Finite Group Databasebeta

← #13147617

Subgroups — #13147617

Order 1728.

712 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6226C211yesmaximal, characteristic, complemented
2C9×#872C211yesmaximal, characteristic, complemented
3C3×#63438C211yesmaximal, characteristic, complemented
4#11721032C211yesmaximal, characteristic
5#11721028C211yesmaximal, characteristic
6#11721024C211yesmaximal, characteristic, complemented
7#11721021C211yesmaximal, characteristic
8#11721011C211yesmaximal, characteristic, complemented
9D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
10#11720996C211yesmaximal, characteristic, complemented
11#11720974C211yesmaximal, characteristic, complemented
12#11720950C211yesmaximal, characteristic, complemented
13#11720928C211yesmaximal, characteristic, complemented
14#11720925C211yesmaximal, characteristic, complemented
15#11720915C211yesmaximal, characteristic, complemented
16#10593919—31nomaximal
17#10589633—31nomaximal
18C2×#6226C2211yescharacteristic
19C2×C4×D3×C9C2211yescharacteristic
20C2×#6194C2211yescharacteristic
21C2×D3×Dic9C2211yescharacteristic
22C2×D3×Dic9C2211yescharacteristic
23C2×Dic3×D9C2211yescharacteristic
24C3×C42×C9C2211yescharacteristic
25C4⋊(C3⋊Dic9)C2211yescharacteristic
26#88534C2211yescharacteristic
27#88534C2211yescharacteristic
28C4×C3⋊Dic9C2211yescharacteristic
29C4×C3⋊Dic9C2211yescharacteristic
30C9×(C2×D3)⋊C4C2211yescharacteristic
31C9×(C2×D3)⋊C4C2211yescharacteristic
32C3×(C2×D9)⋊C4C2211yescharacteristic
33C3×(C2×D9)⋊C4C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C9×Dic3⋊C4C2211yescharacteristic
36C9×Dic3⋊C4C2211yescharacteristic
37C4×C9×Dic3C2211yescharacteristic
38C3×Dic9⋊C4C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40C3×Dic9⋊C4C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D9)⋊Dic3C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44Dic3⋊Dic9C2211yescharacteristic
45Dic3⋊Dic9C2211yescharacteristic
46#88442C2211yescharacteristic
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53C4×#634—31no—
54C3×#876—31no—
55C3×#872D311yescharacteristic
56#63905—31no—
57#63902—31no—
58#63896—31no—
59#63896—31no—
60#63891—31no—
61#63878—31no—
62#63877—31no—
63D3×Dic3⋊C4—31no—
64#63870—31no—
65#63867—31no—
66#63862—31no—
67#63845—31no—
68C9×#117—31no—
69#63491—31no—
70C2×Dic9⋊C4—31no—
71#63460—31no—
72#63458—31no—
73#63451—31no—
74#63451—31no—
75#63448—31no—
76#611⋊C4—31no—
77#63440—31no—
78#63439—31no—
79#63438D311yescharacteristic, complemented
80#63434—31no—
81#63432—31no—
82C4×Dic18—31no—
83C4×Dic18—61no—
84C22×D3×C9C2311yescharacteristic
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×C3⋊Dic9C2311yescharacteristic
93#6226—22no—
94C2×C9×Dic3C2311yescharacteristic
