Finite Group Databasebeta

← #11872787

Subgroups — #11872787

Order 1152.

591 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589727C211yesmaximal, characteristic, complemented
2#10589623C211yesmaximal, characteristic
3C9×#485C211yesmaximal, characteristic, complemented
4#10588729C211yesmaximal, characteristic
5#10588680C211yesmaximal, characteristic, complemented
6#10588571C211yesmaximal, characteristic, complemented
7#10588569C211yesmaximal, characteristic, complemented
8#10588551C211yesmaximal, characteristic, complemented
9#10588532C211yesmaximal, characteristic, complemented
10#10588498C211yesmaximal, characteristic, complemented
11#10588498C211yesmaximal, characteristic, complemented
12#10588497C211yesmaximal, characteristic, complemented
13#10588468C211yesmaximal, characteristic, complemented
14#10588413C211yesmaximal, characteristic
15#10588400C211yesmaximal, characteristic, complemented
16#81498—31nomaximal
17C22×D36C2211yescharacteristic
18C9×C22⋊Q8C2211yescharacteristic
19C9×#117C2211yescharacteristic
20Q8×Dic9C2211yescharacteristic, complemented
21#63506C2211yescharacteristic, complemented
22C2×#3675C2211yescharacteristic
23C2×#3675C2211yescharacteristic
24#63488C2211yescharacteristic
25#63486C2211yescharacteristic
26C2×#3664C2211yescharacteristic
27C2×#3664C2211yescharacteristic
28#63455C2211yescharacteristic
29#63455C2211yescharacteristic
30#63455C2211yescharacteristic
31#63455C2211yescharacteristic
32#63452—21no—
33#63452C2211yescharacteristic, complemented
34#63451—21no—
35#63449C2211yescharacteristic, complemented
36C22⋊C4×D9—21no—
37C22⋊C4×D9—21no—
38#63441—21no—
39#63441—21no—
40C4×D36—21no—
41C4×D36—21no—
42C9×#107C2211yescharacteristic, complemented
43C9×#106C2211yescharacteristic, complemented
44C9×#103C2211yescharacteristic, complemented
45C9×#103C2211yescharacteristic, complemented
46C9×C22⋊C8C2211yescharacteristic
47#63389C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63375C2211yescharacteristic, complemented
51Dic9⋊C8C2211yescharacteristic, complemented
52Dic9⋊C8C2211yescharacteristic, complemented
53C8×Dic9C2211yescharacteristic, complemented
54#63369C2211yescharacteristic
55#63369C2211yescharacteristic
56#63368C2211yescharacteristic, complemented
57#63368C2211yescharacteristic, complemented
58#63367C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5625—31no—
61#5521—31no—
62C3×#485D311yescharacteristic
63#5046—31no—
64#4996—31no—
65#4891—31no—
66#4889—31no—
67#4871—31no—
68#4852—31no—
69#4818—31no—
70#4818—31no—
71#4817—31no—
72#4788—31no—
73#4731—31no—
74#4720—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C2×D36—21no—
79C2×D36—22no—
80C2×D36—22no—
81C2×D36C2311yescharacteristic
82C2×D36C2311yescharacteristic
83C2×C4×D9—21no—
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×Dic18C2311yescharacteristic
88C2×C8×C9C2311yescharacteristic
89C2×C8×C9C2311yescharacteristic
90C9×C4⋊C4—21no—
91C9×C4⋊C4C2311yescharacteristic
92C9×C4⋊C4C2311yescharacteristic
93C9×C4⋊C4C2311yescharacteristic
94C9×C22⋊C4—21no—
95C9×C22⋊C4—21no—
96C42×C9—21no—
97#3676—21no—
98#3676D411yescharacteristic
99#3676D411yescharacteristic
100#3675—22no—
101#3675—22no—
102(C2×D9)⋊C4—21no—
103(C2×D9)⋊C4—21no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4—21no—
106C4⋊Dic9—21no—
107C4⋊Dic9—21no—
108C4⋊Dic9D411yescharacteristic
109C4⋊Dic9D411yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9C2311yescharacteristic
119C4×Dic9C2311yescharacteristic
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122#3664—22no—
123#3664—22no—
124#3123—91noSylow
125C22×D12—31no—
126C3×C22⋊Q8C2×D311yescharacteristic
127C3×#117C2×D311yescharacteristic
128Q8×Dic3—31no—
129#944—31no—
130C2×#215—31no—
131C2×#215—31no—
132#926—31no—
133#924—31no—
134C2×#204—31no—
135C2×#204—31no—
136#893—31no—
