Finite Group Databasebeta

← C3×#23924 #10642531

Subgroups — C3×#23924 #10642531

Order 768.

1952 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#537C211yesmaximal, characteristic, complemented
2C2×C3×#535C211yesmaximal, characteristic, complemented
3C2×C3×#449C212yesmaximal, complemented
4C2×C3×#450C211yesmaximal, characteristic, complemented
5C2×C3×#447C211yesmaximal, characteristic, complemented
6C3×#2000C212yesmaximal, complemented
7C3×#1999C212yesmaximal, complemented
8C3×#1875C211yesmaximal, characteristic, complemented
9C3×#1874C212yesmaximal, complemented
10C3×#1873C211yesmaximal, characteristic, complemented
11C3×#1780C211yesmaximal, characteristic, complemented
12#23924C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C22×C3×#41C2211yescharacteristic, complemented
15C23×C3×D4C2211yescharacteristic
16C22×C3×SD16C2212yes—
17C22×C3×D8C2212yes—
18C3×#537—24no—
19C3×#537—24no—
20C3×#535—28no—
21C2×C3×#127—21no—
22C2×C3×#124—21no—
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic, complemented
26C2×C3×#121—21no—
27C2×C3×#121—21no—
28C2×C3×#121—21no—
29C2×C3×#121C2212yes—
30C2×C3×#121C2212yes—
31C2×C3×#121C2211yescharacteristic
32C2×C3×#121C2211yescharacteristic, complemented
33C2×C3×#120—21no—
34C2×C3×#120—21no—
35C2×C3×#117C2211yescharacteristic
36C22×C3×C4⋊C4C2211yescharacteristic, complemented
37C3×#450—24no—
38C3×#449—28no—
39C3×#447—24no—
40C2×C3×#103C2212yescomplemented
41C2×C3×#102C2212yes—
42C2×C3×#102C2212yes—
43C2×C3×#102C2212yescomplemented
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2212yescomplemented
47C2×C3×C22⋊C8C2212yescomplemented
48C3×#340C2212yescomplemented
49C3×#340C2212yescomplemented
50C2×#537C2×C311yescharacteristic, complemented
51C2×#535C2×C311yescharacteristic, complemented
52C2×#449C2×C312yescomplemented
53C2×#450C2×C311yescharacteristic, complemented
54C2×#447C2×C311yescharacteristic, complemented
55#2000C2×C312yescomplemented
56#1999C2×C312yescomplemented
57#1875C2×C311yescharacteristic, complemented
58#1874C2×C312yescomplemented
59#1873C2×C311yescharacteristic, complemented
60#1780C2×C311yescharacteristic, complemented
61C25×C3—21no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—24no—
65C2×C3×#41—22no—
66C2×C3×#41—22no—
67C2×C3×#41—24no—
68C2×C3×#41—42no—
69C2×C3×#41—42no—
70C22×C3×Q8D411yescharacteristic
71C22×C3×Q8C2311yescharacteristic
72C22×C3×D4—21no—
73C22×C3×D4—22no—
74C22×C3×D4—22no—
75C22×C3×D4—21no—
76C22×C3×D4—21no—
77C22×C3×D4—24no—
78C22×C3×D4—21no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—42no—
82C22×C3×D4D411yescharacteristic
83C22×C3×D4D411yescharacteristic
84C22×C3×D4D411yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C22×C3×D4C2312yes—
87C23×C3×C4—21no—
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C2×C3×SD16—24no—
93C2×C3×SD16—24no—
94C2×C3×SD16—42no—
95C2×C3×D8—24no—
96C2×C3×D8—24no—
97C2×C3×D8—42no—
98C22×C3×C8C2312yes—
99C22×C3×C8C2312yes—
100C3×#127—28no—
101C3×#124—28no—
102C3×C22⋊Q8—28no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8D414yescomplemented
107C3×#121—28no—
108C3×#121—28no—
109C3×#121—28no—
110C3×#121—24no—
111C3×#121—22no—
112C3×#121—24no—
113C3×#121—22no—
114C3×#121—24no—
115C3×#121—22no—
116C3×#121D414yescomplemented
117C3×#121D418yescomplemented
118C3×#120—28no—
119C3×#120—28no—
120C3×#117—24no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C42—21no—
137C3×#103—24no—
138C3×#102—24no—
139C3×#102—24no—
140C3×#102—24no—
141C3×C22⋊C8—22no—
142C3×C22⋊C8—22no—
143C3×C22⋊C8—24no—
