Finite Group Databasebeta

← C3×#139710 #72271638

Subgroups — C3×#139710 #72271638

Order 1536.

1724 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#23910C211yesmaximal, characteristic
2C3×#14473C211yesmaximal, characteristic, complemented
3C3×#12699C211yesmaximal, characteristic, complemented
4C3×#8455C212yesmaximal, complemented
5C3×#7308C212yesmaximal, complemented
6#139710C311yesmaximal, characteristic, direct product factor, Sylow
7C3×#3486C2211yescharacteristic
8C22×C3×#124C2211yescharacteristic
9C2×C3×#454C412yescomplemented
10C3×#3003—21no—
11C2×C3×#386—21no—
12C2×C3×#355—22no—
13C3×#2003—22no—
14C3×#1896—21no—
15C3×#1888C412yescomplemented
16C3×#1784C2212yes—
17C3×#1784C2211yescharacteristic
18C3×#1504—22no—
19C3×#1504—22no—
20C3×#1446C2212yes—
21C3×#1440—22no—
22C3×#1434—21no—
23C3×C22⋊#95—22no—
24#23910C2×C311yescharacteristic
25#14473C2×C311yescharacteristic, complemented
26#12699C2×C311yescharacteristic, complemented
27#8455C2×C312yescomplemented
28#7308C2×C312yescomplemented
29C2×C3×2−1+4C2×C411yescharacteristic, complemented
30C23×C3×Q8C2311yescharacteristic
31C23×C3×D4D411yescharacteristic
32C24×C3×C4—21no—
33C2×C3×AGL(1,ℤ/8)—22no—
34C3×D4×Q8—41no—
35C3×D4×Q8—41no—
36C3×#548—41no—
37C3×#548—41no—
38C3×#536—21no—
39C3×#536—22no—
40C2×C3×#124—22no—
41C2×C3×#124—44no—
42C2×C3×#124C2×C412yes—
43C2×C3×#124D412yes—
44C3×#525—22no—
45C3×#525—21no—
46C3×#519C2×C411yescharacteristic, complemented
47C22×C3×C22⋊C4—22no—
48C22×C3×C22⋊C4—22no—
49C22×C3×C22⋊C4—21no—
50C22×C3×C42D411yescharacteristic
51C3×#454—44no—
52C3×#450—41no—
53C3×#450—41no—
54C3×#447—41no—
55C3×#447—41no—
56C2×C3×#104—22no—
57C3×#418—22no—
58C2×C3×#101—22no—
59C2×C3×#101—21no—
60C2×C3×#101—22no—
61C2×C3×#101C2×C412yescomplemented
62C3×#407—21no—
63C3×#407—22no—
64C3×#386—44no—
65C2×C3×#95—22no—
66C2×C3×#95—22no—
67C2×C3×#95—21no—
68C2×C3×#95—21no—
69C2×C3×#95—22no—
70C2×C3×#95D412yes—
71C2×C3×#95D412yes—
72C3×#355—44no—
73C3×#339—22no—
74C3×#328—42no—
75C3×#328—42no—
76C3×#327—42no—
77C3×#327—42no—
78#3486C22×C311yescharacteristic
79C22×#124C22×C311yescharacteristic
80C2×#454C3×C412yescomplemented
81#3003—21no—
82C2×#386—21no—
83C2×#355—22no—
84#2003—22no—
85#1896—21no—
86#1888C3×C412yescomplemented
87#1784C22×C312yes—
88#1784C22×C311yescharacteristic
89#1504—22no—
90#1504—22no—
91#1446C22×C312yes—
92#1440—22no—
93#1434—21no—
94C22⋊#95—22no—
95C25×C3—21no—
96C3×2−1+4—42no—
97C3×2−1+4—81no—
98C2×C3×#41—21no—
99C2×C3×#41—22no—
100C2×C3×#41—41no—
101C22×C3×Q8—41no—
102C22×C3×Q8—41no—
103C22×C3×Q8—42no—
104C22×C3×Q8—41no—
105C22×C3×Q8—81no—
106C22×C3×Q8C22×C411yescharacteristic
107C22×C3×Q8C2×D411yescharacteristic
108C22×C3×Q8#4112yes—
109C22×C3×D4—24no—
110C22×C3×D4—21no—
111C22×C3×D4—41no—
112C22×C3×D4—41no—
113C22×C3×D4—81no—
114C22×C3×D4C22⋊C412yes—
115C23×C3×C4—22no—
116C23×C3×C4—21no—
117C23×C3×C4—22no—
118C23×C3×C4—44no—
119C23×C3×C4—42no—
120C23×C3×C4—81no—
121C23×C3×C4—82no—
