Finite Group Databasebeta

← C2×C3×#3091 #10679113

Subgroups — C2×C3×#3091 #10679113

Order 768.

2378 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2C22×C3×#117C211yesmaximal, characteristic, complemented
3C3×#3091C2116yesmaximal, direct product factor
4C2×C3×#484C211yesmaximal, characteristic, complemented
5C2×C3×#481C211yesmaximal, characteristic, complemented
6C2×C3×#485C212yesmaximal, complemented
7C2×C3×#482C212yesmaximal, complemented
8C2×C3×#483C211yesmaximal, characteristic, complemented
9C2×C3×#480C211yesmaximal, characteristic, complemented
10C2×C3×#427C212yesmaximal, complemented
11C2×C3×#416C212yesmaximal, complemented
12C22×C3×C22⋊C8C211yesmaximal, characteristic, complemented
13C2×#3091C311yesmaximal, characteristic, direct product factor, Sylow
14C22×C3×#41C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C23×C3×C8C2212yes—
17C3×#525—24no—
18C3×#525C2218yes—
19C2×C3×#123—21no—
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24C2×C3×#120—21no—
25C2×C3×C4×D4—21no—
26C2×C3×C4×D4—21no—
27C2×C3×#117—21no—
28C2×C3×#117—24no—
29C2×C3×#117—21no—
30C2×C3×#117C2212yes—
31C2×C3×#117C2212yes—
32C2×C3×#117C2211yescharacteristic
33C2×C3×#117C2218yescomplemented
34C22×C3×C4⋊C4C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4—21no—
37C22×C3×C42—21no—
38C3×#485C22116yescomplemented
39C3×#484C2218yescomplemented
40C3×#483C2218yescomplemented
41C3×#482C22116yescomplemented
42C3×#481C2218yescomplemented
43C3×#480C2218yescomplemented
44C3×#427C22116yescomplemented
45C2×C3×#107C2212yescomplemented
46C2×C3×#107C2212yescomplemented
47C2×C3×#106C2212yescomplemented
48C2×C3×#106C2212yescomplemented
49C3×#416C22116yescomplemented
50C2×C3×#103C2212yescomplemented
51C2×C3×#103C2212yescomplemented
52C2×C3×#102C2212yescomplemented
53C2×C3×#102C2212yescomplemented
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×C22⋊C8C2211yescharacteristic
56C2×C3×C22⋊C8C2212yes—
57C2×C3×C22⋊C8C2218yescomplemented
58C2×#525C2×C311yescharacteristic
59C22×#117C2×C311yescharacteristic, complemented
60#3091C2×C3116yesdirect product factor
61C2×#484C2×C311yescharacteristic, complemented
62C2×#481C2×C311yescharacteristic, complemented
63C2×#485C2×C312yescomplemented
64C2×#482C2×C312yescomplemented
65C2×#483C2×C311yescharacteristic, complemented
66C2×#480C2×C311yescharacteristic, complemented
67C2×#427C2×C312yescomplemented
68C2×#416C2×C312yescomplemented
69C22×C22⋊C8C2×C311yescharacteristic, complemented
70C25×C3D411yescharacteristic
71C2×C3×#41—22no—
72C2×C3×#41—28no—
73C2×C3×#41C2314yes—
74C22×C3×Q8C2311yescharacteristic
75C22×C3×D4—21no—
76C22×C3×D4—21no—
77C22×C3×D4—21no—
78C22×C3×D4C2311yescharacteristic
79C23×C3×C4—28no—
80C23×C3×C4—21no—
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C23×C3×C4D411yescharacteristic
84C23×C3×C4D414yes—
85C23×C3×C4D411yescharacteristic
86C23×C3×C4D411yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2314yes—
90C23×C3×C4C2311yescharacteristic
91C22×C3×C8—28no—
92C22×C3×C8C2312yes—
93C22×C3×C8C2312yes—
94C22×C3×C8C2318yes—
95C3×#123—28no—
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—22no—
