Finite Group Databasebeta

← #13148073

Subgroups — #13148073

Order 1728.

718 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721723C211yesmaximal, characteristic, complemented
2C3×#63448C211yesmaximal, characteristic
3C9×#878C211yesmaximal, characteristic, complemented
4Dic3×#611C211yesmaximal, characteristic
5#11721260C211yesmaximal, characteristic
6C2×Dic3⋊Dic9C211yesmaximal, characteristic, complemented
7#11721245C211yesmaximal, characteristic, complemented
8#11720984C211yesmaximal, characteristic, complemented
9#11720975C211yesmaximal, characteristic, complemented
10#11720950C211yesmaximal, characteristic, complemented
11#11720946C211yesmaximal, characteristic, complemented
12#11720937C211yesmaximal, characteristic, complemented
13#11720916C211yesmaximal, characteristic, complemented
14#11720916C211yesmaximal, characteristic, complemented
15#11720911C211yesmaximal, characteristic, complemented
16#10594135—31nomaximal
17#10589744—31nomaximal
18C22×C3⋊Dic9C2211yescharacteristic
19C2×C3×#611C2211yescharacteristic
20C22×C9×Dic3C2211yescharacteristic
21C22×C3×Dic9C2211yescharacteristic
22C2×C9×Dic6C2211yescharacteristic
23C2×Dic3×D9C2211yescharacteristic
24C3×C9×C22⋊C4C2211yescharacteristic
25#88551C2211yescharacteristic
26#88534C2211yescharacteristic
27#88534C2211yescharacteristic
28C4×C3⋊Dic9C2211yescharacteristic
29C4×C3⋊Dic9C2211yescharacteristic
30C9×#217C2211yescharacteristic
31C3×(C2×D9)⋊C4C2211yescharacteristic
32C3×(C2×D9)⋊C4C2211yescharacteristic
33C9×C4⋊Dic3C2211yescharacteristic
34C9×Dic3⋊C4C2211yescharacteristic
35C9×Dic3⋊C4C2211yescharacteristic
36C3×C4⋊Dic9C2211yescharacteristic
37C3×C4⋊Dic9C2211yescharacteristic
38(C2×D9)⋊Dic3C2211yescharacteristic
39(C2×D9)⋊Dic3C2211yescharacteristic
40(C2×D9)⋊Dic3C2211yescharacteristic
41Dic3⋊Dic9C2211yescharacteristic
42Dic3⋊Dic9C2211yescharacteristic
43Dic3⋊Dic9C2211yescharacteristic
44Dic3⋊Dic9C2211yescharacteristic
45Dic3⋊Dic9C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47Dic9⋊Dic3C2211yescharacteristic
48Dic9⋊Dic3C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic3×Dic9C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64086—31no—
54C3×#886—31no—
55C3×#878D311yescharacteristic
56Dic3×#67—31no—
57C2×Dic3⋊Dic3—31no—
58#63962—31no—
59#63955—31no—
60#63887—31no—
61#63878—31no—
62#63872—31no—
63#63862—31no—
64#63858—31no—
65#63846—31no—
66#63846—31no—
67#63843—31no—
68C9×C22⋊Q8—31no—
69#63508—31no—
70Q8×Dic9—31no—
71C4×#611—31no—
72C2×C4⋊Dic9—31no—
73#63460—31no—
74#63460—31no—
75#63454—31no—
76#63452—31no—
77#63452—31no—
78#63452—31no—
79#63448—31no—
80#63448D311yescharacteristic
81#63439—31no—
82#63439—31no—
83#63439—61no—
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C2×C3×C4×C9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3⋊Dic9—22no—
89C2×C3⋊Dic9C2311yescharacteristic
