Finite Group Databasebeta

← C3×#84101 #11864257

Subgroups — C3×#84101 #11864257

Order 1152.

2017 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C3×#5830C211yesmaximal, characteristic, complemented
3C2×C3×#949C211yesmaximal, characteristic, complemented
4C22×C3×#213C211yesmaximal, characteristic, complemented
5C3×#5238C214yesmaximal, complemented
6C3×#5234C211yesmaximal, characteristic, complemented
7C3×#5233C211yesmaximal, characteristic, complemented
8C3×#5217C214yesmaximal, complemented
9C3×#5215C211yesmaximal, characteristic, complemented
10C3×#3008—31nomaximal
11#84101C311yesmaximal, characteristic, direct product factor
12C32×H(5,𝔽2)—24no—
13C32×H(5,𝔽2)—24no—
14C2×C32×#41—21no—
15C2×C32×#41C2211yescharacteristic
16C2×C32×#41C2211yescharacteristic
17C2×C32×#41C2212yescomplemented
18C22×C32×D4—22no—
19C22×C32×D4—21no—
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2212yescomplemented
22C22×C3×D12C2211yescharacteristic, complemented
23C3×#949—24no—
24C3×#947—21no—
25C2×C3×#215C2212yescomplemented
26C3×#940—21no—
27C3×#937—22no—
28C2×C3×#213—24no—
29C2×C3×#213C2214yescomplemented
30C2×C3×#213C2212yescomplemented
31C3×#930C2214yescomplemented
32C3×#926C2211yescharacteristic, complemented
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, complemented
41C2×C3×H(5,𝔽2)C2×C311yescharacteristic, complemented
42C2×C3×AGL(1,ℤ/8)—31no—
43C22×C3×D8—31no—
44C3×#535—31no—
45#5830C2×C311yescharacteristic, complemented
46C2×#949C2×C311yescharacteristic, complemented
47C22×#213C2×C311yescharacteristic, complemented
48C3×#449—34no—
49C3×#447—34no—
50C3×#418—31no—
51C3×#416—31no—
52C3×#408—31no—
53#5238C2×C314yescomplemented
54#5234C2×C311yescharacteristic, complemented
55#5233C2×C311yescharacteristic, complemented
56#5217C2×C314yescomplemented
57#5215C2×C311yescharacteristic, complemented
58C24×C32—21no—
59C24×C32—22no—
60C23×C3×D3—21no—
61C32×#41—28no—
62C32×#41—24no—
63C32×#41—24no—
64C32×#41—22no—
65C32×#41—22no—
66C32×#41—22no—
67C32×#41D414yescomplemented
68C2×C32×Q8D411yescharacteristic
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—216no—
71C2×C32×D4—28no—
72C2×C32×D4—21no—
73C2×C32×D4—22no—
74C2×C32×D4—24no—
75C2×C32×D4—24no—
76C2×C32×D4—21no—
77C2×C32×D4—22no—
78C2×C32×D4—22no—
79C2×C32×D4D412yes—
80C2×C32×D4D411yescharacteristic
81C2×C32×D4D414yescomplemented
82C2×C32×D4C2312yes—
83C2×C32×D4C2311yescharacteristic
84C22×C32×C4—21no—
85C22×C32×C4—22no—
86C22×C32×C4C2312yes—
87C22×C32×C4C2311yescharacteristic
88C2×C3×#67—24no—
89C2×C3×D12—22no—
90C2×C3×D12—22no—
91C2×C3×D12—21no—
92C2×C3×D12C2312yes—
93C3×#217—21no—
94C3×#215—24no—
95C3×#213—28no—
96C3×#213—24no—
97C3×(C2×D3)⋊C4—24no—
98C3×C4⋊Dic3C2312yes—
99C3×C4×Dic3—21no—
100C3×#208—22no—
101C2×C3×C3⋊C8—22no—
102C2×C3×C3⋊C8C2312yes—
103C2×C3×C3⋊C8C2312yes—
104#3008—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—21no—
115C2×C3×#41—21no—
116C2×C3×#41—22no—
117C2×C3×#41C2×D311yescharacteristic
118C2×C3×#41C2×D311yescharacteristic
119C2×C3×#41C2×D312yescomplemented
120C2×C3×#41C22×C311yescharacteristic
121C2×C3×#41C22×C311yescharacteristic
122C2×C3×#41C22×C312yescomplemented
