Finite Group Databasebeta

← #13148958

Subgroups — #13148958

Order 1728.

662 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×#888C211yesmaximal, characteristic, complemented
4#11721003C211yesmaximal, characteristic
5#11720996C211yesmaximal, characteristic, complemented
6#11720988C211yesmaximal, characteristic
7#11720984C211yesmaximal, characteristic, complemented
8#11720947C211yesmaximal, characteristic, complemented
9#11720941C211yesmaximal, characteristic
10#11720934C211yesmaximal, characteristic, complemented
11#11720929C211yesmaximal, characteristic, complemented
12#11720926C211yesmaximal, characteristic, complemented
13#11720924C211yesmaximal, characteristic, complemented
14#11720919C211yesmaximal, characteristic, complemented
15#11720917C211yesmaximal, characteristic, complemented
16#10594503—31nomaximal
17#10589837—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C9×Dic6C2211yescharacteristic
21C2×C9×Dic6C2211yescharacteristic
22C2×#6192C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
34C9×Dic3⋊C4C2211yescharacteristic
35C4×C9×Dic3C2211yescharacteristic
36C3×C4⋊Dic9C2211yescharacteristic
37C3×Dic9⋊C4C2211yescharacteristic
38C3×C4×Dic9C2211yescharacteristic
39#88445C2211yescharacteristic
40#88445C2211yescharacteristic
41#88445C2211yescharacteristic
42(C2×D9)⋊Dic3C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44Dic3⋊Dic9C2211yescharacteristic
45#88442C2211yescharacteristic
46#88442C2211yescharacteristic
47Dic9⋊Dic3C2211yescharacteristic
48Dic9⋊Dic3C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64105—31no—
54C3×#898—31no—
55C3×#888D311yescharacteristic
56#63907—31no—
57#63896—31no—
58#63890—31no—
59#63887—31no—
60#63871—31no—
61#63868—31no—
62#63868—31no—
63#63866—31no—
64#63859—31no—
65#63853—31no—
66#63847—31no—
67#63846—31no—
68C9×C4⋊Q8—31no—
69#63509—31no—
70#63508—31no—
71#63508—31no—
72#63506—31no—
73#63460—31no—
74#63460D311yescharacteristic, complemented
75#63458—31no—
76#63458—31no—
77#63458—61no—
78#63456—31no—
79#63456—31no—
80#63451—31no—
81#63451—31no—
82#63438—31no—
83#63438—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—41no—
93#6226—41no—
94C2×C9×Dic3C2311yescharacteristic
95C2×C9×Dic3C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C9×Dic6—41no—
102C9×Dic6—41no—
103#6192—41no—
104Dic3×D9—41no—
105#5735—91no—
106#5712—91no—
107C2×C4×C3⋊D3—31no—
108C2×#634—31no—
109C2×C3×Dic6C2×D311yescharacteristic
110C2×C3×Dic6C2×D311yescharacteristic
111C2×#626—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×Dic3⋊C4—31no—
124C3×Dic3⋊C4C2×D311yescharacteristic
125C3×Dic3⋊C4C2×D311yescharacteristic
126C3×C4×Dic3—31no—
127C3×C4×Dic3C2×D311yescharacteristic
128#3724—31no—
129#3724—31no—
130Dic3⋊Dic3—31no—
131Dic3⋊Dic3—31no—
132Dic3⋊Dic3—31no—
133Dic3⋊Dic3—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136#3722—31no—
137#3722—31no—
138#3722—31no—
139(C2×D3)⋊Dic3—31no—
140(C2×D3)⋊Dic3—31no—
141Dic32—31no—
142C2×Q8×C9—31no—
143C2×Q8×C9—31no—
144C2×D36—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⋊C4C2×D311yescharacteristic
155C42×C9—31no—
156(C2×D9)⋊C4—31no—
157(C2×D9)⋊C4—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—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—61no—
180Dic9⋊C4—61no—
181Dic9⋊C4C2×D311yescharacteristic
182C4×Dic9—31no—
183C4×Dic9C2×D311yescharacteristic
184C22×C3×C9C2411yescharacteristic
185C2×C3⋊D9—21no—
186C2×C3⋊D9—21no—
187C2×C3⋊D9—21no—
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—
197C9×Dic3—21no—
198C9×Dic3—21no—
199C9×Dic3—21no—
