Finite Group Databasebeta

← #11872106

Subgroups — #11872106

Order 1152.

609 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589636C211yesmaximal, characteristic, complemented
2#10589623C211yesmaximal, characteristic, complemented
3C9×#433C211yesmaximal, characteristic, complemented
4#10588530C211yesmaximal, characteristic, complemented
5#10588528C211yesmaximal, characteristic, complemented
6#10588528C211yesmaximal, characteristic, complemented
7#10588526C211yesmaximal, characteristic, complemented
8#10588419C211yesmaximal, characteristic, complemented
9#10588414C211yesmaximal, characteristic
10#10588413C211yesmaximal, characteristic, complemented
11#10588403C211yesmaximal, characteristic, complemented
12#10588392C211yesmaximal, characteristic, complemented
13#10588391C211yesmaximal, characteristic, complemented
14C4×D72C211yesmaximal, characteristic, complemented
15C4×#3664C211yesmaximal, characteristic, complemented
16#79383—31nomaximal
17C22×D36C2211yescharacteristic
18C9×#117C2211yescharacteristic
19#63492C2211yescharacteristic
20#63488C2211yescharacteristic
21#63486C2211yescharacteristic
22C2×D72C2211yescharacteristic
23C2×D72C2211yescharacteristic
24C2×#3664C2211yescharacteristic
25C2×#3664C2211yescharacteristic
26#63460—21no—
27#63458—21no—
28#63455—21no—
29#63455—21no—
30#63447—21no—
31#63445—21no—
32C22⋊C4×D9—21no—
33C22⋊C4×D9—21no—
34#63437C2211yescharacteristic, complemented
35C4×D36C2211yescharacteristic
36C4×D36C2211yescharacteristic
37C4×D36C2211yescharacteristic
38C4×D36C2211yescharacteristic
39C4×D36C2211yescharacteristic, complemented
40#63431C2211yescharacteristic, complemented
41C4×Dic18C2211yescharacteristic, complemented
42C9×C4⋊C8C2211yescharacteristic, complemented
43C9×C4⋊C8C2211yescharacteristic, complemented
44C9×C22⋊C8C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic
46C9×#97C2211yescharacteristic, complemented
47C4×C8×C9C2211yescharacteristic, complemented
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51#63380C2211yescharacteristic
52#63380C2211yescharacteristic, complemented
53#63380C2211yescharacteristic, complemented
54#63378C2211yescharacteristic, complemented
55#63378C2211yescharacteristic, complemented
56#63377C2211yescharacteristic, complemented
57#63377C2211yescharacteristic, complemented
58#63376C2211yescharacteristic, complemented
59#63376C2211yescharacteristic, complemented
60#5534—31no—
61#5521—31no—
62C3×#433D311yescharacteristic
63#4846—31no—
64#4844—31no—
65#4844—31no—
66#4842—31no—
67#4737—31no—
68#4732—31no—
69#4731—31no—
70#4723—31no—
71#4711—31no—
72#4710—31no—
73C4×D24—31no—
74C4×#204—31no—
75C23×D9—21no—
76C22×C4×C9C2311yescharacteristic
77C2×#611—21no—
78C2×D36—21no—
79C2×D36—22no—
80C2×D36—22no—
81C2×D36C2311yescharacteristic
82C2×D36C2311yescharacteristic
83C2×D36C2311yescharacteristic
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×Dic18—21no—
90C2×Dic18C2311yescharacteristic
91C2×C8×C9C2311yescharacteristic
92C2×C8×C9C2311yescharacteristic
93C2×C8×C9C2311yescharacteristic
94C2×C8×C9C2311yescharacteristic
95C9×C4⋊C4D411yescharacteristic
96C9×C4⋊C4D411yescharacteristic
97C9×C22⋊C4D411yescharacteristic
98C9×C22⋊C4D411yescharacteristic
99C42×C9C2311yescharacteristic
100C42×C9C2311yescharacteristic
101#3676—21no—
102#3676—21no—
103(C2×D9)⋊C4—21no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111C4⋊Dic9—21no—
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120D72—22no—
121D72—22no—
122#3664—22no—
123#3664—22no—
124#3118—91noSylow
125C22×D12—31no—
126C3×#117C2×D311yescharacteristic
127#930—31no—
128#926—31no—
129#924—31no—
130C2×D24—31no—
131C2×D24—31no—
132C2×#204—31no—
133C2×#204—31no—
134#898—61no—
135#896—61no—
136#893—61no—
137#893—61no—
138#885—61no—
139#883—61no—
140D3×C22⋊C4—61no—
141D3×C22⋊C4—61no—
142#875—31no—
143C4×D12—31no—
144C4×D12—31no—
145C4×D12—31no—
146C4×D12—31no—
147C4×D12—31no—
