Finite Group Databasebeta

← #11870410

Subgroups — #11870410

Order 1152.

738 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589650C211yesmaximal, characteristic, complemented
2C4×D4×D9C211yesmaximal, characteristic, complemented
3C4×C9×D8C211yesmaximal, characteristic, complemented
4#10588836C211yesmaximal, characteristic, complemented
5#10588830C211yesmaximal, characteristic, complemented
6C4×#3673C211yesmaximal, characteristic, complemented
7C4×#3673C211yesmaximal, characteristic, complemented
8#10588570C211yesmaximal, characteristic, complemented
9#10588562C211yesmaximal, characteristic, complemented
10#10588466C211yesmaximal, characteristic, complemented
11#10588454C211yesmaximal, characteristic, complemented
12#10588453C211yesmaximal, characteristic, complemented
13#10588439C211yesmaximal, characteristic, complemented
14C4×D72C211yesmaximal, characteristic, complemented
15#10588367C211yesmaximal, characteristic, complemented
16#79590—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C2×#3697—21no—
19C22×C4×D9—21no—
20C2×C9×D8C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22C4×D4×C9C2211yescharacteristic, complemented
23#63502C2211yescharacteristic, complemented
24#63500C2211yescharacteristic
25D4×Dic9C2211yescharacteristic
26C2×#3673C2211yescharacteristic
27C2×#3673C2211yescharacteristic
28C4×#611—21no—
29C4×#611—21no—
30C2×D72C2211yescharacteristic
31#63457C2211yescharacteristic
32#63455C2211yescharacteristic
33C4⋊C4×D9C2211yescharacteristic
34#63450C2211yescharacteristic, complemented
35#63447—21no—
36#63446—21no—
37#611⋊C4—21no—
38C22⋊C4×D9—21no—
39C4×D36C2211yescharacteristic
40C4×D36C2211yescharacteristic, complemented
41C42×D9C2211yescharacteristic
42C9×#107C2211yescharacteristic, complemented
43C9×#102C2211yescharacteristic
44C9×#102C2211yescharacteristic, complemented
45C4×C8×C9C2211yescharacteristic, complemented
46#63392C2211yescharacteristic
47#63392C2211yescharacteristic, complemented
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic, complemented
50(C2×D9)⋊C8C2211yescharacteristic
51(C2×D9)⋊C8C2211yescharacteristic
52#63378C2211yescharacteristic, complemented
53Dic9⋊C8C2211yescharacteristic, complemented
54Dic9⋊C8C2211yescharacteristic, complemented
55#63369C2211yescharacteristic
56#63369C2211yescharacteristic, complemented
57#63366C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4×C9⋊C8C2211yescharacteristic, complemented
60#5548—31no—
61C4×D3×D4—31no—
62C3×C4×D8D311yescharacteristic
63#5156—31no—
64#5150—31no—
65C4×#213—31no—
66C4×#213—31no—
67#4890—31no—
68#4882—31no—
69#4786—31no—
70#4774—31no—
71#4773—31no—
72#4759—31no—
73C4×D24—31no—
74#4685—31no—
75C23×D9—21no—
76C2×D4×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C22×C4×C9—21no—
80C2×#611—21no—
81C2×#611—21no—
82C2×#611—21no—
83C2×#611—21no—
84C22×Dic9—21no—
85D4×D9—22no—
86D4×D9—22no—
87#3697—44no—
88C2×D36—21no—
89C2×D36C2311yescharacteristic
90C2×D36C2311yescharacteristic
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×C4×D9—21no—
94C2×C4×D9—21no—
95C2×C4×D9—44no—
96C2×C4×D9D411yescharacteristic
97C2×C4×D9D411yescharacteristic
98C2×C4×D9C2311yescharacteristic
99C2×Dic18—21no—
100C9×D8—22no—
101C2×C8×C9C2311yescharacteristic
102C2×C8×C9C2311yescharacteristic
103C9×C4⋊C4C2311yescharacteristic