123C22×C3×D4—22no—
124C22×C3×D4—24no—
125C22×C3×D4—21no—
126C22×C3×D4—22no—
127C22×C3×D4—21no—
128C22×C3×D4—22no—
129C22×C3×D4—21no—
130C22×C3×D4—22no—
131C22×C3×D4—31no—
132C22×C3×D4C2×D311yescharacteristic
133C22×C3×D4C2×D312yescomplemented
134C22×C3×D4C22×C311yescharacteristic
135C22×C3×D4C22×C312yescomplemented
136C22×D12C22×C311yescharacteristic, complemented
137C3×AGL(1,ℤ/8)—64no—
138C2×C3×SD16—32no—
139C2×C3×D8—34no—
140C2×C3×D8—32no—
141C2×C3×D8—64no—
142C2×C3×M16—31no—
143C22×C3×C8—31no—
144C3×#127—61no—
145C3×#124—61no—
146C3×#121—34no—
147C3×#120—62no—
148C3×#117—31no—
149#949—24no—
150#947—21no—
151C2×#215C22×C312yescomplemented
152#940—21no—
153#937—22no—
154C2×#213—24no—
155C2×#213C22×C312yescomplemented
156C2×#213C22×C314yescomplemented
157#930C22×C314yescomplemented
158#926C22×C311yescharacteristic, complemented
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
177C22×C3×D3—22no—
178C22×C3×D3—42no—
179C22×C3×D3—82no—
180C32×Q8—22no—
181C32×Q8—21no—
182C32×Q8C2×D412yes—
183C32×D4—28no—
184C32×D4—28no—
185C32×D4—24no—
186C32×D4—24no—
187C32×D4—22no—
188C32×D4—24no—
189C32×D4—22no—
190C32×D4—21no—
191C32×D4C2×D412yes—
192C32×D4C2×D414yes—
193C2×C32×C4—28no—
194C2×C32×C4—21no—
195C2×C32×C4—24no—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4C2×D412yes—
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D412yes—
201C2×C32×C4C2×D412yes—
202C2×C32×C4C2411yescharacteristic
203C3×#67—84no—
204C2×C3×Dic3—22no—
205C3×D12—22no—
206C3×D12—22no—
207C3×D12—42no—
208C3×C3⋊C8—22no—
209C3×C3⋊C8—22no—
210C2×H(5,𝔽2)C3×D311yescharacteristic, complemented
211C2×AGL(1,ℤ/8)—31no—
212C22×D8—31no—
213#535—31no—
214#449—34no—
215#447—34no—
216#418—31no—
217#416—31no—
218#408—31no—
219C24×C3—22no—
220C24×C3—24no—
221C24×C3—21no—
222C24×C3—22no—
223C24×C3—21no—
224C24×C3—22no—
225C24×C3—61no—
226C23×D3—21no—
227C3×#41—216no—
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—28no—
231C3×#41—28no—
232C3×#41—24no—
233C3×#41—24no—
234C3×#41—24no—
235C3×#41—24no—
236C3×#41—24no—
237C3×#41—24no—
238C3×#41—24no—
239C3×#41—22no—
240C3×#41—22no—
241C3×#41—22no—
242C3×#41—22no—
243C3×#41—22no—
244C3×#41—22no—
245C3×#41—24no—
246C3×#41#6714yescomplemented
247C3×#41C3×D414yescomplemented
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8#6711yescharacteristic
251C2×C3×Q8C3×D411yescharacteristic
252C2×C3×Q8C22×D311yescharacteristic
253C2×C3×Q8C23×C311yescharacteristic
254C2×C3×D4—22no—
255C2×C3×D4—24no—
256C2×C3×D4—22no—
257C2×C3×D4—24no—
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—21no—
268C2×C3×D4—22no—
269C2×C3×D4—21no—
270C2×C3×D4—22no—
271C2×C3×D4—24no—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—21no—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—21no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—21no—
283C2×C3×D4—24no—
284C2×C3×D4—22no—
285C2×C3×D4—21no—
286C2×C3×D4—32no—
287C2×C3×D4—64no—
288C2×C3×D4—62no—
289C2×C3×D4—62no—
290C2×C3×D4—61no—
291C2×C3×D4#6712yes—
292C2×C3×D4#6711yescharacteristic
293C2×C3×D4#6714yescomplemented
294C2×C3×D4C3×D412yes—
295C2×C3×D4C3×D411yescharacteristic
296C2×C3×D4C3×D414yescomplemented
