Finite Group Databasebeta

← C2×C3×#3007 #10678965

Subgroups — C2×C3×#3007 #10678965

Order 768.

5078 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#41C211yesmaximal, characteristic
2C22×C3×#137C212yesmaximal, complemented
3C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
4C3×#3007C2116yesmaximal, direct product factor
5C2×C3×#452C214yesmaximal, complemented
6C2×C3×#451C212yesmaximal, complemented
7C2×C3×#450C212yesmaximal, complemented
8C2×C3×#417C212yesmaximal, complemented
9C2×C3×#407C211yesmaximal, characteristic, complemented
10C2×#3007C311yesmaximal, characteristic, direct product factor, Sylow
11C22×C3×#41—216no—
12C22×C3×#41—21no—
13C22×C3×#41—24no—
14C22×C3×#41—21no—
15C22×C3×#41C2212yes—
16C22×C3×#41C2218yes—
17C22×C3×#41C2212yes—
18C23×C3×Q8C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic, complemented
20C23×C3×D4—21no—
21C23×C3×D4C2211yescharacteristic
22C24×C3×C4—21no—
23C24×C3×C4C2211yescharacteristic
24C2×C3×#137—216no—
25C2×C3×#137C22116yescomplemented
26C22×C3×Q16C2214yescomplemented
27C22×C3×SD16C2214yescomplemented
28C22×C3×M16C2212yescomplemented
29C2×C3×C22⋊Q8—21no—
30C2×C3×C22⋊Q8—21no—
31C2×C3×C22⋊Q8—24no—
32C2×C3×C22⋊Q8C2212yes—
33C2×C3×C22⋊Q8C2212yescomplemented
34C2×C3×C22⋊Q8C2218yescomplemented
35C22×C3×C4⋊C4—21no—
36C22×C3×C4⋊C4C2211yescharacteristic, complemented
37C22×C3×C22⋊C4—21no—
38C3×#452C22132yescomplemented
39C3×#451C22116yescomplemented
40C3×#450C22116yescomplemented
41C3×#417C22116yescomplemented
42C2×C3×#103C2214yescomplemented
43C2×C3×#102C2214yescomplemented
44C3×#407C2218yescomplemented
45C2×C3×C22⋊C8C2212yes—
46C2×C3×C22⋊C8C2212yescomplemented
47C23×#41C2×C311yescharacteristic
48C22×#137C2×C312yescomplemented
49C22×C22⋊Q8C2×C311yescharacteristic, complemented
50#3007C2×C3116yesdirect product factor
51C2×#452C2×C314yescomplemented
52C2×#451C2×C312yescomplemented
53C2×#450C2×C312yescomplemented
54C2×#417C2×C312yescomplemented
55C2×#407C2×C311yescharacteristic, complemented
56C25×C3—21no—
57C25×C3D411yescharacteristic
58C2×C3×#41—216no—
59C2×C3×#41—264no—
60C2×C3×#41—216no—
61C2×C3×#41—264no—
62C2×C3×#41—28no—
63C2×C3×#41—28no—
64C2×C3×#41—28no—
65C2×C3×#41—28no—
66C2×C3×#41—24no—
67C2×C3×#41—28no—
68C2×C3×#41—24no—
69C2×C3×#41D4116yes—
70C2×C3×#41C2318yes—
71C2×C3×#41C2318yes—
72C22×C3×Q8—28no—
73C22×C3×Q8—22no—
74C22×C3×Q8—21no—
75C22×C3×Q8—22no—
76C22×C3×Q8—21no—
77C22×C3×Q8—28no—
78C22×C3×Q8C2312yes—
79C22×C3×Q8C2314yes—
80C22×C3×Q8C2312yes—
81C22×C3×Q8C2314yescomplemented
82C22×C3×D4—216no—
83C22×C3×D4—28no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—28no—
87C22×C3×D4—22no—
88C22×C3×D4—21no—
89C22×C3×D4C2314yes—
90C22×C3×D4C2312yes—
91C23×C3×C4—216no—
92C23×C3×C4—21no—
93C23×C3×C4—28no—
94C23×C3×C4—22no—
95C23×C3×C4—22no—
96C23×C3×C4—28no—
97C23×C3×C4—21no—
98C23×C3×C4—21no—
99C23×C3×C4D411yescharacteristic
100C23×C3×C4D411yescharacteristic
101C23×C3×C4D414yes—
102C23×C3×C4D411yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2314yes—
106C23×C3×C4C2311yescharacteristic
107C3×#137—264no—
108C2×C3×Q16—216no—
109C2×C3×Q16C23116yescomplemented
110C2×C3×SD16—216no—
111C2×C3×SD16C23116yescomplemented
112C2×C3×M16—28no—
113C2×C3×M16C2318yescomplemented
114C22×C3×C8C2314yes—
115C3×C22⋊Q8—24no—
