Finite Group Databasebeta

← C2×C3×#3105 #10679139

Subgroups — C2×C3×#3105 #10679139

Order 768.

2602 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C22×C3×C4×D4C211yesmaximal, characteristic, complemented
3C3×#3105C2116yesmaximal, direct product factor
4C2×C3×#484C211yesmaximal, characteristic, complemented
5C2×C3×#481C211yesmaximal, characteristic, complemented
6C2×C3×#478C212yesmaximal, complemented
7C2×C3×#463C212yesmaximal, complemented
8C2×C3×#450C211yesmaximal, characteristic, complemented
9C2×C3×#447C211yesmaximal, characteristic
10C2×C3×C4×SD16C212yesmaximal, complemented
11C2×C3×C4×D8C212yesmaximal, complemented
12C2×C3×#431C211yesmaximal, characteristic, complemented
13C2×#3105C311yesmaximal, characteristic, direct product factor, Sylow
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4—21no—
16C22×C3×SD16C2212yes—
17C22×C3×D8C2212yes—
18C3×#529—24no—
19C3×#529C2218yescomplemented
20C2×C3×#126—21no—
21C2×C3×#125C2211yescharacteristic, complemented
22C2×C3×#124C2211yescharacteristic, complemented
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic, complemented
27C2×C3×C4×D4—21no—
28C2×C3×C4×D4—21no—
29C2×C3×C4×D4—24no—
30C2×C3×C4×D4—21no—
31C2×C3×C4×D4C2212yes—
32C2×C3×C4×D4C2212yes—
33C2×C3×C4×D4C2218yescomplemented
34C2×C3×C4×D4C2211yescharacteristic, complemented
35C2×C3×#117—21no—
36C22×C3×C4⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4—21no—
38C22×C3×C42C2211yescharacteristic
39C3×#484C2218yescomplemented
40C3×#481C2218yescomplemented
41C3×#478C22116yescomplemented
42C3×#463C22116yescomplemented
43C3×#450C2218yescomplemented
44C3×#447C2218yes—
45C3×C4×SD16C22116yescomplemented
46C3×C4×D8C22116yescomplemented
47C3×#431C2218yescomplemented
48C2×C3×#107C2212yescomplemented
49C2×C3×#106C2212yescomplemented
50C2×C3×C4⋊C8C2212yescomplemented
51C2×C3×#103C2212yescomplemented
52C2×C3×#102C2212yes—
53C2×C3×#102C2212yes—
54C2×C3×#102C2212yescomplemented
55C2×C3×C22⋊C8C2211yescharacteristic
56C2×C3×C22⋊C8C2211yescharacteristic
57C2×C3×C4×C8C2212yescomplemented
58C2×#529C2×C311yescharacteristic, complemented
59C22×C4×D4C2×C311yescharacteristic, complemented
60#3105C2×C3116yesdirect product factor
61C2×#484C2×C311yescharacteristic, complemented
62C2×#481C2×C311yescharacteristic, complemented
63C2×#478C2×C312yescomplemented
64C2×#463C2×C312yescomplemented
65C2×#450C2×C311yescharacteristic, complemented
66C2×#447C2×C311yescharacteristic
67C2×C4×SD16C2×C312yescomplemented
68C2×C4×D8C2×C312yescomplemented
69C2×#431C2×C311yescharacteristic, complemented
70C25×C3—21no—
71C22×C3×Q8C2311yescharacteristic
72C22×C3×D4—28no—
73C22×C3×D4—21no—
74C22×C3×D4—21no—
75C22×C3×D4—22no—
76C22×C3×D4C2311yescharacteristic
77C22×C3×D4C2314yes—
78C22×C3×D4C2312yes—
79C23×C3×C4—21no—
80C23×C3×C4—22no—
81C23×C3×C4—28no—
82C23×C3×C4—22no—
83C23×C3×C4—21no—
84C23×C3×C4—48no—
85C23×C3×C4D411yescharacteristic
86C23×C3×C4D411yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C2×C3×SD16—28no—
89C2×C3×SD16C2318yes—
90C2×C3×D8—28no—
91C2×C3×D8C2318yes—
92C22×C3×C8C2312yes—
93C22×C3×C8C2312yes—
94C3×#126—28no—
95C3×#125—22no—
96C3×#125C2314yescomplemented
97C3×#124—22no—
98C3×#124C2314yescomplemented