297C2×C3×D4C22×D312yes—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C23×C312yes—
300C2×C3×D4C23×C311yescharacteristic
301C22×C3×C4—22no—
302C22×C3×C4—24no—
303C22×C3×C4—21no—
304C22×C3×C4—22no—
305C22×C3×C4—21no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—21no—
309C22×C3×C4C22×D312yes—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C312yes—
312C22×C3×C4C23×C311yescharacteristic
313C2×#67—24no—
314C2×D12—22no—
315C2×D12—22no—
316C2×D12—21no—
317C2×D12C23×C312yes—
318C3×SD16—64no—
319C3×D8—68no—
320C3×D8—64no—
321C3×M16—62no—
322C2×C3×C8—32no—
323C2×C3×C8—32no—
324C2×C3×C8—62no—
325C3×C4⋊C4—32no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—64no—
328C3×C42—61no—
329#217—21no—
330#215—24no—
331#213—28no—
332#213—24no—
333(C2×D3)⋊C4—24no—
334C4⋊Dic3C23×C312yes—
335C4×Dic3—21no—
336#208—22no—
337C2×C3⋊C8—22no—
338C2×C3⋊C8C23×C312yes—
339C2×C3⋊C8C23×C312yes—
340C22×C32—22no—
341C22×C32—24no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—24no—
345C22×C32—44no—
346C22×C32—42no—
347C22×C32—84no—
348C22×C32—88no—
349C22×C32#12012yes—
350C22×C32C22×D411yescharacteristic
351C2×C3×D3—42no—
352C2×C3×D3—44no—
353C2×C3×D3—84no—
354C32×C4—22no—
355C32×C4—22no—
356C32×C4#12012yes—
357C32×C4C22×D411yescharacteristic
358C32×C4C22×D411yescharacteristic
359C3×Dic3—42no—
360H(5,𝔽2)—24no—
361H(5,𝔽2)—24no—
362C2×#41—21no—
363C2×#41C2×C3×D311yescharacteristic
364C2×#41C2×C3×D311yescharacteristic
365C2×#41C2×C3×D312yescomplemented
366C22×D4—21no—
367C22×D4—22no—
368C22×D4—31no—
369C22×D4C2×C3×D311yescharacteristic
370C22×D4C2×C3×D312yescomplemented
371AGL(1,ℤ/8)—64no—
372C2×SD16—32no—
373C2×D8—34no—
374C2×D8—32no—
375C2×D8—64no—
376C2×M16—31no—
377C22×C8—31no—
378#127—61no—
379#124—61no—
380#121—34no—
381#120—62no—
382#117—31no—
383#103—32no—
384#102—32no—
385#102—34no—
386C22⋊C8—34no—
387C23×C3—22no—
388C23×C3—24no—
389C23×C3—216no—
390C23×C3—28no—
391C23×C3—28no—
392C23×C3—28no—
393C23×C3—21no—
394C23×C3—22no—
395C23×C3—21no—
396C23×C3—22no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—62no—
402C23×C3—82no—
403C23×C3—82no—
404C23×C3—84no—
405C23×C3—84no—
406C23×C3—84no—
407C23×C3—88no—
408C23×C3—122no—
409C23×C3—242no—
410C23×C3C2×#6712yes—
411C23×C3C2×#6711yescharacteristic
412C23×C3C2×C3×D412yes—
413C23×C3C2×C3×D411yescharacteristic
414C22×D3—22no—
415C22×D3—42no—
416C22×D3—82no—
417C3×Q8—24no—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—22no—
421C3×Q8—21no—
422C3×Q8—21no—
423C3×Q8—22no—
424C3×Q8C2×#6712yes—
425C3×Q8C2×C3×D412yes—
426C3×D4—216no—
427C3×D4—216no—
428C3×D4—28no—
429C3×D4—28no—
430C3×D4—28no—
431C3×D4—28no—
432C3×D4—28no—
433C3×D4—28no—
434C3×D4—24no—
435C3×D4—28no—
436C3×D4—24no—
437C3×D4—22no—
438C3×D4—24no—
439C3×D4—24no—
440C3×D4—24no—
441C3×D4—24no—
442C3×D4—22no—
443C3×D4—24no—
444C3×D4—22no—
445C3×D4—24no—
446C3×D4—22no—
447C3×D4—21no—
448C3×D4—22no—
449C3×D4—21no—
450C3×D4—22no—
451C3×D4—24no—
452C3×D4—62no—
453C3×D4—62no—
454C3×D4—122no—
455C3×D4—244no—
456C3×D4C2×#6712yes—
457C3×D4C2×#6714yes—
458C3×D4C2×C3×D412yes—
459C3×D4C2×C3×D414yes—
460C2×C3×C4—22no—
461C2×C3×C4—216no—
462C2×C3×C4—28no—
