Finite Group Databasebeta

← C3×#84084 #11864187

Subgroups — C3×#84084 #11864187

Order 1152.

1953 conjugacy classes of subgroups.

The subgroup lattice has 687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#41C211yesmaximal, characteristic
2C2×C3×#951C212yesmaximal, complemented
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C3×#5239C214yesmaximal, complemented
5C3×#5232C212yesmaximal, complemented
6C3×#5228C212yesmaximal, complemented
7C3×#5218C212yesmaximal, complemented
8C3×#5207C211yesmaximal, characteristic, complemented
9C3×#3007—31nomaximal
10#84084C311yesmaximal, characteristic, direct product factor
11C2×C32×#41—28no—
12C2×C32×#41—21no—
13C2×C32×#41—21no—
14C2×C32×#41C2212yes—
15C2×C32×#41C2212yes—
16C22×C32×Q8C2211yescharacteristic
17C22×C32×D4—21no—
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4—21no—
20C23×C32×C4C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C2×C3×#217—21no—
23C3×#951—28no—
24C2×C3×#216C2214yescomplemented
25C2×C3×#214C2214yescomplemented
26C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
27C3×#924—21no—
28C3×#924—21no—
29C3×#924C2212yes—
30C3×#924C2212yescomplemented
31C2×C3×Dic3⋊C4—21no—
32C2×C3×#208C2212yescomplemented
33C3×#835C2214yescomplemented
34C3×#832C2214yescomplemented
35C3×#830C2212yes—
36C3×#830C2212yescomplemented
37C22×C3×#41—21no—
38C22×C3×#41D311yescharacteristic
39C22×C3×#41C2×C311yescharacteristic
40C2×C3×#137—32no—
41C2×C3×C22⋊Q8—31no—
42C2×#951C2×C312yescomplemented
43C2×#924C2×C311yescharacteristic, complemented
44C3×#452—34no—
45C3×#451—32no—
46C3×#450—32no—
47C3×#417—32no—
48C3×#407—31no—
49#5239C2×C314yescomplemented
50#5232C2×C312yescomplemented
51#5228C2×C312yescomplemented
52#5218C2×C312yescomplemented
53#5207C2×C311yescharacteristic, complemented
54C24×C32—21no—
55C24×C32D411yescharacteristic
56C32×#41—28no—
57C32×#41—28no—
58C32×#41—24no—
59C32×#41—24no—
60C32×#41—24no—
61C32×#41D418yes—
62C2×C32×Q8—24no—
63C2×C32×Q8—21no—
64C2×C32×Q8C2312yes—
65C2×C32×D4—28no—
66C2×C32×D4—22no—
67C2×C32×D4—22no—
68C2×C32×D4—24no—
69C2×C32×D4—21no—
70C2×C32×D4C2312yes—
71C22×C32×C4—28no—
72C22×C32×C4—21no—
73C22×C32×C4—22no—
74C22×C32×C4—22no—
75C22×C32×C4—24no—
76C22×C32×C4D411yescharacteristic
77C22×C32×C4D411yescharacteristic
78C22×C32×C4D411yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C2×C3×Dic6—24no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6C2312yes—
87C3×#217—22no—
88C3×#217—22no—
89C3×#216—28no—
90C3×#214—28no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×#208—24no—
96C2×C3×C3⋊C8C2314yes—
97#3007—31noSylow
98C2×C3×#41—216no—
99C2×C3×#41—22no—
100C2×C3×#41—22no—
101C2×C3×#41—28no—
102C2×C3×#41—28no—
103C2×C3×#41—21no—
104C2×C3×#41—21no—
105C2×C3×#41—21no—
106C2×C3×#41—21no—
107C2×C3×#41—22no—
108C2×C3×#41—22no—
109C2×C3×#41C2×D312yes—
110C2×C3×#41C2×D312yes—
111C2×C3×#41C22×C312yes—
112C2×C3×#41C22×C312yes—
113C22×C3×Q8—21no—
114C22×C3×Q8—31no—
