Finite Group Databasebeta

← #11884519

Subgroups — #11884519

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#547C211yesmaximal, characteristic, complemented
2C2×#63513C211yesmaximal, characteristic, complemented
3C2×#63511C211yesmaximal, characteristic, complemented
4#10589654C211yesmaximal, characteristic, complemented
5#10588919C211yesmaximal, characteristic, complemented
6#10588918C211yesmaximal, characteristic, complemented
7#10588771C211yesmaximal, characteristic, complemented
8#10588763C211yesmaximal, characteristic, complemented
9#10588732C211yesmaximal, characteristic, complemented
10#10588730C211yesmaximal, characteristic, complemented
11#10588727C211yesmaximal, characteristic, complemented
12#10588726C211yesmaximal, characteristic, complemented
13#10588699C211yesmaximal, characteristic, complemented
14#10588694C211yesmaximal, characteristic, complemented
15#10588688C211yesmaximal, characteristic, complemented
16#83528—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×C9×#41C2211yescharacteristic
19C2×#3697C2211yescharacteristic
20C22×Dic18C2211yescharacteristic
21C9×C4⋊Q8C2211yescharacteristic
22C9×#123—21no—
23C9×#123—21no—
24C9×C22⋊Q8C2211yescharacteristic
25C9×C22⋊Q8C2211yescharacteristic
26C9×#121—21no—
27C4×D4×C9C2211yescharacteristic
28C4×D4×C9C2211yescharacteristic
29C2×C9×C4⋊C4—21no—
30#63513—24no—
31#63511—24no—
32C2×#3675C2211yescharacteristic
33C2×#3675C2211yescharacteristic
34C2×#3674C2211yescharacteristic
35C2×#3674C2211yescharacteristic
36C2×#3674C2211yescharacteristic
37C2×#3674C2211yescharacteristic
38#63501—21no—
39C2×#3673C2211yescharacteristic
40C2×#3672C2211yescharacteristic
41C2×#3672C2211yescharacteristic
42#63492C2211yescharacteristic
43#63486C2211yescharacteristic
44C2×#3667C2211yescharacteristic
45C22×C9⋊C8C2211yescharacteristic
46#63458—21no—
47#63447—21no—
48#611⋊C4—21no—
49#63437C2211yescharacteristic
50C4×Dic18C2211yescharacteristic
51#63395C2211yescharacteristic
52#63395C2211yescharacteristic
53#63392C2211yescharacteristic
54#63389C2211yescharacteristic
55#63389C2211yescharacteristic
56#63369C2211yescharacteristic
57#63368C2211yescharacteristic
58#63368C2211yescharacteristic
59#63366C2211yescharacteristic
60C4⋊(C9⋊C8)C2211yescharacteristic
61#63362C2211yescharacteristic
62C3×#547D311yescharacteristic
63C2×#951—31no—
64C2×#950—31no—
65#5552—31no—
66#5239—31no—
67#5238—31no—
68#5090—31no—
69#5086—31no—
70#5051—31no—
71#5050—31no—
72#5049—31no—
73#5047—31no—
74#5018—31no—
75#5016—31no—
76#5011—31no—
77C9×#41—22no—
78C9×#41—22no—
79C9×#41—41no—
80C9×#41—41no—
81C2×Q8×C9C2311yescharacteristic
82C2×Q8×C9C2311yescharacteristic
83C2×D4×C9—21no—
84C2×D4×C9—21no—
85C2×D4×C9D411yescharacteristic
86C2×D4×C9C2311yescharacteristic
87C22×C4×C9—21no—
88C22×C4×C9—21no—
89C22×C4×C9—21no—
90C22×C4×C9C2311yescharacteristic
91C22×C4×C9C2311yescharacteristic
92C2×#611—21no—
93C2×#611—21no—
94C22×Dic9—21no—
95#3697—22no—
96#3697—41no—
97C2×D36C2311yescharacteristic
98C2×C4×D9—21no—
99C2×Dic18—22no—
100C2×Dic18—21no—
101C2×Dic18—41no—
102C2×Dic18C2311yescharacteristic
103C2×Dic18C2311yescharacteristic
104C9×C4⋊C4—21no—
105C9×C4⋊C4—21no—
106C9×C4⋊C4—21no—