122C23×C3×C4—81no—
123C23×C3×C4C2×D411yescharacteristic
124C23×C3×C4C2×D412yes—
125C3×AGL(1,ℤ/8)—44no—
126C3×AGL(1,ℤ/8)—82no—
127C2×C3×SD16—42no—
128C2×C3×D8—42no—
129C2×C3×M16—22no—
130C2×C3×M16—42no—
131C3×C4⋊Q8—41no—
132C3×C4⋊Q8—42no—
133C3×#124—24no—
134C3×#124—24no—
135C3×#124—42no—
136C3×#124—42no—
137C3×#124—48no—
138C3×#124—41no—
139C3×#124—42no—
140C3×#123—42no—
141C3×#123—41no—
142C3×C22⋊Q8—21no—
143C3×C22⋊Q8—21no—
144C3×C22⋊Q8—22no—
145C3×C22⋊Q8—22no—
146C3×C22⋊Q8—41no—
147C3×C22⋊Q8—41no—
148C3×C22⋊Q8—42no—
149C3×C22⋊Q8—42no—
150C3×#121—21no—
151C3×#121—21no—
152C3×#121—22no—
153C3×#121—22no—
154C3×#120—41no—
155C3×C4×Q8—41no—
156C3×C4×Q8—41no—
157C3×C4×D4—41no—
158C3×C4×D4—41no—
159C3×C4×D4—42no—
160C3×C4×D4—42no—
161C3×#117—21no—
162C3×#117—22no—
163C2×C3×C22⋊C4—24no—
164C2×C3×C22⋊C4—24no—
165C2×C3×C22⋊C4—44no—
166C2×C3×C22⋊C4—44no—
167C2×C3×C22⋊C4—44no—
168C2×C3×C22⋊C4—44no—
169C2×C3×C22⋊C4—42no—
170C2×C3×C22⋊C4—82no—
171C2×C3×C22⋊C4—81no—
172C2×C3×C22⋊C4—81no—
173C2×C3×C42—21no—
174C2×C3×C42—42no—
175C2×C3×C42C22⋊C412yes—
176C3×#104—44no—
177C3×#102—42no—
178C3×#102—42no—
179C3×#101—42no—
180C3×#101—44no—
181C3×#101—81no—
182C3×#101—82no—
183C3×C22⋊C8—41no—
184C3×C22⋊C8—41no—
185C3×C22⋊C8—42no—
186C3×C22⋊C8—42no—
187C3×#95—42no—
188C3×#95—42no—
189C3×#95—44no—
190C3×#95—44no—
191C3×#95—82no—
192C3×#95—81no—
193C3×#95—81no—
194C2×2−1+4C2×C3×C411yescharacteristic, complemented
195C23×Q8C23×C311yescharacteristic
196C23×D4C3×D411yescharacteristic
197C24×C4—21no—
198C2×AGL(1,ℤ/8)—22no—
199D4×Q8—41no—
200D4×Q8—41no—
201#548—41no—
202#548—41no—
203#536—21no—
204#536—22no—
205C2×#124—22no—
206C2×#124—44no—
207C2×#124C2×C3×C412yes—
208C2×#124C3×D412yes—
209#525—21no—
210#525—22no—
211#519C2×C3×C411yescharacteristic, complemented
212C22×C22⋊C4—22no—
213C22×C22⋊C4—22no—
214C22×C22⋊C4—21no—
215C22×C42C3×D411yescharacteristic
216#454—44no—
217#450—41no—
218#450—41no—
219#447—41no—
220#447—41no—
221C2×#104—22no—
222#418—22no—
223C2×#101—22no—
224C2×#101—21no—
225C2×#101—22no—
226C2×#101C2×C3×C412yescomplemented
227#407—21no—
228#407—22no—
229#386—44no—
230C2×#95—22no—
231C2×#95—22no—
232C2×#95—21no—
233C2×#95—21no—
234C2×#95—22no—
235C2×#95C3×D412yes—
236C2×#95C3×D412yes—
237#355—44no—
238#339—22no—
239#328—42no—
240#328—42no—
241#327—42no—
242#327—42no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—42no—
247C24×C3—42no—
248C24×C3—42no—
249C24×C3—41no—
250C24×C3—42no—
251C24×C3—41no—
252C24×C3—41no—
253C24×C3—41no—
254C24×C3#12011yescharacteristic
255C3×#41—42no—
256C3×#41—42no—
257C3×#41—82no—
258C3×#41—82no—
259C3×#41—84no—
260C2×C3×Q8—22no—
261C2×C3×Q8—22no—
262C2×C3×Q8—21no—
263C2×C3×Q8—22no—
264C2×C3×Q8—41no—
265C2×C3×Q8—41no—
266C2×C3×Q8—41no—
267C2×C3×Q8—42no—
268C2×C3×Q8—41no—
269C2×C3×Q8—42no—
270C2×C3×Q8—42no—
271C2×C3×Q8—84no—
272C2×C3×Q8—84no—
273C2×C3×Q8—84no—
274C2×C3×D4—21no—
275C2×C3×D4—24no—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4—41no—
