Finite Group Databasebeta

← #11901971

Subgroups — #11901971

Order 1152.

1740 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C9C211yesmaximal, characteristic, complemented
2#10589906C212yesmaximal, complemented
3#10589893C212yesmaximal, complemented
4C2×C4×#611C212yesmaximal, complemented
5#10589666C214yesmaximal, complemented
6#10589662C214yesmaximal, complemented
7#10589649C214yesmaximal, complemented
8#10589640C214yesmaximal, complemented
9#10589617C212yesmaximal, complemented
10#10589596C212yesmaximal, complemented
11#10589595C211yesmaximal, characteristic, complemented
12#10589585C211yesmaximal, characteristic, complemented
13#10589581C212yesmaximal, complemented
14#85776—31nomaximal
15C22×D4×C9C2211yescharacteristic
16C23×C4×C9C2211yescharacteristic
17C23×C4×C9C2211yescharacteristic, complemented
18C22×#611C2212yes—
19C2×#3697C2212yescomplemented
20C22×C4×D9C2212yescomplemented
21C4×D4×C9C2214yescomplemented
22C4×D4×C9C2214yescomplemented
23C2×C9×C4⋊C4C2211yescharacteristic, complemented
24C2×C9×C22⋊C4C2211yescharacteristic
25C2×C9×C22⋊C4C2211yescharacteristic, complemented
26C2×C42×C9C2211yescharacteristic, complemented
27#63515C2214yescomplemented
28C2×#3676C2212yes—
29#63501C2214yes—
30#63501C2214yes—
31#63499C2214yescomplemented
32#63497C2214yescomplemented
33#63492C2212yes—
34#63492C2212yes—
35#63492C2212yescomplemented
36#63491C2214yescomplemented
37#63491C2214yescomplemented
38C4×#611C2214yescomplemented
39C4×#611C2214yescomplemented
40C4×#611C2214yescomplemented
41C4×#611C2214yescomplemented
42C4×#611C2214yescomplemented
43C2×(C2×D9)⋊C4C2212yescomplemented
44#63488C2212yescomplemented
45#63486C2212yescomplemented
46#63486C2212yescomplemented
47#63486C2212yescomplemented
48C2×Dic9⋊C4C2212yescomplemented
49C2×C4×Dic9C2212yescomplemented
50#63460C2214yescomplemented
51#63458C2214yescomplemented
52#63456C2214yescomplemented
53#63451C2214yescomplemented
54#63448C2214yescomplemented
55#63447C2214yescomplemented
56#63446C2214yescomplemented
57#63445C2214yescomplemented
58#63444C2214yescomplemented
59#63441C2214yescomplemented
60#63440C2214yescomplemented
61#63440C2214yescomplemented
62#63438C2214yescomplemented
63#63437C2212yescomplemented
64C4×D36C2212yescomplemented
65#63434C2214yescomplemented
66#63432C2212yescomplemented
67C4×Dic18C2212yescomplemented
68C2×C3×C4×D4D311yescharacteristic
69#5804—32no—
70#5791—32no—
71C2×C4×#67—32no—
72#5564—34no—
73#5560—34no—
74#5547—34no—
75#5538—34no—
76#5515—32no—
77#5494—32no—
78#5493—31no—
79#5483—31no—
80#5479—32no—
81C24×C9C2311yescharacteristic
82C24×C9C2311yescharacteristic
83C23×D9C2312yes—
84C2×D4×C9—24no—
85C2×D4×C9C2314yes—
86C22×C4×C9—42no—
87C22×C4×C9—42no—
88C22×C4×C9C2312yes—
89C22×C4×C9C2311yescharacteristic
90C22×C4×C9C2312yes—
91C22×C4×C9C2311yescharacteristic
92C22×C4×C9C2312yes—
93C22×C4×C9C2311yescharacteristic
94C22×C4×C9C2312yes—
