Finite Group Databasebeta

← C3×#10595072 #13174669

Subgroups — C3×#10595072 #13174669

Order 1728.

1758 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#67C212yesmaximal, complemented
2C3×#64139C211yesmaximal, characteristic, complemented
3C32×#930C211yesmaximal, characteristic, complemented
4C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C3×#63978C212yesmaximal, complemented
6C3×#63923C212yesmaximal, complemented
7C3×#63922C212yesmaximal, complemented
8C3×#63891C212yesmaximal, complemented
9C3×#63890C212yesmaximal, complemented
10C3×#5605—31nomaximal
11C3×#5493—31nomaximal
12#10595072C311yesmaximal, characteristic, direct product factor
13C23×C32×D3C2211yescharacteristic
14C22×C3×D32C2212yescomplemented
15C22×C33×C4C2211yescharacteristic, complemented
16C2×C3×#638C2212yescomplemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C2×C32×#67C2212yescomplemented
19C22×C32×Dic3C2211yescharacteristic, complemented
20C2×C32×D12C2211yescharacteristic, complemented
21C3×D3×#67—28no—
22C2×C3×#626C2212yes—
23C2×C3×#626C2212yescomplemented
24C2×C3×#625C2212yes—
25C2×C3×D3×Dic3C2212yescomplemented
26C3×#3752C2212yescomplemented
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
28C32×(C2×D3)⋊C4C2212yescomplemented
29C32×(C2×D3)⋊C4C2212yescomplemented
30C32×(C2×D3)⋊C4C2212yescomplemented
31C32×C4⋊Dic3C2211yescharacteristic, complemented
32C3×Dic3⋊Dic3C2212yescomplemented
33C3×#3722C2212yescomplemented
34C3×(C2×D3)⋊Dic3C2212yescomplemented
35C22×C3×#67—32no—
36C2×C3×D3×D4—32no—
37C2×D3×#67C2×C312yescomplemented
38C32×#121—31no—
39C2×C32×C22⋊C4—31no—
40#64139C2×C311yescharacteristic, complemented
41C3×#939—32no—
42C3×#937—32no—
43C3×#930—21no—
44C3×#930—31no—
45C3×#930—31no—
46C3×#930—32no—
47C3×#930—61no—
48C3×#930D311yescharacteristic, complemented
49C3×#930C2×C311yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4—21no—
51C2×C3×(C2×D3)⋊C4D311yescharacteristic, complemented
52C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
53C3×#894—32no—
54C3×#886—32no—
55C3×#886—32no—
56C3×#883—32no—
57C3×#882—32no—
58C3×#882—32no—
59C3×#882—32no—
60#63978C2×C312yescomplemented
61#63923C2×C312yescomplemented
62#63922C2×C312yescomplemented
63#63891C2×C312yescomplemented
64#63890C2×C312yescomplemented
65C23×C33C2311yescharacteristic
66C22×C3×C3⋊D3C2312yes—
67C22×C32×D3—41no—
68C22×C32×D3—41no—
69C22×C32×D3D414yescomplemented
70C22×C32×D3C2312yes—
71C22×C32×D3C2312yes—
72C2×C3×D32—24no—
73C2×C3×D32—42no—
74C2×C3×D32—42no—
75C2×C33×C4—41no—
76C2×C33×C4C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C3×#638—24no—
79C2×C3×C3⋊Dic3C2312yes—
80C3×C4⋊(C3⋊D3)—41no—
81C32×#67—24no—
82C2×C32×Dic3—41no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2312yes—
85C32×D12—41no—
86C3×#626—24no—
87C3×#626—42no—
88C3×#625—24no—
89C3×D3×Dic3—24no—
90C3×#534—91no—
91#5605—31no—
92#5493—31no—
93C24×C32—31no—
94C23×C3×D3—21no—
95C23×C3×D3—32no—
96C23×C3×D3—32no—
97C23×C3×D3C2×D311yescharacteristic
98C23×C3×D3C22×C311yescharacteristic
99C22×D32C22×C312yescomplemented
100C2×C32×D4—32no—
101C2×C32×D4—31no—
102C22×C32×C4—21no—
103C22×C32×C4—21no—
104C22×C32×C4—21no—
105C22×C32×C4—31no—
106C22×C32×C4—41no—
107C22×C32×C4C2×D311yescharacteristic, complemented
108C22×C32×C4C2×D311yescharacteristic, complemented
109C22×C32×C4C22×C311yescharacteristic, complemented
110C2×#638C22×C312yescomplemented
111C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
112C2×C3×#67—22no—
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—32no—
119C2×C3×#67—68no—
120C2×C3×#67—62no—
