Finite Group Databasebeta

← C3×#10591376 #13158381

Subgroups — C3×#10591376 #13158381

Order 1728.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×D12C211yesmaximal, characteristic
2C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63658C211yesmaximal, characteristic, complemented
7C32×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#5220—31nomaximal
9C3×#4665—31nomaximal
10#10591376C311yesmaximal, characteristic, direct product factor
11C23×C32×D3C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C32×D12—22no—
19C2×C32×D12—22no—
20C2×C32×D12C414yescomplemented
21C2×C3×D3×Dic3—22no—
22C2×C3×D3×Dic3—22no—
23C2×C3×D3×Dic3—22no—
24C3×(C2×D3)⋊Dic3—22no—
25C3×(C2×D3)⋊Dic3—22no—
26C3×(C2×D3)⋊Dic3—22no—
27C22×C32×D4—31no—
28C23×C3×Dic3—31no—
29C22×C3×D12—21no—
30C22×C3×D12D311yescharacteristic
31C22×C3×D12C2×C311yescharacteristic
32C22×C3×C4×D3—31no—
33C22×D3×Dic3C2×C311yescharacteristic, complemented
34C2×C3×#217—31no—
35C2×C3×#217—31no—
36C2×C3×#217—31no—
37C2×C3×(C2×D3)⋊C4—31no—
38C2×C3×(C2×D3)⋊C4—31no—
39C2×C3×(C2×D3)⋊C4—31no—
40C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
41C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
42C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
43C32×#95—31no—
44#63658C2×C311yescharacteristic, complemented
45C3×C3⋊#95—21no—
46C3×C3⋊#95—31no—
47C3×C3⋊#95—31no—
48C3×C3⋊#95—61no—
49C3×C3⋊#95D311yescharacteristic, complemented
50C3×C3⋊#95C2×C311yescharacteristic, complemented
51C23×C33C2311yescharacteristic
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3—21no—
55C22×C32×D3—21no—
56C22×C32×D3—21no—
57C22×C32×D3—21no—
58C22×C32×D3—21no—
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3C2×C412yes—
63C22×C32×D3C2×C412yescomplemented
64C22×C32×D3D412yes—
65C22×C32×D3D412yes—
66C2×C33×C4—21no—
67C2×C33×C4—21no—
68C2×C33×C4C2×C412yescomplemented
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3—21no—
71C2×C3×C3⋊Dic3—21no—
72C2×C3×C3⋊Dic3—21no—
73C2×C3×C3⋊Dic3—21no—
74C2×C3×C3⋊Dic3D412yescomplemented
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3—21no—
78C2×C32×Dic3—21no—
79C2×C32×Dic3—21no—
80C2×C32×Dic3D412yescomplemented
81C32×D12—28no—
82C3×D3×Dic3—28no—
83C3×#386—91no—
84#5220—31no—
85#4665—31no—
86C24×C32—31no—
87C24×C32—31no—
88C23×C3×D3—21no—
89C23×C3×D3—21no—
90C23×C3×D3C2×D311yescharacteristic
91C23×C3×D3C2×D311yescharacteristic
92C23×C3×D3C22×C311yescharacteristic
93C23×C3×D3C22×C311yescharacteristic
94C2×C32×D4—34no—
95C2×C32×D4—62no—
96C2×C32×D4—62no—
97C22×C32×C4—21no—
98C22×C32×C4—21no—
99C22×C32×C4—21no—
100C22×C32×C4—31no—
101C22×C32×C4—31no—
102C22×C32×C4—41no—
103C22×C32×C4C2×D311yescharacteristic
104C22×C32×C4C2×D311yescharacteristic
105C22×C32×C4C22×C311yescharacteristic
106C22×C3⋊Dic3C22×C311yescharacteristic
107C22×C3⋊Dic3C22×C311yescharacteristic
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—62no—
115C22×C3×Dic3—62no—
116C22×C3×Dic3—62no—
117C22×C3×Dic3—61no—
118C22×C3×Dic3—61no—
119C22×C3×Dic3C2×D311yescharacteristic
120C22×C3×Dic3C2×D311yescharacteristic
121C22×C3×Dic3C22×C311yescharacteristic
122C22×C3×Dic3C22×C311yescharacteristic
123C2×C3×D12—24no—
124C2×C3×D12—24no—
125C2×C3×D12—24no—
126C2×C3×D12—22no—
127C2×C3×D12—22no—