104C9×C4⋊C4C2311yescharacteristic
105C9×C22⋊C4—21no—
106C9×C22⋊C4—21no—
107C42×C9C2311yescharacteristic
108#3676—21no—
109#3676—21no—
110#3673—22no—
111#3673—22no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4—21no—
114(C2×D9)⋊C4—21no—
115(C2×D9)⋊C4—21no—
116C4⋊Dic9C2311yescharacteristic
117C4⋊Dic9C2311yescharacteristic
118Dic9⋊C4—21no—
119Dic9⋊C4—21no—
120C4×Dic9D411yescharacteristic
121C4×Dic9D411yescharacteristic
122C4×Dic9C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125D72—22no—
126#3100—91noSylow
127C2×D3×D4—31no—
128C2×#235—61no—
129C22×C4×D3—61no—
130C2×C3×D8C2×D311yescharacteristic
131C3×C4×D4C2×D311yescharacteristic
132C3×C4×D4C2×D311yescharacteristic
133#940—31no—
134#938—31no—
135D4×Dic3—31no—
136C2×#213—31no—
137C2×#213—31no—
138C4×#67—61no—
139C4×#67—61no—
140C2×D24—31no—
141#895—31no—
142#893—31no—
143D3×C4⋊C4—31no—
144#888—31no—
145#885—61no—
146#884—61no—
147#67⋊C4—61no—
148D3×C22⋊C4—61no—
149C4×D12—31no—
150C4×D12—31no—
151C42×D3—31no—
152C3×#107C2×D311yescharacteristic
153C3×#102C2×D311yescharacteristic
154C3×#102C2×D311yescharacteristic
155C3×C4×C8C2×D311yescharacteristic
156#832—31no—
157#832—31no—
158#821—31no—
159#821—31no—
160(C2×D3)⋊C8—31no—
161(C2×D3)⋊C8—31no—
162#818—31no—
163Dic3⋊C8—31no—
164Dic3⋊C8—31no—
165#809—31no—
166#809—31no—
167#807—31no—
168#807—31no—
169C4×C3⋊C8—31no—
170C23×C9—21no—
171C23×C9—21no—
172C22×D9—24no—
173C22×D9—21no—
174C22×D9—21no—
175C22×D9—42no—
176C22×D9—42no—
177C22×D9C2×D411yescharacteristic
178D4×C9—21no—
179D4×C9—21no—
180D4×C9—21no—
181D4×C9#4112yescomplemented
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—42no—
185C2×C4×C9—42no—
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2411yescharacteristic
189#611—24no—
190#611—42no—
191#611—42no—
192#611—42no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—42no—
196C2×Dic9C2×D411yescharacteristic
197C2×Dic9C2×D411yescharacteristic
198C2×Dic9C2×D411yescharacteristic
199D36—21no—
200D36—21no—
201D36—21no—
202D36—42no—
203D36#4112yescomplemented
204C4×D9—21no—
205C4×D9—21no—
206C4×D9—41no—
207C4×D9—42no—
208C4×D9—42no—
209C4×D9—42no—
210C4×D9—42no—
211C4×D9D814yescomplemented
212Dic18—42no—
213C8×C9—21no—
214C8×C9—21no—
215C9⋊C8—21no—
216C9⋊C8—21no—
217#532—91no—
218C2×C4×D4—91no—
219#480—91no—
220#480—91no—
221#474—91no—
222#474—91no—
223#459—91no—
224#459—91no—
225#447—91no—
226#447—91no—
227C4×D8—91no—
228C4×D8—91no—
229C4×D8—91no—
230C4×D8D911yescharacteristic, complemented
231#431—91no—
232C23×D3—61no—
233C2×C3×D4C22×D311yescharacteristic
234C2×C3×D4C22×D311yescharacteristic
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C2×#67—61no—
238C2×#67—61no—
239C2×#67—61no—
240C2×#67—61no—
241C22×Dic3—61no—
242D3×D4—62no—
243D3×D4—62no—
244#235—124no—
245C2×D12—31no—
246C2×D12—31no—
247C2×D12—61no—
248C2×C4×D3—31no—
249C2×C4×D3—31no—
250C2×C4×D3—31no—
251C2×C4×D3—61no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—124no—
256C2×Dic6—61no—
257C3×D8—22no—
258C2×C3×C8C22×D311yescharacteristic
259C2×C3×C8C22×D311yescharacteristic
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C22⋊C4—21no—
263C3×C22⋊C4—21no—
264C3×C42C22×D311yescharacteristic
265#217—61no—
266#217—61no—
267#213—62no—
268#213—62no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—61no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277C4×Dic3—31no—
