Finite Group Databasebeta

← #13148984

Subgroups — #13148984

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×D36C211yesmaximal, characteristic, complemented
2C2×#88634C211yesmaximal, characteristic, complemented
3#11721750C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×#63457C211yesmaximal, characteristic, complemented
6#11721049C211yesmaximal, characteristic, complemented
7#11721049C211yesmaximal, characteristic, complemented
8#11721048C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721005C211yesmaximal, characteristic, complemented
11#11721003C211yesmaximal, characteristic, complemented
12#11721002C211yesmaximal, characteristic, complemented
13#11720983C211yesmaximal, characteristic, complemented
14#11720981C211yesmaximal, characteristic, complemented
15#11720976C211yesmaximal, characteristic, complemented
16#10594622—31nomaximal
17#10589732—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C4×D3×C9C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic, complemented
25C2×C3×D36C2211yescharacteristic, complemented
26C2×C3×C4×D9C2211yescharacteristic, complemented
27C2×C9×Dic6C2211yescharacteristic, complemented
28C2×#6194C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C2×Dic3×D9C2211yescharacteristic, complemented
35C2×Dic3×D9C2211yescharacteristic, complemented
36D3×D36—24no—
37#88634—24no—
38C3×C9×C4⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88536C2211yescharacteristic, complemented
42#88534C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C9×Dic3⋊C4C2211yescharacteristic, complemented
48C9×Dic3⋊C4C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×D12—31no—
56C2×#3796—31no—
57#64103—31no—
58C3×#896D311yescharacteristic
59C3×#895—31no—
60#63922—31no—
61#63922—31no—
62#63921—31no—
63D3×(C2×D3)⋊C4—31no—
64#63910—31no—
65#63907—31no—
66#63904—31no—
67#63886—31no—
68#63884—31no—
69#63879—31no—
70C2×#3701—31no—
71C22×D36—31no—
72C9×C22⋊Q8—31no—
73#63509—31no—
74C4×#611—31no—
75#63457—31no—
76#63457—31no—
77#63457D311yescharacteristic, complemented
78#63456—31no—
79#63456—31no—
80#63456—61no—
81#63455—31no—
82#63444—31no—
83#63444—31no—
84C22⋊C4×D9—31no—
85C22⋊C4×D9—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×D3×D9—22no—
93C2×D3×D9—22no—
94C2×D3×D9—22no—
95C2×D3×D9—22no—
96C2×D3×D9—41no—
97C2×D3×D9—41no—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C4⋊(C3⋊D9)—22no—
104C4×C3⋊D9—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C4×D3×C9—22no—
110C3×D36—22no—
111C3×D36—22no—
112C3×D36—41no—
113C3×C4×D9—41no—
114C9×Dic6—22no—
115#6194—22no—
116#6192—22no—
117#6192—22no—
118#6192—41no—
119#6192D414yescomplemented
120(C3⋊D9)⋊C4—41no—
121Dic3×D9—22no—
122Dic3×D9—22no—
123#5630—91no—
124#5610—91no—
125C22×D32—31no—
126C22×D32—31no—
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4×C3⋊D3—31no—
129C2×C3×D12—31no—
130C2×C3×D12—31no—
131C2×C3×D12—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×Dic6C2×D311yescharacteristic
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#625—31no—
140C2×#624—31no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143D3×D12—64no—
144#3796—64no—
145C23×D9—31no—
146C23×D9—31no—
147C32×C4⋊C4C2×D311yescharacteristic
148#3752—31no—
149#3752—31no—
150#3752—31no—
