Finite Group Databasebeta

← C3×#10595176 #13174739

Subgroups — C3×#10595176 #13174739

Order 1728.

1330 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64144C211yesmaximal, characteristic, complemented
2C32×#937C211yesmaximal, characteristic
3C32×#936C211yesmaximal, characteristic, complemented
4C3×#67⋊Dic3C212yesmaximal, complemented
5C3×#63969C212yesmaximal, complemented
6C3×D3×#217C212yesmaximal, complemented
7C3×#63956C212yesmaximal, complemented
8C3×#63887C212yesmaximal, complemented
9C3×#63877C212yesmaximal, complemented
10C3×#5679—31nomaximal
11C3×#5587—31nomaximal
12#10595176C311yesmaximal, characteristic, direct product factor
13C23×C32×D3C2211yescharacteristic
14C2×C33×D4C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
16C2×C32×#67C2212yes—
17C2×C32×Dic6C2211yescharacteristic, complemented
18C2×C3×D3×Dic3C2212yes—
19C2×C3×D3×Dic3C2212yes—
20C3×#3757C2212yes—
21C3×#3757C2211yescharacteristic, complemented
22C3×#3750C2212yescomplemented
23C32×#217C2211yescharacteristic
24C32×#217C2212yes—
25C32×#217C2212yescomplemented
26C32×(C2×D3)⋊C4C2212yes—
27C32×C4×Dic3C2211yescharacteristic, complemented
28C3×#3724C2212yescomplemented
29C3×Dic3⋊Dic3C2212yescomplemented
30C3×Dic3⋊Dic3C2212yescomplemented
31C3×(C2×D3)⋊Dic3C2212yes—
32C3×(C2×D3)⋊Dic3C2212yes—
33C3×Dic32C2212yescomplemented
34C32×#124—31no—
35C32×#120—31no—
36#64144C2×C311yescharacteristic, complemented
37C2×C3×#217—32no—
38C3×#946—32no—
39C3×#937—21no—
40C3×#937D311yescharacteristic
41C3×#937C2×C311yescharacteristic
42C3×#936—21no—
43C3×#936D311yescharacteristic, complemented
44C3×#936C2×C311yescharacteristic, complemented
45C3×#935—31no—
46C3×#935—31no—
47C3×#935—32no—
48C3×#935—61no—
49C3×D4×Dic3—32no—
50C3×#883—32no—
51C3×#67⋊C4—32no—
52C3×D3×C22⋊C4—32no—
53C3×#879—32no—
54C3×#879—32no—
55C3×#878—32no—
56C3×#877—32no—
57C3×#872—32no—
58#67⋊Dic3C2×C312yescomplemented
59#63969C2×C312yescomplemented
60D3×#217C2×C312yescomplemented
61#63956C2×C312yescomplemented
62#63887C2×C312yescomplemented
63#63877C2×C312yescomplemented
64C23×C33C2311yescharacteristic
65C23×C33C2311yescharacteristic
66C22×C32×D3—24no—
67C22×C32×D3—41no—
68C22×C32×D3C2312yes—
69C33×D4—41no—
70C2×C33×C4C2311yescharacteristic
71C2×C3×C3⋊Dic3—41no—
72C2×C3×C3⋊Dic3C2312yes—
73C2×C3×C3⋊Dic3C2312yes—
74C32×#67—24no—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78C32×Dic6—41no—
79C3×D3×Dic3—24no—
80C3×D3×Dic3—42no—
81C3×#551—91no—
82#5679—31no—
83#5587—31no—
84C24×C32—31no—
85C23×C3×D3—21no—
86C23×C3×D3C2×D311yescharacteristic
87C23×C3×D3C22×C311yescharacteristic
88C2×C32×Q8—31no—
89C2×C32×D4—21no—
90C2×C32×D4—21no—
91C2×C32×D4—21no—
92C2×C32×D4—32no—
93C2×C32×D4—41no—
94C2×C32×D4C2×D311yescharacteristic
95C2×C32×D4C2×D311yescharacteristic
96C2×C32×D4C22×C311yescharacteristic
97C22×C3⋊Dic3C22×C311yescharacteristic, complemented
98C2×C3×#67—22no—
99C2×C3×#67C2×D312yes—
100C2×C3×#67C22×C312yes—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C22×C3×Dic3—32no—
104C22×C3×Dic3—32no—
105C22×C3×Dic3—61no—
106C2×C3×C4×D3—32no—
107C2×C3×C4×D3—32no—
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2×D311yescharacteristic, complemented
110C2×C3×Dic6C22×C311yescharacteristic, complemented
