Finite Group Databasebeta

← C3×#70036 #11788224

Subgroups — C3×#70036 #11788224

Order 1152.

1301 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×#937C211yesmaximal, characteristic
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C32×#99C211yesmaximal, characteristic, complemented
4C2×C3×#834C211yesmaximal, characteristic, complemented
5C3×#4955C211yesmaximal, characteristic, complemented
6C3×#4527C211yesmaximal, characteristic, complemented
7C3×#4527C211yesmaximal, characteristic, complemented
8C3×#1898—31nomaximal
9#70036C311yesmaximal, characteristic, direct product factor
10C24×C3×D3C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67C412yescomplemented
13C22×C3×C4×D3—21no—
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19C3×#937—21no—
20C3×#937—22no—
21C3×#937—21no—
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×(C2×D3)⋊C4—22no—
24C2×C3×(C2×D3)⋊C4C412yescomplemented
25C3×D3×C22⋊C4—22no—
26C3×D3×C22⋊C4—22no—
27C32×#99—22no—
28C3×#834—22no—
29C2×C3×#120—31no—
30C22×C3×C22⋊C4—31no—
31C2×#937C2×C311yescharacteristic
32C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
33C2×C3×#99—21no—
34C2×C3×#99—31no—
35C2×C3×#99D311yescharacteristic, complemented
36C2×C3×#99C2×C311yescharacteristic, complemented
37C3×#379—31no—
38C2×#834C2×C311yescharacteristic, complemented
39#4955C2×C311yescharacteristic, complemented
40C3×#342—31no—
41C3×#342—31no—
42#4527C2×C311yescharacteristic, complemented
43#4527C2×C311yescharacteristic, complemented
44C24×C32C2×C411yescharacteristic, complemented
45C24×C32C2311yescharacteristic
46C23×C3×D3—21no—
47C23×C3×D3—21no—
48C23×C3×D3—21no—
49C23×C3×D3—21no—
50C23×C3×D3—44no—
51C23×C3×D3C2×C412yes—
52C23×C3×D3D411yescharacteristic
53C23×C3×D3D412yes—
54C23×C3×D3D411yescharacteristic
55C2×C32×D4—21no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4—21no—
60C2×C32×D4—21no—
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4C2×C411yescharacteristic, complemented
64C2×C3×#67—22no—
65C2×C3×#67—22no—
66C2×C3×#67—44no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3C2×C412yescomplemented
70C2×C3×C4×D3—24no—
71C2×C3×C4×D3—44no—
72C32×C22⋊C4—21no—
73C32×C22⋊C4—21no—
74C32×C22⋊C4—21no—
75C32×C22⋊C4D412yescomplemented
76C3×#217—21no—
77C3×#217—21no—
78C3×#217—21no—
79C3×#217—21no—
80C3×#217—21no—
81C3×#217D412yescomplemented
82C3×(C2×D3)⋊C4—24no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—44no—
86#1898—31noSylow
87C25×C3—31no—
88C24×D3C22×C311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—32no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C22×C311yescharacteristic
93C23×C3×C4—61no—
94C22×#67C3×C412yescomplemented
95C22×C4×D3—21no—
96C3×#120—61no—
97C3×#120—62no—
98C3×#120—61no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—62no—
106C2×C3×C22⋊C4—61no—
107C2×C3×C22⋊C4—62no—
108C2×C3×C22⋊C4—62no—
109C2×C3×C22⋊C4C2×D311yescharacteristic
110C2×C3×C22⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C22×C311yescharacteristic
112C2×C3×C22⋊C4C22×C311yescharacteristic
113C2×#217C22×C311yescharacteristic
114C2×#217C22×C311yescharacteristic
115C2×#217C22×C311yescharacteristic
116#937—21no—
117#937—22no—
118#937—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4C3×C412yescomplemented
122D3×C22⋊C4—22no—
123D3×C22⋊C4—22no—
124C3×#99—24no—
125C3×#99—22no—
126C3×#99—22no—
127C3×#99—62no—
128#834—22no—
129C23×C32—21no—
130C23×C32—21no—
131C23×C32—21no—
132C23×C32—42no—
133C23×C32—42no—
134C23×C32C22×C411yescharacteristic
135C23×C32C2×D411yescharacteristic
136C23×C32C2×D411yescharacteristic
137C23×C32C2×D411yescharacteristic
138C23×C32C2×D411yescharacteristic
139C23×C32#4111yescharacteristic
140C23×C32#4111yescharacteristic
141C22×C3×D3—21no—
142C22×C3×D3—21no—
