Finite Group Databasebeta

← #13139911

Subgroups — #13139911

Order 1728.

790 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6194C211yesmaximal, characteristic
2C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
5C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
6C2×Dic3⋊Dic9C211yesmaximal, characteristic, complemented
7#11720572C211yesmaximal, characteristic, complemented
8#10591390—31nomaximal
9#10588641—31nomaximal
10C23×D3×C9C2211yescharacteristic
11C23×C3×D9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C22×C3⋊Dic9C2211yescharacteristic
15C22×C9×Dic3C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C2×#6194—22no—
18C2×#6194—22no—
19C2×#6194—22no—
20C9×(C2×D3)⋊C4—22no—
21C3×(C2×D9)⋊C4—22no—
22(C2×D3)⋊Dic9—22no—
23(C2×D9)⋊Dic3—22no—
24Dic3⋊Dic9—22no—
25C22×#625—31no—
26C2×C3×(C2×D3)⋊C4—31no—
27C2×C3×(C2×D3)⋊C4D311yescharacteristic
28C2×Dic3⋊Dic3—31no—
29C2×(C2×D3)⋊Dic3—31no—
30C2×(C2×D3)⋊Dic3—31no—
31C22×#611—31no—
32#63658—31no—
33C2×C9×C22⋊C4—31no—
34C2×#3676—31no—
35C2×(C2×D9)⋊C4—31no—
36C2×(C2×D9)⋊C4D311yescharacteristic, complemented
37C2×C4⋊Dic9—31no—
38C9⋊#95—31no—
39C9⋊#95—61no—
40C23×C3×C9C2311yescharacteristic
41C22×D3×C9—21no—
42C22×D3×C9—21no—
43C22×D3×C9—21no—
44C22×D3×C9—21no—
45C22×D3×C9—21no—
46C22×D3×C9—21no—
47C22×D3×C9D412yes—
48C22×C3×D9—21no—
49C22×C3×D9—21no—
50C22×C3×D9—21no—
51C22×C3×D9—21no—
52C22×C3×D9—21no—
53C22×C3×D9—21no—
54C22×C3×D9D412yes—
55C2×C3×C4×C9—21no—
56C2×C3×C4×C9—21no—
57C2×C3×C4×C9—21no—
58C2×C3⋊Dic9—21no—
59C2×C3⋊Dic9—21no—
60C2×C3⋊Dic9—21no—
61C2×C3⋊Dic9—21no—
62C2×C3⋊Dic9—21no—
63C2×C3⋊Dic9D412yes—
64C2×C9×Dic3—21no—
65C2×C9×Dic3—21no—
66C2×C9×Dic3D412yescomplemented
67C2×C3×Dic9—21no—
68C2×C3×Dic9—21no—
69C2×C3×Dic9—21no—
70#6194—28no—
71#4961—91no—
72#4959—91no—
73C23×C3×D3—31no—
74C23×C3×D3C2×D311yescharacteristic
75C22×C32×C4C2×D311yescharacteristic
76C22×C3⋊Dic3—31no—
77C22×C3⋊Dic3—31no—
78C22×C3×Dic3—31no—
79C22×C3×Dic3C2×D311yescharacteristic
80C2×#625—62no—
81C2×#625—62no—
82C2×#625—62no—
83C24×C9—31no—
84C23×D9C2×D311yescharacteristic
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—62no—
87Dic3⋊Dic3—62no—
88(C2×D3)⋊Dic3—62no—
89(C2×D3)⋊Dic3—62no—
90C22×C4×C9—21no—
91C22×C4×C9—31no—
92C22×C4×C9C2×D311yescharacteristic
93C2×#611—62no—
94C2×#611—62no—
95C2×#611—62no—
96C22×Dic9—31no—
97C22×Dic9—31no—
98C22×Dic9—61no—
99C22×Dic9—61no—
100C22×Dic9C2×D311yescharacteristic
101C9×C22⋊C4—62no—
102#3676—62no—
103(C2×D9)⋊C4—22no—
104(C2×D9)⋊C4—62no—
105C4⋊Dic9—62no—
106C22×C3×C9C2×D411yescharacteristic
107C22×C3×C9C2×D411yescharacteristic
108C22×C3×C9C2×D411yescharacteristic
109C22×C3×C9C2×D411yescharacteristic
110C22×C3×C9#4111yescharacteristic
111C22×C3×C9#4111yescharacteristic
112C22×C3×C9#4111yescharacteristic
113C2×D3×C9—22no—
114C2×D3×C9—22no—
115C2×D3×C9—22no—
116C2×D3×C9—41no—
117C2×D3×C9—41no—
118C2×D3×C9—41no—
119C2×D3×C9—41no—
120C2×C3×D9—22no—
121C2×C3×D9—22no—
122C2×C3×D9—22no—
123C2×C3×D9—41no—
124C2×C3×D9—41no—
125C2×C3×D9—41no—
126C2×C3×D9—41no—
127C3×C4×C9—41no—
128C3⋊Dic9—22no—
129C3⋊Dic9—41no—
130C9×Dic3—22no—
131C3×Dic9—41no—
132C22×#67—91no—
133C22×#67—91no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—91no—
136C2×#217—91no—
137C2×#217—91no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—91no—