111C2×D3×Dic3C22×C312yes—
112C2×D3×Dic3C22×C312yes—
113C32×C22⋊C4—31no—
114C32×C22⋊C4—32no—
115C32×C22⋊C4—32no—
116C32×C22⋊C4—32no—
117C32×C42—31no—
118#3757C22×C312yes—
119#3757C22×C311yescharacteristic, complemented
120#3750C22×C312yescomplemented
121C3×#217—22no—
122C3×#217—21no—
123C3×#217—22no—
124C3×#217—32no—
125C3×#217—32no—
126C3×#217—31no—
127C3×#217—31no—
128C3×#217—32no—
129C3×#217—32no—
130C3×#217—62no—
131C3×#217—61no—
132C3×#217C2×D311yescharacteristic
133C3×#217C2×D312yes—
134C3×#217C2×D312yescomplemented
135C3×#217C22×C312yes—
136C3×#217C22×C311yescharacteristic
137C3×#217C22×C312yescomplemented
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4C2×D312yes—
142C3×(C2×D3)⋊C4C22×C312yes—
143C3×C4⋊Dic3—32no—
144C3×C4⋊Dic3—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—62no—
152C3×C4×Dic3—21no—
153C3×C4×Dic3—32no—
154C3×C4×Dic3—32no—
155C3×C4×Dic3C2×D311yescharacteristic, complemented
156C3×C4×Dic3C22×C311yescharacteristic, complemented
157#3724C22×C312yescomplemented
158Dic3⋊Dic3C22×C312yescomplemented
159Dic3⋊Dic3C22×C312yescomplemented
160(C2×D3)⋊Dic3C22×C312yes—
161(C2×D3)⋊Dic3C22×C312yes—
162Dic32C22×C312yescomplemented
163C22×C33—22no—
164C22×C33—22no—
165C22×C33—21no—
166C22×C33—21no—
167C22×C33C2411yescharacteristic
168C2×C32×D3—22no—
169C2×C32×D3—22no—
170C2×C32×D3—44no—
171C2×C32×D3#4114yes—
172C33×C4—21no—
173C3×C3⋊Dic3—22no—
174C3×C3⋊Dic3—22no—
175C32×Dic3—22no—
176C32×Dic3—22no—
177C32×Dic3—22no—
178C3×#126—92no—
179C3×#124—31no—
180C3×#124—31no—
181C3×#124—61no—
182C3×#123—92no—
183C3×#123—91no—
184C3×C22⋊Q8—92no—
185C3×#120—31no—
186C3×#120—31no—
187C3×#120—61no—
188C3×C4×D4—92no—
189C3×#117—92no—
190C2×C3×C22⋊C4—92no—
191C2×#217—32no—
192#946—32no—
193#937C3×D311yescharacteristic
194#936C3×D311yescharacteristic, complemented
195#935—31no—
196#935—31no—
197#935—32no—
198#935—61no—
199D4×Dic3—32no—
200#883—32no—
201#67⋊C4—32no—
202D3×C22⋊C4—32no—
203#879—32no—
204#879—32no—
205#878—32no—
206#877—32no—
207#872—32no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—32no—
215C23×C32—41no—
216C23×C32—41no—
217C23×C32—64no—
218C23×C32—121no—
219C23×C32C22×D311yescharacteristic
220C23×C32C22×D311yescharacteristic
221C23×C32C22×D311yescharacteristic
222C23×C32C22×D311yescharacteristic
223C23×C32C23×C311yescharacteristic
224C23×C32C23×C311yescharacteristic
225C22×C3×D3—24no—
226C22×C3×D3—24no—
227C22×C3×D3—22no—
228C22×C3×D3—44no—
229C22×C3×D3—41no—
230C22×C3×D3—41no—
231C22×C3×D3—42no—
232C22×C3×D3C22×D312yes—
233C22×C3×D3C23×C312yes—
234C32×Q8—121no—
235C32×D4—41no—
236C32×D4—41no—
237C32×D4—41no—
238C32×D4—42no—
239C32×D4—42no—
240C32×D4—42no—
241C32×D4—44no—
242C32×D4—64no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—32no—
247C2×C32×C4—32no—
248C2×C32×C4—32no—
249C2×C32×C4—41no—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C23×C311yescharacteristic
253C2×C3⋊Dic3—41no—
254C2×C3⋊Dic3C23×C312yes—
255C2×C3⋊Dic3C23×C312yes—
256C3×#67—24no—
257C3×#67—24no—
258C3×#67—44no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3—64no—
269C2×C3×Dic3—122no—
270C2×C3×Dic3—121no—
271C2×C3×Dic3—121no—
272C2×C3×Dic3—122no—
273C2×C3×Dic3C22×D312yes—
274C2×C3×Dic3C22×D312yes—
275C2×C3×Dic3C22×D312yes—