98C3×C22⋊Q8C2314yes—
99C3×C22⋊Q8C2314yes—
100C3×#121—22no—
101C3×#121—22no—
102C3×#121C2314yes—
103C3×#121C2314yes—
104C3×#120—28no—
105C3×C4×D4—28no—
106C3×C4×D4—28no—
107C3×#117—24no—
108C3×#117—24no—
109C3×#117—28no—
110C3×#117—28no—
111C3×#117—22no—
112C3×#117C2318yes—
113C3×#117C2314yes—
114C3×#117C2318yes—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—28no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C42—22no—
136C2×C3×C42—28no—
137C2×C3×C42—22no—
138C2×C3×C42—21no—
139C3×#107C2318yescomplemented
140C3×#107C2318yescomplemented
141C3×#106C2318yescomplemented
142C3×#106C2318yescomplemented
143C3×#103C2318yescomplemented
144C3×#103C2318yescomplemented
145C3×#102C2318yescomplemented
146C3×#102C2318yescomplemented
147C3×C22⋊C8C2314yes—
148C3×C22⋊C8C2314yes—
149C3×C22⋊C8C2318yes—
150C22×#41C22×C311yescharacteristic
151C24×C4C22×C311yescharacteristic
152C23×C8C22×C312yes—
153#525—24no—
154#525C22×C318yes—
155C2×#123—21no—
156C2×C22⋊Q8C22×C311yescharacteristic
157C2×C22⋊Q8C22×C311yescharacteristic
158C2×#121C22×C311yescharacteristic
159C2×#121C22×C311yescharacteristic
160C2×#120—21no—
161C2×C4×D4—21no—
162C2×C4×D4—21no—
163C2×#117—21no—
164C2×#117—21no—
165C2×#117—24no—
166C2×#117C22×C312yes—
167C2×#117C22×C312yes—
168C2×#117C22×C311yescharacteristic
169C2×#117C22×C318yescomplemented
170C22×C4⋊C4C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172C22×C22⋊C4—21no—
173C22×C42—21no—
174#485C22×C3116yescomplemented
175#484C22×C318yescomplemented
176#483C22×C318yescomplemented
177#482C22×C3116yescomplemented
178#481C22×C318yescomplemented
179#480C22×C318yescomplemented
180#427C22×C3116yescomplemented
181C2×#107C22×C312yescomplemented
182C2×#107C22×C312yescomplemented
183C2×#106C22×C312yescomplemented
184C2×#106C22×C312yescomplemented
185#416C22×C3116yescomplemented
186C2×#103C22×C312yescomplemented
187C2×#103C22×C312yescomplemented
188C2×#102C22×C312yescomplemented
189C2×#102C22×C312yescomplemented
190C2×C22⋊C8C22×C311yescharacteristic
191C2×C22⋊C8C22×C311yescharacteristic
192C2×C22⋊C8C22×C312yes—
193C2×C22⋊C8C22×C318yescomplemented
194C24×C3—24no—
195C24×C3—24no—
196C24×C3—21no—
197C24×C3—42no—
198C24×C3C2×D411yescharacteristic
199C24×C3C2×D414yes—
200C24×C3C2×D411yescharacteristic
201C24×C3C2×D411yescharacteristic
202C3×#41—216no—
203C3×#41—48no—
204C2×C3×Q8—21no—
205C2×C3×Q8—24no—
206C2×C3×Q8C2412yes—
207C2×C3×D4—24no—
208C2×C3×D4—24no—
209C2×C3×D4—24no—
210C2×C3×D4—21no—
211C2×C3×D4—24no—
212C2×C3×D4—44no—
213C2×C3×D4—44no—
214C2×C3×D4—44no—
215C2×C3×D4C2412yes—
216C22×C3×C4—24no—
217C22×C3×C4—24no—
218C22×C3×C4—24no—
219C22×C3×C4—216no—
220C22×C3×C4—24no—
221C22×C3×C4—24no—
222C22×C3×C4—216no—
223C22×C3×C4—24no—
224C22×C3×C4—24no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—24no—
231C22×C3×C4—44no—
232C22×C3×C4—44no—
233C22×C3×C4—44no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D414yes—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D414yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D414yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4#4118yes—
244C22×C3×C4C2412yes—