99C3×#123—28no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8C2314yes—
102C3×#121—22no—
103C3×#121C2314yes—
104C3×C4×Q8—22no—
105C3×C4×Q8C2314yescomplemented
106C3×C4×D4—28no—
107C3×C4×D4—24no—
108C3×C4×D4—24no—
109C3×C4×D4—28no—
110C3×C4×D4—28no—
111C3×C4×D4—22no—
112C3×C4×D4C2318yes—
113C3×C4×D4C2318yes—
114C3×C4×D4C2314yescomplemented
115C3×#117—28no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C22⋊C4—21no—
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×C42—21no—
135C2×C3×C42D411yescharacteristic
136C2×C3×C42D414yes—
137C2×C3×C42D411yescharacteristic
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2314yes—
140C2×C3×C42C2311yescharacteristic
141C3×#107C2318yescomplemented
142C3×#106C2318yescomplemented
143C3×C4⋊C8C2318yescomplemented
144C3×#103C2318yescomplemented
145C3×#102C2318yes—
146C3×#102C2318yes—
147C3×#102C2318yescomplemented
148C3×C22⋊C8C2314yes—
149C3×C22⋊C8C2314yes—
150C3×C4×C8C2318yescomplemented
151C23×D4C22×C311yescharacteristic
152C24×C4—21no—
153C22×SD16C22×C312yes—
154C22×D8C22×C312yes—
155#529—24no—
156#529C22×C318yescomplemented
157C2×#126—21no—
158C2×#125C22×C311yescharacteristic, complemented
159C2×#124C22×C311yescharacteristic, complemented
160C2×#123—21no—
161C2×C22⋊Q8C22×C311yescharacteristic
162C2×#121C22×C311yescharacteristic
163C2×C4×Q8C22×C311yescharacteristic, complemented
164C2×C4×D4—21no—
165C2×C4×D4—21no—
166C2×C4×D4—21no—
167C2×C4×D4—24no—
168C2×C4×D4C22×C312yes—
169C2×C4×D4C22×C312yes—
170C2×C4×D4C22×C318yescomplemented
171C2×C4×D4C22×C311yescharacteristic, complemented
172C2×#117—21no—
173C22×C4⋊C4C22×C311yescharacteristic
174C22×C22⋊C4—21no—
175C22×C42C22×C311yescharacteristic
176#484C22×C318yescomplemented
177#481C22×C318yescomplemented
178#478C22×C3116yescomplemented
179#463C22×C3116yescomplemented
180#450C22×C318yescomplemented
181#447C22×C318yes—
182C4×SD16C22×C3116yescomplemented
183C4×D8C22×C3116yescomplemented
184#431C22×C318yescomplemented
185C2×#107C22×C312yescomplemented
186C2×#106C22×C312yescomplemented
187C2×C4⋊C8C22×C312yescomplemented
188C2×#103C22×C312yescomplemented
189C2×#102C22×C312yes—
190C2×#102C22×C312yes—
191C2×#102C22×C312yescomplemented
192C2×C22⋊C8C22×C311yescharacteristic
193C2×C22⋊C8C22×C311yescharacteristic
194C2×C4×C8C22×C312yescomplemented
195C24×C3—28no—
196C24×C3—24no—
197C24×C3—22no—
198C24×C3—21no—
199C24×C3—44no—
200C24×C3—44no—
201C24×C3C2×D411yescharacteristic
202C2×C3×Q8—21no—
203C2×C3×Q8—24no—
204C2×C3×Q8C2412yes—
205C2×C3×D4—28no—
206C2×C3×D4—216no—
207C2×C3×D4—216no—
208C2×C3×D4—24no—
209C2×C3×D4—24no—
210C2×C3×D4—22no—
211C2×C3×D4—21no—
212C2×C3×D4—24no—
213C2×C3×D4—24no—
214C2×C3×D4—44no—
215C2×C3×D4#4118yes—
216C2×C3×D4C2412yes—
217C2×C3×D4C2414yes—
218C22×C3×C4—24no—
219C22×C3×C4—24no—
220C22×C3×C4—24no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—24no—
225C22×C3×C4—22no—
226C22×C3×C4—24no—
227C22×C3×C4—28no—
228C22×C3×C4—28no—
229C22×C3×C4—48no—
230C22×C3×C4—432no—
231C22×C3×C4—44no—
232C22×C3×C4—44no—
233C22×C3×C4—48no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D414yes—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D414yes—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2412yes—
