Finite Group Databasebeta

← C4×D3×#611 #13150523

Subgroups — C4×D3×#611 #13150523

Order 1728.

1372 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×C9C211yesmaximal, characteristic, complemented
2C2×D3×#611C211yesmaximal, characteristic
3C2×C4×D3×D9C211yesmaximal, characteristic, complemented
4C4×#6233C211yesmaximal, characteristic, complemented
5C3×C4×#611C211yesmaximal, characteristic, complemented
6D3×#3676C211yesmaximal, characteristic, complemented
7Dic3×#611C211yesmaximal, characteristic, complemented
8#11721240C211yesmaximal, characteristic, complemented
9D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
10#11721030C211yesmaximal, characteristic, complemented
11C4×#6195C211yesmaximal, characteristic, complemented
12C4×#6194C211yesmaximal, characteristic, complemented
13D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
14C4×D3×Dic9C211yesmaximal, characteristic, complemented
15#11720976C211yesmaximal, characteristic, complemented
16C4×D3×#67—31nomaximal
17C2×C4×#611—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×C4×C3⋊D9C2211yescharacteristic, complemented
23C2×C3×#611C2211yescharacteristic
24C22×C9×Dic3C2211yescharacteristic, complemented
25C2×C4×D3×C9—24no—
26C2×C4×D3×C9C2211yescharacteristic
27C2×C4×D3×C9C2211yescharacteristic
28C2×C4×D3×C9C2211yescharacteristic, complemented
29C2×C4×D3×C9C2211yescharacteristic, complemented
30C2×C3×C4×D9C2211yescharacteristic, complemented
31D3×#611C418yesdirect product factor
32C2×#6195C2211yescharacteristic
33C2×#6194C2211yescharacteristic
34C2×D3×Dic9C2211yescharacteristic
35C2×D3×Dic9C2211yescharacteristic
36C2×D3×Dic9C2211yescharacteristic
37C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
38C2×Dic3×D9C2211yescharacteristic, complemented
39C4×D3×D9—24no—
40#88551C2211yescharacteristic, complemented
41#88536C2211yescharacteristic, complemented
42#88534C2211yescharacteristic, complemented
43C4×C3⋊Dic9C2211yescharacteristic, complemented
44C3×#3676C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47C3×C4×Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55Dic3×Dic9C2211yescharacteristic, complemented
56C22×C3×C4×D3D311yescharacteristic
57C2×D3×#67—31no—
58C2×C4×D32—31no—
59C4×#638—31no—
60C3×C4×#67—31no—
61Dic3×#67—31no—
62D3×#217—31no—
63#63952—31no—
64D3×(C2×D3)⋊C4—31no—
65#63904—31no—
66C4×#626—31no—
67C4×#625—31no—
68#63879—31no—
69D3×Dic3⋊C4—31no—
70C4×D3×Dic3—31no—
71C23×C4×C9—31no—
72C22×#611—31no—
73C22×C4×D9—31no—
74C2×#3676—31no—
75C4×#611—31no—
76C4×#611—31no—
77C4×#611—31no—
78C4×#611—31no—
79C4×#611—31no—
80C4×#611—31no—
81C4×#611—31no—
82C4×#611—61no—
83C4×#611D311yescharacteristic, direct product factor
84C2×(C2×D9)⋊C4—31no—
85C2×Dic9⋊C4—31no—
86C2×C4×Dic9—31no—
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9—22no—
90C22×D3×C9—22no—
91C22×D3×C9C2×C414yescomplemented
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9C2×C414yescomplemented
98C2×C3×C4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233C2×C414yescomplemented
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C4×C3⋊D9—22no—
106C3×#611C2×C414yescomplemented
107C2×C9×Dic3—22no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C4×D3×C9—22no—
114C4×D3×C9—22no—
115C4×D3×C9—22no—
116C4×D3×C9D414yescomplemented