463C2×C3×C4—28no—
464C2×C3×C4—28no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—62no—
481C2×C3×C4C2×#6712yes—
482C2×C3×C4C2×#6711yescharacteristic
483C2×C3×C4C2×#6712yes—
484C2×C3×C4C2×#6712yes—
485C2×C3×C4C2×C3×D412yes—
486C2×C3×C4C2×C3×D411yescharacteristic
487C2×C3×C4C2×C3×D412yes—
488C2×C3×C4C2×C3×D412yes—
489C2×C3×C4C23×D311yescharacteristic
490C2×C3×C4C24×C311yescharacteristic
491#67—84no—
492C2×Dic3—22no—
493D12—22no—
494D12—22no—
495D12—42no—
496C3×C8—62no—
497C3×C8—62no—
498C3⋊C8—22no—
499C3⋊C8—22no—
500C2×C32—22no—
501C2×C32—42no—
502C2×C32—44no—
503C2×C32—42no—
504C2×C32C2×#12011yescharacteristic
505C2×C32#57612yes—
506C3×D3—82no—
507C24—21no—
508C24—22no—
509C24—61no—
510#41—28no—
511#41—24no—
512#41—24no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41C3×#6714yescomplemented
517C2×Q8C3×#6711yescharacteristic
518C2×Q8C22×C3×D311yescharacteristic
519C2×D4—216no—
520C2×D4—28no—
521C2×D4—21no—
522C2×D4—22no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—21no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—32no—
529C2×D4—64no—
530C2×D4—62no—
531C2×D4—62no—
532C2×D4—61no—
533C2×D4C3×#6712yes—
534C2×D4C3×#6711yescharacteristic
535C2×D4C3×#6714yescomplemented
536C2×D4C22×C3×D312yes—
537C2×D4C22×C3×D311yescharacteristic
538C22×C4—21no—
539C22×C4—22no—
540C22×C4C22×C3×D312yes—
541C22×C4C22×C3×D311yescharacteristic
542SD16—64no—
543D8—68no—
544D8—64no—
545M16—62no—
546C2×C8—32no—
547C2×C8—32no—
548C2×C8—62no—
549C4⋊C4—32no—
550C22⋊C4—61no—
551C22⋊C4—64no—
552C42—61no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—24no—
556C22×C3—28no—
557C22×C3—24no—
558C22×C3—24no—
559C22×C3—24no—
560C22×C3—22no—
561C22×C3—24no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—24no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—21no—
568C22×C3—42no—
569C22×C3—44no—
570C22×C3—48no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—42no—
574C22×C3—44no—
575C22×C3—42no—
576C22×C3—84no—
577C22×C3—84no—
578C22×C3—88no—
579C22×C3—816no—
580C22×C3—88no—
581C22×C3—88no—
582C22×C3—124no—
583C22×C3—122no—
584C22×C3—244no—
585C22×C3#95312yes—
586C22×C3C3×#12012yes—
587C22×C3C22×#6711yescharacteristic
588C22×C3C22×C3×D411yescharacteristic
589C2×D3—44no—
590C2×D3—42no—
591C2×D3—84no—
592C3×C4—24no—
593C3×C4—24no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—122no—
602C3×C4#95312yes—
603C3×C4C3×#12012yes—
604C3×C4C22×#6711yescharacteristic
605C3×C4C22×#6711yescharacteristic
606C3×C4C22×C3×D411yescharacteristic
607C3×C4C22×C3×D411yescharacteristic
608Dic3—42no—
609C32#300811yescharacteristic, complemented, Sylow
610C23—28no—
611C23—21no—
612C23—22no—
613C23—24no—
614C23—62no—
615C23—82no—
616C23—84no—
617C23—122no—
618C23—242no—
619C23C2×C3×#6712yes—
620C23C2×C3×#6711yescharacteristic
621Q8—22no—
622Q8—21no—
623Q8C2×C3×#6712yes—
624D4—28no—
625D4—28no—
626D4—24no—
627D4—24no—
628D4—22no—
629D4—24no—
630D4—22no—
631D4—21no—
632D4—62no—
633D4—62no—
634D4—122no—
635D4—244no—
636D4C2×C3×#6712yes—
637D4C2×C3×#6714yes—
638C2×C4—28no—
639C2×C4—21no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—62no—
644C2×C4C2×C3×#6712yes—
