Finite Group Databasebeta

← #13147555

Subgroups — #13147555

Order 1728.

648 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721713C211yesmaximal, characteristic, complemented
2C3×#63438C211yesmaximal, characteristic, complemented
3C9×#869C211yesmaximal, characteristic, complemented
4#11721003C211yesmaximal, characteristic
5#11720999C211yesmaximal, characteristic, complemented
6#11720994C211yesmaximal, characteristic, complemented
7#11720988C211yesmaximal, characteristic
8#11720986C211yesmaximal, characteristic, complemented
9#11720984C211yesmaximal, characteristic, complemented
10#11720946C211yesmaximal, characteristic, complemented
11#11720942C211yesmaximal, characteristic
12#11720920C211yesmaximal, characteristic, complemented
13#11720918C211yesmaximal, characteristic, complemented
14#11720917C211yesmaximal, characteristic, complemented
15#11720903C211yesmaximal, characteristic, complemented
16#10593957—31nomaximal
17#10589837—31nomaximal
18C2×C9×Dic6C2211yescharacteristic
19C2×C9×Dic6C2211yescharacteristic
20C2×#6192C2211yescharacteristic
21C2×(C3⋊D9)⋊C4C2211yescharacteristic
22C2×Dic3×D9C2211yescharacteristic
23C2×#6189C2211yescharacteristic
24C3×C42×C9C2211yescharacteristic
25#88536C2211yescharacteristic
26#88536C2211yescharacteristic
27#88536C2211yescharacteristic
28#88534C2211yescharacteristic
29#88534C2211yescharacteristic
30#88534C2211yescharacteristic
31C3×(C2×D9)⋊C4C2211yescharacteristic
32C3×(C2×D9)⋊C4C2211yescharacteristic
33C3×(C2×D9)⋊C4C2211yescharacteristic
34C9×C4⋊Dic3C2211yescharacteristic
35C9×C4⋊Dic3C2211yescharacteristic
36C9×C4⋊Dic3C2211yescharacteristic
37C9×C4⋊Dic3C2211yescharacteristic
38C3×Dic9⋊C4C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40C3×Dic9⋊C4C2211yescharacteristic
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45Dic3⋊Dic9C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64085—31no—
54C3×#876—31no—
55C3×#869D311yescharacteristic
56#63907—31no—
57#63899—31no—
58#63895—31no—
59#63890—31no—
60#63888—31no—
61#63887—31no—
62#63858—31no—
63#63854—31no—
64#63848—31no—
65#63847—31no—
66#63846—31no—
67#63839—31no—
68C9×C4⋊Q8—31no—
69#63509—31no—
70#63508—31no—
71#63508—31no—
72#63506—31no—
73#63460—31no—
74#63460—31no—
75#63458—31no—
76#63458—31no—
77#63456—31no—
78#63456—31no—
79#63451—31no—
80#63451—31no—
81#63438—31no—
82#63438—61no—
83#63438D311yescharacteristic, complemented
84C22×C3⋊D9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C2×C3×C4×C9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3⋊Dic9C2311yescharacteristic
90C2×C3⋊Dic9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C9×Dic3C2311yescharacteristic
93C2×C9×Dic3C2311yescharacteristic
94C2×C9×Dic3C2311yescharacteristic
95C2×C9×Dic3C2311yescharacteristic
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C9×Dic6—41no—
100C9×Dic6—41no—