117C3×C4×D9—22no—
118#6195C2×C414yescomplemented
119#6194C2×C414yescomplemented
120D3×Dic9—22no—
121D3×Dic9—22no—
122D3×Dic9C2×C414yescomplemented
123(C3⋊D9)⋊C4—22no—
124Dic3×D9—22no—
125C2×C4×#67—91no—
126C4×D3×D4—91no—
127C23×C3×D3C2×D311yescharacteristic
128C22×D32—31no—
129C22×C32×C4C2×D311yescharacteristic
130C2×#638—31no—
131C2×C4×C3⋊D3—31no—
132C2×C3×#67—31no—
133C22×C3×Dic3C2×D311yescharacteristic
134C2×C3×C4×D3—24no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3C2×D311yescharacteristic
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×C3×C4×D3C2×D311yescharacteristic
139C2×C3×C4×D3C2×D311yescharacteristic
140D3×#67—38no—
141C2×#626—31no—
142C2×#625—31no—
143C2×#624—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C4×D32—64no—
149C24×C9—31no—
150C23×D9—31no—
151#3757—31no—
152#3752—31no—
153#3750—31no—
154C4×C3⋊Dic3—31no—
155C3×#217—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×Dic3⋊C4—31no—
158C3×C4×Dic3—31no—
159#3724—31no—
160Dic3⋊Dic3—31no—
161#3722—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165Dic32—31no—
166Dic32—31no—
167C22×C4×C9—21no—
168C22×C4×C9—31no—
169C22×C4×C9—31no—
170C22×C4×C9—31no—
171C22×C4×C9—31no—
172C22×C4×C9—31no—
173C22×C4×C9—64no—
174C22×C4×C9C2×D311yescharacteristic, complemented
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—38no—
178C2×#611—31no—
179C2×#611—61no—
180C2×#611C2×D311yescharacteristic
181C22×Dic9—31no—
182C22×Dic9—31no—
183C22×Dic9—31no—
184C2×C4×D9—31no—
185C2×C4×D9—31no—
186C2×C4×D9—31no—
187C2×C4×D9—64no—
188C2×C4×D9—61no—
189C2×C4×D9C2×D311yescharacteristic, complemented
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—61no—
194#3676C2×D311yescharacteristic, complemented
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—61no—
199(C2×D9)⋊C4C2×D311yescharacteristic, complemented
200Dic9⋊C4—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—61no—
204Dic9⋊C4C2×D311yescharacteristic, complemented
205C4×Dic9—31no—
206C4×Dic9—31no—
207C4×Dic9—31no—
208C4×Dic9—61no—
209C4×Dic9C2×D311yescharacteristic, complemented
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9C22×C412yescomplemented
213C22×C3×C9C2411yescharacteristic
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3⋊D9C22×C412yescomplemented
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—28no—
220C2×D3×C9C22×C412yes—
221C2×D3×C9C22×C412yescomplemented
222C2×D3×C9C2×D412yes—
223C2×D3×C9#4112yes—
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226C2×C3×D9C22×C412yescomplemented
227D3×D9—28no—
228C3×C4×C9—21no—
229C3×C4×C9C2×D412yescomplemented
230C3⋊Dic9—21no—
231C3⋊Dic9—21no—
232C3⋊Dic9C22×C412yescomplemented
233C9×Dic3—21no—
234C9×Dic3C2×D412yescomplemented
235C3×Dic9—21no—
236C3×Dic9—21no—
237C3×Dic9C22×C412yescomplemented
238C23×C3×C4—31no—
239C22×#67—91no—
240C2×D3×D4—91no—
241C22×C4×D3—91no—
242C22×C4×D3—91no—
243C22×C4×D3D911yescharacteristic, complemented
244C3×C4×D4—91no—
245C2×#217—91no—
246D4×Dic3—91no—
247C4×#67—31no—
248C4×#67—91no—
249C4×#67—91no—
250C4×#67—91no—
251C4×#67—91no—
252C4×#67—91no—
253C4×#67—91no—
254C4×#67—91no—
255C4×#67—91no—
256C4×#67—91no—
257C4×#67—181no—
258C2×(C2×D3)⋊C4—91no—
259C2×Dic3⋊C4—91no—
260C2×C4×Dic3—91no—
261#893—91no—
262D3×C4⋊C4—91no—