140C2×(C2×D3)⋊C4—91no—
141C2×(C2×D3)⋊C4D911yescharacteristic, complemented
142C2×C4⋊Dic3—91no—
143C2×Dic3⋊C4—91no—
144C3⋊#95—91no—
145C3⋊#95—91no—
146C3⋊#95—181no—
147C23×C32C22×D311yescharacteristic
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3—21no—
153C22×C3×D3—21no—
154C22×C3×D3—32no—
155C22×C3×D3—61no—
156C22×C3×D3—61no—
157C22×C3×D3—61no—
158C22×C3×D3—61no—
159C22×C3×D3—61no—
160C22×C3×D3—61no—
161C22×C3×D3D1212yes—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C3⋊Dic3—32no—
166C2×C3⋊Dic3—61no—
167C2×C3⋊Dic3—61no—
168C2×C3⋊Dic3—61no—
169C2×C3⋊Dic3—61no—
170C2×C3⋊Dic3—61no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—61no—
174C2×C3×Dic3—61no—
175C2×C3×Dic3—61no—
176C2×C3×Dic3#6712yes—
177#625—68no—
178C23×C9—21no—
179C23×C9—32no—
180C23×C9—61no—
181C23×C9—61no—
182C23×C9—61no—
183C23×C9—61no—
184C23×C9—61no—
185C23×C9—61no—
186C23×C9C22×D311yescharacteristic
187C22×D9—21no—
188C22×D9—21no—
189C22×D9—21no—
190C22×D9—21no—
191C22×D9—21no—
192C22×D9—21no—
193C22×D9#6712yes—
194C2×C4×C9—22no—
195C2×C4×C9—21no—
196C2×C4×C9—21no—
197C2×C4×C9—21no—
198C2×C4×C9—32no—
199C2×C4×C9—41no—
200C2×C4×C9—41no—
201C2×C4×C9—61no—
202C2×C4×C9—61no—
203#611—68no—
204C2×Dic9—21no—
205C2×Dic9—21no—
206C2×Dic9—21no—
207C2×Dic9—32no—
208C2×Dic9—62no—
209C2×Dic9—61no—
210C2×Dic9—61no—
211C2×Dic9—62no—
212C2×Dic9—61no—
213C2×Dic9—61no—
214C2×Dic9—61no—
215C2×Dic9—121no—
216C2×Dic9—121no—
217C2×Dic9—121no—
218C2×Dic9—121no—
219#394—271noSylow
220C2×C3×C9#12011yescharacteristic
221C2×C3×C9#12111yescharacteristic
222C2×C3×C9#12111yescharacteristic
223C2×C3×C9#12111yescharacteristic
224C2×C3×C9#12311yescharacteristic
225C2×C3×C9#12311yescharacteristic
226C2×C3×C9#12411yescharacteristic
227D3×C9—42no—
228C3×D9—42no—
229C24×C3—31no—
230C24×C3—91no—
231C23×D3—31no—
232C23×D3C2×D911yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—31no—
235C22×C3×C4—91no—
236C22×C3×C4C2×D911yescharacteristic
237C22×C3×C4D3211yescharacteristic
238C2×#67—182no—
239C2×#67—182no—
240C2×#67—182no—
241C2×#67—182no—
242C2×#67—182no—
243C2×#67—182no—
244C22×Dic3—31no—
245C22×Dic3—91no—
246C22×Dic3—91no—
247C22×Dic3—91no—
248C22×Dic3—91no—
249C22×Dic3—181no—
250C22×Dic3—181no—
251C22×Dic3C2×D911yescharacteristic
252C3×C22⋊C4—62no—
253C3×C22⋊C4—182no—
254#217—182no—
255#217—182no—
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—182no—
259(C2×D3)⋊C4—182no—
260C4⋊Dic3—182no—
261Dic3⋊C4—182no—
262C22×C32C2×D1211yescharacteristic
263C22×C32#23511yescharacteristic
264C22×C32D3×D411yescharacteristic
265C22×C32D3×D411yescharacteristic
266C22×C32#23711yescharacteristic
267C22×C32#23711yescharacteristic
268C22×C32C2×#6711yescharacteristic
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—22no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—62no—
277C2×C3×D3—62no—
278C2×C3×D3—62no—
279C2×C3×D3—121no—
280C2×C3×D3—121no—
281C2×C3×D3—121no—
282C2×C3×D3—121no—
283C32×C4—41no—
284C3⋊Dic3—62no—
285C3⋊Dic3—121no—
286C3×Dic3—22no—
287C3×Dic3—121no—
288C22×C9—21no—
289C22×C9—21no—
290C22×C9—21no—
291C22×C9—21no—
292C22×C9—21no—
293C22×C9—21no—
294C22×C9—21no—
295C22×C9—62no—
296C22×C9—62no—
297C22×C9—62no—
298C22×C9—121no—
299C22×C9—121no—
300C22×C9—121no—
301C22×C9—121no—
302C22×C9#23511yescharacteristic
303C22×C9#23511yescharacteristic
