Finite Group Databasebeta

← C3×#71550 #11773273

Subgroups — C3×#71550 #11773273

Order 1152.

2673 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C212yesmaximal, complemented
5C2×C3×C3⋊#95C212yesmaximal, complemented
6C3×#1438—31nomaximal
7#71550C311yesmaximal, characteristic, direct product factor
8C25×C32C2211yescharacteristic
9C24×C3×D3C2211yescharacteristic
10C23×C32×C4C2212yes—
11C22×C3×#67—24no—
12C22×C3×#67—22no—
13C22×C3×#67—22no—
14C22×C3×#67—24no—
15C22×C3×#67C414yescomplemented
16C23×C3×Dic3C2212yes—
17C23×C3×Dic3C2211yescharacteristic
18C2×C32×C22⋊C4—24no—
19C2×C32×C22⋊C4—22no—
20C2×C3×#217—24no—
21C2×C3×#217—22no—
22C2×C3×(C2×D3)⋊C4—24no—
23C2×C3×(C2×D3)⋊C4—24no—
24C2×C3×(C2×D3)⋊C4—24no—
25C3×C3⋊#95—24no—
26C23×C3×D4—31no—
27C23×#67C2×C311yescharacteristic
28C22×C3×C22⋊C4—21no—
29C22×C3×C22⋊C4—32no—
30C22×C3×C22⋊C4—31no—
31C22×C3×C22⋊C4D311yescharacteristic, complemented
32C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
33C22×#217C2×C311yescharacteristic, complemented
34C22×(C2×D3)⋊C4C2×C312yescomplemented
35C2×C3×#95—32no—
36C2×C3⋊#95C2×C312yescomplemented
37C24×C32—22no—
38C24×C32—22no—
39C24×C32—22no—
40C24×C32—22no—
41C24×C32—22no—
42C24×C32—22no—
43C24×C32C2×C412yes—
44C24×C32D412yes—
45C24×C32D412yes—
46C24×C32C2311yescharacteristic
47C23×C3×D3—22no—
48C23×C3×D3—22no—
49C23×C3×D3—21no—
50C23×C3×D3—21no—
51C23×C3×D3—22no—
52C23×C3×D3—22no—
53C23×C3×D3—22no—
54C23×C3×D3C2×C412yes—
55C23×C3×D3D414yes—
56C22×C32×C4—22no—
57C22×C32×C4—22no—
58C22×C32×C4—22no—
59C22×C32×C4—22no—
60C22×C32×C4—22no—
61C22×C32×C4—22no—
62C22×C32×C4D414yescomplemented
63C2×C3×#67—216no—
64C2×C3×#67—216no—
65C2×C3×#67—28no—
66C2×C3×#67—28no—
67C2×C3×#67—28no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—22no—
70C22×C3×Dic3—21no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—22no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3C2×C412yes—
78C22×C3×Dic3D414yes—
79C22×C3×Dic3D414yescomplemented
80C32×C22⋊C4—28no—
81C3×#217—28no—
82C3×(C2×D3)⋊C4—216no—
83#1438—31noSylow
84C25×C3—21no—
85C25×C3—31no—
86C25×C3C2×D311yescharacteristic
87C25×C3C22×C311yescharacteristic
88C24×D3C22×C311yescharacteristic
89C22×C3×D4—34no—
90C22×C3×D4—64no—
91C22×C3×D4—64no—
92C22×C3×D4—62no—
93C22×C3×D4—62no—
94C23×C3×C4—22no—
95C23×C3×C4—31no—
96C23×C3×C4—32no—
97C23×C3×C4C2×D312yes—
98C23×C3×C4C22×C312yes—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—24no—
102C22×#67—24no—
103C22×#67C3×C414yescomplemented
104C23×Dic3C22×C312yes—
105C23×Dic3C22×C311yescharacteristic
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—28no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—64no—
113C2×C3×C22⋊C4—64no—
114C2×C3×C22⋊C4—64no—
115C2×C3×C22⋊C4—62no—
116C2×C3×C22⋊C4—64no—
117C2×#217—22no—
118C2×#217—24no—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—24no—