278C4×Dic3—31no—
279C4×Dic3—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—31no—
282D24—62no—
283C22×C9—22no—
284C22×C9—41no—
285C22×C9—41no—
286C22×C9—41no—
287C22×C9—41no—
288C22×C9—41no—
289C22×C9C22×D411yescharacteristic
290C2×D9—21no—
291C2×D9—21no—
292C2×D9—22no—
293C2×D9—48no—
294C2×D9—41no—
295C2×D9—41no—
296C2×D9—41no—
297C2×D9—41no—
298C2×D9—41no—
299C2×D9C2×D812yes—
300C4×C9—21no—
301C4×C9—41no—
302C4×C9—41no—
303C4×C9C2×D812yes—
304C4×C9C2×#4111yescharacteristic
305C4×C9C2×#4111yescharacteristic
306Dic9—21no—
307Dic9—21no—
308Dic9—41no—
309Dic9—41no—
310Dic9C2×D812yes—
311C2×#41—181no—
312C22×D4—91no—
313C23×C4—181no—
314C2×D8—91no—
315C2×D8—91no—
316C2×D8—91no—
317C2×D8C2×D911yescharacteristic
318C4⋊Q8—91no—
319#127—91no—
320#124—181no—
321#121—91no—
322#121—91no—
323#121—181no—
324C4×D4—91no—
325C4×D4—91no—
326C4×D4—91no—
327C4×D4—91no—
328C4×D4—181no—
329C4×D4—181no—
330C4×D4—181no—
331C4×D4C2×D911yescharacteristic
332C4×D4C2×D911yescharacteristic, complemented
333C2×C4⋊C4—91no—
334C2×C22⋊C4—181no—
335C2×C42—91no—
336#107—91no—
337#107—91no—
338#107—91no—
339#107C2×D911yescharacteristic, complemented
340C4⋊C8—91no—
341C4⋊C8—91no—
342#102—91no—
343#102—91no—
344#102—91no—
345#102—91no—
346#102—91no—
347#102—91no—
348#102C2×D911yescharacteristic
349#102C2×D911yescharacteristic, complemented
350C22⋊C8—91no—
351C22⋊C8—91no—
352C4×C8—91no—
353C4×C8C2×D911yescharacteristic, complemented
354C23×C3—21no—
355C23×C3—21no—
356C22×D3—31no—
357C22×D3—64no—
358C22×D3—61no—
359C22×D3—61no—
360C22×D3—122no—
361C22×D3—122no—
362C3×D4—21no—
363C3×D4—21no—
364C3×D4—21no—
365C3×D4#23512yes—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—64no—
374#67—122no—
375#67—122no—
376#67—122no—
377C2×Dic3—31no—
378C2×Dic3—31no—
379C2×Dic3—31no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—122no—
383D12—32no—
384D12—61no—
385D12—61no—
386D12—61no—
387D12—122no—
388C4×D3—34no—
389C4×D3—61no—
390C4×D3—61no—
391C4×D3—122no—
392C4×D3—121no—
393C4×D3—122no—
394C4×D3—122no—
395C4×D3—122no—
396Dic6—122no—
397C3×C8—21no—
398C3×C8—21no—
399C3⋊C8—61no—
400C3⋊C8—61no—
401C2×C9—42no—
402C2×C9—81no—
403C2×C9#52511yescharacteristic
404C2×C9C22×D811yescharacteristic
405C2×C9#57511yescharacteristic
406D9—22no—
407D9—42no—
408D9—81no—
409C24—181no—
410#41—364no—
411C2×Q8—181no—
412C2×D4—91no—
413C2×D4—91no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4—182no—
419C2×D4—182no—
420C2×D4—181no—
421C2×D4C22×D911yescharacteristic
422C2×D4C22×D911yescharacteristic
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—91no—
426C22×C4—91no—
427C22×C4—91no—
428C22×C4—181no—
429C22×C4—181no—
430C22×C4—181no—
431C22×C4—181no—
432C22×C4—181no—
433C22×C4—364no—
434D8—22no—
435D8—182no—
436D8—182no—
437D8—182no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8C22×D911yescharacteristic
441C2×C8C22×D911yescharacteristic
442C4⋊C4—91no—
443C4⋊C4—91no—
444C4⋊C4—181no—
445C4⋊C4—181no—
446C4⋊C4C22×D911yescharacteristic
447C4⋊C4C22×D911yescharacteristic
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C22⋊C4—181no—
456C42—91no—
457C42—91no—
458C42—91no—
459C42C22×D911yescharacteristic
460C22×C3—22no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3C2×D3×D411yescharacteristic
