Finite Group Databasebeta

← C2×C3×#3005 #10678963

Subgroups — C2×C3×#3005 #10678963

Order 768.

5098 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#41C211yesmaximal, characteristic, complemented
2C22×C3×#137C211yesmaximal, characteristic, complemented
3C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C2×C3×#525C211yesmaximal, characteristic, complemented
5C3×#3005C2116yesmaximal, direct product factor
6C2×C3×#452C214yesmaximal, complemented
7C2×C3×#449C214yesmaximal, complemented
8C2×C3×#419C211yesmaximal, characteristic, complemented
9C2×C3×#418C211yesmaximal, characteristic, complemented
10C2×C3×#407C211yesmaximal, characteristic, complemented
11C2×#3005C311yesmaximal, characteristic, direct product factor, Sylow
12C22×C3×#41—28no—
13C22×C3×#41—28no—
14C22×C3×#41—22no—
15C22×C3×#41—24no—
16C22×C3×#41C2211yescharacteristic
17C22×C3×#41C2214yes—
18C22×C3×#41C2218yescomplemented
19C23×C3×Q8C2211yescharacteristic
20C23×C3×D4—21no—
21C23×C3×D4C2211yescharacteristic
22C24×C3×C4—21no—
23C24×C3×C4C2211yescharacteristic
24C2×C3×#137—28no—
25C2×C3×#137C2218yescomplemented
26C2×C3×AGL(1,ℤ/8)—28no—
27C2×C3×AGL(1,ℤ/8)C2218yescomplemented
28C22×C3×Q16C2212yescomplemented
29C22×C3×SD16C2212yescomplemented
30C22×C3×SD16C2212yescomplemented
31C22×C3×D8C2212yescomplemented
32C22×C3×M16C2211yescharacteristic
33C22×C3×M16C2211yescharacteristic
34C3×#525—24no—
35C3×#525C2218yescomplemented
36C2×C3×#123—21no—
37C2×C3×C22⋊Q8C2212yescomplemented
38C2×C3×#121C2212yescomplemented
39C2×C3×#120—21no—
40C2×C3×C4×D4—22no—
41C2×C3×#117C2211yescharacteristic
42C3×#452C22132yescomplemented
43C3×#449C22132yescomplemented
44C3×#419C2218yescomplemented
45C3×#418C2218yescomplemented
46C2×C3×#103C2214yescomplemented
47C2×C3×#102C2214yescomplemented
48C3×#407C2218yescomplemented
49C2×C3×C22⋊C8C2214yescomplemented
50C23×#41C2×C311yescharacteristic, complemented
51C22×#137C2×C311yescharacteristic, complemented
52C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
53C2×#525C2×C311yescharacteristic, complemented
54#3005C2×C3116yesdirect product factor
55C2×#452C2×C314yescomplemented
56C2×#449C2×C314yescomplemented
57C2×#419C2×C311yescharacteristic, complemented
58C2×#418C2×C311yescharacteristic, complemented
59C2×#407C2×C311yescharacteristic, complemented
60C25×C3—21no—
61C25×C3D411yescharacteristic
62C2×C3×#41—232no—
63C2×C3×#41—264no—
64C2×C3×#41—216no—
65C2×C3×#41—232no—
66C2×C3×#41—216no—
67C2×C3×#41—232no—
68C2×C3×#41—28no—
69C2×C3×#41—216no—
70C2×C3×#41—22no—
71C2×C3×#41—24no—
72C2×C3×#41—24no—
73C2×C3×#41C2314yes—
74C2×C3×#41C23116yes—
75C22×C3×Q8—24no—
76C22×C3×Q8—22no—
77C22×C3×Q8—21no—
78C22×C3×Q8D418yescomplemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2312yes—
81C22×C3×Q8C2314yes—
82C22×C3×D4—216no—
