Finite Group Databasebeta

← C3×#79199 #11860262

Subgroups — C3×#79199 #11860262

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2C3×#5522C211yesmaximal, characteristic, complemented
3C2×C3×#893C211yesmaximal, characteristic, complemented
4C32×#428C211yesmaximal, characteristic, complemented
5C3×Dic3×M16C211yesmaximal, characteristic, complemented
6C3×#5001C211yesmaximal, characteristic, complemented
7C3×#4966C211yesmaximal, characteristic, complemented
8C3×#4889C212yesmaximal, complemented
9C3×#4872C212yesmaximal, complemented
10C3×#4869C212yesmaximal, complemented
11C3×#4852C212yesmaximal, complemented
12C3×C4×AGL(1,ℤ/8)—31nomaximal
13#79199C311yesmaximal, characteristic, direct product factor
14C2×C3×#235C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3—21no—
17C2×C32×M16C2211yescharacteristic
18C32×#117C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C3×#908C418yescomplemented
24C2×C3×D24C2212yes—
25C2×C3×#204C2212yes—
26C3×#893—21no—
27C3×#893—21no—
28C3×#893C2212yes—
29C3×#893C2212yes—
30C3×#893C2211yescharacteristic, complemented
31C3×#893C2211yescharacteristic, complemented
32C3×#887C2211yescharacteristic, complemented
33C3×#887C2211yescharacteristic, complemented
34C3×#67⋊C4—21no—
35C3×#67⋊C4—21no—
36C3×#872—21no—
37C3×C42×D3—21no—
38C32×#107C2212yescomplemented
39C32×#106C2212yescomplemented
40C3×#815C2212yescomplemented
41C3×C8×Dic3C2212yescomplemented
42C3×#810C2212yescomplemented
43C3×#809C2212yes—
44C3×#809C2212yes—
45C3×#809C2212yescomplemented
46C2×C3×AGL(1,ℤ/8)—31no—
47C3×C4×#41—31no—
48C2×C3×C4×D4—31no—
49C2×#908C2×C311yescharacteristic
50#5522C2×C311yescharacteristic, complemented
51C2×#893C2×C311yescharacteristic, complemented
52C3×#442—32no—
53C3×#440—32no—
54C3×C4×SD16—32no—
55C3×C4×D8—32no—
56C3×#428—21no—
57C3×#428D311yescharacteristic, complemented
58C3×#428C2×C311yescharacteristic, complemented
59C3×#418—31no—
60C3×#417—31no—
61C3×C4×M16—31no—
62Dic3×M16C2×C311yescharacteristic, complemented
63#5001C2×C311yescharacteristic, complemented
64#4966C2×C311yescharacteristic, complemented
65#4889C2×C312yescomplemented
66#4872C2×C312yescomplemented
67#4869C2×C312yescomplemented
68#4852C2×C312yescomplemented
69C23×C3×D3—21no—
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C2×C3×#67—21no—
73C22×C3×Dic3D411yescharacteristic
74C22×C3×Dic3D411yescharacteristic
75C3×#235—22no—
76C3×#235C2×C414yescomplemented
77C2×C3×D12—21no—
78C2×C3×D12—22no—
79C2×C3×D12C2×C414yescomplemented
80C2×C3×D12C2312yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—44no—
88C2×C3×Dic6C2311yescharacteristic
89C32×M16C2×C414yescomplemented
90C2×C32×C8C2312yes—
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2312yes—
95C32×C22⋊C4—21no—
96C32×C42—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×(C2×D3)⋊C4—21no—
