Finite Group Databasebeta

← #13150980

Subgroups — #13150980

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×D9C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C9×#935C211yesmaximal, characteristic, complemented
5#11721276C211yesmaximal, characteristic, complemented
6#11721276C211yesmaximal, characteristic, complemented
7#611⋊Dic3C211yesmaximal, characteristic, complemented
8D9×#217C211yesmaximal, characteristic, complemented
9C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
10#11721257C211yesmaximal, characteristic, complemented
11#11721256C211yesmaximal, characteristic, complemented
12#11721002C211yesmaximal, characteristic, complemented
13#11720983C211yesmaximal, characteristic, complemented
14#11720981C211yesmaximal, characteristic, complemented
15#11720939C211yesmaximal, characteristic, complemented
16#10595148—31nomaximal
17#10589756—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C22×C3⋊Dic9C2211yescharacteristic, complemented
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C22×C9×Dic3C2211yescharacteristic, complemented
27C3×D4×D9—24no—
28C2×C3×D36C2211yescharacteristic
29C2×C3×C4×D9C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34#88658—24no—
35C2×Dic3×D9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38#88551C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic, complemented
42C9×#217C2211yescharacteristic, complemented
43C9×#217C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C9×Dic3⋊C4C2211yescharacteristic, complemented
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C3×D3×D4—31no—
56C2×#3804—31no—
57#64148—31no—
58C3×#935D311yescharacteristic
59#63977—31no—
60#63977—31no—
61#67⋊Dic3—31no—
62D3×#217—31no—
63C2×(C2×D3)⋊Dic3—31no—
64#63959—31no—
65#63958—31no—
66#63904—31no—
67#63886—31no—
68#63884—31no—
69#63851—31no—
70C2×D4×D9D311yescharacteristic, complemented
71C2×#3697—31no—
72C9×#123—31no—
73#63501—31no—
74#63501—61no—
75C2×(C2×D9)⋊C4—31no—
76#63458—31no—
77#63457—31no—
78#63456—31no—
79#63455—31no—
80#63447—31no—
81#63446—31no—
82#63444—31no—
83#63444—31no—
84#611⋊C4—31no—
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×C3×D9—22no—
90C22×C3×D9—22no—
91C22×C3×D9—22no—
92C22×C3×D9—22no—
93C22×C3×D9—41no—
94C22×C3×D9—41no—
95C22×C3×D9C2311yescharacteristic
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C3×D4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101#6233—41no—
102C2×C3⋊Dic9—41no—
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C2×C3⋊Dic9C2311yescharacteristic
106C3×#611—22no—
107C3×#611D414yescomplemented
108C2×C9×Dic3—22no—
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C3×D36—22no—
115C3×C4×D9—22no—
116#6192—22no—
117#6192—22no—
118#6192—41no—
119(C3⋊D9)⋊C4—22no—
120Dic3×D9—22no—
121Dic3×D9—41no—
122#6189—22no—
123#5806—91no—
124#5654—91no—
125C23×C3×D3—31no—
126C23×C3×D3—31no—
127C2×C32×D4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130C22×C3⋊Dic3—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C22×C3×Dic3C2×D311yescharacteristic
134C3×D3×D4—64no—
135C2×C3×D12—31no—
136C2×C3×C4×D3—31no—
137C2×#627—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#624—31no—
142#3804—64no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C23×D9C2×D311yescharacteristic
146C23×D9C2×D311yescharacteristic
147#3757—31no—
148#3752—31no—
149#3750—31no—
150C3×#217C2×D311yescharacteristic
151C3×#217C2×D311yescharacteristic
152C3×#217C2×D311yescharacteristic
153C3×Dic3⋊C4C2×D311yescharacteristic
154C3×Dic3⋊C4C2×D311yescharacteristic
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×C9C2×D311yescharacteristic
166C22×C4×C9—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—61no—
170C2×#611—61no—
171C2×#611C2×D311yescharacteristic
172C2×#611C2×D311yescharacteristic
173C22×Dic9—31no—
174C22×Dic9—61no—
175D4×D9—24no—
176#3697—64no—
177C2×D36—31no—
178C2×D36—31no—
179C2×D36—31no—
180C2×D36C2×D311yescharacteristic