83C22×C3×D4—24no—
84C22×C3×D4—28no—
85C22×C3×D4—21no—
86C22×C3×D4—22no—
87C22×C3×D4—22no—
88C22×C3×D4—21no—
89C22×C3×D4—24no—
90C22×C3×D4D418yescomplemented
91C22×C3×D4C2311yescharacteristic
92C22×C3×D4C2312yes—
93C22×C3×D4C2314yes—
94C23×C3×C4—216no—
95C23×C3×C4—21no—
96C23×C3×C4—24no—
97C23×C3×C4—28no—
98C23×C3×C4—24no—
99C23×C3×C4—24no—
100C23×C3×C4—21no—
101C23×C3×C4D411yescharacteristic
102C23×C3×C4D412yes—
103C23×C3×C4D414yes—
104C23×C3×C4C2312yes—
105C23×C3×C4C2314yes—
106C23×C3×C4C2311yescharacteristic
107C3×#137—232no—
108C3×AGL(1,ℤ/8)—232no—
109C2×C3×Q16—28no—
110C2×C3×Q16C2318yescomplemented
111C2×C3×SD16—28no—
112C2×C3×SD16—28no—
113C2×C3×SD16C2318yescomplemented
114C2×C3×SD16C2318yescomplemented
115C2×C3×D8—28no—
116C2×C3×D8C2318yescomplemented
117C2×C3×M16—24no—
118C2×C3×M16—24no—
119C2×C3×M16C2314yes—
120C2×C3×M16C2314yes—
121C22×C3×C8C2312yes—
122C22×C3×C8C2312yes—
123C3×#123—28no—
124C3×C22⋊Q8—24no—
125C3×C22⋊Q8C2318yescomplemented
126C3×#121—24no—
127C3×#121C2318yescomplemented
128C3×#120—28no—
129C3×C4×D4—216no—
130C3×#117—22no—
131C3×#117C2314yes—
132C2×C3×C4⋊C4—22no—
133C2×C3×C4⋊C4C2312yes—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C42—21no—
138C3×#103C23116yescomplemented
139C3×#102C23116yescomplemented
140C3×C22⋊C8C23116yescomplemented
141C22×#41—28no—
142C22×#41—28no—
143C22×#41—22no—
144C22×#41—24no—
145C22×#41C22×C314yes—
146C22×#41C22×C311yescharacteristic
147C22×#41C22×C318yescomplemented
148C23×Q8C22×C311yescharacteristic
149C23×D4—21no—
150C23×D4C22×C311yescharacteristic
151C24×C4—21no—
152C24×C4C22×C311yescharacteristic
153C2×#137—28no—
154C2×#137C22×C318yescomplemented
155C2×AGL(1,ℤ/8)—28no—
156C2×AGL(1,ℤ/8)C22×C318yescomplemented
157C22×Q16C22×C312yescomplemented
158C22×SD16C22×C312yescomplemented
159C22×SD16C22×C312yescomplemented
160C22×D8C22×C312yescomplemented
161C22×M16C22×C311yescharacteristic
162C22×M16C22×C311yescharacteristic
163#525—24no—
164#525C22×C318yescomplemented
165C2×#123—21no—
166C2×C22⋊Q8C22×C312yescomplemented
167C2×#121C22×C312yescomplemented
168C2×#120—21no—
169C2×C4×D4—22no—
170C2×#117C22×C311yescharacteristic
171#452C22×C3132yescomplemented
172#449C22×C3132yescomplemented
173#419C22×C318yescomplemented
174#418C22×C318yescomplemented
175C2×#103C22×C314yescomplemented
176C2×#102C22×C314yescomplemented
177#407C22×C318yescomplemented
178C2×C22⋊C8C22×C314yescomplemented
179C24×C3—28no—
180C24×C3—24no—
181C24×C3—24no—
182C24×C3—22no—
183C24×C3—21no—
184C24×C3—44no—
185C24×C3—48no—
186C24×C3C2×D412yes—
187C24×C3C2×D411yescharacteristic
188C24×C3C2×D414yes—
189C3×#41—264no—
190C3×#41—2128no—
191C3×#41—232no—
192C3×#41—232no—
193C3×#41—28no—
194C3×#41—28no—
195C3×#41—48no—
196C2×C3×Q8—28no—
197C2×C3×Q8—216no—
198C2×C3×Q8—24no—
199C2×C3×Q8—28no—