263#67⋊C4—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—91no—
267C4×D12—91no—
268C42×D3—91no—
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3—31no—
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3—31no—
274C22×C3×D3C4×D314yes—
275C22×C3×D3C22×D311yescharacteristic
276C22×C3×D3C22×D311yescharacteristic
277C2×D32—34no—
278C2×D32—62no—
279C2×D32—62no—
280C2×C32×C4—22no—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283#638—34no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C4×C3⋊D3—62no—
288C3×#67—34no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C3×C4×D3—22no—
296C3×C4×D3—22no—
297C3×C4×D3—22no—
298C3×C4×D3—62no—
299C3×C4×D3#6714yes—
300#626—34no—
301#625—34no—
302#624—62no—
303D3×Dic3—34no—
304D3×Dic3—62no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307C23×C9—21no—
308C23×C9—31no—
309C23×C9—34no—
310C23×C9—31no—
311C23×C9—62no—
312C23×C9—62no—
313C23×C9C22×D311yescharacteristic
314C22×D9—31no—
315C22×D9—34no—
316C22×D9—61no—
317C22×D9—62no—
318C22×D9—62no—
319C22×D9C22×D311yescharacteristic
320C2×C4×C9—22no—
321C2×C4×C9—21no—
322C2×C4×C9—21no—
323C2×C4×C9—31no—
324C2×C4×C9—34no—
325C2×C4×C9—31no—
326C2×C4×C9—42no—
327C2×C4×C9—62no—
328C2×C4×C9—62no—
329C2×C4×C9—62no—
330C2×C4×C9—62no—
331C2×C4×C9C22×D311yescharacteristic
332C2×C4×C9C22×D311yescharacteristic
333#611—34no—
334#611—34no—
335#611—34no—
336#611—64no—
337#611C4×D314yesdirect product factor
338C2×Dic9—31no—
339C2×Dic9—34no—
340C2×Dic9—31no—
341C2×Dic9—31no—
342C2×Dic9—61no—
343C2×Dic9—61no—
344C2×Dic9—61no—
345C2×Dic9—62no—
346C2×Dic9—62no—
347C2×Dic9C22×D311yescharacteristic
348C2×Dic9C22×D311yescharacteristic
349C2×Dic9C22×D311yescharacteristic
350C4×D9—22no—
351C4×D9—62no—
352C4×D9—62no—
353C4×D9—62no—
354C4×D9—122no—
355C2×C4×D4—271noSylow
356C2×C3×C9—22no—
357C2×C3×C9C23×C411yescharacteristic
358C2×C3×C9C22×D411yescharacteristic
359C2×C3×C9C2×#4111yescharacteristic
360C3⋊D9—22no—
361D3×C9—22no—
362D3×C9C4×D414yescomplemented
363C3×D9—22no—
364C24×C3—31no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3C2×D911yescharacteristic
368C2×C3×D4—91no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—64no—
376C22×C3×C4—91no—
377C22×C3×C4C2×D911yescharacteristic, complemented
378C22×C3×C4D3211yescharacteristic
379C2×#67—31no—
380C2×#67—91no—
381C2×#67—98no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—181no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3C2×D911yescharacteristic, complemented
392D3×D4—98no—
393C2×D12—91no—
394C2×C4×D3—24no—
395C2×C4×D3—31no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—181no—
405C2×C4×D3—184no—
406C2×C4×D3—184no—
407C2×C4×D3C2×D911yescharacteristic
408C2×C4×D3C2×D911yescharacteristic
409C2×C4×D3C2×D911yescharacteristic, complemented
410C2×C4×D3C2×D911yescharacteristic, complemented
411C3×C4⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4—91no—
414C3×C42—91no—
415#217—31no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—91no—
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—
430(C2×D3)⋊C4—181no—
431C4⋊Dic3—91no—
432Dic3⋊C4—31no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—181no—
439C4×Dic3—31no—
440C4×Dic3—91no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C4×Dic3—181no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32C2×C4×D312yes—
