Finite Group Databasebeta

← #11872390

Subgroups — #11872390

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×#541C211yesmaximal, characteristic, complemented
2#10589625C211yesmaximal, characteristic
3#10588768C211yesmaximal, characteristic, complemented
4#10588763C211yesmaximal, characteristic, complemented
5#10588747C211yesmaximal, characteristic, complemented
6#10588745C211yesmaximal, characteristic, complemented
7#10588730C211yesmaximal, characteristic
8#10588730C211yesmaximal, characteristic
9#10588724C211yesmaximal, characteristic, complemented
10#10588723C211yesmaximal, characteristic, complemented
11#10588709C211yesmaximal, characteristic, complemented
12C4×#3675C211yesmaximal, characteristic, complemented
13#10588706C211yesmaximal, characteristic, complemented
14C4×#3674C211yesmaximal, characteristic, complemented
15#10588678C211yesmaximal, characteristic, complemented
16#83446—31nomaximal
17C2×#3697C2211yescharacteristic
18C9×C4⋊Q8C2211yescharacteristic
19C9×#126—21no—
20C9×#126—21no—
21C9×#125—21no—
22C9×#125—21no—
23C9×#125C2211yescharacteristic
24C9×C22⋊Q8C2211yescharacteristic
25C9×C22⋊Q8C2211yescharacteristic
26C4×Q8×C9C2211yescharacteristic
27C4×Q8×C9C2211yescharacteristic
28C9×#117C2211yescharacteristic
29C2×#3675C2211yescharacteristic
30C2×#3675C2211yescharacteristic
31C2×#3674C2211yescharacteristic
32C2×#3674C2211yescharacteristic
33C2×C4⋊Dic9C2211yescharacteristic
34#63454—21no—
35C4⋊C4×D9—21no—
36#611⋊C4—21no—
37#611⋊C4—21no—
38C4×D36C2211yescharacteristic
39C4×D36C2211yescharacteristic
40C4×Dic18C2211yescharacteristic
41C4×Dic18C2211yescharacteristic
42#63395C2211yescharacteristic
43#63395C2211yescharacteristic
44#63395C2211yescharacteristic
45#63395C2211yescharacteristic
46#63389C2211yescharacteristic
47#63389C2211yescharacteristic
48#63369C2211yescharacteristic
49#63369C2211yescharacteristic
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×#541D311yescharacteristic
61#5523—31no—
62#5090—31no—
63#5083—31no—
64#5066—31no—
65#5063—31no—
66#5047—31no—
67#5047—31no—
68#5044—31no—
69#5043—31no—
70#5030—31no—
71C4×#216—31no—
72#5026—31no—
73C4×#215—31no—
74#5000—31no—
75C2×Q8×C9C2311yescharacteristic
76C2×Q8×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C2×#611—21no—
79C22×Dic9—21no—
80#3697—22no—
81#3697—22no—
82C2×D36C2311yescharacteristic
83C2×C4×D9—21no—
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×Dic18C2311yescharacteristic
87C9×C4⋊C4—21no—
88C9×C4⋊C4—21no—
89C9×C4⋊C4—21no—
90C9×C4⋊C4—21no—
91C9×C4⋊C4—21no—
92C9×C4⋊C4—21no—
93C9×C4⋊C4—21no—
94C9×C4⋊C4—21no—
95C9×C4⋊C4D411yescharacteristic
96C9×C4⋊C4D411yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C22⋊C4—21no—
100C9×C22⋊C4—21no—
101C9×C22⋊C4D411yescharacteristic
102C9×C22⋊C4D411yescharacteristic
103C42×C9—21no—
104C42×C9—21no—
105C42×C9C2311yescharacteristic
106C42×C9C2311yescharacteristic
107#3675—22no—
108#3675—22no—
109#3674—22no—
110#3674—22no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113C4⋊Dic9—21no—
114C4⋊Dic9C2311yescharacteristic
115C4⋊Dic9C2311yescharacteristic
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×#235—31no—
126C3×C4⋊Q8C2×D311yescharacteristic
127C3×#126—21no—
128C3×#126—21no—
129C3×#125—21no—
130C3×#125—21no—
131C3×#125C2×D311yescharacteristic
132C3×C22⋊Q8C2×D311yescharacteristic
133C3×C22⋊Q8C2×D311yescharacteristic
134C3×C4×Q8C2×D311yescharacteristic
135C3×C4×Q8C2×D311yescharacteristic
136C3×#117C2×D311yescharacteristic
137C2×#216—31no—
138C2×#216—31no—
139C2×#215—31no—
140C2×#215—31no—
141C2×C4⋊Dic3—31no—
142#892—61no—
143D3×C4⋊C4—61no—
144#67⋊C4—61no—
145#67⋊C4—61no—
146C4×D12—31no—
147C4×D12—31no—
148C4×Dic6—31no—
149C4×Dic6—31no—
150#835—31no—
151#835—31no—
152#835—31no—
153#835—31no—
154#830—31no—
155#830—31no—
156#810—31no—
157#810—31no—
158#809—31no—
159#809—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×C9C2×D411yescharacteristic
169C22×D9—21no—
170Q8×C9—21no—
171Q8×C9—21no—
172Q8×C9—21no—
173Q8×C9—21no—
174C2×C4×C9—21no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2×D411yescharacteristic
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2411yescharacteristic
186#611—24no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—81no—
191D36—21no—
192D36#4112yes—
193C4×D9—24no—
194C4×D9—81no—
195C4×D9—81no—
196Dic18—21no—
197Dic18#4112yes—
198C9⋊C8—21no—
199C9⋊C8—21no—
200C9⋊C8—21no—
201C9⋊C8—21no—
202#541D911yescharacteristic, complemented
203#520—91no—
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—
217C2×C3×Q8C22×D311yescharacteristic
