Finite Group Databasebeta

← C3×#10591164 #13158343

Subgroups — C3×#10591164 #13158343

Order 1728.

854 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64139C211yesmaximal, characteristic, complemented
2C32×#930C211yesmaximal, characteristic, complemented
3C22×C32×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×C3×#3714C211yesmaximal, characteristic, complemented
5C3×#63575C211yesmaximal, characteristic, complemented
6C3×#63564C211yesmaximal, characteristic, complemented
7C3×#63563C211yesmaximal, characteristic, complemented
8C3×#5115—31nomaximal
9C3×#5038—31nomaximal
10#10591164C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C2×C3×#638—21no—
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C32×#67—21no—
15C2×C32×D12C2211yescharacteristic
16C3×#3752—21no—
17C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C32×(C2×D3)⋊C4—21no—
19C32×C4⋊Dic3C2211yescharacteristic
20C2×C32×C3⋊C8—22no—
21C2×C32×C3⋊C8C2211yescharacteristic
22C2×C32×C3⋊C8C2211yescharacteristic
23C3×#3714—22no—
24C22×C32×C8—31no—
25C32×#121—31no—
26#64139C2×C311yescharacteristic, complemented
27C2×C3×#213—31no—
28C3×#930—21no—
29C3×#930—31no—
30C3×#930—31no—
31C3×#930—61no—
32C3×#930D311yescharacteristic, complemented
33C3×#930C2×C311yescharacteristic, complemented
34C22×C3×C3⋊C8—21no—
35C22×C3×C3⋊C8D311yescharacteristic, complemented
36C22×C3×C3⋊C8C2×C311yescharacteristic, complemented
37C2×C3×D24—31no—
38C2×#3714C2×C311yescharacteristic, complemented
39C3×#832—31no—
40C3×#821—31no—
41C3×#821—31no—
42C3×#818—31no—
43C3×#809—31no—
44C3×#807—31no—
45#63575C2×C311yescharacteristic, complemented
46#63564C2×C311yescharacteristic, complemented
47#63563C2×C311yescharacteristic, complemented
48C23×C33D411yescharacteristic
49C22×C3×C3⋊D3—21no—
50C22×C32×D3—21no—
51C2×C33×C4—21no—
52C2×C33×C4—21no—
53C2×C33×C4D411yescharacteristic
54C2×C33×C4C2311yescharacteristic
55C3×#638—42no—
56C2×C3×C3⋊Dic3—21no—
57C3×C4⋊(C3⋊D3)—21no—
58C3×C4⋊(C3⋊D3)—21no—
59C32×#67—42no—
60C2×C32×Dic3—21no—
61C32×D12—21no—
62C32×D12—21no—
63C32×C3⋊C8—21no—
64C32×C3⋊C8D412yescomplemented
65C3×#466—91no—
66#5115—31no—
67#5038—31no—
68C2×C32×D4—31no—
69C2×C32×D4—61no—
70C22×C32×C4—21no—
71C22×C32×C4—21no—
72C22×C32×C4—21no—
73C22×C32×C4—41no—
74C22×C32×C4C2×D311yescharacteristic
75C22×C32×C4C2×D311yescharacteristic
76C22×C32×C4C22×C311yescharacteristic
77C2×#638—21no—
78C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
79C2×C3×#67—22no—
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C2×C3×#67—62no—
83C2×C3×#67—61no—
84C2×C3×#67—61no—
85C2×C3×D12—21no—
86C2×C3×D12—31no—
87C2×C3×D12—31no—
88C2×C3×D12—61no—
89C2×C3×D12C2×D311yescharacteristic
90C2×C3×D12C22×C311yescharacteristic
91C2×C32×C8—31no—
92C2×C32×C8—31no—
93C2×C32×C8—62no—
94C32×C4⋊C4—31no—
95C32×C22⋊C4—61no—
96#3752—21no—
97C4⋊(C3⋊Dic3)C22×C311yescharacteristic
98C3×#213—62no—
99C3×(C2×D3)⋊C4—22no—
100C3×(C2×D3)⋊C4—21no—
101C3×(C2×D3)⋊C4—21no—
102C3×(C2×D3)⋊C4—62no—
103C3×(C2×D3)⋊C4—61no—
