Finite Group Databasebeta

← C3×#25769 #10644376

Subgroups — C3×#25769 #10644376

Order 768.

1674 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#546C211yesmaximal, characteristic
2C2×C3×#497C211yesmaximal, characteristic, complemented
3C2×C3×#461C211yesmaximal, characteristic, complemented
4C2×C3×#452C212yesmaximal, complemented
5C2×C3×#450C212yesmaximal, complemented
6C3×#2542C211yesmaximal, characteristic, complemented
7C3×#2001C212yesmaximal, complemented
8C3×#2000C212yesmaximal, complemented
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1955C211yesmaximal, characteristic, complemented
11C3×#1762C211yesmaximal, characteristic, complemented
12#25769C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C22×C3×Q16C2212yescomplemented
16C22×C3×SD16C2212yes—
17C22×C3×SD16C2212yes—
18C3×#546—24no—
19C3×#546—24no—
20C2×C3×C4⋊Q8C2211yescharacteristic, complemented
21C2×C3×#124C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×C22⋊Q8C2212yescomplemented
26C2×C3×#121—21no—
27C2×C3×#121C2211yescharacteristic
28C2×C3×#120—21no—
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C22×C3×C22⋊C4—21no—
32C3×#497—24no—
33C3×#461—24no—
34C3×#452—28no—
35C3×#450—28no—
36C2×C3×C4⋊C8C2211yescharacteristic, complemented
37C2×C3×#103C2212yescomplemented
38C2×C3×#103C2212yescomplemented
39C2×C3×#102C2212yes—
40C2×C3×#102C2212yes—
41C2×C3×C22⋊C8C2212yes—
42C2×C3×C22⋊C8C2212yescomplemented
43C2×C3×#97C2211yescharacteristic, complemented
44C3×#399—21no—
45C3×#399—21no—
46C3×#390—21no—
47C3×#384—21no—
48C3×C4×C4⋊C4C2211yescharacteristic, complemented
49C3×#340C2212yescomplemented
50C2×#546C2×C311yescharacteristic
51C2×#497C2×C311yescharacteristic, complemented
52C2×#461C2×C311yescharacteristic, complemented
53C2×#452C2×C312yescomplemented
54C2×#450C2×C312yescomplemented
55#2542C2×C311yescharacteristic, complemented
56#2001C2×C312yescomplemented
57#2000C2×C312yescomplemented
58#1983C2×C311yescharacteristic, complemented
59#1955C2×C311yescharacteristic, complemented
60#1762C2×C311yescharacteristic, complemented
61C25×C3—21no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—24no—
65C2×C3×#41—42no—
66C22×C3×Q8C2312yes—
67C22×C3×Q8C2311yescharacteristic
68C22×C3×D4—21no—
69C22×C3×D4—21no—
70C22×C3×D4—22no—
71C22×C3×D4—22no—
72C22×C3×D4—24no—
73C22×C3×D4—21no—
74C22×C3×D4—42no—
75C22×C3×D4D411yescharacteristic
76C22×C3×D4C2311yescharacteristic
77C22×C3×D4C2311yescharacteristic
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C2×C3×Q16—24no—
83C2×C3×Q16—24no—
84C2×C3×Q16—42no—
85C2×C3×SD16—24no—
86C2×C3×SD16—24no—
87C2×C3×SD16—24no—
88C2×C3×SD16—24no—
89C2×C3×SD16—24no—
90C2×C3×SD16—42no—
91C22×C3×C8C2312yes—
92C22×C3×C8C2312yes—
93C3×C4⋊Q8—22no—
94C3×C4⋊Q8—22no—
95C3×#124—22no—
96C3×#124D414yes—
97C3×#123—28no—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—24no—
101C3×C22⋊Q8—24no—
102C3×C22⋊Q8—42no—
103C3×C22⋊Q8—42no—
104C3×#121—28no—
105C3×#121—22no—
106C3×#121—22no—
107C3×#120—28no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C3×C4×D4D414yes—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4D411yescharacteristic
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C22⋊C4—28no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4D411yescharacteristic
129C2×C3×C22⋊C4D411yescharacteristic
130C2×C3×C42—21no—
131C2×C3×C42C2311yescharacteristic
132C3×C4⋊C8—22no—
133C3×#103—24no—
134C3×#103—24no—
135C3×#102—24no—
136C3×#102D418yescomplemented