276C2×C3×Dic3C23×C312yes—
277C2×C3×Dic3C23×C312yes—
278C2×C3×Dic3C23×C312yes—
279C3×C4×D3—64no—
280C3×C4×D3—122no—
281C3×Dic6—41no—
282C3×Dic6—41no—
283C3×Dic6—42no—
284D3×Dic3—24no—
285D3×Dic3—42no—
286#551—91noSylow
287C2×C33—41no—
288C2×C33—41no—
289C2×C33C2×#4112yes—
290C2×C33H(5,𝔽2)11yescharacteristic
291C32×D3—24no—
292C24×C3—31no—
293C24×C3—31no—
294C24×C3—61no—
295C23×D3C2×C3×D311yescharacteristic
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—32no—
303C2×C3×D4—32no—
304C2×C3×D4—41no—
305C2×C3×D4—62no—
306C2×C3×D4D3211yescharacteristic
307C2×C3×D4C2×C3×D311yescharacteristic
308C2×C3×D4C2×C3×D311yescharacteristic
309C22×C3×C4—92no—
310C22×C3×C4—92no—
311C22×C3×C4—91no—
312C2×#67C2×C3×D312yes—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—32no—
316C22×Dic3—32no—
317C22×Dic3—61no—
318C2×C4×D3—32no—
319C2×C4×D3—32no—
320C2×Dic6C2×C3×D311yescharacteristic, complemented
321C3×C4⋊C4—92no—
322C3×C4⋊C4—92no—
323C3×C4⋊C4—92no—
324C3×C4⋊C4—92no—
325C3×C22⋊C4—32no—
326C3×C22⋊C4—31no—
327C3×C22⋊C4—32no—
328C3×C22⋊C4—31no—
329C3×C22⋊C4—32no—
330C3×C22⋊C4—32no—
331C3×C22⋊C4—32no—
332C3×C22⋊C4—32no—
333C3×C22⋊C4—62no—
334C3×C22⋊C4—61no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—62no—
337C3×C22⋊C4—92no—
338C3×C22⋊C4—92no—
339C3×C22⋊C4—92no—
340C3×C22⋊C4—91no—
341C3×C42—31no—
342C3×C42—31no—
343C3×C42—61no—
344C3×C42—92no—
345#217—32no—
346#217—32no—
347#217—31no—
348#217—31no—
349#217—32no—
350#217—32no—
351#217—62no—
352#217—61no—
353#217C2×C3×D311yescharacteristic
354#217C2×C3×D312yes—
355#217C2×C3×D312yescomplemented
356(C2×D3)⋊C4—32no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4C2×C3×D312yes—
359C4⋊Dic3—32no—
360C4⋊Dic3—32no—
361Dic3⋊C4—32no—
362Dic3⋊C4—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—32no—
365Dic3⋊C4—32no—
366Dic3⋊C4—32no—
367Dic3⋊C4—62no—
368C4×Dic3—32no—
369C4×Dic3—32no—
370C4×Dic3C2×C3×D311yescharacteristic, complemented
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—22no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—34no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—42no—
395C22×C32—42no—
396C22×C32—42no—
397C22×C32—42no—
398C22×C32—42no—
399C22×C32—42no—
400C22×C32—42no—
401C22×C32—42no—
402C22×C32—62no—
403C22×C32—62no—
404C22×C32—82no—
405C22×C32—82no—
406C22×C32—124no—
407C22×C32C23×D311yescharacteristic
408C22×C32C23×D311yescharacteristic
409C22×C32C24×C311yescharacteristic
410C2×C3×D3—22no—
411C2×C3×D3—22no—
412C2×C3×D3—22no—
413C2×C3×D3—22no—
414C2×C3×D3—24no—
415C2×C3×D3—42no—
416C2×C3×D3—42no—
417C2×C3×D3—44no—
418C2×C3×D3—44no—
419C2×C3×D3—48no—
420C2×C3×D3#23714yes—
421C2×C3×D3C3×#4114yes—
422C32×C4—21no—
423C32×C4—22no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—42no—
429C32×C4—62no—
430C32×C4—62no—
431C32×C4—62no—
432C3⋊Dic3—22no—
433C3⋊Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—42no—
441C3×Dic3—42no—
442C3×Dic3—42no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—62no—
446C3×Dic3—62no—
447C3×Dic3—122no—
448C3×Dic3—122no—
449#126—92no—
450#124—31no—
451#123—92no—
452#123—91no—
453C22⋊Q8—92no—
454#120—31no—
455C4×D4—92no—
456#117—92no—
457C2×C22⋊C4—92no—
458C33#55111yescharacteristic, complemented, Sylow
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—32no—
