Finite Group Databasebeta

← C3×#84105 #11864334

Subgroups — C3×#84105 #11864334

Order 1152.

1953 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×H(5,𝔽2)C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic, complemented
3C2×C3×#951C211yesmaximal, characteristic, complemented
4C22×C3×#214C211yesmaximal, characteristic, complemented
5C3×#5239C214yesmaximal, complemented
6C3×#5234C211yesmaximal, characteristic, complemented
7C3×#5233C211yesmaximal, characteristic, complemented
8C3×#5218C214yesmaximal, complemented
9C3×#5215C211yesmaximal, characteristic, complemented
10C3×#3009—31nomaximal
11#84105C311yesmaximal, characteristic, direct product factor
12C32×H(5,𝔽2)—24no—
13C32×H(5,𝔽2)—24no—
14C2×C32×#41—21no—
15C2×C32×#41C2212yes—
16C2×C32×#41C2211yescharacteristic
17C2×C32×#41C2211yescharacteristic
18C22×C32×D4—22no—
19C22×C32×D4—21no—
20C22×C32×D4C2212yes—
21C22×C32×D4C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23C3×#951—24no—
24C3×#944—21no—
25C2×C3×#216C2212yescomplemented
26C3×#936—21no—
27C3×#935—22no—
28C2×C3×#214—24no—
29C2×C3×#214C2214yescomplemented
30C2×C3×#214C2212yescomplemented
31C3×#926C2211yescharacteristic, complemented
32C3×#924C2214yescomplemented
33C2×C3×#208C2211yescharacteristic, complemented
34C22×C3×C3⋊C8C2211yescharacteristic, complemented
35C3×#835C2212yescomplemented
36C3×#832C2214yescomplemented
37C3×#832C2212yescomplemented
38C3×#830C2214yescomplemented
39C2×C3×H(5,𝔽2)—21no—
40C2×C3×H(5,𝔽2)D311yescharacteristic
41C2×C3×H(5,𝔽2)C2×C311yescharacteristic
42C2×C3×#137—31no—
43C22×C3×SD16—31no—
44C3×#536—31no—
45#5825C2×C311yescharacteristic, complemented
46C2×#951C2×C311yescharacteristic, complemented
47C22×#214C2×C311yescharacteristic, complemented
48C3×#452—34no—
49C3×#450—34no—
50C3×#418—31no—
51C3×#416—31no—
52C3×#408—31no—
53#5239C2×C314yescomplemented
54#5234C2×C311yescharacteristic, complemented
55#5233C2×C311yescharacteristic, complemented
56#5218C2×C314yescomplemented
57#5215C2×C311yescharacteristic, complemented
58C24×C32—22no—
59C24×C32—21no—
60C32×#41—28no—
61C32×#41—24no—
62C32×#41—24no—
63C32×#41—22no—
64C32×#41—22no—
65C32×#41—22no—
66C32×#41D414yes—
67C2×C32×Q8D411yescharacteristic
68C2×C32×Q8C2311yescharacteristic
69C2×C32×D4—216no—
70C2×C32×D4—28no—
71C2×C32×D4—22no—
72C2×C32×D4—21no—
73C2×C32×D4—24no—
74C2×C32×D4—24no—
75C2×C32×D4—22no—
76C2×C32×D4—21no—
77C2×C32×D4—22no—
78C2×C32×D4D412yes—
79C2×C32×D4D411yescharacteristic
80C2×C32×D4D414yes—
81C2×C32×D4C2311yescharacteristic
82C2×C32×D4C2312yes—
83C22×C32×C4—22no—
84C22×C32×C4—21no—
85C22×C32×C4C2312yes—
86C22×C32×C4C2311yescharacteristic
87C22×C3×Dic3—21no—
88C2×C3×Dic6—22no—
89C2×C3×Dic6—22no—
90C2×C3×Dic6—21no—
91C2×C3×Dic6C2312yes—
92C3×#217—24no—
93C3×#217—21no—
94C3×#216—24no—
95C3×#214—28no—
96C3×#214—24no—
97C3×C4⋊Dic3C2312yes—
98C3×Dic3⋊C4—24no—
99C3×C4×Dic3—21no—
100C3×#208—22no—
101C2×C3×C3⋊C8—22no—
102C2×C3×C3⋊C8C2312yes—
103C2×C3×C3⋊C8C2312yes—
104#3009—31noSylow
105C3×H(5,𝔽2)—28no—
106C3×H(5,𝔽2)—28no—
107C3×H(5,𝔽2)—24no—
108C3×H(5,𝔽2)—24no—
109C3×H(5,𝔽2)—24no—
110C3×H(5,𝔽2)—24no—
111C2×C3×#41—22no—
112C2×C3×#41—21no—