645C2×C4C2×C3×#6711yescharacteristic
646C2×C4C2×C3×#6712yes—
647C2×C4C2×C3×#6712yes—
648C2×C4C23×C3×D311yescharacteristic
649C8—62no—
650C8—62no—
651C2×C3—22no—
652C2×C3—22no—
653C2×C3—22no—
654C2×C3—21no—
655C2×C3—42no—
656C2×C3—44no—
657C2×C3—48no—
658C2×C3—44no—
659C2×C3—42no—
660C2×C3—44no—
661C2×C3—42no—
662C2×C3—42no—
663C2×C3—44no—
664C2×C3—42no—
665C2×C3—242no—
666C2×C3#583512yes—
667C2×C3C2×#95311yescharacteristic
668C2×C3C2×C3×#12011yescharacteristic
669C2×C3C3×#57612yes—
670D3—82no—
671C22—22no—
672C22—24no—
673C22—22no—
674C22—24no—
675C22—22no—
676C22—44no—
677C22—42no—
678C22—84no—
679C22—88no—
680C22—124no—
681C22—122no—
682C22—244no—
683C22C3×#95312yes—
684C22C22×C3×#6711yescharacteristic
685C4—22no—
686C4—22no—
687C4—122no—
688C4C3×#95312yes—
689C4C22×C3×#6711yescharacteristic
690C4C22×C3×#6711yescharacteristic
691C3—21no—
692C3#8410111yescharacteristic, direct product factor
693C3C3×#300811yescharacteristic, complemented
694C2—22no—
695C2—42no—
696C2—44no—
697C2—42no—
698C2—242no—
699C2C3×#583512yes—
700C2C2×C3×#95311yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×H(5,𝔽2)C2
socleC22×C32C22×D4
hypercenterC2×C3×H(5,𝔽2)D3
hypocenterC3C3×#3008
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
1. C2×C32×H(5,𝔽2)C2semidirect
2. C3×#5830C2semidirect
3. C2×C3×#949C2semidirect
4. C22×C3×#213C2semidirect
5. C3×#5238C2semidirect
6. C3×#5234C2semidirect
7. C3×#5233C2semidirect
8. C3×#5217C2semidirect
9. C3×#5215C2semidirect
11. #84101C3direct (N × H)
17. C2×C32×#41C22semidirect
21. C22×C32×D4C22semidirect
22. C22×C3×D12C22semidirect
25. C2×C3×#215C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×#213C22semidirect
31. C3×#930C22semidirect
32. C3×#926C22semidirect
33. C2×C3×#208C22semidirect
34. C22×C3×C3⋊C8C22semidirect
35. C3×#835C22semidirect
36. C3×#832C22semidirect
37. C3×#832C22semidirect
38. C3×#830C22semidirect
40. C2×C3×H(5,𝔽2)D3semidirect
41. C2×C3×H(5,𝔽2)C2×C3semidirect
45. #5830C2×C3semidirect
46. C2×#949C2×C3semidirect
47. C22×#213C2×C3semidirect
53. #5238C2×C3semidirect
54. #5234C2×C3semidirect
55. #5233C2×C3semidirect
56. #5217C2×C3semidirect
57. #5215C2×C3semidirect
67. C32×#41D4semidirect
81. C2×C32×D4D4semidirect
119. C2×C3×#41C2×D3semidirect
122. C2×C3×#41C22×C3semidirect
133. C22×C3×D4C2×D3semidirect
135. C22×C3×D4C22×C3semidirect
136. C22×D12C22×C3semidirect
151. C2×#215C22×C3semidirect
155. C2×#213C22×C3semidirect
156. C2×#213C22×C3semidirect
157. #930C22×C3semidirect
158. #926C22×C3semidirect
159. C2×#208C22×C3semidirect
160. C22×C3⋊C8C22×C3semidirect
165. #835C22×C3semidirect
166. #832C22×C3semidirect
167. #832C22×C3semidirect
168. #830C22×C3semidirect
210. C2×H(5,𝔽2)C3×D3semidirect
246. C3×#41#67semidirect
247. C3×#41C3×D4semidirect
293. C2×C3×D4#67semidirect
296. C2×C3×D4C3×D4semidirect
365. C2×#41C2×C3×D3semidirect
370. C22×D4C2×C3×D3semidirect
516. #41C3×#67semidirect
535. C2×D4C3×#67semidirect
609. C32#3008semidirect
692. C3#84101direct (N × H)
693. C3C3×#3008semidirect

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×#58302
C2×C3×#9492
C22×C3×#2132
C3×#52382
C3×#52342
C3×#52332
C3×#52172
C3×#52152
C3×#30083
#841013