104C3×(C2×D3)⋊C4—61no—
105C3×C4⋊Dic3—21no—
106C3×C4⋊Dic3—31no—
107C3×C4⋊Dic3—31no—
108C3×C4⋊Dic3—61no—
109C3×C4⋊Dic3C2×D311yescharacteristic
110C3×C4⋊Dic3C22×C311yescharacteristic
111C2×C3×C3⋊C8—24no—
112C2×C3×C3⋊C8—21no—
113C2×C3×C3⋊C8—21no—
114C2×C3×C3⋊C8—22no—
115C2×C3×C3⋊C8—22no—
116C2×C3×C3⋊C8C2×D311yescharacteristic
117C2×C3×C3⋊C8C2×D311yescharacteristic
118C2×C3×C3⋊C8C22×C311yescharacteristic
119C2×C3×C3⋊C8C22×C311yescharacteristic
120C3×D24—62no—
121#3714—22no—
122C22×C33—21no—
123C22×C33—21no—
124C22×C33D812yescomplemented
125C22×C33C2×D411yescharacteristic
126C2×C3×C3⋊D3—41no—
127C2×C3×C3⋊D3—41no—
128C2×C3×C3⋊D3—41no—
129C2×C32×D3—41no—
130C2×C32×D3—41no—
131C2×C32×D3—41no—
132C33×C4—21no—
133C33×C4C2×D411yescharacteristic
134C33×C4#4111yescharacteristic
135C3×C3⋊Dic3—41no—
136C32×Dic3—41no—
137C2×C3×D8—91no—
138C22×C3×C8—31no—
139C22×C3×C8—31no—
140C22×C3×C8—61no—
141C3×#121—31no—
142C3×#121—31no—
143C3×#121—61no—
144C3×#121—91no—
145C2×#213—31no—
146#930—31no—
147#930—31no—
148#930—61no—
149#930C3×D311yescharacteristic, complemented
150C22×C3⋊C8C3×D311yescharacteristic, complemented
151C2×D24—31no—
152C3×#107—91no—
153C3×#102—91no—
154C3×#102—91no—
155#832—31no—
156#821—31no—
157#821—31no—
158#818—31no—
159#809—31no—
160#807—31no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—41no—
165C23×C32—61no—
166C23×C32D1211yescharacteristic
167C23×C32#6711yescharacteristic
168C23×C32C3×D411yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3×D3—22no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3—62no—
174C22×C3×D3—61no—
175C22×C3×D3—61no—
176C32×D4—61no—
177C32×D4—61no—
178C32×D4—122no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—41no—
194C2×C32×C4—41no—
195C2×C32×C4—41no—
196C2×C32×C4—41no—
197C2×C32×C4—41no—
198C2×C32×C4—41no—
199C2×C32×C4—42no—
200C2×C32×C4—42no—
201C2×C32×C4—61no—
202C2×C32×C4D1211yescharacteristic
203C2×C32×C4#6711yescharacteristic
204C2×C32×C4C3×D411yescharacteristic
205C2×C32×C4C22×D311yescharacteristic
206C2×C32×C4C22×D311yescharacteristic
207C2×C32×C4C23×C311yescharacteristic
208#638—42no—
209C2×C3⋊Dic3—21no—
210C4⋊(C3⋊D3)—21no—
211C4⋊(C3⋊D3)—21no—
212C3×#67—44no—
213C3×#67—42no—
214C3×#67—42no—
215C3×#67—124no—
216C3×#67—122no—
217C3×#67—122no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—62no—
222C2×C3×Dic3—61no—
223C2×C3×Dic3—61no—
224C3×D12—21no—
225C3×D12—21no—
226C3×D12—21no—
227C3×D12—21no—
228C3×D12—41no—
229C3×D12—41no—
230C3×D12—61no—
231C3×D12—61no—
232C3×D12—61no—
233C3×D12—61no—
234C3×D12—121no—
235C3×D12—121no—
236C32×C8—32no—
237C32×C8—61no—
238C3×C3⋊C8—22no—
239C3×C3⋊C8—21no—
240C3×C3⋊C8—21no—
241C3×C3⋊C8—22no—
242C3×C3⋊C8#6712yescomplemented
243C3×C3⋊C8C3×D412yescomplemented
244#466—91noSylow
245C2×C33—22no—
246C2×C33#12111yescharacteristic
247C2×C33C2×D811yescharacteristic
248C2×C33#13511yescharacteristic
249C3×C3⋊D3—81no—
250C32×D3—81no—
251C2×C3×D4—31no—
252C2×C3×D4—31no—
253C2×C3×D4—61no—
254C2×C3×D4—62no—