200C2×C3×Q8—24no—
201C2×C3×Q8—22no—
202C2×C3×Q8—21no—
203C2×C3×Q8—22no—
204C2×C3×Q8—22no—
205C2×C3×Q8C2×D418yes—
206C2×C3×Q8C2×D4116yescomplemented
207C2×C3×Q8C2412yes—
208C2×C3×Q8C2414yes—
209C2×C3×D4—232no—
210C2×C3×D4—264no—
211C2×C3×D4—216no—
212C2×C3×D4—28no—
213C2×C3×D4—24no—
214C2×C3×D4—28no—
215C2×C3×D4—216no—
216C2×C3×D4—24no—
217C2×C3×D4—22no—
218C2×C3×D4—24no—
219C2×C3×D4—28no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—21no—
223C2×C3×D4—48no—
224C2×C3×D4—44no—
225C2×C3×D4C2×D418yes—
226C2×C3×D4C2×D4116yescomplemented
227C2×C3×D4C2412yes—
228C2×C3×D4C2414yes—
229C22×C3×C4—232no—
230C22×C3×C4—264no—
231C22×C3×C4—24no—
232C22×C3×C4—28no—
233C22×C3×C4—24no—
234C22×C3×C4—22no—
235C22×C3×C4—28no—
236C22×C3×C4—216no—
237C22×C3×C4—216no—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—28no—
241C22×C3×C4—28no—
242C22×C3×C4—22no—
243C22×C3×C4—21no—
244C22×C3×C4—24no—
245C22×C3×C4—44no—
246C22×C3×C4C2×D418yes—
247C22×C3×C4C2×D414yes—
248C22×C3×C4C2×D414yes—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D414yes—
253C22×C3×C4C2×D414yes—
254C22×C3×C4C2414yes—
255C22×C3×C4C2412yes—
256C22×C3×C4C2411yescharacteristic
257C3×Q16—216no—
258C3×SD16—216no—
259C3×SD16—216no—
260C3×D8—216no—
261C3×M16—28no—
262C3×M16—28no—
263C2×C3×C8—24no—
264C2×C3×C8—24no—
265C2×C3×C8C2414yes—
266C2×C3×C8C2414yes—
267C3×C4⋊C4—28no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4C2414yes—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—28no—
272C3×C22⋊C4—28no—
273C3×C42—24no—
274C25—21no—
275C25C3×D411yescharacteristic
276C2×#41—232no—
277C2×#41—264no—
278C2×#41—216no—
279C2×#41—232no—
280C2×#41—216no—
281C2×#41—232no—
282C2×#41—28no—
283C2×#41—216no—
284C2×#41—22no—
285C2×#41—24no—
286C2×#41—24no—
287C2×#41C23×C314yes—
288C2×#41C23×C3116yes—
289C22×Q8—24no—
290C22×Q8—21no—
291C22×Q8—22no—
292C22×Q8C3×D418yescomplemented
293C22×Q8C23×C311yescharacteristic
294C22×Q8C23×C312yes—
295C22×Q8C23×C314yes—
296C22×D4—216no—
297C22×D4—24no—
298C22×D4—28no—
299C22×D4—22no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—22no—
303C22×D4—24no—
304C22×D4C3×D418yescomplemented
305C22×D4C23×C311yescharacteristic
306C22×D4C23×C312yes—
307C22×D4C23×C314yes—
308C23×C4—216no—
309C23×C4—21no—
310C23×C4—24no—
311C23×C4—28no—
312C23×C4—24no—
313C23×C4—24no—
314C23×C4—21no—
315C23×C4C3×D412yes—
316C23×C4C3×D411yescharacteristic
317C23×C4C3×D414yes—
318C23×C4C23×C312yes—
319C23×C4C23×C314yes—
320C23×C4C23×C311yescharacteristic
321#137—232no—
322AGL(1,ℤ/8)—232no—
323C2×Q16—28no—
324C2×Q16C23×C318yescomplemented
325C2×SD16—28no—
326C2×SD16—28no—
327C2×SD16C23×C318yescomplemented
328C2×SD16C23×C318yescomplemented
329C2×D8—28no—
330C2×D8C23×C318yescomplemented
331C2×M16—24no—
332C2×M16—24no—
333C2×M16C23×C314yes—
334C2×M16C23×C314yes—