122C3×#95—64no—
123C3⋊#95—24no—
124C23×C32—24no—
125C23×C32—22no—
126C23×C32—24no—
127C23×C32—22no—
128C23×C32—22no—
129C23×C32—22no—
130C23×C32—24no—
131C23×C32—22no—
132C23×C32—24no—
133C23×C32—24no—
134C23×C32—24no—
135C23×C32—22no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32—42no—
140C23×C32—42no—
141C23×C32—42no—
142C23×C32—42no—
143C23×C32—42no—
144C23×C32C22⋊C414yescomplemented
145C23×C32C22×C411yescharacteristic
146C23×C32C2×D411yescharacteristic
147C23×C32C2×D412yes—
148C23×C32C2×D412yes—
149C23×C32C2×D412yes—
150C23×C32C2×D411yescharacteristic
151C23×C32C2×D412yes—
152C23×C32#4112yes—
153C23×C32#4112yes—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—24no—
157C22×C3×D3—24no—
158C22×C3×D3—24no—
159C22×C3×D3—24no—
160C22×C3×D3—24no—
161C22×C3×D3—24no—
162C22×C3×D3—24no—
163C22×C3×D3—24no—
164C22×C3×D3—41no—
165C22×C3×D3—41no—
166C22×C3×D3—42no—
167C22×C3×D3—42no—
168C22×C3×D3—42no—
169C22×C3×D3—42no—
170C22×C3×D3—41no—
171C22×C3×D3—41no—
172C22×C3×D3—42no—
173C22×C3×D3—42no—
174C22×C3×D3C22⋊C414yescomplemented
175C2×C32×C4—24no—
176C2×C32×C4—24no—
177C2×C32×C4—24no—
178C2×C32×C4—42no—
179C2×C32×C4—42no—
180C2×C32×C4—42no—
181C2×C32×C4—42no—
182C3×#67—232no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—42no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3—42no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3C22⋊C414yescomplemented
195C23×D4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—32no—
198C22×C22⋊C4C3×D311yescharacteristic, complemented
199C2×#95—32no—
200C24×C3—24no—
201C24×C3—24no—
202C24×C3—22no—
203C24×C3—22no—
204C24×C3—22no—
205C24×C3—22no—
206C24×C3—22no—
207C24×C3—22no—
208C24×C3—22no—
209C24×C3—22no—
210C24×C3—22no—
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—21no—
218C24×C3—32no—
219C24×C3—34no—
220C24×C3—42no—
221C24×C3—42no—
222C24×C3—42no—
223C24×C3—42no—
224C24×C3—61no—
225C24×C3—62no—
226C24×C3—62no—
227C24×C3—62no—
228C24×C3—62no—
229C24×C3—62no—
230C24×C3—61no—
231C24×C3C4×D312yes—
232C24×C3D1212yes—
233C24×C3#6712yes—
234C24×C3C2×C3×C412yes—
235C24×C3C3×D412yes—
236C24×C3C3×D412yes—
237C24×C3C22×D311yescharacteristic
238C24×C3C23×C311yescharacteristic
239C23×D3—22no—
240C23×D3—22no—
241C23×D3—21no—
242C23×D3—22no—
243C23×D3—21no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3C2×C3×C412yes—
247C23×D3C3×D414yes—
248C2×C3×D4—68no—
249C2×C3×D4—68no—
250C2×C3×D4—616no—
251C2×C3×D4—616no—
252C2×C3×D4—68no—
253C22×C3×C4—24no—
254C22×C3×C4—24no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—24no—
268C22×C3×C4—32no—
269C22×C3×C4—34no—
270C22×C3×C4—34no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—61no—
276C22×C3×C4—62no—
277C22×C3×C4—61no—
278C22×C3×C4—62no—
279C22×C3×C4—62no—
280C22×C3×C4—62no—
281C22×C3×C4—62no—