200C9×Dic3—21no—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×C4⋊Q8—31no—
205C3×#126—91no—
206#947—91no—
207#946—91no—
208#946—91no—
209#944—91no—
210#898—31no—
211#898—91no—
212#898—91no—
213#897—91no—
214#896—91no—
215#896—91no—
216#896—91no—
217#896—181no—
218#894—91no—
219#894—91no—
220#890—91no—
221#889—91no—
222#889—91no—
223#889—91no—
224#888D911yescharacteristic, complemented
225#886—91no—
226#885—91no—
227#883—91no—
228#879—91no—
229#878—91no—
230#878—91no—
231#876—91no—
232#876—91no—
233#876—91no—
234#869—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—121no—
244#634—121no—
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
252C3×Dic6—41no—
253C3×Dic6—41no—
254#626—121no—
255D3×Dic3—121no—
256C22×D9—31no—
257C22×D9—61no—
258C22×D9C22×D311yescharacteristic
259Q8×C9—121no—
260Q8×C9—121no—
261C2×C4×C9—21no—
262C2×C4×C9—21no—
263C2×C4×C9—21no—
264C2×C4×C9—31no—
265C2×C4×C9—31no—
266C2×C4×C9—31no—
267C2×C4×C9—31no—
268C2×C4×C9C22×D311yescharacteristic
269C2×C4×C9C22×D311yescharacteristic
270C2×C4×C9C22×D311yescharacteristic
271C2×Dic9—31no—
272C2×Dic9—31no—
273C2×Dic9—31no—
274C2×Dic9—61no—
275C2×Dic9—61no—
276C2×Dic9—61no—
277C2×Dic9C22×D311yescharacteristic
278C2×Dic9C22×D311yescharacteristic
279C2×Dic9C22×D311yescharacteristic
280D36—121no—
281C4×D9—121no—
282C4×D9—122no—
283C4×D9—121no—
284Dic18—121no—
285Dic18—122no—
286#563—271noSylow
287C2×C3×C9H(5,𝔽2)11yescharacteristic
288C2×C3×C92−1+411yescharacteristic
289C2×C3×C92−1+411yescharacteristic
290C3⋊D9—41no—
291C3×D9—41no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×#67—91no—
295C22×Dic3—91no—
296C2×D12—91no—
297C2×C4×D3—91no—
298C2×C4×D3—91no—
299C2×C4×D3—91no—
300C2×C4×D3—181no—
301C2×Dic6—91no—
302C2×Dic6—91no—
303C2×Dic6—181no—
304C2×Dic6C2×D911yescharacteristic
305C2×Dic6C2×D911yescharacteristic
306C3×C4⋊C4—21no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—91no—
311C3×C4⋊C4—91no—
312C3×C4⋊C4C2×D911yescharacteristic
313C3×C4⋊C4D3211yescharacteristic
314C3×C22⋊C4—91no—
315C3×C22⋊C4—91no—
316C3×C22⋊C4—91no—
317C3×C42—31no—
318C3×C42—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)⋊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—91no—
335(C2×D3)⋊C4—91no—
336(C2×D3)⋊C4—181no—
337(C2×D3)⋊C4—181no—
338C4⋊Dic3—31no—
339C4⋊Dic3—91no—
340C4⋊Dic3—91no—
341C4⋊Dic3—91no—
342C4⋊Dic3—91no—
343C4⋊Dic3—91no—
344C4⋊Dic3—91no—
345C4⋊Dic3C2×D911yescharacteristic
346Dic3⋊C4—31no—
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—91no—
358Dic3⋊C4—91no—
359Dic3⋊C4—91no—
360Dic3⋊C4—91no—
361Dic3⋊C4—181no—
362Dic3⋊C4—181no—
363Dic3⋊C4C2×D911yescharacteristic
364Dic3⋊C4C2×D911yescharacteristic
365C4×Dic3—31no—
366C4×Dic3—91no—
367C4×Dic3—91no—
368C4×Dic3C2×D911yescharacteristic
369C22×C32C23×D311yescharacteristic
370C2×C3⋊D3—61no—
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—61no—
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—62no—
395C2×D9—61no—
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—62no—
414Dic9—61no—
415Dic9—61no—
416Dic9—61no—
417Dic9—121no—
418Dic9—121no—
419C4⋊Q8—31no—
420C4⋊Q8—271no—
421#126—91no—
422#126—271no—
423#126—271no—
424#126—271no—
425#125—271no—
426#125—271no—
427#124—271no—
428#123—271no—
429#123—271no—
430C22⋊Q8—271no—
431C22⋊Q8—271no—
432C22⋊Q8—271no—
433C22⋊Q8—271no—
434C3×C9#56311yescharacteristic, complemented, Sylow
435C23×C3—91no—
436C22×D3—31no—
437C22×D3—91no—
438C22×D3—91no—
439C22×D3—181no—
440C3×Q8—121no—
441C3×Q8—121no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—31no—
446C2×C3×C4—31no—
447C2×C3×C4—31no—
448C2×C3×C4—31no—
