Finite Group Databasebeta

← #13150570

Subgroups — #13150570

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D9×#67C211yesmaximal, characteristic, complemented
2C2×#88662C211yesmaximal, characteristic, complemented
3C4×#6233C211yesmaximal, characteristic, complemented
4C9×#930C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
6#11721285C211yesmaximal, characteristic, complemented
7#11721265C211yesmaximal, characteristic, complemented
8#11721050C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10#11721044C211yesmaximal, characteristic, complemented
11#11721041C211yesmaximal, characteristic, complemented
12#11721028C211yesmaximal, characteristic, complemented
13#11721016C211yesmaximal, characteristic, complemented
14#11720999C211yesmaximal, characteristic, complemented
15#11720942C211yesmaximal, characteristic, complemented
16#10595083—31nomaximal
17#10589712—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×C4×C3⋊D9C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic
24C2×C9×#67C2211yescharacteristic, complemented
25C22×C3×Dic9C2211yescharacteristic, complemented
26C2×C9×D12C2211yescharacteristic, complemented
27D9×#67—24no—
28C2×#6195C2211yescharacteristic, complemented
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31C2×#6194C2211yescharacteristic, complemented
32#88662—24no—
33C2×D3×Dic9C2211yescharacteristic, complemented
34C2×#6192C2211yescharacteristic
35C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic
37C2×#6189C2211yescharacteristic, complemented
38#88551C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C4×C3⋊Dic9C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C9×C4⋊Dic3C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54#88442C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3804—31no—
57C4×#638—31no—
58C3×#930D311yescharacteristic
59C2×C3×(C2×D3)⋊C4—31no—
60#63976—31no—
61#63961—31no—
62#63922—31no—
63#63921—31no—
64#63915—31no—
65#63912—31no—
66#63902—31no—
67#63899—31no—
68#63885—31no—
69#63854—31no—
70C2×#3699—31no—
71C2×D4×D9—31no—
72C9×#121—31no—
73#63501—31no—
74#63499—31no—
75#63499—31no—
76#63497—31no—
77C4×#611—31no—
78C4×#611—61no—
79C2×(C2×D9)⋊C4D311yescharacteristic, complemented
80#63458—31no—
81#63456—31no—
82#63447—31no—
83#63446—31no—
84#611⋊C4—31no—
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9—22no—
91C22×C3×D9—22no—
92C22×C3×D9—41no—
93C22×C3×D9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9—41no—
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233D414yescomplemented
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C4×C3⋊D9—41no—
106C9×#67—22no—
107C9×#67—22no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9—22no—
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C9×D12—41no—
114#6195—22no—
115#6194—22no—
116#6194—22no—
117#6194—41no—
118D3×Dic9—22no—
119#6192—22no—
120(C3⋊D9)⋊C4—22no—
121Dic3×D9—22no—
122#6189—22no—
123#5610—91no—
124#5490—91no—
125C23×C3×D3—31no—
126C22×D32—31no—
127C22×C32×C4C2×D311yescharacteristic
128C2×#638—31no—
129C2×C4×C3⋊D3—31no—
130C2×C3×#67C2×D311yescharacteristic
131C2×C3×#67C2×D311yescharacteristic
132C22×C3×Dic3—31no—
133C2×C3×D12C2×D311yescharacteristic
134D3×#67—64no—
135C2×#627—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#625—31no—
139C2×#625—31no—
140C2×#625—31no—
141C2×#624—31no—
142#3804—64no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C23×D9—31no—
146C23×D9C2×D311yescharacteristic
147#3757—31no—
148#3752—31no—
149#3750—31no—
150C4×C3⋊Dic3—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×(C2×D3)⋊C4C2×D311yescharacteristic
157C3×C4⋊Dic3C2×D311yescharacteristic
158#3724—31no—
159#3724—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164C2×D4×C9—31no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C22×C4×C9—21no—
168C22×C4×C9C2×D311yescharacteristic, complemented
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—61no—
175C22×Dic9—31no—
176C22×Dic9C2×D311yescharacteristic, complemented
177#3699—64no—
178D4×D9—64no—
179C2×D36—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—61no—