95C22×C4×C9C2311yescharacteristic
96C22×C4×C9C2311yescharacteristic
97C2×#611—28no—
98C2×#611C2314yes—
99C2×#611C2314yes—
100C2×#611C2314yes—
101C2×#611C2314yes—
102C22×Dic9C2312yes—
103C22×Dic9C2312yes—
104C22×Dic9C2312yes—
105#3697—44no—
106C2×D36C2312yes—
107C2×D36C2312yes—
108C2×C4×D9—44no—
109C2×C4×D9C2314yes—
110C2×C4×D9C2314yes—
111C2×Dic18C2312yes—
112C2×Dic18C2312yes—
113C9×C4⋊C4C2314yes—
114C9×C22⋊C4C2314yes—
115C9×C22⋊C4C2314yes—
116C42×C9C2312yes—
117C42×C9C2312yes—
118#3676C2314yes—
119#3676C2314yes—
120#3676C2314yes—
121#3676C2314yes—
122(C2×D9)⋊C4C2314yes—
123(C2×D9)⋊C4C2314yes—
124(C2×D9)⋊C4C2314yes—
125(C2×D9)⋊C4C2314yes—
126(C2×D9)⋊C4C2314yes—
127(C2×D9)⋊C4C2314yes—
128C4⋊Dic9C2312yes—
129C4⋊Dic9C2312yes—
130C4⋊Dic9C2312yes—
131C4⋊Dic9C2312yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2314yes—
134Dic9⋊C4C2314yes—
135Dic9⋊C4C2314yes—
136Dic9⋊C4C2314yes—
137Dic9⋊C4C2314yes—
138C4×Dic9C2314yes—
139C4×Dic9C2314yes—
140#3459—91noSylow
141C22×C3×D4C2×D311yescharacteristic
142C23×C3×C4C2×D311yescharacteristic
143C23×C3×C4C2×D311yescharacteristic
144C22×#67—32no—
145C2×#235—32no—
146C22×C4×D3—32no—
147C3×C4×D4C2×D314yes—
148C3×C4×D4C2×D314yes—
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C22⋊C4C2×D311yescharacteristic
151C2×C3×C22⋊C4C2×D311yescharacteristic
152C2×C3×C42C2×D311yescharacteristic
153#953—34no—
154C2×#217—32no—
155#939—34no—
156#939—34no—
157#937—34no—
158#935—34no—
159#930—32no—
160#930—32no—
161#930—32no—
162#929—34no—
163#929—34no—
164C4×#67—34no—
165C4×#67—34no—
166C4×#67—34no—
167C4×#67—34no—
168C4×#67—34no—
169C2×(C2×D3)⋊C4—32no—
170#926—32no—
171#924—32no—
172#924—32no—
173#924—32no—
174C2×Dic3⋊C4—32no—
175C2×C4×Dic3—32no—
176#898—34no—
177#896—34no—
178#894—34no—
179#889—34no—
180#886—34no—
181#885—34no—
182#884—34no—
183#883—34no—
184#882—34no—
185#879—34no—
186#878—34no—
187#878—34no—
188#876—34no—
189#875—32no—
190C4×D12—32no—
191#872—34no—
192#870—32no—
193C4×Dic6—32no—
194C23×C9—22no—
195C23×C9—41no—
196C23×C9—41no—
197C23×C9—41no—
198C23×C9—41no—
199C23×C9#4114yescomplemented
200C23×C9C2412yes—
201C23×C9C2411yescharacteristic
202C23×C9C2412yes—
203C22×D9—24no—
204C22×D9—42no—
205C22×D9—42no—
206C22×D9C2414yes—
207D4×C9—28no—
208C2×C4×C9—22no—
209C2×C4×C9—24no—
210C2×C4×C9—24no—
211C2×C4×C9—22no—
212C2×C4×C9—41no—
213C2×C4×C9—42no—
214C2×C4×C9—41no—
215C2×C4×C9—42no—
216C2×C4×C9—41no—
217C2×C4×C9C2412yes—
218C2×C4×C9C2412yes—
219C2×C4×C9C2411yescharacteristic
220C2×C4×C9C2412yes—
221C2×C4×C9C2412yes—
222C2×C4×C9C2411yescharacteristic
223#611—28no—
224#611—28no—
225#611—44no—
226#611—44no—
227C2×Dic9—24no—
228C2×Dic9—42no—
229C2×Dic9—42no—
230C2×Dic9C2414yes—
231C2×Dic9C2414yes—
232C2×Dic9C2414yes—
233D36—42no—
234D36—42no—
235C4×D9—28no—
236C4×D9—44no—
237Dic18—42no—
238Dic18—42no—
239#543—91no—
240#539—94no—
241#539—92no—
242#538—94no—
243#538—92no—
