Finite Group Databasebeta

← C3×#10595208 #13174757

Subgroups — C3×#10595208 #13174757

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×#64146C211yesmaximal, characteristic
2C32×#936C211yesmaximal, characteristic, complemented
3C32×#935C211yesmaximal, characteristic, complemented
4C3×#63975C212yesmaximal, complemented
5C3×#63974C212yesmaximal, complemented
6C3×#63956C212yesmaximal, complemented
7C3×#63952C212yesmaximal, complemented
8C3×#63888C212yesmaximal, complemented
9C3×#63836C212yesmaximal, complemented
10C3×#5679—31nomaximal
11C3×#5659—31nomaximal
12#10595208C311yesmaximal, characteristic, direct product factor
13C23×C3×C3⋊D3C2211yescharacteristic
14C2×C33×D4C2211yescharacteristic
15C2×C3×#638C2212yes—
16C22×C32×Dic3C2211yescharacteristic, complemented
17C2×C32×Dic6C2211yescharacteristic, complemented
18C2×C3×#624C2212yes—
19C2×C3×#624C2212yes—
20C3×#3757C2211yescharacteristic
21C3×#3752C2212yes—
22C32×#217C2212yes—
23C32×#217C2212yes—
24C32×#217C2212yescomplemented
25C32×#217C2211yescharacteristic, complemented
26C32×Dic3⋊C4C2212yescomplemented
27C32×C4×Dic3C2211yescharacteristic, complemented
28C3×#3724C2212yescomplemented
29C3×Dic3⋊Dic3C2212yescomplemented
30C3×Dic3⋊Dic3C2212yescomplemented
31C3×#3722C2212yes—
32C3×#3722C2212yes—
33C3×Dic32C2212yescomplemented
34C32×#124—31no—
35C32×#123—31no—
36#64146C2×C311yescharacteristic
37C3×#946—32no—
38C3×#937—31no—
39C3×#937—31no—
40C3×#937—61no—
41C3×#936—21no—
42C3×#936D311yescharacteristic, complemented
43C3×#936C2×C311yescharacteristic, complemented
44C3×#935—21no—
45C3×#935D311yescharacteristic, complemented
46C3×#935C2×C311yescharacteristic, complemented
47C3×C4×#67—32no—
48C3×#896—32no—
49C3×#892—32no—
50C3×#883—32no—
51C3×#883—32no—
52C3×#67⋊C4—32no—
53C3×D3×C22⋊C4—32no—
54C3×D3×C22⋊C4—32no—
55C3×#879—32no—
56C3×#879—32no—
57C3×#872—32no—
58#63975C2×C312yescomplemented
59#63974C2×C312yescomplemented
60#63956C2×C312yescomplemented
61#63952C2×C312yescomplemented
62#63888C2×C312yescomplemented
63#63836C2×C312yescomplemented
64C23×C33C2311yescharacteristic
65C23×C33C2311yescharacteristic
66C22×C3×C3⋊D3—24no—
67C22×C3×C3⋊D3—41no—
68C22×C3×C3⋊D3C2312yes—
69C33×D4—41no—
70C2×C33×C4C2311yescharacteristic
71C3×#638—24no—
72C2×C3×C3⋊Dic3C2312yes—
73C2×C32×Dic3—41no—
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78C32×Dic6—41no—
79C3×#624—24no—
80C3×#624—42no—
81C3×#551—91no—
82#5679—31no—
83#5659—31no—
84C23×C3⋊D3C22×C311yescharacteristic
85C23×C3×D3—31no—
86C23×C3×D3—31no—
87C23×C3×D3—61no—
88C2×C32×Q8—31no—
89C2×C32×D4—21no—
90C2×C32×D4—21no—
91C2×C32×D4—21no—
92C2×C32×D4—41no—
93C2×C32×D4C2×D311yescharacteristic
94C2×C32×D4C2×D311yescharacteristic
95C2×C32×D4C22×C311yescharacteristic
96C22×C32×C4—31no—
97C2×#638C22×C312yes—
98C2×C3×#67—32no—
99C2×C3×#67—32no—
100C2×C3×#67—62no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3C2×D311yescharacteristic, complemented
103C22×C3×Dic3C22×C311yescharacteristic, complemented