184C2×Dic18—31no—
185C9×C4⋊C4—31no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188#3676—31no—
189#3676—31no—
190#3676—31no—
191#3676—61no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—61no—
196(C2×D9)⋊C4C2×D311yescharacteristic
197(C2×D9)⋊C4C2×D311yescharacteristic
198(C2×D9)⋊C4C2×D311yescharacteristic, complemented
199(C2×D9)⋊C4C2×D311yescharacteristic, complemented
200Dic9⋊C4—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—61no—
204C4×Dic9—31no—
205C4×Dic9—61no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9C2×D412yes—
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9C2×D412yes—
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×C3×D9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—44no—
225C2×C3×D9#4112yescomplemented
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9C2×D412yes—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C22×#67—91no—
237C2×#237—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#121—31no—
241C2×C3×C22⋊C4—91no—
242#953—91no—
243#939—91no—
244#937—91no—
245#937—91no—
246#935—91no—
247#930D911yescharacteristic, complemented
248#929—91no—
249C4×#67—91no—
250C4×#67—91no—
251C4×#67—181no—
252C2×(C2×D3)⋊C4—31no—
253#896—91no—
254#894—91no—
255#885—91no—
256#885—91no—
257#884—91no—
258#884—91no—
259#884—91no—
260#883—91no—
261#882—91no—
262#67⋊C4—91no—
263#67⋊C4—91no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—62no—
272C22×C3×D3—62no—
273C22×C3×D3—121no—
274C22×C3×D3C22×D311yescharacteristic
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4—41no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282#638—34no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C4×C3⋊D3—121no—
287C3×#67—22no—
288C3×#67—22no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C3×D12—41no—
295#627—62no—
296#626—62no—
297#626—62no—
298#625—62no—
299#625—62no—
300#625—121no—
301#624—62no—
302D3×Dic3—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9—31no—
307C23×C9C22×D311yescharacteristic
308C22×D9—22no—
309C22×D9—22no—
310C22×D9—31no—
311C22×D9—41no—
312C22×D9—61no—
313C22×D9—62no—
314C22×D9—62no—
315C22×D9—121no—
316C22×D9C22×D311yescharacteristic
317C22×D9C22×D311yescharacteristic
318D4×C9—62no—
319D4×C9—62no—
320D4×C9—121no—
321C2×C4×C9—21no—
322C2×C4×C9—21no—
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9—41no—
326C2×C4×C9—42no—
327C2×C4×C9C22×D311yescharacteristic
328C2×C4×C9C22×D311yescharacteristic
329#611—34no—
330#611—64no—
331#611—62no—
332#611—62no—
333#611—62no—
334#611—121no—
335C2×Dic9—22no—
336C2×Dic9—31no—
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—61no—
342C2×Dic9—62no—
343C2×Dic9C22×D311yescharacteristic
344C2×Dic9C22×D311yescharacteristic
345D36—62no—
346C4×D9—62no—
347C4×D9—62no—
348C4×D9—121no—
349C4×D9—122no—
350Dic18—62no—
351#546—271noSylow
352C2×C3×C9—22no—
353C2×C3×C9C22×D411yescharacteristic
354C2×C3×C9C2×#4111yescharacteristic
355C2×C3×C9H(5,𝔽2)11yescharacteristic
356C3⋊D9—22no—
357D3×C9—41no—
358D3×C9—41no—
359C3×D9—22no—
360C3×D9—41no—
361C24×C3—91no—
362C23×D3—31no—
363C23×D3—91no—
364C23×D3—91no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C22×C3×C4—21no—
369C22×C3×C4—91no—
370C22×C3×C4C2×D911yescharacteristic, complemented
371C22×C3×C4D3211yescharacteristic
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—181no—
383C2×#67—184no—
384C2×#67C2×D911yescharacteristic
385C2×#67C2×D911yescharacteristic, complemented
386C22×Dic3—31no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389#237—184no—
390D3×D4—184no—
391#235—184no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12C2×D911yescharacteristic, complemented
395C2×C4×D3—91no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—181no—
402C2×Dic6—91no—
403C2×Dic6—91no—
404C3×C4⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—181no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—91no—
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—181no—
429(C2×D3)⋊C4C2×D911yescharacteristic, complemented
430(C2×D3)⋊C4C2×D911yescharacteristic, complemented
431C4⋊Dic3C2×D911yescharacteristic, complemented