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×Q8C22×C311yescharacteristic
117C22×C3×D4—22no—
118C22×C3×D4—21no—
119C22×C3×D4—21no—
120C22×C3×D4—21no—
121C22×C3×D4C2×D311yescharacteristic
122C22×C3×D4C22×C311yescharacteristic
123C23×C3×C4—22no—
124C23×C3×C4—21no—
125C23×C3×C4—21no—
126C23×C3×C4—21no—
127C23×C3×C4C2×D311yescharacteristic
128C23×C3×C4C22×C311yescharacteristic
129C22×Dic6C22×C311yescharacteristic, complemented
130C3×#137—68no—
131C2×C3×Q16—34no—
132C2×C3×SD16—34no—
133C2×C3×M16—32no—
134C3×C22⋊Q8—32no—
135C3×C22⋊Q8—32no—
136C3×C22⋊Q8—61no—
137C3×C22⋊Q8—61no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—61no—
140C2×C3×C22⋊C4—61no—
141C2×#217—21no—
142#951—28no—
143C2×#216C22×C314yescomplemented
144C2×#214C22×C314yescomplemented
145C2×C4⋊Dic3C22×C311yescharacteristic, complemented
146#924—21no—
147#924—21no—
148#924C22×C312yes—
149#924C22×C312yescomplemented
150C2×Dic3⋊C4—21no—
151C2×#208C22×C312yescomplemented
152C3×#103—34no—
153C3×#102—34no—
154C3×C22⋊C8—32no—
155C3×C22⋊C8—32no—
156#835C22×C314yescomplemented
157#832C22×C314yescomplemented
158#830C22×C312yes—
159#830C22×C312yescomplemented
160C23×C32—24no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—41no—
165C23×C32—42no—
166C23×C32—42no—
167C23×C32C2×D411yescharacteristic
168C23×C32C2×D411yescharacteristic
169C23×C32C2×D411yescharacteristic
170C32×Q8—24no—
171C32×Q8—22no—
172C32×Q8C2×D414yes—
173C32×D4—28no—
174C32×D4—24no—
175C32×D4—28no—
176C32×D4—22no—
177C32×D4C2×D414yes—
178C2×C32×C4—24no—
179C2×C32×C4—28no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—28no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D414yes—
191C2×C32×C4C2411yescharacteristic
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—42no—
195C2×C3×Dic3—42no—
196C3×Dic6—24no—
197C3×Dic6—42no—
198C3×C3⋊C8—24no—
199C22×#41C3×D311yescharacteristic
200C2×#137—32no—
201C2×C22⋊Q8—31no—
202#452—34no—
203#451—32no—
204#450—32no—
205#417—32no—
206#407—31no—
207C24×C3—22no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3#6711yescharacteristic
212C24×C3C3×D411yescharacteristic
213C3×#41—216no—
214C3×#41—216no—
215C3×#41—28no—
216C3×#41—28no—
217C3×#41—28no—
218C3×#41—28no—
219C3×#41—28no—
220C3×#41—28no—
221C3×#41—28no—
222C3×#41—24no—
223C3×#41—24no—
224C3×#41—24no—
225C3×#41—24no—
226C3×#41—24no—
227C3×#41—24no—
228C3×#41—28no—
229C3×#41#6718yes—
230C3×#41C3×D418yes—
231C2×C3×Q8—28no—
232C2×C3×Q8—22no—
233C2×C3×Q8—24no—
234C2×C3×Q8—24no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—22no—
238C2×C3×Q8—32no—
239C2×C3×Q8—61no—
240C2×C3×Q8—64no—
241C2×C3×Q8C22×D312yes—
242C2×C3×Q8C23×C312yes—
243C2×C3×D4—216no—
244C2×C3×D4—28no—
245C2×C3×D4—28no—
246C2×C3×D4—24no—
247C2×C3×D4—24no—
248C2×C3×D4—28no—
249C2×C3×D4—22no—
250C2×C3×D4—22no—
251C2×C3×D4—22no—
252C2×C3×D4—22no—
253C2×C3×D4—22no—
254C2×C3×D4—24no—
255C2×C3×D4—24no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—22no—
259C2×C3×D4C22×D312yes—