137C3×C22⋊C8—24no—
138C3×C22⋊C8—24no—
139C3×#97—22no—
140C3×#95—21no—
141C22×#41C22×C311yescharacteristic
142C23×D4C22×C311yescharacteristic
143C22×Q16C22×C312yescomplemented
144C22×SD16C22×C312yes—
145C22×SD16C22×C312yes—
146#546—24no—
147#546—24no—
148C2×C4⋊Q8C22×C311yescharacteristic, complemented
149C2×#124C22×C311yescharacteristic
150C2×#123—21no—
151C2×C22⋊Q8C22×C311yescharacteristic
152C2×C22⋊Q8C22×C312yes—
153C2×C22⋊Q8C22×C312yescomplemented
154C2×#121—21no—
155C2×#121C22×C311yescharacteristic
156C2×#120—21no—
157C2×C4×D4C22×C311yescharacteristic
158C2×C4×D4C22×C311yescharacteristic
159C22×C22⋊C4—21no—
160#497—24no—
161#461—24no—
162#452—28no—
163#450—28no—
164C2×C4⋊C8C22×C311yescharacteristic, complemented
165C2×#103C22×C312yescomplemented
166C2×#103C22×C312yescomplemented
167C2×#102C22×C312yes—
168C2×#102C22×C312yes—
169C2×C22⋊C8C22×C312yes—
170C2×C22⋊C8C22×C312yescomplemented
171C2×#97C22×C311yescharacteristic, complemented
172#399—21no—
173#399—21no—
174#390—21no—
175#384—21no—
176C4×C4⋊C4C22×C311yescharacteristic, complemented
177#340C22×C312yescomplemented
178C24×C3—21no—
179C24×C3—24no—
180C24×C3—21no—
181C24×C3—44no—
182C24×C3—42no—
183C24×C3—42no—
184C24×C3—82no—
185C24×C3C2×D411yescharacteristic
186C24×C3C2×D411yescharacteristic
187C3×#41—48no—
188C3×#41—44no—
189C3×#41—44no—
190C2×C3×Q8—21no—
191C2×C3×Q8—22no—
192C2×C3×Q8—22no—
193C2×C3×Q8—22no—
194C2×C3×Q8—22no—
195C2×C3×Q8—22no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8C2×D412yes—
200C2×C3×D4—24no—
201C2×C3×D4—24no—
202C2×C3×D4—22no—
203C2×C3×D4—24no—
204C2×C3×D4—22no—
205C2×C3×D4—21no—
206C2×C3×D4—22no—
207C2×C3×D4—21no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—41no—
211C2×C3×D4—44no—
212C2×C3×D4—48no—
213C2×C3×D4—44no—
214C2×C3×D4—44no—
215C2×C3×D4—44no—
216C2×C3×D4—82no—
217C2×C3×D4C2×D412yes—
218C2×C3×D4C2×D414yes—
219C2×C3×D4C2×D412yes—
220C22×C3×C4—24no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—24no—
233C22×C3×C4—22no—
234C22×C3×C4—44no—
235C22×C3×C4—82no—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2411yescharacteristic
241C3×Q16—48no—
242C3×SD16—48no—
243C3×SD16—48no—
244C2×C3×C8—22no—
245C2×C3×C8—22no—
246C2×C3×C8—22no—
247C2×C3×C8—22no—
248C2×C3×C8—22no—
249C2×C3×C8C2×D414yes—
250C3×C4⋊C4—24no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—44no—
255C3×C4⋊C4—44no—
256C3×C4⋊C4—42no—
257C3×C4⋊C4—42no—
258C3×C4⋊C4C2×D414yes—
259C3×C4⋊C4C2×D412yes—
260C3×C22⋊C4—24no—
261C3×C22⋊C4—24no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—24no—
265C3×C22⋊C4—24no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—44no—
268C3×C22⋊C4—44no—
269C3×C42—42no—
270C3×C42C2×D412yes—
271C3×C42C2×D412yes—
272C25—21no—
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—24no—
276C2×#41—42no—
277C22×Q8C23×C312yes—
278C22×Q8C23×C311yescharacteristic
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—24no—
284C22×D4—21no—
285C22×D4—42no—
286C22×D4C3×D411yescharacteristic
287C22×D4C23×C311yescharacteristic
288C22×D4C23×C311yescharacteristic
289C23×C4—21no—
290C23×C4—21no—
291C23×C4C23×C311yescharacteristic
292C23×C4C23×C311yescharacteristic
293C2×Q16—24no—
294C2×Q16—24no—
295C2×Q16—42no—
296C2×SD16—24no—
297C2×SD16—24no—
298C2×SD16—24no—
299C2×SD16—24no—
300C2×SD16—24no—
301C2×SD16—42no—
302C22×C8C23×C312yes—
303C22×C8C23×C312yes—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306#124—22no—
307#124C3×D414yes—