255C2×C3×D4—61no—
256C2×C3×D4—61no—
257C2×C3×D4—91no—
258C2×C3×D4—181no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—41no—
263C22×C3×C4D3211yescharacteristic
264C22×C3×C4C2×C3×D311yescharacteristic
265C22×C3×C4C2×C3×D311yescharacteristic
266C2×#67—21no—
267C2×#67—62no—
268C2×#67—61no—
269C2×#67—61no—
270C2×D12—31no—
271C2×D12—31no—
272C2×D12—61no—
273C2×D12C2×C3×D311yescharacteristic
274C3×D8—182no—
275C2×C3×C8—31no—
276C2×C3×C8—31no—
277C2×C3×C8—31no—
278C2×C3×C8—31no—
279C2×C3×C8—61no—
280C2×C3×C8—61no—
281C2×C3×C8—62no—
282C2×C3×C8—62no—
283C2×C3×C8—64no—
284C3×C4⋊C4—31no—
285C3×C4⋊C4—31no—
286C3×C4⋊C4—61no—
287C3×C4⋊C4—91no—
288C3×C22⋊C4—62no—
289C3×C22⋊C4—61no—
290C3×C22⋊C4—61no—
291C3×C22⋊C4—181no—
292#213—62no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297C4⋊Dic3—31no—
298C4⋊Dic3—31no—
299C4⋊Dic3—61no—
300C4⋊Dic3C2×C3×D311yescharacteristic
301C2×C3⋊C8—22no—
302C2×C3⋊C8C2×C3×D311yescharacteristic
303C2×C3⋊C8C2×C3×D311yescharacteristic
304D24—62no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—42no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32—42no—
326C22×C32—42no—
327C22×C32—121no—
328C22×C32—121no—
329C22×C32—121no—
330C22×C32D2412yescomplemented
331C22×C32#21312yescomplemented
332C22×C32C3×D812yescomplemented
333C22×C32C2×D1211yescharacteristic
334C22×C32C2×#6711yescharacteristic
335C22×C32C2×C3×D411yescharacteristic
336C2×C3⋊D3—41no—
337C2×C3⋊D3—41no—
338C2×C3⋊D3—41no—
339C2×C3×D3—42no—
340C2×C3×D3—42no—
341C2×C3×D3—42no—
342C2×C3×D3—41no—
343C2×C3×D3—41no—
344C2×C3×D3—41no—
345C2×C3×D3—41no—
346C2×C3×D3—41no—
347C2×C3×D3—41no—
348C2×C3×D3—122no—
349C2×C3×D3—122no—
350C2×C3×D3—122no—
351C2×C3×D3—121no—
352C2×C3×D3—121no—
353C2×C3×D3—121no—
354C2×C3×D3—121no—
355C2×C3×D3—121no—
356C2×C3×D3—121no—
357C32×C4—21no—
358C32×C4—22no—
359C32×C4—21no—
360C32×C4—21no—
361C32×C4—21no—
362C32×C4—21no—
363C32×C4—21no—
364C32×C4—21no—
365C32×C4—21no—
366C32×C4—21no—
367C32×C4—41no—
368C32×C4—41no—
369C32×C4—41no—
370C32×C4—41no—
371C32×C4—42no—
372C32×C4—121no—
373C32×C4#23511yescharacteristic
374C32×C4D3×D411yescharacteristic
375C32×C4#23711yescharacteristic
376C32×C4C2×#6711yescharacteristic
377C32×C4C2×C3×D411yescharacteristic
378C32×C4C3×#4111yescharacteristic
379C3⋊Dic3—41no—
380C3×Dic3—42no—
381C3×Dic3—41no—
382C3×Dic3—41no—
383C3×Dic3—122no—
384C3×Dic3—121no—
385C3×Dic3—121no—
386C2×D8—91no—
387C22×C8—31no—
388#121—31no—
389#121—91no—
390#107—91no—
391#102—91no—
392#102—91no—
393C33#46611yescharacteristic, complemented, Sylow
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—41no—
398C23×C3—62no—
399C23×C3—61no—
400C23×C3—61no—
401C23×C3—181no—
402C23×C3#62611yescharacteristic
403C23×C3C3×D1211yescharacteristic
404C23×C3C3×#6711yescharacteristic
405C22×D3—21no—
406C22×D3—62no—
407C22×D3—61no—
408C22×D3—61no—
409C3×D4—61no—
410C3×D4—61no—
411C3×D4—61no—
412C3×D4—61no—
413C3×D4—121no—
414C3×D4—121no—
415C3×D4—124no—
416C3×D4—122no—
417C3×D4—122no—
418C3×D4—181no—