151#3750—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×Dic3⋊C4C2×D311yescharacteristic
157C3×Dic3⋊C4C2×D311yescharacteristic
158#3722—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163Dic32—31no—
164C2×Q8×C9—31no—
165C22×C4×C9—31no—
166C2×#611—31no—
167#3701—64no—
168C2×D36—31no—
169C2×D36—31no—
170C2×D36—31no—
171C2×D36—31no—
172C2×D36—31no—
173C2×D36—64no—
174C2×D36—61no—
175C2×D36C2×D311yescharacteristic
176C2×D36C2×D311yescharacteristic, complemented
177C2×D36C2×D311yescharacteristic, complemented
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—61no—
183C2×C4×D9C2×D311yescharacteristic, complemented
184C9×C4⋊C4—21no—
185C9×C4⋊C4—31no—
186C9×C4⋊C4—31no—
187C9×C4⋊C4C2×D311yescharacteristic, complemented
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190#3676—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
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—61no—
199(C2×D9)⋊C4—61no—
200(C2×D9)⋊C4—61no—
201(C2×D9)⋊C4C2×D311yescharacteristic, complemented
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203Dic9⋊C4—31no—
204Dic9⋊C4—61no—
205C4×Dic9—31no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9C2×D412yes—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9#4112yescomplemented
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—21no—
224C2×C3×D9C2×D412yes—
225D3×D9—44no—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3×C4×C9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C9×Dic3C2×D412yes—
235C3×Dic9—21no—
236C2×#239—91no—
237C2×#237—91no—
238C2×D3×D4—91no—
239C22×D12—91no—
240C3×C22⋊Q8—31no—
241C3×#121—91no—
242#947—91no—
243#939—91no—
244#937—91no—
245#937—91no—
246#935—91no—
247C4×#67—91no—
248C4×#67—91no—
249C2×(C2×D3)⋊C4—91no—
250#896D911yescharacteristic, complemented
251#895—31no—
252#895—91no—
253#895—91no—
254#894—91no—
255#894—91no—
256#894—91no—
257#894—181no—
258#893—91no—
259#885—91no—
260#884—91no—
261#882—91no—
262#882—91no—
263#67⋊C4—91no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—91no—
267C22×C3⋊D3—31no—
268C22×C3⋊D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3C22×D311yescharacteristic
273C2×D32—62no—
274C2×D32—62no—
275C2×D32—62no—
276C2×D32—62no—
277C2×D32—121no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C4⋊(C3⋊D3)—62no—
285C4×C3⋊D3—62no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C3×D12—62no—
291C3×D12—62no—
292C3×D12—121no—
293C3×C4×D3—22no—
294C3×C4×D3—121no—
295C3×Dic6—22no—
296#626—34no—
297#626—62no—
298#626—62no—
299#626—121no—
300#625—62no—
301#624—121no—
302D3×Dic3—62no—
303D3×Dic3—62no—
304C23×C9—31no—
305C22×D9—31no—
306C22×D9—31no—
307C22×D9—61no—
308C22×D9—61no—
309C22×D9—62no—
310C22×D9—62no—
311C22×D9—62no—
312C22×D9—62no—
313C22×D9—121no—
314C22×D9—121no—
315C22×D9C22×D311yescharacteristic
316C22×D9C22×D311yescharacteristic
317C22×D9C22×D311yescharacteristic
318Q8×C9—62no—
319C2×C4×C9—21no—
320C2×C4×C9—21no—
321C2×C4×C9—21no—
322C2×C4×C9—31no—
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9—62no—
326C2×C4×C9C22×D311yescharacteristic
327C2×C4×C9C22×D311yescharacteristic
328C2×C4×C9C22×D311yescharacteristic
329#611—62no—
330C2×Dic9—31no—
331C2×Dic9—31no—
332C2×Dic9—61no—
333C2×Dic9—61no—
334C2×Dic9C22×D311yescharacteristic
335D36—22no—
336D36—22no—
337D36—34no—
338D36—41no—
339D36—62no—
340D36—62no—