244#534—92no—
245#534—91no—
246#529—94no—
247#529—92no—
248#525—92no—
249#525—94no—
250C2×C4×D4—92no—
251C2×C4×D4D911yescharacteristic, complemented
252C24×C3C22×D311yescharacteristic
253C24×C3C22×D311yescharacteristic
254C23×D3—32no—
255C2×C3×D4—24no—
256C2×C3×D4C22×D314yes—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4C22×D312yes—
260C22×C3×C4C22×D312yes—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D312yes—
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D312yes—
267C22×C3×C4C22×D311yescharacteristic
268C2×#67—34no—
269C2×#67—34no—
270C2×#67—34no—
271C2×#67—34no—
272C2×#67—68no—
273C22×Dic3—32no—
274C22×Dic3—32no—
275C22×Dic3—32no—
276#235—124no—
277C2×D12—32no—
278C2×D12—32no—
279C2×C4×D3—34no—
280C2×C4×D3—34no—
281C2×C4×D3—124no—
282C2×Dic6—32no—
283C2×Dic6—32no—
284C3×C4⋊C4C22×D314yes—
285C3×C22⋊C4C22×D314yes—
286C3×C22⋊C4C22×D314yes—
287C3×C42C22×D312yes—
288C3×C42C22×D312yes—
289#217—34no—
290#217—34no—
291#217—34no—
292#217—34no—
293(C2×D3)⋊C4—34no—
294(C2×D3)⋊C4—34no—
295(C2×D3)⋊C4—34no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4—34no—
299C4⋊Dic3—32no—
300C4⋊Dic3—32no—
301C4⋊Dic3—32no—
302C4⋊Dic3—32no—
303Dic3⋊C4—34no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307Dic3⋊C4—34no—
308Dic3⋊C4—34no—
309C4×Dic3—34no—
310C4×Dic3—34no—
311C22×C9—22no—
312C22×C9—21no—
313C22×C9—22no—
314C22×C9—21no—
315C22×C9—22no—
316C22×C9—22no—
317C22×C9—22no—
318C22×C9—44no—
319C22×C9—44no—
320C22×C9C2×#4114yes—
321C22×C9C2×#4112yes—
322C22×C9C2511yescharacteristic
323C2×D9—24no—
324C2×D9—24no—
325C2×D9—24no—
326C2×D9—48no—
327C4×C9—22no—
328C4×C9—22no—
329C4×C9—22no—
330C4×C9—21no—
331C4×C9—22no—
332C4×C9H(5,𝔽2)12yes—
333Dic9—24no—
334Dic9—24no—
335Dic9—24no—
336C2×#41—92no—
337C22×D4—92no—
338C22×D4C2×D911yescharacteristic
339C23×C4—92no—
340C23×C4C2×D911yescharacteristic
341C23×C4C2×D911yescharacteristic, complemented
342#126—94no—
343#126—94no—
344#126—94no—
345#125—94no—
346#125—92no—
347#124—94no—
348#124—92no—
349#123—94no—
350#123—94no—
351#123—94no—
352#123—94no—
353#123—94no—
354#123—94no—
355C22⋊Q8—92no—
356C22⋊Q8—92no—
357C22⋊Q8—92no—
358C22⋊Q8—94no—
359C22⋊Q8—94no—
360C22⋊Q8—94no—
361#121—94no—
362#121—94no—
363#121—92no—
364#121—92no—
365#121—92no—
366#121—94no—
367#120—94no—
368#120—94no—
369#120—94no—
370C4×Q8—92no—
371C4×D4—94no—
372C4×D4—94no—
373C4×D4—94no—
374C4×D4—94no—
375C4×D4—94no—
376C4×D4—92no—
377C4×D4C2×D914yescomplemented
378C4×D4C2×D914yescomplemented
379#117—92no—
380#117—94no—
381C2×C4⋊C4—92no—
382C2×C4⋊C4C2×D911yescharacteristic, complemented
383C2×C22⋊C4—92no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4C2×D911yescharacteristic
386C2×C22⋊C4C2×D911yescharacteristic, complemented
387C2×C42—92no—
388C2×C42C2×D911yescharacteristic, complemented
389C23×C3—22no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3#23514yes—