116C3×C22⋊Q8—28no—
117C3×C22⋊Q8—28no—
118C3×C22⋊Q8—24no—
119C3×C22⋊Q8C2318yes—
120C3×C22⋊Q8C2318yescomplemented
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—28no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2314yescomplemented
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—28no—
130C2×C3×C22⋊C4—22no—
131C3×#103C23116yescomplemented
132C3×#102C23116yescomplemented
133C3×C22⋊C8C2318yes—
134C3×C22⋊C8C2318yescomplemented
135C22×#41—216no—
136C22×#41—21no—
137C22×#41—24no—
138C22×#41—21no—
139C22×#41C22×C312yes—
140C22×#41C22×C318yes—
141C22×#41C22×C312yes—
142C23×Q8C22×C311yescharacteristic
143C23×Q8C22×C311yescharacteristic, complemented
144C23×D4—21no—
145C23×D4C22×C311yescharacteristic
146C24×C4—21no—
147C24×C4C22×C311yescharacteristic
148C2×#137—216no—
149C2×#137C22×C3116yescomplemented
150C22×Q16C22×C314yescomplemented
151C22×SD16C22×C314yescomplemented
152C22×M16C22×C312yescomplemented
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8C22×C312yes—
157C2×C22⋊Q8C22×C312yescomplemented
158C2×C22⋊Q8C22×C318yescomplemented
159C22×C4⋊C4—21no—
160C22×C4⋊C4C22×C311yescharacteristic, complemented
161C22×C22⋊C4—21no—
162#452C22×C3132yescomplemented
163#451C22×C3116yescomplemented
164#450C22×C3116yescomplemented
165#417C22×C3116yescomplemented
166C2×#103C22×C314yescomplemented
167C2×#102C22×C314yescomplemented
168#407C22×C318yescomplemented
169C2×C22⋊C8C22×C312yes—
170C2×C22⋊C8C22×C312yescomplemented
171C24×C3—28no—
172C24×C3—24no—
173C24×C3—24no—
174C24×C3—24no—
175C24×C3—22no—
176C24×C3—42no—
177C24×C3—44no—
178C24×C3—44no—
179C24×C3C2×D411yescharacteristic
180C24×C3C2×D414yes—
181C24×C3C2×D411yescharacteristic
182C24×C3C2×D411yescharacteristic
183C3×#41—264no—
184C3×#41—232no—
185C3×#41—264no—
186C3×#41—216no—
187C3×#41—216no—
188C3×#41—232no—
189C3×#41—216no—
190C3×#41C2×D4132yes—
191C2×C3×Q8—216no—
192C2×C3×Q8—28no—
193C2×C3×Q8—216no—
194C2×C3×Q8—24no—
195C2×C3×Q8—24no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—24no—
199C2×C3×Q8—28no—
200C2×C3×Q8—216no—
201C2×C3×Q8—44no—
202C2×C3×Q8—48no—
203C2×C3×Q8C2×D418yes—
204C2×C3×Q8C2414yes—
205C2×C3×Q8C2414yes—
206C2×C3×D4—264no—
207C2×C3×D4—216no—
208C2×C3×D4—28no—
209C2×C3×D4—216no—
210C2×C3×D4—216no—
211C2×C3×D4—28no—
212C2×C3×D4—28no—
213C2×C3×D4—216no—
214C2×C3×D4—24no—
215C2×C3×D4—22no—
216C2×C3×D4—24no—
217C2×C3×D4C2×D418yes—
218C2×C3×D4C2414yes—
219C22×C3×C4—28no—
220C22×C3×C4—264no—
221C22×C3×C4—216no—
222C22×C3×C4—24no—
223C22×C3×C4—24no—
224C22×C3×C4—22no—
225C22×C3×C4—24no—
226C22×C3×C4—216no—
227C22×C3×C4—24no—
228C22×C3×C4—216no—
229C22×C3×C4—28no—
230C22×C3×C4—28no—
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4—216no—
234C22×C3×C4—24no—
235C22×C3×C4—24no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—44no—
239C22×C3×C4—44no—
240C22×C3×C4C2×D414yes—
241C22×C3×C4C2×D414yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×D414yes—
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D418yes—
250C22×C3×C4C2412yes—
251C22×C3×C4C2412yes—
252C22×C3×C4C2412yes—
253C22×C3×C4C2411yescharacteristic
254C3×Q16—232no—
255C3×SD16—232no—
256C3×M16—216no—
257C2×C3×C8—28no—
258C2×C3×C8C2418yes—
259C3×C4⋊C4—28no—
260C3×C4⋊C4—28no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—24no—