128C2×C3×D12—22no—
129C2×C3×D12—22no—
130C2×C3×D12Dic314yescomplemented
131C2×C3×D12C3×C414yescomplemented
132C2×C3×C4×D3—62no—
133C2×C3×C4×D3—62no—
134C2×C3×C4×D3—62no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C3×#217—62no—
139C3×#217—62no—
140C3×#217—62no—
141C3×(C2×D3)⋊C4—62no—
142C3×(C2×D3)⋊C4—62no—
143C3×(C2×D3)⋊C4—62no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147C22×C33C22×C411yescharacteristic
148C22×C33C2×D411yescharacteristic
149C22×C33C2×D411yescharacteristic
150C22×C33C2×D411yescharacteristic
151C22×C33C2×D411yescharacteristic
152C22×C33#4111yescharacteristic
153C22×C33#4111yescharacteristic
154C2×C32×D3—22no—
155C2×C32×D3—22no—
156C2×C32×D3—22no—
157C2×C32×D3—22no—
158C2×C32×D3—22no—
159C2×C32×D3—22no—
160C2×C32×D3—22no—
161C2×C32×D3—22no—
162C2×C32×D3—22no—
163C2×C32×D3—41no—
164C2×C32×D3—41no—
165C2×C32×D3—41no—
166C2×C32×D3—41no—
167C2×C32×D3C22⋊C414yescomplemented
168C33×C4—22no—
169C3×C3⋊Dic3—22no—
170C3×C3⋊Dic3—41no—
171C32×Dic3—22no—
172C32×Dic3—41no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—61no—
176C23×C3×C4—91no—
177C23×Dic3—31no—
178C22×D12C3×D311yescharacteristic
179C22×C4×D3—31no—
180C2×C3×C22⋊C4—91no—
181C2×C3×C22⋊C4—91no—
182C2×C3×C22⋊C4—91no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95—61no—
192C3×#95—91no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—61no—
196C3⋊#95C3×D311yescharacteristic, complemented
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—32no—
201C23×C32—32no—
202C23×C32—32no—
203C23×C32—32no—
204C23×C32—41no—
205C23×C32—61no—
206C23×C32—61no—
207C23×C32—61no—
208C23×C32—61no—
209C23×C32—61no—
210C23×C32—61no—
211C23×C32—61no—
212C23×C32—61no—
213C23×C32—61no—
214C23×C32—61no—
215C23×C32C22×D311yescharacteristic
216C23×C32C22×D311yescharacteristic
217C23×C32C23×C311yescharacteristic
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—22no—
227C22×C3×D3—22no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—22no—
241C22×C3×D3—22no—
242C22×C3×D3—22no—
243C22×C3×D3—22no—
244C22×C3×D3—41no—
245C22×C3×D3—41no—
246C22×C3×D3—41no—
247C22×C3×D3—41no—
248C22×C3×D3—41no—
249C22×C3×D3—41no—
250C22×C3×D3—41no—
251C22×C3×D3—41no—
252C22×C3×D3C2×Dic312yes—
253C22×C3×D3C2×Dic312yescomplemented
254C22×C3×D3#6712yes—
255C22×C3×D3#6712yes—
256C22×C3×D3C2×C3×C412yes—
257C22×C3×D3C2×C3×C412yescomplemented
258C22×C3×D3C3×D412yes—
259C22×C3×D3C3×D412yes—
260C32×D4—68no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—22no—
264C2×C32×C4—22no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—22no—
270C2×C32×C4—22no—
271C2×C32×C4—22no—
272C2×C32×C4—32no—
273C2×C32×C4—42no—
274C2×C32×C4—41no—
275C2×C32×C4—41no—
276C2×C32×C4—41no—
277C2×C32×C4—41no—
278C2×C32×C4—42no—
279C2×C32×C4—42no—
280C2×C32×C4—61no—
281C2×C32×C4—61no—
282C2×C32×C4—61no—
283C2×C32×C4—61no—
284C2×C32×C4—61no—
285C2×C32×C4C4×D312yescomplemented
286C2×C32×C4C2×Dic312yescomplemented
287C2×C32×C4C2×C3×C412yescomplemented
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3—21no—
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3C3×D412yescomplemented
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—41no—
309C2×C3×Dic3—41no—
310C2×C3×Dic3—41no—