90C2×C3⋊Dic9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C3×#611—22no—
94C2×C9×Dic3—22no—
95C2×C9×Dic3C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C3×Dic9—22no—
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C9×Dic6—22no—
104Dic3×D9—22no—
105#5650—91no—
106#5642—91no—
107C22×C3⋊Dic3—31no—
108C2×C3×#67—31no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3C2×D311yescharacteristic
111C2×C3×Dic6C2×D311yescharacteristic
112C2×D3×Dic3—31no—
113C32×C22⋊C4C2×D311yescharacteristic
114#3757—31no—
115#3750—31no—
116#3750—31no—
117C4×C3⋊Dic3—31no—
118C4×C3⋊Dic3—31no—
119C3×#217C2×D311yescharacteristic
120C3×(C2×D3)⋊C4—31no—
121C3×(C2×D3)⋊C4—31no—
122C3×C4⋊Dic3—31no—
123C3×C4⋊Dic3—31no—
124C3×C4⋊Dic3C2×D311yescharacteristic
125C3×Dic3⋊C4C2×D311yescharacteristic
126C3×Dic3⋊C4C2×D311yescharacteristic
127Dic3⋊Dic3—31no—
128Dic3⋊Dic3—31no—
129Dic3⋊Dic3—31no—
130Dic3⋊Dic3—31no—
131Dic3⋊Dic3—31no—
132Dic3⋊Dic3—31no—
133Dic3⋊Dic3—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136(C2×D3)⋊Dic3—31no—
137(C2×D3)⋊Dic3—31no—
138(C2×D3)⋊Dic3—31no—
139Dic32—31no—
140Dic32—31no—
141Dic32—31no—
142C2×Q8×C9—31no—
143C22×C4×C9—31no—
144C2×#611C2×D311yescharacteristic
145C22×Dic9—31no—
146C22×Dic9—61no—
147C22×Dic9C2×D311yescharacteristic
148C2×C4×D9—31no—
149C9×C4⋊C4—31no—
150C9×C4⋊C4—31no—
151C9×C4⋊C4—31no—
152C9×C22⋊C4—21no—
153C9×C22⋊C4—31no—
154C9×C22⋊C4C2×D311yescharacteristic
155#3676—31no—
156#3676—61no—
157(C2×D9)⋊C4—31no—
158(C2×D9)⋊C4—31no—
159(C2×D9)⋊C4—31no—
160(C2×D9)⋊C4C2×D311yescharacteristic
161(C2×D9)⋊C4C2×D311yescharacteristic
162C4⋊Dic9—31no—
163C4⋊Dic9—31no—
164C4⋊Dic9—31no—
165C4⋊Dic9—31no—
166C4⋊Dic9—31no—
167C4⋊Dic9—31no—
168C4⋊Dic9C2×D311yescharacteristic
169C4⋊Dic9C2×D311yescharacteristic
170Dic9⋊C4—31no—
171Dic9⋊C4—31no—
172Dic9⋊C4—31no—
173Dic9⋊C4—31no—
174Dic9⋊C4—31no—
175Dic9⋊C4—61no—
176Dic9⋊C4—61no—
177C4×Dic9—31no—
178C4×Dic9—31no—
179C4×Dic9—31no—
180C4×Dic9—31no—
181C4×Dic9—31no—
182C4×Dic9—61no—
183C4×Dic9—61no—
184C22×C3×C9—21no—
185C22×C3×C9—21no—
186C22×C3×C9#4112yes—
187C22×C3×C9C2411yescharacteristic
188C2×C3×D9—21no—
189C2×C3×D9—21no—
190C2×C3×D9—21no—
191C3×C4×C9—21no—
192C3×C4×C9—21no—
193C3⋊Dic9—21no—
194C3⋊Dic9—21no—
195C3⋊Dic9—21no—
196C3⋊Dic9—21no—
197C9×Dic3—21no—
198C9×Dic3—21no—
199C9×Dic3—21no—
200C9×Dic3#4112yes—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×#123—91no—
205C3×C22⋊Q8—31no—
206#946—91no—
207Q8×Dic3—91no—
208#935—91no—
209D4×Dic3—91no—
210C4×#67—91no—
211#926—91no—
212C2×C4⋊Dic3—91no—
213C2×Dic3⋊C4—91no—
214#898—91no—
215#898—91no—
216#892—91no—
217#890—91no—
218#890—91no—
219#890—91no—
220#890—91no—
221#889—91no—
222#889—91no—
223#887—91no—
224#886—31no—
225#886—91no—
226#879—91no—
227#879—91no—
228#878—91no—
229#878D911yescharacteristic, complemented
230#877—91no—
231#877—91no—
232#877—91no—
233#877—91no—
234#877—181no—
235C23×C32C22×D311yescharacteristic
