Finite Group Databasebeta

← C3×#10591467 #13158476

Subgroups — C3×#10591467 #13158476

Order 1728.

1160 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic
2C2×C32×#214C211yesmaximal, characteristic, complemented
3C3×#63871C211yesmaximal, characteristic, complemented
4C2×C3×#3717C211yesmaximal, characteristic, complemented
5C32×#832C211yesmaximal, characteristic, complemented
6C3×#63564C211yesmaximal, characteristic, complemented
7C3×#63557C211yesmaximal, characteristic, complemented
8C3×#5169—31nomaximal
9C3×#4776—31nomaximal
10#10591467C311yesmaximal, characteristic, direct product factor
11C23×C3×C3⋊D3—21no—
12C2×C33×D4C2211yescharacteristic
13C2×C3×#638—21no—
14C3×D4×C3⋊D3—22no—
15C3×D4×C3⋊D3—22no—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×Dic6C2211yescharacteristic, complemented
19C32×#214—22no—
20C32×C4⋊Dic3C2211yescharacteristic, complemented
21C2×C32×C3⋊C8C2211yescharacteristic, complemented
22C2×C32×C3⋊C8C2211yescharacteristic, complemented
23C3×Dic3⋊Dic3—21no—
24C3×#3722—21no—
25C3×#3717—22no—
26C2×D4×C3⋊D3C2×C311yescharacteristic
27C2×C3×D3×D4—31no—
28C2×C3×D3×D4—31no—
29C2×C3×D3×D4—61no—
30C2×C32×SD16—31no—
31C3×#946—31no—
32C2×C3×#215—31no—
33C2×C3×#214—21no—
34C2×C3×#214D311yescharacteristic, complemented
35C2×C3×#214C2×C311yescharacteristic, complemented
36C2×C3×#204—31no—
37C3×#897—31no—
38#63871C2×C311yescharacteristic, complemented
39C2×#3717C2×C311yescharacteristic, complemented
40C32×#102—31no—
41C3×#832—21no—
42C3×#832D311yescharacteristic, complemented
43C3×#832C2×C311yescharacteristic, complemented
44C3×#821—31no—
45C3×(C2×D3)⋊C8—31no—
46C3×(C2×D3)⋊C8—31no—
47C3×#809—31no—
48#63564C2×C311yescharacteristic, complemented
49#63557C2×C311yescharacteristic, complemented
50C23×C33—21no—
51C22×C3×C3⋊D3—24no—
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—42no—
54C22×C3×C3⋊D3—42no—
55C22×C3×C3⋊D3D411yescharacteristic
56C33×D4—21no—
57C33×D4D412yes—
58C2×C33×C4C2311yescharacteristic
59C3×#638—24no—
60C2×C3×C3⋊Dic3D411yescharacteristic
61C3×C4⋊(C3⋊D3)—21no—
62C3×C4⋊(C3⋊D3)D412yes—
63C3×C4×C3⋊D3—21no—
64C3×C4×C3⋊D3—21no—
65C2×C32×Dic3—21no—
66C2×C32×Dic3—21no—
67C32×Dic6—21no—
68C32×Dic6—21no—
69C32×C3⋊C8—21no—
70C32×C3⋊C8—21no—
71C3×#450—91no—
72#5169—31no—
73#4776—31no—
74C23×C3⋊D3—21no—
75C23×C3×D3—61no—
76C23×C3×D3—61no—
77C23×C3×D3—62no—
78C2×C32×Q8—31no—
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4—21no—
82C2×C32×D4—41no—
83C2×C32×D4C2×D311yescharacteristic
84C2×C32×D4C2×D311yescharacteristic
85C2×C32×D4C22×C311yescharacteristic
86C2×#638—21no—
87D4×C3⋊D3—22no—
88D4×C3⋊D3—22no—
89C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
90C2×C4×C3⋊D3C22×C311yescharacteristic
91C2×C3×#67—61no—
92C2×C3×#67—61no—
93C2×C3×#67—62no—
94C3×D3×D4—62no—
95C3×D3×D4—62no—
96C3×D3×D4—64no—
97C3×D3×D4—64no—
98C3×D3×D4—62no—
99C3×D3×D4—62no—
100C2×C3×D12—31no—
101C2×C3×D12—31no—
102C2×C3×D12—61no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—61no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2×D311yescharacteristic, complemented
108C2×C3×Dic6C22×C311yescharacteristic, complemented
109C32×SD16—62no—
110C2×C32×C8—31no—
111C2×C32×C8—31no—
112C32×C4⋊C4—31no—
113C3×#215—62no—