95C2×C9×Dic3C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C4×D3×C9—22no—
101#6194—22no—
102D3×Dic9—22no—
103D3×Dic9—22no—
104Dic3×D9—22no—
105#5708—91no—
106#5531—91no—
107C2×#634—31no—
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×#625—31no—
110C2×D3×Dic3—31no—
111C2×D3×Dic3—31no—
112C2×D3×Dic3—31no—
113C32×C42C2×D311yescharacteristic
114C4⋊(C3⋊Dic3)—31no—
115#3750—31no—
116#3750—31no—
117C4×C3⋊Dic3—31no—
118C4×C3⋊Dic3—31no—
119C3×(C2×D3)⋊C4—31no—
120C3×(C2×D3)⋊C4—31no—
121C3×(C2×D3)⋊C4—31no—
122C3×(C2×D3)⋊C4C2×D311yescharacteristic
123C3×(C2×D3)⋊C4C2×D311yescharacteristic
124C3×Dic3⋊C4—31no—
125C3×Dic3⋊C4—31no—
126C3×Dic3⋊C4—31no—
127C3×Dic3⋊C4C2×D311yescharacteristic
128C3×Dic3⋊C4C2×D311yescharacteristic
129C3×C4×Dic3C2×D311yescharacteristic
130#3724—31no—
131#3724—31no—
132#3724—31no—
133Dic3⋊Dic3—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—31no—
138(C2×D3)⋊Dic3—31no—
139(C2×D3)⋊Dic3—31no—
140(C2×D3)⋊Dic3—31no—
141Dic32—31no—
142C22×C4×C9—31no—
143C2×#611—31no—
144C22×Dic9—31no—
145C22×Dic9—31no—
146C2×C4×D9—31no—
147C2×Dic18—31no—
148C2×Dic18—61no—
149C9×C4⋊C4—31no—
150C9×C4⋊C4—31no—
151C9×C22⋊C4—31no—
152C9×C22⋊C4—31no—
153C42×C9—21no—
154C42×C9—31no—
155C42×C9C2×D311yescharacteristic
156#3676—31no—
157(C2×D9)⋊C4—31no—
158(C2×D9)⋊C4—31no—
159(C2×D9)⋊C4C2×D311yescharacteristic
160(C2×D9)⋊C4C2×D311yescharacteristic
161(C2×D9)⋊C4C2×D311yescharacteristic
162C4⋊Dic9—31no—
163C4⋊Dic9—31no—
164C4⋊Dic9—31no—
165C4⋊Dic9—61no—
166Dic9⋊C4—31no—
167Dic9⋊C4—31no—
168Dic9⋊C4—31no—
169Dic9⋊C4—31no—
170Dic9⋊C4—31no—
171Dic9⋊C4—31no—
172Dic9⋊C4—31no—
173Dic9⋊C4—31no—
174Dic9⋊C4—61no—
175Dic9⋊C4—61no—
176Dic9⋊C4C2×D311yescharacteristic
177Dic9⋊C4C2×D311yescharacteristic
178Dic9⋊C4C2×D311yescharacteristic
179C4×Dic9—31no—
180C4×Dic9—31no—
181C4×Dic9—31no—
182C4×Dic9—61no—
183C4×Dic9—61no—
184C22×C3×C9C2411yescharacteristic
185C2×D3×C9—21no—
186C2×D3×C9—21no—
187C2×D3×C9#4112yes—
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—
197C3⋊Dic9#4112yes—
198C9×Dic3—21no—
199C9×Dic3—21no—
200C9×Dic3—21no—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×#126—91no—
205C3×#117—31no—
206#929—91no—
207C2×Dic3⋊C4—91no—
208#898—91no—
209#896—91no—
210#896—91no—
211#892—91no—
212D3×C4⋊C4—91no—
213#890—91no—
214#889—91no—
215#889—91no—
216#889—91no—
217#889—91no—
218#886—91no—
219#883—91no—
220#883—91no—
221#67⋊C4—91no—
222#67⋊C4—91no—
223#879—91no—
224#878—91no—
225#878—91no—
226#877—91no—
227#877—91no—
228#876—31no—
229#872—91no—
230#872D911yescharacteristic, complemented
231#870—91no—
232C4×Dic6—91no—
233C4×Dic6—91no—
234C4×Dic6—181no—
235C22×C3×D3—31no—
236C22×C3×D3C22×D311yescharacteristic
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—