243C22×C3×C4C2411yescharacteristic
244C3×SD16—216no—
245C3×D8—216no—
246C2×C3×C8—24no—
247C2×C3×C8—24no—
248C2×C3×C8C2414yes—
249C2×C3×C8C2414yes—
250C3×C4⋊C4—24no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—24no—
253C3×C4⋊C4—24no—
254C3×C4⋊C4—24no—
255C3×C4⋊C4—24no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4C2412yes—
259C3×C4⋊C4C2412yes—
260C3×C4⋊C4C2414yes—
261C3×C22⋊C4—24no—
262C3×C22⋊C4—28no—
263C3×C22⋊C4—28no—
264C3×C22⋊C4—24no—
265C3×C22⋊C4—24no—
266C3×C22⋊C4—24no—
267C3×C22⋊C4—24no—
268C3×C42—24no—
269C3×C42C2×D414yes—
270C3×C42C2×D412yes—
271C3×C42C2×D412yes—
272C3×C42C2×D414yes—
273C3×C42C2412yes—
274C3×C42C2412yes—
275C25—21no—
276C22×Q8C23×C311yescharacteristic
277C22×D4—28no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—22no—
281C22×D4C23×C314yes—
282C22×D4C23×C311yescharacteristic
283C22×D4C23×C312yes—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—28no—
289C23×C4—48no—
290C23×C4C3×D411yescharacteristic
291C23×C4C3×D411yescharacteristic
292C23×C4C23×C311yescharacteristic
293C2×SD16—28no—
294C2×SD16C23×C318yes—
295C2×D8—28no—
296C2×D8C23×C318yes—
297C22×C8C23×C312yes—
298C22×C8C23×C312yes—
299#126—28no—
300#125—22no—
301#125C23×C314yescomplemented
302#124—22no—
303#124C23×C314yescomplemented
304#123—28no—
305C22⋊Q8—22no—
306C22⋊Q8C23×C314yes—
307#121—22no—
308#121C23×C314yes—
309C4×Q8—22no—
310C4×Q8C23×C314yescomplemented
311C4×D4—28no—
312C4×D4—24no—
313C4×D4—24no—
314C4×D4—28no—
315C4×D4—28no—
316C4×D4—22no—
317C4×D4C23×C318yes—
318C4×D4C23×C318yes—
319C4×D4C23×C314yescomplemented
320#117—28no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4C23×C312yes—
328C2×C4⋊C4C23×C314yes—
329C2×C4⋊C4C23×C311yescharacteristic
330C2×C4⋊C4C23×C311yescharacteristic
331C2×C22⋊C4—21no—
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×C42—21no—
340C2×C42C3×D411yescharacteristic
341C2×C42C3×D411yescharacteristic
342C2×C42C3×D414yes—
343C2×C42C23×C311yescharacteristic
344C2×C42C23×C311yescharacteristic
345C2×C42C23×C314yes—
346#107C23×C318yescomplemented
347#106C23×C318yescomplemented
348C4⋊C8C23×C318yescomplemented
349#103C23×C318yescomplemented
350#102C23×C318yes—
351#102C23×C318yes—
352#102C23×C318yescomplemented
353C22⋊C8C23×C314yes—
354C22⋊C8C23×C314yes—
355C4×C8C23×C318yescomplemented
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—216no—
359C23×C3—28no—
360C23×C3—24no—
361C23×C3—22no—
362C23×C3—48no—
363C23×C3—432no—
364C23×C3—48no—
365C23×C3—44no—
366C23×C3—44no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3#13514yes—
371C23×C3C22×D412yes—
372C23×C3C22×D411yescharacteristic
373C3×Q8—24no—
374C3×Q8—42no—
375C3×D4—216no—
376C3×D4—28no—
377C3×D4—24no—
378C3×D4—24no—
379C3×D4—48no—
380C3×D4—42no—
381C3×D4C2×#4118yes—
382C2×C3×C4—22no—
383C2×C3×C4—28no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—28no—
389C2×C3×C4—24no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—416no—
395C2×C3×C4—48no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—44no—
400C2×C3×C4—48no—
401C2×C3×C4—416no—
402C2×C3×C4AGL(1,ℤ/8)14yes—
403C2×C3×C4C22×D412yes—
404C2×C3×C4C22×D412yes—
405C2×C3×C4C22×D412yes—
406C2×C3×C4C22×D412yes—
