031—31no—
65#5030—31no—
66C4×#216—31no—
67#5022—31no—
68#5019—31no—
69#5018—31no—
70C4×#214—31no—
71#5009—31no—
72#5000—31no—
73#4971—31no—
74#4970—31no—
75C9×#41—22no—
76C9×#41—22no—
77C2×Q8×C9C2311yescharacteristic
78C2×D4×C9—21no—
79C2×D4×C9C2311yescharacteristic
80C22×C4×C9—21no—
81C22×C4×C9—21no—
82C22×C4×C9—21no—
83C22×C4×C9—21no—
84C22×C4×C9C2311yescharacteristic
85C2×Dic18C2311yescharacteristic
86C2×Dic18C2311yescharacteristic
87C9×C4⋊C4—21no—
88C9×C4⋊C4—21no—
89C9×C4⋊C4—21no—
90C9×C4⋊C4D411yescharacteristic
91C9×C4⋊C4D411yescharacteristic
92C9×C4⋊C4C2311yescharacteristic
93C9×C4⋊C4C2311yescharacteristic
94C9×C22⋊C4—21no—
95C9×C22⋊C4—21no—
96C9×C22⋊C4D411yescharacteristic
97C9×C22⋊C4D411yescharacteristic
98C42×C9—21no—
99C42×C9—21no—
100C42×C9C2311yescharacteristic
101C42×C9C2311yescharacteristic
102#3676—21no—
103#3676—21no—
104#3674—22no—
105#3674—22no—
106#3672—22no—
107#3672—22no—
108C4⋊Dic9—21no—
109C4⋊Dic9—21no—
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3120—91noSylow
125C2×C3×#41C2×D311yescharacteristic
126C3×C4×Q8C2×D311yescharacteristic
127C3×C4×Q8C2×D311yescharacteristic
128C3×C4×D4—21no—
129C3×C4×D4—21no—
130C3×C4×D4C2×D311yescharacteristic
131C3×C4×D4C2×D311yescharacteristic
132C3×#117—21no—
133C3×#117C2×D311yescharacteristic
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×#216—31no—
137C2×#216—31no—
138C2×#214—31no—
139C2×#214—31no—
140#924—31no—
141#924—31no—
142#889—61no—
143#889—61no—
144#879—61no—
145#879—61no—
146#870—31no—
147#869—31no—
148C4×Dic6—31no—
149C4×Dic6—31no—
150#835—31no—
151#835—31no—
152#832—31no—
153#832—31no—
154#830—31no—
155#830—31no—
156#810—31no—
157#810—31no—
158#810—31no—
159#810—31no—
160#808—31no—
161#808—31no—
162#807—31no—
163#807—31no—
164C4⋊(C3⋊C8)—31no—
165C4⋊(C3⋊C8)—31no—
166#803—31no—
167C4×C3⋊C8—31no—
168C23×C9—21no—
169C23×C9C2×D411yescharacteristic
170Q8×C9—21no—
171Q8×C9#4112yes—
172D4×C9—24no—
173D4×C9—21no—
174D4×C9#4112yes—
175C2×C4×C9—24no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—81no—
182C2×C4×C9—81no—
183C2×C4×C9—81no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2411yescharacteristic
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194Dic18—21no—
195Dic18—21no—
196Dic18—21no—
197Dic18—21no—
198C9⋊C8—21no—
199C9⋊C8—21no—
200C9⋊C8—21no—
201C9⋊C8—21no—
202#541—91no—
203#520D911yescharacteristic
204#484—91no—
205#483—91no—
206#479—91no—
207#478—91no—
208#462—91no—
209#461—91no—
210#452—91no—
211#452—91no—
212#441—91no—
213#440—91no—
214C4×Q16—91no—
215C4×SD16—91no—
216#433—91no—
217C3×#41—22no—
218C3×#41—22no—
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4C22×D311yescharacteristic
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4C22×D311yescharacteristic
227C2×Dic6—31no—
228C2×Dic6—31no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4#6711yescharacteristic
233C3×C4⋊C4#6711yescharacteristic
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4#6711yescharacteristic
239C3×C22⋊C4#6711yescharacteristic
240C3×C42—21no—
241C3×C42—21no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—61no—
245#217—61no—
246#216—62no—
247#216—62no—
248#214—62no—
249#214—62no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—61no—
259Dic3⋊C4—61no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C22×C9—21no—
267C22×C9—22no—
268C22×C9—21no—
269C22×C9—21no—
270C22×C9—41no—
271C22×C9—41no—
272C22×C9C22×D411yescharacteristic
273C4×C9—21no—
274C4×C9—22no—
275C4×C9—21no—
276C4×C9—21no—
277C4×C9—21no—
278C4×C9—21no—
279C4×C9—41no—
280C4×C9—41no—
281C4×C9C2×#4111yescharacteristic
282C4×C9C2×#4111yescharacteristic
283Dic9—41no—
284Dic9—41no—
285Dic9—41no—
286Dic9—41no—
287C2×#41C2×D911yescharacteristic
288C2×Q16—91no—
289C2×Q16—91no—
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8—91no—
293#126—181no—
294#126—181no—
295#125—91no—
296#125—181no—
297#125—181no—
298C22⋊Q8—91no—
299C22⋊Q8—91no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8C2×D911yescharacteristic