113C2×C3×#41—21no—
114C2×C3×#41—22no—
115C2×C3×#41—21no—
116C2×C3×#41—21no—
117C2×C3×#41C2×D312yes—
118C2×C3×#41C2×D311yescharacteristic
119C2×C3×#41C2×D311yescharacteristic
120C2×C3×#41C22×C312yes—
121C2×C3×#41C22×C311yescharacteristic
122C2×C3×#41C22×C311yescharacteristic
123C22×C3×Q8—31no—
124C22×C3×D4—24no—
125C22×C3×D4—22no—
126C22×C3×D4—22no—
127C22×C3×D4—21no—
128C22×C3×D4—22no—
129C22×C3×D4—21no—
130C22×C3×D4—22no—
131C22×C3×D4—21no—
132C22×C3×D4C2×D312yes—
133C22×C3×D4C2×D311yescharacteristic
134C22×C3×D4C22×C312yes—
135C22×C3×D4C22×C311yescharacteristic
136C22×Dic6C22×C311yescharacteristic, complemented
137C3×#137—64no—
138C2×C3×Q16—32no—
139C2×C3×SD16—34no—
140C2×C3×SD16—32no—
141C2×C3×SD16—64no—
142C2×C3×M16—31no—
143C22×C3×C8—31no—
144C3×C4⋊Q8—61no—
145C3×#124—61no—
146C3×#123—62no—
147C3×C22⋊Q8—34no—
148C3×#117—31no—
149#951—24no—
150#944—21no—
151C2×#216C22×C312yescomplemented
152#936—21no—
153#935—22no—
154C2×#214—24no—
155C2×#214C22×C312yescomplemented
156C2×#214C22×C314yescomplemented
157#926C22×C311yescharacteristic, complemented
158#924C22×C314yescomplemented
159C2×#208C22×C311yescharacteristic, complemented
160C22×C3⋊C8C22×C311yescharacteristic, complemented
161C3×#103—32no—
162C3×#102—32no—
163C3×#102—34no—
164C3×C22⋊C8—34no—
165#835C22×C312yescomplemented
166#832C22×C314yescomplemented
167#832C22×C312yescomplemented
168#830C22×C314yescomplemented
169C23×C32—28no—
170C23×C32—22no—
171C23×C32—21no—
172C23×C32—24no—
173C23×C32—82no—
174C23×C32—84no—
175C23×C32C2×D412yes—
176C23×C32C2×D411yescharacteristic
177C32×Q8—22no—
178C32×Q8—21no—
179C32×Q8C2×D412yes—
180C32×D4—28no—
181C32×D4—28no—
182C32×D4—24no—
183C32×D4—24no—
184C32×D4—22no—
185C32×D4—24no—
186C32×D4—22no—
187C32×D4—21no—
188C32×D4C2×D412yes—
189C32×D4C2×D414yes—
190C2×C32×C4—28no—
191C2×C32×C4—21no—
192C2×C32×C4—24no—
193C2×C32×C4—22no—
194C2×C32×C4—22no—
195C2×C32×C4C2×D412yes—
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2×D412yes—
198C2×C32×C4C2×D412yes—
199C2×C32×C4C2411yescharacteristic
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—42no—
203C3×Dic6—22no—
204C3×Dic6—22no—
205C3×Dic6—42no—
206C3×C3⋊C8—22no—
207C3×C3⋊C8—22no—
208C2×H(5,𝔽2)C3×D311yescharacteristic
209C2×#137—31no—
210C22×SD16—31no—
211#536—31no—
212#452—34no—
213#450—34no—
214#418—31no—
215#416—31no—
216#408—31no—
217C24×C3—24no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—21no—
221C24×C3—22no—
222C24×C3—21no—
223C3×#41—216no—
224C3×#41—28no—
225C3×#41—28no—
226C3×#41—28no—
227C3×#41—28no—
228C3×#41—24no—
229C3×#41—24no—
230C3×#41—24no—
231C3×#41—24no—
232C3×#41—24no—
233C3×#41—24no—
234C3×#41—24no—
235C3×#41—22no—
236C3×#41—22no—
237C3×#41—22no—
238C3×#41—22no—
239C3×#41—22no—
240C3×#41—22no—
241C3×#41—24no—
242C3×#41#6714yes—
243C3×#41C3×D414yes—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—32no—
247C2×C3×Q8—61no—
248C2×C3×Q8—62no—
249C2×C3×Q8—62no—
250C2×C3×Q8#6711yescharacteristic
251C2×C3×Q8C3×D411yescharacteristic
252C2×C3×Q8C22×D311yescharacteristic
253C2×C3×Q8C23×C311yescharacteristic
254C2×C3×D4—24no—
255C2×C3×D4—22no—
256C2×C3×D4—24no—
257C2×C3×D4—22no—
