Finite Group Databasebeta

← C3×#10595168 #13174731

Subgroups — C3×#10595168 #13174731

Order 1728.

1810 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3C32×#940C211yesmaximal, characteristic, complemented
4C32×#936C211yesmaximal, characteristic, complemented
5C3×#63981C214yesmaximal, complemented
6C3×#63971C214yesmaximal, complemented
7C3×#63911C211yesmaximal, characteristic, complemented
8C3×#63874C211yesmaximal, characteristic, complemented
9C3×#63864C211yesmaximal, characteristic, complemented
10C3×#5715—31nomaximal
11C3×#5674—31nomaximal
12#10595168C311yesmaximal, characteristic, direct product factor
13C23×C3×C3⋊D3C2212yes—
14C2×C33×D4C2211yescharacteristic
15C2×C3×#638C2212yes—
16C3×D4×C3⋊D3—24no—
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C32×#67C2214yescomplemented
20C2×C32×D12C2211yescharacteristic, complemented
21C2×C32×Dic6C2211yescharacteristic, complemented
22C2×C3×#626C2212yes—
23C2×C3×#626C2214yescomplemented
24C2×C3×D3×Dic3C2212yescomplemented
25C3×#3796—24no—
26C32×#217C2214yescomplemented
27C32×C4×Dic3C2211yescharacteristic, complemented
28C32×C4×Dic3C2211yescharacteristic, complemented
29C3×#3724C2212yescomplemented
30C3×#3722C2212yes—
31C3×#3722C2214yescomplemented
32C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
33C2×C3×#239—31no—
34C2×C3×#237—31no—
35C2×C3×D3×D4—31no—
36C2×C3×D3×D4—31no—
37C2×C3×D3×D4—61no—
38C2×#3796C2×C311yescharacteristic, complemented
39C32×#127—31no—
40C32×#124—31no—
41C3×#947—31no—
42C3×#940—21no—
43C3×#940—31no—
44C3×#940D311yescharacteristic, complemented
45C3×#940C2×C311yescharacteristic, complemented
46C3×#939—34no—
47C3×#937—34no—
48C3×#936—21no—
49C3×#936D311yescharacteristic, complemented
50C3×#936C2×C311yescharacteristic, complemented
51C3×#884—34no—
52C3×#882—34no—
53C3×#875—31no—
54C3×#874—31no—
55C3×#872—31no—
56C3×#872—31no—
57#63981C2×C314yescomplemented
58#63971C2×C314yescomplemented
59#63911C2×C311yescharacteristic, complemented
60#63874C2×C311yescharacteristic, complemented
61#63864C2×C311yescharacteristic, complemented
62C23×C33C2312yes—
63C22×C3×C3⋊D3—24no—
64C22×C3×C3⋊D3—44no—
65C22×C3×C3⋊D3C2312yes—
66C22×C3×C3⋊D3C2311yescharacteristic
67C22×C32×D3C2312yes—
68C33×D4—22no—
69C2×C33×C4C2311yescharacteristic
70C3×#638—24no—
71C2×C3×C3⋊Dic3C2311yescharacteristic
72C3×C4⋊(C3⋊D3)—22no—
73C3×C4×C3⋊D3D414yescomplemented
74C32×#67—44no—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78C32×D12—22no—
79C32×Dic6—22no—
80C3×#626—24no—
81C3×#626—44no—
82C3×D3×Dic3—24no—
83C3×#535—91no—
84#5715—31no—
85#5674—31no—
86C23×C3⋊D3C22×C312yes—
87C23×C3×D3—32no—
88C23×C3×D3—32no—
89C23×C3×D3—62no—
90C2×C32×Q8—31no—
91C2×C32×D4—21no—
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4—34no—
95C2×C32×D4—31no—
96C2×C32×D4—41no—
97C2×C32×D4C2×D311yescharacteristic
98C2×C32×D4C2×D311yescharacteristic
99C2×C32×D4C22×C311yescharacteristic