341D36—62no—
342D36—122no—
343D36—121no—
344C4×D9—41no—
345C4×D9—62no—
346C4×D9—62no—
347C4×D9—62no—
348C4×D9—122no—
349C4×D9—121no—
350#546—271noSylow
351C2×C3×C9C22×D411yescharacteristic
352C2×C3×C9C2×#4111yescharacteristic
353C2×C3×C9H(5,𝔽2)11yescharacteristic
354C3⋊D9—22no—
355C3⋊D9—41no—
356D3×C9—22no—
357C3×D9—22no—
358C3×D9—41no—
359C3×D9—41no—
360C23×D3—91no—
361C23×D3—91no—
362C23×D3—91no—
363C23×D3—91no—
364C2×C3×Q8—31no—
365C2×C3×D4—91no—
366C2×C3×D4—91no—
367C2×C3×D4—91no—
368C22×C3×C4—31no—
369C22×C3×C4—91no—
370C2×#67—91no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C22×Dic3—91no—
377C22×Dic3—91no—
378#239—184no—
379#237—184no—
380D3×D4—184no—
381C2×D12—31no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—91no—
385C2×D12—91no—
386C2×D12—91no—
387C2×D12—91no—
388C2×D12—91no—
389C2×D12—91no—
390C2×D12—181no—
391C2×D12—184no—
392C2×C4×D3—31no—
393C2×C4×D3—91no—
394C2×C4×D3—91no—
395C2×C4×D3—91no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—181no—
400C2×C4×D3C2×D911yescharacteristic
401C2×Dic6C2×D911yescharacteristic, complemented
402C3×C4⋊C4—21no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4C2×D911yescharacteristic, complemented
406C3×C4⋊C4D3211yescharacteristic
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
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—91no—
429(C2×D3)⋊C4—181no—
430(C2×D3)⋊C4—181no—
431(C2×D3)⋊C4—181no—
432(C2×D3)⋊C4C2×D911yescharacteristic
433(C2×D3)⋊C4C2×D911yescharacteristic
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—181no—
437Dic3⋊C4C2×D911yescharacteristic, complemented
438Dic3⋊C4C2×D911yescharacteristic, complemented
439C4×Dic3—91no—
440C4×Dic3—91no—
441C22×C32C23×D311yescharacteristic
442C2×C3⋊D3—32no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—32no—
451C2×C3×D3—61no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3#23912yes—
460D32—124no—
461D32—124no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—61no—
470C3×Dic3D3×D412yes—
471C22×C9—21no—
472C22×C9—32no—
473C22×C9—61no—
474C22×C9—61no—
475C22×C9C23×D311yescharacteristic
476C2×D9—21no—
477C2×D9—21no—
478C2×D9—21no—
479C2×D9—21no—
480C2×D9—21no—
481C2×D9—21no—
482C2×D9—21no—
483C2×D9—21no—
484C2×D9—32no—
485C2×D9—62no—
486C2×D9—61no—
487C2×D9—61no—
488C2×D9—61no—
489C2×D9—61no—
490C2×D9—61no—
491C2×D9—121no—
492C2×D9—121no—
493C2×D9—121no—
494C2×D9—121no—
495C2×D9—121no—
496C2×D9—124no—
497C2×D9—124no—
498C2×D9D3×D412yes—
499C4×C9—21no—
500C4×C9—21no—
501C4×C9—21no—
502C4×C9—32no—
503C4×C9—41no—
504C4×C9—41no—
505C4×C9—41no—
506C4×C9—61no—
507C4×C9—61no—
508Dic9—21no—
509Dic9—61no—
510Dic9—61no—
511Dic9—121no—
512Dic9—121no—
513C2×#41—271no—
514C22×D4—271no—
515#124—271no—
516#123—271no—
517#123—271no—
518C22⋊Q8—31no—
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—31no—
530C23×C3—91no—
531C23×C3—91no—
532C23×C3—91no—
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—31no—
536C22×D3—91no—
537C22×D3—91no—
538C22×D3—91no—
539C22×D3—91no—
540C22×D3—181no—
541C22×D3—181no—
542C22×D3—182no—
543C22×D3—182no—
544C22×D3—182no—
545C22×D3—182no—
546C22×D3—182no—
547C22×D3—182no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—361no—
551C22×D3—361no—
552C22×D3—361no—
553C22×D3—361no—
554C22×D3C22×D911yescharacteristic
555C3×Q8—62no—