450C22×C32C23×D311yescharacteristic
451C2×C3⋊D3—32no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—61no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—28no—
457C2×C3×D3—32no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3C2×C4×D312yes—
461C2×C3×D3C2×C4×D312yes—
462C2×C3×D3#23512yes—
463C2×C3×D3C2×#6712yes—
464D32—68no—
465C32×C4—21no—
466C32×C4C2×#6712yes—
467C3⋊Dic3—32no—
468C3⋊Dic3—61no—
469C3⋊Dic3—61no—
470C3×Dic3—21no—
471C3×Dic3—32no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3C2×#6712yes—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—22no—
479C22×C9—32no—
480C22×C9—32no—
481C22×C9—32no—
482C22×C9—32no—
483C22×C9—41no—
484C22×C9—41no—
485C22×C9—68no—
486C22×C9—61no—
487C22×C9—61no—
488C22×C9C2×C4×D312yescomplemented
489C22×C9C23×D311yescharacteristic
490C2×D9—21no—
491C2×D9—21no—
492C2×D9—32no—
493C2×D9—62no—
494C2×D9—68no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—121no—
498C2×D9—121no—
499C2×D9C2×C4×D312yescomplemented
500C4×C9—21no—
501C4×C9—22no—
502C4×C9—32no—
503C4×C9—41no—
504C4×C9—61no—
505C4×C9D3×D412yescomplemented
506Dic9—21no—
507Dic9—21no—
508Dic9—32no—
509Dic9—62no—
510Dic9—61no—
511Dic9—61no—
512Dic9—121no—
513Dic9—121no—
514Dic9C2×C4×D312yescomplemented
515C22×D4—271no—
516C23×C4—31no—
517C23×C4—271no—
518C4×D4—91no—
519C4×D4—271no—
520C4×D4—271no—
521C4×D4—271no—
522C4×D4—271no—
523C4×D4—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C4⋊C4—271no—
527C2×C22⋊C4—271no—
528C2×C22⋊C4—271no—
529C2×C42—271no—
530C3×C9C2×C4×D411yescharacteristic, complemented, Sylow
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—34no—
535C23×C3—62no—
536C23×C3—62no—
537C23×C3—91no—
538C23×C3C22×D911yescharacteristic
539C23×C3C2×D3211yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—31no—
543C22×D3—94no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—94no—
547C22×D3—181no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3C4×D914yescomplemented
553C22×D3C22×D911yescharacteristic
554C22×D3C22×D911yescharacteristic
555C3×D4—94no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—31no—
561C2×C3×C4—34no—
562C2×C3×C4—31no—
563C2×C3×C4—42no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—91no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—182no—
572C2×C3×C4C22×D911yescharacteristic
573C2×C3×C4C22×D911yescharacteristic
574C2×C3×C4C2×D3211yescharacteristic
575C2×C3×C4C2×D3211yescharacteristic
576#67—34no—
577#67—94no—
578#67—94no—
579#67—94no—
580#67—94no—
581#67—94no—
582#67—184no—
583C2×Dic3—22no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—94no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—181no—
595C2×Dic3—181no—
596C2×Dic3—181no—
597C2×Dic3—182no—
598C2×Dic3—182no—
599C2×Dic3—182no—
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602D12—94no—
603C4×D3—22no—
604C4×D3—22no—
605C4×D3—22no—
606C4×D3—62no—
607C4×D3—94no—
608C4×D3—182no—
609C4×D3—182no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—362no—
616C4×D3#61114yesdirect product factor
617C2×C32—22no—
618C2×C32C22×C4×D311yescharacteristic
619C2×C32C2×#23511yescharacteristic
620C2×C32C22×#6711yescharacteristic
621C3⋊D3—62no—
622C3×D3—22no—
623C3×D3—62no—