245C22×C3×C4C2412yes—
246C22×C3×C4C2411yescharacteristic
247C22×C3×C4C2412yes—
248C2×C3×C8—24no—
249C2×C3×C8—24no—
250C2×C3×C8—216no—
251C2×C3×C8C2414yes—
252C2×C3×C8C2414yes—
253C3×C4⋊C4—24no—
254C3×C4⋊C4—24no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4C2414yes—
262C3×C4⋊C4C2414yes—
263C3×C4⋊C4C2412yes—
264C3×C4⋊C4C2412yes—
265C3×C22⋊C4—28no—
266C3×C22⋊C4—28no—
267C3×C22⋊C4—24no—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—24no—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272C3×C42—28no—
273C3×C42—28no—
274C3×C42—24no—
275C25C3×D411yescharacteristic
276C2×#41—22no—
277C2×#41—28no—
278C2×#41C23×C314yes—
279C22×Q8C23×C311yescharacteristic
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C23×C311yescharacteristic
284C23×C4—28no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4C3×D411yescharacteristic
289C23×C4C3×D411yescharacteristic
290C23×C4C3×D414yes—
291C23×C4C3×D411yescharacteristic
292C23×C4C23×C311yescharacteristic
293C23×C4C23×C311yescharacteristic
294C23×C4C23×C314yes—
295C23×C4C23×C311yescharacteristic
296C22×C8—28no—
297C22×C8C23×C312yes—
298C22×C8C23×C312yes—
299C22×C8C23×C318yes—
300#123—28no—
301C22⋊Q8—22no—
302C22⋊Q8—22no—
303C22⋊Q8C23×C314yes—
304C22⋊Q8C23×C314yes—
305#121—22no—
306#121—22no—
307#121C23×C314yes—
308#121C23×C314yes—
309#120—28no—
310C4×D4—28no—
311C4×D4—28no—
312#117—24no—
313#117—24no—
314#117—28no—
315#117—28no—
316#117—22no—
317#117C23×C318yes—
318#117C23×C318yes—
319#117C23×C314yes—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4C23×C312yes—
327C2×C4⋊C4C23×C312yes—
328C2×C4⋊C4C23×C314yes—
329C2×C4⋊C4C23×C314yes—
330C2×C4⋊C4C23×C311yescharacteristic
331C2×C4⋊C4C23×C311yescharacteristic
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—28no—
343C2×C42—21no—
344#107C23×C318yescomplemented
345#107C23×C318yescomplemented
346#106C23×C318yescomplemented
347#106C23×C318yescomplemented
348#103C23×C318yescomplemented
349#103C23×C318yescomplemented
350#102C23×C318yescomplemented
351#102C23×C318yescomplemented
352C22⋊C8C23×C314yes—
353C22⋊C8C23×C314yes—
354C22⋊C8C23×C318yes—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—28no—
360C23×C3—22no—
361C23×C3—28no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—44no—
366C23×C3—416no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3#12314yes—
371C23×C3#13514yes—
372C23×C3C22×D412yes—
373C23×C3C22×D412yes—
374C23×C3C22×D412yes—
375C23×C3C22×D411yescharacteristic
376C3×Q8—24no—
377C3×Q8—42no—
378C3×D4—24no—
379C3×D4—48no—
380C3×D4—48no—
381C3×D4—48no—
382C3×D4—42no—
383C2×C3×C4—28no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—28no—
387C2×C3×C4—28no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—48no—
398C2×C3×C4—42no—
399C2×C3×C4—48no—
400C2×C3×C4—44no—
401C2×C3×C4—42no—
402C2×C3×C4—44no—
403C2×C3×C4—42no—
404C2×C3×C4—48no—
405C2×C3×C4#12314yes—
406C2×C3×C4#12318yes—
407C2×C3×C4C22×D412yes—
408C2×C3×C4C22×D412yes—
409C2×C3×C4C22×D412yes—
410C2×C3×C4C22×D411yescharacteristic
411C2×C3×C4C2×#4114yes—
412C2×C3×C4C2×#4118yes—
413C2×C3×C4C2511yescharacteristic
414C3×C8—24no—
415C3×C8—24no—
416C24—24no—
417C24—24no—