258C2×C3×D4—232no—
259C2×C3×D4—216no—
260C2×C3×D4—216no—
261C2×C3×D4—216no—
262C2×C3×D4—28no—
263C2×C3×D4—28no—
264C2×C3×D4—28no—
265C2×C3×D4—28no—
266C2×C3×D4—24no—
267C2×C3×D4—22no—
268C2×C3×D4—21no—
269C2×C3×D4—22no—
270C2×C3×D4—21no—
271C2×C3×D4—24no—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—22no—
276C2×C3×D4—21no—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C2×C3×D4—21no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—21no—
283C2×C3×D4—24no—
284C2×C3×D4—21no—
285C2×C3×D4—22no—
286C2×C3×D4#6712yes—
287C2×C3×D4#6711yescharacteristic
288C2×C3×D4#6714yes—
289C2×C3×D4C3×D412yes—
290C2×C3×D4C3×D411yescharacteristic
291C2×C3×D4C3×D414yes—
292C2×C3×D4C22×D311yescharacteristic
293C2×C3×D4C22×D312yes—
294C2×C3×D4C23×C311yescharacteristic
295C2×C3×D4C23×C312yes—
296C22×C3×C4—24no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—21no—
300C22×C3×C4—22no—
301C22×C3×C4—21no—
302C22×C3×C4—22no—
303C22×C3×C4—21no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D312yes—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C23×C312yes—
308C22×C3×C4C23×C311yescharacteristic
309C22×Dic3—21no—
310C2×Dic6—22no—
311C2×Dic6—22no—
312C2×Dic6—21no—
313C2×Dic6C23×C312yes—
314C3×Q16—64no—
315C3×SD16—68no—
316C3×SD16—64no—
317C3×M16—62no—
318C2×C3×C8—32no—
319C2×C3×C8—32no—
320C2×C3×C8—62no—
321C3×C4⋊C4—32no—
322C3×C4⋊C4—64no—
323C3×C22⋊C4—61no—
324C3×C22⋊C4—64no—
325C3×C42—61no—
326#217—24no—
327#217—21no—
328#216—24no—
329#214—28no—
330#214—24no—
331C4⋊Dic3C23×C312yes—
332Dic3⋊C4—24no—
333C4×Dic3—21no—
334#208—22no—
335C2×C3⋊C8—22no—
336C2×C3⋊C8C23×C312yes—
337C2×C3⋊C8C23×C312yes—
338C22×C32—22no—
339C22×C32—24no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—24no—
343C22×C32—44no—
344C22×C32—42no—
345C22×C32—84no—
346C22×C32—88no—
347C22×C32#12012yes—
348C22×C32C22×D411yescharacteristic
349C32×C4—22no—
350C32×C4—22no—
351C32×C4#12012yes—
352C32×C4C22×D411yescharacteristic
353C32×C4C22×D411yescharacteristic
354C3×Dic3—42no—
355C3×Dic3—42no—
356H(5,𝔽2)—24no—
357H(5,𝔽2)—24no—
358C2×#41—21no—
359C2×#41C2×C3×D312yes—
360C2×#41C2×C3×D311yescharacteristic
361C2×#41C2×C3×D311yescharacteristic
362C22×Q8—31no—
363C22×D4—22no—
364C22×D4—21no—
365C22×D4C2×C3×D312yes—
366C22×D4C2×C3×D311yescharacteristic
367#137—64no—
368C2×Q16—32no—
369C2×SD16—34no—
370C2×SD16—32no—
371C2×SD16—64no—
372C2×M16—31no—
373C22×C8—31no—
374C4⋊Q8—61no—
375#124—61no—
376#123—62no—
377C22⋊Q8—34no—
378#117—31no—
379#103—32no—
380#102—32no—
381#102—34no—
382C22⋊C8—34no—
383C23×C3—24no—
384C23×C3—22no—
385C23×C3—216no—
386C23×C3—28no—
387C23×C3—28no—
388C23×C3—28no—
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3—21no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—22no—
396C23×C3—21no—
397C23×C3—82no—
398C23×C3—82no—
399C23×C3—84no—
400C23×C3—84no—
401C23×C3—84no—
402C23×C3—88no—
403C23×C3C2×#6712yes—
404C23×C3C2×#6711yescharacteristic
405C23×C3C2×C3×D412yes—
406C23×C3C2×C3×D411yescharacteristic
407C3×Q8—24no—
408C3×Q8—22no—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—21no—
412C3×Q8—21no—
413C3×Q8—22no—
414C3×Q8—62no—
415C3×Q8—62no—
416C3×Q8—122no—