466C23×C3—32no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—62no—
470C23×C3—64no—
471C23×C3—64no—
472C23×C3—124no—
473C23×C3—121no—
474C23×C3—121no—
475C23×C3—122no—
476C23×C3C2×D3211yescharacteristic
477C23×C3C2×D3211yescharacteristic
478C23×C3C22×C3×D311yescharacteristic
479C23×C3C22×C3×D311yescharacteristic
480C23×C3C22×C3×D311yescharacteristic
481C23×C3C22×C3×D311yescharacteristic
482C22×D3—24no—
483C22×D3—41no—
484C22×D3C22×C3×D312yes—
485C3×Q8—121no—
486C3×Q8—121no—
487C3×Q8—122no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—42no—
492C3×D4—42no—
493C3×D4—42no—
494C3×D4—44no—
495C3×D4—64no—
496C3×D4—64no—
497C3×D4—124no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—41no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—92no—
512C2×C3×C4—92no—
513C2×C3×C4—184no—
514C2×C3×C4—362no—
515C2×C3×C4—361no—
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C22×C3×D311yescharacteristic
518C2×C3×C4C22×C3×D311yescharacteristic
519#67—24no—
520C2×Dic3—32no—
521C2×Dic3—32no—
522C2×Dic3—32no—
523C2×Dic3—32no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—64no—
527C2×Dic3—122no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3C22×C3×D312yes—
532C2×Dic3C22×C3×D312yes—
533C2×Dic3C22×C3×D312yes—
534C4×D3—64no—
535C4×D3—122no—
536Dic6—41no—
537C2×C32—22no—
538C2×C32—21no—
539C2×C32—22no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—22no—
543C2×C32—42no—
544C2×C32—41no—
545C2×C32—41no—
546C2×C32—41no—
547C2×C32—42no—
548C2×C32—42no—
549C2×C32—41no—
550C2×C32—41no—
551C2×C32—41no—
552C2×C32—41no—
553C2×C32—64no—
554C2×C32—81no—
555C2×C32—81no—
556C2×C32—81no—
557C2×C32—81no—
558C2×C32—82no—
559C2×C32—82no—
560C2×C32C2×#23712yes—
561C2×C32#100411yescharacteristic
562C2×C32#100411yescharacteristic
563C2×C32D3×#4112yes—
564C2×C32C2×C3×#4112yes—
565C2×C32C3×H(5,𝔽2)11yescharacteristic
566C3×D3—24no—
567C3×D3—24no—
568C3×D3—44no—
569C24—31no—
570C2×Q8—31no—
571C2×D4—32no—
572C2×D4C3×D3211yescharacteristic
573C22×C4—92no—
574C22×C4—92no—
575C22×C4—91no—
576C4⋊C4—92no—
577C4⋊C4—92no—
578C4⋊C4—92no—
579C4⋊C4—92no—
580C22⋊C4—32no—
581C22⋊C4—32no—
582C22⋊C4—31no—
583C22⋊C4—32no—
584C22⋊C4—92no—
585C22⋊C4—92no—
586C22⋊C4—92no—
587C22⋊C4—91no—
588C42—31no—
589C42—92no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—34no—
608C22×C3—34no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—64no—
623C22×C3—62no—
624C22×C3—62no—
625C22×C3—62no—
626C22×C3—62no—
627C22×C3—82no—
628C22×C3—82no—
629C22×C3—122no—
630C22×C3—122no—
631C22×C3—124no—
632C22×C3—124no—
633C22×C3—128no—
634C22×C3C22×D3211yescharacteristic
635C22×C3C23×C3×D311yescharacteristic
636C22×C3C23×C3×D311yescharacteristic
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—44no—
640C2×D3C3×#23714yes—
641C3×C4—22no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—42no—
648C3×C4—62no—
649C3×C4—62no—
650C3×C4—62no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—122no—
655C3×C4—122no—
656C3×C4—122no—
657C3×C4—182no—
658C3×C4—182no—
659Dic3—22no—
660Dic3—22no—
661Dic3—22no—
662Dic3—62no—
663Dic3—62no—
664Dic3—62no—
665Dic3—62no—
666Dic3—122no—
667Dic3—122no—
668C32—21no—
669C32—21no—
670C32—21no—
671C32—41no—
