Finite Group Databasebeta

← C3×#10590330 #13157345

Subgroups — C3×#10590330 #13157345

Order 1728.

698 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×D12C211yesmaximal, characteristic
2C2×C3×#3711C211yesmaximal, characteristic, complemented
3C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#63630C211yesmaximal, characteristic, complemented
5C32×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5011—31nomaximal
9C3×#4836—31nomaximal
10#10590330C311yesmaximal, characteristic, direct product factor
11C2×C32×D12C411yescharacteristic
12C2×C32×C4×D3C2211yescharacteristic
13C2×C32×C4×D3C2211yescharacteristic
14C33×C42C2211yescharacteristic
15C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
17C32×(C2×D3)⋊C4C411yescharacteristic
18C32×(C2×D3)⋊C4C411yescharacteristic
19C32×C4⋊Dic3C411yescharacteristic
20C2×C32×C3⋊C8C2211yescharacteristic
21C2×C32×C3⋊C8C2211yescharacteristic
22C3×#3711—22no—
23C3×D3×C3⋊C8—22no—
24C32×C4×D4—31no—
25C2×C3×#208—31no—
26C22×C3×C3⋊C8—31no—
27C2×C3×ΓL(1,𝔽25)—31no—
28C2×C3×D3×C8—31no—
29C3×C4×D12—21no—
30C3×C4×D12D311yescharacteristic
31C3×C4×D12C2×C311yescharacteristic
32C2×#3711C2×C311yescharacteristic, complemented
33C2×D3×C3⋊C8C2×C311yescharacteristic, complemented
34C32×C4⋊C8—31no—
35#63630C2×C311yescharacteristic, complemented
36C3×#830—31no—
37C3×#830—31no—
38C3×(C2×D3)⋊C8—31no—
39C3×(C2×D3)⋊C8—31no—
40C3×C4⋊(C3⋊C8)—21no—
41C3×C4⋊(C3⋊C8)D311yescharacteristic, complemented
42C3×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
43C3×#803—31no—
44C3×#803—31no—
45C3×#803—61no—
46(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
47(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
48C22×C32×D3C2×C411yescharacteristic
49C22×C32×D3C2×C411yescharacteristic
50C2×C33×C4C2×C411yescharacteristic
51C2×C33×C4C2×C411yescharacteristic
52C2×C33×C4C2311yescharacteristic
53C2×C32×Dic3C2×C411yescharacteristic
54C2×C32×Dic3C2×C411yescharacteristic
55C32×D12—22no—
56C32×C4×D3—21no—
57C32×C4×D3—21no—
58C32×C4×D3—21no—
59C32×C4×D3—21no—
60C3×C3⋊(C3⋊C8)—21no—
61C3×C3⋊(C3⋊C8)D412yescomplemented
62C32×C3⋊C8—21no—
63C32×C3⋊C8—21no—
64C3×#435—91no—
65#5011—31no—
66#4836—31no—
67C2×C32×D4—31no—
68C22×C32×C4—31no—
69C22×C32×C4—31no—
70C2×C3×D12—21no—
71C2×C3×D12Dic311yescharacteristic
72C2×C3×D12C3×C411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3C2×D311yescharacteristic
76C2×C3×C4×D3C2×D311yescharacteristic
77C2×C3×C4×D3C22×C311yescharacteristic
78C2×C3×C4×D3C22×C311yescharacteristic
79C2×C32×C8—31no—
80C2×C32×C8—31no—
81C32×C4⋊C4—31no—
82C32×C22⋊C4—31no—
83C32×C22⋊C4—31no—
84C32×C42—21no—
85C32×C42—21no—
86C32×C42—21no—
87C32×C42—41no—
88C32×C42C2×D311yescharacteristic
89C32×C42C2×D311yescharacteristic
90C32×C42C22×C311yescharacteristic
91C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
92C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4Dic311yescharacteristic
96C3×(C2×D3)⋊C4Dic311yescharacteristic