107C9×C4⋊C4—21no—
108C9×C4⋊C4D411yescharacteristic
109C9×C4⋊C4C2311yescharacteristic
110C9×C22⋊C4—21no—
111C9×C22⋊C4—21no—
112C9×C22⋊C4—21no—
113C9×C22⋊C4D411yescharacteristic
114C9×C22⋊C4D411yescharacteristic
115C42×C9C2311yescharacteristic
116#3676—21no—
117#3675—22no—
118#3675—41no—
119#3674—22no—
120#3674—22no—
121#3674—22no—
122#3674—41no—
123#3673—22no—
124#3672—22no—
125#3672D414yescomplemented
126(C2×D9)⋊C4—21no—
127(C2×D9)⋊C4—21no—
128(C2×D9)⋊C4—21no—
129C4⋊Dic9C2311yescharacteristic
130Dic9⋊C4—21no—
131Dic9⋊C4—21no—
132C4×Dic9—21no—
133#3667—22no—
134C2×C9⋊C8—22no—
135C2×C9⋊C8C2311yescharacteristic
136C2×C9⋊C8C2311yescharacteristic
137C2×C9⋊C8C2311yescharacteristic
138C2×C9⋊C8C2311yescharacteristic
139#3269—91noSylow
140C2×C3×#41C2×D311yescharacteristic
141C2×C3×#41C2×D311yescharacteristic
142C2×#235—31no—
143C22×Dic6—31no—
144C3×C4⋊Q8C2×D311yescharacteristic
145C3×#123—21no—
146C3×#123—21no—
147C3×C22⋊Q8C2×D311yescharacteristic
148C3×C22⋊Q8C2×D311yescharacteristic
149C3×#121—21no—
150C3×C4×D4C2×D311yescharacteristic
151C3×C4×D4C2×D311yescharacteristic
152C2×C3×C4⋊C4—21no—
153#951—64no—
154#950—64no—
155C2×#216—31no—
156C2×#216—31no—
157C2×#216—31no—
158C2×#216—31no—
159C2×#215—31no—
160C2×#215—31no—
161#939—61no—
162C2×#214—31no—
163C2×#214—31no—
164C2×#213—31no—
165#930—31no—
166#924—31no—
167C2×#208—31no—
168C22×C3⋊C8—31no—
169#896—61no—
170#885—61no—
171#67⋊C4—61no—
172#875—31no—
173C4×Dic6—31no—
174#835—31no—
175#835—31no—
176#832—31no—
177#830—31no—
178#830—31no—
179#810—31no—
180#810—31no—
181#809—31no—
182#807—31no—
183C4⋊(C3⋊C8)—31no—
184#803—31no—
185C23×C9—21no—
186C23×C9C2×D411yescharacteristic
187C23×C9C2×D411yescharacteristic
188C22×D9—21no—
189Q8×C9—21no—
190Q8×C9—21no—
191Q8×C9—21no—
192Q8×C9—21no—
193D4×C9—21no—
194D4×C9—41no—
195D4×C9—42no—
196D4×C9—42no—
197D4×C9C2×D412yes—
198C2×C4×C9—21no—
199C2×C4×C9—21no—
200C2×C4×C9—21no—
201C2×C4×C9—21no—
202C2×C4×C9—21no—
203C2×C4×C9—21no—
204C2×C4×C9—21no—
205C2×C4×C9—42no—
206C2×C4×C9—42no—
207C2×C4×C9—42no—
208C2×C4×C9C2×D411yescharacteristic
209C2×C4×C9C2×D411yescharacteristic
210C2×C4×C9C2×D411yescharacteristic
211C2×C4×C9C2×D411yescharacteristic
212C2×C4×C9C2411yescharacteristic
213#611—42no—
214#611—42no—
215C2×Dic9—21no—
216C2×Dic9—21no—
217C2×Dic9—21no—
218C2×Dic9—42no—
219D36—21no—
220D36—21no—
221C4×D9—42no—
222Dic18—21no—
223Dic18—21no—
224Dic18—21no—
225Dic18—42no—
226Dic18C2×D412yes—
227C9⋊C8—21no—
228C9⋊C8—21no—
229C9⋊C8—21no—
230C9⋊C8C2×D412yes—
231C2×#137—91no—
232C2×#135—91no—
233#548—91no—
234#547D911yescharacteristic, complemented
235#497—91no—
236#468—91no—
237#467—91no—
238#463—91no—
239#462—91no—
240#452—91no—
241#452—91no—
242#451—91no—
243#449—91no—
244#440—91no—
245#435—91no—
246C3×#41—22no—
247C3×#41—22no—
248C3×#41—41no—
249C3×#41—41no—
250C2×C3×Q8C22×D311yescharacteristic
251C2×C3×Q8C22×D311yescharacteristic
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4#6711yescharacteristic
255C2×C3×D4C22×D311yescharacteristic
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C2×#67—61no—
262C2×#67—61no—
263C22×Dic3—61no—
264#235—62no—
265#235—121no—
266C2×D12—31no—
267C2×C4×D3—61no—