148#869—31no—
149C4×Dic6—31no—
150C3×C4⋊C8C2×D311yescharacteristic
151C3×C4⋊C8C2×D311yescharacteristic
152C3×C22⋊C8C2×D311yescharacteristic
153C3×C22⋊C8C2×D311yescharacteristic
154C3×#97C2×D311yescharacteristic
155C3×C4×C8C2×D311yescharacteristic
156#821—31no—
157#821—31no—
158#821—31no—
159#821—31no—
160#821—31no—
161#821—31no—
162#818—31no—
163#818—31no—
164#817—31no—
165#817—31no—
166#816—31no—
167#816—31no—
168C23×C9C2×D411yescharacteristic
169C22×D9—21no—
170C22×D9—21no—
171C22×D9—24no—
172C22×D9—21no—
173C22×D9—81no—
174C22×D9—81no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9C2×D411yescharacteristic
178C2×C4×C9C2×D411yescharacteristic
179C2×C4×C9C2×D411yescharacteristic
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2×D411yescharacteristic
182C2×C4×C9C2411yescharacteristic
183#611—81no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189D36—24no—
190D36—21no—
191D36—21no—
192D36—21no—
193D36—21no—
194D36#4112yes—
195D36#4112yes—
196C4×D9—81no—
197C4×D9—81no—
198C4×D9—81no—
199C4×D9—81no—
200C4×D9—81no—
201Dic18—21no—
202Dic18—21no—
203Dic18—81no—
204C8×C9—21no—
205C8×C9—21no—
206C8×C9—21no—
207C8×C9—21no—
208#542—91no—
209#518—91no—
210#485—91no—
211#482—91no—
212#476—91no—
213#474—91no—
214#463—91no—
215#463—91no—
216#450—91no—
217#447—91no—
218#442—91no—
219#440—91no—
220C4×SD16—91no—
221C4×D8—91no—
222#433D911yescharacteristic, complemented
223C23×D3—61no—
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—61no—
226C2×D12—31no—
227C2×D12—31no—
228C2×D12—31no—
229C2×D12—62no—
230C2×D12—62no—
231C2×D12—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×Dic6—31no—
238C2×Dic6—61no—
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C3×C4⋊C4D1211yescharacteristic
244C3×C4⋊C4D1211yescharacteristic
245C3×C22⋊C4D1211yescharacteristic
246C3×C22⋊C4D1211yescharacteristic
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#217—61no—
250#217—61no—
251(C2×D3)⋊C4—61no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266C4×Dic3—61no—
267C4×Dic3—61no—
268D24—62no—
269D24—62no—
270#204—62no—
271#204—62no—
272C22×C9—21no—
273C22×C9—21no—
274C22×C9—21no—
275C22×C9C22×D411yescharacteristic
276C2×D9—22no—
277C2×D9—22no—
278C2×D9—41no—
279C2×D9—41no—
280C2×D9—41no—
281C2×D9—41no—
282C2×D9—41no—
283C2×D9—41no—
284C2×D9—41no—
285C2×D9—84no—
286C4×C9—21no—
287C4×C9—21no—
288C4×C9—21no—
289C4×C9—21no—
290C4×C9—21no—
291C4×C9C2×#4111yescharacteristic
292C4×C9C2×#4111yescharacteristic
293Dic9—41no—
294Dic9—41no—
295Dic9—41no—
296Dic9—41no—
297Dic9—41no—
298C22×D4—91no—
299C2×SD16—91no—
300C2×SD16—91no—
301C2×D8—91no—
302C2×D8—91no—
303C4⋊Q8—91no—
304#126—181no—
305#124—91no—
306#124—181no—
307#123—181no—
308C22⋊Q8—91no—
309C22⋊Q8—181no—
310#121—91no—
311C4×Q8—91no—
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—181no—
318C4×D4—181no—
319#117—91no—
320#117C2×D911yescharacteristic
321C2×C22⋊C4—181no—
322C2×C22⋊C4—181no—
323#107—91no—
324#107—91no—
325#106—91no—
326#106—91no—
327C4⋊C8C2×D911yescharacteristic, complemented
328C4⋊C8C2×D911yescharacteristic, complemented
329#103—91no—
330#103—91no—
331#102—91no—
332#102—91no—
333#102—91no—
334#102—91no—
335#102—91no—
336#102—91no—
337C22⋊C8C2×D911yescharacteristic
338C22⋊C8C2×D911yescharacteristic
339#97C2×D911yescharacteristic, complemented
340C4×C8C2×D911yescharacteristic, complemented
341C23×C3C2×D1211yescharacteristic
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—64no—
345C22×D3—61no—
346C22×D3—241no—
347C22×D3—241no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356#67—241no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362D12—32no—
363D12—32no—
364D12—64no—
365D12—61no—
366D12—61no—
367D12—61no—
368D12—61no—
369C4×D3—241no—
370C4×D3—241no—
371C4×D3—241no—
372C4×D3—241no—
373C4×D3—241no—
374Dic6—61no—
375Dic6—61no—
376Dic6—241no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—21no—
380C3×C8—21no—