99C3×(C2×D3)⋊C4—22no—
100C3×(C2×D3)⋊C4—22no—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3—21no—
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3D411yescharacteristic
107C3×C4×Dic3C2311yescharacteristic
108C3×C4×Dic3C2311yescharacteristic
109C3×#208—22no—
110C2×C3×C3⋊C8C2312yes—
111C3×D24C2×C418yescomplemented
112C3×#204C2×C418yescomplemented
113C4×AGL(1,ℤ/8)—31noSylow
114C2×C3×#41—31no—
115C22×C3×D4—31no—
116C23×C3×C4—61no—
117C2×#235C22×C311yescharacteristic
118C22×D12C22×C311yescharacteristic
119C22×C4×D3—21no—
120C3×AGL(1,ℤ/8)—38no—
121C2×C3×SD16—32no—
122C2×C3×D8—32no—
123C2×C3×M16—21no—
124C2×C3×M16—31no—
125C2×C3×M16C2×D311yescharacteristic
126C2×C3×M16C22×C311yescharacteristic
127C3×C4×Q8—31no—
128C3×C4×Q8—31no—
129C3×C4×D4—32no—
130C3×C4×D4—32no—
131C3×C4×D4—31no—
132C3×C4×D4—31no—
133C3×C4×D4—61no—
134C3×C4×D4—61no—
135C3×C4×D4—61no—
136C3×C4×D4—61no—
137C3×#117—21no—
138C3×#117—61no—
139C3×#117C2×D311yescharacteristic
140C3×#117C22×C311yescharacteristic
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4C2×D311yescharacteristic
143C2×C3×C4⋊C4C22×C311yescharacteristic
144C2×C3×C22⋊C4—61no—
145C2×C3×C42—31no—
146C2×C3×C42—61no—
147C2×(C2×D3)⋊C4—21no—
148C2×C4×Dic3C22×C311yescharacteristic
149C2×#208C22×C311yescharacteristic
150#908C3×C418yescomplemented
151C2×D24C22×C312yes—
152C2×#204C22×C312yes—
153#893—21no—
154#893—21no—
155#893C22×C312yes—
156#893C22×C312yes—
157#893C22×C311yescharacteristic, complemented
158#893C22×C311yescharacteristic, complemented
159#887C22×C311yescharacteristic, complemented
160#887C22×C311yescharacteristic, complemented
161#67⋊C4—21no—
162#67⋊C4—21no—
163#872—21no—
164C42×D3—21no—
165C3×#107—22no—
166C3×#107C2×D312yescomplemented
167C3×#107C22×C312yescomplemented
168C3×#106—22no—
169C3×#106C2×D312yescomplemented
170C3×#106C22×C312yescomplemented
171C3×#103—32no—
172C3×#102—32no—
173C3×#102—32no—
174C3×#102—32no—
175C3×#97—32no—
176C3×C4×C8—32no—
177#815C22×C312yescomplemented
178C8×Dic3C22×C312yescomplemented
179#810C22×C312yescomplemented
180#809C22×C312yes—
181#809C22×C312yes—
182#809C22×C312yescomplemented
183C23×C32C2×D411yescharacteristic
184C22×C3×D3—24no—
185C22×C3×D3—22no—
186C22×C3×D3—21no—
187C22×C3×D3—42no—
188C22×C3×D3—42no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—22no—
192C2×C32×C4—42no—
193C2×C32×C4C22×C412yes—
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4#4112yes—
196C2×C32×C4C2411yescharacteristic
197C3×#67—24no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—41no—
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—24no—
206C3×D12—22no—
207C3×D12—21no—
208C3×D12C22×C414yes—
209C3×D12C22×C412yescomplemented
210C3×C4×D3—24no—
211C3×C4×D3—42no—
212C3×C4×D3—44no—