556C3×D4—182no—
557C3×D4—182no—
558C3×D4—361no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—62no—
566C2×C3×C4—91no—
567C2×C3×C4—361no—
568C2×C3×C4C22×D911yescharacteristic
569C2×C3×C4C22×D911yescharacteristic
570C2×C3×C4C22×D911yescharacteristic
571C2×C3×C4C2×D3211yescharacteristic
572C2×C3×C4C2×D3211yescharacteristic
573C2×C3×C4C2×D3211yescharacteristic
574#67—94no—
575#67—182no—
576#67—182no—
577#67—182no—
578#67—182no—
579#67—361no—
580C2×Dic3—31no—
581C2×Dic3—91no—
582C2×Dic3—91no—
583C2×Dic3—91no—
584C2×Dic3—91no—
585C2×Dic3—181no—
586C2×Dic3—181no—
587C2×Dic3—182no—
588C2×Dic3—182no—
589C2×Dic3C22×D911yescharacteristic
590C2×Dic3C22×D911yescharacteristic
591C2×Dic3C22×D911yescharacteristic
592D12—62no—
593D12—62no—
594D12—94no—
595D12—121no—
596D12—182no—
597D12—182no—
598D12—182no—
599D12—182no—
600D12—362no—
601D12—361no—
602C4×D3—22no—
603C4×D3—121no—
604C4×D3—182no—
605C4×D3—182no—
606C4×D3—182no—
607C4×D3—182no—
608C4×D3—362no—
609C4×D3—361no—
610C4×D3—361no—
611Dic6—22no—
612C2×C32C2×D3×D411yescharacteristic
613C2×C32C2×#23911yescharacteristic
614C2×C32#100911yescharacteristic
615C3⋊D3—62no—
616C3⋊D3—121no—
617C3×D3—22no—
618C3×D3—62no—
619C3×D3—121no—
620C3×D3—121no—
621C2×C9—21no—
622C2×C9—21no—
623C2×C9—21no—
624C2×C9—62no—
625C2×C9C2×D3×D411yescharacteristic
626C2×C9#100411yescharacteristic
627C2×C9D3×#4111yescharacteristic
628D9—22no—
629D9—41no—
630D9—41no—
631D9—62no—
632D9—122no—
633D9—121no—
634D9—241no—
635C24—271no—
636C24—271no—
637#41—544no—
638C2×Q8—31no—
639C2×D4—91no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—271no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—544no—
649C22×C4—31no—
650C22×C4—91no—
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—271no—
658C4⋊C4D3×D911yescharacteristic, complemented
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—91no—
662C22⋊C4—91no—
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—32no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—92no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3—181no—
682C22×C3—181no—
683C22×C3—181no—
684C22×C3—181no—
685C22×C3C23×D911yescharacteristic
686C22×C3C22×D3211yescharacteristic
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—32no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—92no—
699C2×D3—92no—
700C2×D3—182no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—181no—
704C2×D3—181no—
705C2×D3—181no—
706C2×D3—181no—
707C2×D3—181no—
708C2×D3—181no—
709C2×D3—181no—
710C2×D3—181no—
711C2×D3—361no—
712C2×D3—361no—
713C2×D3—361no—
714C2×D3—361no—
715C2×D3—361no—
716C2×D3—364no—
717C2×D3—364no—
718C2×D3—364no—
719C2×D3—364no—
720C2×D3#370112yescomplemented
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—32no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—61no—
732C3×C4—61no—
733C3×C4—181no—
734Dic3—21no—
735Dic3—21no—
736Dic3—61no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740Dic3—181no—
741Dic3—361no—
742Dic3—361no—
743Dic3D4×D912yes—
744C32#563011yescharacteristic
745C9—21no—
746C9#561011yescharacteristic, complemented
747C23—31no—
748C23—91no—
749C23—91no—
750C23—91no—
751C23—271no—
752C23—271no—
753C23—542no—
754C23—542no—
755C23—542no—
756C23—542no—
757C23—1081no—
758C23—1081no—
759Q8—62no—
760D4—182no—
761D4—182no—