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—32no—
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×#624C22×C312yes—
112C2×#624C22×C312yes—
113C32×C4⋊C4—32no—
114C32×C22⋊C4—32no—
115C32×C22⋊C4—32no—
116C32×C22⋊C4—32no—
117C32×C22⋊C4—31no—
118C32×C42—31no—
119#3757C22×C311yescharacteristic
120#3752C22×C312yes—
121C3×#217—22no—
122C3×#217—22no—
123C3×#217—21no—
124C3×#217—22no—
125C3×#217—31no—
126C3×#217—31no—
127C3×#217—61no—
128C3×#217C2×D312yes—
129C3×#217C2×D312yes—
130C3×#217C2×D311yescharacteristic, complemented
131C3×#217C2×D312yescomplemented
132C3×#217C22×C312yes—
133C3×#217C22×C312yes—
134C3×#217C22×C311yescharacteristic, complemented
135C3×#217C22×C312yescomplemented
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—62no—
143C3×C4⋊Dic3—32no—
144C3×C4⋊Dic3—32no—
145C3×Dic3⋊C4—22no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4C2×D312yescomplemented
151C3×Dic3⋊C4C22×C312yescomplemented
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#3722C22×C312yes—
161#3722C22×C312yes—
162Dic32C22×C312yescomplemented
163C22×C33—22no—
164C22×C33—22no—
165C22×C33—21no—
166C22×C33—21no—
167C22×C33C2411yescharacteristic
168C2×C3×C3⋊D3—22no—
169C2×C3×C3⋊D3—22no—
170C2×C3×C3⋊D3—44no—
171C2×C3×C3⋊D3#4114yes—
172C33×C4—21no—
173C3×C3⋊Dic3—22no—
174C32×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—31no—
183C3×#123—31no—
184C3×#123—61no—
185C3×#123—92no—
186C3×C22⋊Q8—92no—
187C3×#120—91no—
188C3×C4×D4—92no—
189C3×#117—92no—
190C2×C3×C22⋊C4—92no—
191#946—32no—
192#937—31no—
193#937—31no—
194#937—61no—
195#936C3×D311yescharacteristic, complemented
196#935C3×D311yescharacteristic, complemented
197C4×#67—32no—
198#896—32no—
199#892—32no—
200#883—32no—
201#883—32no—
202#67⋊C4—32no—
203D3×C22⋊C4—32no—
204D3×C22⋊C4—32no—
205#879—32no—
206#879—32no—
207#872—32no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—41no—
215C23×C32—41no—
216C23×C32C22×D311yescharacteristic
217C23×C32C22×D311yescharacteristic
218C23×C32C22×D311yescharacteristic
219C23×C32C22×D311yescharacteristic
220C23×C32C23×C311yescharacteristic
221C23×C32C23×C311yescharacteristic
222C22×C3⋊D3—24no—
223C22×C3⋊D3—41no—
224C22×C3⋊D3C23×C312yes—
225C22×C3×D3—32no—
226C22×C3×D3—32no—
227C22×C3×D3—62no—
228C22×C3×D3—64no—
229C22×C3×D3—64no—
230C22×C3×D3—124no—
231C22×C3×D3—121no—
232C22×C3×D3—121no—
233C22×C3×D3—122no—
234C32×Q8—121no—
235C32×D4—41no—
236C32×D4—41no—
237C32×D4—41no—
238C32×D4—42no—
239C32×D4—42no—
240C32×D4—42no—
241C32×D4—44no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—32no—
246C2×C32×C4—32no—
247C2×C32×C4—32no—
248C2×C32×C4—32no—
249C2×C32×C4—41no—
250C2×C32×C4—121no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C23×C311yescharacteristic
254#638—24no—
255C2×C3⋊Dic3C23×C312yes—
256C3×#67—64no—
257C3×#67—64no—
258C3×#67—124no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3—42no—
268C2×C3×Dic3—62no—
269C2×C3×Dic3C22×D312yes—
270C2×C3×Dic3C22×D312yes—
271C2×C3×Dic3C22×D312yes—