100C2×#638C22×C312yes—
101D4×C3⋊D3—24no—
102C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
103C2×C4×C3⋊D3C22×C311yescharacteristic
104C2×C3×#67—24no—
105C2×C3×#67—32no—
106C2×C3×#67—32no—
107C2×C3×#67—32no—
108C2×C3×#67—34no—
109C2×C3×#67—62no—
110C2×C3×#67C2×D314yescomplemented
111C2×C3×#67C22×C314yescomplemented
112C22×C3×Dic3—32no—
113C3×#239—64no—
114C3×#237—64no—
115C3×D3×D4—64no—
116C3×D3×D4—64no—
117C3×D3×D4—68no—
118C2×C3×D12—21no—
119C2×C3×D12—32no—
120C2×C3×D12—31no—
121C2×C3×D12—31no—
122C2×C3×D12—34no—
123C2×C3×D12—61no—
124C2×C3×D12C2×D311yescharacteristic, complemented
125C2×C3×D12C22×C311yescharacteristic, complemented
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—61no—
130C2×C3×Dic6—21no—
131C2×C3×Dic6C2×D311yescharacteristic, complemented
132C2×C3×Dic6C22×C311yescharacteristic, complemented
133C2×#626C22×C312yes—
134C2×#626C22×C314yescomplemented
135C2×D3×Dic3C22×C312yescomplemented
136#3796—24no—
137C32×C22⋊C4—34no—
138C32×C42—31no—
139C32×C42—31no—
140C3×#217—24no—
141C3×#217C2×D314yescomplemented
142C3×#217C22×C314yescomplemented
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—34no—
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4—34no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×C4×Dic3—21no—
150C3×C4×Dic3—21no—
151C3×C4×Dic3C2×D311yescharacteristic, complemented
152C3×C4×Dic3C2×D311yescharacteristic, complemented
153C3×C4×Dic3C22×C311yescharacteristic, complemented
154C3×C4×Dic3C22×C311yescharacteristic, complemented
155#3724C22×C312yescomplemented
156#3722C22×C312yes—
157#3722C22×C314yescomplemented
158C22×C33—22no—
159C22×C33—24no—
160C22×C33C2411yescharacteristic
161C2×C3×C3⋊D3—22no—
162C2×C3×C3⋊D3—22no—
163C2×C3×C3⋊D3—24no—
164C2×C3×C3⋊D3—48no—
165C2×C3×C3⋊D3C2×D412yes—
166C2×C32×D3—22no—
167C2×C32×D3—24no—
168C33×C4C2×D412yes—
169C3×C3⋊Dic3C2×D412yes—
170C32×Dic3—22no—
171C32×Dic3—22no—
172C32×Dic3—22no—
173C2×C3×#41—91no—
174C22×C3×D4—91no—
175C2×#239—31no—
176C2×#237—31no—
177C2×D3×D4—31no—
178C2×D3×D4—31no—
179C2×D3×D4—61no—
180C3×#127—31no—
181C3×#127—31no—
182C3×#127—61no—
183C3×#127—91no—
184C3×#124—31no—
185C3×#124—31no—
186C3×#124—61no—
187C3×#124—91no—
188C3×#121—94no—
189C3×#120—94no—
190C3×#117—91no—
191#947—31no—
192#940—31no—
193#940C3×D311yescharacteristic, complemented
194#939—34no—
195#937—34no—
196#936C3×D311yescharacteristic, complemented
197#884—34no—
198#882—34no—
199#875—31no—
200#874—31no—
201#872—31no—
202#872—31no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—32no—
207C23×C32—42no—
208C23×C32C22×D312yes—
209C23×C32C22×D312yes—
210C23×C32C23×C312yes—
211C22×C3⋊D3—24no—
212C22×C3⋊D3—44no—
213C22×C3⋊D3C23×C312yes—
214C22×C3⋊D3C23×C311yescharacteristic
215C22×C3×D3—22no—
216C22×C3×D3—31no—
217C22×C3×D3—31no—
218C22×C3×D3—32no—
219C22×C3×D3—32no—
220C22×C3×D3—61no—
221C22×C3×D3—62no—