407C2×C3×C4C22×D411yescharacteristic
408C2×C3×C4C22×D412yes—
409C2×C3×C4C2×#4114yes—
410C2×C3×C4C2511yescharacteristic
411C3×C8—24no—
412C3×C8—24no—
413C24—28no—
414C24—24no—
415C24—22no—
416C24—21no—
417C24—44no—
418C24—44no—
419C24C2×C3×D411yescharacteristic
420C2×Q8—21no—
421C2×Q8—24no—
422C2×Q8C24×C312yes—
423C2×D4—28no—
424C2×D4—216no—
425C2×D4—216no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—44no—
433C2×D4C3×#4118yes—
434C2×D4C24×C312yes—
435C2×D4C24×C314yes—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—48no—
448C22×C4—432no—
449C22×C4—44no—
450C22×C4—48no—
451C22×C4—44no—
452C22×C4C2×C3×D411yescharacteristic
453C22×C4C2×C3×D412yes—
454C22×C4C2×C3×D411yescharacteristic
455C22×C4C2×C3×D411yescharacteristic
456C22×C4C2×C3×D414yes—
457C22×C4C2×C3×D411yescharacteristic
458C22×C4C2×C3×D414yes—
459C22×C4C2×C3×D411yescharacteristic
460C22×C4C24×C312yes—
461C22×C4C24×C311yescharacteristic
462SD16—216no—
463D8—216no—
464C2×C8—24no—
465C2×C8—24no—
466C2×C8C24×C314yes—
467C2×C8C24×C314yes—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4C24×C312yes—
477C4⋊C4C24×C312yes—
478C4⋊C4C24×C314yes—
479C22⋊C4—24no—
480C22⋊C4—28no—
481C22⋊C4—28no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C42—24no—
487C42C2×C3×D414yes—
488C42C2×C3×D412yes—
489C42C2×C3×D412yes—
490C42C2×C3×D414yes—
491C42C24×C312yes—
492C42C24×C312yes—
493C22×C3—28no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—28no—
497C22×C3—432no—
498C22×C3—416no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—84no—
505C22×C3#52512yes—
506C22×C3C2×#13514yes—
507C22×C3C2×#13512yes—
508C22×C3C2×AGL(1,ℤ/8)12yes—
509C22×C3C23×D411yescharacteristic
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—42no—
515C3×C4—42no—
516C3×C4—42no—
517C3×C4—44no—
518C3×C4#52512yes—
519C3×C4C2×AGL(1,ℤ/8)14yes—
520C3×C4C22×#4112yes—
521C23—22no—
522C23—22no—
523C23—216no—
524C23—24no—
525C23—28no—
526C23—22no—
527C23—48no—
528C23—432no—
529C23—48no—
530C23—44no—
531C23—44no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23C3×#13514yes—
536C23C22×C3×D412yes—
537C23C22×C3×D411yescharacteristic
538Q8—24no—
539Q8—42no—
540D4—216no—
541D4—24no—
542D4—24no—
543D4—28no—
544D4—48no—
545D4—42no—
546D4C2×C3×#4118yes—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—28no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—416no—
560C2×C4—48no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—416no—
566C2×C4—48no—
567C2×C4C3×AGL(1,ℤ/8)14yes—
568C2×C4C22×C3×D412yes—
569C2×C4C22×C3×D412yes—
570C2×C4C22×C3×D412yes—
571C2×C4C22×C3×D412yes—
572C2×C4C22×C3×D412yes—
573C2×C4C22×C3×D411yescharacteristic
574C2×C4C2×C3×#4114yes—
575C2×C4C25×C311yescharacteristic
576C8—24no—
577C8—24no—
578C2×C3—24no—
579C2×C3—48no—
580C2×C3—82no—
581C2×C3#310514yesdirect product factor
582C2×C3C2×#52511yescharacteristic
583C2×C3C22×#13511yescharacteristic
584C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
585C22—22no—
586C22—22no—
587C22—28no—
588C22—28no—
589C22—432no—
590C22—44no—
591C22—44no—
592C22—416no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—84no—
597C22C3×#52512yes—
598C22C2×C3×#13514yes—
599C22C2×C3×#13512yes—
600C22C2×C3×AGL(1,ℤ/8)12yes—