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9C2×D311yescharacteristic
185C2×Dic18—31no—
186C9×C4⋊C4—31no—
187C9×C4⋊C4—31no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4—31no—
191#3676—31no—
192#3676—61no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—61no—
202Dic9⋊C4—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—61no—
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×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—44no—
224C2×C3×D9—44no—
225C2×C3×D9C2×D412yes—
226C2×C3×D9#4112yescomplemented
227C3×C4×C9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C9×Dic3—21no—
235C3×Dic9C2×D412yes—
236C22×C3×D4—91no—
237C2×#237—91no—
238C2×D3×D4—31no—
239C2×#235—91no—
240C3×#123—31no—
241#953—91no—
242#953—91no—
243C2×#217—91no—
244C2×#217—91no—
245#939—91no—
246#939—91no—
247#939—91no—
248#939—181no—
249#938—91no—
250#936—91no—
251#935—91no—
252#935D911yescharacteristic, complemented
253D4×Dic3—91no—
254C4×#67—91no—
255C2×(C2×D3)⋊C4—91no—
256#924—91no—
257#896—91no—
258#895—91no—
259#894—91no—
260#893—91no—
261#885—91no—
262#884—91no—
263#882—91no—
264#882—91no—
265#67⋊C4—91no—
266D3×C22⋊C4—91no—
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C22×C3⋊D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—62no—
274C22×C3×D3—62no—
275C22×C3×D3—62no—
276C22×C3×D3—62no—
277C22×C3×D3—121no—
278C22×C3×D3—121no—
279C32×D4—22no—
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—121no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—121no—
287C3×#67—34no—
288C3×#67—62no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C3×D12—62no—
296C3×C4×D3—62no—
297#627—62no—
298#626—62no—
299#626—62no—
300#626—121no—
301#624—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—21no—
306C23×C9C22×D311yescharacteristic
307C23×C9C22×D311yescharacteristic
308C22×D9—22no—
309C22×D9—22no—
310C22×D9—22no—
311C22×D9—22no—
312C22×D9—31no—
313C22×D9—41no—
314C22×D9—41no—
315C22×D9—61no—
316C22×D9C22×D311yescharacteristic
317C22×D9C22×D311yescharacteristic
318C22×D9C22×D311yescharacteristic
319D4×C9—22no—
320D4×C9—42no—
321C2×C4×C9—21no—
322C2×C4×C9—31no—
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9—31no—
326C2×C4×C9—62no—
327C2×C4×C9C22×D311yescharacteristic
328#611—22no—
329#611—62no—
330#611—122no—
331#611—121no—
332#611—122no—
333#611#6714yescomplemented
334C2×Dic9—31no—
335C2×Dic9—31no—
336C2×Dic9—31no—
337C2×Dic9—61no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—121no—
341C2×Dic9—122no—
342C2×Dic9C22×D311yescharacteristic
343D36—22no—
344D36—62no—
345D36—62no—
346D36—121no—
347C4×D9—22no—
348C4×D9—62no—
349C4×D9—62no—
350C4×D9—121no—
351Dic18—62no—
352#546—271noSylow
353C2×C3×C9—22no—
354C2×C3×C9—41no—
355C2×C3×C9C22×D411yescharacteristic
356C2×C3×C9C2×#4111yescharacteristic
357C2×C3×C9H(5,𝔽2)11yescharacteristic
358C3⋊D9—41no—
359C3×D9—22no—
360C3×D9—22no—
361C3×D9—41no—
362C24×C3—91no—
363C24×C3—91no—
364C23×D3—31no—
365C23×D3—31no—
366C2×C3×D4—21no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C2×C3×D4—91no—
370C2×C3×D4—184no—
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×#67—91no—
384C2×#67—181no—
385C2×#67—181no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—181no—
391C22×Dic3C2×D911yescharacteristic, complemented
392#237—184no—
393D3×D4—64no—
394#235—184no—
395C2×D12—31no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12—91no—
399C2×C4×D3—31no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
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—91no—
420#217—181no—
421#217C2×D911yescharacteristic, complemented
422#217C2×D911yescharacteristic, complemented
423#217C2×D911yescharacteristic, complemented
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—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—181no—
434C4⋊Dic3—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—181no—
439Dic3⋊C4C2×D911yescharacteristic, complemented
440Dic3⋊C4C2×D911yescharacteristic, complemented