304C22×C9D3×D411yescharacteristic
305C22×C9D3×D411yescharacteristic
306C22×C9D3×D411yescharacteristic
307C22×C9#23711yescharacteristic
308C22×C9C2×#6711yescharacteristic
309C2×D9—22no—
310C2×D9—22no—
311C2×D9—22no—
312C2×D9—41no—
313C2×D9—41no—
314C2×D9—41no—
315C2×D9—41no—
316C4×C9—42no—
317C4×C9—41no—
318C4×C9—62no—
319Dic9—41no—
320Dic9—62no—
321Dic9—122no—
322Dic9—122no—
323Dic9—121no—
324C22×D4—271no—
325C2×C4⋊C4—271no—
326C2×C22⋊C4—31no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—271no—
329C2×C22⋊C4—271no—
330#95—271no—
331C3×C9#39411yescharacteristic, complemented, Sylow
332C23×C3—21no—
333C23×C3—32no—
334C23×C3—61no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—61no—
339C23×C3—61no—
340C23×C3—92no—
341C23×C3—181no—
342C23×C3—181no—
343C23×C3—181no—
344C23×C3—181no—
345C23×C3—181no—
346C23×C3—181no—
347C23×C3C22×D911yescharacteristic
348C23×C3C2×D3211yescharacteristic
349C22×D3—21no—
350C22×D3—21no—
351C22×D3—21no—
352C22×D3—21no—
353C22×D3—21no—
354C22×D3—21no—
355C22×D3—32no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—61no—
359C22×D3—61no—
360C22×D3—61no—
361C22×D3—61no—
362C22×D3D3612yes—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—32no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—181no—
376C2×C3×C4—181no—
377C2×C3×C4—181no—
378#67—188no—
379#67—188no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—92no—
386C2×Dic3—92no—
387C2×Dic3—182no—
388C2×Dic3—181no—
389C2×Dic3—181no—
390C2×Dic3—181no—
391C2×Dic3—181no—
392C2×Dic3—182no—
393C2×Dic3—181no—
394C2×Dic3—181no—
395C2×Dic3—181no—
396C2×Dic3—181no—
397C2×Dic3—181no—
398C2×Dic3—181no—
399C2×Dic3—361no—
400C2×Dic3—361no—
401C2×Dic3—361no—
402C2×Dic3—361no—
403C2×Dic3#61112yescomplemented
404C2×C32#88211yescharacteristic
405C2×C32#88311yescharacteristic
406C2×C32#88511yescharacteristic
407C2×C32#88611yescharacteristic
408C2×C32#93011yescharacteristic
409C2×C32#93811yescharacteristic
410C2×C32#93911yescharacteristic
411C3×D3—42no—
412C3×D3—122no—
413C2×C9—21no—
414C2×C9—21no—
415C2×C9—21no—
416C2×C9—21no—
417C2×C9—21no—
418C2×C9—21no—
419C2×C9—21no—
420C2×C9—122no—
421C2×C9#88311yescharacteristic
422C2×C9#88411yescharacteristic
423C2×C9#88411yescharacteristic
424C2×C9#88511yescharacteristic
425C2×C9#92911yescharacteristic
426C2×C9#93711yescharacteristic
427C2×C9#93911yescharacteristic
428D9—42no—
429C24—31no—
430C24—91no—
431C2×D4—542no—
432C2×D4—542no—
433C2×D4—542no—
434C22×C4—31no—
435C22×C4—91no—
436C22×C4—271no—
437C22×C4—271no—
438C22×C4D3×D911yescharacteristic
439C4⋊C4—542no—
440C22⋊C4—62no—
441C22⋊C4—182no—
442C22⋊C4—542no—
443C22⋊C4—542no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—62no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—121no—
455C22×C3—121no—
456C22×C3—121no—
457C22×C3—121no—
458C22×C3—182no—
459C22×C3—182no—
460C22×C3—182no—
461C22×C3—361no—
462C22×C3—361no—
463C22×C3—361no—
464C22×C3—361no—
465C22×C3C2×D3611yescharacteristic
466C22×C3#369711yescharacteristic
467C22×C3D4×D911yescharacteristic
468C22×C3D4×D911yescharacteristic
469C22×C3#369911yescharacteristic
470C22×C3#369911yescharacteristic
471C22×C3C2×#61111yescharacteristic
472C22×C3#379511yescharacteristic
473C22×C3#379811yescharacteristic
474C22×C3D3×D1211yescharacteristic
475C22×C3#380211yescharacteristic