144C3×C22⋊C8—42no—
145C22×#41C22×C311yescharacteristic
146C22×#41C22×C311yescharacteristic, complemented
147C23×D4C22×C311yescharacteristic
148C22×SD16C22×C312yes—
149C22×D8C22×C312yes—
150#537—24no—
151#537—24no—
152#535—28no—
153C2×#127—21no—
154C2×#124—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8C22×C311yescharacteristic
157C2×C22⋊Q8C22×C311yescharacteristic, complemented
158C2×#121—21no—
159C2×#121—21no—
160C2×#121—21no—
161C2×#121C22×C312yes—
162C2×#121C22×C312yes—
163C2×#121C22×C311yescharacteristic
164C2×#121C22×C311yescharacteristic, complemented
165C2×#120—21no—
166C2×#120—21no—
167C2×#117C22×C311yescharacteristic
168C22×C4⋊C4C22×C311yescharacteristic, complemented
169#450—24no—
170#449—28no—
171#447—24no—
172C2×#103C22×C312yescomplemented
173C2×#102C22×C312yes—
174C2×#102C22×C312yes—
175C2×#102C22×C312yescomplemented
176C2×C22⋊C8C22×C311yescharacteristic
177C2×C22⋊C8C22×C311yescharacteristic
178C2×C22⋊C8C22×C312yescomplemented
179C2×C22⋊C8C22×C312yescomplemented
180#340C22×C312yescomplemented
181#340C22×C312yescomplemented
182C24×C3—24no—
183C24×C3—22no—
184C24×C3—21no—
185C24×C3—42no—
186C24×C3—42no—
187C24×C3—82no—
188C24×C3—82no—
189C24×C3C2×D411yescharacteristic
190C24×C3C2×D411yescharacteristic
191C24×C3C2×D411yescharacteristic
192C3×#41—48no—
193C3×#41—48no—
194C3×#41—48no—
195C3×#41—48no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—21no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8—41no—
202C2×C3×Q8C2×D412yes—
203C2×C3×D4—24no—
204C2×C3×D4—24no—
205C2×C3×D4—22no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—22no—
209C2×C3×D4—28no—
210C2×C3×D4—24no—
211C2×C3×D4—28no—
212C2×C3×D4—24no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—21no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—48no—
224C2×C3×D4—48no—
225C2×C3×D4—41no—
226C2×C3×D4—41no—
227C2×C3×D4—41no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—82no—
233C2×C3×D4—82no—
234C2×C3×D4—82no—
235C2×C3×D4—82no—
236C2×C3×D4—82no—
237C2×C3×D4—82no—
238C2×C3×D4C2×D412yes—
239C2×C3×D4C2×D414yes—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—24no—
246C22×C3×C4—22no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—24no—
251C22×C3×C4—22no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4—82no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D414yes—
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2411yescharacteristic
265C3×SD16—48no—
266C3×D8—48no—
267C2×C3×C8—22no—
268C2×C3×C8—22no—
269C2×C3×C8—22no—
270C2×C3×C8—22no—
271C2×C3×C8—22no—
272C2×C3×C8—22no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4C2×D412yes—
280C3×C4⋊C4C2×D412yes—
281C3×C4⋊C4C2×D414yes—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—28no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—28no—
288C3×C22⋊C4—24no—
289C3×C42—24no—
290C25—21no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—24no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—24no—
297C2×#41—42no—
298C2×#41—42no—
299C22×Q8C3×D411yescharacteristic
300C22×Q8C23×C311yescharacteristic
301C22×D4—21no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—24no—
307C22×D4—21no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—42no—
311C22×D4C3×D411yescharacteristic
312C22×D4C3×D411yescharacteristic
313C22×D4C3×D411yescharacteristic
314C22×D4C23×C312yes—
315C22×D4C23×C311yescharacteristic
316C23×C4—21no—
317C23×C4—21no—
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320C23×C4C23×C311yescharacteristic
321C2×SD16—24no—
322C2×SD16—24no—