213C3×C4×D3—42no—
214C3×C4×D3—44no—
215C3×Dic6—21no—
216C3×Dic6C22×C412yescomplemented
217C32×C8C22×C414yescomplemented
218C3×C3⋊C8—22no—
219C2×AGL(1,ℤ/8)—31no—
220C4×#41—31no—
221C2×C4×D4—31no—
222#442—32no—
223#440—32no—
224C4×SD16—32no—
225C4×D8—32no—
226#428C3×D311yescharacteristic, complemented
227#418—31no—
228#417—31no—
229C4×M16—31no—
230C24×C3—61no—
231C23×D3—21no—
232C3×#41—34no—
233C3×#41—62no—
234C2×C3×Q8—31no—
235C2×C3×D4—34no—
236C2×C3×D4—31no—
237C2×C3×D4—32no—
238C2×C3×D4—61no—
239C2×C3×D4—61no—
240C2×C3×D4—62no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—41no—
247C22×C3×C4—61no—
248C22×C3×C4—61no—
249C22×C3×C4—62no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252C22×C3×C4—124no—
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C23×C311yescharacteristic
255C2×#67—21no—
256C22×Dic3C3×D411yescharacteristic
257C22×Dic3C3×D411yescharacteristic
258#235—22no—
259#235C2×C3×C414yescomplemented
260C2×D12—21no—
261C2×D12—22no—
262C2×D12C2×C3×C414yescomplemented
263C2×D12C23×C312yes—
264C2×D12C23×C311yescharacteristic
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—22no—
269C2×C4×D3—22no—
270C2×C4×D3—44no—
271C2×Dic6C23×C311yescharacteristic
272C3×SD16—38no—
273C3×D8—38no—
274C3×M16—24no—
275C3×M16—62no—
276C3×M16C4×D314yescomplemented
277C3×M16C2×C3×C414yescomplemented
278C2×C3×C8—22no—
279C2×C3×C8—32no—
280C2×C3×C8C22×D312yes—
281C2×C3×C8C23×C312yes—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—41no—
288C3×C4⋊C4—61no—
289C3×C4⋊C4—61no—
290C3×C4⋊C4C22×D311yescharacteristic
291C3×C4⋊C4C22×D311yescharacteristic
292C3×C4⋊C4C22×D312yes—
293C3×C4⋊C4C23×C311yescharacteristic
294C3×C4⋊C4C23×C311yescharacteristic
295C3×C4⋊C4C23×C312yes—
296C3×C22⋊C4—21no—
297C3×C22⋊C4—21no—
298C3×C22⋊C4—41no—
299C3×C22⋊C4—62no—
300C3×C22⋊C4—62no—
301C3×C22⋊C4—61no—
302C3×C22⋊C4—61no—
303C3×C42—21no—
304C3×C42—21no—
305C3×C42—31no—
306C3×C42—31no—
307C3×C42—31no—
308C3×C42—31no—
309C3×C42—41no—
310C3×C42—61no—
311C3×C42—61no—
312(C2×D3)⋊C4—21no—
313(C2×D3)⋊C4—21no—
314(C2×D3)⋊C4—22no—
315(C2×D3)⋊C4—22no—
316Dic3⋊C4—21no—
317Dic3⋊C4—21no—
318C4×Dic3—21no—
319C4×Dic3—21no—
320C4×Dic3C3×D411yescharacteristic
321C4×Dic3C3×D411yescharacteristic
322C4×Dic3C23×C311yescharacteristic
323C4×Dic3C23×C311yescharacteristic
324#208—22no—
325C2×C3⋊C8C23×C312yes—
326D24C2×C3×C418yescomplemented
327#204C2×C3×C418yescomplemented
328C22×C32—21no—
329C22×C32—21no—
330C22×C32C4×D412yes—
331C22×C32C22×D411yescharacteristic
332C2×C3×D3—22no—
333C2×C3×D3—24no—
334C2×C3×D3—48no—
335C2×C3×D3—42no—
336C2×C3×D3—41no—
337C2×C3×D3—41no—
338C2×C3×D3—42no—
339C32×C4—42no—
340C32×C4—41no—
341C32×C4—41no—
342C32×C4C4×D412yes—
343C32×C4C23×C411yescharacteristic
344C32×C4C2×#4111yescharacteristic
345C3×Dic3—22no—