282C22×C3×C4—62no—
283C22×C3×C4—62no—
284C22×C3×C4#6714yescomplemented
285C22×C3×C4C3×D414yescomplemented
286C2×#67—216no—
287C2×#67—216no—
288C2×#67—28no—
289C2×#67—28no—
290C2×#67—28no—
291C22×Dic3—21no—
292C22×Dic3—22no—
293C22×Dic3—21no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3C2×C3×C412yes—
301C22×Dic3C3×D414yes—
302C22×Dic3C3×D414yescomplemented
303C3×C22⋊C4—216no—
304C3×C22⋊C4—28no—
305C3×C22⋊C4—28no—
306C3×C22⋊C4—616no—
307C3×C22⋊C4—68no—
308#217—28no—
309(C2×D3)⋊C4—216no—
310C22×C32—24no—
311C22×C32—24no—
312C22×C32—24no—
313C22×C32—44no—
314C22×C32—44no—
315C22×C32—44no—
316C22×C32—44no—
317C22×C32—44no—
318C22×C32—44no—
319C22×C32C2×C22⋊C411yescharacteristic
320C22×C32C2×C22⋊C411yescharacteristic
321C22×C32C2×C22⋊C411yescharacteristic
322C22×C32C4×D412yes—
323C22×C32C4×D412yes—
324C22×C32#12012yes—
325C22×C32#12011yescharacteristic
326C22×C32#12012yes—
327C22×C32#12012yes—
328C22×C32#12011yescharacteristic
329C22×C32#12112yes—
330C22×C32#12112yes—
331C22×C32#12112yes—
332C22×C32#12112yes—
333C22×C32#12112yes—
334C22×C32#12112yes—
335C22×C32#12312yes—
336C22×C32#12311yescharacteristic
337C22×C32#12311yescharacteristic
338C22×C32#12412yes—
339C22×C32#12712yes—
340C2×C3×D3—24no—
341C2×C3×D3—28no—
342C2×C3×D3—42no—
343C2×C3×D3—42no—
344C2×C3×D3—44no—
345C2×C3×D3—44no—
346C2×C3×D3—44no—
347C2×C3×D3—44no—
348C2×C3×D3—44no—
349C32×C4—44no—
350C3×Dic3—24no—
351C3×Dic3—44no—
352C25—31no—
353C25C2×C3×D311yescharacteristic
354C22×D4—34no—
355C22×D4—64no—
356C22×D4—64no—
357C22×D4—62no—
358C22×D4—62no—
359C23×C4—31no—
360C23×C4—32no—
361C23×C4C2×C3×D312yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4—62no—
368C2×C22⋊C4—64no—
369#95—64no—
370C23×C3—24no—
371C23×C3—28no—
372C23×C3—24no—
373C23×C3—28no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—24no—
379C23×C3—22no—
380C23×C3—24no—
381C23×C3—22no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—24no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—34no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—44no—
412C23×C3—42no—
413C23×C3—44no—
414C23×C3—42no—
415C23×C3—44no—
416C23×C3—44no—
417C23×C3—44no—
418C23×C3—44no—
419C23×C3—44no—
420C23×C3—44no—
421C23×C3—44no—
422C23×C3—44no—
423C23×C3—44no—
424C23×C3—44no—
425C23×C3—42no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—62no—
442C23×C3—64no—
443C23×C3—64no—
444C23×C3—64no—
445C23×C3—64no—
446C23×C3—62no—
447C23×C3—64no—
448C23×C3—64no—
449C23×C3—64no—
450C23×C3—64no—
451C23×C3—121no—
452C23×C3—122no—
453C23×C3—122no—
454C23×C3—121no—
455C23×C3—121no—
456C23×C3—122no—
457C23×C3—122no—
458C23×C3—122no—
459C23×C3—122no—
460C23×C3—121no—
461C23×C3(C2×D3)⋊C414yescomplemented
462C23×C3C3×C22⋊C414yescomplemented
463C23×C3C2×C4×D311yescharacteristic
464C23×C3C2×D1211yescharacteristic
465C23×C3#23512yes—