263C3×C4⋊C4C2414yes—
264C3×C22⋊C4—28no—
265C3×C22⋊C4—28no—
266C25—21no—
267C25C3×D411yescharacteristic
268C2×#41—216no—
269C2×#41—264no—
270C2×#41—216no—
271C2×#41—264no—
272C2×#41—28no—
273C2×#41—28no—
274C2×#41—28no—
275C2×#41—28no—
276C2×#41—24no—
277C2×#41—28no—
278C2×#41—24no—
279C2×#41C3×D4116yes—
280C2×#41C23×C318yes—
281C2×#41C23×C318yes—
282C22×Q8—28no—
283C22×Q8—21no—
284C22×Q8—22no—
285C22×Q8—21no—
286C22×Q8—22no—
287C22×Q8—28no—
288C22×Q8C23×C312yes—
289C22×Q8C23×C314yes—
290C22×Q8C23×C312yes—
291C22×Q8C23×C314yescomplemented
292C22×D4—216no—
293C22×D4—22no—
294C22×D4—28no—
295C22×D4—22no—
296C22×D4—28no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4C23×C314yes—
300C22×D4C23×C312yes—
301C23×C4—216no—
302C23×C4—21no—
303C23×C4—22no—
304C23×C4—28no—
305C23×C4—22no—
306C23×C4—28no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4C3×D411yescharacteristic
310C23×C4C3×D411yescharacteristic
311C23×C4C3×D411yescharacteristic
312C23×C4C3×D414yes—
313C23×C4C23×C311yescharacteristic
314C23×C4C23×C311yescharacteristic
315C23×C4C23×C314yes—
316C23×C4C23×C311yescharacteristic
317#137—264no—
318C2×Q16—216no—
319C2×Q16C23×C3116yescomplemented
320C2×SD16—216no—
321C2×SD16C23×C3116yescomplemented
322C2×M16—28no—
323C2×M16C23×C318yescomplemented
324C22×C8C23×C314yes—
325C22⋊Q8—24no—
326C22⋊Q8—28no—
327C22⋊Q8—28no—
328C22⋊Q8—24no—
329C22⋊Q8C23×C318yes—
330C22⋊Q8C23×C318yescomplemented
331C2×C4⋊C4—22no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4C23×C312yes—
337C2×C4⋊C4C23×C314yescomplemented
338C2×C22⋊C4—22no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—22no—
341#103C23×C3116yescomplemented
342#102C23×C3116yescomplemented
343C22⋊C8C23×C318yes—
344C22⋊C8C23×C318yescomplemented
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—216no—
350C23×C3—28no—
351C23×C3—22no—
352C23×C3—28no—
353C23×C3—22no—
354C23×C3—28no—
355C23×C3—22no—
356C23×C3—24no—
357C23×C3—44no—
358C23×C3—416no—
359C23×C3—432no—
360C23×C3—48no—
361C23×C3—44no—
362C23×C3—48no—
363C23×C3—44no—
364C23×C3#12014yes—
365C23×C3#13714yescomplemented
366C23×C3C22×D412yes—
367C23×C3C22×D412yes—
368C23×C3C22×D412yes—
369C23×C3C22×D411yescharacteristic
370C3×Q8—216no—
371C3×Q8—28no—
372C3×Q8—24no—
373C3×Q8—28no—
374C3×Q8—48no—
375C3×Q8—44no—
376C3×Q8C22×D418yes—
377C3×D4—232no—
378C3×D4—216no—
379C3×D4—232no—
380C3×D4—28no—
381C3×D4—24no—
382C3×D4C22×D418yes—
383C2×C3×C4—216no—
384C2×C3×C4—232no—
385C2×C3×C4—22no—
386C2×C3×C4—28no—
387C2×C3×C4—22no—
388C2×C3×C4—28no—
389C2×C3×C4—24no—
390C2×C3×C4—28no—
391C2×C3×C4—232no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—28no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—48no—
400C2×C3×C4—48no—
401C2×C3×C4—44no—
402C2×C3×C4—44no—
403C2×C3×C4#12014yes—
404C2×C3×C4#12018yes—
405C2×C3×C4C22×D412yes—
406C2×C3×C4C22×D412yes—
407C2×C3×C4C22×D412yes—
408C2×C3×C4C22×D411yescharacteristic
409C2×C3×C4C22×D414yes—
410C2×C3×C4C22×D418yes—
411C2×C3×C4C2511yescharacteristic
412C3×C8—28no—
413C24—28no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—22no—
418C24—42no—
419C24—44no—
420C24—44no—
421C24C2×C3×D411yescharacteristic
422C24C2×C3×D414yes—
423C24C2×C3×D411yescharacteristic
424C24C2×C3×D411yescharacteristic