311C2×C3×Dic3—41no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—68no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—62no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—121no—
326C2×C3×Dic3—121no—
327C2×C3×Dic3—121no—
328C2×C3×Dic3—121no—
329C2×C3×Dic3D1212yescomplemented
330C2×C3×Dic3C3×D412yescomplemented
331C3×D12—216no—
332C3×D12—28no—
333C3×D12—28no—
334C3×C4×D3—68no—
335D3×Dic3—28no—
336#386—91noSylow
337C2×C33C2×C22⋊C411yescharacteristic
338C2×C33C4×D411yescharacteristic
339C2×C33C4×D411yescharacteristic
340C2×C33#12011yescharacteristic
341C2×C33#12111yescharacteristic
342C2×C33#12111yescharacteristic
343C2×C33#12311yescharacteristic
344C32×D3—24no—
345C32×D3—42no—
346C24×C3—31no—
347C24×C3—31no—
348C24×C3—31no—
349C24×C3—31no—
350C24×C3—61no—
351C24×C3—61no—
352C23×D3C2×C3×D311yescharacteristic
353C23×D3C2×C3×D311yescharacteristic
354C2×C3×D4—34no—
355C2×C3×D4—34no—
356C2×C3×D4—64no—
357C2×C3×D4—62no—
358C2×C3×D4—62no—
359C2×C3×D4—62no—
360C2×C3×D4—62no—
361C2×C3×D4—64no—
362C2×C3×D4—64no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—41no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C22×C3×C4—91no—
374C22×C3×C4—91no—
375C22×C3×C4—182no—
376C22×C3×C4—182no—
377C22×C3×C4—182no—
378C22×C3×C4D3211yescharacteristic
379C22×C3×C4C2×C3×D311yescharacteristic
380C22×C3×C4C2×C3×D311yescharacteristic
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—62no—
390C22×Dic3C2×C3×D311yescharacteristic
391C22×Dic3C2×C3×D311yescharacteristic
392C2×D12—22no—
393C2×D12—22no—
394C2×D12C3×Dic314yescomplemented
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C3×C22⋊C4—182no—
399C3×C22⋊C4—182no—
400C3×C22⋊C4—182no—
401#217—62no—
402#217—62no—
403#217—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—34no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—62no—
437C22×C32—62no—
438C22×C32—62no—
439C22×C32—62no—
440C22×C32—62no—
441C22×C32—62no—
442C22×C32—62no—
443C22×C32—62no—
444C22×C32—62no—
445C22×C32—121no—
446C22×C32—121no—
447C22×C32—121no—
448C22×C32—121no—
449C22×C32C2×C4×D311yescharacteristic
450C22×C32C2×D1211yescharacteristic
451C22×C32#23511yescharacteristic
452C22×C32D3×D411yescharacteristic
453C22×C32D3×D411yescharacteristic
454C22×C32D3×D411yescharacteristic
455C22×C32D3×D411yescharacteristic
456C22×C32D3×D411yescharacteristic
457C22×C32#23711yescharacteristic
458C22×C32#23711yescharacteristic
459C22×C32#23911yescharacteristic
460C22×C32C22×Dic311yescharacteristic
461C22×C32C2×#6711yescharacteristic
462C22×C32C2×#6711yescharacteristic
463C22×C32C22×C3×C411yescharacteristic
464C22×C32C2×C3×D411yescharacteristic
465C22×C32C2×C3×D411yescharacteristic
466C22×C32C2×C3×D411yescharacteristic
467C22×C32C2×C3×D411yescharacteristic
468C22×C32C3×#4111yescharacteristic
469C22×C32C3×#4111yescharacteristic
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—24no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—24no—
490C2×C3×D3—42no—
491C2×C3×D3—42no—
492C2×C3×D3—42no—
493C2×C3×D3—42no—
494C2×C3×D3—42no—
495C2×C3×D3—42no—
496C2×C3×D3—42no—
497C2×C3×D3—42no—
498C2×C3×D3—42no—
499C2×C3×D3—42no—
500C2×C3×D3—42no—
501C2×C3×D3—42no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3#21714yescomplemented