281C2×C3×D4—41no—
282C2×C3×D4—41no—
283C2×C3×D4—81no—
284C2×C3×D4—81no—
285C2×C3×D4—84no—
286C2×C3×D4—84no—
287C2×C3×D4#9914yes—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—24no—
294C22×C3×C4—22no—
295C22×C3×C4—41no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—41no—
299C22×C3×C4—42no—
300C22×C3×C4—42no—
301C22×C3×C4—42no—
302C22×C3×C4—41no—
303C22×C3×C4—42no—
304C22×C3×C4—42no—
305C22×C3×C4—42no—
306C22×C3×C4—42no—
307C22×C3×C4—41no—
308C22×C3×C4—42no—
309C22×C3×C4—42no—
310C22×C3×C4—42no—
311C22×C3×C4—42no—
312C22×C3×C4—42no—
313C22×C3×C4—42no—
314C22×C3×C4—42no—
315C22×C3×C4—42no—
316C22×C3×C4—42no—
317C22×C3×C4—84no—
318C22×C3×C4—88no—
319C22×C3×C4—88no—
320C22×C3×C4—84no—
321C22×C3×C4—84no—
322C22×C3×C4C2×C22⋊C411yescharacteristic
323C22×C3×C4C4×D412yes—
324C22×C3×C4#12112yes—
325C22×C3×C4#12311yescharacteristic
326C3×SD16—84no—
327C3×D8—84no—
328C3×M16—42no—
329C3×M16—42no—
330C3×M16—82no—
331C3×M16—82no—
332C2×C3×C8—42no—
333C2×C3×C8—82no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—22no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—42no—
339C3×C4⋊C4—42no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—41no—
342C3×C22⋊C4—48no—
343C3×C22⋊C4—48no—
344C3×C22⋊C4—42no—
345C3×C22⋊C4—42no—
346C3×C22⋊C4—41no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—41no—
351C3×C22⋊C4—88no—
352C3×C22⋊C4—84no—
353C3×C42—22no—
354C3×C42—22no—
355C3×C42—42no—
356C3×C42—41no—
357C3×C42—42no—
358C25—21no—
3592−1+4—42no—
3602−1+4—81no—
361C2×#41—21no—
362C2×#41—22no—
363C2×#41—41no—
364C22×Q8—41no—
365C22×Q8—41no—
366C22×Q8—42no—
367C22×Q8—41no—
368C22×Q8—81no—
369C22×Q8C22×C3×C411yescharacteristic
370C22×Q8C2×C3×D411yescharacteristic
371C22×Q8C3×#4112yes—
372C22×D4—24no—
373C22×D4—21no—
374C22×D4—41no—
375C22×D4—41no—
376C22×D4—81no—
377C22×D4C3×C22⋊C412yes—
378C23×C4—21no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—44no—
382C23×C4—42no—
383C23×C4—81no—
384C23×C4—82no—
385C23×C4—81no—
386C23×C4C2×C3×D411yescharacteristic
387C23×C4C2×C3×D412yes—
388AGL(1,ℤ/8)—44no—
389AGL(1,ℤ/8)—82no—
390C2×SD16—42no—
391C2×D8—42no—
392C2×M16—22no—
393C2×M16—42no—
394C4⋊Q8—41no—
395C4⋊Q8—42no—
396#124—24no—
397#124—24no—
398#124—42no—
399#124—42no—
400#124—48no—
401#124—41no—
402#124—42no—
403#123—42no—
404#123—41no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—41no—
410C22⋊Q8—41no—
411C22⋊Q8—42no—
412C22⋊Q8—42no—
413#121—22no—
414#121—22no—
415#121—21no—
416#121—21no—
417#120—41no—
418C4×Q8—41no—
419C4×Q8—41no—
420C4×D4—41no—
421C4×D4—41no—
422C4×D4—42no—
423C4×D4—42no—
424#117—21no—
425#117—22no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—82no—
434C2×C22⋊C4—81no—
435C2×C22⋊C4—81no—
436C2×C42—21no—
437C2×C42—42no—
438C2×C42C3×C22⋊C412yes—
439#104—44no—
440#102—42no—
441#102—42no—
442#101—42no—
443#101—44no—
444#101—81no—
445#101—82no—
446C22⋊C8—41no—
447C22⋊C8—41no—
448C22⋊C8—42no—
449C22⋊C8—42no—
450#95—42no—
451#95—42no—
452#95—44no—
453#95—44no—