244#634—62no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3C22×D311yescharacteristic
249C2×C3×Dic3C22×D311yescharacteristic
250C2×C3×Dic3C22×D311yescharacteristic
251C3×C4×D3—22no—
252#625—62no—
253D3×Dic3—62no—
254D3×Dic3—62no—
255D3×Dic3—62no—
256C23×C9—31no—
257C22×D9C22×D311yescharacteristic
258C2×C4×C9—21no—
259C2×C4×C9—21no—
260C2×C4×C9—21no—
261C2×C4×C9—31no—
262C2×C4×C9—31no—
263C2×C4×C9—31no—
264C2×C4×C9—62no—
265C2×C4×C9C22×D311yescharacteristic
266C2×C4×C9C22×D311yescharacteristic
267C2×C4×C9C22×D311yescharacteristic
268#611—62no—
269C2×Dic9—31no—
270C2×Dic9—31no—
271C2×Dic9—31no—
272C2×Dic9—31no—
273C2×Dic9—61no—
274C2×Dic9—61no—
275C2×Dic9—61no—
276C2×Dic9—61no—
277C2×Dic9—62no—
278C2×Dic9—62no—
279C2×Dic9C22×D311yescharacteristic
280C2×Dic9C22×D311yescharacteristic
281C2×Dic9C22×D311yescharacteristic
282C4×D9—62no—
283Dic18—62no—
284Dic18—64no—
285#552—271noSylow
286C2×C3×C9C2×#4111yescharacteristic
287C2×C3×C9C2×#4111yescharacteristic
288C2×C3×C92−1+411yescharacteristic
289D3×C9—22no—
290C3×D9—41no—
291C22×C3×C4—31no—
292C2×#67—91no—
293C2×#67—91no—
294C22×Dic3—91no—
295C22×Dic3—91no—
296C22×Dic3—91no—
297C2×C4×D3—91no—
298C2×C4×D3—91no—
299C2×C4×D3—91no—
300C2×C4×D3C2×D911yescharacteristic
301C2×Dic6—91no—
302C2×Dic6—91no—
303C2×Dic6—181no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4—91no—
308C3×C4⋊C4—91no—
309C3×C22⋊C4—31no—
310C3×C22⋊C4—31no—
311C3×C22⋊C4—91no—
312C3×C22⋊C4—91no—
313C3×C22⋊C4—91no—
314C3×C42—21no—
315C3×C42—31no—
316C3×C42C2×D911yescharacteristic
317C3×C42D3211yescharacteristic
318#217—91no—
319#217—91no—
320#217—91no—
321(C2×D3)⋊C4—31no—
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—
327(C2×D3)⋊C4C2×D911yescharacteristic
328(C2×D3)⋊C4C2×D911yescharacteristic
329C4⋊Dic3—91no—
330C4⋊Dic3—91no—
331C4⋊Dic3—91no—
332C4⋊Dic3—91no—
333C4⋊Dic3—91no—
334C4⋊Dic3—91no—
335C4⋊Dic3—91no—
336C4⋊Dic3—181no—
337Dic3⋊C4—31no—
338Dic3⋊C4—31no—
339Dic3⋊C4—31no—
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—91no—
353Dic3⋊C4—91no—
354Dic3⋊C4—91no—
355Dic3⋊C4—181no—
356Dic3⋊C4—181no—
357Dic3⋊C4C2×D911yescharacteristic
358Dic3⋊C4C2×D911yescharacteristic
359C4×Dic3—91no—
360C4×Dic3—91no—
361C4×Dic3—91no—
362C4×Dic3—91no—
363C4×Dic3—91no—
364C4×Dic3—91no—
365C4×Dic3—181no—
366C4×Dic3—181no—
367C4×Dic3C2×D911yescharacteristic
368C22×C32C23×D311yescharacteristic
369C2×C3×D3—21no—
370C2×C3×D3—21no—
371C2×C3×D3—61no—
372C2×C3×D3—61no—
373C2×C3×D3—61no—
374C2×C3×D3#23512yes—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4—21no—
378C3⋊Dic3—32no—
379C3⋊Dic3—61no—
380C3⋊Dic3—61no—
381C3⋊Dic3—61no—
382C3×Dic3—21no—
383C3×Dic3—21no—
384C3×Dic3—21no—
385C3×Dic3—61no—
386C3×Dic3—61no—
387C3×Dic3—61no—
388C22×C9—21no—