335C22×C8C23×C312yes—
336C22×C8C23×C312yes—
337#123—28no—
338C22⋊Q8—24no—
339C22⋊Q8C23×C318yescomplemented
340#121—24no—
341#121C23×C318yescomplemented
342#120—28no—
343C4×D4—216no—
344#117—22no—
345#117C23×C314yes—
346C2×C4⋊C4—22no—
347C2×C4⋊C4C23×C312yes—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C42—21no—
352#103C23×C3116yescomplemented
353#102C23×C3116yescomplemented
354C22⋊C8C23×C3116yescomplemented
355C23×C3—24no—
356C23×C3—28no—
357C23×C3—24no—
358C23×C3—28no—
359C23×C3—216no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—22no—
364C23×C3—48no—
365C23×C3—416no—
366C23×C3—432no—
367C23×C3—416no—
368C23×C3—48no—
369C23×C3—42no—
370C23×C3—44no—
371C23×C3#12014yes—
372C23×C3C22×D414yes—
373C23×C3C22×D412yes—
374C23×C3C22×D411yescharacteristic
375C3×Q8—28no—
376C3×Q8—216no—
377C3×Q8—24no—
378C3×Q8—22no—
379C3×Q8—22no—
380C3×Q8—42no—
381C3×Q8C22×D418yes—
382C3×D4—264no—
383C3×D4—28no—
384C3×D4—216no—
385C3×D4—24no—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—416no—
389C3×D4—48no—
390C3×D4—42no—
391C3×D4C22×D418yes—
392C2×C3×C4—264no—
393C2×C3×C4—28no—
394C2×C3×C4—24no—
395C2×C3×C4—28no—
396C2×C3×C4—216no—
397C2×C3×C4—24no—
398C2×C3×C4—216no—
399C2×C3×C4—28no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—42no—
405C2×C3×C4—44no—
406C2×C3×C4—48no—
407C2×C3×C4#12014yes—
408C2×C3×C4#12018yes—
409C2×C3×C4C22×D414yes—
410C2×C3×C4C22×D412yes—
411C2×C3×C4C22×D411yescharacteristic
412C2×C3×C4C22×D412yes—
413C2×C3×C4C22×D412yes—
414C2×C3×C4C22×D414yes—
415C2×C3×C4C22×D414yes—
416C2×C3×C4C2511yescharacteristic
417C3×C8—24no—
418C3×C8—24no—
419C24—24no—
420C24—28no—
421C24—22no—
422C24—24no—
423C24—21no—
424C24—44no—
425C24—48no—
426C24C2×C3×D412yes—
427C24C2×C3×D411yescharacteristic
428C24C2×C3×D414yes—
429#41—264no—
430#41—2128no—
431#41—232no—
432#41—232no—
433#41—28no—
434#41—28no—
435#41—48no—
436C2×Q8—28no—
437C2×Q8—216no—
438C2×Q8—24no—
439C2×Q8—22no—
440C2×Q8—24no—
441C2×Q8—28no—
442C2×Q8—21no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8C2×C3×D418yes—
446C2×Q8C2×C3×D4116yescomplemented
447C2×Q8C24×C312yes—
448C2×Q8C24×C314yes—
449C2×D4—232no—
450C2×D4—264no—
451C2×D4—216no—
452C2×D4—28no—
453C2×D4—24no—
454C2×D4—28no—
455C2×D4—216no—
456C2×D4—24no—
457C2×D4—28no—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—48no—
464C2×D4—44no—
465C2×D4C2×C3×D418yes—
466C2×D4C2×C3×D4116yescomplemented
467C2×D4C24×C312yes—
468C2×D4C24×C314yes—
469C22×C4—232no—
470C22×C4—264no—
471C22×C4—24no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—28no—
476C22×C4—216no—
477C22×C4—216no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—44no—
486C22×C4C2×C3×D412yes—
487C22×C4C2×C3×D418yes—
488C22×C4C2×C3×D414yes—
489C22×C4C2×C3×D414yes—
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D412yes—