454#95—82no—
455#95—81no—
456#95—81no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—22no—
462C23×C3—24no—
463C23×C3—42no—
464C23×C3—44no—
465C23×C3—42no—
466C23×C3—44no—
467C23×C3—42no—
468C23×C3—42no—
469C23×C3—44no—
470C23×C3—44no—
471C23×C3—44no—
472C23×C3—44no—
473C23×C3—42no—
474C23×C3—42no—
475C23×C3—41no—
476C23×C3—82no—
477C23×C3—81no—
478C23×C3—82no—
479C23×C3—82no—
480C23×C3—82no—
481C23×C3—81no—
482C23×C3—82no—
483C23×C3—81no—
484C23×C3—81no—
485C23×C3—82no—
486C23×C3#38611yescharacteristic
487C23×C3B(4,𝔽2)11yescharacteristic
488C23×C3B(4,𝔽2)11yescharacteristic
489C3×Q8—44no—
490C3×Q8—42no—
491C3×Q8—82no—
492C3×Q8—84no—
493C3×Q8—82no—
494C3×D4—44no—
495C3×D4—42no—
496C3×D4—82no—
497C3×D4—84no—
498C3×D4—82no—
499C3×D4—81no—
500C3×D4—81no—
501C3×D4—81no—
502C3×D4—81no—
503C3×D4—82no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4—44no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—44no—
521C2×C3×C4—44no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—42no—
526C2×C3×C4—82no—
527C2×C3×C4—82no—
528C2×C3×C4—82no—
529C2×C3×C4—84no—
530C2×C3×C4—82no—
531C2×C3×C4—82no—
532C2×C3×C4—82no—
533C2×C3×C4—82no—
534C2×C3×C4—82no—
535C2×C3×C4—816no—
536C2×C3×C4—82no—
537C2×C3×C4—82no—
538C2×C3×C4—82no—
539C2×C3×C4—82no—
540C2×C3×C4—82no—
541C2×C3×C4—82no—
542C2×C3×C4—82no—
543C2×C3×C4—82no—
544C2×C3×C4C2×#9912yes—
545C3×C8—82no—
546C3×C8—162no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—42no—
551C24—42no—
552C24—41no—
553C24—42no—
554C24—41no—
555C24—42no—
556C24—41no—
557C24—41no—
558C24C3×#12011yescharacteristic
559#41—42no—
560#41—42no—
561#41—82no—
562#41—82no—
563#41—84no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—41no—
569C2×Q8—41no—
570C2×Q8—41no—
571C2×Q8—42no—
572C2×Q8—41no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—84no—
576C2×Q8—84no—
577C2×Q8—84no—
578C2×D4—21no—
579C2×D4—24no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—84no—
590C2×D4—84no—
591C2×D4C3×#9914yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—41no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—84no—
622C22×C4—88no—
623C22×C4—88no—
624C22×C4—84no—
625C22×C4—84no—
626C22×C4C2×C3×C22⋊C411yescharacteristic
627C22×C4C3×C4×D412yes—
628C22×C4C3×#12112yes—
629C22×C4C3×#12311yescharacteristic
630SD16—84no—
631D8—84no—
632M16—42no—
633M16—42no—
634M16—82no—
635M16—82no—
636C2×C8—42no—
637C2×C8—82no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—41no—
655C22⋊C4—88no—
656C22⋊C4—84no—
657C42—22no—
658C42—22no—
659C42—42no—
660C42—41no—
661C42—42no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—48no—
673C22×C3—44no—
674C22×C3—82no—
675C22×C3—82no—
676C22×C3—84no—
677C22×C3—84no—
678C22×C3—84no—
679C22×C3—82no—
680C22×C3—82no—
681C22×C3—82no—
682C22×C3—82no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3#188911yescharacteristic
687C22×C3#189811yescharacteristic
688C22×C3#191311yescharacteristic
689C22×C3#220211yescharacteristic