97C3×(C2×D3)⋊C4C3×C411yescharacteristic
98C3×(C2×D3)⋊C4C3×C411yescharacteristic
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3Dic311yescharacteristic
101C3×C4⋊Dic3C3×C411yescharacteristic
102C3×#208—62no—
103C2×C3×C3⋊C8—21no—
104C2×C3×C3⋊C8—21no—
105C2×C3×C3⋊C8—31no—
106C2×C3×C3⋊C8—31no—
107C2×C3×C3⋊C8—31no—
108C2×C3×C3⋊C8—31no—
109C2×C3×C3⋊C8—62no—
110C2×C3×C3⋊C8—61no—
111C2×C3×C3⋊C8—61no—
112C2×C3×C3⋊C8C2×D311yescharacteristic
113C2×C3×C3⋊C8C2×D311yescharacteristic
114C2×C3×C3⋊C8C22×C311yescharacteristic
115C2×C3×C3⋊C8C22×C311yescharacteristic
116C3×ΓL(1,𝔽25)—62no—
117C3×D3×C8—62no—
118#3711—22no—
119D3×C3⋊C8—22no—
120C22×C33C22×C411yescharacteristic
121C2×C32×D3—21no—
122C2×C32×D3—21no—
123C2×C32×D3—21no—
124C2×C32×D3—21no—
125C2×C32×D3—21no—
126C2×C32×D3M1612yescomplemented
127C33×C4—21no—
128C33×C4—21no—
129C33×C4C2×D411yescharacteristic
130C33×C4#4111yescharacteristic
131C32×Dic3—21no—
132C32×Dic3—21no—
133C2×C3×M16—91no—
134C22×C3×C8—91no—
135C3×C4×D4—31no—
136C3×C4×D4—31no—
137C3×C4×D4—61no—
138C2×#208—31no—
139C22×C3⋊C8—31no—
140C2×ΓL(1,𝔽25)—31no—
141C2×D3×C8—31no—
142C4×D12C3×D311yescharacteristic
143C3×C4⋊C8—31no—
144C3×C4⋊C8—31no—
145C3×C4⋊C8—61no—
146C3×C22⋊C8—91no—
147C3×C22⋊C8—91no—
148C3×#97—91no—
149#830—31no—
150#830—31no—
151(C2×D3)⋊C8—31no—
152(C2×D3)⋊C8—31no—
153C4⋊(C3⋊C8)C3×D311yescharacteristic, complemented
154#803—31no—
155#803—31no—
156#803—61no—
157C23×C32—31no—
158C23×C32—31no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3C2×Dic311yescharacteristic
162C22×C3×D3C2×Dic311yescharacteristic
163C22×C3×D3C2×C3×C411yescharacteristic
164C22×C3×D3C2×C3×C411yescharacteristic
165C32×D4—62no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—31no—
176C2×C32×C4—31no—
177C2×C32×C4—41no—
178C2×C32×C4—41no—
179C2×C32×C4—41no—
180C2×C32×C4—61no—
181C2×C32×C4—61no—
182C2×C32×C4—61no—
183C2×C32×C4—61no—
184C2×C32×C4C4×D311yescharacteristic
185C2×C32×C4C4×D311yescharacteristic
186C2×C32×C4C2×Dic311yescharacteristic
187C2×C32×C4C2×Dic311yescharacteristic
188C2×C32×C4C2×C3×C411yescharacteristic
189C2×C32×C4C2×C3×C411yescharacteristic
190C2×C32×C4C22×D311yescharacteristic
191C2×C32×C4C22×D311yescharacteristic
192C2×C32×C4C23×C311yescharacteristic
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3C2×Dic311yescharacteristic
196C2×C3×Dic3C2×Dic311yescharacteristic
197C2×C3×Dic3C2×C3×C411yescharacteristic
198C2×C3×Dic3C2×C3×C411yescharacteristic
199C3×D12—24no—
200C3×D12—22no—
201C3×D12—22no—
202C3×C4×D3—21no—
203C3×C4×D3—21no—
204C3×C4×D3—21no—
205C3×C4×D3—21no—
206C3×C4×D3—21no—
207C3×C4×D3—21no—
208C3×C4×D3—21no—
209C3×C4×D3—21no—
210C3×C4×D3—41no—
211C3×C4×D3—41no—
212C3×C4×D3—41no—
213C3×C4×D3—41no—
214C32×C8—61no—
215C32×C8—61no—
216C3⋊(C3⋊C8)—21no—
217C3⋊(C3⋊C8)C3×D412yescomplemented
218C3×C3⋊C8—21no—
219C3×C3⋊C8—21no—
220C3×C3⋊C8—21no—
221C3×C3⋊C8—21no—
222C3×C3⋊C8—32no—
223C3×C3⋊C8—32no—