346C3×Dic3—21no—
347C3×Dic3—21no—
348C3×Dic3—21no—
349C3×Dic3AGL(1,ℤ/8)12yescomplemented
350C2×#41—31no—
351C22×D4—31no—
352C23×C4—61no—
353AGL(1,ℤ/8)—38no—
354C2×SD16—32no—
355C2×D8—32no—
356C2×M16—31no—
357C2×M16C2×C3×D311yescharacteristic
358C4×Q8—31no—
359C4×Q8—31no—
360C4×D4—32no—
361C4×D4—32no—
362C4×D4—31no—
363C4×D4—31no—
364C4×D4—61no—
365C4×D4—61no—
366C4×D4—61no—
367C4×D4—61no—
368#117—61no—
369#117C2×C3×D311yescharacteristic
370C2×C4⋊C4C2×C3×D311yescharacteristic
371C2×C22⋊C4—61no—
372C2×C42—31no—
373C2×C42—61no—
374#107C2×C3×D312yescomplemented
375#106C2×C3×D312yescomplemented
376#103—32no—
377#102—32no—
378#102—32no—
379#102—32no—
380#97—32no—
381C4×C8—32no—
382C23×C3—21no—
383C23×C3—64no—
384C23×C3—61no—
385C23×C3—62no—
386C23×C3—122no—
387C23×C3—122no—
388C23×C3D3×D411yescharacteristic
389C23×C3C2×C3×D411yescharacteristic
390C22×D3—24no—
391C22×D3—21no—
392C22×D3—22no—
393C22×D3—42no—
394C22×D3—42no—
395C3×Q8—32no—
396C3×Q8—61no—
397C3×D4—34no—
398C3×D4—32no—
399C3×D4—64no—
400C3×D4—64no—
401C3×D4—62no—
402C3×D4—61no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—31no—
414C2×C3×C4—31no—
415C2×C3×C4—31no—
416C2×C3×C4—31no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—62no—
423C2×C3×C4—61no—
424C2×C3×C4—64no—
425C2×C3×C4—82no—
426C2×C3×C4—122no—
427C2×C3×C4—124no—
428C2×C3×C4—122no—
429C2×C3×C4—124no—
430C2×C3×C4—121no—
431C2×C3×C4C2×C4×D312yes—
432C2×C3×C4D3×D411yescharacteristic
433C2×C3×C4#23912yes—
434C2×C3×C4C22×C3×C412yes—
435C2×C3×C4C2×C3×D411yescharacteristic
436C2×C3×C4C3×#4112yes—
437C2×C3×C4C23×D311yescharacteristic
438C2×C3×C4C24×C311yescharacteristic
439#67—24no—
440C2×Dic3—21no—
441C2×Dic3—22no—
442C2×Dic3—41no—
443C2×Dic3C2×C3×D411yescharacteristic
444C2×Dic3C2×C3×D411yescharacteristic
445C2×Dic3C2×C3×D411yescharacteristic
446C2×Dic3C2×C3×D411yescharacteristic
447D12—24no—
448D12—22no—
449D12—21no—
450D12C22×C3×C414yes—
451D12C22×C3×C412yescomplemented
452C4×D3—24no—
453C4×D3—42no—
454C4×D3—44no—
455C4×D3—42no—
456C4×D3—44no—
457Dic6—21no—
458Dic6C22×C3×C412yescomplemented
459C3×C8—24no—
460C3×C8—62no—
461C3×C8C2×C4×D314yescomplemented
462C3×C8C22×C3×C414yescomplemented
463C3⋊C8—22no—
464C2×C32—22no—
465C2×C32C2×C4×D411yescharacteristic
466C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
467C2×C32#57511yescharacteristic
468C3×D3—42no—
469C3×D3—44no—
470C24—61no—
471#41—34no—
472#41—62no—
473C2×Q8—31no—
474C2×D4—31no—
475C2×D4—32no—
476C2×D4—34no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—62no—
480C22×C4—21no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—62no—
486C22×C4—62no—
487C22×C4—61no—
488C22×C4—124no—
489C22×C4C22×C3×D311yescharacteristic
490SD16—38no—
491D8—38no—
492M16—62no—
493M16C3×C4×D314yescomplemented
494C2×C8—32no—
