Finite Group Databasebeta

← #13148963

Subgroups — #13148963

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#11721753C211yesmaximal, characteristic, complemented
2C3×#63460C211yesmaximal, characteristic, complemented
3C9×#889C211yesmaximal, characteristic, complemented
4#11720996C211yesmaximal, characteristic, complemented
5#11720991C211yesmaximal, characteristic, complemented
6#11720988C211yesmaximal, characteristic
7#11720969C211yesmaximal, characteristic, complemented
8#11720949C211yesmaximal, characteristic, complemented
9#11720941C211yesmaximal, characteristic
10#11720940C211yesmaximal, characteristic
11#11720934C211yesmaximal, characteristic, complemented
12#11720927C211yesmaximal, characteristic, complemented
13#11720923C211yesmaximal, characteristic, complemented
14#11720921C211yesmaximal, characteristic, complemented
15#11720905C211yesmaximal, characteristic, complemented
16#10594504—31nomaximal
17#10589801—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×#6192C2211yescharacteristic
21C2×Dic3×D9C2211yescharacteristic
22C2×#6189C2211yescharacteristic
23C2×#6189C2211yescharacteristic
24C3×C9×C4⋊C4C2211yescharacteristic
25#88536C2211yescharacteristic
26#88536C2211yescharacteristic
27C4⋊(C3⋊Dic9)C2211yescharacteristic
28C4⋊(C3⋊Dic9)C2211yescharacteristic
29C3×(C2×D9)⋊C4C2211yescharacteristic
30C3×(C2×D9)⋊C4C2211yescharacteristic
31C3×(C2×D9)⋊C4C2211yescharacteristic
32C9×C4⋊Dic3C2211yescharacteristic
33C9×Dic3⋊C4C2211yescharacteristic
34C9×Dic3⋊C4C2211yescharacteristic
35C9×Dic3⋊C4C2211yescharacteristic
36C9×Dic3⋊C4C2211yescharacteristic
37C4×C9×Dic3C2211yescharacteristic
38C3×C4⋊Dic9C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40C3×C4×Dic9C2211yescharacteristic
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64106—31no—
54C3×#898—31no—
55C3×#889D311yescharacteristic
56#63918—31no—
57#63896—31no—
58#63893—31no—
59#63890—31no—
60#63869—31no—
61#63868—31no—
62#63865—31no—
63#63861—31no—
64#63853—31no—
65#63852—31no—
66#63848—31no—
67#63840—31no—
68C9×#125—31no—
69#63460—31no—
70#63460—31no—
71#63460—31no—
72#63460D311yescharacteristic, complemented
73#63459—31no—
74#63459—31no—
75#63459—61no—
76#63458—31no—
77#63458—31no—
78#63456—31no—
79#63456—31no—
80#63450—31no—
81#63450—31no—
82#63437—31no—
83#63432—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
101#6192—41no—
102Dic3×D9—41no—
103#6189—41no—
104#6189—41no—
105#5712—91no—
106#5699—91no—
107C2×C4×C3⋊D3—31no—
108C2×#634—31no—
109C2×#627—31no—
110C2×#627—31no—
111C2×#626—31no—
112C2×D3×Dic3—31no—
113C32×C4⋊C4C2×D311yescharacteristic
114#3752—31no—
115#3752—31no—
116C4⋊(C3⋊Dic3)—31no—
117C4⋊(C3⋊Dic3)—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×Dic3⋊C4C2×D311yescharacteristic
127C3×Dic3⋊C4C2×D311yescharacteristic
128C3×C4×Dic3—31no—
129C3×C4×Dic3C2×D311yescharacteristic
130#3724—31no—
131#3724—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×D36—31no—
143C2×C4×D9—31no—
144C2×C4×D9—31no—
145C2×C4×D9—61no—
146C2×Dic18—31no—
147C2×Dic18—31no—
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—31no—
164(C2×D9)⋊C4—31no—
165(C2×D9)⋊C4—61no—
166(C2×D9)⋊C4—61no—
167(C2×D9)⋊C4C2×D311yescharacteristic
168(C2×D9)⋊C4C2×D311yescharacteristic
169(C2×D9)⋊C4C2×D311yescharacteristic
170C4⋊Dic9—31no—
171C4⋊Dic9—31no—
172C4⋊Dic9—31no—
173C4⋊Dic9—61no—
174C4⋊Dic9—61no—
175C4⋊Dic9C2×D311yescharacteristic
176Dic9⋊C4—31no—
177Dic9⋊C4—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
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×#126—91no—
205C3×#125—31no—
206#898—31no—
207#898—91no—
208#898—91no—
209#898—91no—
210#898—91no—
211#897—91no—
212#897—91no—
213#897—91no—
214#897—181no—
215#896—91no—
216#896—91no—
217#896—91no—
218#894—91no—
219#894—91no—
220#890—91no—
221#889D911yescharacteristic, complemented
222#888—91no—
223#888—91no—
224#888—91no—
225#886—91no—
226#885—91no—