466C23×C3D3×D412yes—
467C23×C3D3×D412yes—
468C23×C3D3×D412yes—
469C23×C3#23712yes—
470C23×C3C2×#6711yescharacteristic
471C23×C3C2×#6712yes—
472C23×C3C22×C3×C411yescharacteristic
473C23×C3C2×C3×D411yescharacteristic
474C23×C3C2×C3×D412yes—
475C23×C3C2×C3×D412yes—
476C23×C3C2×C3×D412yes—
477C23×C3C2×C3×D411yescharacteristic
478C23×C3C2×C3×D412yes—
479C23×C3C3×#4112yes—
480C23×C3C3×#4112yes—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—24no—
484C22×D3—24no—
485C22×D3—24no—
486C22×D3—24no—
487C22×D3—24no—
488C22×D3—24no—
489C22×D3—24no—
490C22×D3—24no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3C3×C22⋊C414yescomplemented
502C3×D4—632no—
503C2×C3×C4—28no—
504C2×C3×C4—24no—
505C2×C3×C4—24no—
506C2×C3×C4—24no—
507C2×C3×C4—24no—
508C2×C3×C4—24no—
509C2×C3×C4—24no—
510C2×C3×C4—34no—
511C2×C3×C4—44no—
512C2×C3×C4—44no—
513C2×C3×C4—44no—
514C2×C3×C4—44no—
515C2×C3×C4—44no—
516C2×C3×C4—44no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—42no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4—42no—
524C2×C3×C4—42no—
525C2×C3×C4—62no—
526C2×C3×C4—64no—
527C2×C3×C4—62no—
528C2×C3×C4—64no—
529C2×C3×C4—64no—
530C2×C3×C4—64no—
531C2×C3×C4—64no—
532C2×C3×C4—122no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536#67—232no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—24no—
540C2×Dic3—24no—
541C2×Dic3—24no—
542C2×Dic3—24no—
543C2×Dic3—24no—
544C2×Dic3—42no—
545C2×Dic3—42no—
546C2×Dic3—42no—
547C2×Dic3—42no—
548C2×Dic3C3×C22⋊C414yescomplemented
549C2×C32—44no—
550C2×C32#37911yescharacteristic
551C2×C32#38612yes—
552C2×C32#38611yescharacteristic
553C2×C32#38611yescharacteristic
554C2×C32#39012yes—
555C2×C32#39212yes—
556C2×C32#39212yes—
557C2×C32#39412yes—
558C2×C32#39412yes—
559C3×D3—44no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—32no—
567C24—34no—
568C24—61no—
569C24—62no—
570C24—62no—
571C24—62no—
572C24—62no—
573C24—62no—
574C24—61no—
575C24C3×C4×D312yes—
576C24C3×D1212yes—
577C24C3×#6712yes—
578C24C22×C3×D311yescharacteristic
579C2×D4—68no—
580C2×D4—68no—
581C2×D4—616no—
582C2×D4—616no—
583C2×D4—68no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—32no—
591C22×C4—34no—
592C22×C4—34no—
593C22×C4—61no—
594C22×C4—62no—
595C22×C4—61no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4C3×#6714yescomplemented
603C22⋊C4—28no—
604C22⋊C4—616no—
605C22⋊C4—68no—
606C22×C3—28no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—21no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—48no—
637C22×C3—48no—
638C22×C3—48no—
639C22×C3—48no—
640C22×C3—48no—
641C22×C3—48no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—44no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3—44no—
648C22×C3—44no—
649C22×C3—44no—
650C22×C3—44no—
651C22×C3—44no—
652C22×C3—44no—
653C22×C3—44no—
654C22×C3—64no—
655C22×C3—68no—