672C32#558711yescharacteristic, complemented
673C32#567911yescharacteristic, complemented
674C32C3×#55111yescharacteristic, complemented
675C23—32no—
676C23—64no—
677C23—121no—
678C23C2×C3×D3211yescharacteristic
679C23C2×C3×D3211yescharacteristic
680Q8—121no—
681D4—41no—
682D4—64no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—92no—
687C2×C4—92no—
688C2×C4—184no—
689C2×C4—362no—
690C2×C4—361no—
691C2×C4C2×C3×D3211yescharacteristic
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—22no—
696C2×C3—22no—
697C2×C3—22no—
698C2×C3—42no—
699C2×C3—42no—
700C2×C3—41no—
701C2×C3—41no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—42no—
708C2×C3—64no—
709C2×C3—64no—
710C2×C3—81no—
711C2×C3—81no—
712C2×C3—81no—
713C2×C3—81no—
714C2×C3—82no—
715C2×C3—82no—
716C2×C3—124no—
717C2×C3D3×#23712yes—
718C2×C3#6433011yescharacteristic
719C2×C3C2×C3×#23712yes—
720C2×C3C3×#100411yescharacteristic
721C2×C3C3×#100411yescharacteristic
722C2×C3C3×D3×#4112yes—
723D3—24no—
724C22—21no—
725C22—21no—
726C22—22no—
727C22—22no—
728C22—34no—
729C22—62no—
730C22—62no—
731C22—124no—
732C22C22×C3×D3211yescharacteristic
733C4—21no—
734C4—62no—
735C4—62no—
736C4—62no—
737C4—182no—
738C4—182no—
739C3—21no—
740C3—21no—
741C3—21no—
742C3—41no—
743C3#1059517611yescharacteristic, direct product factor
744C3C3×#558711yescharacteristic, complemented
745C3C3×#567911yescharacteristic, complemented
746C2—41no—
747C2—41no—
748C2—64no—
749C2C3×D3×#23712yes—
750C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC32×#937C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64144C2semidirect
3. C32×#936C2semidirect
4. C3×#67⋊Dic3C2semidirect
5. C3×#63969C2semidirect
6. C3×D3×#217C2semidirect
7. C3×#63956C2semidirect
8. C3×#63887C2semidirect
9. C3×#63877C2semidirect
12. #10595176C3direct (N × H)
15. C22×C3×C3⋊Dic3C22semidirect
17. C2×C32×Dic6C22semidirect
21. C3×#3757C22semidirect
22. C3×#3750C22semidirect
25. C32×#217C22semidirect
27. C32×C4×Dic3C22semidirect
28. C3×#3724C22semidirect
29. C3×Dic3⋊Dic3C22semidirect
30. C3×Dic3⋊Dic3C22semidirect
33. C3×Dic32C22semidirect
36. #64144C2×C3semidirect
43. C3×#936D3semidirect
44. C3×#936C2×C3semidirect
58. #67⋊Dic3C2×C3semidirect
59. #63969C2×C3semidirect
60. D3×#217C2×C3semidirect
61. #63956C2×C3semidirect
62. #63887C2×C3semidirect
63. #63877C2×C3semidirect
97. C22×C3⋊Dic3C22×C3semidirect
109. C2×C3×Dic6C2×D3semidirect
110. C2×C3×Dic6C22×C3semidirect
119. #3757C22×C3semidirect
120. #3750C22×C3semidirect
134. C3×#217C2×D3semidirect
137. C3×#217C22×C3semidirect
155. C3×C4×Dic3C2×D3semidirect
156. C3×C4×Dic3C22×C3semidirect
157. #3724C22×C3semidirect
158. Dic3⋊Dic3C22×C3semidirect
159. Dic3⋊Dic3C22×C3semidirect
162. Dic32C22×C3semidirect
194. #936C3×D3semidirect
320. C2×Dic6C2×C3×D3semidirect
355. #217C2×C3×D3semidirect
370. C4×Dic3C2×C3×D3semidirect
458. C33#551semidirect
672. C32#5587semidirect
673. C32#5679semidirect
674. C32C3×#551semidirect
743. C3#10595176direct (N × H)
744. C3C3×#5587semidirect
745. C3C3×#5679semidirect

Maximal subgroups

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

subgroupindex
C3×#641442
C32×#9372
C32×#9362
C3×#67⋊Dic32
C3×#639692
C3×D3×#2172
C3×#639562
C3×#638872
C3×#638772
C3×#56793
C3×#55873
#105951763