476C22×C3#380511yescharacteristic
477C22×C3D3×#6711yescharacteristic
478C22×C3D3×#6711yescharacteristic
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—41no—
483C2×D3—41no—
484C2×D3—41no—
485C2×D3—41no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—121no—
490C2×D3—121no—
491C2×D3—121no—
492C2×D3—121no—
493C3×C4—42no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—62no—
497C3×C4—361no—
498Dic3—22no—
499Dic3—121no—
500Dic3—182no—
501Dic3—182no—
502Dic3—362no—
503Dic3—362no—
504Dic3—361no—
505Dic3—361no—
506C32#496111yescharacteristic
507C9—21no—
508C9#495911yescharacteristic, complemented
509C23—32no—
510C23—61no—
511C23—61no—
512C23—61no—
513C23—61no—
514C23—61no—
515C23—61no—
516C23—92no—
517C23—181no—
518C23—181no—
519C23—181no—
520C23—181no—
521C23—181no—
522C23—181no—
523C23C2×D3×D911yescharacteristic
524D4—548no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—32no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—272no—
535C2×C4—541no—
536C2×C4—541no—
537C2×C4—541no—
538C2×C4—541no—
539C2×C4—541no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—122no—
548C2×C3—362no—
549C2×C3#6344411yescharacteristic
550C2×C3#6344511yescharacteristic
551C2×C3#6344711yescharacteristic
552C2×C3#6344811yescharacteristic
553C2×C3#6349211yescharacteristic
554C2×C3#6350011yescharacteristic
555C2×C3#6350111yescharacteristic
556C2×C3#6388511yescharacteristic
557C2×C3#6389111yescharacteristic
558C2×C3#6390511yescharacteristic
559C2×C3#6390611yescharacteristic
560C2×C3#6391511yescharacteristic
561C2×C3#6392211yescharacteristic
562C2×C3#6397011yescharacteristic
563D3—42no—
564D3—122no—
565C22—62no—
566C22—62no—
567C22—62no—
568C22—121no—
569C22—121no—
570C22—121no—
571C22—121no—
572C22—182no—
573C22—182no—
574C22—182no—
575C22—361no—
576C22—361no—
577C22—361no—
578C22—361no—
579C22#8863811yescharacteristic
580C22#8864011yescharacteristic
581C22D3×D3611yescharacteristic
582C22#8864611yescharacteristic
583C22#8866311yescharacteristic
584C22D3×#61111yescharacteristic
585C22D9×#6711yescharacteristic
586C4—41no—
587C4—62no—
588C4—361no—
589C4—542no—
590C4—1081no—
591C3—21no—
592C3#1058864111yescharacteristic, complemented
593C3#1059139011yescharacteristic
594C2—122no—
595C2—362no—
596C2#1172101611yescharacteristic
597C2#1172102111yescharacteristic
598C2#1172103111yescharacteristic
599C2#1172103411yescharacteristic
600C2#1172104411yescharacteristic
601C2#1172104911yescharacteristic
602C2#1172127011yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutator, cosocleC23×C3×C9C23
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC22×#6194C2
hypercenterC22×C4D3×D9
hypocenterC3×C9#394
LCSG ▷ C23×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C9×(C2×D3)⋊C4C2semidirect
3. C2×C3×(C2×D9)⋊C4C2semidirect
4. C2×(C2×D3)⋊Dic9C2semidirect
5. C2×(C2×D9)⋊Dic3C2semidirect
6. C2×Dic3⋊Dic9C2semidirect
7. #11720572C2semidirect
36. C2×(C2×D9)⋊C4D3semidirect
66. C2×C9×Dic3D4semidirect
141. C2×(C2×D3)⋊C4D9semidirect
331. C3×C9#394semidirect
403. C2×Dic3#611semidirect
508. C9#4959semidirect
592. C3#10588641semidirect

Maximal subgroups

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

subgroupindex
C22×#61942
C2×C9×(C2×D3)⋊C42
C2×C3×(C2×D9)⋊C42
C2×(C2×D3)⋊Dic92
C2×(C2×D9)⋊Dic32
C2×Dic3⋊Dic92
#117205722
#105913903
#105886413