441C4×Dic3—91no—
442C4×Dic3—91no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32D3×D412yes—
449C22×C32C23×D311yescharacteristic
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3×D3—32no—
454C2×C3×D3—32no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—124no—
463C2×C3×D3—124no—
464C32×C4—21no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—32no—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—22no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—41no—
483C22×C9—41no—
484C22×C9—41no—
485C22×C9C2×#6712yes—
486C22×C9C23×D311yescharacteristic
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—21no—
492C2×D9—21no—
493C2×D9—21no—
494C2×D9—44no—
495C2×D9—44no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9#23712yescomplemented
503C2×D9C2×#6712yes—
504C4×C9—21no—
505C4×C9—41no—
506C4×C9—61no—
507C4×C9—61no—
508C4×C9—61no—
509C4×C9—61no—
510Dic9—62no—
511Dic9—61no—
512Dic9—61no—
513Dic9—61no—
514Dic9—121no—
515Dic9—121no—
516Dic9C2×#6712yes—
517C2×#41—271no—
518C22×D4—91no—
519#124—271no—
520#123—31no—
521#123—271no—
522C22⋊Q8—271no—
523#121—271no—
524#121—271no—
525#121—271no—
526#120—271no—
527#120—271no—
528C4×D4—271no—
529C4×D4—271no—
530C2×C22⋊C4—271no—
531C2×C22⋊C4—271no—
532C3×C9#54611yescharacteristic, complemented, Sylow
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—91no—
536C23×C3—91no—
537C23×C3—91no—
538C23×C3—182no—
539C23×C3—182no—
540C23×C3—182no—
541C23×C3—182no—
542C23×C3—361no—
543C23×C3—361no—
544C23×C3C22×D911yescharacteristic
545C23×C3C22×D911yescharacteristic
546C23×C3C2×D3211yescharacteristic
547C23×C3C2×D3211yescharacteristic
548C22×D3—31no—
549C22×D3—31no—
550C22×D3—31no—
551C22×D3—62no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—62no—
555C22×D3—91no—
556C22×D3—91no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—181no—
560C3×D4—22no—
561C3×D4—22no—
562C3×D4—42no—
563C3×D4—94no—
564C3×D4—182no—
565C3×D4—182no—
566C2×C3×C4—21no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—62no—
572C2×C3×C4—91no—
573C2×C3×C4—182no—
574C2×C3×C4C22×D911yescharacteristic
575C2×C3×C4C2×D3211yescharacteristic
576#67—34no—
577#67—62no—
578#67—182no—
579#67—182no—
580#67—182no—
581#67—182no—
582#67—362no—
583#67—361no—
584#67—361no—
585#67—361no—
586#67—362no—
587C2×Dic3—22no—
588C2×Dic3—31no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—181no—
596C2×Dic3—181no—
597C2×Dic3—181no—
598C2×Dic3—182no—
599C2×Dic3—361no—
600C2×Dic3—361no—
601C2×Dic3—361no—
602C2×Dic3—362no—
603C2×Dic3C22×D911yescharacteristic
604C2×Dic3C22×D911yescharacteristic
605C2×Dic3C22×D911yescharacteristic
606C2×Dic3C22×D911yescharacteristic
607D12—62no—
608D12—182no—
609D12—182no—
610D12—361no—
611C4×D3—62no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—361no—
616Dic6—182no—
617Dic6—182no—
618C2×C32—22no—
619C2×C32—41no—
620C2×C32C2×D3×D411yescharacteristic
621C2×C32D3×#4111yescharacteristic
622C2×C32#100911yescharacteristic
623C3⋊D3—121no—
624C3×D3—62no—
625C3×D3—62no—
626C3×D3—121no—
627C2×C9—22no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—21no—
631C2×C9—42no—
632C2×C9—41no—
633C2×C9—81no—
634C2×C9C2×#23711yescharacteristic
635C2×C9#100411yescharacteristic
636C2×C9C22×#6711yescharacteristic
637D9—22no—
638D9—22no—
639D9—41no—
640D9—121no—
641D9—241no—
642C24—91no—
643C24—91no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—91no—
647C2×D4—91no—
648C2×D4—91no—
649C2×D4—184no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4D3×D911yescharacteristic
656C22×C4—31no—
657C22×C4—91no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C42—271no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—22no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—92no—
697C22×C3—92no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3—181no—
704C22×C3—181no—
705C22×C3—364no—
706C22×C3—364no—
707C22×C3D4×D912yes—
708C22×C3C23×D911yescharacteristic
709C22×C3D3×#6712yes—