224C3×C3⋊C8—41no—
225C3×C3⋊C8—41no—
226C3×C3⋊C8—62no—
227C3×C3⋊C8—62no—
228C3×C3⋊C8—61no—
229C3×C3⋊C8—61no—
230#435—91noSylow
231C2×C33C4×D411yescharacteristic
232C2×C33C2×M1611yescharacteristic
233C2×C33#13111yescharacteristic
234C32×D3—22no—
235C32×D3—41no—
236C2×C3×D4—31no—
237C2×C3×D4—31no—
238C2×C3×D4—61no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C2×D12C3×Dic311yescharacteristic
246C2×C4×D3C2×C3×D311yescharacteristic
247C2×C4×D3C2×C3×D311yescharacteristic
248C3×M16—182no—
249C2×C3×C8—31no—
250C2×C3×C8—31no—
251C2×C3×C8—31no—
252C2×C3×C8—31no—
253C2×C3×C8—61no—
254C2×C3×C8—61no—
255C2×C3×C8—91no—
256C2×C3×C8—91no—
257C2×C3×C8—182no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—61no—
261C3×C22⋊C4—31no—
262C3×C22⋊C4—31no—
263C3×C22⋊C4—31no—
264C3×C22⋊C4—31no—
265C3×C22⋊C4—61no—
266C3×C22⋊C4—61no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42—41no—
271C3×C42D3211yescharacteristic
272C3×C42C2×C3×D311yescharacteristic
273C3×C42C2×C3×D311yescharacteristic
274(C2×D3)⋊C4C3×Dic311yescharacteristic
275(C2×D3)⋊C4C3×Dic311yescharacteristic
276C4⋊Dic3C3×Dic311yescharacteristic
277#208—62no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—31no—
282C2×C3⋊C8—61no—
283C2×C3⋊C8—61no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8C2×C3×D311yescharacteristic
286C2×C3⋊C8C2×C3×D311yescharacteristic
287ΓL(1,𝔽25)—62no—
288D3×C8—62no—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32—32no—
293C22×C32—41no—
294C22×C32—61no—
295C22×C32—61no—
296C22×C32—61no—
297C22×C32—61no—
298C22×C32—61no—
299C22×C32C2×C4×D311yescharacteristic
300C22×C32C22×Dic311yescharacteristic
301C22×C32C22×C3×C411yescharacteristic
302C2×C3×D3—21no—
303C2×C3×D3—21no—
304C2×C3×D3—21no—
305C2×C3×D3—21no—
306C2×C3×D3—22no—
307C2×C3×D3—21no—
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—22no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3—41no—
318C2×C3×D3#20812yescomplemented
319C2×C3×D3C3×M1612yescomplemented
320C32×C4—21no—
321C32×C4—21no—
322C32×C4—22no—
323C32×C4—22no—
324C32×C4—21no—
325C32×C4—21no—
326C32×C4—21no—
327C32×C4—21no—
328C32×C4—21no—
329C32×C4—21no—
330C32×C4—21no—
331C32×C4—21no—
332C32×C4—21no—
333C32×C4—21no—
334C32×C4—41no—
335C32×C4—41no—
336C32×C4—41no—
337C32×C4—41no—
338C32×C4—41no—
339C32×C4—41no—
340C32×C4—42no—
341C32×C4—42no—
342C32×C4—61no—
343C32×C4—61no—
344C32×C4D3×D411yescharacteristic
345C32×C4D3×D411yescharacteristic
346C32×C4#23711yescharacteristic
347C32×C4#23911yescharacteristic
348C32×C4C2×C3×D411yescharacteristic
349C32×C4C3×#4111yescharacteristic
350C3×Dic3—21no—
351C3×Dic3—21no—
352C3×Dic3—21no—
353C3×Dic3—21no—
354C3×Dic3—41no—
355C3×Dic3—41no—
356C2×M16—91no—
357C22×C8—91no—
358C4×D4—31no—
359C4⋊C8—31no—
360C22⋊C8—91no—
361C22⋊C8—91no—
362#97—91no—
363C33#43511yescharacteristic, complemented, Sylow
364C23×C3—31no—
365C23×C3—31no—
366C23×C3—31no—
367C23×C3—31no—
368C23×C3—61no—
369C23×C3—61no—