762D4—274no—
763D4—361no—
764D4—542no—
765D4—542no—
766D4—542no—
767D4—542no—
768D4—1081no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—62no—
773C2×C4—91no—
774C2×C4—271no—
775C2×C4—271no—
776C2×C4—361no—
777C2×C4—542no—
778C2×C4—542no—
779C2×C4—542no—
780C2×C4—1081no—
781C2×C4C2×D3×D911yescharacteristic
782C2×C4C2×D3×D911yescharacteristic
783C2×C4C2×D3×D911yescharacteristic
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—62no—
788C2×C3—182no—
789C2×C3—361no—
790C2×C3—361no—
791C2×C3C2×D4×D911yescharacteristic
792C2×C3C2×#370111yescharacteristic
793C2×C3#6371511yescharacteristic
794C2×C3#6430711yescharacteristic
795C2×C3D32×D411yescharacteristic
796C2×C3D3×#23911yescharacteristic
797D3—22no—
798D3—62no—
799D3—121no—
800D3—121no—
801D3—182no—
802D3—182no—
803D3—362no—
804D3—361no—
805D3—361no—
806D3—721no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—92no—
811C22—181no—
812C22—181no—
813C22—181no—
814C22—181no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—272no—
820C22—541no—
821C22—541no—
822C22—541no—
823C22—541no—
824C22—541no—
825C22—1084no—
826C22—1084no—
827C22C22×D3×D911yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—32no—
832C4—61no—
833C4—61no—
834C4—181no—
835C4—541no—
836C4—541no—
837C3—21no—
838C3#1058973211yescharacteristic, complemented
839C3#1059462211yescharacteristic
840C2—62no—
841C2—182no—
842C2—361no—
843C2—361no—
844C2—542no—
845C2—1081no—
846C2#1172247711yescharacteristic
847C2D3×D4×D911yescharacteristic
848C2D3×#370111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#546
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. C2×D3×D36C2semidirect
2. C2×#88634C2semidirect
3. #11721750C2semidirect
4. C9×#896C2semidirect
5. C3×#63457C2semidirect
6. #11721049C2semidirect
7. #11721049C2semidirect
8. #11721048C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721005C2semidirect
11. #11721003C2semidirect
12. #11721002C2semidirect
13. #11720983C2semidirect
14. #11720981C2semidirect
15. #11720976C2semidirect
21. C2×C4×C3⋊D9C22semidirect
24. C2×C3×D36C22semidirect
25. C2×C3×D36C22semidirect
26. C2×C3×C4×D9C22semidirect
27. C2×C9×Dic6C22semidirect
31. C2×#6192C22semidirect
32. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C2×Dic3×D9C22semidirect
35. C2×Dic3×D9C22semidirect
38. C3×C9×C4⋊C4C22semidirect
39. #88536C22semidirect
40. #88536C22semidirect
41. #88536C22semidirect
42. #88534C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C9×Dic3⋊C4C22semidirect
48. C9×Dic3⋊C4C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
77. #63457D3semidirect
119. #6192D4semidirect
176. C2×D36C2×D3semidirect
177. C2×D36C2×D3semidirect
183. C2×C4×D9C2×D3semidirect
187. C9×C4⋊C4C2×D3semidirect
201. (C2×D9)⋊C4C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
215. C2×D3×C9#41semidirect
250. #896D9semidirect
401. C2×Dic6C2×D9semidirect
405. C3×C4⋊C4C2×D9semidirect
437. Dic3⋊C4C2×D9semidirect
438. Dic3⋊C4C2×D9semidirect
528. C3×C9#546semidirect
658. C4⋊C4D3×D9semidirect
720. C2×D3#3701semidirect
746. C9#5610semidirect
838. C3#10589732semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D362
C2×#886342
#117217502
C9×#8962
C3×#634572
#117210492
#117210482
D9×(C2×D3)⋊C42
#117210052
#117210032
#117210022
#117209832
#117209812
#117209762
#105946223
#105897323