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—181no—
439C4×Dic3—91no—
440C4×Dic3—91no—
441C4×Dic3—181no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32D3×D412yes—
445C22×C32C23×D311yescharacteristic
446C2×C3⋊D3—32no—
447C2×C3⋊D3—61no—
448C2×C3⋊D3—61no—
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—32no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—124no—
462D32—124no—
463C32×C4—21no—
464C32×C4—21no—
465C3⋊Dic3—32no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C22×C9—21no—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—22no—
476C22×C9—41no—
477C22×C9—41no—
478C22×C9—61no—
479C22×C9—61no—
480C22×C9—61no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9D3×D412yes—
485C22×C9C23×D311yescharacteristic
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—32no—
492C2×D9—44no—
493C2×D9—62no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—121no—
497C2×D9—121no—
498C2×D9—124no—
499C2×D9#23512yescomplemented
500C4×C9—22no—
501C4×C9—21no—
502C4×C9—21no—
503C4×C9—41no—
504C4×C9—61no—
505C4×C9—61no—
506Dic9—21no—
507Dic9—21no—
508Dic9—32no—
509Dic9—62no—
510Dic9—61no—
511Dic9—61no—
512Dic9—121no—
513Dic9—121no—
514C2×#41—271no—
515C22×D4—271no—
516#124—271no—
517#123—271no—
518#123—271no—
519C22⋊Q8—271no—
520#121—31no—
521#121—271no—
522#121—271no—
523#120—271no—
524#120—271no—
525C4×D4—271no—
526C4×D4—271no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—271no—
529C3×C9#54611yescharacteristic, complemented, Sylow
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—91no—
534C23×C3—91no—
535C23×C3—182no—
536C23×C3—182no—
537C23×C3—361no—
538C23×C3C22×D911yescharacteristic
539C23×C3C2×D3211yescharacteristic
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—121no—
547C22×D3—181no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—361no—
553C22×D3—361no—
554C22×D3C22×D911yescharacteristic
555C22×D3C22×D911yescharacteristic
556C3×D4—62no—
557C3×D4—62no—
558C3×D4—121no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—42no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—182no—
569C2×C3×C4C22×D911yescharacteristic
570C2×C3×C4C22×D911yescharacteristic
571C2×C3×C4C2×D3211yescharacteristic
572C2×C3×C4C2×D3211yescharacteristic
573#67—22no—
574#67—22no—
575#67—94no—
576#67—94no—
577#67—184no—
578#67—182no—
579#67—182no—
580#67—182no—
581#67—182no—
582#67—182no—
583#67—182no—
584#67—361no—
585#67—361no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—62no—
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—182no—
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602D12—41no—
603D12—182no—
604D12—182no—
605C4×D3—182no—
606C4×D3—182no—
607C4×D3—182no—
608C4×D3—182no—
609C4×D3—361no—
610C4×D3—361no—
611C4×D3—362no—
612Dic6—182no—
613Dic6—182no—
614C2×C32—22no—
615C2×C32C2×D3×D411yescharacteristic
616C2×C32#100411yescharacteristic
617C2×C32D3×#4111yescharacteristic
618C3⋊D3—62no—
619C3×D3—41no—
620C3×D3—41no—
621C3×D3—62no—
622C3×D3—121no—
623C2×C9—22no—
624C2×C9—21no—
625C2×C9—21no—
626C2×C9—21no—
627C2×C9—42no—
628C2×C9—121no—
629C2×C9—121no—
630C2×C9C2×#23511yescharacteristic
631C2×C9C2×D3×D411yescharacteristic
632C2×C9#100411yescharacteristic
633D9—22no—
634D9—41no—
635D9—62no—
636D9—122no—
637C24—91no—
638C24—271no—
639#41—544no—
640C2×Q8—271no—
641C2×D4—31no—
642C2×D4—31no—
643C2×D4—31no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
650C2×D4—544no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4D3×D911yescharacteristic, complemented
657C4⋊C4—31no—
658C4⋊C4—271no—
659C4⋊C4—271no—
660C4⋊C4—271no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—91no—
664C22⋊C4—91no—
665C22⋊C4—91no—
666C22⋊C4—91no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C42—271no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—22no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—92no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—364no—
695C22×C3D4×D912yes—
696C22×C3C23×D911yescharacteristic
697C22×C3#380212yes—
698C22×C3C22×D3211yescharacteristic
