Finite Group Databasebeta

← #13151146

Subgroups — #13151146

Order 1728.

1080 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D4×C9C211yesmaximal, characteristic, complemented
2C2×#88663C211yesmaximal, characteristic, complemented
3#11721835C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic, complemented
5#11721286C211yesmaximal, characteristic, complemented
6#11721286C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8D3×#3676C211yesmaximal, characteristic, complemented
9#11721270C211yesmaximal, characteristic, complemented
10C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
11#11721263C211yesmaximal, characteristic, complemented
12#11721016C211yesmaximal, characteristic, complemented
13#11721015C211yesmaximal, characteristic, complemented
14#11720976C211yesmaximal, characteristic, complemented
15#11720955C211yesmaximal, characteristic, complemented
16#10595150—31nomaximal
17#10589908—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C23×D3×C9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic, complemented
25C2×C3×#611C2211yescharacteristic, complemented
26C22×C3×Dic9C2211yescharacteristic, complemented
27D3×D4×C9—24no—
28C2×C9×D12C2211yescharacteristic
29C2×C4×D3×C9C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31C2×#6194C2211yescharacteristic, complemented
32C2×#6194C2211yescharacteristic, complemented
33#88663—24no—
34C2×D3×Dic9C2211yescharacteristic, complemented
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38#88551C2211yescharacteristic, complemented
39#88551C2211yescharacteristic, complemented
40#88551C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42#88534C2211yescharacteristic, complemented
43C3×#3676C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52(C2×D3)⋊Dic9C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C3×D3×D4D311yescharacteristic
56C2×#3805—31no—
57#64144—31no—
58C3×#939—31no—
59#63976—31no—
60#63976—31no—
61Dic3×#67—31no—
62#63970—31no—
63D3×#217—31no—
64C2×(C2×D3)⋊Dic3—31no—
65#63959—31no—
66#63885—31no—
67#63884—31no—
68#63879—31no—
69#63851—31no—
70C22×D4×C9—31no—
71C2×#3699—31no—
72#63515—31no—
73#63515—31no—
74C2×#3676—31no—
75C2×#3676—31no—
76#63501—31no—
77#63501D311yescharacteristic, complemented
78#63500—31no—
79#63498—31no—
80#63497—31no—
81#63497—31no—
82#63497—61no—
83D4×Dic9—31no—
84C4×#611—31no—
85#63486—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×D3×C9—22no—
89C22×D3×C9—22no—
90C22×D3×C9—22no—
91C22×D3×C9—22no—
92C22×D3×C9—41no—
93C22×D3×C9—41no—
94C22×D3×C9C2311yescharacteristic
95C22×D3×C9C2311yescharacteristic
96C22×D3×C9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C3×D4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3⋊Dic9—22no—
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C9×#67—22no—
106C9×#67D414yescomplemented
107C3×#611—22no—
108C3×#611—41no—
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9—41no—
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C9×D12—22no—
115C4×D3×C9—22no—
116#6194—22no—
117#6194—22no—
118#6194—41no—
119D3×Dic9—22no—
120D3×Dic9—41no—
121Dic3×D9—22no—
122#6189—22no—
123#5806—91no—
124#5610—91no—
125C23×C3×D3C2×D311yescharacteristic
126C23×C3×D3C2×D311yescharacteristic
127C2×C32×D4C2×D311yescharacteristic
128C22×C3⋊Dic3—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×#67C2×D311yescharacteristic
133C22×C3×Dic3—31no—
134C3×D3×D4—24no—
135C2×C3×D12C2×D311yescharacteristic
136C2×C3×C4×D3C2×D311yescharacteristic
137C2×#627—31no—
138C2×#625—31no—
139C2×#625—31no—
140C2×#625—31no—
141#3805—64no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C24×C9—31no—
146C24×C9—31no—
147#3757—31no—
148#3757—31no—
149#3757—31no—
150#3750—31no—
151#3750—31no—
152C3×#217—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×Dic3⋊C4—31no—
155Dic3⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163Dic32—31no—
164C2×D4×C9—21no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C2×D4×C9—31no—
168C2×D4×C9—64no—
169C2×D4×C9C2×D311yescharacteristic
170C22×C4×C9—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611C2×D311yescharacteristic, complemented