395C23×C3C23×D312yes—
396C23×C3C23×D311yescharacteristic
397C23×C3C23×D312yes—
398C22×D3—34no—
399C22×D3—64no—
400C22×D3—122no—
401C22×D3—122no—
402C3×D4—28no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—41no—
408C2×C3×C4—42no—
409C2×C3×C4—41no—
410C2×C3×C4—42no—
411C2×C3×C4—41no—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D312yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D311yescharacteristic
418#67—68no—
419#67—68no—
420#67—124no—
421#67—124no—
422C2×Dic3—34no—
423C2×Dic3—34no—
424C2×Dic3—34no—
425C2×Dic3—64no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428D12—122no—
429D12—122no—
430C4×D3—68no—
431C4×D3—124no—
432Dic6—122no—
433Dic6—122no—
434C2×C9—24no—
435C2×C9—22no—
436C2×C9—42no—
437C2×C9C22×#4111yescharacteristic
438C2×C9C2×H(5,𝔽2)11yescharacteristic
439C2×C9#58511yescharacteristic
440D9—44no—
441C24—92no—
442C24C22×D911yescharacteristic
443C24C22×D911yescharacteristic
444#41—364no—
445C2×Q8—92no—
446C2×Q8—92no—
447C2×D4—24no—
448C2×D4—94no—
449C2×D4—94no—
450C2×D4—94no—
451C2×D4—94no—
452C2×D4—92no—
453C2×D4—92no—
454C2×D4—188no—
455C2×D4C22×D914yes—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—92no—
459C22×C4—92no—
460C22×C4—92no—
461C22×C4—94no—
462C22×C4—94no—
463C22×C4—364no—
464C22×C4C22×D911yescharacteristic
465C22×C4C22×D912yes—
466C22×C4C22×D911yescharacteristic
467C22×C4C22×D912yes—
468C22×C4C22×D911yescharacteristic
469C22×C4C22×D912yes—
470C22×C4C22×D911yescharacteristic
471C22×C4C22×D911yescharacteristic
472C22×C4C22×D912yes—
473C4⋊C4—94no—
474C4⋊C4—94no—
475C4⋊C4—94no—
476C4⋊C4—92no—
477C4⋊C4—94no—
478C4⋊C4—92no—
479C4⋊C4—94no—
480C4⋊C4—92no—
481C4⋊C4—94no—
482C4⋊C4—92no—
483C4⋊C4C22×D914yes—
484C22⋊C4—94no—
485C22⋊C4—94no—
486C22⋊C4—94no—
487C22⋊C4—94no—
488C22⋊C4—94no—
489C22⋊C4—94no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—94no—
493C22⋊C4—94no—
494C22⋊C4C22×D914yes—
495C22⋊C4C22×D914yes—
496C42—94no—
497C42—94no—
498C42C22×D912yes—
499C42C22×D912yes—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—44no—
508C22×C3—44no—
509C22×C3C2×#23514yes—
510C22×C3C2×#23512yes—
511C22×C3C24×D311yescharacteristic
512C2×D3—64no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—128no—
516C3×C4—22no—
517C3×C4—22no—
518C3×C4—22no—
519C3×C4—21no—
520C3×C4—22no—
521C3×C4#100412yes—
522Dic3—64no—
523Dic3—64no—
524Dic3—64no—
525C9#345911yescharacteristic, complemented, Sylow
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—94no—
532C23—184no—
533C23—362no—
534C23—362no—
535C23#369714yescomplemented
536C23C23×D912yes—
537C23C23×D911yescharacteristic
538C23C23×D912yes—
539Q8—362no—
540Q8—362no—
541D4—28no—
542D4—188no—
543D4—188no—
544D4—362no—
545D4—362no—
546D4—364no—
547D4—364no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—94no—
558C2×C4—94no—
559C2×C4—94no—
560C2×C4—184no—
561C2×C4—188no—
562C2×C4—364no—
563C2×C4—362no—
564C2×C4—362no—