222C22×C3×D3—64no—
223C22×C3×D3—64no—
224C22×C3×D3—68no—
225C22×C3×D3—124no—
226C22×C3×D3—124no—
227C22×C3×D3—128no—
228C22×C3×D3C22×D312yes—
229C22×C3×D3C23×C312yes—
230C32×Q8—62no—
231C32×D4—22no—
232C32×D4—24no—
233C32×D4—22no—
234C32×D4—22no—
235C32×D4—42no—
236C32×D4—42no—
237C32×D4—44no—
238C32×D4—62no—
239C32×D4—124no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—32no—
244C2×C32×C4—32no—
245C2×C32×C4—32no—
246C2×C32×C4—41no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C23×C311yescharacteristic
250#638—24no—
251C2×C3⋊Dic3C23×C311yescharacteristic
252C4⋊(C3⋊D3)—22no—
253C4×C3⋊D3C3×D414yescomplemented
254C3×#67—44no—
255C3×#67—44no—
256C3×#67—48no—
257C3×#67—64no—
258C3×#67—64no—
259C3×#67—64no—
260C3×#67—68no—
261C3×#67—124no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—64no—
269C2×C3×Dic3C22×D312yes—
270C2×C3×Dic3C22×D312yes—
271C2×C3×Dic3C22×D312yes—
272C2×C3×Dic3C23×C312yes—
273C2×C3×Dic3C23×C312yes—
274C2×C3×Dic3C23×C312yes—
275C3×D12—22no—
276C3×D12—22no—
277C3×D12—42no—
278C3×D12—64no—
279C3×D12—64no—
280C3×D12—62no—
281C3×D12—62no—
282C3×D12—124no—
283C3×C4×D3—34no—
284C3×C4×D3—34no—
285C3×C4×D3—64no—
286C3×C4×D3—64no—
287C3×Dic6—22no—
288C3×Dic6—22no—
289C3×Dic6—42no—
290#626—24no—
291#626—44no—
292D3×Dic3—24no—
293#535—91noSylow
294C2×C33—42no—
295C2×C33C22×D411yescharacteristic
296C2×C33H(5,𝔽2)12yes—
297C3×C3⋊D3—22no—
298C3×C3⋊D3—42no—
299C32×D3—42no—
300C24×C3—92no—
301C23×D3—32no—
302C23×D3—32no—
303C23×D3—62no—
304C3×#41—184no—
305C2×C3×Q8—31no—
306C2×C3×Q8—31no—
307C2×C3×Q8—61no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—34no—
312C2×C3×D4—34no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—41no—
316C2×C3×D4—61no—
317C2×C3×D4—64no—
318C2×C3×D4—92no—
319C2×C3×D4—94no—
320C2×C3×D4—92no—
321C2×C3×D4—91no—
322C2×C3×D4—184no—
323C2×C3×D4D3211yescharacteristic
324C2×C3×D4C2×C3×D311yescharacteristic
325C2×C3×D4C2×C3×D311yescharacteristic
326C22×C3×C4—92no—
327C22×C3×C4—91no—
328C2×#67—32no—
329C2×#67—32no—
330C2×#67—32no—
331C2×#67—34no—
332C2×#67—62no—
333C2×#67C2×C3×D314yescomplemented
334C22×Dic3—32no—
335#239—64no—
336#237—64no—
337D3×D4—64no—
338D3×D4—64no—
339D3×D4—68no—
340C2×D12—32no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—34no—
344C2×D12—61no—
345C2×D12C2×C3×D311yescharacteristic, complemented
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—32no—
349C2×C4×D3—61no—
350C2×Dic6C2×C3×D311yescharacteristic, complemented
351C3×C4⋊C4—92no—
352C3×C22⋊C4—34no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—64no—
355C3×C22⋊C4—92no—
356C3×C22⋊C4—94no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—31no—
360C3×C42—31no—
361C3×C42—61no—
362C3×C42—61no—
363#217C2×C3×D314yescomplemented
364(C2×D3)⋊C4—32no—
365(C2×D3)⋊C4—32no—
366(C2×D3)⋊C4—34no—
367(C2×D3)⋊C4—34no—
368Dic3⋊C4—32no—
369Dic3⋊C4—32no—
370C4×Dic3C2×C3×D311yescharacteristic, complemented