425#41—264no—
426#41—232no—
427#41—264no—
428#41—216no—
429#41—216no—
430#41—232no—
431#41—216no—
432#41C2×C3×D4132yes—
433C2×Q8—216no—
434C2×Q8—28no—
435C2×Q8—216no—
436C2×Q8—24no—
437C2×Q8—22no—
438C2×Q8—24no—
439C2×Q8—22no—
440C2×Q8—24no—
441C2×Q8—28no—
442C2×Q8—216no—
443C2×Q8—44no—
444C2×Q8—48no—
445C2×Q8C2×C3×D418yes—
446C2×Q8C24×C314yes—
447C2×Q8C24×C314yes—
448C2×D4—264no—
449C2×D4—216no—
450C2×D4—28no—
451C2×D4—216no—
452C2×D4—216no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—216no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4C2×C3×D418yes—
460C2×D4C24×C314yes—
461C22×C4—28no—
462C22×C4—264no—
463C22×C4—216no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—216no—
469C22×C4—24no—
470C22×C4—216no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—216no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4C2×C3×D411yescharacteristic
483C22×C4C2×C3×D411yescharacteristic
484C22×C4C2×C3×D414yes—
485C22×C4C2×C3×D414yes—
486C22×C4C2×C3×D412yes—
487C22×C4C2×C3×D412yes—
488C22×C4C2×C3×D414yes—
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C2×C3×D412yes—
491C22×C4C2×C3×D418yes—
492C22×C4C24×C312yes—
493C22×C4C24×C312yes—
494C22×C4C24×C311yescharacteristic
495C22×C4C24×C312yes—
496Q16—232no—
497SD16—232no—
498M16—216no—
499C2×C8—28no—
500C2×C8C24×C318yes—
501C4⋊C4—28no—
502C4⋊C4—28no—
503C4⋊C4—22no—
504C4⋊C4—24no—
505C4⋊C4C24×C314yes—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C22×C3—22no—
509C22×C3—28no—
510C22×C3—28no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—28no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—416no—
519C22×C3—432no—
520C22×C3—44no—
521C22×C3—416no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3C2×#12014yes—
525C22×C3C2×#12012yes—
526C22×C3C2×#13712yes—
527C22×C3C2×#13714yescomplemented
528C22×C3#57512yes—
529C22×C3C23×D411yescharacteristic
530C3×C4—22no—
531C3×C4—28no—
532C3×C4—22no—
533C3×C4—44no—
534C3×C4—44no—
535C3×C4C2×#12014yes—
536C3×C4C2×#12012yes—
537C3×C4C23×D412yes—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—216no—
543C23—22no—
544C23—28no—
545C23—22no—
546C23—24no—
547C23—28no—
548C23—22no—
549C23—28no—
550C23—44no—
551C23—416no—
552C23—432no—
553C23—48no—
554C23—44no—
555C23—48no—
556C23—44no—
557C23C3×#12014yes—
558C23C3×#13714yescomplemented
559C23C22×C3×D412yes—
560C23C22×C3×D412yes—
561C23C22×C3×D412yes—
562C23C22×C3×D411yescharacteristic
563Q8—216no—
564Q8—24no—
565Q8—28no—
566Q8—28no—
567Q8—48no—
568Q8—44no—
569Q8C22×C3×D418yes—
570D4—232no—
571D4—216no—
572D4—232no—
573D4—24no—
574D4—28no—
575D4C22×C3×D418yes—
576C2×C4—216no—
577C2×C4—232no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—28no—
581C2×C4—22no—
582C2×C4—28no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—28no—
586C2×C4—232no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—28no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—48no—
593C2×C4—44no—
594C2×C4—48no—
595C2×C4—44no—
596C2×C4C3×#12014yes—
597C2×C4C3×#12018yes—
598C2×C4C22×C3×D412yes—
599C2×C4C22×C3×D412yes—
600C2×C4C22×C3×D414yes—
601C2×C4C22×C3×D418yes—
602C2×C4C22×C3×D412yes—
603C2×C4C22×C3×D411yescharacteristic
604C2×C4C25×C311yescharacteristic
605C8—28no—
606C2×C3—24no—
607C2×C3—24no—
608C2×C3—42no—