236C22×C3×D3—31no—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C3⋊Dic3—31no—
240C2×C3⋊Dic3—31no—
241C2×C3⋊Dic3—31no—
242C2×C3⋊Dic3—31no—
243C2×C3⋊Dic3—62no—
244C3×#67—62no—
245C2×C3×Dic3—22no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3—31no—
249C2×C3×Dic3—62no—
250C2×C3×Dic3C22×D311yescharacteristic
251C2×C3×Dic3C22×D311yescharacteristic
252C2×C3×Dic3C22×D311yescharacteristic
253C2×C3×Dic3C22×D311yescharacteristic
254C3×Dic6—22no—
255D3×Dic3—62no—
256C23×C9—21no—
257C23×C9C22×D311yescharacteristic
258C22×D9C22×D311yescharacteristic
259Q8×C9—62no—
260C2×C4×C9—21no—
261C2×C4×C9—21no—
262C2×C4×C9—31no—
263C2×C4×C9—31no—
264C2×C4×C9—31no—
265C2×C4×C9—31no—
266C2×C4×C9—62no—
267C2×C4×C9C22×D311yescharacteristic
268C2×C4×C9C22×D311yescharacteristic
269#611—22no—
270C2×Dic9—22no—
271C2×Dic9—31no—
272C2×Dic9—31no—
273C2×Dic9—31no—
274C2×Dic9—31no—
275C2×Dic9—61no—
276C2×Dic9—61no—
277C2×Dic9—61no—
278C2×Dic9—61no—
279C2×Dic9—64no—
280C2×Dic9—62no—
281C2×Dic9C22×D311yescharacteristic
282C2×Dic9C22×D311yescharacteristic
283C2×Dic9C22×D311yescharacteristic
284C4×D9—62no—
285#552—271noSylow
286C2×C3×C9—22no—
287C2×C3×C9C2×#4111yescharacteristic
288C2×C3×C9C2×#4111yescharacteristic
289C2×C3×C92−1+411yescharacteristic
290C3×D9—41no—
291C2×C3×Q8—31no—
292C2×C3×D4—91no—
293C22×C3×C4—31no—
294C22×C3×C4—91no—
295C2×#67—31no—
296C22×Dic3—31no—
297C22×Dic3—91no—
298C22×Dic3—91no—
299C22×Dic3—91no—
300C22×Dic3—181no—
301C22×Dic3C2×D911yescharacteristic
302C2×C4×D3—91no—
303C2×Dic6C2×D911yescharacteristic
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—91no—
308C3×C4⋊C4—91no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—31no—
311C3×C22⋊C4—91no—
312C3×C22⋊C4—91no—
313C3×C22⋊C4C2×D911yescharacteristic
314C3×C22⋊C4D3211yescharacteristic
315#217—91no—
316#217—91no—
317#217—91no—
318#217—91no—
319#217—91no—
320#217—181no—
321#217C2×D911yescharacteristic
322(C2×D3)⋊C4—31no—
323(C2×D3)⋊C4—31no—
324(C2×D3)⋊C4—91no—
325(C2×D3)⋊C4—91no—
326(C2×D3)⋊C4—91no—
327C4⋊Dic3—31no—
328C4⋊Dic3—31no—
329C4⋊Dic3—91no—
330C4⋊Dic3—91no—
331C4⋊Dic3—91no—
332C4⋊Dic3—91no—
333C4⋊Dic3—91no—
334C4⋊Dic3—91no—
335C4⋊Dic3—91no—
336C4⋊Dic3—91no—
337C4⋊Dic3—91no—
338C4⋊Dic3C2×D911yescharacteristic
339Dic3⋊C4—91no—
340Dic3⋊C4—91no—
341Dic3⋊C4—91no—
342Dic3⋊C4—91no—
343Dic3⋊C4—91no—
344Dic3⋊C4—91no—
345Dic3⋊C4—91no—
346Dic3⋊C4—91no—
347Dic3⋊C4—91no—
348Dic3⋊C4—91no—
349Dic3⋊C4—91no—
350Dic3⋊C4—91no—
351Dic3⋊C4—91no—
352Dic3⋊C4—181no—
353Dic3⋊C4—181no—
354Dic3⋊C4C2×D911yescharacteristic
355Dic3⋊C4C2×D911yescharacteristic
356C4×Dic3—91no—
357C4×Dic3—91no—
358C4×Dic3—91no—
359C4×Dic3—91no—
360C4×Dic3—91no—
361C4×Dic3—91no—
362C4×Dic3—91no—
363C4×Dic3—91no—
364C4×Dic3—91no—
365C4×Dic3—91no—
366C4×Dic3—181no—
367C4×Dic3—181no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32#23912yes—
371C22×C32C23×D311yescharacteristic