260C2×C3×D4C23×C312yes—
261C22×C3×C4—22no—
262C22×C3×C4—216no—
263C22×C3×C4—28no—
264C22×C3×C4—28no—
265C22×C3×C4—24no—
266C22×C3×C4—24no—
267C22×C3×C4—28no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—24no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—24no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—61no—
283C22×C3×C4—61no—
284C22×C3×C4#6711yescharacteristic
285C22×C3×C4#6711yescharacteristic
286C22×C3×C4#6711yescharacteristic
287C22×C3×C4C3×D411yescharacteristic
288C22×C3×C4C3×D411yescharacteristic
289C22×C3×C4C3×D411yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C23×C311yescharacteristic
294C22×C3×C4C23×C311yescharacteristic
295C22×C3×C4C23×C311yescharacteristic
296C22×Dic3—21no—
297C22×Dic3—21no—
298C2×Dic6—24no—
299C2×Dic6—21no—
300C2×Dic6C23×C312yes—
301C3×Q16—68no—
302C3×SD16—68no—
303C3×M16—64no—
304C2×C3×C8—34no—
305C3×C4⋊C4—32no—
306C3×C4⋊C4—62no—
307C3×C4⋊C4—62no—
308C3×C4⋊C4—61no—
309C3×C22⋊C4—62no—
310C3×C22⋊C4—62no—
311#217—22no—
312#217—22no—
313#216—28no—
314#214—28no—
315C4⋊Dic3—21no—
316C4⋊Dic3C23×C312yes—
317Dic3⋊C4—22no—
318Dic3⋊C4—22no—
319#208—24no—
320C2×C3⋊C8C23×C314yes—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—24no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—44no—
330C22×C32—48no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32#12012yes—
334C22×C32#13712yescomplemented
335C22×C32C22×D411yescharacteristic
336C32×C4—21no—
337C32×C4—24no—
338C32×C4—21no—
339C32×C4#12012yes—
340C32×C4C22×D412yes—
341C3×Dic3—42no—
342C3×Dic3—42no—
343C2×#41—28no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41C2×C3×D312yes—
347C2×#41C2×C3×D312yes—
348C22×Q8—31no—
349C22×Q8C2×C3×D311yescharacteristic
350C22×D4—21no—
351C22×D4C2×C3×D311yescharacteristic
352C23×C4—21no—
353C23×C4C2×C3×D311yescharacteristic
354#137—68no—
355C2×Q16—34no—
356C2×SD16—34no—
357C2×M16—32no—
358C22⋊Q8—32no—
359C22⋊Q8—32no—
360C22⋊Q8—61no—
361C22⋊Q8—61no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C22⋊C4—61no—
365#103—34no—
366#102—34no—
367C22⋊C8—32no—
368C22⋊C8—32no—
369C23×C3—28no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—42no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—42no—
387C23×C3—44no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—44no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3C2×#6711yescharacteristic
394C23×C3C2×#6711yescharacteristic
395C23×C3C2×#6711yescharacteristic
396C23×C3C2×C3×D411yescharacteristic
397C23×C3C2×C3×D411yescharacteristic
398C23×C3C2×C3×D411yescharacteristic
399C3×Q8—28no—
400C3×Q8—24no—
401C3×Q8—24no—
402C3×Q8—24no—
403C3×Q8—22no—
404C3×Q8—22no—
405C3×Q8—24no—
406C3×Q8—64no—
407C3×Q8—122no—
408C3×Q8C2×#6714yes—
409C3×Q8C2×C3×D414yes—
410C3×D4—216no—
411C3×D4—28no—
412C3×D4—28no—
413C3×D4—24no—
414C3×D4—28no—
415C3×D4—24no—
416C3×D4—216no—
417C3×D4—24no—
418C3×D4—28no—
419C3×D4—28no—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—24no—