308#123—28no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—24no—
312C22⋊Q8—24no—
313C22⋊Q8—42no—
314C22⋊Q8—42no—
315#121—28no—
316#121—22no—
317#121—22no—
318#120—28no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4C3×D414yes—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C3×D411yescharacteristic
329C2×C4⋊C4C23×C311yescharacteristic
330C2×C4⋊C4C23×C312yes—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4C3×D411yescharacteristic
340C2×C22⋊C4C3×D411yescharacteristic
341C2×C42—21no—
342C2×C42C23×C311yescharacteristic
343C4⋊C8—22no—
344#103—24no—
345#103—24no—
346#102—24no—
347#102C3×D418yescomplemented
348C22⋊C8—24no—
349C22⋊C8—24no—
350#97—22no—
351#95—21no—
352C23×C3—21no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—24no—
356C23×C3—21no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—22no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—22no—
364C23×C3—48no—
365C23×C3—48no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—42no—
373C23×C3—88no—
374C23×C3—84no—
375C23×C3—88no—
376C23×C3#13712yes—
377C23×C3C22×D411yescharacteristic
378C3×Q8—24no—
379C3×Q8—41no—
380C3×Q8—41no—
381C3×Q8—42no—
382C3×Q8—42no—
383C3×Q8—42no—
384C3×Q8—42no—
385C3×D4—22no—
386C3×D4—24no—
387C3×D4—24no—
388C3×D4—44no—
389C3×D4—48no—
390C3×D4—48no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—84no—
394C3×D4#12714yes—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—48no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—84no—
420C2×C3×C4#12012yes—
421C2×C3×C4#12012yes—
422C2×C3×C4C22×D411yescharacteristic
423C2×C3×C4C22×D412yes—
424C2×C3×C4C22×D411yescharacteristic
425C2×C3×C4H(5,𝔽2)12yes—
426C3×C8—24no—
427C3×C8—42no—
428C24—21no—
429C24—24no—
430C24—21no—
431C24—44no—
432C24—42no—
433C24—42no—
434C24—82no—
435C24C2×C3×D411yescharacteristic
436C24C2×C3×D411yescharacteristic
437#41—48no—
438#41—44no—
439#41—44no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8C2×C3×D412yes—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—22no—
453C2×D4—24no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—41no—
461C2×D4—44no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—82no—
467C2×D4C2×C3×D412yes—
468C2×D4C2×C3×D414yes—
469C2×D4C2×C3×D412yes—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—44no—
485C22×C4—82no—
486C22×C4C2×C3×D411yescharacteristic
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C24×C311yescharacteristic
491Q16—48no—
492SD16—48no—
493SD16—48no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8C2×C3×D414yes—
500C4⋊C4—24no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—44no—
505C4⋊C4—44no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4C2×C3×D414yes—
509C4⋊C4C2×C3×D412yes—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—22no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—22no—
517C22⋊C4—44no—
518C22⋊C4—44no—
519C42—42no—
520C42C2×C3×D412yes—
521C42C2×C3×D412yes—
522C22×C3—24no—
523C22×C3—22no—
524C22×C3—24no—
525C22×C3—41no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—41no—
529C22×C3—44no—
530C22×C3—42no—
531C22×C3—44no—
532C22×C3—41no—
533C22×C3—42no—
534C22×C3—41no—
535C22×C3—42no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—816no—
541C22×C3—82no—
542C22×C3—82no—
543C22×C3C2×#12011yescharacteristic
544C22×C3D4212yes—
545C22×C3C2×#13711yescharacteristic
546C22×C3#57511yescharacteristic
547C22×C3#57712yes—
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—41no—
551C3×C4—41no—