389C22×C9—32no—
390C22×C9—61no—
391C22×C9—61no—
392C22×C9C23×D311yescharacteristic
393C2×D9—21no—
394C2×D9—21no—
395C2×D9—21no—
396C4×C9—22no—
397C4×C9—22no—
398C4×C9—21no—
399C4×C9—21no—
400C4×C9—21no—
401C4×C9—41no—
402C4×C9—61no—
403C4×C9—61no—
404C4×C9—61no—
405Dic9—21no—
406Dic9—21no—
407Dic9—21no—
408Dic9—32no—
409Dic9—62no—
410Dic9—62no—
411Dic9—61no—
412Dic9—61no—
413Dic9—61no—
414Dic9—121no—
415Dic9—121no—
416#126—91no—
417#126—271no—
418#125—271no—
419#125—271no—
420#125—271no—
421#123—271no—
422#123—271no—
423C22⋊Q8—271no—
424C22⋊Q8—271no—
425C4×Q8—271no—
426C4×D4—271no—
427#117—31no—
428#117—271no—
429#117—271no—
430C2×C4⋊C4—271no—
431C3×C9#55211yescharacteristic, complemented, Sylow
432C23×C3—31no—
433C23×C3—91no—
434C22×D3—31no—
435C22×D3C22×D911yescharacteristic
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—62no—
443C2×C3×C4—91no—
444C2×C3×C4—91no—
445C2×C3×C4—91no—
446C2×C3×C4C22×D911yescharacteristic
447C2×C3×C4C22×D911yescharacteristic
448C2×C3×C4C22×D911yescharacteristic
449C2×C3×C4C2×D3211yescharacteristic
450C2×C3×C4C2×D3211yescharacteristic
451C2×C3×C4C2×D3211yescharacteristic
452#67—182no—
453#67—182no—
454C2×Dic3—31no—
455C2×Dic3—31no—
456C2×Dic3—31no—
457C2×Dic3—91no—
458C2×Dic3—91no—
459C2×Dic3—91no—
460C2×Dic3—91no—
461C2×Dic3—91no—
462C2×Dic3—91no—
463C2×Dic3—91no—
464C2×Dic3—91no—
465C2×Dic3—181no—
466C2×Dic3—181no—
467C2×Dic3—181no—
468C2×Dic3—181no—
469C2×Dic3—182no—
470C2×Dic3—182no—
471C2×Dic3—182no—
472C2×Dic3C22×D911yescharacteristic
473C2×Dic3C22×D911yescharacteristic
474C2×Dic3C22×D911yescharacteristic
475C4×D3—22no—
476C4×D3—182no—
477C4×D3—182no—
478C4×D3—182no—
479Dic6—182no—
480Dic6—182no—
481Dic6—184no—
482C2×C32C2×#23511yescharacteristic
483C2×C32D3×#4111yescharacteristic
484C2×C32#101011yescharacteristic
485C3×D3—22no—
486C3×D3—121no—
487C2×C9—21no—
488C2×C9—21no—
489C2×C9—21no—
490C2×C9—62no—
491C2×C9D3×#4111yescharacteristic
492C2×C9D3×#4111yescharacteristic
493C2×C9#101011yescharacteristic
494D9—41no—
495C2×Q8—271no—
496C2×D4—271no—
497C22×C4—31no—
498C22×C4—271no—
499C22×C4—271no—
500C22×C4—271no—
501C4⋊C4—31no—
502C4⋊C4—31no—
503C4⋊C4—91no—
504C4⋊C4—91no—
505C4⋊C4—91no—
506C4⋊C4—271no—
507C4⋊C4—271no—
508C4⋊C4—271no—
509C4⋊C4—271no—
510C4⋊C4—271no—
511C4⋊C4—271no—
512C4⋊C4—271no—
513C4⋊C4—271no—
514C4⋊C4—271no—
515C4⋊C4—271no—
516C4⋊C4—271no—
517C22⋊C4—31no—
518C22⋊C4—31no—
519C22⋊C4—91no—
520C22⋊C4—91no—
521C22⋊C4—91no—
522C22⋊C4—271no—
523C22⋊C4—271no—
524C22⋊C4—271no—
525C42—31no—
526C42—271no—
527C42—271no—
528C42—271no—
529C42D3×D911yescharacteristic
530C22×C3—21no—
531C22×C3—32no—
532C22×C3—61no—
533C22×C3—61no—
534C22×C3—181no—
535C22×C3—181no—
536C22×C3—181no—
537C22×C3C23×D911yescharacteristic