114C3×#214—24no—
115C3×#214—22no—
116C3×#214—22no—
117C3×(C2×D3)⋊C4—61no—
118C3×(C2×D3)⋊C4—61no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—61no—
121C3×C4⋊Dic3C2×D311yescharacteristic, complemented
122C3×C4⋊Dic3C22×C311yescharacteristic, complemented
123C3×Dic3⋊C4—61no—
124C2×C3×C3⋊C8—21no—
125C2×C3×C3⋊C8—21no—
126C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
127C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
128C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
129C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
130C3×#204—62no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3717—22no—
134C22×C33—22no—
135C22×C33—41no—
136C22×C33—41no—
137C22×C33C2×D411yescharacteristic
138C2×C3×C3⋊D3—21no—
139C2×C3×C3⋊D3—21no—
140C2×C3×C3⋊D3—22no—
141C2×C3×C3⋊D3—48no—
142C2×C3×C3⋊D3—41no—
143C2×C3×C3⋊D3—41no—
144C2×C3×C3⋊D3SD1612yescomplemented
145C33×C4C2×D411yescharacteristic
146C33×C4C2×D411yescharacteristic
147C3×C3⋊Dic3—21no—
148C32×Dic3—41no—
149C32×Dic3—41no—
150C22×C3×D4—91no—
151C2×D3×D4—31no—
152C2×D3×D4—31no—
153C2×D3×D4—61no—
154C2×C3×SD16—31no—
155C2×C3×SD16—31no—
156C2×C3×SD16—61no—
157C2×C3×SD16—91no—
158C3×C22⋊Q8—91no—
159#946—31no—
160C2×#215—31no—
161C2×#214C3×D311yescharacteristic, complemented
162C2×#204—31no—
163#897—31no—
164C3×#102—31no—
165C3×#102—31no—
166C3×#102—61no—
167C3×#102—91no—
168C3×C22⋊C8—91no—
169#832C3×D311yescharacteristic, complemented
170#821—31no—
171(C2×D3)⋊C8—31no—
172(C2×D3)⋊C8—31no—
173#809—31no—
174C23×C32—21no—
175C23×C32—22no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—41no—
179C23×C32—41no—
180C23×C32—42no—
181C22×C3⋊D3—24no—
182C22×C3⋊D3—21no—
183C22×C3⋊D3—42no—
184C22×C3⋊D3—42no—
185C22×C3⋊D3C3×D411yescharacteristic
186C22×C3×D3—31no—
187C22×C3×D3—31no—
188C22×C3×D3—61no—
189C22×C3×D3—62no—
190C22×C3×D3—68no—
191C22×C3×D3—64no—
192C22×C3×D3—64no—
193C22×C3×D3—61no—
194C22×C3×D3—61no—
195C22×C3×D3—122no—
196C22×C3×D3—122no—
197C22×C3×D3—124no—
198C22×C3×D3—124no—
199C22×C3×D3—122no—
200C22×C3×D3—122no—
201C32×Q8—61no—
202C32×Q8—61no—
203C32×D4—21no—
204C32×D4—22no—
205C32×D4—21no—
206C32×D4—21no—
207C32×D4—22no—
208C32×D4—22no—
209C32×D4—22no—
210C32×D4—42no—
211C32×D4—41no—
212C32×D4—41no—
213C32×D4—42no—
214C32×D4D1212yes—
215C32×D4#6712yes—
216C32×D4C3×D412yes—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—41no—
221C2×C32×C4—61no—
222C2×C32×C4—61no—
223C2×C32×C4C22×D311yescharacteristic
224C2×C32×C4C22×D311yescharacteristic
225C2×C32×C4C23×C311yescharacteristic
226#638—24no—
227C2×C3⋊Dic3C3×D411yescharacteristic
228C4⋊(C3⋊D3)—21no—
229C4⋊(C3⋊D3)C3×D412yes—
230C4×C3⋊D3—21no—
231C4×C3⋊D3—21no—
232C3×#67—68no—
233C3×#67—64no—
234C3×#67—64no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—31no—
240C2×C3×Dic3—31no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C2×C3×Dic3—61no—
244C3×D12—32no—
245C3×D12—32no—
246C3×D12—62no—
247C3×D12—62no—
248C3×D12—61no—
249C3×D12—61no—
250C3×C4×D3—62no—
251C3×C4×D3—62no—
252C3×C4×D3—61no—
253C3×C4×D3—61no—
254C3×C4×D3—61no—
255C3×C4×D3—61no—
256C3×Dic6—22no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6—41no—
262C32×C8—61no—
263C32×C8—61no—
264C3×C3⋊C8—22no—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—41no—