690C22×C3#220311yescharacteristic
691C22×C3#220412yes—
692C3×C4—22no—
693C3×C4—42no—
694C3×C4—41no—
695C3×C4—42no—
696C3×C4—82no—
697C3×C4—84no—
698C3×C4—81no—
699C3×C4—81no—
700C3×C4—81no—
701C3×C4—162no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—24no—
708C23—42no—
709C23—44no—
710C23—42no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—82no—
722C23—81no—
723C23—82no—
724C23—82no—
725C23—82no—
726C23—82no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C3×#38611yescharacteristic
732C23C3×B(4,𝔽2)11yescharacteristic
733C23C3×B(4,𝔽2)11yescharacteristic
734Q8—44no—
735Q8—42no—
736Q8—82no—
737Q8—84no—
738Q8—82no—
739D4—44no—
740D4—42no—
741D4—82no—
742D4—84no—
743D4—82no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—82no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4—82no—
774C2×C4—84no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4—82no—
778C2×C4—82no—
779C2×C4—82no—
780C2×C4—816no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4—82no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—82no—
788C2×C4—82no—
789C2×C4C2×C3×#9912yes—
790C8—82no—
791C8—162no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—84no—
798C2×C3—161no—
799C2×C3#949511yescharacteristic
800C2×C3#1305511yescharacteristic
801C2×C3#1305711yescharacteristic
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—48no—
813C22—44no—
814C22—82no—
815C22—82no—
816C22—84no—
817C22—84no—
818C22—84no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22C3×#188911yescharacteristic
827C22C3×#189811yescharacteristic
828C22C3×#191311yescharacteristic
829C22C3×#220211yescharacteristic
830C22C3×#220311yescharacteristic
831C22C3×#220412yes—
832C4—22no—
833C4—42no—
834C4—41no—
835C4—42no—
836C4—84no—
837C4—82no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—162no—
842C3#13971011yescharacteristic, direct product factor, Sylow
843C2—21no—
844C2—21no—
845C2—22no—
846C2—21no—
847C2—21no—
848C2—84no—
849C2—161no—
850C2C3×#949511yescharacteristic
851C2C3×#1305511yescharacteristic
852C2C3×#1305711yescharacteristic
subgroupG/H
center, socleC22×C3#1889
commutatorC22×Q8C22×C3×C4
Frattini, cosocleC23×Q8C23×C3
prime radicalC3×#23910C2
LCSG ▷ C22×Q8 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C23×C3×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#14473C2semidirect
3. C3×#12699C2semidirect
4. C3×#8455C2semidirect
5. C3×#7308C2semidirect
6. #139710C3direct (N × H)
9. C2×C3×#454C4semidirect
15. C3×#1888C4semidirect
25. #14473C2×C3semidirect
26. #12699C2×C3semidirect
27. #8455C2×C3semidirect
28. #7308C2×C3semidirect
29. C2×C3×2−1+4C2×C4semidirect
46. C3×#519C2×C4semidirect
61. C2×C3×#101C2×C4semidirect
80. C2×#454C3×C4semidirect
86. #1888C3×C4semidirect
194. C2×2−1+4C2×C3×C4semidirect
211. #519C2×C3×C4semidirect
226. C2×#101C2×C3×C4semidirect
842. C3#139710direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#239102
C3×#144732
C3×#126992
C3×#84552
C3×#73082
#1397103