137#893—31no—
138#893—31no—
139#893—31no—
140#890—31no—
141#890—61no—
142#889—61no—
143#887—31no—
144D3×C22⋊C4—61no—
145D3×C22⋊C4—61no—
146#879—61no—
147#879—61no—
148C4×D12—61no—
149C4×D12—61no—
150C3×#107C2×D311yescharacteristic
151C3×#106C2×D311yescharacteristic
152C3×#103C2×D311yescharacteristic
153C3×#103C2×D311yescharacteristic
154C3×C22⋊C8C2×D311yescharacteristic
155#830—31no—
156#821—31no—
157#821—31no—
158#815—31no—
159Dic3⋊C8—31no—
160Dic3⋊C8—31no—
161C8×Dic3—31no—
162#810—31no—
163#810—31no—
164#809—31no—
165#809—31no—
166#808—31no—
167#807—31no—
168C23×C9C2×D411yescharacteristic
169C22×D9—21no—
170C22×D9—21no—
171C22×D9—24no—
172C22×D9—81no—
173C22×D9—81no—
174Q8×C9—21no—
175Q8×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2411yescharacteristic
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9C2×D411yescharacteristic
187C2×Dic9C2×D411yescharacteristic
188C2×Dic9C2×D411yescharacteristic
189C2×Dic9C2×D411yescharacteristic
190D36—24no—
191D36—21no—
192D36—21no—
193D36#4112yes—
194D36#4112yes—
195C4×D9—81no—
196C4×D9—81no—
197C4×D9—81no—
198C4×D9—81no—
199Dic18—21no—
200Dic18—21no—
201C8×C9—21no—
202C8×C9—21no—
203C9⋊C8—21no—
204C9⋊C8—21no—
205#541—91no—
206#518—91no—
207#485—91no—
208#485D911yescharacteristic, complemented
209#478—91no—
210#478—91no—
211#461—91no—
212#461—91no—
213#450—91no—
214#450—91no—
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16—91no—
219#433—91no—
220C23×D3—61no—
221C2×C3×Q8C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×D12—31no—
224C2×D12—31no—
225C2×D12—62no—
226C2×D12—62no—
227C2×D12—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×Dic6—31no—
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C3×C4⋊C4—21no—
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C42—21no—
242#217—31no—
243#217—31no—
244#217—61no—
245#215—62no—
246#215—62no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—61no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261C4×Dic3—31no—
262C4×Dic3—31no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267#204—62no—
268#204—62no—
269C22×C9—21no—
270C22×C9—21no—
271C22×C9—21no—
272C22×C9C22×D411yescharacteristic
273C2×D9—22no—
274C2×D9—22no—
275C2×D9—41no—
276C2×D9—41no—
277C2×D9—41no—
278C2×D9—41no—
279C2×D9—84no—
280C4×C9—21no—
281C4×C9—41no—
282C4×C9—41no—
283C4×C9—41no—
284C4×C9—41no—
285C4×C9C2×#4111yescharacteristic
286C4×C9C2×#4111yescharacteristic
287Dic9—21no—
288Dic9—21no—
289Dic9—21no—
290Dic9—21no—
291Dic9—41no—
292Dic9—41no—
293C22×D4—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16—91no—
297C2×SD16—91no—
298C4⋊Q8—91no—
299#126—181no—
300#126—181no—
301#125—91no—
302#125—181no—
303#125—181no—
304C22⋊Q8—91no—
305C22⋊Q8C2×D911yescharacteristic
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—91no—
311C4×D4—91no—
312C4×D4—181no—
313C4×D4—181no—
314#117—91no—
315#117C2×D911yescharacteristic
316C2×C22⋊C4—181no—
317C2×C22⋊C4—181no—
318#107—91no—
319#107C2×D911yescharacteristic, complemented
320#106—91no—
321#106C2×D911yescharacteristic, complemented
322C4⋊C8—91no—
323C4⋊C8—91no—
324#103—91no—
325#103—91no—
326#103C2×D911yescharacteristic, complemented
327#103C2×D911yescharacteristic, complemented
328#102—91no—
329#102—91no—
330#102—91no—
331#102—91no—
332C22⋊C8—91no—
333C22⋊C8C2×D911yescharacteristic
334#97—91no—
335C4×C8—91no—
336C23×C3D3×D411yescharacteristic
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—64no—
340C22×D3—241no—
341C22×D3—241no—
342C3×Q8—21no—
343C3×Q8—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—31no—
353C2×Dic3—31no—
354C2×Dic3—31no—
355C2×Dic3—31no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358D12—32no—
359D12—32no—
360D12—64no—
361D12—61no—
362D12—61no—
363C4×D3—241no—
364C4×D3—241no—
365C4×D3—241no—
366C4×D3—241no—
367Dic6—61no—