601C22C23×C3×D411yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—44no—
609C4—42no—
610C4C3×#52512yes—
611C4C2×C3×AGL(1,ℤ/8)14yes—
612C4C22×C3×#4112yes—
613C3C2×#310511yescharacteristic, direct product factor, Sylow
614C2—24no—
615C2—48no—
616C2—82no—
617C2C3×#310514yesdirect product factor
618C2C2×C3×#52511yescharacteristic
619C2C22×C3×#13511yescharacteristic
620C2C22×C3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3×C4C2×D4
commutator, Frattini, cosocleC2×C4C25×C3
socleC23×C3C22×D4
prime radicalC2×C3×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C4 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. C22×C3×C4×D4C2semidirect
3. C3×#3105C2direct (N × H)
4. C2×C3×#484C2semidirect
5. C2×C3×#481C2semidirect
6. C2×C3×#478C2semidirect
7. C2×C3×#463C2semidirect
8. C2×C3×#450C2semidirect
10. C2×C3×C4×SD16C2semidirect
11. C2×C3×C4×D8C2semidirect
12. C2×C3×#431C2semidirect
13. C2×#3105C3direct (N × H)
19. C3×#529C22semidirect
21. C2×C3×#125C22semidirect
22. C2×C3×#124C22semidirect
26. C2×C3×C4×Q8C22semidirect
33. C2×C3×C4×D4C22semidirect
34. C2×C3×C4×D4C22semidirect
39. C3×#484C22semidirect
40. C3×#481C22semidirect
41. C3×#478C22semidirect
42. C3×#463C22semidirect
43. C3×#450C22semidirect
45. C3×C4×SD16C22semidirect
46. C3×C4×D8C22semidirect
47. C3×#431C22semidirect
48. C2×C3×#107C22semidirect
49. C2×C3×#106C22semidirect
50. C2×C3×C4⋊C8C22semidirect
51. C2×C3×#103C22semidirect
54. C2×C3×#102C22semidirect
57. C2×C3×C4×C8C22semidirect
58. C2×#529C2×C3semidirect
59. C22×C4×D4C2×C3semidirect
60. #3105C2×C3direct (N × H)
61. C2×#484C2×C3semidirect
62. C2×#481C2×C3semidirect
63. C2×#478C2×C3semidirect
64. C2×#463C2×C3semidirect
65. C2×#450C2×C3semidirect
67. C2×C4×SD16C2×C3semidirect
68. C2×C4×D8C2×C3semidirect
69. C2×#431C2×C3semidirect
96. C3×#125C23semidirect
98. C3×#124C23semidirect
105. C3×C4×Q8C23semidirect
114. C3×C4×D4C23semidirect
141. C3×#107C23semidirect
142. C3×#106C23semidirect
143. C3×C4⋊C8C23semidirect
144. C3×#103C23semidirect
147. C3×#102C23semidirect
150. C3×C4×C8C23semidirect
156. #529C22×C3semidirect
158. C2×#125C22×C3semidirect
159. C2×#124C22×C3semidirect
163. C2×C4×Q8C22×C3semidirect
170. C2×C4×D4C22×C3semidirect
171. C2×C4×D4C22×C3semidirect
176. #484C22×C3semidirect
177. #481C22×C3semidirect
178. #478C22×C3semidirect
179. #463C22×C3semidirect
180. #450C22×C3semidirect
182. C4×SD16C22×C3semidirect
183. C4×D8C22×C3semidirect
184. #431C22×C3semidirect
185. C2×#107C22×C3semidirect
186. C2×#106C22×C3semidirect
187. C2×C4⋊C8C22×C3semidirect
188. C2×#103C22×C3semidirect
191. C2×#102C22×C3semidirect
194. C2×C4×C8C22×C3semidirect
301. #125C23×C3semidirect
303. #124C23×C3semidirect
310. C4×Q8C23×C3semidirect
319. C4×D4C23×C3semidirect
346. #107C23×C3semidirect
347. #106C23×C3semidirect
348. C4⋊C8C23×C3semidirect
349. #103C23×C3semidirect
352. #102C23×C3semidirect
355. C4×C8C23×C3semidirect
581. C2×C3#3105direct (N × H)
613. C3C2×#3105direct (N × H)
617. C2C3×#3105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C22×C3×C4×D42
C3×#31052
C2×C3×#4842
C2×C3×#4812
C2×C3×#4782
C2×C3×#4632
C2×C3×#4502
C2×C3×#4472
C2×C3×C4×SD162
C2×C3×C4×D82
C2×C3×#4312
C2×#31053