227#883—91no—
228#879—91no—
229#878—91no—
230#878—91no—
231#876—91no—
232#875—91no—
233#870—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
252#627—121no—
253#627—121no—
254#626—121no—
255D3×Dic3—121no—
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—121no—
279C4×D9—121no—
280C4×D9—121no—
281C4×D9—122no—
282Dic18—121no—
283Dic18—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×#67—91no—
293C22×Dic3—91no—
294C2×D12—91no—
295C2×C4×D3—91no—
296C2×C4×D3—91no—
297C2×C4×D3—91no—
298C2×C4×D3—181no—
299C2×Dic6—91no—
300C2×Dic6—91no—
301C2×Dic6—91no—
302C2×Dic6—91no—
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—91no—
335(C2×D3)⋊C4—91no—
336(C2×D3)⋊C4—91no—
337(C2×D3)⋊C4—91no—
338(C2×D3)⋊C4—181no—
339(C2×D3)⋊C4—181no—
340C4⋊Dic3—31no—
341C4⋊Dic3—91no—
342C4⋊Dic3—91no—
343C4⋊Dic3—91no—
344C4⋊Dic3—91no—
345C4⋊Dic3—91no—
346C4⋊Dic3—91no—
347C4⋊Dic3—91no—
348C4⋊Dic3—91no—
349C4⋊Dic3—181no—
350C4⋊Dic3—181no—
351C4⋊Dic3C2×D911yescharacteristic
352Dic3⋊C4—31no—
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⋊C4C2×D911yescharacteristic
362Dic3⋊C4C2×D911yescharacteristic
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—22no—
401C4×C9—21no—
402C4×C9—21no—
403C4×C9—21no—
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—61no—
414Dic9—61no—
415Dic9—61no—
416Dic9—121no—
417Dic9—121no—
418Dic9—121no—
419C4⋊Q8—271no—
420C4⋊Q8—271no—
421#126—91no—
422#126—271no—
423#126—271no—
424#126—271no—
425#125—31no—
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—
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—361no—
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—361no—
470C2×Dic3C22×D911yescharacteristic
471C2×Dic3C22×D911yescharacteristic
472C2×Dic3C22×D911yescharacteristic
473C2×Dic3C22×D911yescharacteristic
474D12—361no—
475C4×D3—361no—
476C4×D3—361no—
477C4×D3—361no—
478C4×D3—362no—
479Dic6—361no—
480Dic6—361no—
481Dic6—361no—
482Dic6—361no—
483Dic6—361no—
484Dic6—361no—
485Dic6—362no—
486C2×C32#100711yescharacteristic
487C2×C32#100911yescharacteristic
488C2×C32#101011yescharacteristic
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—271no—
501C2×Q8—271no—
502C2×Q8—271no—
503C2×D4—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—
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—22no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
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—181no—
577Dic3—181no—
578Dic3—181no—
579Dic3—181no—
580Dic3—181no—
581Dic3—181no—
582Dic3—361no—
583Dic3—361no—
584Dic3—361no—
585C32#569911yescharacteristic
586C9—21no—
587C9#571211yescharacteristic, complemented
588C23—91no—
589C23—271no—
590Q8—1081no—
591Q8—1081no—
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#6371311yescharacteristic
614C2×C3#6371511yescharacteristic
615C2×C3#6371611yescharacteristic
616C2×C3#6430811yescharacteristic
617C2×C3#6430911yescharacteristic
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#1058980111yescharacteristic, complemented
645C3#1059450411yescharacteristic
646C2—361no—
647C2—1081no—
648C2#1172247811yescharacteristic
649C2#1172249411yescharacteristic
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. #11721753C2semidirect
2. C3×#63460C2semidirect
3. C9×#889C2semidirect
4. #11720996C2semidirect
5. #11720991C2semidirect
7. #11720969C2semidirect
8. #11720949C2semidirect
11. #11720934C2semidirect
12. #11720927C2semidirect
13. #11720923C2semidirect
14. #11720921C2semidirect
15. #11720905C2semidirect
72. #63460D3semidirect
221. #889D9semidirect
434. C3×C9#563semidirect
587. C9#5712semidirect
644. C3#10589801semidirect

Maximal subgroups

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

subgroupindex
#117217532
C3×#634602
C9×#8892
#117209962
#117209912
#117209882
#117209692
#117209492
#117209412
#117209402
#117209342
#117209272
#117209232
#117209212
#117209052
#105945043
#105898013