710C22×C3C22×D3211yescharacteristic
711C2×D3—32no—
712C2×D3—32no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—124no—
721C2×D3—124no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—181no—
728C2×D3—361no—
729C2×D3—361no—
730C2×D3—361no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—41no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—61no—
738C3×C4—92no—
739Dic3—21no—
740Dic3—21no—
741Dic3—21no—
742Dic3—21no—
743Dic3—32no—
744Dic3—182no—
745Dic3—181no—
746Dic3—181no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—361no—
752Dic3—361no—
753C32#565411yescharacteristic
754C9—21no—
755C9#580611yescharacteristic, complemented
756C23—91no—
757C23—91no—
758C23—91no—
759C23—182no—
760C23—182no—
761C23—182no—
762C23—182no—
763C23—271no—
764C23—361no—
765C23—361no—
766C23C2×D3×D911yescharacteristic
767C23C2×D3×D911yescharacteristic
768Q8—542no—
769D4—22no—
770D4—94no—
771D4—182no—
772D4—182no—
773D4—542no—
774D4—542no—
775D4—542no—
776D4—1081no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—31no—
782C2×C4—62no—
783C2×C4—91no—
784C2×C4—182no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—271no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—1081no—
791C2×C4—1081no—
792C2×C4C2×D3×D911yescharacteristic
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—42no—
799C2×C3—41no—
800C2×C3—41no—
801C2×C3—81no—
802C2×C3—182no—
803C2×C3—182no—
804C2×C3—361no—
805C2×C3C2×D4×D911yescharacteristic
806C2×C3#41×D911yescharacteristic
807C2×C3#6371511yescharacteristic
808C2×C3D3×#23711yescharacteristic
809C2×C3#6431411yescharacteristic
810C2×C3C2×D3×#6711yescharacteristic
811D3—62no—
812D3—62no—
813D3—121no—
814D3—361no—
815D3—361no—
816D3—721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—92no—
823C22—92no—
824C22—181no—
825C22—181no—
826C22—181no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—364no—
832C22—364no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22D9×#6712yes—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—61no—
840C4—61no—
841C4—61no—
842C4—61no—
843C4—92no—
844C4—541no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058975611yescharacteristic, complemented
849C3#1059514811yescharacteristic
850C2—22no—
851C2—41no—
852C2—182no—
853C2—182no—
854C2—361no—
855C2—1081no—
856C2D9×#23711yescharacteristic
857C2#1172250111yescharacteristic
858C2C2×D9×#6711yescharacteristic
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×C3×D4×D9C2semidirect
2. C2×#88658C2semidirect
3. #11721839C2semidirect
4. C9×#935C2semidirect
5. #11721276C2semidirect
6. #11721276C2semidirect
7. #611⋊Dic3C2semidirect
8. D9×#217C2semidirect
9. C2×(C2×D9)⋊Dic3C2semidirect
10. #11721257C2semidirect
11. #11721256C2semidirect
12. #11721002C2semidirect
13. #11720983C2semidirect
14. #11720981C2semidirect
15. #11720939C2semidirect
21. C2×#6233C22semidirect
22. C2×#6233C22semidirect
23. C22×C3⋊Dic9C22semidirect
26. C22×C9×Dic3C22semidirect
31. C2×#6192C22semidirect
32. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×Dic3×D9C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
38. #88551C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C9×#217C22semidirect
42. C9×#217C22semidirect
43. C9×#217C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C9×Dic3⋊C4C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
70. C2×D4×D9D3semidirect
107. C3×#611D4semidirect
226. C2×C3×D9#41semidirect
252. #935D9semidirect
333. #611#67semidirect
391. C22×Dic3C2×D9semidirect
421. #217C2×D9semidirect
422. #217C2×D9semidirect
423. #217C2×D9semidirect
439. Dic3⋊C4C2×D9semidirect
440. Dic3⋊C4C2×D9semidirect
502. C2×D9#237semidirect
532. C3×C9#546semidirect
755. C9#5806semidirect
848. C3#10589756semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×D92
C2×#886582
#117218392
C9×#9352
#117212762
#611⋊Dic32
D9×#2172
C2×(C2×D9)⋊Dic32
#117212572
#117212562
#117210022
#117209832
#117209812
#117209392
#105951483
#105897563