624C3×D3C4×#6714yes—
625C2×C9—22no—
626C2×C9—21no—
627C2×C9—21no—
628C2×C9—21no—
629C2×C9—34no—
630C2×C9—42no—
631C2×C9—62no—
632C2×C9C22×C4×D311yescharacteristic
633C2×C9C2×D3×D411yescharacteristic
634C2×C9D3×#4111yescharacteristic
635D9—22no—
636D9—62no—
637D9—122no—
638C24—31no—
639C24—271no—
640C2×D4—91no—
641C2×D4—271no—
642C2×D4—278no—
643C2×D4—271no—
644C2×D4—271no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—64no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C22×C4—271no—
658C22×C4—544no—
659C22×C4D3×D911yescharacteristic, complemented
660C4⋊C4—91no—
661C4⋊C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C22⋊C4—91no—
665C22⋊C4—91no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C42—91no—
673C42—271no—
674C42—271no—
675C42—271no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—22no—
682C22×C3—32no—
683C22×C3—32no—
684C22×C3—32no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—68no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—92no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3C2×C4×D912yescomplemented
695C22×C3C23×D911yescharacteristic
696C22×C3C4×D3212yes—
697C22×C3C22×D3211yescharacteristic
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—28no—
701C2×D3—32no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—92no—
705C2×D3—92no—
706C2×D3—182no—
707C2×D3—188no—
708C2×D3—181no—
709C2×D3—181no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—188no—
713C2×D3—361no—
714C2×D3—361no—
715C2×D3C2×C4×D912yes—
716C2×D3C2×C4×D912yescomplemented
717C2×D3#369712yes—
718C2×D3C2×#61112yes—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—22no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—61no—
725C3×C4—92no—
726C3×C4—181no—
727C3×C4—181no—
728C3×C4C2×#61112yescomplemented
729C3×C4D3×#6712yes—
730Dic3—21no—
731Dic3—32no—
732Dic3—61no—
733Dic3—61no—
734Dic3—92no—
735Dic3—92no—
736Dic3—182no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740Dic3—181no—
741Dic3—361no—
742Dic3—361no—
743Dic3C2×#61112yescomplemented
744C32C2×C4×#6711yescharacteristic
745C9—21no—
746C9C4×D3×D411yescharacteristic, complemented
747C23—31no—
748C23—31no—
749C23—34no—
750C23—62no—
751C23—62no—
752C23—91no—
753C23—274no—
754C23—271no—
755C23—542no—
756C23—542no—
757C23C2×D3×D911yescharacteristic
758D4—94no—
759D4—274no—
760D4—274no—
761D4—274no—
762C2×C4—22no—
763C2×C4—31no—
764C2×C4—34no—
765C2×C4—31no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—182no—
774C2×C4—274no—
775C2×C4—271no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—542no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—542no—
783C2×C4C2×D3×D911yescharacteristic
784C2×C4C2×D3×D911yescharacteristic
785C2×C3—22no—
786C2×C3—22no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—34no—
791C2×C3—42no—
792C2×C3—62no—
793C2×C3—182no—
794C2×C3C22×C4×D911yescharacteristic
795C2×C3C2×#369711yescharacteristic
796C2×C3C22×#61111yescharacteristic
797C2×C3C2×C4×D3211yescharacteristic
798C2×C3D3×#23511yescharacteristic
799C2×C3C2×D3×#6711yescharacteristic
800D3—22no—
801D3—62no—
802D3—182no—
803D3—182no—
804D3—362no—
805D3C4×#61114yesdirect product factor
806C22—21no—
807C22—21no—
808C22—32no—
809C22—32no—
810C22—32no—
811C22—32no—
812C22—68no—
813C22—61no—
814C22—61no—
