Finite Group Databasebeta

← #11872565

Subgroups — #11872565

Order 1152.

555 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
1#10589914C211yesmaximal, characteristic, complemented
2#10589745C211yesmaximal, characteristic
3C9×#451C211yesmaximal, characteristic, complemented
4#10588908C211yesmaximal, characteristic
5#10588865C211yesmaximal, characteristic, complemented
6#10588865C211yesmaximal, characteristic, complemented
7#10588864C211yesmaximal, characteristic, complemented
8Q16×Dic9C211yesmaximal, characteristic, complemented
9#10588725C211yesmaximal, characteristic, complemented
10#10588497C211yesmaximal, characteristic, complemented
11#10588473C211yesmaximal, characteristic, complemented
12#10588471C211yesmaximal, characteristic, complemented
13#10588468C211yesmaximal, characteristic, complemented
14#10588419C211yesmaximal, characteristic
15#10588400C211yesmaximal, characteristic, complemented
16#80176—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C2×C9×Q16C2211yescharacteristic
19C2×C9×Q16C2211yescharacteristic
20C9×C22⋊Q8C2211yescharacteristic
21#63509C2211yescharacteristic
22Q8×Dic9—21no—
23Q8×Dic9—21no—
24Q8×Dic9C2211yescharacteristic
25Q8×Dic9C2211yescharacteristic
26Q8×Dic9C2211yescharacteristic
27Q8×Dic9C2211yescharacteristic
28Q8×Dic9C2211yescharacteristic
29C2×#3675C2211yescharacteristic
30C2×#3675C2211yescharacteristic
31#63492C2211yescharacteristic
32#63488—21no—
33#63488—21no—
34#63488C2211yescharacteristic
35#63488C2211yescharacteristic
36#63460—21no—
37#63459—21no—
38#63455C2211yescharacteristic
39#63450C2211yescharacteristic
40#63447—21no—
41#63445—21no—
42C9×#103C2211yescharacteristic
43C9×#103C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45#63395C2211yescharacteristic
46#63395C2211yescharacteristic
47#63395C2211yescharacteristic
48#63395C2211yescharacteristic
49#63389C2211yescharacteristic
50#63380C2211yescharacteristic
51#63380C2211yescharacteristic
52#63378C2211yescharacteristic
53#63377C2211yescharacteristic
54#63375C2211yescharacteristic
55Dic9⋊C8C2211yescharacteristic
56Dic9⋊C8C2211yescharacteristic
57C8×Dic9C2211yescharacteristic
58#63367C2211yescharacteristic
59#63366C2211yescharacteristic
60#5812—31no—
61#5643—31no—
62C3×#451D311yescharacteristic
63#5227—31no—
64#5185—31no—
65#5185—31no—
66#5184—31no—
67Dic3×Q16—31no—
68#5045—31no—
69#4817—31no—
70#4793—31no—
71#4791—31no—
72#4788—31no—
73#4737—31no—
74#4720—31no—
75C2×Q8×C9—22no—
76C2×Q8×C9—22no—
77C2×Q8×C9—21no—
78C2×Q8×C9C2311yescharacteristic
79C2×Q8×C9C2311yescharacteristic
80C2×Q8×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C22×C4×C9C2311yescharacteristic
83C2×#611—21no—
84C2×D36C2311yescharacteristic
85C2×C4×D9—21no—
86C2×Dic18—21no—
87C9×Q16—22no—
88C9×Q16—22no—
89C2×C8×C9C2311yescharacteristic
90C2×C8×C9C2311yescharacteristic
91C9×C4⋊C4—21no—
92C9×C4⋊C4C2311yescharacteristic
93C9×C22⋊C4—21no—
94#3676—21no—
95#3676D411yescharacteristic
96#3676D411yescharacteristic
97#3675—22no—
98#3675—22no—
99(C2×D9)⋊C4—21no—
100(C2×D9)⋊C4—21no—
101(C2×D9)⋊C4—21no—
102(C2×D9)⋊C4—21no—
103C4⋊Dic9—21no—
104C4⋊Dic9—21no—
105C4⋊Dic9—21no—
106C4⋊Dic9—21no—
107C4⋊Dic9—21no—
108C4⋊Dic9D411yescharacteristic
109C4⋊Dic9D411yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113Dic9⋊C4—21no—
114C4×Dic9—21no—
115C4×Dic9—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C4×Dic9C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3121—91noSylow
125C22×C3×Q8C2×D311yescharacteristic
126C2×C3×Q16C2×D311yescharacteristic
127C2×C3×Q16C2×D311yescharacteristic