381C2×C9—41no—
382C2×C9#52511yescharacteristic
383C2×C9#57611yescharacteristic
384C2×C9#57711yescharacteristic
385D9—42no—
386D9—42no—
387D9—81no—
388C24—181no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×D4—91no—
392C2×D4—91no—
393C2×D4—91no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4C22×D911yescharacteristic
404SD16—182no—
405SD16—182no—
406D8—182no—
407D8—182no—
408C2×C8C22×D911yescharacteristic
409C2×C8C22×D911yescharacteristic
410C2×C8C22×D911yescharacteristic
411C2×C8C22×D911yescharacteristic
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4D3611yescharacteristic
420C4⋊C4D3611yescharacteristic
421C22⋊C4—181no—
422C22⋊C4—181no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4D3611yescharacteristic
432C22⋊C4D3611yescharacteristic
433C42—181no—
434C42—181no—
435C42C22×D911yescharacteristic
436C42C22×D911yescharacteristic
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3C22×D1211yescharacteristic
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—244no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4D3×#4111yescharacteristic
457C3×C4D3×#4111yescharacteristic
458Dic3—121no—
459Dic3—121no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463C9#311811yescharacteristic, complemented, Sylow
464C23—184no—
465C23—181no—
466C23—181no—
467C23—181no—
468C23—721no—
469C23—721no—
470C23C2×D3611yescharacteristic
471Q8—181no—
472Q8—181no—
473Q8—721no—
474D4—92no—
475D4—92no—
476D4—184no—
477D4—181no—
478D4—181no—
479D4—181no—
480D4—181no—
481D4—721no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—721no—
490C2×C4—721no—
491C2×C4—721no—
492C2×C4—721no—
493C2×C4—721no—
494C2×C4C2×D3611yescharacteristic
495C2×C4C2×D3611yescharacteristic
496C2×C4C2×D3611yescharacteristic
497C2×C4C2×D3611yescharacteristic
498C2×C4C2×D3611yescharacteristic
499C2×C4C23×D911yescharacteristic
500C8—21no—
501C8—21no—
502C8—21no—
503C8—21no—
504C2×C3—41no—
505C2×C3#552411yescharacteristic
506C2×C3#575111yescharacteristic
507C2×C3#575211yescharacteristic
508D3—122no—
509D3—122no—
510D3—241no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—182no—
515C22—182no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22—724no—
524C22C22×D3611yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—361no—
531C4—361no—
532C4—361no—
533C4—361no—
534C4—361no—
535C4#41×D911yescharacteristic
536C4#41×D911yescharacteristic
537C3#7938311yescharacteristic
538C2—41no—
539C2—362no—
540C2—362no—
541C2—721no—
542C2#1058962611yescharacteristic
543C2#1058985311yescharacteristic
544C2#1058985411yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#433C2
socleC22×C3C22×D12
prime radical#10588414C2
hypercenter#433D9
hypocenterC9#3118
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #10589636C2semidirect
2. #10589623C2semidirect
3. C9×#433C2semidirect
4. #10588530C2semidirect
5. #10588528C2semidirect
6. #10588528C2semidirect
7. #10588526C2semidirect
8. #10588419C2semidirect
10. #10588413C2semidirect
11. #10588403C2semidirect
12. #10588392C2semidirect
13. #10588391C2semidirect
14. C4×D72C2semidirect
15. C4×#3664C2semidirect
34. #63437C22semidirect
39. C4×D36C22semidirect
40. #63431C22semidirect
41. C4×Dic18C22semidirect
42. C9×C4⋊C8C22semidirect
43. C9×C4⋊C8C22semidirect
46. C9×#97C22semidirect
47. C4×C8×C9C22semidirect
52. #63380C22semidirect
53. #63380C22semidirect
54. #63378C22semidirect
55. #63378C22semidirect
56. #63377C22semidirect
57. #63377C22semidirect
58. #63376C22semidirect
59. #63376C22semidirect
222. #433D9semidirect
327. C4⋊C8C2×D9semidirect
328. C4⋊C8C2×D9semidirect
339. #97C2×D9semidirect
340. C4×C8C2×D9semidirect
463. C9#3118semidirect

Maximal subgroups

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

subgroupindex
#105896362
#105896232
C9×#4332
#105885302
#105885282
#105885262
#105884192
#105884142
#105884132
#105884032
#105883922
#105883912
C4×D722
C4×#36642
#793833