368Dic6—61no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C2×C9—41no—
374C2×C9#52511yescharacteristic
375C2×C9#57711yescharacteristic
376C2×C9#57711yescharacteristic
377D9—42no—
378D9—42no—
379C24—181no—
380C2×Q8—91no—
381C2×Q8C22×D911yescharacteristic
382C2×D4—91no—
383C2×D4—91no—
384C2×D4—182no—
385C2×D4—182no—
386C2×D4—181no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4C22×D911yescharacteristic
392SD16—182no—
393SD16—182no—
394SD16—182no—
395SD16—182no—
396C2×C8—91no—
397C2×C8—91no—
398C2×C8C22×D911yescharacteristic
399C2×C8C22×D911yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—91no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4C22×D911yescharacteristic
412C4⋊C4C22×D911yescharacteristic
413C4⋊C4C22×D911yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—91no—
417C22⋊C4—91no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C42—21no—
424C42—91no—
425C42—91no—
426C42—181no—
427C42—181no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3C2×D3×D411yescharacteristic
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—244no—
439C3×C4—21no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4D3×#4111yescharacteristic
445C3×C4D3×#4111yescharacteristic
446Dic3—61no—
447Dic3—61no—
448Dic3—61no—
449Dic3—61no—
450Dic3—121no—
451Dic3—121no—
452C9#312311yescharacteristic, complemented, Sylow
453C23—184no—
454C23—181no—
455C23—181no—
456C23—721no—
457C23—721no—
458C23D4×D911yescharacteristic
459Q8—21no—
460Q8—21no—
461Q8—181no—
462Q8—181no—
463D4—92no—
464D4—92no—
465D4—184no—
466D4—181no—
467D4—181no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—91no—
475C2×C4—91no—
476C2×C4—91no—
477C2×C4—91no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4—721no—
482C2×C4—721no—
483C2×C4—721no—
484C2×C4D4×D911yescharacteristic
485C2×C4C23×D911yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—41no—
491C2×C3#565611yescharacteristic
492C2×C3#577011yescharacteristic
493C2×C3#577811yescharacteristic
494D3—122no—
495D3—122no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—182no—
500C22—182no—
501C22—361no—
502C22—361no—
503C22—361no—
504C22—361no—
505C22—724no—
506C22C2×D4×D911yescharacteristic
507C4—21no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—181no—
513C4—181no—
514C4—181no—
515C4—181no—
516C4—361no—
517C4—361no—
518C4#41×D911yescharacteristic
519C4#41×D911yescharacteristic
520C3#8149811yescharacteristic
521C2—41no—
522C2—362no—
523C2—362no—
524C2#1058975811yescharacteristic
525C2#1058987211yescharacteristic
526C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#485C2
socleC22×C3C2×D3×D4
prime radicalC22×D36C22
hypercenter#485D9
hypocenterC9#3123
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #10589727C2semidirect
3. C9×#485C2semidirect
5. #10588680C2semidirect
6. #10588571C2semidirect
7. #10588569C2semidirect
8. #10588551C2semidirect
9. #10588532C2semidirect
10. #10588498C2semidirect
11. #10588498C2semidirect
12. #10588497C2semidirect
13. #10588468C2semidirect
15. #10588400C2semidirect
20. Q8×Dic9C22semidirect
21. #63506C22semidirect
33. #63452C22semidirect
35. #63449C22semidirect
42. C9×#107C22semidirect
43. C9×#106C22semidirect
44. C9×#103C22semidirect
45. C9×#103C22semidirect
50. #63375C22semidirect
51. Dic9⋊C8C22semidirect
52. Dic9⋊C8C22semidirect
53. C8×Dic9C22semidirect
56. #63368C22semidirect
57. #63368C22semidirect
58. #63367C22semidirect
59. #63366C22semidirect
208. #485D9semidirect
319. #107C2×D9semidirect
321. #106C2×D9semidirect
326. #103C2×D9semidirect
327. #103C2×D9semidirect
452. C9#3123semidirect

Maximal subgroups

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

subgroupindex
#105897272
#105896232
C9×#4852
#105887292
#105886802
#105885712
#105885692
#105885512
#105885322
#105884982
#105884972
#105884682
#105884132
#105884002
#814983