303C4×Q8C2×D911yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C2×D911yescharacteristic
307C4×D4C2×D911yescharacteristic
308#117—21no—
309#117C2×D911yescharacteristic
310C2×C4⋊C4—21no—
311C2×C4⋊C4C2×D911yescharacteristic
312#107—91no—
313#107—91no—
314#106—91no—
315#106—91no—
316C4⋊C8—91no—
317C4⋊C8—91no—
318#103—91no—
319#103—91no—
320#103—91no—
321#103—91no—
322#103—91no—
323#103—91no—
324#102—91no—
325#102—91no—
326C22⋊C8—91no—
327C22⋊C8—91no—
328#97—91no—
329C4×C8—91no—
330C23×C3—21no—
331C23×C3C2×#6711yescharacteristic
332C3×Q8—21no—
333C3×Q8#23512yes—
334C3×D4—24no—
335C3×D4—21no—
336C3×D4#23512yes—
337C2×C3×C4—24no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—81no—
344C2×C3×C4—81no—
345C2×C3×C4—81no—
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356Dic6—61no—
357Dic6—61no—
358Dic6—61no—
359Dic6—61no—
360C3⋊C8—61no—
361C3⋊C8—61no—
362C3⋊C8—61no—
363C3⋊C8—61no—
364C2×C9—41no—
365C2×C9—42no—
366C2×C9#52511yescharacteristic
367C2×C9#57711yescharacteristic
368C2×C9#57811yescharacteristic
369#41—22no—
370#41—22no—
371C2×Q8—91no—
372C2×Q8—91no—
373C2×Q8C22×D911yescharacteristic
374C2×D4—21no—
375C2×D4C22×D911yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4C22×D911yescharacteristic
381Q16—182no—
382Q16—182no—
383SD16—182no—
384SD16—182no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8—91no—
388C2×C8—91no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4—181no—
402C4⋊C4#61111yescharacteristic
403C4⋊C4#61111yescharacteristic
404C4⋊C4C22×D911yescharacteristic
405C4⋊C4C22×D911yescharacteristic
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C22⋊C4#61111yescharacteristic
411C22⋊C4#61111yescharacteristic
412C42—21no—
413C42—21no—
414C42—181no—
415C42—181no—
416C42C22×D911yescharacteristic
417C42C22×D911yescharacteristic
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3C22×#6711yescharacteristic
425C3×C4—21no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4C2×#23511yescharacteristic
434C3×C4C2×#23511yescharacteristic
435Dic3—121no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439C9#312011yescharacteristic, complemented, Sylow
440C23—21no—
441C23C2×#61111yescharacteristic
442Q8—21no—
443Q8—181no—
444Q8—181no—
445Q8—181no—
446Q8—181no—
447Q8#369712yes—
448D4—24no—
449D4—21no—
450D4#369712yes—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4C2×#61111yescharacteristic
465C2×C4C2×#61111yescharacteristic
466C2×C4C2×#61111yescharacteristic
467C2×C4C2×#61111yescharacteristic
468C2×C4C2×#61111yescharacteristic
469C2×C4C23×D911yescharacteristic
470C8—181no—
471C8—181no—
472C8—181no—
473C8—181no—
474C2×C3—41no—
475C2×C3—42no—
476C2×C3#579111yescharacteristic
477C2×C3#583611yescharacteristic
478C2×C3#583811yescharacteristic
479C22—21no—
480C22—22no—
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22C22×#61111yescharacteristic
486C4—21no—
487C4—22no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—41no—
493C4—41no—
494C4—361no—
495C4—361no—
496C4—361no—
497C4—361no—
498C4C2×#369711yescharacteristic
499C4C2×#369711yescharacteristic
500C3#8257511yescharacteristic
501C2—41no—
502C2—42no—
503C2#1058989311yescharacteristic
504C2#1058993811yescharacteristic
505C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#520C2
socleC22×C3C22×#67
prime radicalC2×C3×#41C2×D3
hypercenter#520D9
hypocenterC9#3120
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
2. #10589620C2semidirect
5. #10588707C2semidirect
6. #10588706C2semidirect
7. C4×#3674C2semidirect
8. #10588704C2semidirect
9. #10588695C2semidirect
10. #10588694C2semidirect
11. C4×#3672C2semidirect
12. #10588692C2semidirect
13. #10588678C2semidirect
14. #10588647C2semidirect
15. #10588646C2semidirect
439. C9#3120semidirect

Maximal subgroups

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

subgroupindex
C9×#5202
#105896202
#105889182
#105887072
#105887062
C4×#36742
#105887042
#105886952
#105886942
C4×#36722
#105886922
#105886782
#105886472
#105886462
#825753