565C2×C4C23×D912yes—
566C2×C4C23×D912yes—
567C2×C4C23×D911yescharacteristic
568C2×C4C23×D912yes—
569C2×C4C23×D912yes—
570C2×C4C23×D911yescharacteristic
571C2×C3—24no—
572C2×C3—22no—
573C2×C3—42no—
574C2×C3C22×#23511yescharacteristic
575C2×C3C2×#100411yescharacteristic
576C2×C3#596411yescharacteristic
577D3—124no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—44no—
586C22—44no—
587C22—184no—
588C22—184no—
589C22—184no—
590C22—368no—
591C22C2×#369712yes—
592C22C2×#369714yes—
593C22C24×D911yescharacteristic
594C4—22no—
595C4—21no—
596C4—22no—
597C4—22no—
598C4—22no—
599C4—184no—
600C4—184no—
601C4—184no—
602C4#6371012yes—
603C3#8577611yescharacteristic
604C2—22no—
605C2—24no—
606C2—42no—
607C2—364no—
608C2C22×#369711yescharacteristic
609C2C2×#6371011yescharacteristic
610C2#1059313911yescharacteristic
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC2×C4×D4×C9C2
hypercenterC2×C4×D4D9
hypocenterC9#3459
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C9C2semidirect
2. #10589906C2semidirect
3. #10589893C2semidirect
4. C2×C4×#611C2semidirect
5. #10589666C2semidirect
6. #10589662C2semidirect
7. #10589649C2semidirect
8. #10589640C2semidirect
9. #10589617C2semidirect
10. #10589596C2semidirect
11. #10589595C2semidirect
12. #10589585C2semidirect
13. #10589581C2semidirect
17. C23×C4×C9C22semidirect
19. C2×#3697C22semidirect
20. C22×C4×D9C22semidirect
21. C4×D4×C9C22semidirect
22. C4×D4×C9C22semidirect
23. C2×C9×C4⋊C4C22semidirect
25. C2×C9×C22⋊C4C22semidirect
26. C2×C42×C9C22semidirect
27. #63515C22semidirect
31. #63499C22semidirect
32. #63497C22semidirect
35. #63492C22semidirect
36. #63491C22semidirect
37. #63491C22semidirect
38. C4×#611C22semidirect
39. C4×#611C22semidirect
40. C4×#611C22semidirect
41. C4×#611C22semidirect
42. C4×#611C22semidirect
43. C2×(C2×D9)⋊C4C22semidirect
44. #63488C22semidirect
45. #63486C22semidirect
46. #63486C22semidirect
47. #63486C22semidirect
48. C2×Dic9⋊C4C22semidirect
49. C2×C4×Dic9C22semidirect
50. #63460C22semidirect
51. #63458C22semidirect
52. #63456C22semidirect
53. #63451C22semidirect
54. #63448C22semidirect
55. #63447C22semidirect
56. #63446C22semidirect
57. #63445C22semidirect
58. #63444C22semidirect
59. #63441C22semidirect
60. #63440C22semidirect
61. #63440C22semidirect
62. #63438C22semidirect
63. #63437C22semidirect
64. C4×D36C22semidirect
65. #63434C22semidirect
66. #63432C22semidirect
67. C4×Dic18C22semidirect
199. C23×C9#41semidirect
251. C2×C4×D4D9semidirect
341. C23×C4C2×D9semidirect
377. C4×D4C2×D9semidirect
378. C4×D4C2×D9semidirect
382. C2×C4⋊C4C2×D9semidirect
386. C2×C22⋊C4C2×D9semidirect
388. C2×C42C2×D9semidirect
525. C9#3459semidirect
535. C23#3697semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C92
#105899062
#105898932
C2×C4×#6112
#105896662
#105896622
#105896492
#105896402
#105896172
#105895962
#105895952
#105895852
#105895812
#857763