423C3×D4C2×#6714yes—
424C3×D4C2×C3×D414yes—
425C2×C3×C4—24no—
426C2×C3×C4—28no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—216no—
432C2×C3×C4—28no—
433C2×C3×C4—28no—
434C2×C3×C4—24no—
435C2×C3×C4—216no—
436C2×C3×C4—24no—
437C2×C3×C4—24no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—28no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—28no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—24no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—122no—
460C2×C3×C4—122no—
461C2×C3×C4C2×#6711yescharacteristic
462C2×C3×C4C2×#6711yescharacteristic
463C2×C3×C4C2×#6711yescharacteristic
464C2×C3×C4C2×#6714yes—
465C2×C3×C4C2×C3×D411yescharacteristic
466C2×C3×C4C2×C3×D411yescharacteristic
467C2×C3×C4C2×C3×D411yescharacteristic
468C2×C3×C4C2×C3×D414yes—
469C2×C3×C4C23×D311yescharacteristic
470C2×C3×C4C24×C311yescharacteristic
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475Dic6—24no—
476Dic6—42no—
477C3×C8—64no—
478C3⋊C8—24no—
479C2×C32—22no—
480C2×C32—22no—
481C2×C32—41no—
482C2×C32—44no—
483C2×C32C2×#12011yescharacteristic
484C2×C32C2×#13711yescharacteristic
485C2×C32#57511yescharacteristic
486C24—21no—
487C24C3×#6711yescharacteristic
488#41—28no—
489#41—28no—
490#41—24no—
491#41—24no—
492#41—24no—
493#41C3×#6718yes—
494C2×Q8—24no—
495C2×Q8—21no—
496C2×Q8—32no—
497C2×Q8—61no—
498C2×Q8—64no—
499C2×Q8C22×C3×D312yes—
500C2×D4—28no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—24no—
504C2×D4—21no—
505C2×D4C22×C3×D312yes—
506C22×C4—28no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4C3×#6711yescharacteristic
514C22×C4C3×#6711yescharacteristic
515C22×C4C3×#6711yescharacteristic
516C22×C4C22×C3×D311yescharacteristic
517C22×C4C22×C3×D311yescharacteristic
518C22×C4C22×C3×D311yescharacteristic
519Q16—68no—
520SD16—68no—
521M16—64no—
522C2×C8—34no—
523C4⋊C4—32no—
524C4⋊C4—61no—
525C4⋊C4—62no—
526C4⋊C4—62no—
527C22⋊C4—62no—
528C22⋊C4—62no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—22no—
540C22×C3—28no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—24no—
547C22×C3—21no—
548C22×C3—24no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—21no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—48no—
559C22×C3—416no—
560C22×C3—48no—
561C22×C3—48no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3#95112yescomplemented
569C22×C3#95312yes—
570C22×C3C3×#12012yes—
571C22×C3C3×#13712yescomplemented
572C22×C3C22×#6711yescharacteristic
573C22×C3C22×C3×D411yescharacteristic
574C3×C4—22no—
575C3×C4—28no—
576C3×C4—22no—
577C3×C4—21no—
578C3×C4—24no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—24no—
582C3×C4—21no—
583C3×C4—22no—
584C3×C4—22no—
585C3×C4—122no—
586C3×C4—122no—
587C3×C4#95312yes—
588C3×C4C3×#12012yes—
589C3×C4C22×#6712yes—
590C3×C4C22×C3×D412yes—
591Dic3—42no—
592Dic3—42no—
593C32#300711yescharacteristic, complemented, Sylow
594C23—24no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—41no—
599C23—42no—