372C2×C3×D3—61no—
373C2×C3×D3—61no—
374C2×C3×D3—61no—
375C32×C4—21no—
376C32×C4—21no—
377C3⋊Dic3—61no—
378C3⋊Dic3—61no—
379C3⋊Dic3—61no—
380C3⋊Dic3—61no—
381C3×Dic3—21no—
382C3×Dic3—21no—
383C3×Dic3—21no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3—61no—
387C3×Dic3#23712yes—
388C22×C9—21no—
389C22×C9—21no—
390C22×C9—21no—
391C22×C9—22no—
392C22×C9—41no—
393C22×C9—41no—
394C22×C9#23712yes—
395C22×C9C23×D311yescharacteristic
396C2×D9—21no—
397C2×D9—21no—
398C2×D9—21no—
399C4×C9—21no—
400C4×C9—21no—
401C4×C9—32no—
402C4×C9—41no—
403C4×C9—41no—
404C4×C9—61no—
405C4×C9—61no—
406C4×C9—61no—
407Dic9—21no—
408Dic9—21no—
409Dic9—21no—
410Dic9—62no—
411Dic9—62no—
412Dic9—61no—
413Dic9—61no—
414Dic9—61no—
415Dic9—61no—
416Dic9—121no—
417Dic9—121no—
418#126—271no—
419#126—271no—
420#125—271no—
421#125—271no—
422#125—271no—
423#123—91no—
424#123—271no—
425C22⋊Q8—31no—
426C22⋊Q8—271no—
427C4×Q8—271no—
428C4×D4—271no—
429#117—271no—
430#117—271no—
431#117—271no—
432C2×C4⋊C4—271no—
433C3×C9#55211yescharacteristic, complemented, Sylow
434C23×C3—21no—
435C23×C3—91no—
436C23×C3C22×D911yescharacteristic
437C23×C3C2×D3211yescharacteristic
438C22×D3—31no—
439C3×Q8—62no—
440C3×D4—182no—
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—62no—
448C2×C3×C4—91no—
449C2×C3×C4—91no—
450C2×C3×C4—91no—
451C2×C3×C4—182no—
452C2×C3×C4C22×D911yescharacteristic
453C2×C3×C4C22×D911yescharacteristic
454C2×C3×C4C2×D3211yescharacteristic
455C2×C3×C4C2×D3211yescharacteristic
456#67—62no—
457C2×Dic3—22no—
458C2×Dic3—31no—
459C2×Dic3—31no—
460C2×Dic3—31no—
461C2×Dic3—62no—
462C2×Dic3—91no—
463C2×Dic3—91no—
464C2×Dic3—91no—
465C2×Dic3—91no—
466C2×Dic3—91no—
467C2×Dic3—91no—
468C2×Dic3—91no—
469C2×Dic3—91no—
470C2×Dic3—181no—
471C2×Dic3—181no—
472C2×Dic3—181no—
473C2×Dic3—181no—
474C2×Dic3—184no—
475C2×Dic3—182no—
476C2×Dic3—182no—
477C2×Dic3—182no—
478C2×Dic3C22×D911yescharacteristic
479C2×Dic3C22×D911yescharacteristic
480C2×Dic3C22×D911yescharacteristic
481C2×Dic3C22×D911yescharacteristic
482C4×D3—182no—
483Dic6—22no—
484C2×C32—22no—
485C2×C32C2×#23711yescharacteristic
486C2×C32C2×#23911yescharacteristic
487C2×C32#101011yescharacteristic
488C3×D3—121no—
489C2×C9—22no—
490C2×C9—21no—
491C2×C9—21no—
492C2×C9—21no—
493C2×C9—42no—
494C2×C9C2×#23711yescharacteristic
495C2×C9D3×#4111yescharacteristic
496C2×C9#101011yescharacteristic
497D9—41no—
498C2×Q8—31no—
499C2×D4—91no—
500C22×C4—31no—
501C22×C4—91no—
502C22×C4—271no—
503C22×C4—271no—
504C4⋊C4—31no—
505C4⋊C4—31no—
506C4⋊C4—31no—
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—
518C4⋊C4—271no—
519C4⋊C4—271no—
520C22⋊C4—31no—
521C22⋊C4—91no—
522C22⋊C4—91no—
523C22⋊C4—271no—
524C22⋊C4—271no—
525C22⋊C4—271no—
526C22⋊C4—271no—
527C22⋊C4D3×D911yescharacteristic
528C42—271no—
529C42—271no—
530C42—271no—
531C42—271no—
532C42—271no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—22no—