128C3×C22⋊Q8C2×D311yescharacteristic
129#947—31no—
130Q8×Dic3—31no—
131Q8×Dic3—31no—
132Q8×Dic3—31no—
133Q8×Dic3—31no—
134Q8×Dic3—31no—
135Q8×Dic3—61no—
136Q8×Dic3—61no—
137C2×#215—31no—
138C2×#215—31no—
139#930—31no—
140#926—31no—
141#926—31no—
142#926—61no—
143#926—61no—
144#898—61no—
145#897—61no—
146#893—31no—
147#888—31no—
148#885—61no—
149#883—61no—
150C3×#103C2×D311yescharacteristic
151C3×#103C2×D311yescharacteristic
152C3×C22⋊C8C2×D311yescharacteristic
153#835—31no—
154#835—31no—
155#835—31no—
156#835—31no—
157#830—31no—
158#821—31no—
159#821—31no—
160#818—31no—
161#817—31no—
162#815—31no—
163Dic3⋊C8—31no—
164Dic3⋊C8—31no—
165C8×Dic3—31no—
166#808—31no—
167#807—31no—
168C23×C9C2×D411yescharacteristic
169C22×D9—21no—
170Q8×C9—24no—
171Q8×C9—21no—
172Q8×C9—21no—
173Q8×C9—21no—
174Q8×C9—21no—
175Q8×C9#4112yes—
176Q8×C9#4112yes—
177C2×C4×C9—24no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2411yescharacteristic
186#611—81no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9C2×D411yescharacteristic
191C2×Dic9C2×D411yescharacteristic
192C2×Dic9C2×D411yescharacteristic
193C2×Dic9C2×D411yescharacteristic
194D36—21no—
195D36—21no—
196C4×D9—81no—
197Dic18—81no—
198C8×C9—21no—
199C8×C9—21no—
200C9⋊C8—21no—
201C9⋊C8—21no—
202#542—91no—
203#519—91no—
204#485—91no—
205#482—91no—
206#477—91no—
207#475—91no—
208#464—91no—
209#464—91no—
210#451D911yescharacteristic, complemented
211#448—91no—
212#441—91no—
213#440—91no—
214C4×Q16—91no—
215C4×SD16—91no—
216#433—91no—
217C2×C3×Q8—22no—
218C2×C3×Q8—22no—
219C2×C3×Q8—21no—
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C22×D311yescharacteristic
223C22×C3×C4—21no—
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—61no—
226C2×D12—31no—
227C2×C4×D3—61no—
228C2×Dic6—61no—
229C3×Q16—22no—
230C3×Q16—22no—
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C3×C4⋊C4—21no—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C22⋊C4—21no—
236#217—31no—
237#217—31no—
238#217—61no—
239#215—62no—
240#215—62no—
241(C2×D3)⋊C4—61no—
242(C2×D3)⋊C4—61no—
243(C2×D3)⋊C4—61no—
244(C2×D3)⋊C4—61no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—31no—
249C4⋊Dic3—31no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255Dic3⋊C4—61no—
256C4×Dic3—31no—
257C4×Dic3—31no—
258C4×Dic3—61no—
259C4×Dic3—61no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C22×C9—21no—
267C22×C9—21no—
268C22×C9—21no—
269C22×C9C22×D411yescharacteristic
270C2×D9—41no—
271C2×D9—41no—
272C2×D9—41no—
273C4×C9—22no—
274C4×C9—22no—
275C4×C9—21no—
276C4×C9—41no—
277C4×C9—41no—
278C4×C9C2×#4111yescharacteristic
279C4×C9C2×#4111yescharacteristic
280Dic9—21no—
281Dic9—21no—
282Dic9—21no—
283Dic9—21no—
284Dic9—41no—
285Dic9—41no—
286Dic9—41no—
287C22×Q8C2×D911yescharacteristic
288C2×Q16C2×D911yescharacteristic
289C2×Q16C2×D911yescharacteristic
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8—91no—
293#126—181no—
294#124—91no—
295#124—181no—
296#123—181no—
297C22⋊Q8—181no—
298C22⋊Q8C2×D911yescharacteristic
299#121—91no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—181no—
306C4×Q8—181no—
307C4×D4—91no—
308#117—91no—
309#117—91no—
310#117—181no—
311#117—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#103C2×D911yescharacteristic
323#103C2×D911yescharacteristic
324#102—91no—
325#102—91no—
326C22⋊C8—91no—
327C22⋊C8C2×D911yescharacteristic
328#97—91no—
329C4×C8—91no—
330C23×C3D3×D411yescharacteristic
331C22×D3—61no—
332C3×Q8—24no—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8—21no—
336C3×Q8—21no—