600C23—42no—
601C23C2×C3×#6711yescharacteristic
602C23C2×C3×#6711yescharacteristic
603C23C2×C3×#6711yescharacteristic
604Q8—24no—
605Q8—22no—
606Q8—64no—
607Q8—122no—
608Q8C2×C3×#6714yes—
609D4—28no—
610D4—24no—
611D4—28no—
612D4—22no—
613D4C2×C3×#6714yes—
614C2×C4—24no—
615C2×C4—28no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—62no—
624C2×C4—62no—
625C2×C4—122no—
626C2×C4—122no—
627C2×C4C2×C3×#6711yescharacteristic
628C2×C4C2×C3×#6711yescharacteristic
629C2×C4C2×C3×#6711yescharacteristic
630C2×C4C2×C3×#6714yes—
631C2×C4C23×C3×D311yescharacteristic
632C8—64no—
633C2×C3—24no—
634C2×C3—22no—
635C2×C3—22no—
636C2×C3—22no—
637C2×C3—22no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—42no—
642C2×C3—42no—
643C2×C3—48no—
644C2×C3—41no—
645C2×C3—44no—
646C2×C3—41no—
647C2×C3—44no—
648C2×C3#582211yescharacteristic
649C2×C3C2×#95111yescharacteristic
650C2×C3C2×#95311yescharacteristic
651C2×C3C2×C3×#12011yescharacteristic
652C2×C3C2×C3×#13711yescharacteristic
653C2×C3C3×#57511yescharacteristic
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—24no—
662C22—44no—
663C22—48no—
664C22—42no—
665C22—42no—
666C22C3×#95112yescomplemented
667C22C3×#95312yes—
668C22C22×C3×#6711yescharacteristic
669C4—21no—
670C4—24no—
671C4—21no—
672C4—122no—
673C4—122no—
674C4C3×#95312yes—
675C4C22×C3×#6712yes—
676C3—21no—
677C3#8408411yescharacteristic, direct product factor
678C3C3×#300711yescharacteristic, complemented
679C2—22no—
680C2—22no—
681C2—41no—
682C2—44no—
683C2C3×#582211yescharacteristic
684C2C2×C3×#95111yescharacteristic
685C2C2×C3×#95311yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC22×C32×#41C2
socleC22×C32C22×D4
hypercenterC22×C3×#41D3
hypocenterC3C3×#3007
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×C3×#924C2semidirect
4. C3×#5239C2semidirect
5. C3×#5232C2semidirect
6. C3×#5228C2semidirect
7. C3×#5218C2semidirect
8. C3×#5207C2semidirect
10. #84084C3direct (N × H)
21. C22×C3×Dic6C22semidirect
24. C2×C3×#216C22semidirect
25. C2×C3×#214C22semidirect
26. C2×C3×C4⋊Dic3C22semidirect
30. C3×#924C22semidirect
32. C2×C3×#208C22semidirect
33. C3×#835C22semidirect
34. C3×#832C22semidirect
36. C3×#830C22semidirect
42. C2×#951C2×C3semidirect
43. C2×#924C2×C3semidirect
49. #5239C2×C3semidirect
50. #5232C2×C3semidirect
51. #5228C2×C3semidirect
52. #5218C2×C3semidirect
53. #5207C2×C3semidirect
129. C22×Dic6C22×C3semidirect
143. C2×#216C22×C3semidirect
144. C2×#214C22×C3semidirect
145. C2×C4⋊Dic3C22×C3semidirect
149. #924C22×C3semidirect
151. C2×#208C22×C3semidirect
156. #835C22×C3semidirect
157. #832C22×C3semidirect
159. #830C22×C3semidirect
334. C22×C32#137semidirect
568. C22×C3#951semidirect
571. C22×C3C3×#137semidirect
593. C32#3007semidirect
666. C22C3×#951semidirect
677. C3#84084direct (N × H)
678. C3C3×#3007semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#412
C2×C3×#9512
C2×C3×#9242
C3×#52392
C3×#52322
C3×#52282
C3×#52182
C3×#52072
C3×#30073
#840843