270#450—91noSylow
271C2×C33—42no—
272C2×C33#12011yescharacteristic
273C2×C33C2×SD1611yescharacteristic
274C2×C33AGL(1,ℤ/8)11yescharacteristic
275C3×C3⋊D3—22no—
276C3×C3⋊D3—42no—
277C24×C3—181no—
278C23×D3—61no—
279C23×D3—61no—
280C23×D3—62no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—41no—
288C2×C3×D4—91no—
289C2×C3×D4—181no—
290C2×C3×D4—182no—
291C2×C3×D4—182no—
292C2×C3×D4D3211yescharacteristic
293C2×C3×D4C2×C3×D311yescharacteristic
294C2×C3×D4C2×C3×D311yescharacteristic
295C22×C3×C4—91no—
296C2×#67—61no—
297C2×#67—61no—
298C2×#67—62no—
299D3×D4—62no—
300D3×D4—62no—
301D3×D4—64no—
302D3×D4—64no—
303D3×D4—62no—
304D3×D4—62no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—61no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—61no—
311C2×Dic6C2×C3×D311yescharacteristic, complemented
312C3×SD16—64no—
313C3×SD16—62no—
314C3×SD16—62no—
315C3×SD16—182no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C2×C3×C8—31no—
320C2×C3×C8—61no—
321C2×C3×C8—61no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—181no—
326C3×C22⋊C4—181no—
327#215—62no—
328#214—22no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331C4⋊Dic3—61no—
332C4⋊Dic3C2×C3×D311yescharacteristic, complemented
333Dic3⋊C4—61no—
334C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
335C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
336#204—62no—
337C22×C32—22no—
338C22×C32—24no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—41no—
345C22×C32—42no—
346C22×C32—42no—
347C22×C32—44no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—81no—
357C22×C32—81no—
358C22×C32—81no—
359C22×C32—81no—
360C22×C32—82no—
361C22×C32—82no—
362C22×C32D3×D411yescharacteristic
363C22×C32D3×D411yescharacteristic
364C22×C32C2×C3×D411yescharacteristic
365C2×C3⋊D3—21no—
366C2×C3⋊D3—21no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—48no—
369C2×C3⋊D3—41no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3C3×SD1612yescomplemented
372C2×C3×D3—32no—
373C2×C3×D3—32no—
374C2×C3×D3—62no—
375C2×C3×D3—62no—
376C2×C3×D3—62no—
377C2×C3×D3—61no—
378C2×C3×D3—61no—
379C2×C3×D3—61no—
380C2×C3×D3—61no—
381C2×C3×D3—64no—
382C2×C3×D3—62no—
383C2×C3×D3—62no—
384C2×C3×D3—1216no—
385C2×C3×D3—128no—
386C2×C3×D3—128no—
387C2×C3×D3—122no—
388C2×C3×D3—122no—
389C2×C3×D3—121no—
390C2×C3×D3—121no—
391C2×C3×D3—121no—
392C2×C3×D3—121no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4—121no—
402C32×C4—121no—
403C32×C4C2×D1211yescharacteristic
404C32×C4D3×D411yescharacteristic
405C32×C4D3×D411yescharacteristic
406C32×C4C2×#6711yescharacteristic
407C32×C4C2×C3×D411yescharacteristic
408C32×C4C2×C3×D411yescharacteristic
409C3⋊Dic3—21no—
410C3×Dic3—42no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—62no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—81no—
419C22×D4—91no—
420C2×SD16—31no—
421C2×SD16—91no—
422C22⋊Q8—91no—
423#102—31no—
424#102—91no—
425C22⋊C8—91no—
426C33#45011yescharacteristic, complemented, Sylow
427C23×C3—22no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—42no—
434C23×C3—91no—
435C23×C3—184no—
436C23×C3—181no—
437C23×C3—362no—
438C23×C3—362no—
439C22×D3—31no—
440C22×D3—31no—
441C22×D3—61no—
442C22×D3—62no—