218C2×C3×Q8C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—61no—
221C22×Dic3—61no—
222#235—62no—
223#235—62no—
224C2×D12—31no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×Dic6—31no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4#6711yescharacteristic
238C3×C4⋊C4#6711yescharacteristic
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C22⋊C4—21no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4#6711yescharacteristic
244C3×C22⋊C4#6711yescharacteristic
245C3×C42—21no—
246C3×C42—21no—
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#216—62no—
250#216—62no—
251#215—62no—
252#215—62no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—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—21no—
268C22×C9—21no—
269C22×C9C22×D411yescharacteristic
270C2×D9—22no—
271C2×D9—41no—
272C2×D9—41no—
273C4×C9—21no—
274C4×C9—21no—
275C4×C9—21no—
276C4×C9—21no—
277C4×C9—21no—
278C4×C9—41no—
279C4×C9—41no—
280C4×C9—41no—
281C4×C9—41no—
282C4×C9C2×#4111yescharacteristic
283C4×C9C2×#4111yescharacteristic
284Dic9—22no—
285Dic9—41no—
286Dic9—41no—
287C2×#41—91no—
288C2×Q16—91no—
289C2×Q16—91no—
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8C2×D911yescharacteristic
293#126—21no—
294#126—21no—
295#125—21no—
296#125—21no—
297#125C2×D911yescharacteristic
298C22⋊Q8C2×D911yescharacteristic
299C22⋊Q8C2×D911yescharacteristic
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8C2×D911yescharacteristic
303C4×Q8C2×D911yescharacteristic
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—181no—
307C4×D4—181no—
308#117—181no—
309#117C2×D911yescharacteristic
310C2×C4⋊C4—91no—
311C2×C4⋊C4—181no—
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×C3C2×#6711yescharacteristic
331C22×D3—61no—
332C3×Q8—21no—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—64no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—241no—
353D12—32no—
354D12—61no—
355C4×D3—64no—
356C4×D3—241no—
357C4×D3—241no—
358Dic6—32no—
359Dic6—61no—
360C3⋊C8—61no—
361C3⋊C8—61no—
362C3⋊C8—61no—
363C3⋊C8—61no—
364C2×C9—41no—
365C2×C9#52511yescharacteristic
366C2×C9#57711yescharacteristic
367C2×C9#57811yescharacteristic
368D9—42no—
369#41—182no—
370#41—182no—
371C2×Q8—91no—
372C2×Q8C22×D911yescharacteristic
373C2×Q8C22×D911yescharacteristic
374C2×D4—91no—
375C2×D4—181no—
376C22×C4—181no—
377C22×C4—181no—
378C22×C4—181no—
379C22×C4—181no—
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—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—91no—
398C4⋊C4—91no—
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—21no—
420C22×C3—21no—
421C22×C3C22×#6711yescharacteristic
422C2×D3—62no—
423C2×D3—121no—
424C2×D3—121no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4D3×#4111yescharacteristic
435C3×C4D3×#4111yescharacteristic
436Dic3—62no—
437Dic3—121no—
438Dic3—121no—
439C9#312011yescharacteristic, complemented, Sylow
440C23—181no—
441C23C2×#61111yescharacteristic
442Q8—21no—
443Q8—21no—
444Q8—21no—
445Q8—21no—
446Q8—92no—
447Q8—181no—
448D4—92no—
449D4—184no—
450D4—181no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—184no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—721no—
462C2×C4—721no—
463C2×C4—721no—
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#582811yescharacteristic
476C2×C3#583711yescharacteristic
477C2×C3#583811yescharacteristic
478D3—122no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—182no—
483C22—361no—
484C22—361no—
485C22C22×#61111yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—182no—
496C4—361no—
497C4—361no—
498C4#41×D911yescharacteristic
499C4#41×D911yescharacteristic
500C3#8344611yescharacteristic
501C2—41no—
502C2—362no—
503C2#1058993011yescharacteristic
504C2#1058993911yescharacteristic
505C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#541C2
socleC22×C3C22×#67
prime radicalC2×#3697C22
hypercenter#541D9
hypocenterC9#3120
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C9×#541C2semidirect
3. #10588768C2semidirect
4. #10588763C2semidirect
5. #10588747C2semidirect
6. #10588745C2semidirect
9. #10588724C2semidirect
10. #10588723C2semidirect
11. #10588709C2semidirect
12. C4×#3675C2semidirect
13. #10588706C2semidirect
14. C4×#3674C2semidirect
15. #10588678C2semidirect
202. #541D9semidirect
439. C9#3120semidirect

Maximal subgroups

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

subgroupindex
C9×#5412
#105896252
#105887682
#105887632
#105887472
#105887452
#105887302
#105887242
#105887232
#105887092
C4×#36752
#105887062
C4×#36742
#105886782
#834463