371C4×Dic3C2×C3×D311yescharacteristic, complemented
372C22×C32—22no—
373C22×C32—24no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—24no—
377C22×C32—24no—
378C22×C32—24no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—41no—
383C22×C32—42no—
384C22×C32—42no—
385C22×C32—44no—
386C22×C32—44no—
387C22×C32—44no—
388C22×C32—44no—
389C22×C32—62no—
390C22×C32—64no—
391C22×C32—84no—
392C22×C32C23×D311yescharacteristic
393C22×C32C23×D311yescharacteristic
394C22×C32C24×C311yescharacteristic
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—24no—
398C2×C3⋊D3—48no—
399C2×C3⋊D3C2×C3×D412yes—
400C2×C3×D3—22no—
401C2×C3×D3—24no—
402C2×C3×D3—22no—
403C2×C3×D3—24no—
404C2×C3×D3—32no—
405C2×C3×D3—32no—
406C2×C3×D3—42no—
407C2×C3×D3—44no—
408C2×C3×D3—62no—
409C2×C3×D3—64no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—64no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—64no—
416C2×C3×D3—64no—
417C2×C3×D3—124no—
418C2×C3×D3—1216no—
419C2×C3×D3—128no—
420C2×C3×D3—128no—
421C32×C4—22no—
422C32×C4—22no—
423C32×C4—22no—
424C32×C4—42no—
425C32×C4—62no—
426C32×C4—62no—
427C32×C4—62no—
428C32×C4D3×D412yes—
429C32×C4D3×D412yes—
430C32×C4C2×C3×D412yes—
431C3⋊Dic3C2×C3×D412yes—
432C3×Dic3—24no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—32no—
440C3×Dic3—32no—
441C3×Dic3—42no—
442C3×Dic3—42no—
443C3×Dic3—62no—
444C2×#41—91no—
445C22×D4—91no—
446#127—31no—
447#127—91no—
448#124—31no—
449#124—91no—
450#121—94no—
451#120—94no—
452#117—91no—
453C33#53511yescharacteristic, complemented, Sylow
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—32no—
458C23×C3—32no—
459C23×C3—42no—
460C23×C3—62no—
461C23×C3—91no—
462C23×C3—92no—
463C23×C3—184no—
464C23×C3—364no—
465C23×C3C2×D3212yes—
466C23×C3C22×C3×D312yes—
467C23×C3C22×C3×D312yes—
468C22×D3—31no—
469C22×D3—31no—
470C22×D3—32no—
471C22×D3—32no—
472C22×D3—61no—
473C22×D3—62no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—68no—
477C22×D3—124no—
478C22×D3—124no—
479C22×D3—128no—
480C22×D3C22×C3×D312yes—
481C3×Q8—62no—
482C3×Q8—62no—
483C3×Q8—122no—
484C3×D4—24no—
485C3×D4—22no—
486C3×D4—22no—
487C3×D4—22no—
488C3×D4—42no—
489C3×D4—42no—
490C3×D4—44no—
491C3×D4—62no—
492C3×D4—62no—
493C3×D4—122no—
494C3×D4—124no—
495C3×D4—124no—
496C3×D4—128no—
497C3×D4—184no—
498C3×D4—184no—
499C3×D4—182no—
500C3×D4—364no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—41no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—91no—
515C2×C3×C4—94no—
516C2×C3×C4—184no—
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C22×C3×D311yescharacteristic
519C2×C3×C4C22×C3×D311yescharacteristic
520#67—44no—
521#67—64no—
522#67—64no—
523#67—64no—
524#67—68no—
525#67—124no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—64no—
530C2×Dic3C22×C3×D312yes—
531C2×Dic3C22×C3×D312yes—
532C2×Dic3C22×C3×D312yes—
533D12—22no—
534D12—64no—