419C3×D4—181no—
420C3×D4—362no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—62no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—181no—
447C2×C3×C4#62611yescharacteristic
448C2×C3×C4C3×D1211yescharacteristic
449C2×C3×C4C3×#6711yescharacteristic
450C2×C3×C4C2×D3211yescharacteristic
451C2×C3×C4C22×C3×D311yescharacteristic
452C2×C3×C4C22×C3×D311yescharacteristic
453#67—42no—
454#67—124no—
455#67—122no—
456#67—122no—
457C2×Dic3—21no—
458C2×Dic3—62no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461D12—21no—
462D12—21no—
463D12—61no—
464D12—61no—
465D12—61no—
466D12—61no—
467D12—121no—
468D12—121no—
469C3×C8—32no—
470C3×C8—32no—
471C3×C8—62no—
472C3×C8—62no—
473C3×C8—61no—
474C3×C8—61no—
475C3⋊C8—21no—
476C3⋊C8C3×#6712yescomplemented
477C2×C32—22no—
478C2×C32—24no—
479C2×C32—22no—
480C2×C32—22no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—41no—
491C2×C32—41no—
492C2×C32—41no—
493C2×C32—42no—
494C2×C32—42no—
495C2×C32—44no—
496C2×C32—241no—
497C2×C32C2×D2411yescharacteristic
498C2×C32#90411yescharacteristic
499C2×C32#93011yescharacteristic
500C2×C32C2×#21311yescharacteristic
501C2×C32#93911yescharacteristic
502C2×C32#95011yescharacteristic
503C2×C32C3×#12111yescharacteristic
504C2×C32C2×C3×D811yescharacteristic
505C2×C32C3×#13511yescharacteristic
506C3⋊D3—81no—
507C3×D3—82no—
508C3×D3—81no—
509C3×D3—81no—
510C3×D3—242no—
511C3×D3—241no—
512C3×D3—241no—
513C2×D4—31no—
514C2×D4—61no—
515C2×D4—91no—
516C2×D4—181no—
517C22×C4C3×D3211yescharacteristic
518D8—182no—
519C2×C8—31no—
520C2×C8—31no—
521C2×C8—62no—
522C4⋊C4—31no—
523C4⋊C4—91no—
524C22⋊C4—61no—
525C22⋊C4—181no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—41no—
547C22×C3—42no—
548C22×C3—122no—
549C22×C3—122no—
550C22×C3—122no—
551C22×C3—121no—
552C22×C3—121no—
553C22×C3—121no—
554C22×C3—121no—
555C22×C3—121no—
556C22×C3—121no—
557C22×C3—361no—
558C22×C3—361no—
559C22×C3—361no—
560C22×C3#371412yescomplemented
561C22×C3C3×D2412yescomplemented
562C22×C3C3×#21312yescomplemented
563C22×C3C2×#62611yescharacteristic
564C22×C3C2×C3×D1211yescharacteristic
565C22×C3C2×C3×#6711yescharacteristic
566C2×D3—41no—
567C2×D3—41no—
568C2×D3—41no—
569C2×D3—122no—
570C2×D3—122no—
571C2×D3—122no—
572C2×D3—121no—
573C2×D3—121no—
574C2×D3—121no—
575C2×D3—121no—
576C2×D3—121no—
577C2×D3—121no—
578C3×C4—22no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—42no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—122no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4—361no—
597C3×C4#380411yescharacteristic
598C3×C4D3×#6711yescharacteristic
599C3×C4C3×#23511yescharacteristic
600C3×C4C3×D3×D411yescharacteristic
601C3×C4C3×#23711yescharacteristic
602C3×C4C2×C3×#6711yescharacteristic
603Dic3—41no—
604Dic3—122no—
605Dic3—121no—
606Dic3—121no—
607C32—21no—
608C32—21no—
609C32—21no—
610C32—41no—
611C32#503811yescharacteristic, complemented
612C32#511511yescharacteristic, complemented
613C32C3×#46611yescharacteristic, complemented
614C23—61no—