656C22×C3—124no—
657C22×C3—122no—
658C22×C3—122no—
659C22×C3—124no—
660C22×C3—124no—
661C22×C3—124no—
662C22×C3—124no—
663C22×C3D3×C22⋊C411yescharacteristic
664C22×C3D3×C22⋊C411yescharacteristic
665C22×C3#67⋊C412yes—
666C22×C3#88212yes—
667C22×C3#88211yescharacteristic
668C22×C3#88312yes—
669C22×C3#88412yes—
670C22×C3#88412yes—
671C22×C3#88512yes—
672C22×C3#88611yescharacteristic
673C22×C3C2×(C2×D3)⋊C411yescharacteristic
674C22×C3C4×#6712yes—
675C22×C3#92911yescharacteristic
676C22×C3#93012yes—
677C22×C3#93712yes—
678C22×C3#93712yes—
679C22×C3#93812yes—
680C22×C3#93912yes—
681C22×C3#93912yes—
682C22×C3#94012yes—
683C22×C3#95311yescharacteristic
684C22×C3C2×C3×C22⋊C411yescharacteristic
685C22×C3C2×C3×C22⋊C411yescharacteristic
686C22×C3C2×C3×C22⋊C411yescharacteristic
687C22×C3C3×C4×D412yes—
688C22×C3C3×C4×D412yes—
689C22×C3C3×#12012yes—
690C22×C3C3×#12011yescharacteristic
691C22×C3C3×#12012yes—
692C22×C3C3×#12012yes—
693C22×C3C3×#12011yescharacteristic
694C22×C3C3×#12112yes—
695C22×C3C3×#12112yes—
696C22×C3C3×#12112yes—
697C22×C3C3×#12112yes—
698C22×C3C3×#12112yes—
699C22×C3C3×#12112yes—
700C22×C3C3×#12312yes—
701C22×C3C3×#12311yescharacteristic
702C22×C3C3×#12311yescharacteristic
703C22×C3C3×#12412yes—
704C22×C3C3×#12712yes—
705C2×D3—24no—
706C2×D3—28no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—44no—
710C2×D3—44no—
711C2×D3—44no—
712C2×D3—44no—
713C2×D3—44no—
714C3×C4—48no—
715C3×C4—44no—
716C3×C4—44no—
717C3×C4—64no—
718C3×C4—124no—
719Dic3—24no—
720Dic3—44no—
721C32#143811yescharacteristic, complemented, Sylow
722C23—22no—
723C23—22no—
724C23—24no—
725C23—22no—
726C23—24no—
727C23—22no—
728C23—24no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—22no—
734C23—34no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—62no—
744C23—64no—
745C23—64no—
746C23—64no—
747C23—64no—
748C23—62no—
749C23—64no—
750C23—64no—
751C23—64no—
752C23—64no—
753C23—121no—
754C23—122no—
755C23—122no—
756C23—121no—
757C23—121no—
758C23—122no—
759C23—122no—
760C23—122no—
761C23—122no—
762C23—121no—
763C23C3×(C2×D3)⋊C414yescomplemented
764C23C2×C3×C4×D311yescharacteristic
765C23C2×C3×D1211yescharacteristic
766C23C3×#23512yes—
767C23C3×D3×D412yes—
768C23C3×D3×D412yes—
769C23C3×D3×D412yes—
770C23C3×#23712yes—
771C23C2×C3×#6711yescharacteristic
772C23C2×C3×#6712yes—
773D4—632no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—34no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—62no—
783C2×C4—64no—
784C2×C4—62no—
785C2×C4—64no—
786C2×C4—64no—
787C2×C4—64no—
788C2×C4—64no—
789C2×C4—122no—
790C2×C4—122no—
791C2×C4—122no—
792C2×C4—122no—
793C2×C3—21no—
794C2×C3—22no—
795C2×C3—22no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—22no—
799C2×C3—22no—
800C2×C3—22no—
801C2×C3—22no—
802C2×C3—48no—
803C2×C3—44no—
804C2×C3—44no—
805C2×C3—124no—
