Finite Group Databasebeta

← #13139905

Subgroups — #13139905

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C22×#6195C211yesmaximal, characteristic
3C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
5C2×#88445C211yesmaximal, characteristic, complemented
6C3×C9⋊#95C211yesmaximal, characteristic, complemented
7#11720331C211yesmaximal, characteristic, complemented
8#10591387—31nomaximal
9#10588636—31nomaximal
10C23×C3⋊D9C2211yescharacteristic
11C23×D3×C9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C2×C4×C3⋊D9—22no—
15C2×C4×C3⋊D9—22no—
16C2×C4×C3⋊D9—22no—
17C22×C9×Dic3C2211yescharacteristic
18C22×C3×Dic9C2211yescharacteristic
19C22×C3×Dic9C2211yescharacteristic
20C2×#6195—22no—
21C2×#6195—22no—
22C2×#6195C414yescomplemented
23C9×(C2×D3)⋊C4—22no—
24(C2×D3)⋊Dic9—22no—
25#88445—22no—
26C22×C4×C3⋊D3—31no—
27C22×#626—31no—
28C2×C3×(C2×D3)⋊C4D311yescharacteristic
29C2×#3722—31no—
30C2×(C2×D3)⋊Dic3—31no—
31C22×#611—31no—
32C22×C4×D9—31no—
33C22×C4×D9—61no—
34C3×C3⋊#95—31no—
35#63579—31no—
36C2×C9×C22⋊C4—31no—
37C2×#3676—31no—
38C2×(C2×D9)⋊C4—31no—
39C9⋊#95—31no—
40C9⋊#95D311yescharacteristic, complemented
41C23×C3×C9C2311yescharacteristic
42C22×C3⋊D9—21no—
43C22×C3⋊D9—21no—
44C22×C3⋊D9—21no—
45C22×C3⋊D9—21no—
46C22×C3⋊D9C2×C412yes—
47C22×C3⋊D9D412yes—
48C22×C3⋊D9D412yes—
49C22×D3×C9—21no—
50C22×D3×C9—21no—
51C22×D3×C9—21no—
52C22×D3×C9—21no—
53C22×D3×C9—21no—
54C22×D3×C9—21no—
55C22×D3×C9C2×C412yescomplemented
56C2×C3×C4×C9—21no—
57C2×C3×C4×C9—21no—
58C2×C3×C4×C9D412yescomplemented
59C2×C3⋊Dic9—21no—
60C2×C3⋊Dic9—21no—
61C2×C3⋊Dic9D412yescomplemented
62C4×C3⋊D9—28no—
63C2×C9×Dic3—21no—
64C2×C9×Dic3—21no—
65C2×C9×Dic3—21no—
66C2×C3×Dic9—21no—
67C2×C3×Dic9—21no—
68C2×C3×Dic9—21no—
69C2×C3×Dic9—21no—
70C2×C3×Dic9—21no—
71C2×C3×Dic9C2×C412yescomplemented
72#6195—28no—
73#4956—91no—
74#4665—91no—
75C23×C3⋊D3—31no—
76C23×C3×D3C2×D311yescharacteristic
77C22×C32×C4C2×D311yescharacteristic
78C22×C3⋊Dic3—31no—
79C2×C4×C3⋊D3—62no—
80C2×C4×C3⋊D3—62no—
81C2×C4×C3⋊D3—62no—
82C22×C3×Dic3—31no—
83C22×C3×Dic3—31no—
84C22×C3×Dic3C2×D311yescharacteristic
85C2×#626—34no—
86C2×#626—62no—
87C2×#626—62no—
88C24×C9—31no—
89C23×D9—31no—
90C23×D9—61no—
91C3×(C2×D3)⋊C4—22no—
92#3722—62no—
93(C2×D3)⋊Dic3—62no—
94C22×C4×C9—21no—
95C22×C4×C9—31no—
96C22×C4×C9C2×D311yescharacteristic
97C2×#611—34no—
98C2×#611—62no—
99C2×#611—62no—
100C22×Dic9—31no—
101C22×Dic9—61no—
102C22×Dic9C2×D311yescharacteristic
103C22×Dic9C2×D311yescharacteristic
104C2×C4×D9—62no—
105C2×C4×D9—62no—
106C2×C4×D9—64no—
107C2×C4×D9—64no—
108C2×C4×D9—64no—
109C2×C4×D9—62no—
110C9×C22⋊C4—62no—
111#3676—62no—
112(C2×D9)⋊C4—62no—
113C22×C3×C9C22×C411yescharacteristic
114C22×C3×C9C2×D411yescharacteristic
115C22×C3×C9C2×D411yescharacteristic
116C22×C3×C9C2×D411yescharacteristic