443C22×D3—68no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—122no—
449C22×D3—122no—
450C22×D3—124no—
451C22×D3—124no—
452C22×D3—122no—
453C22×D3—122no—
454C3×Q8—62no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—121no—
460C3×D4—22no—
461C3×D4—21no—
462C3×D4—21no—
463C3×D4—21no—
464C3×D4—22no—
465C3×D4—22no—
466C3×D4—22no—
467C3×D4—41no—
468C3×D4—41no—
469C3×D4—42no—
470C3×D4—42no—
471C3×D4—92no—
472C3×D4—184no—
473C3×D4—181no—
474C3×D4#62612yes—
475C3×D4C3×D1212yes—
476C3×D4C3×#6712yes—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—41no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—91no—
486C2×C3×C4—121no—
487C2×C3×C4—121no—
488C2×C3×C4—181no—
489C2×C3×C4—181no—
490C2×C3×C4C2×D3211yescharacteristic
491C2×C3×C4C22×C3×D311yescharacteristic
492C2×C3×C4C22×C3×D311yescharacteristic
493#67—68no—
494#67—64no—
495#67—64no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—61no—
501D12—32no—
502D12—32no—
503D12—62no—
504D12—62no—
505D12—61no—
506D12—61no—
507C4×D3—62no—
508C4×D3—62no—
509C4×D3—61no—
510C4×D3—61no—
511C4×D3—61no—
512C4×D3—61no—
513Dic6—21no—
514Dic6—21no—
515C3×C8—62no—
516C3×C8—61no—
517C3×C8—61no—
518C3×C8—61no—
519C3×C8—61no—
520C3×C8—121no—
521C3⋊C8—21no—
522C3⋊C8—21no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—41no—
535C2×C32—42no—
536C2×C32—44no—
537C2×C32—42no—
538C2×C32—42no—
539C2×C32—82no—
540C2×C32—82no—
541C2×C32—84no—
542C2×C32#88211yescharacteristic
543C2×C32#91111yescharacteristic
544C2×C32D3×SD1611yescharacteristic
545C2×C32D3×SD1611yescharacteristic
546C2×C32#91411yescharacteristic
547C2×C32#93711yescharacteristic
548C2×C32C3×#12011yescharacteristic
549C2×C32C2×C3×SD1611yescharacteristic
550C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
551C3⋊D3—22no—
552C3⋊D3—42no—
553C3×D3—64no—
554C3×D3—62no—
555C3×D3—62no—
556C3×D3—124no—
557C3×D3—122no—
558C3×D3—122no—
559C24—181no—
560C2×Q8—31no—
561C2×D4—91no—
562C2×D4—181no—
563C2×D4—182no—
564C2×D4—182no—
565C2×D4C3×D3211yescharacteristic
566C22×C4—91no—
567SD16—62no—
568SD16—182no—
569C2×C8—31no—
570C2×C8—31no—
571C4⋊C4—31no—
572C4⋊C4—181no—
573C22⋊C4—181no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—44no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—92no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3—182no—
603C22×C3—368no—
604C22×C3—361no—
605C22×C3—361no—
606C22×C3#381111yescharacteristic
607C22×C3C3×D3×D411yescharacteristic
608C22×C3C3×D3×D411yescharacteristic
609C2×D3—32no—
610C2×D3—32no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—64no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—1216no—
622C2×D3—128no—
623C2×D3—128no—
624C2×D3—122no—
625C2×D3—122no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—122no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—181no—
644C3×C4—241no—
645C3×C4C2×#62611yescharacteristic
646C3×C4#381111yescharacteristic
647C3×C4C2×C3×D1211yescharacteristic
648C3×C4C3×D3×D411yescharacteristic
649C3×C4C3×D3×D411yescharacteristic
650C3×C4C2×C3×#6711yescharacteristic
651Dic3—41no—
652Dic3—41no—
653Dic3—62no—
654Dic3—61no—
655Dic3—61no—
656C32—21no—
657C32—21no—
658C32—21no—
659C32—41no—
660C32#477611yescharacteristic, complemented