806C2×C3#495511yescharacteristic
807C2×C3#495612yes—
808C2×C3#495712yes—
809C2×C3#495811yescharacteristic
810C2×C3#495912yes—
811C2×C3#496012yes—
812C2×C3#496112yes—
813C2×C3#521311yescharacteristic
814C2×C3#522312yes—
815C2×C3C3×#37911yescharacteristic
816C2×C3C3×#38612yes—
817C2×C3C3×#38611yescharacteristic
818C2×C3C3×#38611yescharacteristic
819C2×C3C3×#39012yes—
820C2×C3C3×#39212yes—
821C2×C3C3×#39212yes—
822C2×C3C3×#39412yes—
823C2×C3C3×#39412yes—
824D3—44no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—64no—
835C22—68no—
836C22—124no—
837C22—122no—
838C22—122no—
839C22—124no—
840C22—124no—
841C22—124no—
842C22—124no—
843C22C3×D3×C22⋊C411yescharacteristic
844C22C3×D3×C22⋊C411yescharacteristic
845C22C3×#67⋊C412yes—
846C22C3×#88212yes—
847C22C3×#88211yescharacteristic
848C22C3×#88312yes—
849C22C3×#88412yes—
850C22C3×#88412yes—
851C22C3×#88512yes—
852C22C3×#88611yescharacteristic
853C22C2×C3×(C2×D3)⋊C411yescharacteristic
854C22C3×C4×#6712yes—
855C22C3×#92911yescharacteristic
856C22C3×#93012yes—
857C22C3×#93712yes—
858C22C3×#93712yes—
859C22C3×#93812yes—
860C22C3×#93912yes—
861C22C3×#93912yes—
862C22C3×#94012yes—
863C22C3×#95311yescharacteristic
864C4—44no—
865C4—64no—
866C4—124no—
867C3—21no—
868C3#7155011yescharacteristic, direct product factor
869C3C3×#143811yescharacteristic, complemented
870C2—44no—
871C2—124no—
872C2C3×#495511yescharacteristic
873C2C3×#495612yes—
874C2C3×#495712yes—
875C2C3×#495811yescharacteristic
876C2C3×#495912yes—
877C2C3×#496012yes—
878C2C3×#496112yes—
879C2C3×#521311yescharacteristic
880C2C3×#522312yes—
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
prime radicalC23×C3×#67C2
cosocleC24×C3C23×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C3×#1438
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C32×C22⋊C4C2semidirect
3. C22×C3×#217C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C2×C3×C3⋊#95C2semidirect
7. #71550C3direct (N × H)
15. C22×C3×#67C4semidirect
31. C22×C3×C22⋊C4D3semidirect
32. C22×C3×C22⋊C4C2×C3semidirect
33. C22×#217C2×C3semidirect
34. C22×(C2×D3)⋊C4C2×C3semidirect
36. C2×C3⋊#95C2×C3semidirect
62. C22×C32×C4D4semidirect
79. C22×C3×Dic3D4semidirect
103. C22×#67C3×C4semidirect
144. C23×C32C22⋊C4semidirect
174. C22×C3×D3C22⋊C4semidirect
194. C2×C3×Dic3C22⋊C4semidirect
198. C22×C22⋊C4C3×D3semidirect
284. C22×C3×C4#67semidirect
285. C22×C3×C4C3×D4semidirect
302. C22×Dic3C3×D4semidirect
461. C23×C3(C2×D3)⋊C4semidirect
462. C23×C3C3×C22⋊C4semidirect
501. C22×D3C3×C22⋊C4semidirect
548. C2×Dic3C3×C22⋊C4semidirect
602. C22×C4C3×#67semidirect
721. C32#1438semidirect
763. C23C3×(C2×D3)⋊C4semidirect
868. C3#71550direct (N × H)
869. C3C3×#1438semidirect

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×C32×C22⋊C42
C22×C3×#2172
C22×C3×(C2×D3)⋊C42
C2×C3×C3⋊#952
C3×#14383
#715503