370C22×D3C2×C3×Dic311yescharacteristic
371C22×D3C2×C3×Dic311yescharacteristic
372C3×D4—62no—
373C3×D4—62no—
374C3×D4—64no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—31no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—121no—
402C2×C3×C4—121no—
403C2×C3×C4—121no—
404C2×C3×C4—121no—
405C2×C3×C4D3×Dic311yescharacteristic
406C2×C3×C4D3×Dic311yescharacteristic
407C2×C3×C4C3×C4×D311yescharacteristic
408C2×C3×C4C3×C4×D311yescharacteristic
409C2×C3×C4C2×C3×Dic311yescharacteristic
410C2×C3×C4C2×C3×Dic311yescharacteristic
411C2×C3×C4C2×D3211yescharacteristic
412C2×C3×C4C22×C3×D311yescharacteristic
413C2×C3×C4C22×C3×D311yescharacteristic
414C2×Dic3C2×C3×Dic311yescharacteristic
415C2×Dic3C2×C3×Dic311yescharacteristic
416D12—22no—
417C4×D3—21no—
418C4×D3—21no—
419C4×D3—21no—
420C4×D3—21no—
421C3×C8—61no—
422C3×C8—61no—
423C3×C8—61no—
424C3×C8—61no—
425C3×C8—92no—
426C3×C8—121no—
427C3×C8—121no—
428C3×C8—181no—
429C3⋊C8—21no—
430C3⋊C8—21no—
431C3⋊C8—32no—
432C3⋊C8—32no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C3⋊C8—61no—
436C3⋊C8—61no—
437C2×C32—21no—
438C2×C32—21no—
439C2×C32—21no—
440C2×C32—21no—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32—21no—
445C2×C32—21no—
446C2×C32—41no—
447C2×C32—41no—
448C2×C32—41no—
449C2×C32—62no—
450C2×C32—121no—
451C2×C32#89311yescharacteristic
452C2×C32#90111yescharacteristic
453C2×C32D3×M1611yescharacteristic
454C2×C32C2×#20811yescharacteristic
455C2×C32D4×Dic311yescharacteristic
456C2×C32#94811yescharacteristic
457C2×C32C3×C4×D411yescharacteristic
458C2×C32C2×C3×M1611yescharacteristic
459C2×C32C3×#13111yescharacteristic
460C3×D3—22no—
461C3×D3—22no—
462C3×D3—42no—
463C3×D3—42no—
464C3×D3—41no—
465C3×D3—41no—
466C2×D4—31no—
467C22×C4—31no—
468C22×C4—31no—
469M16—182no—
470C2×C8—31no—
471C2×C8—31no—
472C2×C8—91no—
473C2×C8—91no—
474C2×C8—182no—
475C4⋊C4—31no—
476C22⋊C4—31no—
477C22⋊C4—31no—
478C42C3×D3211yescharacteristic
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—32no—
483C22×C3—32no—
484C22×C3—41no—
485C22×C3—62no—
486C22×C3—62no—
487C22×C3—61no—
488C22×C3—61no—
489C22×C3—61no—
490C22×C3—61no—
491C22×C3—61no—
492C22×C3—61no—
493C22×C3—61no—
494C22×C3—61no—
495C22×C3—61no—
496C22×C3—61no—
497C22×C3—121no—
498C22×C3—121no—
499C22×C3—121no—
500C22×C3—121no—
501C22×C3C2×D3×Dic311yescharacteristic
502C22×C3C2×C3×C4×D311yescharacteristic
503C22×C3C22×C3×Dic311yescharacteristic
504C2×D3—21no—
505C2×D3—21no—
506C2×D3—21no—
507C2×D3—21no—
508C2×D3—21no—
509C2×D3C3×#20812yescomplemented
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—41no—
525C3×C4—41no—
526C3×C4—41no—
527C3×C4—41no—
528C3×C4—42no—
529C3×C4—42no—
530C3×C4—41no—
531C3×C4—41no—
532C3×C4—61no—
533C3×C4—61no—
534C3×C4—61no—
535C3×C4—61no—
536C3×C4—121no—
537C3×C4—121no—
538C3×C4#379611yescharacteristic
539C3×C4#380211yescharacteristic
540C3×C4C3×D3×D411yescharacteristic
541C3×C4C3×D3×D411yescharacteristic