268C2×Dic6—31no—
269C2×Dic6—31no—
270C2×Dic6—62no—
271C2×Dic6—61no—
272C2×Dic6—121no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4#6711yescharacteristic
278C3×C4⋊C4C22×D311yescharacteristic
279C3×C22⋊C4—21no—
280C3×C22⋊C4—21no—
281C3×C22⋊C4—21no—
282C3×C22⋊C4#6711yescharacteristic
283C3×C22⋊C4#6711yescharacteristic
284C3×C42C22×D311yescharacteristic
285#217—61no—
286#216—62no—
287#216—62no—
288#216—62no—
289#216—121no—
290#215—62no—
291#215—121no—
292#214—34no—
293#214—62no—
294#213—62no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—61no—
298C4⋊Dic3—31no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301C4×Dic3—61no—
302#208—62no—
303C2×C3⋊C8—31no—
304C2×C3⋊C8—31no—
305C2×C3⋊C8—31no—
306C2×C3⋊C8—31no—
307C2×C3⋊C8—62no—
308C22×C9—21no—
309C22×C9—21no—
310C22×C9—22no—
311C22×C9—21no—
312C22×C9—21no—
313C22×C9—21no—
314C22×C9—21no—
315C22×C9—41no—
316C22×C9—41no—
317C22×C9C22×D411yescharacteristic
318C2×D9—41no—
319C2×D9—41no—
320C2×D9—41no—
321C4×C9—21no—
322C4×C9—21no—
323C4×C9—21no—
324C4×C9—21no—
325C4×C9—41no—
326C4×C9—41no—
327C4×C9—41no—
328C4×C9C22×D411yescharacteristic
329C4×C9H(5,𝔽2)11yescharacteristic
330Dic9—22no—
331Dic9—41no—
332Dic9—41no—
333C2×#41—91no—
334C2×#41C2×D911yescharacteristic
335C2×#41C2×D911yescharacteristic
336C22×Q8—91no—
337#137—184no—
338#135—184no—
339C2×Q16—91no—
340C2×Q16—91no—
341C2×Q16—91no—
342C2×Q16—91no—
343C2×SD16—91no—
344C2×SD16—91no—
345C2×SD16—91no—
346C2×SD16—91no—
347C2×D8—91no—
348C2×M16—91no—
349C22×C8—91no—
350C4⋊Q8C2×D911yescharacteristic
351#124—91no—
352#124—181no—
353#123—21no—
354#123—21no—
355C22⋊Q8—91no—
356C22⋊Q8—181no—
357C22⋊Q8C2×D911yescharacteristic
358C22⋊Q8C2×D911yescharacteristic
359#121—21no—
360#121—91no—
361#121—181no—
362C4×Q8—91no—
363C4×D4—181no—
364C4×D4C2×D911yescharacteristic
365C4×D4C2×D911yescharacteristic
366C2×C4⋊C4—21no—
367#107—91no—
368C4⋊C8—91no—
369#103—91no—
370#103—91no—
371#103—91no—
372#103—91no—
373#102—91no—
374#102—91no—
375C22⋊C8—91no—
376C22⋊C8—91no—
377#97—91no—
378C23×C3—21no—
379C23×C3C2×#6711yescharacteristic
380C23×C3C2×#6711yescharacteristic
381C22×D3—61no—
382C3×Q8—21no—
383C3×Q8—21no—
384C3×Q8—21no—
385C3×Q8—21no—
386C3×D4—21no—
387C3×D4—41no—
388C3×D4—42no—
389C3×D4—42no—
390C3×D4D3×D412yes—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C2×#6711yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—122no—
407#67—122no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—122no—
412D12—61no—
413D12—61no—
414C4×D3—122no—
415Dic6—32no—
416Dic6—61no—
417Dic6—61no—
418Dic6—61no—
419Dic6—122no—
420C3⋊C8—32no—
421C3⋊C8—61no—
422C3⋊C8—61no—
423C3⋊C8—61no—
424C2×C9—41no—
425C2×C9—41no—
426C2×C9—42no—
427C2×C9D4211yescharacteristic
428C2×C9#57511yescharacteristic
429C2×C9#57811yescharacteristic
430D9—81no—
431#41—22no—
432#41—22no—
433#41—41no—
434#41—41no—
435#41—182no—
436#41—361no—
437C2×Q8—91no—
438C2×Q8—91no—
439C2×Q8—182no—
440C2×Q8—181no—
441C2×Q8—361no—
442C2×Q8C22×D911yescharacteristic
443C2×Q8C22×D911yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—91no—
447C2×D4—181no—
448C2×D4—181no—
449C2×D4#61111yescharacteristic
450C2×D4C22×D911yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—181no—