535D12—64no—
536D12—62no—
537D12—62no—
538D12—124no—
539C4×D3—34no—
540C4×D3—34no—
541C4×D3—64no—
542C4×D3—64no—
543Dic6—22no—
544C2×C32—22no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—22no—
549C2×C32—22no—
550C2×C32—41no—
551C2×C32—42no—
552C2×C32—42no—
553C2×C32—44no—
554C2×C32—42no—
555C2×C32—42no—
556C2×C32—82no—
557C2×C32—82no—
558C2×C32—84no—
559C2×C32—122no—
560C2×C32C2×D3×D411yescharacteristic
561C2×C32C2×D3×D411yescharacteristic
562C2×C32#100412yes—
563C2×C32#100912yes—
564C2×C32C22×C3×D411yescharacteristic
565C2×C32C3×H(5,𝔽2)12yes—
566C3⋊D3—22no—
567C3⋊D3—42no—
568C3×D3—42no—
569C3×D3—42no—
570C3×D3—64no—
571C3×D3—62no—
572C3×D3—62no—
573C3×D3—82no—
574C3×D3—124no—
575C3×D3—122no—
576C3×D3—122no—
577C24—92no—
578#41—184no—
579C2×Q8—31no—
580C2×D4—34no—
581C2×D4—31no—
582C2×D4—92no—
583C2×D4—94no—
584C2×D4—92no—
585C2×D4—91no—
586C2×D4—184no—
587C2×D4C3×D3211yescharacteristic
588C22×C4—92no—
589C22×C4—91no—
590C4⋊C4—92no—
591C22⋊C4—34no—
592C22⋊C4—92no—
593C22⋊C4—94no—
594C42—31no—
595C42—31no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—44no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—44no—
612C22×C3—41no—
613C22×C3—64no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—64no—
617C22×C3—84no—
618C22×C3—92no—
619C22×C3—122no—
620C22×C3—124no—
621C22×C3—182no—
622C22×C3—184no—
623C22×C3—182no—
624C22×C3—368no—
625C22×C3C22×D3211yescharacteristic
626C22×C3C23×C3×D311yescharacteristic
627C22×C3C23×C3×D311yescharacteristic
628C2×D3—22no—
629C2×D3—24no—
630C2×D3—32no—
631C2×D3—32no—
632C2×D3—62no—
633C2×D3—64no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—64no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—124no—
642C2×D3—1216no—
643C2×D3—128no—
644C2×D3—128no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—42no—
649C3×C4—64no—
650C3×C4—62no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—92no—
657C3×C4—122no—
658C3×C4—122no—
659C3×C4#381112yes—
660C3×C4C3×D3×D412yes—
661C3×C4C3×D3×D412yes—
662Dic3—22no—
663Dic3—22no—
664Dic3—22no—
665Dic3—32no—
666Dic3—32no—
667Dic3—62no—
668C32—21no—
669C32—21no—
670C32—21no—
671C32—41no—
672C32#567411yescharacteristic, complemented
673C32#571511yescharacteristic, complemented
674C32C3×#53511yescharacteristic, complemented
675C23—32no—
676C23—91no—
677C23—92no—
678C23—184no—
679C23—364no—
680C23C2×C3×D3212yes—
681Q8—62no—
682D4—22no—
683D4—62no—
684D4—124no—
685D4—184no—
686D4—184no—
687D4—182no—
688D4—364no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—91no—
693C2×C4—94no—
694C2×C4—184no—
695C2×C4C2×C3×D3211yescharacteristic
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—22no—
700C2×C3—22no—
701C2×C3—22no—
702C2×C3—44no—
703C2×C3—42no—
704C2×C3—42no—
705C2×C3—42no—
706C2×C3—41no—
707C2×C3—42no—
708C2×C3—82no—
709C2×C3—82no—
710C2×C3—84no—
711C2×C3—122no—
712C2×C3—122no—
713C2×C3—182no—