417C3×Q8C2×#6712yes—
418C3×Q8C2×C3×D412yes—
419C3×D4—216no—
420C3×D4—216no—
421C3×D4—28no—
422C3×D4—28no—
423C3×D4—28no—
424C3×D4—28no—
425C3×D4—28no—
426C3×D4—28no—
427C3×D4—28no—
428C3×D4—24no—
429C3×D4—24no—
430C3×D4—22no—
431C3×D4—24no—
432C3×D4—24no—
433C3×D4—24no—
434C3×D4—24no—
435C3×D4—22no—
436C3×D4—24no—
437C3×D4—22no—
438C3×D4—24no—
439C3×D4—22no—
440C3×D4—21no—
441C3×D4—22no—
442C3×D4—21no—
443C3×D4—22no—
444C3×D4—24no—
445C3×D4C2×#6712yes—
446C3×D4C2×#6714yes—
447C3×D4C2×C3×D412yes—
448C3×D4C2×C3×D414yes—
449C2×C3×C4—22no—
450C2×C3×C4—216no—
451C2×C3×C4—28no—
452C2×C3×C4—28no—
453C2×C3×C4—28no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—122no—
472C2×C3×C4C2×#6712yes—
473C2×C3×C4C2×#6711yescharacteristic
474C2×C3×C4C2×#6712yes—
475C2×C3×C4C2×#6712yes—
476C2×C3×C4C2×C3×D412yes—
477C2×C3×C4C2×C3×D411yescharacteristic
478C2×C3×C4C2×C3×D412yes—
479C2×C3×C4C2×C3×D412yes—
480C2×C3×C4C23×D311yescharacteristic
481C2×C3×C4C24×C311yescharacteristic
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—42no—
485Dic6—22no—
486Dic6—22no—
487Dic6—42no—
488C3×C8—62no—
489C3×C8—62no—
490C3⋊C8—22no—
491C3⋊C8—22no—
492C2×C32—22no—
493C2×C32—42no—
494C2×C32—44no—
495C2×C32—42no—
496C2×C32C2×#12011yescharacteristic
497C2×C32#57712yes—
498C24—22no—
499C24—21no—
500#41—28no—
501#41—24no—
502#41—24no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41C3×#6714yes—
507C2×Q8—32no—
508C2×Q8—61no—
509C2×Q8—62no—
510C2×Q8—62no—
511C2×Q8C3×#6711yescharacteristic
512C2×Q8C22×C3×D311yescharacteristic
513C2×D4—216no—
514C2×D4—28no—
515C2×D4—22no—
516C2×D4—21no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—22no—
522C2×D4C3×#6712yes—
523C2×D4C3×#6711yescharacteristic
524C2×D4C3×#6714yes—
525C2×D4C22×C3×D311yescharacteristic
526C2×D4C22×C3×D312yes—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—61no—
530C22×C4C22×C3×D312yes—
531C22×C4C22×C3×D311yescharacteristic
532Q16—64no—
533SD16—68no—
534SD16—64no—
535M16—62no—
536C2×C8—32no—
537C2×C8—32no—
538C2×C8—62no—
539C4⋊C4—32no—
540C4⋊C4—64no—
541C22⋊C4—61no—
542C22⋊C4—64no—
543C42—61no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—24no—
547C22×C3—28no—
548C22×C3—24no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—22no—
552C22×C3—24no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—24no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—21no—
559C22×C3—42no—
560C22×C3—44no—
561C22×C3—48no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—42no—
565C22×C3—44no—
566C22×C3—42no—
567C22×C3—84no—
568C22×C3—84no—
569C22×C3—88no—
570C22×C3—816no—
571C22×C3—88no—
572C22×C3—88no—
573C22×C3#95312yes—
574C22×C3C3×#12012yes—
575C22×C3C22×#6711yescharacteristic
576C22×C3C22×C3×D411yescharacteristic
577C3×C4—24no—
578C3×C4—24no—
579C3×C4—22no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—22no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—122no—
587C3×C4—122no—
588C3×C4#95312yes—
589C3×C4C3×#12012yes—
590C3×C4C22×#6711yescharacteristic
591C3×C4C22×#6711yescharacteristic
592C3×C4C22×C3×D411yescharacteristic
593C3×C4C22×C3×D411yescharacteristic
594Dic3—42no—
595Dic3—42no—