117C22×C3×C9C2×D411yescharacteristic
118C22×C3×C9#4111yescharacteristic
119C22×C3×C9#4111yescharacteristic
120C2×C3⋊D9—22no—
121C2×C3⋊D9—22no—
122C2×C3⋊D9—22no—
123C2×C3⋊D9—22no—
124C2×C3⋊D9—22no—
125C2×C3⋊D9—22no—
126C2×C3⋊D9C22⋊C414yescomplemented
127C2×D3×C9—22no—
128C2×D3×C9—22no—
129C2×D3×C9—22no—
130C2×D3×C9—41no—
131C2×D3×C9—41no—
132C2×D3×C9—41no—
133C2×D3×C9—41no—
134C3×C4×C9—22no—
135C3⋊Dic9—22no—
136C9×Dic3—41no—
137C3×Dic9—22no—
138C3×Dic9—41no—
139C22×#67—91no—
140C22×D12—91no—
141C22×C4×D3—91no—
142C22×C4×D3—91no—
143C22×C4×D3—181no—
144C2×C3×C22⋊C4—31no—
145C2×#217—91no—
146C2×(C2×D3)⋊C4—91no—
147C2×(C2×D3)⋊C4—91no—
148C2×(C2×D3)⋊C4—91no—
149C2×(C2×D3)⋊C4D911yescharacteristic, complemented
150C3×#95—91no—
151C3⋊#95—31no—
152C3⋊#95—91no—
153C3⋊#95—91no—
154C23×C32C22×D311yescharacteristic
155C22×C3⋊D3—32no—
156C22×C3⋊D3—32no—
157C22×C3⋊D3—32no—
158C22×C3⋊D3—61no—
159C22×C3⋊D3—61no—
160C22×C3⋊D3—61no—
161C22×C3⋊D3—61no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3C4×D312yes—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4#6712yes—
172C2×C3⋊Dic3—32no—
173C2×C3⋊Dic3—61no—
174C2×C3⋊Dic3—61no—
175C4×C3⋊D3—68no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—32no—
180C2×C3×Dic3—61no—
181C2×C3×Dic3—61no—
182C2×C3×Dic3—61no—
183C2×C3×Dic3—61no—
184C2×C3×Dic3—61no—
185#626—68no—
186C23×C9—21no—
187C23×C9—32no—
188C23×C9—61no—
189C23×C9—61no—
190C23×C9—61no—
191C23×C9—61no—
192C23×C9—61no—
193C23×C9—61no—
194C23×C9C22×D311yescharacteristic
195C22×D9—32no—
196C22×D9—32no—
197C22×D9—32no—
198C22×D9—62no—
199C22×D9—62no—
200C22×D9—62no—
201C22×D9—62no—
202C22×D9—62no—
203C22×D9—62no—
204C22×D9—62no—
205C22×D9—61no—
206C22×D9—61no—
207C22×D9—61no—
208C22×D9—61no—
209C2×C4×C9—22no—
210C2×C4×C9—22no—
211C2×C4×C9—21no—
212C2×C4×C9—21no—
213C2×C4×C9—22no—
214C2×C4×C9—61no—
215C2×C4×C9—61no—
216C2×C4×C9—61no—
217C2×C4×C9D1212yescomplemented
218#611—68no—
219C2×Dic9—21no—
220C2×Dic9—21no—
221C2×Dic9—21no—
222C2×Dic9—21no—
223C2×Dic9—21no—
224C2×Dic9—32no—
225C2×Dic9—62no—
226C2×Dic9—62no—
227C2×Dic9—62no—
228C2×Dic9—61no—
229C2×Dic9—61no—
230C2×Dic9C4×D312yescomplemented
231C4×D9—616no—
232C4×D9—68no—
233#386—271noSylow
234C2×C3×C9C2×C22⋊C411yescharacteristic
235C2×C3×C9C4×D411yescharacteristic
236C2×C3×C9C4×D411yescharacteristic
237C2×C3×C9#12011yescharacteristic
238C2×C3×C9#12111yescharacteristic
239C2×C3×C9#12111yescharacteristic
240C2×C3×C9#12311yescharacteristic
241C3⋊D9—24no—
242D3×C9—42no—
243C24×C3—31no—
244C23×D3—91no—
245C23×D3—91no—
246C23×D3—181no—
247C23×D3C2×D911yescharacteristic
248C22×C3×C4—21no—
249C22×C3×C4—31no—
250C22×C3×C4—91no—
251C22×C3×C4—91no—
252C22×C3×C4C2×D911yescharacteristic
253C22×C3×C4D3211yescharacteristic
254C2×#67—94no—
255C2×#67—182no—
256C2×#67—182no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—91no—
