Finite Group Databasebeta

← #13148942

Subgroups — #13148942

Order 1728.

716 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721752C211yesmaximal, characteristic, complemented
2C3×#63460C211yesmaximal, characteristic, complemented
3C9×#890C211yesmaximal, characteristic, complemented
4#11721000C211yesmaximal, characteristic, complemented
5#11720996C211yesmaximal, characteristic, complemented
6#11720978C211yesmaximal, characteristic
7#11720974C211yesmaximal, characteristic, complemented
8#11720946C211yesmaximal, characteristic, complemented
9#11720942C211yesmaximal, characteristic
10#11720942C211yesmaximal, characteristic
11#11720919C211yesmaximal, characteristic, complemented
12#11720918C211yesmaximal, characteristic, complemented
13#11720913C211yesmaximal, characteristic, complemented
14#11720899C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10594478—31nomaximal
17#10589795—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×#6192C2211yescharacteristic
21C2×(C3⋊D9)⋊C4C2211yescharacteristic
22C2×(C3⋊D9)⋊C4C2211yescharacteristic
23C2×Dic3×D9C2211yescharacteristic
24C3×C9×C4⋊C4C2211yescharacteristic
25#88536C2211yescharacteristic
26#88536C2211yescharacteristic
27#88534C2211yescharacteristic
28#88534C2211yescharacteristic
29C3×(C2×D9)⋊C4C2211yescharacteristic
30C3×(C2×D9)⋊C4C2211yescharacteristic
31C3×(C2×D9)⋊C4C2211yescharacteristic
32C9×C4⋊Dic3C2211yescharacteristic
33C9×C4⋊Dic3C2211yescharacteristic
34C9×C4⋊Dic3C2211yescharacteristic
35C9×Dic3⋊C4C2211yescharacteristic
36C9×Dic3⋊C4C2211yescharacteristic
37C4×C9×Dic3C2211yescharacteristic
38C3×C4⋊Dic9C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40C3×C4×Dic9C2211yescharacteristic
41#88445C2211yescharacteristic
42(C2×D9)⋊Dic3C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44Dic3⋊Dic9C2211yescharacteristic
45#88442C2211yescharacteristic
46#88442C2211yescharacteristic
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic3×Dic9C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64105—31no—
54C3×#898—31no—
55C3×#890D311yescharacteristic
56#63900—31no—
57#63896—31no—
58#63881—31no—
59#63877—31no—
60#63858—31no—
61#63854—31no—
62#63854—31no—
63#63847—31no—
64#63847—31no—
65#63844—31no—
66#63836—31no—
67#63836—31no—
68C9×#125—31no—
69#63460—31no—
70#63460D311yescharacteristic, complemented
71#63458—31no—
72#63458—31no—
73#63458—61no—
74#63456—31no—
75#63456—31no—
76#63455—31no—
77#63454—31no—
78C4⋊C4×D9—31no—
79#63451—31no—
80#63451—31no—
81#63449—31no—
82#63434—31no—
83#63434—31no—
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
92C4×C3⋊D9—22no—
93#6226—22no—
94C2×C9×Dic3C2311yescharacteristic
95C2×C9×Dic3C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101#6192—22no—
102(C3⋊D9)⋊C4—22no—
103(C3⋊D9)⋊C4—22no—
104Dic3×D9—22no—
105#5708—91no—
106#5693—91no—
107C2×C4×C3⋊D3—31no—
108C2×#634—31no—
109C2×#626—31no—
110C2×#624—31no—
111C2×#624—31no—
112C2×D3×Dic3—31no—
113C32×C4⋊C4C2×D311yescharacteristic
114#3752—31no—
115#3752—31no—
116#3750—31no—
117#3750—31no—
118C3×(C2×D3)⋊C4—31no—
119C3×(C2×D3)⋊C4—31no—
120C3×(C2×D3)⋊C4—31no—
121C3×C4⋊Dic3—31no—
122C3×C4⋊Dic3C2×D311yescharacteristic
123C3×C4⋊Dic3C2×D311yescharacteristic
124C3×C4⋊Dic3C2×D311yescharacteristic