101#6192—41no—
102(C3⋊D9)⋊C4—41no—
103Dic3×D9—41no—
104#6189—41no—
105#5735—91no—
106#5712—91no—
107C2×C3×Dic6C2×D311yescharacteristic
108C2×C3×Dic6C2×D311yescharacteristic
109C2×#627—31no—
110C2×#626—31no—
111C2×#624—31no—
112C2×D3×Dic3—31no—
113C32×C42C2×D311yescharacteristic
114#3752—31no—
115#3752—31no—
116#3752—31no—
117#3750—31no—
118#3750—31no—
119#3750—31no—
120C3×(C2×D3)⋊C4—31no—
121C3×(C2×D3)⋊C4—31no—
122C3×(C2×D3)⋊C4—31no—
123C3×C4⋊Dic3C2×D311yescharacteristic
124C3×C4⋊Dic3C2×D311yescharacteristic
125C3×C4⋊Dic3C2×D311yescharacteristic
126C3×C4⋊Dic3C2×D311yescharacteristic
127C3×Dic3⋊C4—31no—
128C3×Dic3⋊C4—31no—
129C3×Dic3⋊C4—31no—
130#3724—31no—
131#3724—31no—
132Dic3⋊Dic3—31no—
133Dic3⋊Dic3—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136#3722—31no—
137#3722—31no—
138(C2×D3)⋊Dic3—31no—
139(C2×D3)⋊Dic3—31no—
140Dic32—31no—
141Dic32—31no—
142C2×Q8×C9—31no—
143C2×Q8×C9—31no—
144C2×D36—31no—
145C2×C4×D9—31no—
146C2×C4×D9—31no—
147C2×Dic18—31no—
148C9×C4⋊C4—31no—
149C9×C4⋊C4—31no—
150C9×C4⋊C4—31no—
151C9×C4⋊C4—31no—
152C42×C9—21no—
153C42×C9C2×D311yescharacteristic
154(C2×D9)⋊C4—31no—
155(C2×D9)⋊C4—31no—
156(C2×D9)⋊C4—31no—
157(C2×D9)⋊C4—31no—
158(C2×D9)⋊C4—31no—
159(C2×D9)⋊C4—31no—
160(C2×D9)⋊C4—31no—
161(C2×D9)⋊C4—61no—
162(C2×D9)⋊C4—61no—
163(C2×D9)⋊C4—61no—
164(C2×D9)⋊C4C2×D311yescharacteristic
165(C2×D9)⋊C4C2×D311yescharacteristic
166(C2×D9)⋊C4C2×D311yescharacteristic
167C4⋊Dic9—31no—
168C4⋊Dic9—31no—
169Dic9⋊C4—31no—
170Dic9⋊C4—31no—
171Dic9⋊C4—31no—
172Dic9⋊C4—31no—
173Dic9⋊C4—31no—
174Dic9⋊C4—31no—
175Dic9⋊C4—31no—
176Dic9⋊C4—61no—
177Dic9⋊C4—61no—
178Dic9⋊C4—61no—
179Dic9⋊C4C2×D311yescharacteristic
180Dic9⋊C4C2×D311yescharacteristic
181Dic9⋊C4C2×D311yescharacteristic
182C4×Dic9—31no—
183C4×Dic9—31no—
184C22×C3×C9C2411yescharacteristic
185C2×C3⋊D9—21no—
186C2×C3⋊D9—21no—
187C2×C3⋊D9—21no—
188C2×C3×D9—21no—
189C2×C3×D9—21no—
190C2×C3×D9—21no—
191C3×C4×C9—21no—
192C3×C4×C9—21no—
193C3×C4×C9—21no—
194C3⋊Dic9—21no—
195C3⋊Dic9—21no—
196C3⋊Dic9—21no—
197C9×Dic3—21no—
198C9×Dic3—21no—
199C9×Dic3—21no—
200C9×Dic3—21no—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×C4⋊Q8—31no—
205C3×#126—91no—
206#947—91no—
207#946—91no—
208#946—91no—
209#944—91no—
210#898—91no—
211#898—91no—
212#898—91no—
213#897—91no—
214#896—91no—
215#896—91no—
216#896—91no—
217#894—91no—
218#894—91no—
219#890—91no—
220#889—91no—
221#889—91no—
222#889—91no—
223#888—91no—
224#886—91no—
225#885—91no—
226#883—91no—
227#879—91no—
228#878—91no—
229#878—91no—
230#876—31no—
231#876—91no—
232#876—91no—
233#876—181no—
234#869D911yescharacteristic, complemented
235C22×C3⋊D3—31no—
236C22×C3×D3—31no—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240C2×C3⋊Dic3—31no—
241C2×C3⋊Dic3—31no—
242C2×C3⋊Dic3—31no—
243C2×C3×Dic3—31no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3C22×D311yescharacteristic