455C22×C4—181no—
456C22×C4C22×D911yescharacteristic
457C22×C4C22×D911yescharacteristic
458Q16—182no—
459Q16—182no—
460Q16—182no—
461Q16—361no—
462SD16—94no—
463SD16—182no—
464SD16—182no—
465SD16—361no—
466D8—182no—
467M16—182no—
468C2×C8—91no—
469C2×C8—91no—
470C2×C8—91no—
471C2×C8—91no—
472C2×C8—182no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—91no—
478C4⋊C4—181no—
479C4⋊C4—181no—
480C4⋊C4#61111yescharacteristic
481C4⋊C4C22×D911yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—181no—
486C22⋊C4—181no—
487C22⋊C4—181no—
488C22⋊C4—181no—
489C22⋊C4#61111yescharacteristic
490C22⋊C4#61111yescharacteristic
491C42—181no—
492C42C22×D911yescharacteristic
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3C22×#6711yescharacteristic
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—121no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—41no—
513C3×C4C2×D3×D411yescharacteristic
514C3×C4#100411yescharacteristic
515Dic3—62no—
516Dic3—121no—
517Dic3—121no—
518C9#326911yescharacteristic, complemented, Sylow
519C23—21no—
520C23—181no—
521C23C2×#61111yescharacteristic
522C23C2×#61111yescharacteristic
523Q8—21no—
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—92no—
528Q8—181no—
529Q8—181no—
530Q8—181no—
531Q8—362no—
532D4—21no—
533D4—41no—
534D4—42no—
535D4—42no—
536D4—181no—
537D4—181no—
538D4—362no—
539D4—362no—
540D4D4×D912yes—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—362no—
555C2×C4—362no—
556C2×C4C2×#61111yescharacteristic
557C2×C4C2×#61111yescharacteristic
558C2×C4C2×#61111yescharacteristic
559C2×C4C2×#61111yescharacteristic
560C2×C4C23×D911yescharacteristic
561C8—92no—
562C8—181no—
563C8—181no—
564C8—181no—
565C2×C3—41no—
566C2×C3—41no—
567C2×C3—42no—
568C2×C3D4×#6711yescharacteristic
569C2×C3#582211yescharacteristic
570C2×C3#583811yescharacteristic
571D3—241no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—361no—
582C22—361no—
583C22—361no—
584C22C22×#61111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—182no—
593C4—361no—
594C4—361no—
595C4C2×D4×D911yescharacteristic
596C4#6371011yescharacteristic
597C3#8352811yescharacteristic
598C2—41no—
599C2—41no—
600C2—42no—
601C2—721no—
602C2D4×#61111yescharacteristic
603C2#1058992511yescharacteristic
604C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#547C2
socleC22×C3C22×#67
hypercenter#547D9
hypocenterC9#3269
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C9×#547C2semidirect
2. C2×#63513C2semidirect
3. C2×#63511C2semidirect
4. #10589654C2semidirect
5. #10588919C2semidirect
6. #10588918C2semidirect
7. #10588771C2semidirect
8. #10588763C2semidirect
9. #10588732C2semidirect
10. #10588730C2semidirect
11. #10588727C2semidirect
12. #10588726C2semidirect
13. #10588699C2semidirect
14. #10588694C2semidirect
15. #10588688C2semidirect
125. #3672D4semidirect
234. #547D9semidirect
518. C9#3269semidirect

Maximal subgroups

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

subgroupindex
C9×#5472
C2×#635132
C2×#635112
#105896542
#105889192
#105889182
#105887712
#105887632
#105887322
#105887302
#105887272
#105887262
#105886992
#105886942
#105886882
#835283