815C22—92no—
816C22—181no—
817C22—181no—
818C22—272no—
819C22—548no—
820C22—541no—
821C22—541no—
822C22C4×D3×D912yescomplemented
823C22C22×D3×D911yescharacteristic
824C4—21no—
825C4—32no—
826C4—61no—
827C4—92no—
828C4—181no—
829C4—181no—
830C4—272no—
831C4—541no—
832C4—541no—
833C4D3×#61112yesdirect product factor
834C3—21no—
835C3C2×C4×#61111yescharacteristic, complemented
836C3C4×D3×#6711yescharacteristic
837C2—22no—
838C2—34no—
839C2—62no—
840C2—182no—
841C2—542no—
842C2C2×C4×D3×D911yescharacteristic
843C2D3×#369711yescharacteristic
844C2C2×D3×#61111yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
prime radicalC2×D3×#611C2
cosocleC22×C3×C9C24
hypercenterC22×C4D3×D9
hypocenterC3×C9C2×C4×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D3×C9C2semidirect
3. C2×C4×D3×D9C2semidirect
4. C4×#6233C2semidirect
5. C3×C4×#611C2semidirect
6. D3×#3676C2semidirect
7. Dic3×#611C2semidirect
8. #11721240C2semidirect
9. D3×(C2×D9)⋊C4C2semidirect
10. #11721030C2semidirect
11. C4×#6195C2semidirect
12. C4×#6194C2semidirect
13. D3×Dic9⋊C4C2semidirect
14. C4×D3×Dic9C2semidirect
15. #11720976C2semidirect
20. C22×C3×C4×C9C22semidirect
22. C2×C4×C3⋊D9C22semidirect
24. C22×C9×Dic3C22semidirect
28. C2×C4×D3×C9C22semidirect
29. C2×C4×D3×C9C22semidirect
30. C2×C3×C4×D9C22semidirect
31. D3×#611C4direct (N × H)
37. C2×(C3⋊D9)⋊C4C22semidirect
38. C2×Dic3×D9C22semidirect
40. #88551C22semidirect
41. #88536C22semidirect
42. #88534C22semidirect
43. C4×C3⋊Dic9C22semidirect
44. C3×#3676C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×Dic9⋊C4C22semidirect
47. C3×C4×Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
55. Dic3×Dic9C22semidirect
83. C4×#611D3direct (N × H)
91. C22×D3×C9C2×C4semidirect
97. C2×D3×D9C2×C4semidirect
101. #6233C2×C4semidirect
106. C3×#611C2×C4semidirect
116. C4×D3×C9D4semidirect
118. #6195C2×C4semidirect
119. #6194C2×C4semidirect
122. D3×Dic9C2×C4semidirect
174. C22×C4×C9C2×D3semidirect
189. C2×C4×D9C2×D3semidirect
194. #3676C2×D3semidirect
199. (C2×D9)⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
209. C4×Dic9C2×D3semidirect
212. C22×C3×C9C22×C4semidirect
216. C2×C3⋊D9C22×C4semidirect
221. C2×D3×C9C22×C4semidirect
226. C2×C3×D9C22×C4semidirect
229. C3×C4×C9C2×D4semidirect
232. C3⋊Dic9C22×C4semidirect
234. C9×Dic3C2×D4semidirect
237. C3×Dic9C22×C4semidirect
243. C22×C4×D3D9semidirect
337. #611C4×D3direct (N × H)
362. D3×C9C4×D4semidirect
377. C22×C3×C4C2×D9semidirect
391. C22×Dic3C2×D9semidirect
409. C2×C4×D3C2×D9semidirect
410. C2×C4×D3C2×D9semidirect
488. C22×C9C2×C4×D3semidirect
499. C2×D9C2×C4×D3semidirect
505. C4×C9D3×D4semidirect
514. Dic9C2×C4×D3semidirect
530. C3×C9C2×C4×D4semidirect
552. C22×D3C4×D9semidirect
616. C4×D3#611direct (N × H)
659. C22×C4D3×D9semidirect
694. C22×C3C2×C4×D9semidirect
716. C2×D3C2×C4×D9semidirect
728. C3×C4C2×#611semidirect
743. Dic3C2×#611semidirect
746. C9C4×D3×D4semidirect
805. D3C4×#611direct (N × H)
822. C22C4×D3×D9semidirect
833. C4D3×#611direct (N × H)
835. C3C2×C4×#611semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D3×C92
C2×D3×#6112
C2×C4×D3×D92
C4×#62332
C3×C4×#6112
D3×#36762
Dic3×#6112
#117212402
D3×(C2×D9)⋊C42
#117210302
C4×#61952
C4×#61942
D3×Dic9⋊C42
C4×D3×Dic92
#117209762
C4×D3×#673
C2×C4×#6113