247C2×C3×Dic3C22×D311yescharacteristic
248C2×C3×Dic3C22×D311yescharacteristic
249C2×C3×Dic3C22×D311yescharacteristic
250C3×Dic6—41no—
251C3×Dic6—41no—
252#627—121no—
253#626—121no—
254#624—121no—
255D3×Dic3—121no—
256C22×D9—31no—
257C22×D9—61no—
258C22×D9C22×D311yescharacteristic
259Q8×C9—121no—
260Q8×C9—121no—
261C2×C4×C9—21no—
262C2×C4×C9—21no—
263C2×C4×C9—21no—
264C2×C4×C9—31no—
265C2×C4×C9—31no—
266C2×C4×C9—31no—
267C2×C4×C9—31no—
268C2×C4×C9C22×D311yescharacteristic
269C2×C4×C9C22×D311yescharacteristic
270C2×C4×C9C22×D311yescharacteristic
271C2×Dic9—31no—
272C2×Dic9—31no—
273C2×Dic9—31no—
274C2×Dic9—61no—
275C2×Dic9—61no—
276C2×Dic9—61no—
277C2×Dic9C22×D311yescharacteristic
278C2×Dic9C22×D311yescharacteristic
279C2×Dic9C22×D311yescharacteristic
280D36—121no—
281C4×D9—121no—
282C4×D9—121no—
283Dic18—121no—
284#563—271noSylow
285C2×C3×C9H(5,𝔽2)11yescharacteristic
286C2×C3×C92−1+411yescharacteristic
287C2×C3×C92−1+411yescharacteristic
288C3⋊D9—41no—
289C3×D9—41no—
290C2×C3×Q8—31no—
291C2×C3×Q8—31no—
292C2×#67—91no—
293C22×Dic3—91no—
294C2×D12—91no—
295C2×C4×D3—91no—
296C2×C4×D3—91no—
297C2×C4×D3—91no—
298C2×Dic6—91no—
299C2×Dic6—91no—
300C2×Dic6C2×D911yescharacteristic
301C2×Dic6C2×D911yescharacteristic
302C3×C4⋊C4—31no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4—91no—
308C3×C4⋊C4—91no—
309C3×C22⋊C4—91no—
310C3×C22⋊C4—91no—
311C3×C22⋊C4—91no—
312C3×C42—21no—
313C3×C42C2×D911yescharacteristic
314C3×C42D3211yescharacteristic
315#217—91no—
316#217—91no—
317(C2×D3)⋊C4—31no—
318(C2×D3)⋊C4—31no—
319(C2×D3)⋊C4—31no—
320(C2×D3)⋊C4—91no—
321(C2×D3)⋊C4—91no—
322(C2×D3)⋊C4—91no—
323(C2×D3)⋊C4—91no—
324(C2×D3)⋊C4—91no—
325(C2×D3)⋊C4—91no—
326(C2×D3)⋊C4—91no—
327(C2×D3)⋊C4—91no—
328(C2×D3)⋊C4—91no—
329(C2×D3)⋊C4—91no—
330(C2×D3)⋊C4—91no—
331(C2×D3)⋊C4—91no—
332(C2×D3)⋊C4—181no—
333(C2×D3)⋊C4—181no—
334(C2×D3)⋊C4—181no—
335C4⋊Dic3—91no—
336C4⋊Dic3—91no—
337C4⋊Dic3—91no—
338C4⋊Dic3—91no—
339C4⋊Dic3C2×D911yescharacteristic
340C4⋊Dic3C2×D911yescharacteristic
341C4⋊Dic3C2×D911yescharacteristic
342C4⋊Dic3C2×D911yescharacteristic
343Dic3⋊C4—31no—
344Dic3⋊C4—31no—
345Dic3⋊C4—31no—
346Dic3⋊C4—91no—
347Dic3⋊C4—91no—
348Dic3⋊C4—91no—
349Dic3⋊C4—91no—
350Dic3⋊C4—91no—
351Dic3⋊C4—91no—
352Dic3⋊C4—91no—
353Dic3⋊C4—91no—
354Dic3⋊C4—91no—
355Dic3⋊C4—91no—
356Dic3⋊C4—91no—
357Dic3⋊C4—91no—
358Dic3⋊C4—91no—
359Dic3⋊C4—91no—
360Dic3⋊C4—181no—
361Dic3⋊C4—181no—
362Dic3⋊C4—181no—
363C4×Dic3—91no—
364C4×Dic3—91no—
365C4×Dic3—91no—
366C4×Dic3—91no—
367C22×C32C23×D311yescharacteristic
368C2×C3⋊D3—61no—
369C2×C3⋊D3—61no—
370C2×C3⋊D3—61no—
371C2×C3×D3—61no—
372C2×C3×D3—61no—
373C2×C3×D3—61no—
374C32×C4—21no—
375C32×C4—21no—
376C32×C4—21no—
377C3⋊Dic3—61no—
378C3⋊Dic3—61no—
379C3⋊Dic3—61no—
380C3×Dic3—21no—
381C3×Dic3—21no—
382C3×Dic3—21no—