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3—21no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—21no—
150C22×C3×D3—24no—
151C22×C3×D3—24no—
152C22×C3×D3—42no—
153C22×C3×D3—42no—
154C22×C3×D3—42no—
155C22×C3×D3—44no—
156C22×C3×D3—44no—
157C22×C3×D3—44no—
158C22×C3×D3—44no—
159C22×C3×D3C22⋊C412yes—
160C22×C3×D3C22⋊C412yes—
161C32×D4—41no—
162C32×D4—41no—
163C32×D4—41no—
164C32×D4—41no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—41no—
170C2×C32×C4—42no—
171C2×C32×C4—42no—
172C3×#67—44no—
173C3×#67—44no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—42no—
177C2×C3×Dic3—42no—
178C2×C3×Dic3—42no—
179C2×C3×Dic3—41no—
180C3×C4×D3—48no—
181C2×#120—31no—
182C22×C22⋊C4—31no—
183C2×#99—31no—
184C2×#99C3×D311yescharacteristic, complemented
185#379—31no—
186#342—31no—
187#342—31no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—31no—
191C24×C3—32no—
192C24×C3—32no—
193C24×C3—31no—
194C24×C3—61no—
195C24×C3—61no—
196C24×C3—61no—
197C24×C3—61no—
198C24×C3—124no—
199C24×C3C4×D311yescharacteristic, complemented
200C24×C3C2×C3×C411yescharacteristic, complemented
201C24×C3C22×D311yescharacteristic
202C24×C3C23×C311yescharacteristic
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—44no—
208C23×D3C2×C3×C412yes—
209C23×D3C3×D411yescharacteristic
210C23×D3C3×D412yes—
211C23×D3C3×D411yescharacteristic
212C2×C3×D4—22no—
213C2×C3×D4—22no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—41no—
227C2×C3×D4—41no—
228C2×C3×D4—41no—
229C2×C3×D4—41no—
230C2×C3×D4—62no—
231C2×C3×D4—62no—
232C2×C3×D4—124no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—32no—
239C22×C3×C4—41no—
240C22×C3×C4—41no—
241C22×C3×C4—64no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4—124no—
245C22×C3×C4C4×D311yescharacteristic, complemented
246C22×C3×C4C2×C3×C411yescharacteristic, complemented
247C2×#67—22no—
248C2×#67—22no—
249C2×#67—44no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3C2×C3×C412yescomplemented
253C2×C4×D3—24no—
254C2×C4×D3—44no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—21no—
259C3×C22⋊C4—21no—
260C3×C22⋊C4—21no—
261C3×C22⋊C4—21no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—32no—
264C3×C22⋊C4—41no—
265C3×C22⋊C4—41no—
266C3×C22⋊C4—62no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—64no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C22⋊C4—61no—
274C3×C22⋊C4—124no—
275C3×C22⋊C4#6712yescomplemented
276C3×C22⋊C4C3×D412yescomplemented
277#217—21no—
278#217—21no—
279#217—21no—
280#217—21no—
281#217—21no—
282#217C3×D412yescomplemented
283(C2×D3)⋊C4—24no—
284(C2×D3)⋊C4—22no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—44no—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32—42no—
296C22×C32—81no—
297C22×C32—81no—
298C22×C32C2×C22⋊C411yescharacteristic
299C22×C32C4×D411yescharacteristic
300C22×C32C4×D411yescharacteristic
301C22×C32#12011yescharacteristic
302C22×C32#12111yescharacteristic
303C22×C32#12111yescharacteristic
304C22×C32#12311yescharacteristic
305C2×C3×D3—24no—
306C2×C3×D3—24no—
307C2×C3×D3—22no—
308C2×C3×D3—22no—
309C2×C3×D3—22no—
310C2×C3×D3—22no—
311C2×C3×D3—22no—
312C2×C3×D3—44no—
313C2×C3×D3—44no—
314C2×C3×D3—44no—
315C2×C3×D3—44no—
316C2×C3×D3—42no—
317C2×C3×D3—42no—
318C2×C3×D3#9914yescomplemented
319C32×C4—41no—
320C32×C4—42no—
321C32×C4—81no—
322C3×Dic3—42no—
323C3×Dic3—42no—
324C3×Dic3—81no—
325C25—31no—
326C22×D4—32no—
327C22×D4C2×C3×D311yescharacteristic
328C23×C4—61no—
329#120—61no—
330#120—62no—
331#120—61no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—32no—
335C2×C22⋊C4—31no—
336C2×C22⋊C4—62no—
337C2×C22⋊C4—61no—
338C2×C22⋊C4—62no—
339C2×C22⋊C4—62no—
340C2×C22⋊C4C2×C3×D311yescharacteristic
341C2×C22⋊C4C2×C3×D311yescharacteristic
342#99—22no—
343#99—62no—
344C23×C3—22no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—32no—