542C3×C4C3×#23711yescharacteristic
543C3×C4C3×#23911yescharacteristic
544Dic3—21no—
545Dic3—21no—
546C32—21no—
547C32—21no—
548C32—21no—
549C32—41no—
550C32#483611yescharacteristic, complemented
551C32#501111yescharacteristic, complemented
552C32C3×#43511yescharacteristic, complemented
553C23—31no—
554C23—31no—
555D4—62no—
556C2×C4—31no—
557C2×C4—31no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4C3×D3×Dic311yescharacteristic
563C2×C4C3×D3×Dic311yescharacteristic
564C2×C4C2×C3×D3211yescharacteristic
565C8—61no—
566C8—61no—
567C8—92no—
568C8—181no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—41no—
579C2×C3—41no—
580C2×C3—41no—
581C2×C3—62no—
582C2×C3—62no—
583C2×C3—122no—
584C2×C3—122no—
585C2×C3—121no—
586C2×C3—121no—
587C2×C3D3×#20811yescharacteristic
588C2×C3#6381411yescharacteristic
589C2×C3#6389811yescharacteristic
590C2×C3C3×#89311yescharacteristic
591C2×C3C3×#90111yescharacteristic
592C2×C3C3×D3×M1611yescharacteristic
593C2×C3C2×C3×#20811yescharacteristic
594C2×C3C3×D4×Dic311yescharacteristic
595C2×C3C3×#94811yescharacteristic
596D3—22no—
597D3—41no—
598C22—32no—
599C22—61no—
600C22—61no—
601C22—61no—
602C22—61no—
603C22—61no—
604C22C2×C3×D3×Dic311yescharacteristic
605C4—21no—
606C4—21no—
607C4—61no—
608C4—61no—
609C4C3×#379611yescharacteristic
610C4C3×#380211yescharacteristic
611C3—21no—
612C3—21no—
613C3—21no—
614C3—41no—
615C3#1059033011yescharacteristic, direct product factor
616C3C3×#483611yescharacteristic, complemented
617C3C3×#501111yescharacteristic, complemented
618C2—62no—
619C2—121no—
620C2C3×D3×#20811yescharacteristic
621C2C3×#6381411yescharacteristic
622C2C3×#6389811yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC33×C42C22
socleC22×C33C22×C4
prime radicalC2×C32×D12C4
cosocleC2×C32×C4C23×C3
hypercenterC3×C42D32
hypocenterC32C3×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3711C2semidirect
3. C2×C3×D3×C3⋊C8C2semidirect
4. C3×#63630C2semidirect
5. C32×C4⋊(C3⋊C8)C2semidirect
6. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10590330C3direct (N × H)
32. C2×#3711C2×C3semidirect
33. C2×D3×C3⋊C8C2×C3semidirect
35. #63630C2×C3semidirect
41. C3×C4⋊(C3⋊C8)D3semidirect
42. C3×C4⋊(C3⋊C8)C2×C3semidirect
46. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
47. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
61. C3×C3⋊(C3⋊C8)D4semidirect
126. C2×C32×D3M16semidirect
153. C4⋊(C3⋊C8)C3×D3semidirect
217. C3⋊(C3⋊C8)C3×D4semidirect
318. C2×C3×D3#208semidirect
319. C2×C3×D3C3×M16semidirect
363. C33#435semidirect
509. C2×D3C3×#208semidirect
550. C32#4836semidirect
551. C32#5011semidirect
552. C32C3×#435semidirect
615. C3#10590330direct (N × H)
616. C3C3×#4836semidirect
617. C3C3×#5011semidirect

Maximal subgroups

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

subgroupindex
C32×C4×D122
C2×C3×#37112
C2×C3×D3×C3⋊C82
C3×#636302
C32×C4⋊(C3⋊C8)2
C3×(C2×D3)⋊(C3⋊C8)2
C3×#50113
C3×#48363
#105903303