495C2×C8C22×C3×D312yes—
496C4⋊C4—21no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4C22×C3×D311yescharacteristic
500C4⋊C4C22×C3×D311yescharacteristic
501C4⋊C4C22×C3×D312yes—
502C22⋊C4—21no—
503C22⋊C4—62no—
504C22⋊C4—62no—
505C22⋊C4—61no—
506C22⋊C4—61no—
507C42—21no—
508C42—31no—
509C42—31no—
510C42—31no—
511C42—31no—
512C42—61no—
513C42—61no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—22no—
519C22×C3—21no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—62no—
523C22×C3—64no—
524C22×C3—128no—
525C22×C3—122no—
526C22×C3—121no—
527C22×C3—121no—
528C22×C3—122no—
529C22×C3#89312yes—
530C22×C3C3×C4×D412yes—
531C22×C3C2×D3×D411yescharacteristic
532C22×C3C22×C3×D411yescharacteristic
533C2×D3—22no—
534C2×D3—24no—
535C2×D3—48no—
536C2×D3—42no—
537C2×D3—41no—
538C2×D3—41no—
539C2×D3—42no—
540C3×C4—22no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—32no—
544C3×C4—42no—
545C3×C4—41no—
546C3×C4—41no—
547C3×C4—42no—
548C3×C4—41no—
549C3×C4—41no—
550C3×C4—62no—
551C3×C4—61no—
552C3×C4—61no—
553C3×C4—61no—
554C3×C4—82no—
555C3×C4—81no—
556C3×C4—81no—
557C3×C4#89312yes—
558C3×C4C3×C4×D412yes—
559C3×C4C22×C4×D311yescharacteristic
560C3×C4C2×#23911yescharacteristic
561C3×C4C23×C3×C411yescharacteristic
562C3×C4C2×C3×#4111yescharacteristic
563Dic3—21no—
564Dic3—21no—
565Dic3—21no—
566Dic3—22no—
567Dic3C3×AGL(1,ℤ/8)12yescomplemented
568C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
569C23—64no—
570C23—61no—
571C23—62no—
572C23—122no—
573C23—122no—
574C23C3×D3×D411yescharacteristic
575Q8—32no—
576Q8—61no—
577D4—32no—
578D4—34no—
579D4—64no—
580D4—64no—
581D4—62no—
582D4—61no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—31no—
587C2×C4—31no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—42no—
591C2×C4—62no—
592C2×C4—61no—
593C2×C4—64no—
594C2×C4—124no—
595C2×C4—122no—
596C2×C4—124no—
597C2×C4—122no—
598C2×C4—121no—
599C2×C4C2×C3×C4×D312yes—
600C2×C4C3×D3×D411yescharacteristic
601C2×C4C3×#23912yes—
602C2×C4C23×C3×D311yescharacteristic
603C8—62no—
604C8C2×C3×C4×D314yescomplemented
605C2×C3—22no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—42no—
611C2×C3—124no—
612C2×C3—122no—
613C2×C3C2×#89311yescharacteristic
614C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
615C2×C3#577711yescharacteristic
616C2×C3C2×C3×C4×D411yescharacteristic
617C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
618C2×C3C3×#57511yescharacteristic
619D3—44no—
620D3—42no—
621C22—21no—
622C22—21no—
623C22—62no—
624C22—64no—
625C22—128no—
626C22—122no—
627C22—121no—
628C22—121no—
629C22—122no—
630C22C3×#89312yes—
631C22C2×C3×D3×D411yescharacteristic
632C4—32no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—62no—
637C4—61no—
638C4—61no—
639C4—61no—
640C4C3×#89312yes—