359C23×C3—32no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—64no—
367C23×C3—64no—
368C23×C3—64no—
369C23×C3—61no—
370C23×C3—61no—
371C23×C3—62no—
372C23×C3—61no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3—61no—
376C23×C3—62no—
377C23×C3—82no—
378C23×C3—82no—
379C23×C3—122no—
380C23×C3—122no—
381C23×C3—122no—
382C23×C3—124no—
383C23×C3—124no—
384C23×C3—124no—
385C23×C3—124no—
386C23×C3C2×C4×D311yescharacteristic
387C23×C3#23511yescharacteristic
388C23×C3D3×D411yescharacteristic
389C23×C3D3×D411yescharacteristic
390C23×C3D3×D411yescharacteristic
391C23×C3#23711yescharacteristic
392C23×C3C2×#6711yescharacteristic
393C23×C3C22×C3×C411yescharacteristic
394C23×C3C2×C3×D411yescharacteristic
395C23×C3C2×C3×D411yescharacteristic
396C23×C3C2×C3×D411yescharacteristic
397C23×C3C2×C3×D411yescharacteristic
398C23×C3C3×#4111yescharacteristic
399C23×C3C3×#4111yescharacteristic
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—24no—
403C22×D3—22no—
404C22×D3—22no—
405C22×D3—21no—
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—21no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—44no—
415C22×D3—44no—
416C22×D3—44no—
417C22×D3—44no—
418C22×D3C3×C22⋊C412yes—
419C22×D3C3×C22⋊C412yes—
420C3×D4—42no—
421C3×D4—42no—
422C3×D4—42no—
423C3×D4—42no—
424C3×D4—41no—
425C3×D4—41no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—124no—
433C3×D4—124no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—82no—
456C2×C3×C4—82no—
457C2×C3×C4—128no—
458C2×C3×C4—122no—
459C2×C3×C4—122no—
460C2×C3×C4—122no—
461C2×C3×C4—121no—
462#67—44no—
463#67—44no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—41no—
470C4×D3—48no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32—81no—
478C2×C32#38611yescharacteristic
479C2×C32C2×#9912yes—
480C3×D3—24no—
481C3×D3—42no—
482C24—31no—
483C24—32no—
484C24—32no—
485C24—31no—
486C24—61no—
487C24—61no—
488C24—61no—
489C24—61no—
490C24—124no—
491C24C3×C4×D311yescharacteristic, complemented
492C24C22×C3×D311yescharacteristic
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—62no—
500C2×D4—62no—
501C2×D4—124no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—32no—
505C22×C4—64no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—124no—
509C22×C4C3×C4×D311yescharacteristic, complemented
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—32no—
514C22⋊C4—62no—
515C22⋊C4—62no—
516C22⋊C4—64no—
517C22⋊C4—61no—
518C22⋊C4—61no—
519C22⋊C4—61no—
520C22⋊C4—61no—
521C22⋊C4—61no—
522C22⋊C4—124no—
523C22⋊C4C3×#6712yescomplemented
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—34no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—42no—
550C22×C3—41no—
551C22×C3—42no—
552C22×C3—41no—
553C22×C3—42no—
554C22×C3—64no—
555C22×C3—64no—
556C22×C3—62no—
557C22×C3—62no—
558C22×C3—62no—
559C22×C3—62no—
560C22×C3—62no—
561C22×C3—82no—
562C22×C3—81no—
563C22×C3—81no—
564C22×C3—81no—
565C22×C3—81no—
566C22×C3—81no—
567C22×C3—81no—
568C22×C3—81no—
569C22×C3—81no—
570C22×C3—82no—
571C22×C3—82no—
572C22×C3—124no—
573C22×C3—124no—
574C22×C3—124no—
575C22×C3—124no—
576C22×C3—122no—
577C22×C3—122no—
578C22×C3D3×C22⋊C411yescharacteristic
579C22×C3#67⋊C411yescharacteristic
580C22×C3#88311yescharacteristic
581C22×C3#88411yescharacteristic
582C22×C3C4×#6711yescharacteristic
583C22×C3#93711yescharacteristic
584C22×C3#93811yescharacteristic
585C22×C3C2×C3×C22⋊C411yescharacteristic
586C22×C3C3×C4×D411yescharacteristic
587C22×C3C3×C4×D411yescharacteristic
588C22×C3C3×#12011yescharacteristic
589C22×C3C3×#12111yescharacteristic
590C22×C3C3×#12111yescharacteristic
591C22×C3C3×#12311yescharacteristic
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—44no—
600C2×D3—44no—
601C2×D3—44no—
602C2×D3—44no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3C3×#9914yescomplemented
606C3×C4—42no—