661C32#516911yescharacteristic, complemented
662C32C3×#45011yescharacteristic, complemented
663C23—21no—
664C23—91no—
665C23—184no—
666C23—181no—
667C23—362no—
668C23—362no—
669Q8—61no—
670Q8—61no—
671D4—21no—
672D4—92no—
673D4—184no—
674D4—181no—
675D4C3×#62612yes—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—91no—
679C2×C4—181no—
680C2×C4—181no—
681C2×C4C2×C3×D3211yescharacteristic
682C8—61no—
683C8—61no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—44no—
694C2×C3—42no—
695C2×C3—42no—
696C2×C3—42no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—41no—
700C2×C3—82no—
701C2×C3—82no—
702C2×C3—84no—
703C2×C3—182no—
704C2×C3—362no—
705C2×C3#6393011yescharacteristic
706C2×C3#6393711yescharacteristic
707C2×C3#6398111yescharacteristic
708C2×C3C3×#88211yescharacteristic
709C2×C3C3×#91111yescharacteristic
710C2×C3C3×D3×SD1611yescharacteristic
711C2×C3C3×D3×SD1611yescharacteristic
712C2×C3C3×#91411yescharacteristic
713C2×C3C3×#93711yescharacteristic
714D3—64no—
715D3—62no—
716D3—62no—
717D3—124no—
718D3—122no—
719D3—122no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—92no—
724C22—181no—
725C22—181no—
726C22—182no—
727C22—368no—
728C22—361no—
729C22—361no—
730C22C3×#381111yescharacteristic
731C4—121no—
732C4—121no—
733C4—181no—
734C4C2×C3×#62611yescharacteristic
735C4C3×#381111yescharacteristic
736C3—21no—
737C3—21no—
738C3—21no—
739C3—41no—
740C3#1059146711yescharacteristic, direct product factor
741C3C3×#477611yescharacteristic, complemented
742C3C3×#516911yescharacteristic, complemented
743C2—42no—
744C2—182no—
745C2—362no—
746C2C3×#6393011yescharacteristic
747C2C3×#6393711yescharacteristic
748C2C3×#6398111yescharacteristic
subgroupG/H
centerC22×C3#3811
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
prime radicalC2×C3×D4×C3⋊D3C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C2×C32×#214C2semidirect
3. C3×#63871C2semidirect
4. C2×C3×#3717C2semidirect
5. C32×#832C2semidirect
6. C3×#63564C2semidirect
7. C3×#63557C2semidirect
10. #10591467C3direct (N × H)
18. C2×C32×Dic6C22semidirect
20. C32×C4⋊Dic3C22semidirect
21. C2×C32×C3⋊C8C22semidirect
22. C2×C32×C3⋊C8C22semidirect
34. C2×C3×#214D3semidirect
35. C2×C3×#214C2×C3semidirect
38. #63871C2×C3semidirect
39. C2×#3717C2×C3semidirect
42. C3×#832D3semidirect
43. C3×#832C2×C3semidirect
48. #63564C2×C3semidirect
49. #63557C2×C3semidirect
107. C2×C3×Dic6C2×D3semidirect
108. C2×C3×Dic6C22×C3semidirect
121. C3×C4⋊Dic3C2×D3semidirect
122. C3×C4⋊Dic3C22×C3semidirect
126. C2×C3×C3⋊C8C2×D3semidirect
127. C2×C3×C3⋊C8C2×D3semidirect
128. C2×C3×C3⋊C8C22×C3semidirect
129. C2×C3×C3⋊C8C22×C3semidirect
144. C2×C3×C3⋊D3SD16semidirect
161. C2×#214C3×D3semidirect
169. #832C3×D3semidirect
311. C2×Dic6C2×C3×D3semidirect
332. C4⋊Dic3C2×C3×D3semidirect
334. C2×C3⋊C8C2×C3×D3semidirect
335. C2×C3⋊C8C2×C3×D3semidirect
371. C2×C3⋊D3C3×SD16semidirect
426. C33#450semidirect
660. C32#4776semidirect
661. C32#5169semidirect
662. C32C3×#450semidirect
740. C3#10591467direct (N × H)
741. C3C3×#4776semidirect
742. C3C3×#5169semidirect

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×C32×#2142
C3×#638712
C2×C3×#37172
C32×#8322
C3×#635642
C3×#635572
C3×#51693
C3×#47763
#105914673