337C3×Q8#23712yes—
338C3×Q8#23712yes—
339C2×C3×C4—24no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—241no—
349C2×Dic3—31no—
350C2×Dic3—31no—
351C2×Dic3—31no—
352C2×Dic3—31no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356D12—61no—
357D12—61no—
358C4×D3—241no—
359Dic6—241no—
360C3×C8—21no—
361C3×C8—21no—
362C3⋊C8—61no—
363C3⋊C8—61no—
364C2×C9—41no—
365C2×C9#52511yescharacteristic
366C2×C9#57711yescharacteristic
367C2×C9#57811yescharacteristic
368D9—81no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—21no—
372C2×Q8—181no—
373C2×Q8C22×D911yescharacteristic
374C2×Q8C22×D911yescharacteristic
375C2×Q8C22×D911yescharacteristic
376C2×D4—91no—
377C2×D4—181no—
378C22×C4—21no—
379C22×C4—181no—
380C22×C4C22×D911yescharacteristic
381Q16—22no—
382Q16—22no—
383SD16—182no—
384SD16—182no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8C22×D911yescharacteristic
388C2×C8C22×D911yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—91no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—91no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4C22×D911yescharacteristic
402C22⋊C4—21no—
403C22⋊C4—91no—
404C22⋊C4—91no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C42—91no—
411C42—91no—
412C42—181no—
413C42—181no—
414C42—181no—
415C42—181no—
416C42—181no—
417C42—181no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—121no—
425C3×C4—22no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4C2×#23711yescharacteristic
431C3×C4C2×#23711yescharacteristic
432Dic3—61no—
433Dic3—61no—
434Dic3—61no—
435Dic3—61no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439C9#312111yescharacteristic, complemented, Sylow
440C23—181no—
441C23D4×D911yescharacteristic
442Q8—24no—
443Q8—21no—
444Q8—21no—
445Q8—21no—
446Q8—21no—
447Q8—721no—
448Q8#369912yes—
449Q8#369912yes—
450D4—181no—
451D4—181no—
452D4—721no—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—91no—
461C2×C4—91no—
462C2×C4—91no—
463C2×C4—91no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—721no—
468C2×C4D4×D911yescharacteristic
469C2×C4C23×D911yescharacteristic
470C8—21no—
471C8—21no—
472C8—181no—
473C8—181no—
474C2×C3—41no—
475C2×C3#558611yescharacteristic
476C2×C3#576611yescharacteristic
477C2×C3#577811yescharacteristic
478D3—241no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—361no—
483C22—361no—
484C22—361no—
485C22C2×D4×D911yescharacteristic
486C4—22no—
487C4—22no—
488C4—21no—
489C4—41no—
490C4—41no—
491C4—181no—
492C4—181no—
493C4—181no—
494C4—181no—
495C4—361no—
496C4—361no—
497C4—361no—
498C4C2×#369911yescharacteristic
499C4C2×#369911yescharacteristic
500C3#8017611yescharacteristic
501C2—41no—
502C2—721no—
503C2#1058968811yescharacteristic
504C2#1058986811yescharacteristic
505C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#451C2
socleC22×C3C2×D3×D4
prime radical#63492C22
hypercenter#451D9
hypocenterC9#3121
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #10589914C2semidirect
3. C9×#451C2semidirect
5. #10588865C2semidirect
6. #10588865C2semidirect
7. #10588864C2semidirect
8. Q16×Dic9C2semidirect
9. #10588725C2semidirect
10. #10588497C2semidirect
11. #10588473C2semidirect
12. #10588471C2semidirect
13. #10588468C2semidirect
15. #10588400C2semidirect
210. #451D9semidirect
439. C9#3121semidirect

Maximal subgroups

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

subgroupindex
#105899142
#105897452
C9×#4512
#105889082
#105888652
#105888642
Q16×Dic92
#105887252
#105884972
#105884732
#105884712
#105884682
#105884192
#105884002
#801763