175C2×#611C2×D311yescharacteristic, complemented
176C22×Dic9—31no—
177C22×Dic9—31no—
178C22×Dic9—31no—
179C22×Dic9—61no—
180C22×Dic9C2×D311yescharacteristic, complemented
181#3699—64no—
182C2×C4×D9—31no—
183C2×Dic18—31no—
184#3676—31no—
185#3676—31no—
186#3676—31no—
187#3676—31no—
188#3676—31no—
189#3676—31no—
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—31no—
194#3676—61no—
195#3676—61no—
196#3676—61no—
197#3676C2×D311yescharacteristic, complemented
198(C2×D9)⋊C4C2×D311yescharacteristic, complemented
199C4⋊Dic9—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4—61no—
203Dic9⋊C4—61no—
204Dic9⋊C4C2×D311yescharacteristic, complemented
205C4×Dic9—31no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9C2×D412yes—
212C22×C3×C9C2411yescharacteristic
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—44no—
221C2×D3×C9—44no—
222C2×D3×C9C2×D412yes—
223C2×D3×C9#4112yescomplemented
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226C2×C3×D9—21no—
227C3×C4×C9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9—21no—
232C9×Dic3C2×D412yes—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C22×C3×D4—31no—
237C2×#237—91no—
238C2×#237—91no—
239C2×D3×D4D911yescharacteristic, complemented
240C3×#121—91no—
241#953—91no—
242#953—91no—
243C2×#217—91no—
244C2×#217—91no—
245#939—31no—
246#939—91no—
247#939—91no—
248#938—91no—
249#937—91no—
250#937—91no—
251#936—91no—
252#935—91no—
253#935—91no—
254#935—91no—
255#935—181no—
256D4×Dic3—91no—
257C4×#67—91no—
258C4×#67—91no—
259C2×(C2×D3)⋊C4—91no—
260#924—91no—
261#896—91no—
262#894—91no—
263#885—91no—
264#884—91no—
265#67⋊C4—91no—
266D3×C22⋊C4—91no—
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3—31no—
274C22×C3×D3—41no—
275C22×C3×D3—41no—
276C22×C3×D3C22×D311yescharacteristic
277C22×C3×D3C22×D311yescharacteristic
278C22×C3×D3C22×D311yescharacteristic
279C32×D4—22no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—62no—
286C3×#67—22no—
287C3×#67—62no—
288C3×#67—121no—
289C3×#67#6714yes—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—121no—
294C2×C3×Dic3C22×D311yescharacteristic
295C3×D12—22no—
296C3×C4×D3—22no—
297#627—62no—
298#625—62no—
299#625—62no—
300#625—121no—
301D3×Dic3—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—21no—
306C23×C9—31no—
307C23×C9—31no—
308C23×C9—31no—
309C23×C9—62no—
310C23×C9—62no—
311C23×C9—62no—
312C23×C9—62no—
313C23×C9—121no—
314C23×C9—121no—
315C23×C9C22×D311yescharacteristic
316C23×C9C22×D311yescharacteristic
317C22×D9C22×D311yescharacteristic
318D4×C9—22no—
319D4×C9—34no—
320D4×C9—42no—
321D4×C9—62no—
322D4×C9—62no—
323C2×C4×C9—21no—
324C2×C4×C9—31no—
325C2×C4×C9—62no—
326C2×C4×C9C22×D311yescharacteristic
327#611—22no—
328#611—41no—
329#611—62no—
330#611—62no—
331#611—121no—
332C2×Dic9—31no—
333C2×Dic9—31no—
334C2×Dic9—31no—
335C2×Dic9—31no—
336C2×Dic9—41no—
337C2×Dic9—61no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—62no—
342C2×Dic9—62no—
343C2×Dic9—122no—
344C2×Dic9—121no—
345C2×Dic9C22×D311yescharacteristic
346C2×Dic9C22×D311yescharacteristic
347C2×Dic9C22×D311yescharacteristic
348C4×D9—62no—
349Dic18—62no—
350#546—271noSylow
351C2×C3×C9—22no—
352C2×C3×C9—41no—
353C2×C3×C9C22×D411yescharacteristic
354C2×C3×C9C2×#4111yescharacteristic
355C2×C3×C9H(5,𝔽2)11yescharacteristic
356D3×C9—22no—
357D3×C9—22no—
358D3×C9—41no—
359C3×D9—41no—
360C24×C3—31no—
361C24×C3—31no—
362C23×D3C2×D911yescharacteristic
363C23×D3C2×D911yescharacteristic
364C2×C3×D4—21no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—64no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C2×C3×D4C2×D911yescharacteristic
372C2×C3×D4D3211yescharacteristic
373C22×C3×C4—31no—
374C22×C3×C4—91no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67C2×D911yescharacteristic
384C2×#67C2×D911yescharacteristic
385C22×Dic3—31no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—181no—
392#237—184no—
393#237—184no—
394D3×D4—24no—
395C2×D12C2×D911yescharacteristic
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3C2×D911yescharacteristic
400C2×Dic6—91no—
401C2×Dic6—91no—
402C3×C4⋊C4—91no—
403C3×C22⋊C4—91no—
404C3×C22⋊C4—91no—
405#217—31no—
406#217—91no—
407#217—91no—