552C3×C4—42no—
553C3×C4—42no—
554C3×C4—44no—
555C3×C4—82no—
556C3×C4C2×#12711yescharacteristic
557C3×C4#53511yescharacteristic
558C3×C4D4212yes—
559C23—21no—
560C23—22no—
561C23—21no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—22no—
569C23—21no—
570C23—22no—
571C23—48no—
572C23—48no—
573C23—41no—
574C23—41no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—42no—
580C23—88no—
581C23—84no—
582C23—88no—
583C23C3×#13712yes—
584C23C22×C3×D411yescharacteristic
585Q8—24no—
586Q8—41no—
587Q8—41no—
588Q8—42no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592D4—22no—
593D4—24no—
594D4—24no—
595D4—44no—
596D4—48no—
597D4—48no—
598D4—41no—
599D4—41no—
600D4—84no—
601D4C3×#12714yes—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—48no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—84no—
627C2×C4C3×#12012yes—
628C2×C4C3×#12012yes—
629C2×C4C22×C3×D411yescharacteristic
630C2×C4C22×C3×D412yes—
631C2×C4C22×C3×D411yescharacteristic
632C2×C4C3×H(5,𝔽2)12yes—
633C8—24no—
634C8—42no—
635C2×C3—42no—
636C2×C3—44no—
637C2×C3—81no—
638C2×C3—82no—
639C2×C3#243311yescharacteristic
640C2×C3#300711yescharacteristic
641C2×C3#300911yescharacteristic
642C2×C3#326612yes—
643C2×C3#326712yes—
644C22—24no—
645C22—22no—
646C22—24no—
647C22—41no—
648C22—42no—
649C22—42no—
650C22—41no—
651C22—44no—
652C22—42no—
653C22—44no—
654C22—41no—
655C22—42no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—816no—
663C22—82no—
664C22—82no—
665C22C2×C3×#12011yescharacteristic
666C22C3×D4212yes—
667C22C2×C3×#13711yescharacteristic
668C22C3×#57511yescharacteristic
669C22C3×#57712yes—
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—42no—
675C4—42no—
676C4—44no—
677C4—82no—
678C4C2×C3×#12711yescharacteristic
679C4C3×#53511yescharacteristic
680C4C3×D4212yes—
681C3#2576911yescharacteristic, direct product factor, Sylow
682C2—42no—
683C2—44no—
684C2—81no—
685C2—82no—
686C2C3×#243311yescharacteristic
687C2C3×#300711yescharacteristic
688C2C3×#300911yescharacteristic
689C2C3×#326612yes—
690C2C3×#326712yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#497C2semidirect
3. C2×C3×#461C2semidirect
4. C2×C3×#452C2semidirect
5. C2×C3×#450C2semidirect
6. C3×#2542C2semidirect
7. C3×#2001C2semidirect
8. C3×#2000C2semidirect
9. C3×#1983C2semidirect
10. C3×#1955C2semidirect
11. C3×#1762C2semidirect
12. #25769C3direct (N × H)
15. C22×C3×Q16C22semidirect
20. C2×C3×C4⋊Q8C22semidirect
25. C2×C3×C22⋊Q8C22semidirect
36. C2×C3×C4⋊C8C22semidirect
37. C2×C3×#103C22semidirect
38. C2×C3×#103C22semidirect
42. C2×C3×C22⋊C8C22semidirect
43. C2×C3×#97C22semidirect
48. C3×C4×C4⋊C4C22semidirect
49. C3×#340C22semidirect
51. C2×#497C2×C3semidirect
52. C2×#461C2×C3semidirect
53. C2×#452C2×C3semidirect
54. C2×#450C2×C3semidirect
55. #2542C2×C3semidirect
56. #2001C2×C3semidirect
57. #2000C2×C3semidirect
58. #1983C2×C3semidirect
59. #1955C2×C3semidirect
60. #1762C2×C3semidirect
136. C3×#102D4semidirect
143. C22×Q16C22×C3semidirect
148. C2×C4⋊Q8C22×C3semidirect
153. C2×C22⋊Q8C22×C3semidirect
164. C2×C4⋊C8C22×C3semidirect
165. C2×#103C22×C3semidirect
166. C2×#103C22×C3semidirect
170. C2×C22⋊C8C22×C3semidirect
171. C2×#97C22×C3semidirect
176. C4×C4⋊C4C22×C3semidirect
177. #340C22×C3semidirect
347. #102C3×D4semidirect
681. C3#25769direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5462
C2×C3×#4972
C2×C3×#4612
C2×C3×#4522
C2×C3×#4502
C3×#25422
C3×#20012
C3×#20002
C3×#19832
C3×#19552
C3×#17622
#257693