641C4C22×C3×C4×D311yescharacteristic
642C4C2×C3×#23911yescharacteristic
643C3—21no—
644C3#7919911yescharacteristic, direct product factor
645C3C3×C4×AGL(1,ℤ/8)11yescharacteristic, complemented
646C2—22no—
647C2—124no—
648C2—122no—
649C2C2×C3×#89311yescharacteristic
650C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
651C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC2×C3×#908C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#428D3
hypocenterC3C3×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#428

Complements

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

NH ≅ G/Ntype
2. C3×#5522C2semidirect
3. C2×C3×#893C2semidirect
4. C32×#428C2semidirect
5. C3×Dic3×M16C2semidirect
6. C3×#5001C2semidirect
7. C3×#4966C2semidirect
8. C3×#4889C2semidirect
9. C3×#4872C2semidirect
10. C3×#4869C2semidirect
11. C3×#4852C2semidirect
13. #79199C3direct (N × H)
23. C3×#908C4semidirect
30. C3×#893C22semidirect
31. C3×#893C22semidirect
32. C3×#887C22semidirect
33. C3×#887C22semidirect
38. C32×#107C22semidirect
39. C32×#106C22semidirect
40. C3×#815C22semidirect
41. C3×C8×Dic3C22semidirect
42. C3×#810C22semidirect
45. C3×#809C22semidirect
50. #5522C2×C3semidirect
51. C2×#893C2×C3semidirect
57. C3×#428D3semidirect
58. C3×#428C2×C3semidirect
62. Dic3×M16C2×C3semidirect
63. #5001C2×C3semidirect
64. #4966C2×C3semidirect
65. #4889C2×C3semidirect
66. #4872C2×C3semidirect
67. #4869C2×C3semidirect
68. #4852C2×C3semidirect
76. C3×#235C2×C4semidirect
79. C2×C3×D12C2×C4semidirect
89. C32×M16C2×C4semidirect
111. C3×D24C2×C4semidirect
112. C3×#204C2×C4semidirect
150. #908C3×C4semidirect
157. #893C22×C3semidirect
158. #893C22×C3semidirect
159. #887C22×C3semidirect
160. #887C22×C3semidirect
166. C3×#107C2×D3semidirect
167. C3×#107C22×C3semidirect
169. C3×#106C2×D3semidirect
170. C3×#106C22×C3semidirect
177. #815C22×C3semidirect
178. C8×Dic3C22×C3semidirect
179. #810C22×C3semidirect
182. #809C22×C3semidirect
209. C3×D12C22×C4semidirect
216. C3×Dic6C22×C4semidirect
217. C32×C8C22×C4semidirect
226. #428C3×D3semidirect
259. #235C2×C3×C4semidirect
262. C2×D12C2×C3×C4semidirect
276. C3×M16C4×D3semidirect
277. C3×M16C2×C3×C4semidirect
326. D24C2×C3×C4semidirect
327. #204C2×C3×C4semidirect
349. C3×Dic3AGL(1,ℤ/8)semidirect
374. #107C2×C3×D3semidirect
375. #106C2×C3×D3semidirect
451. D12C22×C3×C4semidirect
458. Dic6C22×C3×C4semidirect
461. C3×C8C2×C4×D3semidirect
462. C3×C8C22×C3×C4semidirect
493. M16C3×C4×D3semidirect
567. Dic3C3×AGL(1,ℤ/8)semidirect
568. C32C4×AGL(1,ℤ/8)semidirect
604. C8C2×C3×C4×D3semidirect
644. C3#79199direct (N × H)
645. C3C3×C4×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C3×#55222
C2×C3×#8932
C32×#4282
C3×Dic3×M162
C3×#50012
C3×#49662
C3×#48892
C3×#48722
C3×#48692
C3×#48522
C3×C4×AGL(1,ℤ/8)3
#791993