511C2×C3×D3C3×C22⋊C414yescomplemented
512C32×C4—22no—
513C32×C4—24no—
514C32×C4—22no—
515C32×C4—22no—
516C32×C4—42no—
517C32×C4—42no—
518C32×C4—44no—
519C32×C4—62no—
520C32×C4—121no—
521C3⋊Dic3—22no—
522C3⋊Dic3—41no—
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—42no—
526C3×Dic3—42no—
527C3×Dic3—41no—
528C3×Dic3—41no—
529C3×Dic3—62no—
530C3×Dic3—62no—
531C3×Dic3—122no—
532C3×Dic3—122no—
533C3×Dic3—121no—
534C3×Dic3—121no—
535C22×D4—31no—
536C23×C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540#95—31no—
541#95—91no—
542C33#38611yescharacteristic, complemented, Sylow
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—32no—
550C23×C3—32no—
551C23×C3—32no—
552C23×C3—32no—
553C23×C3—32no—
554C23×C3—41no—
555C23×C3—62no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—62no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—121no—
582C23×C3—121no—
583C23×C3—121no—
584C23×C3—121no—
585C23×C3—121no—
586C23×C3—121no—
587C23×C3—121no—
588C23×C3—121no—
589C23×C3C2×D3211yescharacteristic
590C23×C3C22×C3×D311yescharacteristic
591C23×C3C22×C3×D311yescharacteristic
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3C2×C3×Dic312yes—
603C22×D3C2×C3×Dic312yescomplemented
604C22×D3C3×#6712yes—
605C22×D3C3×#6712yes—
606C3×D4—68no—
607C3×D4—68no—
608C3×D4—616no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—42no—
627C2×C3×C4—42no—
628C2×C3×C4—42no—
629C2×C3×C4—62no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—62no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—92no—
642C2×C3×C4—121no—
643C2×C3×C4—121no—
644C2×C3×C4—121no—
645C2×C3×C4—121no—
646C2×C3×C4—188no—
647C2×C3×C4—181no—
648C2×C3×C4—181no—
649C2×C3×C4—181no—
650C2×C3×C4—181no—
651C2×C3×C4—181no—
652C2×C3×C4D3×Dic312yescomplemented
653C2×C3×C4C3×C4×D312yescomplemented
654C2×C3×C4C2×C3×Dic312yescomplemented
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—62no—
663C2×Dic3—68no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—62no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—121no—
676C2×Dic3—121no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3C3×D1212yescomplemented
680D12—28no—
681C4×D3—68no—
682C2×C32—21no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—21no—
693C2×C32—21no—
694C2×C32—21no—
695C2×C32—21no—
696C2×C32—21no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—21no—
700C2×C32—21no—
701C2×C32—21no—
702C2×C32—21no—
703C2×C32—41no—
704C2×C32—41no—
705C2×C32—41no—
706C2×C32—41no—
707C2×C32—41no—
708C2×C32—41no—
709C2×C32—41no—
710C2×C32—64no—
711C2×C32—122no—
712C2×C32C4×D1211yescharacteristic
713C2×C32D3×C22⋊C411yescharacteristic
714C2×C32#88211yescharacteristic
715C2×C32#88411yescharacteristic
716C2×C32#89311yescharacteristic
717C2×C32#89411yescharacteristic
718C2×C32#89511yescharacteristic
719C2×C32D4×Dic311yescharacteristic
720C2×C32D4×Dic311yescharacteristic
721C2×C32#93511yescharacteristic
722C2×C32#93711yescharacteristic
723C2×C32#93911yescharacteristic
724C2×C32#93911yescharacteristic
725C2×C32C2×#21711yescharacteristic
726C2×C32C2×C3×C22⋊C411yescharacteristic
727C2×C32C3×C4×D411yescharacteristic
728C2×C32C3×C4×D411yescharacteristic
729C2×C32C3×#12011yescharacteristic
730C2×C32C3×#12111yescharacteristic