125C3×Dic3⋊C4—31no—
126C3×Dic3⋊C4C2×D311yescharacteristic
127C3×Dic3⋊C4C2×D311yescharacteristic
128C3×C4×Dic3—31no—
129C3×C4×Dic3C2×D311yescharacteristic
130#3724—31no—
131#3724—31no—
132#3724—31no—
133#3724—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136#3722—31no—
137(C2×D3)⋊Dic3—31no—
138(C2×D3)⋊Dic3—31no—
139Dic32—31no—
140Dic32—31no—
141Dic32—31no—
142C2×D36—31no—
143C2×C4×D9—31no—
144C2×C4×D9—31no—
145C2×C4×D9—31no—
146C2×C4×D9—31no—
147C2×C4×D9—61no—
148C2×Dic18—31no—
149C2×Dic18—61no—
150C9×C4⋊C4—21no—
151C9×C4⋊C4—31no—
152C9×C4⋊C4—31no—
153C9×C4⋊C4—31no—
154C9×C4⋊C4—31no—
155C9×C4⋊C4—31no—
156C9×C4⋊C4C2×D311yescharacteristic
157C42×C9—31no—
158(C2×D9)⋊C4—31no—
159(C2×D9)⋊C4—31no—
160(C2×D9)⋊C4—31no—
161(C2×D9)⋊C4—31no—
162(C2×D9)⋊C4—31no—
163(C2×D9)⋊C4—61no—
164(C2×D9)⋊C4—61no—
165(C2×D9)⋊C4C2×D311yescharacteristic
166(C2×D9)⋊C4C2×D311yescharacteristic
167(C2×D9)⋊C4C2×D311yescharacteristic
168C4⋊Dic9—31no—
169C4⋊Dic9C2×D311yescharacteristic
170Dic9⋊C4—31no—
171Dic9⋊C4—31no—
172Dic9⋊C4—31no—
173Dic9⋊C4—31no—
174Dic9⋊C4—31no—
175Dic9⋊C4—31no—
176Dic9⋊C4—31no—
177Dic9⋊C4—61no—
178Dic9⋊C4—61no—
179Dic9⋊C4C2×D311yescharacteristic
180C4×Dic9—31no—
181C4×Dic9—31no—
182C4×Dic9—31no—
183C4×Dic9C2×D311yescharacteristic
184C22×C3×C9C2411yescharacteristic
185C2×C3⋊D9—21no—
186C2×C3⋊D9—21no—
187C2×C3⋊D9#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#4112yes—
197C9×Dic3—21no—
198C9×Dic3—21no—
199C9×Dic3—21no—
200C9×Dic3—21no—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×#126—91no—
205C3×#125—31no—
206#898—31no—
207#898—91no—
208#896—91no—
209#896—91no—
210#896—91no—
211#896—181no—
212#894—91no—
213#894—91no—
214#893—91no—
215#892—91no—
216#892—91no—
217D3×C4⋊C4—91no—
218D3×C4⋊C4—91no—
219#890D911yescharacteristic, complemented
220#889—91no—
221#889—91no—
222#889—91no—
223#889—91no—
224#887—91no—
225#883—91no—
226#883—91no—
227#67⋊C4—91no—
228#879—91no—
229#878—91no—
230#877—91no—
231#872—91no—
232#872—91no—
233#872—91no—
234C4×Dic6—91no—
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—
243C4×C3⋊D3—62no—
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
251C2×C3×Dic3C22×D311yescharacteristic
252#626—62no—
253#624—62no—
254#624—62no—
255D3×Dic3—62no—
256C22×D9—31no—
257C22×D9—61no—
258C22×D9C22×D311yescharacteristic
259C2×C4×C9—21no—
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×C9C22×D311yescharacteristic
267C2×C4×C9C22×D311yescharacteristic
268C2×C4×C9C22×D311yescharacteristic
269C2×Dic9—31no—
270C2×Dic9—31no—
271C2×Dic9—31no—
272C2×Dic9—61no—
273C2×Dic9—61no—
274C2×Dic9—61no—
275C2×Dic9C22×D311yescharacteristic
276C2×Dic9C22×D311yescharacteristic
277C2×Dic9C22×D311yescharacteristic
278D36—62no—
279C4×D9—62no—
280C4×D9—62no—
281C4×D9—62no—
282C4×D9—62no—
283C4×D9—122no—
284Dic18—62no—
285Dic18—122no—
286#552—271noSylow
287C2×C3×C9C2×#4111yescharacteristic
288C2×C3×C9C2×#4111yescharacteristic
289C2×C3×C92−1+411yescharacteristic
290C3⋊D9—22no—
291C3×D9—41no—
292C2×#67—91no—
293C22×Dic3—91no—
294C2×D12—91no—
295C2×C4×D3—91no—
296C2×C4×D3—91no—
297C2×C4×D3—91no—
298C2×C4×D3—91no—
299C2×C4×D3—91no—
300C2×C4×D3—91no—
301C2×C4×D3—91no—
302C2×C4×D3—181no—
303C2×Dic6—91no—
304C2×Dic6—91no—