596C32#300911yescharacteristic, complemented, Sylow
597C23—28no—
598C23—22no—
599C23—21no—
600C23—24no—
601C23—82no—
602C23—84no—
603C23C2×C3×#6712yes—
604C23C2×C3×#6711yescharacteristic
605Q8—22no—
606Q8—21no—
607Q8—62no—
608Q8—62no—
609Q8—122no—
610Q8C2×C3×#6712yes—
611D4—28no—
612D4—28no—
613D4—24no—
614D4—24no—
615D4—22no—
616D4—24no—
617D4—22no—
618D4—21no—
619D4C2×C3×#6712yes—
620D4C2×C3×#6714yes—
621C2×C4—28no—
622C2×C4—21no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—122no—
629C2×C4C2×C3×#6712yes—
630C2×C4C2×C3×#6711yescharacteristic
631C2×C4C2×C3×#6712yes—
632C2×C4C2×C3×#6712yes—
633C2×C4C23×C3×D311yescharacteristic
634C8—62no—
635C8—62no—
636C2×C3—22no—
637C2×C3—22no—
638C2×C3—22no—
639C2×C3—21no—
640C2×C3—42no—
641C2×C3—44no—
642C2×C3—48no—
643C2×C3—44no—
644C2×C3—42no—
645C2×C3—44no—
646C2×C3—42no—
647C2×C3—42no—
648C2×C3—44no—
649C2×C3—42no—
650C2×C3#583612yes—
651C2×C3C2×#95311yescharacteristic
652C2×C3C2×C3×#12011yescharacteristic
653C2×C3C3×#57712yes—
654C22—22no—
655C22—24no—
656C22—22no—
657C22—24no—
658C22—22no—
659C22—44no—
660C22—42no—
661C22—84no—
662C22—88no—
663C22C3×#95312yes—
664C22C22×C3×#6711yescharacteristic
665C4—22no—
666C4—22no—
667C4—122no—
668C4—122no—
669C4C3×#95312yes—
670C4C22×C3×#6711yescharacteristic
671C4C22×C3×#6711yescharacteristic
672C3—21no—
673C3#8410511yescharacteristic, direct product factor
674C3C3×#300911yescharacteristic, complemented
675C2—22no—
676C2—42no—
677C2—44no—
678C2—42no—
679C2C3×#583612yes—
680C2C2×C3×#95311yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC2×C32×H(5,𝔽2)C2
socleC22×C32C22×D4
hypercenterC2×C3×H(5,𝔽2)D3
hypocenterC3C3×#3009
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C2×C3×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C3×#5825C2semidirect
3. C2×C3×#951C2semidirect
4. C22×C3×#214C2semidirect
5. C3×#5239C2semidirect
6. C3×#5234C2semidirect
7. C3×#5233C2semidirect
8. C3×#5218C2semidirect
9. C3×#5215C2semidirect
11. #84105C3direct (N × H)
22. C22×C3×Dic6C22semidirect
25. C2×C3×#216C22semidirect
29. C2×C3×#214C22semidirect
30. C2×C3×#214C22semidirect
31. C3×#926C22semidirect
32. C3×#924C22semidirect
33. C2×C3×#208C22semidirect
34. C22×C3×C3⋊C8C22semidirect
35. C3×#835C22semidirect
36. C3×#832C22semidirect
37. C3×#832C22semidirect
38. C3×#830C22semidirect
45. #5825C2×C3semidirect
46. C2×#951C2×C3semidirect
47. C22×#214C2×C3semidirect
53. #5239C2×C3semidirect
54. #5234C2×C3semidirect
55. #5233C2×C3semidirect
56. #5218C2×C3semidirect
57. #5215C2×C3semidirect
136. C22×Dic6C22×C3semidirect
151. C2×#216C22×C3semidirect
155. C2×#214C22×C3semidirect
156. C2×#214C22×C3semidirect
157. #926C22×C3semidirect
158. #924C22×C3semidirect
159. C2×#208C22×C3semidirect
160. C22×C3⋊C8C22×C3semidirect
165. #835C22×C3semidirect
166. #832C22×C3semidirect
167. #832C22×C3semidirect
168. #830C22×C3semidirect
596. C32#3009semidirect
673. C3#84105direct (N × H)
674. C3C3×#3009semidirect

Maximal subgroups

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

subgroupindex
C2×C32×H(5,𝔽2)2
C3×#58252
C2×C3×#9512
C22×C3×#2142
C3×#52392
C3×#52342
C3×#52332
C3×#52182
C3×#52152
C3×#30093
#841053