260C22×Dic3—91no—
261C22×Dic3—181no—
262C22×Dic3C2×D911yescharacteristic
263C2×D12—94no—
264C2×D12—182no—
265C2×D12—182no—
266C2×C4×D3—182no—
267C2×C4×D3—182no—
268C2×C4×D3—182no—
269C2×C4×D3—182no—
270C2×C4×D3—184no—
271C2×C4×D3—184no—
272C2×C4×D3—184no—
273C2×C4×D3—182no—
274C2×C4×D3—182no—
275C3×C22⋊C4—62no—
276#217—182no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—182no—
279(C2×D3)⋊C4—182no—
280(C2×D3)⋊C4—182no—
281C22×C32C2×C4×D311yescharacteristic
282C22×C32#23511yescharacteristic
283C22×C32D3×D411yescharacteristic
284C22×C32D3×D411yescharacteristic
285C22×C32D3×D411yescharacteristic
286C22×C32#23711yescharacteristic
287C22×C32C2×#6711yescharacteristic
288C2×C3⋊D3—34no—
289C2×C3⋊D3—62no—
290C2×C3⋊D3—62no—
291C2×C3⋊D3—62no—
292C2×C3⋊D3—62no—
293C2×C3⋊D3—62no—
294C2×C3⋊D3—62no—
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3—41no—
299C2×C3×D3—41no—
300C2×C3×D3—41no—
301C2×C3×D3—41no—
302C32×C4—22no—
303C3⋊Dic3—62no—
304C3×Dic3—41no—
305C3×Dic3—62no—
306C3×Dic3—121no—
307C22×C9—21no—
308C22×C9—21no—
309C22×C9—21no—
310C22×C9—21no—
311C22×C9—21no—
312C22×C9—21no—
313C22×C9—21no—
314C22×C9—62no—
315C22×C9—62no—
316C22×C9—62no—
317C22×C9—121no—
318C22×C9—121no—
319C22×C9—121no—
320C22×C9—121no—
321C22×C9C2×C4×D311yescharacteristic
322C22×C9C2×D1211yescharacteristic
323C22×C9#23511yescharacteristic
324C22×C9D3×D411yescharacteristic
325C22×C9D3×D411yescharacteristic
326C22×C9D3×D411yescharacteristic
327C22×C9#23911yescharacteristic
328C2×D9—34no—
329C2×D9—64no—
330C2×D9—64no—
331C2×D9—64no—
332C2×D9—64no—
333C2×D9—64no—
334C2×D9—64no—
335C2×D9—64no—
336C2×D9—62no—
337C2×D9—62no—
338C2×D9—62no—
339C2×D9—62no—
340C2×D9—62no—
341C2×D9—62no—
342C4×C9—24no—
343C4×C9—22no—
344C4×C9—121no—
345Dic9—22no—
346Dic9—41no—
347Dic9—64no—
348Dic9—62no—
349C22×D4—271no—
350C23×C4—271no—
351C2×C22⋊C4—31no—
352C2×C22⋊C4—271no—
353C2×C22⋊C4—271no—
354#95—91no—
355#95—271no—
356C3×C9#38611yescharacteristic, complemented, Sylow
357C23×C3—21no—
358C23×C3—32no—
359C23×C3—61no—
360C23×C3—61no—
361C23×C3—61no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3C22×D911yescharacteristic
366C23×C3C2×D3211yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—21no—
370C22×D3—21no—
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—92no—
374C22×D3—92no—
375C22×D3—92no—
376C22×D3—92no—
377C22×D3—92no—
378C22×D3—92no—
379C22×D3—182no—
380C22×D3—182no—
381C22×D3—182no—
382C22×D3—182no—
383C22×D3—182no—
384C22×D3—182no—
385C22×D3—182no—
386C22×D3—181no—
387C22×D3—181no—
388C22×D3—181no—
389C22×D3—181no—
390C22×D3—181no—
391C22×D3—181no—
392C22×D3—181no—
393C22×D3—181no—
394C22×D3C4×D912yescomplemented
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—92no—
406C2×C3×C4—181no—
407C2×C3×C4—181no—