305C2×Dic6—181no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—91no—
313C3×C4⋊C4—91no—
314C3×C4⋊C4C2×D911yescharacteristic
315C3×C4⋊C4D3211yescharacteristic
316C3×C22⋊C4—91no—
317C3×C22⋊C4—91no—
318C3×C22⋊C4—91no—
319C3×C42—31no—
320C3×C42—91no—
321#217—91no—
322#217—91no—
323(C2×D3)⋊C4—31no—
324(C2×D3)⋊C4—31no—
325(C2×D3)⋊C4—31no—
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—91no—
333(C2×D3)⋊C4—91no—
334(C2×D3)⋊C4—181no—
335(C2×D3)⋊C4—181no—
336C4⋊Dic3—31no—
337C4⋊Dic3—91no—
338C4⋊Dic3—91no—
339C4⋊Dic3C2×D911yescharacteristic
340C4⋊Dic3C2×D911yescharacteristic
341C4⋊Dic3C2×D911yescharacteristic
342Dic3⋊C4—31no—
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—91no—
356Dic3⋊C4—91no—
357Dic3⋊C4—181no—
358Dic3⋊C4—181no—
359Dic3⋊C4C2×D911yescharacteristic
360Dic3⋊C4C2×D911yescharacteristic
361C4×Dic3—31no—
362C4×Dic3—91no—
363C4×Dic3—91no—
364C4×Dic3—91no—
365C4×Dic3—91no—
366C4×Dic3—91no—
367C4×Dic3—91no—
368C4×Dic3C2×D911yescharacteristic
369C22×C32C23×D311yescharacteristic
370C2×C3⋊D3—32no—
371C2×C3⋊D3—61no—
372C2×C3⋊D3—61no—
373C2×C3×D3—61no—
374C2×C3×D3—61no—
375C2×C3×D3—61no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—21no—
379C3⋊Dic3—32no—
380C3⋊Dic3—61no—
381C3⋊Dic3—61no—
382C3×Dic3—21no—
383C3×Dic3—21no—
384C3×Dic3—21no—
385C3×Dic3—21no—
386C3×Dic3—61no—
387C3×Dic3—61no—
388C3×Dic3—61no—
389C22×C9—21no—
390C22×C9C23×D311yescharacteristic
391C2×D9—21no—
392C2×D9—21no—
393C2×D9—21no—
394C2×D9—32no—
395C2×D9—62no—
396C2×D9—61no—
397C2×D9—61no—
398C2×D9—121no—
399C2×D9—121no—
400C4×C9—21no—
401C4×C9—21no—
402C4×C9—21no—
403C4×C9—41no—
404C4×C9—41no—
405C4×C9—41no—
406C4×C9—61no—
407C4×C9—61no—
408C4×C9—61no—
409C4×C9—61no—
410Dic9—21no—
411Dic9—21no—
412Dic9—21no—
413Dic9—32no—
414Dic9—62no—
415Dic9—61no—
416Dic9—61no—
417Dic9—121no—
418Dic9—121no—
419#126—91no—
420#126—271no—
421#125—31no—
422#125—271no—
423#125—271no—
424#123—271no—
425#123—271no—
426C22⋊Q8—271no—
427C22⋊Q8—271no—
428C4×Q8—271no—
429C4×D4—271no—
430#117—271no—
431#117—271no—
432#117—271no—
433C2×C4⋊C4—271no—
434C3×C9#55211yescharacteristic, complemented, Sylow
435C23×C3—91no—
436C22×D3—31no—
437C22×D3—91no—
438C22×D3—91no—
439C22×D3—181no—
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—182no—
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—182no—
470C2×Dic3C22×D911yescharacteristic
471C2×Dic3C22×D911yescharacteristic
472C2×Dic3C22×D911yescharacteristic
473C2×Dic3C22×D911yescharacteristic
474D12—182no—
475C4×D3—182no—
476C4×D3—182no—
477C4×D3—182no—
478C4×D3—182no—
479C4×D3—182no—
480C4×D3—182no—
481C4×D3—182no—
482C4×D3—362no—
483Dic6—182no—
484Dic6—182no—
485Dic6—362no—
486C2×C32#100711yescharacteristic
487C2×C32D3×#4111yescharacteristic
488C2×C32D3×#4111yescharacteristic
489C3⋊D3—62no—
490C3×D3—121no—
491C2×C9—21no—
492C2×C9—21no—
493C2×C9—21no—
494C2×C9D3×#4111yescharacteristic
495C2×C9D3×#4111yescharacteristic
496C2×C9#101011yescharacteristic
497D9—41no—
498D9—62no—
499D9—122no—
500C2×Q8—271no—
501C2×D4—271no—
502C22×C4—271no—
503C22×C4—271no—
504C22×C4—271no—
505C22×C4—271no—
506C4⋊C4—31no—
507C4⋊C4—31no—
508C4⋊C4—31no—
509C4⋊C4—31no—
510C4⋊C4—31no—
511C4⋊C4—91no—
512C4⋊C4—91no—
513C4⋊C4—271no—
514C4⋊C4—271no—