492C22×C4C2×C3×D414yes—
493C22×C4C2×C3×D414yes—
494C22×C4C24×C314yes—
495C22×C4C24×C311yescharacteristic
496C22×C4C24×C312yes—
497Q16—216no—
498SD16—216no—
499SD16—216no—
500D8—216no—
501M16—28no—
502M16—28no—
503C2×C8—24no—
504C2×C8—24no—
505C2×C8C24×C314yes—
506C2×C8C24×C314yes—
507C4⋊C4—28no—
508C4⋊C4—22no—
509C4⋊C4C24×C314yes—
510C22⋊C4—24no—
511C22⋊C4—28no—
512C22⋊C4—28no—
513C42—24no—
514C22×C3—28no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3—28no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—416no—
521C22×C3—432no—
522C22×C3—48no—
523C22×C3—416no—
524C22×C3—48no—
525C22×C3—42no—
526C22×C3—44no—
527C22×C3—84no—
528C22×C3C2×#12014yes—
529C22×C3C2×#12012yes—
530C22×C3#57514yes—
531C22×C3C23×D411yescharacteristic
532C3×C4—24no—
533C3×C4—28no—
534C3×C4—42no—
535C3×C4—44no—
536C3×C4C2×#12014yes—
537C3×C4C2×#12012yes—
538C3×C4C23×D411yescharacteristic
539C3×C4C23×D411yescharacteristic
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—28no—
545C23—24no—
546C23—28no—
547C23—216no—
548C23—22no—
549C23—48no—
550C23—416no—
551C23—432no—
552C23—416no—
553C23—48no—
554C23—44no—
555C23—42no—
556C23C3×#12014yes—
557C23C22×C3×D414yes—
558C23C22×C3×D412yes—
559C23C22×C3×D411yescharacteristic
560Q8—24no—
561Q8—28no—
562Q8—216no—
563Q8—22no—
564Q8—22no—
565Q8—42no—
566Q8C22×C3×D418yes—
567D4—264no—
568D4—24no—
569D4—22no—
570D4—22no—
571D4—28no—
572D4—216no—
573D4—416no—
574D4—48no—
575D4—42no—
576D4C22×C3×D418yes—
577C2×C4—264no—
578C2×C4—24no—
579C2×C4—28no—
580C2×C4—24no—
581C2×C4—28no—
582C2×C4—216no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—216no—
586C2×C4—28no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—44no—
590C2×C4—42no—
591C2×C4—48no—
592C2×C4C3×#12014yes—
593C2×C4C3×#12018yes—
594C2×C4C22×C3×D414yes—
595C2×C4C22×C3×D412yes—
596C2×C4C22×C3×D412yes—
597C2×C4C22×C3×D414yes—
598C2×C4C22×C3×D414yes—
599C2×C4C22×C3×D412yes—
600C2×C4C22×C3×D411yescharacteristic
601C2×C4C25×C311yescharacteristic
602C8—24no—
603C8—24no—
604C2×C3—24no—
605C2×C3—44no—
606C2×C3—48no—
607C2×C3—82no—
608C2×C3#300514yesdirect product factor
609C2×C3C22×#12011yescharacteristic
610C2×C3C2×#57512yes—
611C22—28no—
612C22—24no—
613C22—24no—
614C22—28no—
615C22—24no—
616C22—24no—
617C22—416no—
618C22—432no—
619C22—48no—
620C22—416no—
621C22—48no—
622C22—42no—
623C22—44no—
624C22—84no—
625C22C2×C3×#12014yes—
626C22C2×C3×#12012yes—
627C22C3×#57514yes—
628C22C23×C3×D411yescharacteristic
629C4—24no—
630C4—28no—
631C4—42no—
632C4—44no—
633C4C2×C3×#12014yes—
634C4C2×C3×#12012yes—
635C4C23×C3×D411yescharacteristic
636C4C23×C3×D411yescharacteristic
637C3C2×#300511yescharacteristic, direct product factor, Sylow
638C2—24no—
639C2—44no—
640C2—48no—
641C2—82no—
642C2C3×#300514yesdirect product factor