615C23—181no—
616C23C3×#62611yescharacteristic
617D4—61no—
618D4—61no—
619D4—122no—
620D4—181no—
621D4—181no—
622D4—362no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—61no—
626C2×C4—181no—
627C2×C4C3×#62611yescharacteristic
628C2×C4C2×C3×D3211yescharacteristic
629C8—32no—
630C8—61no—
631C2×C3—24no—
632C2×C3—22no—
633C2×C3—22no—
634C2×C3—22no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—42no—
645C2×C3—42no—
646C2×C3—44no—
647C2×C3—41no—
648C2×C3—41no—
649C2×C3—41no—
650C2×C3—242no—
651C2×C3—241no—
652C2×C3—241no—
653C2×C3—721no—
654C2×C3C2×#371411yescharacteristic
655C2×C3#6382911yescharacteristic
656C2×C3#6397811yescharacteristic
657C2×C3C2×C3×D2411yescharacteristic
658C2×C3C3×#90411yescharacteristic
659C2×C3C3×#93011yescharacteristic
660C2×C3C2×C3×#21311yescharacteristic
661C2×C3C3×#93911yescharacteristic
662C2×C3C3×#95011yescharacteristic
663D3—81no—
664D3—242no—
665D3—241no—
666D3—241no—
667C22—21no—
668C22—21no—
669C22—121no—
670C22—121no—
671C22—121no—
672C22—361no—
673C22—361no—
674C22—361no—
675C22C3×#371412yescomplemented
676C22C2×C3×#62611yescharacteristic
677C4—21no—
678C4—121no—
679C4—361no—
680C4C3×#380411yescharacteristic
681C4C3×D3×#6711yescharacteristic
682C3—21no—
683C3—21no—
684C3—21no—
685C3—41no—
686C3#1059116411yescharacteristic, direct product factor
687C3C3×#503811yescharacteristic, complemented
688C3C3×#511511yescharacteristic, complemented
689C2—22no—
690C2—241no—
691C2—721no—
692C2C2×C3×#371411yescharacteristic
693C2C3×#6382911yescharacteristic
694C2C3×#6397811yescharacteristic
subgroupG/H
centerC22×C3C2×#626
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC22×C33C2×D4
hypercenterC22×C3×C4D32
hypocenterC32C3×#466
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#64139C2semidirect
2. C32×#930C2semidirect
3. C22×C32×C3⋊C8C2semidirect
4. C2×C3×#3714C2semidirect
5. C3×#63575C2semidirect
6. C3×#63564C2semidirect
7. C3×#63563C2semidirect
10. #10591164C3direct (N × H)
26. #64139C2×C3semidirect
32. C3×#930D3semidirect
33. C3×#930C2×C3semidirect
35. C22×C3×C3⋊C8D3semidirect
36. C22×C3×C3⋊C8C2×C3semidirect
38. C2×#3714C2×C3semidirect
45. #63575C2×C3semidirect
46. #63564C2×C3semidirect
47. #63563C2×C3semidirect
64. C32×C3⋊C8D4semidirect
124. C22×C33D8semidirect
149. #930C3×D3semidirect
150. C22×C3⋊C8C3×D3semidirect
242. C3×C3⋊C8#67semidirect
243. C3×C3⋊C8C3×D4semidirect
330. C22×C32D24semidirect
331. C22×C32#213semidirect
332. C22×C32C3×D8semidirect
393. C33#466semidirect
476. C3⋊C8C3×#67semidirect
560. C22×C3#3714semidirect
561. C22×C3C3×D24semidirect
562. C22×C3C3×#213semidirect
611. C32#5038semidirect
612. C32#5115semidirect
613. C32C3×#466semidirect
675. C22C3×#3714semidirect
686. C3#10591164direct (N × H)
687. C3C3×#5038semidirect
688. C3C3×#5115semidirect

Maximal subgroups

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

subgroupindex
C3×#641392
C32×#9302
C22×C32×C3⋊C82
C2×C3×#37142
C3×#635752
C3×#635642
C3×#635632
C3×#51153
C3×#50383
#105911643