418C24—21no—
419C24—42no—
420C24C2×C3×D411yescharacteristic
421C24C2×C3×D414yes—
422C24C2×C3×D411yescharacteristic
423C24C2×C3×D411yescharacteristic
424#41—216no—
425#41—48no—
426C2×Q8—21no—
427C2×Q8—24no—
428C2×Q8C24×C312yes—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—21no—
433C2×D4—24no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4C24×C312yes—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—216no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—216no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4C2×C3×D411yescharacteristic
457C22×C4C2×C3×D414yes—
458C22×C4C2×C3×D411yescharacteristic
459C22×C4C2×C3×D412yes—
460C22×C4C2×C3×D414yes—
461C22×C4C2×C3×D412yes—
462C22×C4C2×C3×D414yes—
463C22×C4C2×C3×D411yescharacteristic
464C22×C4C2×C3×D412yes—
465C22×C4C3×#4118yes—
466C22×C4C24×C312yes—
467C22×C4C24×C312yes—
468C22×C4C24×C311yescharacteristic
469C22×C4C24×C312yes—
470C2×C8—24no—
471C2×C8—24no—
472C2×C8—216no—
473C2×C8C24×C314yes—
474C2×C8C24×C314yes—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—24no—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4C24×C314yes—
484C4⋊C4C24×C314yes—
485C4⋊C4C24×C312yes—
486C4⋊C4C24×C312yes—
487C22⋊C4—28no—
488C22⋊C4—28no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C42—28no—
495C42—28no—
496C42—24no—
497C22×C3—28no—
498C22×C3—28no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—416no—
507C22×C3—44no—
508C22×C3—42no—
509C22×C3—42no—
510C22×C3—42no—
511C22×C3—84no—
512C22×C3C2×#12314yes—
513C22×C3C2×#12312yes—
514C22×C3C2×#13514yes—
515C22×C3C2×#13512yes—
516C22×C3#57512yes—
517C22×C3C23×D411yescharacteristic
518C3×C4—22no—
519C3×C4—22no—
520C3×C4—42no—
521C3×C4—44no—
522C3×C4—42no—
523C3×C4—44no—
524C3×C4—42no—
525C3×C4C2×#12314yes—
526C3×C4C2×#12312yes—
527C3×C4C22×#4112yes—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—28no—
533C23—22no—
534C23—22no—
535C23—28no—
536C23—22no—
537C23—22no—
538C23—44no—
539C23—416no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23C3×#12314yes—
544C23C3×#13514yes—
545C23C22×C3×D412yes—
546C23C22×C3×D412yes—
547C23C22×C3×D412yes—
548C23C22×C3×D411yescharacteristic
549Q8—24no—
550Q8—42no—
551D4—24no—
552D4—48no—
553D4—48no—
554D4—48no—
555D4—42no—
556C2×C4—28no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—28no—
562C2×C4—28no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—48no—
571C2×C4—48no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—48no—
578C2×C4C3×#12314yes—
579C2×C4C3×#12318yes—
580C2×C4C22×C3×D412yes—
581C2×C4C22×C3×D412yes—
582C2×C4C22×C3×D412yes—
583C2×C4C22×C3×D411yescharacteristic
584C2×C4C2×C3×#4114yes—
585C2×C4C2×C3×#4118yes—
586C2×C4C25×C311yescharacteristic
587C8—24no—
588C8—24no—
589C2×C3—24no—
590C2×C3—24no—
591C2×C3—42no—
592C2×C3—82no—
593C2×C3#309114yesdirect product factor
594C2×C3C22×#12311yescharacteristic
595C2×C3C22×#13511yescharacteristic
596C2×C3C2×#57511yescharacteristic
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—28no—
602C22—28no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—416no—
607C22—44no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—84no—