731C2×C32C3×#12111yescharacteristic
732C2×C32C3×#12311yescharacteristic
733C3×D3—24no—
734C3×D3—24no—
735C3×D3—44no—
736C3×D3—44no—
737C3×D3—42no—
738C3×D3—42no—
739C24—31no—
740C24—31no—
741C2×D4—34no—
742C2×D4—62no—
743C2×D4—62no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—91no—
747C22×C4—91no—
748C22×C4—182no—
749C22×C4—182no—
750C22×C4—182no—
751C22×C4C3×D3211yescharacteristic
752C22⋊C4—182no—
753C22⋊C4—182no—
754C22⋊C4—182no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—34no—
777C22×C3—34no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—64no—
786C22×C3—64no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—122no—
806C22×C3—122no—
807C22×C3—122no—
808C22×C3—122no—
809C22×C3—122no—
810C22×C3—122no—
811C22×C3—122no—
812C22×C3—122no—
813C22×C3—122no—
814C22×C3—122no—
815C22×C3—122no—
816C22×C3—122no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3#379511yescharacteristic
826C22×C3#379611yescharacteristic
827C22×C3D3×D1211yescharacteristic
828C22×C3#380211yescharacteristic
829C22×C3C2×D3×Dic311yescharacteristic
830C22×C3D3×#6711yescharacteristic
831C22×C3D3×#6711yescharacteristic
832C22×C3C2×C3×C4×D311yescharacteristic
833C22×C3C2×C3×D1211yescharacteristic
834C22×C3C3×#23511yescharacteristic
835C22×C3C3×D3×D411yescharacteristic
836C22×C3C3×D3×D411yescharacteristic
837C22×C3C3×D3×D411yescharacteristic
838C22×C3C3×D3×D411yescharacteristic
839C22×C3C3×D3×D411yescharacteristic
840C22×C3C3×#23711yescharacteristic
841C22×C3C3×#23711yescharacteristic
842C22×C3C3×#23911yescharacteristic
843C22×C3C22×C3×Dic311yescharacteristic
844C22×C3C2×C3×#6711yescharacteristic
845C22×C3C2×C3×#6711yescharacteristic
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3C3×#21714yescomplemented
860C3×C4—24no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—42no—
865C3×C4—42no—
866C3×C4—44no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—122no—
870C3×C4—122no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4—182no—
874C3×C4—361no—
875Dic3—22no—
876Dic3—41no—
877Dic3—62no—
878Dic3—62no—
879Dic3—122no—
880Dic3—122no—
881Dic3—121no—
882Dic3—121no—
883C32—21no—
884C32—21no—
885C32—21no—
886C32—41no—
887C32#466511yescharacteristic, complemented
888C32#522011yescharacteristic, complemented
889C32C3×#38611yescharacteristic, complemented
890C23—32no—
891C23—32no—
892C23—32no—
893C23—32no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—61no—
904C23C2×C3×D3211yescharacteristic
905D4—68no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—32no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—92no—
915C2×C4—188no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—181no—
919C2×C4—181no—
920C2×C4—181no—
921C2×C4C3×D3×Dic312yescomplemented
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—41no—
944C2×C3—41no—
945C2×C3—41no—
946C2×C3—41no—
947C2×C3—41no—
948C2×C3—41no—
949C2×C3—41no—
950C2×C3—64no—
951C2×C3—64no—
952C2×C3—124no—
953C2×C3—124no—
954C2×C3—122no—
955C2×C3—122no—
956C2×C3#6388411yescharacteristic
957C2×C3#6388511yescharacteristic
958C2×C3#6388611yescharacteristic
959C2×C3Dic3×D1211yescharacteristic
960C2×C3#6389811yescharacteristic
961C2×C3#6392211yescharacteristic
962C2×C3D3×#21711yescharacteristic