538C22×C3C22×D3211yescharacteristic
539C2×D3—21no—
540C2×D3—21no—
541C2×D3—61no—
542C2×D3—61no—
543C2×D3—61no—
544C2×D3#369712yes—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—41no—
554C3×C4—61no—
555C3×C4—61no—
556C3×C4—61no—
557C3×C4—181no—
558C3×C4—181no—
559C3×C4—181no—
560Dic3—21no—
561Dic3—21no—
562Dic3—21no—
563Dic3—61no—
564Dic3—61no—
565Dic3—61no—
566Dic3—92no—
567Dic3—92no—
568Dic3—182no—
569Dic3—182no—
570Dic3—181no—
571Dic3—181no—
572Dic3—181no—
573Dic3—181no—
574Dic3—181no—
575Dic3—181no—
576Dic3—361no—
577Dic3—361no—
578C32#553111yescharacteristic
579C9—21no—
580C9#570811yescharacteristic, complemented
581C23—31no—
582C23—91no—
583Q8—542no—
584D4—542no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—31no—
588C2×C4—62no—
589C2×C4—91no—
590C2×C4—91no—
591C2×C4—91no—
592C2×C4—271no—
593C2×C4—271no—
594C2×C4—271no—
595C2×C4—271no—
596C2×C4—542no—
597C2×C4—542no—
598C2×C4—542no—
599C2×C4C2×D3×D911yescharacteristic
600C2×C4C2×D3×D911yescharacteristic
601C2×C4C2×D3×D911yescharacteristic
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—62no—
606C2×C3—361no—
607C2×C3C2×#369711yescharacteristic
608C2×C3#41×D911yescharacteristic
609C2×C3#6371611yescharacteristic
610C2×C3#6429811yescharacteristic
611C2×C3D3×#23511yescharacteristic
612C2×C3#6430611yescharacteristic
613D3—22no—
614D3—121no—
615C22—32no—
616C22—61no—
617C22—61no—
618C22—181no—
619C22—181no—
620C22—181no—
621C22C22×D3×D911yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—61no—
626C4—61no—
627C4—61no—
628C4—181no—
629C4—181no—
630C4—181no—
631C4—272no—
632C4—541no—
633C4—541no—
634C4—541no—
635C3—21no—
636C3#1058963311yescharacteristic, complemented
637C3#1059391911yescharacteristic
638C2—62no—
639C2—361no—
640C2#1172246511yescharacteristic
641C2D3×#369711yescharacteristic
642C2#1172247511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C42×C9C22
socleC22×C32C23×D3
prime radicalC2×#6194C22
hypercenterC42D3×D9
hypocenterC3×C9#552
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×#6226C2semidirect
2. C9×#872C2semidirect
3. C3×#63438C2semidirect
6. #11721024C2semidirect
8. #11721011C2semidirect
9. D3×Dic9⋊C4C2semidirect
10. #11720996C2semidirect
11. #11720974C2semidirect
12. #11720950C2semidirect
13. #11720928C2semidirect
14. #11720925C2semidirect
15. #11720915C2semidirect
79. #63438D3semidirect
230. #872D9semidirect
431. C3×C9#552semidirect
580. C9#5708semidirect
636. C3#10589633semidirect

Maximal subgroups

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

subgroupindex
C4×#62262
C9×#8722
C3×#634382
#117210322
#117210282
#117210242
#117210212
#117210112
D3×Dic9⋊C42
#117209962
#117209742
#117209502
#117209282
#117209252
#117209152
#105939193
#105896333