323C2×SD16—42no—
324C2×D8—24no—
325C2×D8—24no—
326C2×D8—42no—
327C22×C8C23×C312yes—
328C22×C8C23×C312yes—
329#127—28no—
330#124—28no—
331C22⋊Q8—28no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8C3×D414yescomplemented
336#121—28no—
337#121—28no—
338#121—28no—
339#121—24no—
340#121—22no—
341#121—24no—
342#121—22no—
343#121—24no—
344#121—22no—
345#121C3×D418yescomplemented
346#121C3×D414yescomplemented
347#120—28no—
348#120—28no—
349#117—24no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4C23×C311yescharacteristic
356C2×C4⋊C4C23×C311yescharacteristic
357C2×C4⋊C4C23×C312yes—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C42—21no—
366#103—24no—
367#102—24no—
368#102—24no—
369#102—24no—
370C22⋊C8—22no—
371C22⋊C8—22no—
372C22⋊C8—24no—
373C22⋊C8—42no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—21no—
383C23×C3—22no—
384C23×C3—24no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—48no—
390C23×C3—41no—
391C23×C3—42no—
392C23×C3—41no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—84no—
401C23×C3—84no—
402C23×C3—88no—
403C23×C3—88no—
404C23×C3#12012yes—
405C23×C3#12012yes—
406C23×C3C22×D411yescharacteristic
407C3×Q8—24no—
408C3×Q8—44no—
409C3×Q8—42no—
410C3×D4—24no—
411C3×D4—24no—
412C3×D4—24no—
413C3×D4—44no—
414C3×D4—44no—
415C3×D4—48no—
416C3×D4—44no—
417C3×D4—48no—
418C3×D4—42no—
419C3×D4—42no—
420C3×D4—42no—
421C3×D4—84no—
422C3×D4—88no—
423C3×D4—84no—
424C3×D4—88no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—48no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—84no—
450C2×C3×C4#12012yes—
451C2×C3×C4#12012yes—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D412yes—
455C2×C3×C4H(5,𝔽2)12yes—
456C3×C8—42no—
457C3×C8—42no—
458C24—24no—
459C24—21no—
460C24—22no—
461C24—42no—
462C24—42no—
463C24—82no—
464C24—82no—
465C24C2×C3×D411yescharacteristic
466C24C2×C3×D411yescharacteristic
467C24C2×C3×D411yescharacteristic
468#41—48no—
469#41—48no—
470#41—48no—
471#41—48no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—21no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—41no—
478C2×Q8C2×C3×D412yes—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—28no—
486C2×D4—24no—
487C2×D4—28no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—82no—
509C2×D4—82no—
510C2×D4—82no—
511C2×D4—82no—
512C2×D4—82no—
513C2×D4—82no—
514C2×D4C2×C3×D412yes—
515C2×D4C2×C3×D414yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—82no—
534C22×C4C2×C3×D411yescharacteristic
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D414yes—
538C22×C4C2×C3×D412yes—
539C22×C4C2×C3×D412yes—
540C22×C4C24×C311yescharacteristic
541SD16—48no—
542D8—48no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—22no—
555C4⋊C4C2×C3×D412yes—
556C4⋊C4C2×C3×D412yes—
557C4⋊C4C2×C3×D414yes—
558C22⋊C4—24no—
559C22⋊C4—28no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—28no—
564C22⋊C4—24no—
565C42—24no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—24no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—41no—
578C22×C3—44no—
579C22×C3—42no—
580C22×C3—41no—
581C22×C3—42no—
582C22×C3—41no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—44no—
586C22×C3—44no—
587C22×C3—816no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3—82no—
593C22×C3—82no—
594C22×C3C2×#12011yescharacteristic
595C22×C3C2×#12011yescharacteristic
596C22×C3#53411yescharacteristic
597C22×C3#57612yes—
598C22×C3#57712yes—
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—41no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—44no—