272C2×C3×Dic3C22×D312yes—
273C2×C3×Dic3C23×C312yes—
274C2×C3×Dic3C23×C312yes—
275C2×C3×Dic3C23×C312yes—
276C2×C3×Dic3C23×C312yes—
277C3×C4×D3—64no—
278C3×C4×D3—64no—
279C3×C4×D3—122no—
280C3×C4×D3—122no—
281C3×Dic6—41no—
282C3×Dic6—41no—
283C3×Dic6—42no—
284#624—24no—
285#624—42no—
286#551—91noSylow
287C2×C33—41no—
288C2×C33—41no—
289C2×C33C2×#4112yes—
290C2×C33H(5,𝔽2)11yescharacteristic
291C3×C3⋊D3—24no—
292C24×C3—91no—
293C23×D3—31no—
294C23×D3—31no—
295C23×D3—61no—
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—41no—
303C2×C3×D4—92no—
304C2×C3×D4D3211yescharacteristic
305C2×C3×D4C2×C3×D311yescharacteristic
306C2×C3×D4C2×C3×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—92no—
311C22×C3×C4—92no—
312C2×#67—32no—
313C2×#67—32no—
314C2×#67—62no—
315C22×Dic3C2×C3×D311yescharacteristic, complemented
316C2×C4×D3—32no—
317C2×C4×D3—32no—
318C2×C4×D3—32no—
319C2×C4×D3—32no—
320C2×Dic6C2×C3×D311yescharacteristic, complemented
321C3×C4⋊C4—32no—
322C3×C4⋊C4—32no—
323C3×C4⋊C4—62no—
324C3×C4⋊C4—92no—
325C3×C4⋊C4—92no—
326C3×C4⋊C4—92no—
327C3×C22⋊C4—32no—
328C3×C22⋊C4—32no—
329C3×C22⋊C4—32no—
330C3×C22⋊C4—31no—
331C3×C22⋊C4—32no—
332C3×C22⋊C4—32no—
333C3×C22⋊C4—32no—
334C3×C22⋊C4—31no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—62no—
338C3×C22⋊C4—62no—
339C3×C22⋊C4—92no—
340C3×C22⋊C4—92no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4—92no—
343C3×C42—31no—
344C3×C42—31no—
345C3×C42—61no—
346C3×C42—92no—
347#217—31no—
348#217—31no—
349#217—61no—
350#217C2×C3×D312yes—
351#217C2×C3×D312yes—
352#217C2×C3×D311yescharacteristic, complemented
353#217C2×C3×D312yescomplemented
354(C2×D3)⋊C4—32no—
355(C2×D3)⋊C4—32no—
356(C2×D3)⋊C4—32no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—32no—
360(C2×D3)⋊C4—62no—
361C4⋊Dic3—32no—
362C4⋊Dic3—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—32no—
365Dic3⋊C4—32no—
366Dic3⋊C4—32no—
367Dic3⋊C4C2×C3×D312yescomplemented
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—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—22no—
379C22×C32—22no—
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—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—42no—
394C22×C32—42no—
395C22×C32—42no—
396C22×C32—42no—
397C22×C32—42no—
398C22×C32—42no—
399C22×C32—42no—
400C22×C32—42no—
401C22×C32—82no—
402C22×C32—82no—
403C22×C32C23×D311yescharacteristic
404C22×C32C23×D311yescharacteristic
405C22×C32C24×C311yescharacteristic
406C2×C3⋊D3—22no—
407C2×C3⋊D3—22no—
408C2×C3⋊D3—44no—
409C2×C3⋊D3C3×#4114yes—
410C2×C3×D3—34no—
411C2×C3×D3—34no—
412C2×C3×D3—64no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—62no—
416C2×C3×D3—62no—
417C2×C3×D3—122no—
418C2×C3×D3—122no—
419C2×C3×D3—124no—
420C2×C3×D3—124no—
421C2×C3×D3—128no—
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—
432C32×C4—62no—
433C3⋊Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—42no—
443C3×Dic3—42no—
444C3×Dic3—42no—
445C3×Dic3—42no—
446C3×Dic3—62no—
447C3×Dic3—62no—
448C3×Dic3—122no—