467C2×D3—32no—
468C2×D3—61no—
469C2×D3—61no—
470C2×D3—62no—
471C2×D3—128no—
472C2×D3—121no—
473C2×D3—121no—
474C2×D3—121no—
475C2×D3—121no—
476C2×D3—121no—
477C3×C4—21no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4D3×D812yes—
481C3×C4C2×#23511yescharacteristic
482C3×C4D3×#4111yescharacteristic
483Dic3—32no—
484Dic3—61no—
485Dic3—61no—
486Dic3—121no—
487Dic3—121no—
488C9#310011yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—91no—
492C23—184no—
493C23—181no—
494C23—181no—
495C23—362no—
496C23—362no—
497Q8—362no—
498D4—21no—
499D4—21no—
500D4—21no—
501D4—92no—
502D4—184no—
503D4—181no—
504D4—181no—
505D4—181no—
506D4—362no—
507D4—362no—
508D4—362no—
509D4—362no—
510D4#369712yescomplemented
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—91no—
516C2×C4—94no—
517C2×C4—91no—
518C2×C4—91no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—361no—
524C2×C4—362no—
525C2×C4—362no—
526C2×C4—362no—
527C2×C4—362no—
528C2×C4—362no—
529C2×C4D4×D911yescharacteristic
530C2×C4D4×D911yescharacteristic
531C2×C4C23×D911yescharacteristic
532C8—21no—
533C8—21no—
534C8—181no—
535C8—181no—
536C2×C3—42no—
537C2×C3—81no—
538C2×C3#554711yescharacteristic
539C2×C3C2×D3×D811yescharacteristic
540C2×C3#576811yescharacteristic
541D3—62no—
542D3—122no—
543D3—241no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—92no—
551C22—181no—
552C22—181no—
553C22—182no—
554C22—368no—
555C22—361no—
556C22—361no—
557C22—361no—
558C22—361no—
559C22—361no—
560C22C2×D4×D911yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—92no—
565C4—181no—
566C4—181no—
567C4—361no—
568C4—361no—
569C4D8×D912yes—
570C4C2×#369711yescharacteristic
571C4#41×D911yescharacteristic
572C3#7959011yescharacteristic
573C2—42no—
574C2—81no—
575C2—182no—
576C2—362no—
577C2—721no—
578C2#1058964911yescharacteristic
579C2C2×D8×D911yescharacteristic
580C2#1058987011yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×D8C2
socleC22×C3C2×D3×D4
hypercenterC4×D8D9
hypocenterC9#3100
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10589650C2semidirect
2. C4×D4×D9C2semidirect
3. C4×C9×D8C2semidirect
4. #10588836C2semidirect
5. #10588830C2semidirect
6. C4×#3673C2semidirect
7. C4×#3673C2semidirect
8. #10588570C2semidirect
9. #10588562C2semidirect
10. #10588466C2semidirect
11. #10588454C2semidirect
12. #10588453C2semidirect
13. #10588439C2semidirect
14. C4×D72C2semidirect
15. #10588367C2semidirect
22. C4×D4×C9C22semidirect
23. #63502C22semidirect
34. #63450C22semidirect
40. C4×D36C22semidirect
42. C9×#107C22semidirect
44. C9×#102C22semidirect
45. C4×C8×C9C22semidirect
47. #63392C22semidirect
49. #63380C22semidirect
52. #63378C22semidirect
53. Dic9⋊C8C22semidirect
54. Dic9⋊C8C22semidirect
56. #63369C22semidirect
57. #63366C22semidirect
58. #63366C22semidirect
59. C4×C9⋊C8C22semidirect
181. D4×C9#41semidirect
203. D36#41semidirect
211. C4×D9D8semidirect
230. C4×D8D9semidirect
332. C4×D4C2×D9semidirect
339. #107C2×D9semidirect
349. #102C2×D9semidirect
353. C4×C8C2×D9semidirect
488. C9#3100semidirect
510. D4#3697semidirect

Maximal subgroups

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

subgroupindex
#105896502
C4×D4×D92
C4×C9×D82
#105888362
#105888302
C4×#36732
#105885702
#105885622
#105884662
#105884542
#105884532
#105884392
C4×D722
#105883672
#795903