607C3×C4—42no—
608C3×C4—42no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—82no—
612C3×C4—81no—
613C3×C4—81no—
614C3×C4—82no—
615C3×C4—122no—
616C3×C4—122no—
617C3×C4—241no—
618Dic3—42no—
619Dic3—42no—
620Dic3—81no—
621C32#189811yescharacteristic, complemented, Sylow
622C23—21no—
623C23—21no—
624C23—21no—
625C23—32no—
626C23—32no—
627C23—42no—
628C23—42no—
629C23—64no—
630C23—64no—
631C23—64no—
632C23—61no—
633C23—61no—
634C23—62no—
635C23—61no—
636C23—62no—
637C23—62no—
638C23—61no—
639C23—62no—
640C23—122no—
641C23—122no—
642C23—122no—
643C23—124no—
644C23—124no—
645C23—124no—
646C23—124no—
647C23C2×C3×C4×D311yescharacteristic
648C23C3×#23511yescharacteristic
649C23C3×D3×D411yescharacteristic
650C23C3×D3×D411yescharacteristic
651C23C3×D3×D411yescharacteristic
652C23C3×#23711yescharacteristic
653C23C2×C3×#6711yescharacteristic
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—124no—
659D4—124no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—128no—
670C2×C4—122no—
671C2×C4—122no—
672C2×C4—122no—
673C2×C4—121no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—22no—
688C2×C3—41no—
689C2×C3—41no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—41no—
693C2×C3—41no—
694C2×C3—64no—
695C2×C3—82no—
696C2×C3—81no—
697C2×C3—81no—
698C2×C3—122no—
699C2×C3D3×#9912yes—
700C2×C3#495611yescharacteristic
701C2×C3C3×#38611yescharacteristic
702C2×C3C2×C3×#9912yes—
703D3—24no—
704D3—42no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—34no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—64no—
716C22—64no—
717C22—62no—
718C22—62no—
719C22—62no—
720C22—62no—
721C22—62no—
722C22—81no—
723C22—81no—
724C22—124no—
725C22—124no—
726C22—124no—
727C22—124no—
728C22—122no—
729C22—122no—
730C22C3×D3×C22⋊C411yescharacteristic
731C22C3×#67⋊C411yescharacteristic
732C22C3×#88311yescharacteristic
733C22C3×#88411yescharacteristic
734C22C3×C4×#6711yescharacteristic
735C22C3×#93711yescharacteristic
736C22C3×#93811yescharacteristic
737C4—42no—
738C4—41no—
739C4—81no—
740C4—122no—
741C4—122no—
742C4—241no—
743C3—21no—
744C3#7003611yescharacteristic, direct product factor
745C3C3×#189811yescharacteristic, complemented
746C2—21no—
747C2—21no—
748C2—21no—
749C2—21no—
750C2—21no—
751C2—21no—
752C2—64no—
753C2—81no—
754C2—122no—
755C2C3×D3×#9912yes—
756C2C3×#495611yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC2×C32×#99C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#937C2
cosocleC24×C3C23×C3
hypercenterC2×C3×#99D3
hypocenterC3C3×#1898
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C22⋊C4C2semidirect
3. C2×C32×#99C2semidirect
4. C2×C3×#834C2semidirect
5. C3×#4955C2semidirect
6. C3×#4527C2semidirect
7. C3×#4527C2semidirect
9. #70036C3direct (N × H)
12. C22×C3×#67C4semidirect
24. C2×C3×(C2×D3)⋊C4C4semidirect
32. C2×D3×C22⋊C4C2×C3semidirect
35. C2×C3×#99D3semidirect
36. C2×C3×#99C2×C3semidirect
38. C2×#834C2×C3semidirect
39. #4955C2×C3semidirect
42. #4527C2×C3semidirect
43. #4527C2×C3semidirect
44. C24×C32C2×C4semidirect
63. C22×C32×C4C2×C4semidirect
69. C22×C3×Dic3C2×C4semidirect
75. C32×C22⋊C4D4semidirect
81. C3×#217D4semidirect
94. C22×#67C3×C4semidirect
121. C2×(C2×D3)⋊C4C3×C4semidirect
184. C2×#99C3×D3semidirect
199. C24×C3C4×D3semidirect
200. C24×C3C2×C3×C4semidirect
245. C22×C3×C4C4×D3semidirect
246. C22×C3×C4C2×C3×C4semidirect
252. C22×Dic3C2×C3×C4semidirect
275. C3×C22⋊C4#67semidirect
276. C3×C22⋊C4C3×D4semidirect
282. #217C3×D4semidirect
318. C2×C3×D3#99semidirect
491. C24C3×C4×D3semidirect
509. C22×C4C3×C4×D3semidirect
523. C22⋊C4C3×#67semidirect
605. C2×D3C3×#99semidirect
621. C32#1898semidirect
744. C3#70036direct (N × H)
745. C3C3×#1898semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9372
C2×C3×D3×C22⋊C42
C2×C32×#992
C2×C3×#8342
C3×#49552
C3×#45272
C3×#18983
#700363