515C4⋊C4—271no—
516C4⋊C4—271no—
517C4⋊C4—271no—
518C4⋊C4—271no—
519C4⋊C4—271no—
520C4⋊C4—271no—
521C4⋊C4D3×D911yescharacteristic
522C22⋊C4—91no—
523C22⋊C4—91no—
524C22⋊C4—91no—
525C22⋊C4—271no—
526C22⋊C4—271no—
527C22⋊C4—271no—
528C22⋊C4—271no—
529C22⋊C4—271no—
530C42—31no—
531C42—91no—
532C42—271no—
533C42—271no—
534C42—271no—
535C22×C3—21no—
536C22×C3—181no—
537C22×C3—181no—
538C22×C3—181no—
539C22×C3C23×D911yescharacteristic
540C22×C3C22×D3211yescharacteristic
541C2×D3—61no—
542C2×D3—61no—
543C2×D3—61no—
544C2×D3—92no—
545C2×D3—92no—
546C2×D3—182no—
547C2×D3—181no—
548C2×D3—181no—
549C2×D3—181no—
550C2×D3—181no—
551C2×D3—361no—
552C2×D3—361no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—41no—
560C3×C4—41no—
561C3×C4—41no—
562C3×C4—61no—
563C3×C4—61no—
564C3×C4—61no—
565C3×C4—61no—
566C3×C4—181no—
567C3×C4—181no—
568C3×C4—181no—
569Dic3—21no—
570Dic3—21no—
571Dic3—21no—
572Dic3—21no—
573Dic3—61no—
574Dic3—61no—
575Dic3—61no—
576Dic3—92no—
577Dic3—92no—
578Dic3—182no—
579Dic3—181no—
580Dic3—181no—
581Dic3—181no—
582Dic3—181no—
583Dic3—361no—
584Dic3—361no—
585C32#569311yescharacteristic
586C9—21no—
587C9#570811yescharacteristic, complemented
588C23—91no—
589C23—271no—
590Q8—542no—
591D4—542no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—91no—
597C2×C4—91no—
598C2×C4—91no—
599C2×C4—271no—
600C2×C4—271no—
601C2×C4—271no—
602C2×C4—542no—
603C2×C4—542no—
604C2×C4—542no—
605C2×C4—542no—
606C2×C4C2×D3×D911yescharacteristic
607C2×C4C2×D3×D911yescharacteristic
608C2×C4C2×D3×D911yescharacteristic
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—361no—
613C2×C3#6371311yescharacteristic
614C2×C3#41×D911yescharacteristic
615C2×C3#41×D911yescharacteristic
616C2×C3#6429711yescharacteristic
617C2×C3#6431211yescharacteristic
618C2×C3#6431911yescharacteristic
619D3—121no—
620D3—182no—
621D3—182no—
622D3—362no—
623C22—181no—
624C22—181no—
625C22—181no—
626C22—272no—
627C22—541no—
628C22—541no—
629C22C22×D3×D911yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—61no—
634C4—61no—
635C4—61no—
636C4—61no—
637C4—181no—
638C4—181no—
639C4—181no—
640C4—272no—
641C4—541no—
642C4—541no—
643C3—21no—
644C3#1058979511yescharacteristic, complemented
645C3#1059447811yescharacteristic
646C2—361no—
647C2—542no—
648C2#1172245811yescharacteristic
649C2#1172249811yescharacteristic
650C2#1172251411yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#6192C22
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#552
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721752C2semidirect
2. C3×#63460C2semidirect
3. C9×#890C2semidirect
4. #11721000C2semidirect
5. #11720996C2semidirect
7. #11720974C2semidirect
8. #11720946C2semidirect
11. #11720919C2semidirect
12. #11720918C2semidirect
13. #11720913C2semidirect
14. #11720899C2semidirect
15. #11720898C2semidirect
70. #63460D3semidirect
219. #890D9semidirect
434. C3×C9#552semidirect
587. C9#5708semidirect
644. C3#10589795semidirect

Maximal subgroups

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

subgroupindex
#117217522
C3×#634602
C9×#8902
#117210002
#117209962
#117209782
#117209742
#117209462
#117209422
#117209192
#117209182
#117209132
#117208992
#117208982
#105944783
#105897953