714C2×C3—242no—
715C2×C3—362no—
716C2×C3#6431412yes—
717C2×C3C2×#381111yescharacteristic
718C2×C3C2×C3×D3×D411yescharacteristic
719C2×C3C2×C3×D3×D411yescharacteristic
720C2×C3C3×#100412yes—
721C2×C3C3×#100912yes—
722D3—42no—
723D3—64no—
724D3—62no—
725D3—62no—
726D3—124no—
727D3—122no—
728D3—122no—
729C22—22no—
730C22—24no—
731C22—62no—
732C22—64no—
733C22—92no—
734C22—182no—
735C22—182no—
736C22—184no—
737C22—368no—
738C22C22×C3×D3211yescharacteristic
739C4—62no—
740C4—62no—
741C4—62no—
742C4—92no—
743C4C3×#381112yes—
744C3—21no—
745C3—21no—
746C3—21no—
747C3—41no—
748C3#1059516811yescharacteristic, direct product factor
749C3C3×#567411yescharacteristic, complemented
750C3C3×#571511yescharacteristic, complemented
751C2—42no—
752C2—122no—
753C2—182no—
754C2—362no—
755C2C3×#6431412yes—
756C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#535
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. C2×C3×D4×C3⋊D3C2semidirect
2. C2×C3×#3796C2semidirect
3. C32×#940C2semidirect
4. C32×#936C2semidirect
5. C3×#63981C2semidirect
6. C3×#63971C2semidirect
7. C3×#63911C2semidirect
8. C3×#63874C2semidirect
9. C3×#63864C2semidirect
12. #10595168C3direct (N × H)
19. C2×C32×#67C22semidirect
20. C2×C32×D12C22semidirect
21. C2×C32×Dic6C22semidirect
23. C2×C3×#626C22semidirect
24. C2×C3×D3×Dic3C22semidirect
26. C32×#217C22semidirect
27. C32×C4×Dic3C22semidirect
28. C32×C4×Dic3C22semidirect
29. C3×#3724C22semidirect
31. C3×#3722C22semidirect
32. C2×D4×C3⋊D3C2×C3semidirect
38. C2×#3796C2×C3semidirect
44. C3×#940D3semidirect
45. C3×#940C2×C3semidirect
49. C3×#936D3semidirect
50. C3×#936C2×C3semidirect
57. #63981C2×C3semidirect
58. #63971C2×C3semidirect
59. #63911C2×C3semidirect
60. #63874C2×C3semidirect
61. #63864C2×C3semidirect
73. C3×C4×C3⋊D3D4semidirect
110. C2×C3×#67C2×D3semidirect
111. C2×C3×#67C22×C3semidirect
124. C2×C3×D12C2×D3semidirect
125. C2×C3×D12C22×C3semidirect
131. C2×C3×Dic6C2×D3semidirect
132. C2×C3×Dic6C22×C3semidirect
134. C2×#626C22×C3semidirect
135. C2×D3×Dic3C22×C3semidirect
141. C3×#217C2×D3semidirect
142. C3×#217C22×C3semidirect
151. C3×C4×Dic3C2×D3semidirect
152. C3×C4×Dic3C2×D3semidirect
153. C3×C4×Dic3C22×C3semidirect
154. C3×C4×Dic3C22×C3semidirect
155. #3724C22×C3semidirect
157. #3722C22×C3semidirect
193. #940C3×D3semidirect
196. #936C3×D3semidirect
253. C4×C3⋊D3C3×D4semidirect
333. C2×#67C2×C3×D3semidirect
345. C2×D12C2×C3×D3semidirect
350. C2×Dic6C2×C3×D3semidirect
363. #217C2×C3×D3semidirect
370. C4×Dic3C2×C3×D3semidirect
371. C4×Dic3C2×C3×D3semidirect
453. C33#535semidirect
672. C32#5674semidirect
673. C32#5715semidirect
674. C32C3×#535semidirect
748. C3#10595168direct (N × H)
749. C3C3×#5674semidirect
750. C3C3×#5715semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C3×#37962
C32×#9402
C32×#9362
C3×#639812
C3×#639712
C3×#639112
C3×#638742
C3×#638642
C3×#57153
C3×#56743
#105951683