449#126—92no—
450#124—31no—
451#123—31no—
452#123—92no—
453C22⋊Q8—92no—
454#120—91no—
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—41no—
466C23×C3—41no—
467C23×C3—92no—
468C23×C3—184no—
469C23×C3—361no—
470C23×C3C2×D3211yescharacteristic
471C23×C3C2×D3211yescharacteristic
472C23×C3C22×C3×D311yescharacteristic
473C23×C3C22×C3×D311yescharacteristic
474C23×C3C22×C3×D311yescharacteristic
475C23×C3C22×C3×D311yescharacteristic
476C22×D3—32no—
477C22×D3—32no—
478C22×D3—62no—
479C22×D3—64no—
480C22×D3—64no—
481C22×D3—124no—
482C22×D3—121no—
483C22×D3—121no—
484C22×D3—122no—
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—184no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
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—62no—
512C2×C3×C4—92no—
513C2×C3×C4—121no—
514C2×C3×C4—121no—
515C2×C3×C4—122no—
516C2×C3×C4—184no—
517C2×C3×C4—362no—
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C22×C3×D311yescharacteristic
520C2×C3×C4C22×C3×D311yescharacteristic
521#67—64no—
522#67—64no—
523#67—124no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—41no—
527C2×Dic3—62no—
528C2×Dic3C22×C3×D312yes—
529C2×Dic3C22×C3×D312yes—
530C2×Dic3C22×C3×D312yes—
531C2×Dic3C22×C3×D312yes—
532C4×D3—64no—
533C4×D3—64no—
534C4×D3—122no—
535C4×D3—122no—
536Dic6—41no—
537C2×C32—22no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—22no—
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—81no—
554C2×C32—81no—
555C2×C32—81no—
556C2×C32—81no—
557C2×C32—82no—
558C2×C32—82no—
559C2×C32#100411yescharacteristic
560C2×C32#100411yescharacteristic
561C2×C32D3×#4112yes—
562C2×C32D3×#4112yes—
563C2×C32C2×C3×#4112yes—
564C2×C32C3×H(5,𝔽2)11yescharacteristic
565C3⋊D3—24no—
566C3×D3—64no—
567C3×D3—64no—
568C3×D3—124no—
569C24—91no—
570C2×Q8—31no—
571C2×D4—92no—
572C2×D4C3×D3211yescharacteristic
573C22×C4—31no—
574C22×C4—92no—
575C22×C4—92no—
576C4⋊C4—32no—
577C4⋊C4—92no—
578C4⋊C4—92no—
579C4⋊C4—92no—
580C22⋊C4—32no—
581C22⋊C4—32no—
582C22⋊C4—32no—
583C22⋊C4—31no—
584C22⋊C4—92no—
585C22⋊C4—92no—
586C22⋊C4—91no—
587C22⋊C4—92no—
588C42—31no—
589C42—92no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—82no—
621C22×C3—82no—
622C22×C3—94no—
623C22×C3—182no—
624C22×C3—182no—
625C22×C3—364no—
626C22×C3C22×D3211yescharacteristic
627C22×C3C23×C3×D311yescharacteristic
628C22×C3C23×C3×D311yescharacteristic
629C2×D3—34no—
630C2×D3—34no—
631C2×D3—64no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—122no—
637C2×D3—122no—
638C2×D3—124no—
639C2×D3—124no—
640C2×D3—128no—
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—62no—
655C3×C4—62no—
656C3×C4—122no—
657C3×C4—122no—
658C3×C4—122no—
659C3×C4—122no—
660C3×C4—182no—
661Dic3—22no—
662Dic3—22no—
663Dic3—22no—
664Dic3—22no—
665Dic3—62no—
666Dic3—62no—
667Dic3—122no—
668C32—21no—
669C32—21no—
670C32—21no—
671C32—41no—
672C32#565911yescharacteristic, complemented
673C32#567911yescharacteristic, complemented
674C32C3×#55111yescharacteristic, complemented
675C23—92no—