538C22×C3—21no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—181no—
542C22×C3—181no—
543C22×C3—181no—
544C22×C3#370112yes—
545C22×C3C23×D911yescharacteristic
546C22×C3#379612yes—
547C22×C3C22×D3211yescharacteristic
548C2×D3—61no—
549C2×D3—61no—
550C2×D3—61no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—32no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—61no—
559C3×C4—61no—
560C3×C4—61no—
561C3×C4—181no—
562C3×C4—181no—
563C3×C4—181no—
564Dic3—21no—
565Dic3—21no—
566Dic3—21no—
567Dic3—61no—
568Dic3—61no—
569Dic3—61no—
570Dic3—182no—
571Dic3—182no—
572Dic3—181no—
573Dic3—181no—
574Dic3—181no—
575Dic3—181no—
576Dic3—181no—
577Dic3—181no—
578Dic3—181no—
579Dic3—181no—
580Dic3—361no—
581Dic3—361no—
582Dic3#369912yes—
583C32#564211yescharacteristic
584C9—21no—
585C9#565011yescharacteristic, complemented
586C23—91no—
587C23C2×D3×D911yescharacteristic
588Q8—62no—
589D4—182no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—62no—
595C2×C4—91no—
596C2×C4—91no—
597C2×C4—91no—
598C2×C4—182no—
599C2×C4—271no—
600C2×C4—271no—
601C2×C4—271no—
602C2×C4—271no—
603C2×C4—542no—
604C2×C4—542no—
605C2×C4C2×D3×D911yescharacteristic
606C2×C4C2×D3×D911yescharacteristic
607C2×C3—22no—
608C2×C3—22no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—42no—
613C2×C3—361no—
614C2×C3C2×#369911yescharacteristic
615C2×C3C2×#370111yescharacteristic
616C2×C3#6371611yescharacteristic
617C2×C3C2×#379611yescharacteristic
618C2×C3#6430911yescharacteristic
619C2×C3D3×#23711yescharacteristic
620D3—121no—
621C22—21no—
622C22—21no—
623C22—181no—
624C22—181no—
625C22—181no—
626C22#8863412yes—
627C22C22×D3×D911yescharacteristic
628C4—21no—
629C4—21no—
630C4—32no—
631C4—61no—
632C4—61no—
633C4—61no—
634C4—181no—
635C4—181no—
636C4—181no—
637C4—541no—
638C4—541no—
639C4—541no—
640C4—541no—
641C3—21no—
642C3#1058974411yescharacteristic, complemented
643C3#1059413511yescharacteristic
644C2—22no—
645C2—361no—
646C2C2×#8863411yescharacteristic
647C2#1172249411yescharacteristic
648C2D3×#369911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×C3×#611C22
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#552
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721723C2semidirect
3. C9×#878C2semidirect
6. C2×Dic3⋊Dic9C2semidirect
7. #11721245C2semidirect
8. #11720984C2semidirect
9. #11720975C2semidirect
10. #11720950C2semidirect
11. #11720946C2semidirect
12. #11720937C2semidirect
13. #11720916C2semidirect
14. #11720916C2semidirect
15. #11720911C2semidirect
229. #878D9semidirect
433. C3×C9#552semidirect
585. C9#5650semidirect
642. C3#10589744semidirect

Maximal subgroups

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

subgroupindex
#117217232
C3×#634482
C9×#8782
Dic3×#6112
#117212602
C2×Dic3⋊Dic92
#117212452
#117209842
#117209752
#117209502
#117209462
#117209372
#117209162
#117209112
#105941353
#105897443