606C3×C4D4212yes—
607C3×C4D4212yes—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—22no—
618C23—21no—
619C23—22no—
620C23—24no—
621C23—21no—
622C23—21no—
623C23—48no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—41no—
633C23—42no—
634C23—84no—
635C23—84no—
636C23—88no—
637C23—88no—
638C23C3×#12012yes—
639C23C3×#12012yes—
640C23C22×C3×D411yescharacteristic
641Q8—24no—
642Q8—44no—
643Q8—42no—
644D4—24no—
645D4—24no—
646D4—24no—
647D4—44no—
648D4—44no—
649D4—48no—
650D4—44no—
651D4—48no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—84no—
656D4—88no—
657D4—84no—
658D4—88no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—48no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4C3×#12012yes—
685C2×C4C3×#12012yes—
686C2×C4C22×C3×D411yescharacteristic
687C2×C4C22×C3×D411yescharacteristic
688C2×C4C22×C3×D412yes—
689C2×C4C3×H(5,𝔽2)12yes—
690C8—42no—
691C8—42no—
692C2×C3—42no—
693C2×C3—42no—
694C2×C3—81no—
695C2×C3—82no—
696C2×C3—84no—
697C2×C3#240311yescharacteristic
698C2×C3#300811yescharacteristic
699C2×C3#301011yescharacteristic
700C2×C3#301212yes—
701C2×C3#319812yes—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—24no—
707C22—42no—
708C22—42no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—41no—
714C22—44no—
715C22—42no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—44no—
722C22—44no—
723C22—816no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22C2×C3×#12011yescharacteristic
731C22C2×C3×#12011yescharacteristic
732C22C3×#53411yescharacteristic
733C22C3×#57612yes—
734C22C3×#57712yes—
735C4—22no—
736C4—22no—
737C4—41no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—44no—
742C4C3×D4212yes—
743C4C3×D4212yes—
744C3#2392411yescharacteristic, direct product factor, Sylow
745C2—42no—
746C2—42no—
747C2—81no—
748C2—84no—
749C2—82no—
750C2C3×#240311yescharacteristic
751C2C3×#300811yescharacteristic
752C2C3×#301011yescharacteristic
753C2C3×#301212yes—
754C2C3×#319812yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#537C2semidirect
2. C2×C3×#535C2semidirect
3. C2×C3×#449C2semidirect
4. C2×C3×#450C2semidirect
5. C2×C3×#447C2semidirect
6. C3×#2000C2semidirect
7. C3×#1999C2semidirect
8. C3×#1875C2semidirect
9. C3×#1874C2semidirect
10. C3×#1873C2semidirect
11. C3×#1780C2semidirect
12. #23924C3direct (N × H)
14. C22×C3×#41C22semidirect
25. C2×C3×C22⋊Q8C22semidirect
32. C2×C3×#121C22semidirect
36. C22×C3×C4⋊C4C22semidirect
40. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
46. C2×C3×C22⋊C8C22semidirect
47. C2×C3×C22⋊C8C22semidirect
48. C3×#340C22semidirect
49. C3×#340C22semidirect
50. C2×#537C2×C3semidirect
51. C2×#535C2×C3semidirect
52. C2×#449C2×C3semidirect
53. C2×#450C2×C3semidirect
54. C2×#447C2×C3semidirect
55. #2000C2×C3semidirect
56. #1999C2×C3semidirect
57. #1875C2×C3semidirect
58. #1874C2×C3semidirect
59. #1873C2×C3semidirect
60. #1780C2×C3semidirect
106. C3×C22⋊Q8D4semidirect
116. C3×#121D4semidirect
117. C3×#121D4semidirect
146. C22×#41C22×C3semidirect
157. C2×C22⋊Q8C22×C3semidirect
164. C2×#121C22×C3semidirect
168. C22×C4⋊C4C22×C3semidirect
172. C2×#103C22×C3semidirect
175. C2×#102C22×C3semidirect
178. C2×C22⋊C8C22×C3semidirect
179. C2×C22⋊C8C22×C3semidirect
180. #340C22×C3semidirect
181. #340C22×C3semidirect
335. C22⋊Q8C3×D4semidirect
345. #121C3×D4semidirect
346. #121C3×D4semidirect
744. C3#23924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5372
C2×C3×#5352
C2×C3×#4492
C2×C3×#4502
C2×C3×#4472
C3×#20002
C3×#19992
C3×#18752
C3×#18742
C3×#18732
C3×#17802
#239243