408C2×C3×C4—181no—
409C2×C3×C4—181no—
410C2×C3×C4—181no—
411C2×C3×C4#61112yescomplemented
412C2×C3×C4#62612yes—
413#67—188no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—32no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—92no—
424C2×Dic3—92no—
425C2×Dic3—182no—
426C2×Dic3—182no—
427C2×Dic3—182no—
428C2×Dic3—181no—
429C2×Dic3—181no—
430C2×Dic3—181no—
431C2×Dic3—181no—
432D12—188no—
433C4×D3—188no—
434C4×D3—1816no—
435C4×D3—188no—
436C2×C32D3×C22⋊C411yescharacteristic
437C2×C32#67⋊C411yescharacteristic
438C2×C32#88311yescharacteristic
439C2×C32#88411yescharacteristic
440C2×C32C4×#6711yescharacteristic
441C2×C32#93711yescharacteristic
442C2×C32#93811yescharacteristic
443C3⋊D3—64no—
444C3×D3—42no—
445C2×C9—21no—
446C2×C9—21no—
447C2×C9—21no—
448C2×C9—21no—
449C2×C9—21no—
450C2×C9—21no—
451C2×C9—21no—
452C2×C9—122no—
453C2×C9C4×D1211yescharacteristic
454C2×C9D3×C22⋊C411yescharacteristic
455C2×C9#88211yescharacteristic
456C2×C9#88411yescharacteristic
457C2×C9#89311yescharacteristic
458C2×C9#89411yescharacteristic
459C2×C9#89511yescharacteristic
460D9—68no—
461D9—64no—
462C24—31no—
463C24—271no—
464C2×D4—274no—
465C2×D4—542no—
466C2×D4—542no—
467C22×C4—31no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—271no—
471C22×C4—542no—
472C22×C4—542no—
473C22×C4—542no—
474C22×C4D3×D911yescharacteristic
475C22⋊C4—62no—
476C22⋊C4—542no—
477C22⋊C4—542no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—62no—
486C22×C3—62no—
487C22×C3—62no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3C2×C4×D911yescharacteristic
493C22×C3#369711yescharacteristic
494C22×C3D4×D911yescharacteristic
495C22×C3D4×D911yescharacteristic
496C22×C3D4×D911yescharacteristic
497C22×C3#369911yescharacteristic
498C22×C3C2×#61111yescharacteristic
499C22×C3#379611yescharacteristic
500C22×C3#379811yescharacteristic
501C22×C3C4×D3211yescharacteristic
502C22×C3#380211yescharacteristic
503C22×C3C2×#62611yescharacteristic
504C22×C3#381111yescharacteristic
505C22×C3#381111yescharacteristic
506C2×D3—22no—
507C2×D3—22no—
508C2×D3—22no—
509C2×D3—41no—
510C2×D3—41no—
511C2×D3—41no—
512C2×D3—41no—
513C2×D3—94no—
514C2×D3—94no—
515C2×D3—184no—
516C2×D3—184no—
517C2×D3—184no—
518C2×D3—184no—
519C2×D3—184no—
520C2×D3—184no—
521C2×D3—184no—
522C2×D3—182no—
523C2×D3—182no—
524C2×D3—182no—
525C2×D3—182no—
526C2×D3—182no—
527C2×D3—182no—
528C2×D3—182no—
529C2×D3—182no—
530C2×D3—182no—
531C2×D3—182no—
532C2×D3—182no—
533C2×D3—182no—
534C3×C4—24no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—121no—
538C3×C4—182no—
539C3×C4—361no—
540Dic3—41no—
541Dic3—62no—
542Dic3—121no—
543Dic3—184no—
544Dic3—182no—
545Dic3—182no—
546C32#495611yescharacteristic
547C9—21no—
548C9#466511yescharacteristic, complemented
549C23—32no—
550C23—61no—
551C23—61no—
552C23—61no—