676C23—184no—
677C23—361no—
678C23C2×C3×D3211yescharacteristic
679C23C2×C3×D3211yescharacteristic
680Q8—121no—
681D4—41no—
682D4—184no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—92no—
688C2×C4—121no—
689C2×C4—184no—
690C2×C4—362no—
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—81no—
709C2×C3—81no—
710C2×C3—81no—
711C2×C3—81no—
712C2×C3—82no—
713C2×C3—82no—
714C2×C3—184no—
715C2×C3#6431212yes—
716C2×C3#6433011yescharacteristic
717C2×C3C3×#100411yescharacteristic
718C2×C3C3×#100411yescharacteristic
719C2×C3C3×D3×#4112yes—
720C2×C3C3×D3×#4112yes—
721D3—64no—
722D3—64no—
723D3—124no—
724C22—21no—
725C22—21no—
726C22—22no—
727C22—22no—
728C22—94no—
729C22—182no—
730C22—182no—
731C22—364no—
732C22C22×C3×D3211yescharacteristic
733C4—21no—
734C4—62no—
735C4—62no—
736C4—62no—
737C4—62no—
738C4—182no—
739C3—21no—
740C3—21no—
741C3—21no—
742C3—41no—
743C3#1059520811yescharacteristic, direct product factor
744C3C3×#565911yescharacteristic, complemented
745C3C3×#567911yescharacteristic, complemented
746C2—41no—
747C2—41no—
748C2—184no—
749C2C3×#6431212yes—
750C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC3×#64146C2
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
2. C32×#936C2semidirect
3. C32×#935C2semidirect
4. C3×#63975C2semidirect
5. C3×#63974C2semidirect
6. C3×#63956C2semidirect
7. C3×#63952C2semidirect
8. C3×#63888C2semidirect
9. C3×#63836C2semidirect
12. #10595208C3direct (N × H)
16. C22×C32×Dic3C22semidirect
17. C2×C32×Dic6C22semidirect
24. C32×#217C22semidirect
25. C32×#217C22semidirect
26. C32×Dic3⋊C4C22semidirect
27. C32×C4×Dic3C22semidirect
28. C3×#3724C22semidirect
29. C3×Dic3⋊Dic3C22semidirect
30. C3×Dic3⋊Dic3C22semidirect
33. C3×Dic32C22semidirect
42. C3×#936D3semidirect
43. C3×#936C2×C3semidirect
45. C3×#935D3semidirect
46. C3×#935C2×C3semidirect
58. #63975C2×C3semidirect
59. #63974C2×C3semidirect
60. #63956C2×C3semidirect
61. #63952C2×C3semidirect
62. #63888C2×C3semidirect
63. #63836C2×C3semidirect
102. C22×C3×Dic3C2×D3semidirect
103. C22×C3×Dic3C22×C3semidirect
109. C2×C3×Dic6C2×D3semidirect
110. C2×C3×Dic6C22×C3semidirect
130. C3×#217C2×D3semidirect
131. C3×#217C2×D3semidirect
134. C3×#217C22×C3semidirect
135. C3×#217C22×C3semidirect
150. C3×Dic3⋊C4C2×D3semidirect
151. C3×Dic3⋊C4C22×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
195. #936C3×D3semidirect
196. #935C3×D3semidirect
315. C22×Dic3C2×C3×D3semidirect
320. C2×Dic6C2×C3×D3semidirect
352. #217C2×C3×D3semidirect
353. #217C2×C3×D3semidirect
367. Dic3⋊C4C2×C3×D3semidirect
370. C4×Dic3C2×C3×D3semidirect
458. C33#551semidirect
672. C32#5659semidirect
673. C32#5679semidirect
674. C32C3×#551semidirect
743. C3#10595208direct (N × H)
744. C3C3×#5659semidirect
745. C3C3×#5679semidirect

Maximal subgroups

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

subgroupindex
C3×#641462
C32×#9362
C32×#9352
C3×#639752
C3×#639742
C3×#639562
C3×#639522
C3×#638882
C3×#638362
C3×#56793
C3×#56593
#105952083