383C3×Dic3—21no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3—61no—
387C22×C9—21no—
388C22×C9C23×D311yescharacteristic
389C2×D9—21no—
390C2×D9—21no—
391C2×D9—21no—
392C2×D9—61no—
393C2×D9—61no—
394C2×D9—61no—
395C2×D9—121no—
396C2×D9—121no—
397C2×D9—121no—
398C4×C9—21no—
399C4×C9—21no—
400C4×C9—21no—
401C4×C9—41no—
402C4×C9—41no—
403C4×C9—41no—
404C4×C9—61no—
405C4×C9—61no—
406C4×C9—61no—
407C4×C9—61no—
408Dic9—21no—
409Dic9—21no—
410Dic9—21no—
411Dic9—61no—
412Dic9—61no—
413Dic9—61no—
414Dic9—121no—
415Dic9—121no—
416Dic9—121no—
417C4⋊Q8—31no—
418C4⋊Q8—271no—
419#126—91no—
420#126—271no—
421#126—271no—
422#126—271no—
423#125—271no—
424#125—271no—
425#124—271no—
426#123—271no—
427#123—271no—
428C22⋊Q8—271no—
429C22⋊Q8—271no—
430C22⋊Q8—271no—
431C22⋊Q8—271no—
432C3×C9#56311yescharacteristic, complemented, Sylow
433C23×C3—91no—
434C22×D3—31no—
435C22×D3—91no—
436C22×D3—91no—
437C22×D3—181no—
438C3×Q8—121no—
439C3×Q8—121no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—31no—
444C2×C3×C4—31no—
445C2×C3×C4—31no—
446C2×C3×C4—31no—
447C2×C3×C4—91no—
448C2×C3×C4—91no—
449C2×C3×C4—91no—
450C2×C3×C4C22×D911yescharacteristic
451C2×C3×C4C22×D911yescharacteristic
452C2×C3×C4C22×D911yescharacteristic
453C2×C3×C4C2×D3211yescharacteristic
454C2×C3×C4C2×D3211yescharacteristic
455C2×C3×C4C2×D3211yescharacteristic
456#67—361no—
457C2×Dic3—31no—
458C2×Dic3—31no—
459C2×Dic3—31no—
460C2×Dic3—91no—
461C2×Dic3—91no—
462C2×Dic3—91no—
463C2×Dic3—91no—
464C2×Dic3—91no—
465C2×Dic3—91no—
466C2×Dic3—181no—
467C2×Dic3—181no—
468C2×Dic3—181no—
469C2×Dic3—361no—
470C2×Dic3C22×D911yescharacteristic
471C2×Dic3C22×D911yescharacteristic
472C2×Dic3C22×D911yescharacteristic
473C2×Dic3C22×D911yescharacteristic
474D12—361no—
475C4×D3—361no—
476C4×D3—361no—
477C4×D3—361no—
478Dic6—41no—
479Dic6—41no—
480Dic6—361no—
481Dic6—361no—
482C2×C32#100411yescharacteristic
483C2×C32#100711yescharacteristic
484C2×C32#100711yescharacteristic
485C3⋊D3—121no—
486C3×D3—121no—
487C2×C9—21no—
488C2×C9—21no—
489C2×C9—21no—
490C2×C9#100911yescharacteristic
491C2×C9#101011yescharacteristic
492C2×C9#101011yescharacteristic
493D9—41no—
494D9—121no—
495D9—241no—
496C2×Q8—31no—
497C2×Q8—31no—
498C2×Q8—271no—
499C2×D4—271no—
500C22×C4—271no—
501C22×C4—271no—
502C4⋊C4—31no—
503C4⋊C4—31no—
504C4⋊C4—31no—
505C4⋊C4—31no—
506C4⋊C4—91no—
507C4⋊C4—91no—
508C4⋊C4—91no—
509C4⋊C4—271no—
510C4⋊C4—271no—
511C4⋊C4—271no—
512C4⋊C4—271no—
513C4⋊C4—271no—
514C4⋊C4—271no—
515C4⋊C4—271no—
516C4⋊C4—271no—
517C4⋊C4—271no—
518C22⋊C4—91no—
519C22⋊C4—91no—
520C22⋊C4—91no—
521C22⋊C4—271no—
522C22⋊C4—271no—
523C22⋊C4—271no—
524C22⋊C4—271no—
525C22⋊C4—271no—
526C22⋊C4—271no—
527C22⋊C4—271no—
528C42—271no—
529C42—271no—
530C42D3×D911yescharacteristic
531C22×C3—21no—
532C22×C3—181no—
533C22×C3—181no—
534C22×C3—181no—
535C22×C3C23×D911yescharacteristic