963C2×C3C3×C4×D1211yescharacteristic
964C2×C3C3×D3×C22⋊C411yescharacteristic
965C2×C3C3×#88211yescharacteristic
966C2×C3C3×#88411yescharacteristic
967C2×C3C3×#89311yescharacteristic
968C2×C3C3×#89411yescharacteristic
969C2×C3C3×#89511yescharacteristic
970C2×C3C3×D4×Dic311yescharacteristic
971C2×C3C3×D4×Dic311yescharacteristic
972C2×C3C3×#93511yescharacteristic
973C2×C3C3×#93711yescharacteristic
974C2×C3C3×#93911yescharacteristic
975C2×C3C3×#93911yescharacteristic
976C2×C3C2×C3×#21711yescharacteristic
977D3—24no—
978D3—42no—
979C22—34no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—62no—
988C22—62no—
989C22—121no—
990C22—121no—
991C22—121no—
992C22—121no—
993C22C3×#379511yescharacteristic
994C22C3×#379611yescharacteristic
995C22C3×D3×D1211yescharacteristic
996C22C3×#380211yescharacteristic
997C22C2×C3×D3×Dic311yescharacteristic
998C22C3×D3×#6711yescharacteristic
999C22C3×D3×#6711yescharacteristic
1000C4—22no—
1001C4—62no—
1002C4—121no—
1003C4—182no—
1004C4—361no—
1005C3—21no—
1006C3—21no—
1007C3—21no—
1008C3—41no—
1009C3#1059137611yescharacteristic, direct product factor
1010C3C3×#466511yescharacteristic, complemented
1011C3C3×#522011yescharacteristic, complemented
1012C2—64no—
1013C2—122no—
1014C2C3×#6388411yescharacteristic
1015C2C3×#6388511yescharacteristic
1016C2C3×#6388611yescharacteristic
1017C2C3×Dic3×D1211yescharacteristic
1018C2C3×#6389811yescharacteristic
1019C2C3×#6392211yescharacteristic
1020C2C3×D3×#21711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC22×C32×D12C2
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#386
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×D3×Dic3C2semidirect
3. C2×C3×(C2×D3)⋊Dic3C2semidirect
4. C2×C3×(C2×D3)⋊Dic3C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
6. C3×#63658C2semidirect
7. C32×C3⋊#95C2semidirect
10. #10591376C3direct (N × H)
20. C2×C32×D12C4semidirect
33. C22×D3×Dic3C2×C3semidirect
40. C2×(C2×D3)⋊Dic3C2×C3semidirect
41. C2×(C2×D3)⋊Dic3C2×C3semidirect
42. C2×(C2×D3)⋊Dic3C2×C3semidirect
44. #63658C2×C3semidirect
49. C3×C3⋊#95D3semidirect
50. C3×C3⋊#95C2×C3semidirect
63. C22×C32×D3C2×C4semidirect
68. C2×C33×C4C2×C4semidirect
74. C2×C3×C3⋊Dic3D4semidirect
80. C2×C32×Dic3D4semidirect
130. C2×C3×D12Dic3semidirect
131. C2×C3×D12C3×C4semidirect
167. C2×C32×D3C22⋊C4semidirect
196. C3⋊#95C3×D3semidirect
253. C22×C3×D3C2×Dic3semidirect
257. C22×C3×D3C2×C3×C4semidirect
285. C2×C32×C4C4×D3semidirect
286. C2×C32×C4C2×Dic3semidirect
287. C2×C32×C4C2×C3×C4semidirect
293. C2×C3⋊Dic3C3×D4semidirect
329. C2×C3×Dic3D12semidirect
330. C2×C3×Dic3C3×D4semidirect
394. C2×D12C3×Dic3semidirect
510. C2×C3×D3#217semidirect
511. C2×C3×D3C3×C22⋊C4semidirect
542. C33#386semidirect
603. C22×D3C2×C3×Dic3semidirect
652. C2×C3×C4D3×Dic3semidirect
653. C2×C3×C4C3×C4×D3semidirect
654. C2×C3×C4C2×C3×Dic3semidirect
679. C2×Dic3C3×D12semidirect
859. C2×D3C3×#217semidirect
887. C32#4665semidirect
888. C32#5220semidirect
889. C32C3×#386semidirect
921. C2×C4C3×D3×Dic3semidirect
1009. C3#10591376direct (N × H)
1010. C3C3×#4665semidirect
1011. C3C3×#5220semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D122
C22×C3×D3×Dic32
C2×C3×(C2×D3)⋊Dic32
C3×#636582
C32×C3⋊#952
C3×#52203
C3×#46653
#105913763