612C22C2×C3×#12314yes—
613C22C2×C3×#12312yes—
614C22C2×C3×#13514yes—
615C22C2×C3×#13512yes—
616C22C3×#57512yes—
617C22C23×C3×D411yescharacteristic
618C4—22no—
619C4—22no—
620C4—42no—
621C4—44no—
622C4—42no—
623C4—44no—
624C4—42no—
625C4C2×C3×#12314yes—
626C4C2×C3×#12312yes—
627C4C22×C3×#4112yes—
628C3C2×#309111yescharacteristic, direct product factor, Sylow
629C2—24no—
630C2—24no—
631C2—42no—
632C2—82no—
633C2C3×#309114yesdirect product factor
634C2C22×C3×#12311yescharacteristic
635C2C22×C3×#13511yescharacteristic
636C2C2×C3×#57511yescharacteristic
subgroupG/H
centerC22×C3×C4C2×D4
commutator, Frattini, cosocleC2×C4C25×C3
socleC23×C3C22×D4
prime radicalC2×C3×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C4 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×#117C2semidirect
3. C3×#3091C2direct (N × H)
4. C2×C3×#484C2semidirect
5. C2×C3×#481C2semidirect
6. C2×C3×#485C2semidirect
7. C2×C3×#482C2semidirect
8. C2×C3×#483C2semidirect
9. C2×C3×#480C2semidirect
10. C2×C3×#427C2semidirect
11. C2×C3×#416C2semidirect
12. C22×C3×C22⋊C8C2semidirect
13. C2×#3091C3direct (N × H)
33. C2×C3×#117C22semidirect
38. C3×#485C22semidirect
39. C3×#484C22semidirect
40. C3×#483C22semidirect
41. C3×#482C22semidirect
42. C3×#481C22semidirect
43. C3×#480C22semidirect
44. C3×#427C22semidirect
45. C2×C3×#107C22semidirect
46. C2×C3×#107C22semidirect
47. C2×C3×#106C22semidirect
48. C2×C3×#106C22semidirect
49. C3×#416C22semidirect
50. C2×C3×#103C22semidirect
51. C2×C3×#103C22semidirect
52. C2×C3×#102C22semidirect
53. C2×C3×#102C22semidirect
57. C2×C3×C22⋊C8C22semidirect
59. C22×#117C2×C3semidirect
60. #3091C2×C3direct (N × H)
61. C2×#484C2×C3semidirect
62. C2×#481C2×C3semidirect
63. C2×#485C2×C3semidirect
64. C2×#482C2×C3semidirect
65. C2×#483C2×C3semidirect
66. C2×#480C2×C3semidirect
67. C2×#427C2×C3semidirect
68. C2×#416C2×C3semidirect
69. C22×C22⋊C8C2×C3semidirect
139. C3×#107C23semidirect
140. C3×#107C23semidirect
141. C3×#106C23semidirect
142. C3×#106C23semidirect
143. C3×#103C23semidirect
144. C3×#103C23semidirect
145. C3×#102C23semidirect
146. C3×#102C23semidirect
169. C2×#117C22×C3semidirect
174. #485C22×C3semidirect
175. #484C22×C3semidirect
176. #483C22×C3semidirect
177. #482C22×C3semidirect
178. #481C22×C3semidirect
179. #480C22×C3semidirect
180. #427C22×C3semidirect
181. C2×#107C22×C3semidirect
182. C2×#107C22×C3semidirect
183. C2×#106C22×C3semidirect
184. C2×#106C22×C3semidirect
185. #416C22×C3semidirect
186. C2×#103C22×C3semidirect
187. C2×#103C22×C3semidirect
188. C2×#102C22×C3semidirect
189. C2×#102C22×C3semidirect
193. C2×C22⋊C8C22×C3semidirect
344. #107C23×C3semidirect
345. #107C23×C3semidirect
346. #106C23×C3semidirect
347. #106C23×C3semidirect
348. #103C23×C3semidirect
349. #103C23×C3semidirect
350. #102C23×C3semidirect
351. #102C23×C3semidirect
593. C2×C3#3091direct (N × H)
628. C3C2×#3091direct (N × H)
633. C2C3×#3091direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C22×C3×#1172
C3×#30912
C2×C3×#4842
C2×C3×#4812
C2×C3×#4852
C2×C3×#4822
C2×C3×#4832
C2×C3×#4802
C2×C3×#4272
C2×C3×#4162
C22×C3×C22⋊C82
C2×#30913