408#217—91no—
409#217—91no—
410#217—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—181no—
420#217—181no—
421#217—181no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430C4⋊Dic3—91no—
431Dic3⋊C4—31no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—181no—
438Dic3⋊C4—181no—
439C4×Dic3—91no—
440C4×Dic3—91no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32C2×#6712yes—
447C22×C32C23×D311yescharacteristic
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—44no—
456C2×C3×D3—44no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3#23712yes—
461C2×C3×D3C2×#6712yes—
462C32×C4—21no—
463C3⋊Dic3—61no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—61no—
470C3×Dic3C2×#6712yes—
471C22×C9—21no—
472C22×C9—21no—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—22no—
478C22×C9—32no—
479C22×C9—32no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—41no—
483C22×C9—41no—
484C22×C9—41no—
485C22×C9—61no—
486C22×C9—61no—
487C22×C9—61no—
488C22×C9—61no—
489C22×C9—61no—
490C22×C9—61no—
491C22×C9—61no—
492C22×C9—124no—
493C22×C9—124no—
494C22×C9D3×D412yes—
495C22×C9C23×D311yescharacteristic
496C2×D9—21no—
497C2×D9—21no—
498C2×D9—21no—
499C4×C9—21no—
500C4×C9—32no—
501C4×C9—41no—
502Dic9—21no—
503Dic9—21no—
504Dic9—21no—
505Dic9—61no—
506Dic9—61no—
507Dic9—61no—
508Dic9—61no—
509Dic9—121no—
510Dic9—121no—
511Dic9—121no—
512Dic9—121no—
513C2×#41—271no—
514C22×D4—31no—
515#124—271no—
516#123—271no—
517#123—271no—
518C22⋊Q8—271no—
519#121—91no—
520#121—271no—
521#121—271no—
522#120—271no—
523#120—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C22⋊C4—271no—
527C2×C22⋊C4—271no—
528C3×C9#54611yescharacteristic, complemented, Sylow
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—62no—
535C23×C3—62no—
536C23×C3—62no—
537C23×C3—62no—
538C23×C3—91no—
539C23×C3—121no—
540C23×C3—121no—
541C23×C3C22×D911yescharacteristic
542C23×C3C22×D911yescharacteristic
543C23×C3C2×D3211yescharacteristic
544C23×C3C2×D3211yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—31no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3C22×D911yescharacteristic
553C22×D3C22×D911yescharacteristic
554C22×D3C22×D911yescharacteristic
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—34no—
558C3×D4—42no—
559C3×D4—62no—
560C3×D4—62no—
561C3×D4—182no—
562C3×D4—361no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—62no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—91no—
569C2×C3×C4—361no—
570C2×C3×C4C22×D911yescharacteristic
571C2×C3×C4C2×D3211yescharacteristic
572#67—22no—
573#67—62no—
574#67—121no—
575#67—182no—
576#67—182no—
577#67—182no—
578#67—182no—
579#67—361no—
580#67—361no—
581#67#61114yescomplemented
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—91no—
586C2×Dic3—91no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—121no—
594C2×Dic3—181no—
595C2×Dic3—181no—
596C2×Dic3—181no—
597C2×Dic3—181no—
598C2×Dic3—182no—
599C2×Dic3—182no—
600C2×Dic3—182no—
601C2×Dic3—182no—
602C2×Dic3—362no—
603C2×Dic3—361no—
604C2×Dic3C22×D911yescharacteristic
605D12—22no—
606C4×D3—22no—
607C4×D3—182no—
608C4×D3—182no—
609C4×D3—361no—
610Dic6—182no—
611Dic6—182no—
612C2×C32—22no—
613C2×C32—41no—
614C2×C32C2×#23711yescharacteristic
615C2×C32#100411yescharacteristic
616C2×C32C22×#6711yescharacteristic
617C3×D3—22no—
618C3×D3—22no—
619C3×D3—41no—
620C3×D3—121no—
621C2×C9—22no—
622C2×C9—21no—
623C2×C9—21no—
624C2×C9—21no—
625C2×C9—42no—
626C2×C9—41no—
627C2×C9—62no—
628C2×C9—62no—
629C2×C9—81no—
630C2×C9—121no—
631C2×C9C2×D3×D411yescharacteristic
632C2×C9#100411yescharacteristic
633C2×C9D3×#4111yescharacteristic
634D9—41no—
635C24—31no—
636C24—31no—
637#41—544no—
638C2×Q8—271no—
639C2×D4—31no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—64no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4D3×D911yescharacteristic
649C22×C4—31no—
650C22×C4—91no—
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C4⋊C4—91no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C42—271no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—22no—
684C22×C3—32no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—124no—