643C2C22×C3×#12011yescharacteristic
644C2C2×C3×#57512yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC2×C4C25×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C3×#41C2semidirect
2. C22×C3×#137C2semidirect
3. C22×C3×AGL(1,ℤ/8)C2semidirect
4. C2×C3×#525C2semidirect
5. C3×#3005C2direct (N × H)
6. C2×C3×#452C2semidirect
7. C2×C3×#449C2semidirect
8. C2×C3×#419C2semidirect
9. C2×C3×#418C2semidirect
10. C2×C3×#407C2semidirect
11. C2×#3005C3direct (N × H)
18. C22×C3×#41C22semidirect
25. C2×C3×#137C22semidirect
27. C2×C3×AGL(1,ℤ/8)C22semidirect
28. C22×C3×Q16C22semidirect
29. C22×C3×SD16C22semidirect
30. C22×C3×SD16C22semidirect
31. C22×C3×D8C22semidirect
35. C3×#525C22semidirect
37. C2×C3×C22⋊Q8C22semidirect
38. C2×C3×#121C22semidirect
42. C3×#452C22semidirect
43. C3×#449C22semidirect
44. C3×#419C22semidirect
45. C3×#418C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×#102C22semidirect
48. C3×#407C22semidirect
49. C2×C3×C22⋊C8C22semidirect
50. C23×#41C2×C3semidirect
51. C22×#137C2×C3semidirect
52. C22×AGL(1,ℤ/8)C2×C3semidirect
53. C2×#525C2×C3semidirect
54. #3005C2×C3direct (N × H)
55. C2×#452C2×C3semidirect
56. C2×#449C2×C3semidirect
57. C2×#419C2×C3semidirect
58. C2×#418C2×C3semidirect
59. C2×#407C2×C3semidirect
78. C22×C3×Q8D4semidirect
90. C22×C3×D4D4semidirect
110. C2×C3×Q16C23semidirect
113. C2×C3×SD16C23semidirect
114. C2×C3×SD16C23semidirect
116. C2×C3×D8C23semidirect
125. C3×C22⋊Q8C23semidirect
127. C3×#121C23semidirect
138. C3×#103C23semidirect
139. C3×#102C23semidirect
140. C3×C22⋊C8C23semidirect
147. C22×#41C22×C3semidirect
154. C2×#137C22×C3semidirect
156. C2×AGL(1,ℤ/8)C22×C3semidirect
157. C22×Q16C22×C3semidirect
158. C22×SD16C22×C3semidirect
159. C22×SD16C22×C3semidirect
160. C22×D8C22×C3semidirect
164. #525C22×C3semidirect
166. C2×C22⋊Q8C22×C3semidirect
167. C2×#121C22×C3semidirect
171. #452C22×C3semidirect
172. #449C22×C3semidirect
173. #419C22×C3semidirect
174. #418C22×C3semidirect
175. C2×#103C22×C3semidirect
176. C2×#102C22×C3semidirect
177. #407C22×C3semidirect
178. C2×C22⋊C8C22×C3semidirect
206. C2×C3×Q8C2×D4semidirect
226. C2×C3×D4C2×D4semidirect
292. C22×Q8C3×D4semidirect
304. C22×D4C3×D4semidirect
324. C2×Q16C23×C3semidirect
327. C2×SD16C23×C3semidirect
328. C2×SD16C23×C3semidirect
330. C2×D8C23×C3semidirect
339. C22⋊Q8C23×C3semidirect
341. #121C23×C3semidirect
352. #103C23×C3semidirect
353. #102C23×C3semidirect
354. C22⋊C8C23×C3semidirect
446. C2×Q8C2×C3×D4semidirect
466. C2×D4C2×C3×D4semidirect
608. C2×C3#3005direct (N × H)
637. C3C2×#3005direct (N × H)
642. C2C3×#3005direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#412
C22×C3×#1372
C22×C3×AGL(1,ℤ/8)2
C2×C3×#5252
C3×#30052
C2×C3×#4522
C2×C3×#4492
C2×C3×#4192
C2×C3×#4182
C2×C3×#4072
C2×#30053