449C2×C3×C4—91no—
450C2×C3×C4—91no—
451C2×C3×C4—91no—
452C2×C3×C4C22×D911yescharacteristic
453C2×C3×C4C22×D911yescharacteristic
454C2×C3×C4C22×D911yescharacteristic
455C2×C3×C4C2×D3211yescharacteristic
456C2×C3×C4C2×D3211yescharacteristic
457C2×C3×C4C2×D3211yescharacteristic
458#67—361no—
459C2×Dic3—31no—
460C2×Dic3—31no—
461C2×Dic3—31no—
462C2×Dic3—91no—
463C2×Dic3—91no—
464C2×Dic3—91no—
465C2×Dic3—91no—
466C2×Dic3—91no—
467C2×Dic3—91no—
468C2×Dic3—181no—
469C2×Dic3—181no—
470C2×Dic3—181no—
471C2×Dic3—361no—
472C2×Dic3C22×D911yescharacteristic
473C2×Dic3C22×D911yescharacteristic
474C2×Dic3C22×D911yescharacteristic
475C2×Dic3C22×D911yescharacteristic
476D12—361no—
477C4×D3—361no—
478C4×D3—361no—
479C4×D3—362no—
480C4×D3—361no—
481Dic6—41no—
482Dic6—41no—
483Dic6—361no—
484Dic6—361no—
485Dic6—362no—
486C2×C32#100411yescharacteristic
487C2×C32#100711yescharacteristic
488C2×C32#100711yescharacteristic
489C3⋊D3—121no—
490C3×D3—121no—
491C2×C9—21no—
492C2×C9—21no—
493C2×C9—21no—
494C2×C9#100911yescharacteristic
495C2×C9#101011yescharacteristic
496C2×C9#101011yescharacteristic
497D9—41no—
498D9—122no—
499D9—121no—
500C2×Q8—31no—
501C2×Q8—31no—
502C2×Q8—271no—
503C2×D4—271no—
504C22×C4—271no—
505C22×C4—271no—
506C4⋊C4—31no—
507C4⋊C4—31no—
508C4⋊C4—31no—
509C4⋊C4—91no—
510C4⋊C4—91no—
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—
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—
530C22⋊C4—271no—
531C22⋊C4—271no—
532C42—31no—
533C42—91no—
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—182no—
545C2×D3—181no—
546C2×D3—181no—
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—182no—
577Dic3—181no—
578Dic3—181no—
579Dic3—181no—
580Dic3—181no—
581Dic3—181no—
582Dic3—181no—
583Dic3—361no—
584Dic3—361no—
585C32#573511yescharacteristic
586C9—21no—
587C9#571211yescharacteristic, complemented
588C23—91no—
589C23—271no—
590Q8—121no—
591Q8—121no—
592Q8—1081no—
593D4—1081no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—31no—
598C2×C4—91no—
599C2×C4—91no—
600C2×C4—91no—
601C2×C4—271no—
602C2×C4—271no—
603C2×C4—271no—
604C2×C4—1081no—
605C2×C4—1081no—
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#6371011yescharacteristic
614C2×C3#6371311yescharacteristic
615C2×C3#6371311yescharacteristic
616C2×C3#6429711yescharacteristic
617C2×C3#6431411yescharacteristic
618C2×C3#6431511yescharacteristic
619D3—121no—
620D3—362no—
621D3—361no—
622D3—361no—
623C22—181no—
624C22—181no—
625C22—181no—
626C22—541no—
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—541no—
641C4—541no—
642C4—541no—
643C3—21no—
644C3#1058983711yescharacteristic, complemented
645C3#1059450311yescharacteristic
646C2—361no—
647C2—1081no—
648C2#1172245811yescharacteristic
649C2#1172250011yescharacteristic
650C2#1172251011yescharacteristic
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#563
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×#888C2semidirect
5. #11720996C2semidirect
7. #11720984C2semidirect
8. #11720947C2semidirect
10. #11720934C2semidirect
11. #11720929C2semidirect
12. #11720926C2semidirect
13. #11720924C2semidirect
14. #11720919C2semidirect
15. #11720917C2semidirect
74. #63460D3semidirect
224. #888D9semidirect
434. C3×C9#563semidirect
587. C9#5712semidirect
644. C3#10589837semidirect

Maximal subgroups

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

subgroupindex
#117217522
C3×#634602
C9×#8882
#117210032
#117209962
#117209882
#117209842
#117209472
#117209412
#117209342
#117209292
#117209262
#117209242
#117209192
#117209172
#105945033
#105898373