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—32no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—92no—
712C2×D3—92no—
713C2×D3—124no—
714C2×D3—182no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—361no—
720C2×D3—361no—
721C2×D3—364no—
722C2×D3—364no—
723C3×C4—22no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—41no—
729C3×C4—61no—
730C3×C4—61no—
731C3×C4—181no—
732C3×C4—181no—
733Dic3—21no—
734Dic3—21no—
735Dic3—61no—
736Dic3—61no—
737Dic3—92no—
738Dic3—92no—
739Dic3—182no—
740Dic3—181no—
741Dic3—181no—
742Dic3—181no—
743Dic3—181no—
744Dic3—361no—
745Dic3—361no—
746C32#561011yescharacteristic
747C9—21no—
748C9#549011yescharacteristic, complemented
749C23—31no—
750C23—31no—
751C23—91no—
752C23—91no—
753C23—182no—
754C23—182no—
755C23—271no—
756C23—361no—
757C23—542no—
758C23—542no—
759C23—1081no—
760C23C2×D3×D911yescharacteristic
761Q8—542no—
762D4—62no—
763D4—62no—
764D4—121no—
765D4—274no—
766D4—542no—
767D4—542no—
768D4—542no—
769D4—542no—
770D4—1081no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—41no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—182no—
777C2×C4—271no—
778C2×C4—271no—
779C2×C4—271no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—542no—
783C2×C4—1081no—
784C2×C4C2×D3×D911yescharacteristic
785C2×C4C2×D3×D911yescharacteristic
786C2×C3—22no—
787C2×C3—22no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—42no—
792C2×C3—121no—
793C2×C3—121no—
794C2×C3—182no—
795C2×C3—361no—
796C2×C3C2×D4×D911yescharacteristic
797C2×C3#6371011yescharacteristic
798C2×C3#41×D911yescharacteristic
799C2×C3C2×#380211yescharacteristic
800C2×C3D3×#23511yescharacteristic
801C2×C3#6433011yescharacteristic
802D3—41no—
803D3—41no—
804D3—62no—
805D3—121no—
806D3—182no—
807D3—182no—
808D3—362no—
809C22—21no—
810C22—21no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—92no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—181no—
823C22—272no—
824C22—364no—
825C22—541no—
826C22—541no—
827C22—1084no—
828C22#8864612yes—
829C22C22×D3×D911yescharacteristic
830C4—21no—
831C4—21no—
832C4—61no—
833C4—61no—
834C4—181no—
835C4—181no—
836C4—272no—
837C4—541no—
838C4—541no—
839C3—21no—
840C3#1058971211yescharacteristic, complemented
841C3#1059508311yescharacteristic
842C2—22no—
843C2—121no—
844C2—121no—
845C2—182no—
846C2—361no—
847C2—542no—
848C2C2×#8864611yescharacteristic
849C2D9×#23511yescharacteristic
850C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×D9×#67C2semidirect
2. C2×#88662C2semidirect
3. C4×#6233C2semidirect
4. C9×#930C2semidirect
5. C2×C3×(C2×D9)⋊C4C2semidirect
6. #11721285C2semidirect
7. #11721265C2semidirect
8. #11721050C2semidirect
9. #11721048C2semidirect
10. #11721044C2semidirect
11. #11721041C2semidirect
12. #11721028C2semidirect
13. #11721016C2semidirect
14. #11720999C2semidirect
15. #11720942C2semidirect
20. C22×C3×C4×C9C22semidirect
22. C2×C4×C3⋊D9C22semidirect
24. C2×C9×#67C22semidirect
25. C22×C3×Dic9C22semidirect
26. C2×C9×D12C22semidirect
28. C2×#6195C22semidirect
31. C2×#6194C22semidirect
33. C2×D3×Dic9C22semidirect
35. C2×(C3⋊D9)⋊C4C22semidirect
37. C2×#6189C22semidirect
38. #88551C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C4×C3⋊Dic9C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C9×C4⋊Dic3C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. #88442C22semidirect
54. #88442C22semidirect
79. C2×(C2×D9)⋊C4D3semidirect
101. #6233D4semidirect
168. C22×C4×C9C2×D3semidirect
176. C22×Dic9C2×D3semidirect
198. (C2×D9)⋊C4C2×D3semidirect
199. (C2×D9)⋊C4C2×D3semidirect
225. C2×C3×D9#41semidirect
247. #930D9semidirect
370. C22×C3×C4C2×D9semidirect
385. C2×#67C2×D9semidirect
394. C2×D12C2×D9semidirect
429. (C2×D3)⋊C4C2×D9semidirect
430. (C2×D3)⋊C4C2×D9semidirect
431. C4⋊Dic3C2×D9semidirect
499. C2×D9#235semidirect
529. C3×C9#546semidirect
656. C22×C4D3×D9semidirect
748. C9#5490semidirect
840. C3#10589712semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×#886622
C4×#62332
C9×#9302
C2×C3×(C2×D9)⋊C42
#117212852
#117212652
#117210502
#117210482
#117210442
#117210412
#117210282
#117210162
#117209992
#117209422
#105950833
#105897123