553C23—61no—
554C23—61no—
555C23—61no—
556C23—272no—
557C23—272no—
558C23—272no—
559C23—541no—
560C23—541no—
561C23—541no—
562C23—541no—
563C23C2×D3×D911yescharacteristic
564D4—548no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—92no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—181no—
574C2×C4—181no—
575C2×C4—181no—
576C2×C4—272no—
577C2×C4—548no—
578C2×C4—541no—
579C2×C4—541no—
580C2×C4#619512yescomplemented
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—122no—
589C2×C3C22⋊C4×D911yescharacteristic
590C2×C3#611⋊C411yescharacteristic
591C2×C3#6344511yescharacteristic
592C2×C3#6344611yescharacteristic
593C2×C3C4×#61111yescharacteristic
594C2×C3#6349911yescharacteristic
595C2×C3#6350011yescharacteristic
596C2×C3#6385311yescharacteristic
597C2×C3#6388111yescharacteristic
598C2×C3C4×#62611yescharacteristic
599C2×C3#6391211yescharacteristic
600C2×C3#6391611yescharacteristic
601C2×C3#6392111yescharacteristic
602C2×C3#6398111yescharacteristic
603D3—42no—
604D3—188no—
605D3—184no—
606D3—184no—
607C22—62no—
608C22—62no—
609C22—62no—
610C22—121no—
611C22—121no—
612C22—121no—
613C22—121no—
614C22—274no—
615C22—542no—
616C22—542no—
617C22—542no—
618C22—542no—
619C22—542no—
620C22—542no—
621C22#8863911yescharacteristic
622C22#8864011yescharacteristic
623C22C4×D3×D911yescharacteristic
624C22#8864611yescharacteristic
625C22C2×#619511yescharacteristic
626C22#8866811yescharacteristic
627C22#8866811yescharacteristic
628C4—22no—
629C4—121no—
630C4—182no—
631C4—361no—
632C4—542no—
633C3—21no—
634C3#1058863611yescharacteristic, complemented
635C3#1059138711yescharacteristic
636C2—122no—
637C2—544no—
638C2#1172095711yescharacteristic
639C2#1172101411yescharacteristic
640C2C4×#619511yescharacteristic
641C2#1172104111yescharacteristic
642C2#1172104511yescharacteristic
643C2#1172104811yescharacteristic
644C2#1172129111yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC22×#6195C2
cosocleC23×C3×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9#386
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊D9C2semidirect
3. C2×C9×(C2×D3)⋊C4C2semidirect
4. C2×(C2×D3)⋊Dic9C2semidirect
5. C2×#88445C2semidirect
6. C3×C9⋊#95C2semidirect
7. #11720331C2semidirect
22. C2×#6195C4semidirect
40. C9⋊#95D3semidirect
55. C22×D3×C9C2×C4semidirect
58. C2×C3×C4×C9D4semidirect
61. C2×C3⋊Dic9D4semidirect
71. C2×C3×Dic9C2×C4semidirect
126. C2×C3⋊D9C22⋊C4semidirect
149. C2×(C2×D3)⋊C4D9semidirect
217. C2×C4×C9D12semidirect
230. C2×Dic9C4×D3semidirect
356. C3×C9#386semidirect
394. C22×D3C4×D9semidirect
411. C2×C3×C4#611semidirect
548. C9#4665semidirect
580. C2×C4#6195semidirect
634. C3#10588636semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊D92
C22×#61952
C2×C9×(C2×D3)⋊C42
C2×(C2×D3)⋊Dic92
C2×#884452
C3×C9⋊#952
#117203312
#105913873
#105886363