536C22×C3C22×D3211yescharacteristic
537C2×D3—61no—
538C2×D3—61no—
539C2×D3—61no—
540C2×D3—181no—
541C2×D3—181no—
542C2×D3—181no—
543C2×D3—181no—
544C2×D3—181no—
545C2×D3—181no—
546C2×D3—361no—
547C2×D3—361no—
548C2×D3—361no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—41no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—61no—
559C3×C4—61no—
560C3×C4—61no—
561C3×C4—61no—
562C3×C4—181no—
563C3×C4—181no—
564C3×C4—181no—
565Dic3—21no—
566Dic3—21no—
567Dic3—21no—
568Dic3—21no—
569Dic3—61no—
570Dic3—61no—
571Dic3—61no—
572Dic3—181no—
573Dic3—181no—
574Dic3—181no—
575Dic3—181no—
576Dic3—181no—
577Dic3—181no—
578Dic3—361no—
579Dic3—361no—
580Dic3—361no—
581C32#573511yescharacteristic
582C9—21no—
583C9#571211yescharacteristic, complemented
584C23—91no—
585C23—271no—
586Q8—121no—
587Q8—121no—
588Q8—1081no—
589D4—1081no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—91no—
595C2×C4—91no—
596C2×C4—91no—
597C2×C4—271no—
598C2×C4—271no—
599C2×C4—271no—
600C2×C4—1081no—
601C2×C4—1081no—
602C2×C4C2×D3×D911yescharacteristic
603C2×C4C2×D3×D911yescharacteristic
604C2×C4C2×D3×D911yescharacteristic
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—361no—
609C2×C3#6371011yescharacteristic
610C2×C3#6371311yescharacteristic
611C2×C3#6371311yescharacteristic
612C2×C3#6429711yescharacteristic
613C2×C3#6429711yescharacteristic
614C2×C3#6430711yescharacteristic
615D3—121no—
616D3—361no—
617D3—361no—
618D3—721no—
619C22—181no—
620C22—181no—
621C22—181no—
622C22—541no—
623C22—541no—
624C22—541no—
625C22C22×D3×D911yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—61no—
630C4—61no—
631C4—61no—
632C4—61no—
633C4—181no—
634C4—181no—
635C4—181no—
636C4—541no—
637C4—541no—
638C4—541no—
639C3—21no—
640C3#1058983711yescharacteristic, complemented
641C3#1059395711yescharacteristic
642C2—361no—
643C2—1081no—
644C2#1172245811yescharacteristic
645C2#1172245811yescharacteristic
646C2#1172247611yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C42×C9C22
socleC22×C32C23×D3
prime radicalC2×#6192C22
hypercenterC42D3×D9
hypocenterC3×C9#563
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #11721713C2semidirect
2. C3×#63438C2semidirect
3. C9×#869C2semidirect
5. #11720999C2semidirect
6. #11720994C2semidirect
8. #11720986C2semidirect
9. #11720984C2semidirect
10. #11720946C2semidirect
12. #11720920C2semidirect
13. #11720918C2semidirect
14. #11720917C2semidirect
15. #11720903C2semidirect
83. #63438D3semidirect
234. #869D9semidirect
432. C3×C9#563semidirect
583. C9#5712semidirect
640. C3#10589837semidirect

Maximal subgroups

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

subgroupindex
#117217132
C3×#634382
C9×#8692
#117210032
#117209992
#117209942
#117209882
#117209862
#117209842
#117209462
#117209422
#117209202
#117209182
#117209172
#117209032
#105939573
#105898373