699C22×C3—124no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3C2×#61112yes—
704C22×C3C23×D911yescharacteristic
705C22×C3D3×#6712yes—
706C22×C3C22×D3211yescharacteristic
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—44no—
715C2×D3—44no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3#369912yescomplemented
720C2×D3C2×#61112yes—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—32no—
724C3×C4—41no—
725C3×C4—181no—
726C3×C4—181no—
727C3×C4—181no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—181no—
732Dic3—181no—
733Dic3—181no—
734Dic3—181no—
735Dic3—181no—
736Dic3—181no—
737Dic3—181no—
738Dic3—181no—
739Dic3—361no—
740Dic3—361no—
741Dic3—361no—
742Dic3—361no—
743Dic3C2×#61112yes—
744C32#580611yescharacteristic
745C9—21no—
746C9#561011yescharacteristic, complemented
747C23—31no—
748C23—31no—
749C23—31no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23—91no—
755C23—121no—
756C23—121no—
757C23C2×D3×D911yescharacteristic
758C23C2×D3×D911yescharacteristic
759Q8—542no—
760D4—22no—
761D4—34no—
762D4—62no—
763D4—62no—
764D4—182no—
765D4—361no—
766D4—542no—
767D4—542no—
768D4—1081no—
769C2×C4—31no—
770C2×C4—62no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—271no—
775C2×C4—271no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—361no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—1081no—
783C2×C4C2×D3×D911yescharacteristic
784C2×C3—22no—
785C2×C3—22no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—42no—
790C2×C3—41no—
791C2×C3—41no—
792C2×C3—62no—
793C2×C3—62no—
794C2×C3—81no—
795C2×C3—121no—
796C2×C3—361no—
797C2×C3C2×#369911yescharacteristic
798C2×C3#6371011yescharacteristic
799C2×C3C22×#61111yescharacteristic
800C2×C3D3×#23711yescharacteristic
801C2×C3#6431311yescharacteristic
802C2×C3C2×D3×#6711yescharacteristic
803D3—22no—
804D3—22no—
805D3—41no—
806D3—121no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—32no—
813C22—32no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—61no—
821C22—124no—
822C22—124no—
823C22—181no—
824C22—181no—
825C22—181no—
826C22D3×#61112yes—
827C22C22×D3×D911yescharacteristic
828C4—21no—
829C4—32no—
830C4—181no—
831C4—181no—
832C4—181no—
833C4—541no—
834C4—541no—
835C4—541no—
836C4—541no—
837C3—21no—
838C3#1058990811yescharacteristic, complemented
839C3#1059515011yescharacteristic
840C2—22no—
841C2—41no—
842C2—62no—
843C2—62no—
844C2—121no—
845C2—361no—
846C2D3×#369911yescharacteristic
847C2#1172249911yescharacteristic
848C2C2×D3×#61111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D3×D4×C9C2semidirect
2. C2×#88663C2semidirect
3. #11721835C2semidirect
4. C3×#63501C2semidirect
5. #11721286C2semidirect
6. #11721286C2semidirect
7. #67×Dic9C2semidirect
8. D3×#3676C2semidirect
9. #11721270C2semidirect
10. C2×(C2×D3)⋊Dic9C2semidirect
11. #11721263C2semidirect
12. #11721016C2semidirect
13. #11721015C2semidirect
14. #11720976C2semidirect
15. #11720955C2semidirect
21. C22×C3⋊Dic9C22semidirect
24. C2×C3×#611C22semidirect
25. C2×C3×#611C22semidirect
26. C22×C3×Dic9C22semidirect
31. C2×#6194C22semidirect
32. C2×#6194C22semidirect
34. C2×D3×Dic9C22semidirect
35. C2×D3×Dic9C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
38. #88551C22semidirect
39. #88551C22semidirect
40. #88551C22semidirect
41. #88534C22semidirect
42. #88534C22semidirect
43. C3×#3676C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×Dic9⋊C4C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. (C2×D3)⋊Dic9C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic3×Dic9C22semidirect
77. #63501D3semidirect
106. C9×#67D4semidirect
174. C2×#611C2×D3semidirect
175. C2×#611C2×D3semidirect
180. C22×Dic9C2×D3semidirect
197. #3676C2×D3semidirect
198. (C2×D9)⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
223. C2×D3×C9#41semidirect
239. C2×D3×D4D9semidirect
528. C3×C9#546semidirect
581. #67#611semidirect
719. C2×D3#3699semidirect
746. C9#5610semidirect
838. C3#10589908semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D4×C92
C2×#886632
#117218352
C3×#635012
#117212862
#67×Dic92
D3×#36762
#117212702
C2×(C2×D3)⋊Dic92
#117212632
#117210162
#117210152
#117209762
#117209552
#105951503
#105899083