609C2×C3—48no—
610C2×C3#300714yesdirect product factor
611C2×C3C22×#12011yescharacteristic
612C2×C3C22×#13711yescharacteristic
613C2×C3C2×#57511yescharacteristic
614C22—22no—
615C22—28no—
616C22—28no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—28no—
622C22—22no—
623C22—22no—
624C22—416no—
625C22—432no—
626C22—44no—
627C22—416no—
628C22—44no—
629C22—44no—
630C22C2×C3×#12014yes—
631C22C2×C3×#12012yes—
632C22C2×C3×#13712yes—
633C22C2×C3×#13714yescomplemented
634C22C3×#57512yes—
635C22C23×C3×D411yescharacteristic
636C4—22no—
637C4—28no—
638C4—22no—
639C4—44no—
640C4—44no—
641C4C2×C3×#12014yes—
642C4C2×C3×#12012yes—
643C4C23×C3×D412yes—
644C3C2×#300711yescharacteristic, direct product factor, Sylow
645C2—24no—
646C2—24no—
647C2—42no—
648C2—48no—
649C2C3×#300714yesdirect product factor
650C2C22×C3×#12011yescharacteristic
651C2C22×C3×#13711yescharacteristic
652C2C2×C3×#57511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC2×C4C25×C3
prime radicalC23×C3×#41C2
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
2. C22×C3×#137C2semidirect
3. C22×C3×C22⋊Q8C2semidirect
4. C3×#3007C2direct (N × H)
5. C2×C3×#452C2semidirect
6. C2×C3×#451C2semidirect
7. C2×C3×#450C2semidirect
8. C2×C3×#417C2semidirect
9. C2×C3×#407C2semidirect
10. C2×#3007C3direct (N × H)
19. C23×C3×Q8C22semidirect
25. C2×C3×#137C22semidirect
26. C22×C3×Q16C22semidirect
27. C22×C3×SD16C22semidirect
28. C22×C3×M16C22semidirect
33. C2×C3×C22⋊Q8C22semidirect
34. C2×C3×C22⋊Q8C22semidirect
36. C22×C3×C4⋊C4C22semidirect
38. C3×#452C22semidirect
39. C3×#451C22semidirect
40. C3×#450C22semidirect
41. C3×#417C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
44. C3×#407C22semidirect
46. C2×C3×C22⋊C8C22semidirect
48. C22×#137C2×C3semidirect
49. C22×C22⋊Q8C2×C3semidirect
50. #3007C2×C3direct (N × H)
51. C2×#452C2×C3semidirect
52. C2×#451C2×C3semidirect
53. C2×#450C2×C3semidirect
54. C2×#417C2×C3semidirect
55. C2×#407C2×C3semidirect
81. C22×C3×Q8C23semidirect
109. C2×C3×Q16C23semidirect
111. C2×C3×SD16C23semidirect
113. C2×C3×M16C23semidirect
120. C3×C22⋊Q8C23semidirect
127. C2×C3×C4⋊C4C23semidirect
131. C3×#103C23semidirect
132. C3×#102C23semidirect
134. C3×C22⋊C8C23semidirect
143. C23×Q8C22×C3semidirect
149. C2×#137C22×C3semidirect
150. C22×Q16C22×C3semidirect
151. C22×SD16C22×C3semidirect
152. C22×M16C22×C3semidirect
157. C2×C22⋊Q8C22×C3semidirect
158. C2×C22⋊Q8C22×C3semidirect
160. C22×C4⋊C4C22×C3semidirect
162. #452C22×C3semidirect
163. #451C22×C3semidirect
164. #450C22×C3semidirect
165. #417C22×C3semidirect
166. C2×#103C22×C3semidirect
167. C2×#102C22×C3semidirect
168. #407C22×C3semidirect
170. C2×C22⋊C8C22×C3semidirect
291. C22×Q8C23×C3semidirect
319. C2×Q16C23×C3semidirect
321. C2×SD16C23×C3semidirect
323. C2×M16C23×C3semidirect
330. C22⋊Q8C23×C3semidirect
337. C2×C4⋊C4C23×C3semidirect
341. #103C23×C3semidirect
342. #102C23×C3semidirect
344. C22⋊C8C23×C3semidirect
365. C23×C3#137semidirect
527. C22×C3C2×#137semidirect
558. C23C3×#137semidirect
610. C2×C3#3007direct (N × H)
633. C22C2×C3×#137semidirect
644. C3C2×#3007direct (N × H)
649. C2C3×#3007direct (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×C22⋊Q82
C3×#30072
C2×C3×#4522
C2×C3×#4512
C2×C3×#4502
C2×C3×#4172
C2×C3×#4072
C2×#30073