121C2×C3×#67C2×D312yescomplemented
122C2×C3×#67C22×C312yescomplemented
123C22×C3×Dic3—21no—
124C22×C3×Dic3—32no—
125C22×C3×Dic3C2×D311yescharacteristic, complemented
126C22×C3×Dic3C22×C311yescharacteristic, complemented
127C3×D3×D4—68no—
128C2×C3×D12—21no—
129C2×C3×D12—32no—
130C2×C3×D12—32no—
131C2×C3×D12—31no—
132C2×C3×D12—31no—
133C2×C3×D12—61no—
134C2×C3×D12C2×D311yescharacteristic, complemented
135C2×C3×D12C22×C311yescharacteristic, complemented
136C2×C3×C4×D3—32no—
137D3×#67—28no—
138C2×#626C22×C312yes—
139C2×#626C22×C312yescomplemented
140C2×#625C22×C312yes—
141C2×D3×Dic3C22×C312yescomplemented
142C32×C4⋊C4—31no—
143C32×C22⋊C4—32no—
144C32×C22⋊C4—32no—
145C32×C22⋊C4—32no—
146#3752C22×C312yescomplemented
147C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
148C3×#217—32no—
149C3×(C2×D3)⋊C4—22no—
150C3×(C2×D3)⋊C4—22no—
151C3×(C2×D3)⋊C4—22no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—32no—
155C3×(C2×D3)⋊C4—32no—
156C3×(C2×D3)⋊C4—32no—
157C3×(C2×D3)⋊C4—62no—
158C3×(C2×D3)⋊C4C2×D312yescomplemented
159C3×(C2×D3)⋊C4C2×D312yescomplemented
160C3×(C2×D3)⋊C4C2×D312yescomplemented
161C3×(C2×D3)⋊C4C22×C312yescomplemented
162C3×(C2×D3)⋊C4C22×C312yescomplemented
163C3×(C2×D3)⋊C4C22×C312yescomplemented
164C3×C4⋊Dic3—21no—
165C3×C4⋊Dic3—31no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—32no—
168C3×C4⋊Dic3—61no—
169C3×C4⋊Dic3C2×D311yescharacteristic, complemented
170C3×C4⋊Dic3C22×C311yescharacteristic, complemented
171C3×Dic3⋊C4—32no—
172Dic3⋊Dic3C22×C312yescomplemented
173#3722C22×C312yescomplemented
174(C2×D3)⋊Dic3C22×C312yescomplemented
175C22×C33—21no—
176C22×C33—21no—
177C22×C33C2×D412yes—
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—22no—
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—22no—
182C2×C32×D3—22no—
183C2×C32×D3—22no—
184C2×C32×D3—22no—
185C2×C32×D3—22no—
186C2×C32×D3—22no—
187C2×C32×D3—44no—
188C2×C32×D3C2×D414yes—
189C3×D32—48no—
190C33×C4—21no—
191C33×C4—21no—
192C3×C3⋊Dic3—22no—
193C32×Dic3—22no—
194C32×Dic3—22no—
195C22×C3×D4—92no—
196C22×#67—32no—
197C2×D3×D4—32no—
198C3×#123—92no—
199C3×#123—92no—
200C3×#121—31no—
201C3×#121—31no—
202C3×#121—61no—
203C3×#121—92no—
204C3×#121—91no—
205C3×#120—92no—
206C3×#120—92no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4—61no—
210#939—32no—
211#937—32no—
212#930—31no—
213#930—31no—
214#930—32no—
215#930—61no—
216#930C3×D311yescharacteristic, complemented
217C2×(C2×D3)⋊C4C3×D311yescharacteristic, complemented
218#894—32no—
219#886—32no—
220#886—32no—
221#883—32no—
222#882—32no—
223#882—32no—
224#882—32no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—32no—
229C23×C32—34no—
230C23×C32—32no—
231C23×C32—41no—
232C23×C32—121no—
233C23×C32—121no—
234C23×C32C22×D311yescharacteristic
235C23×C32C22×D311yescharacteristic
236C23×C32C23×C311yescharacteristic
237C22×C3⋊D3C23×C312yes—
238C22×C3×D3—24no—
239C22×C3×D3—22no—
240C22×C3×D3—22no—
241C22×C3×D3—32no—
242C22×C3×D3—32no—
243C22×C3×D3—41no—
244C22×C3×D3—41no—
245C22×C3×D3—41no—
246C22×C3×D3—41no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3—62no—
250C22×C3×D3—64no—
251C22×C3×D3—64no—
252C22×C3×D3—122no—
253C22×C3×D3—122no—
254C22×C3×D3—122no—
255C22×C3×D3—122no—
256C22×C3×D3D1214yescomplemented
257C22×C3×D3C3×D414yescomplemented
258C22×C3×D3C22×D312yes—
259C22×C3×D3C22×D312yes—
260C22×C3×D3C23×C312yes—
261C22×C3×D3C23×C312yes—
262C2×D32—24no—
263C2×D32—42no—
264C2×D32—42no—
265C32×D4—64no—
266C32×D4—121no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—32no—
274C2×C32×C4—32no—
275C2×C32×C4—41no—
276C2×C32×C4—41no—
277C2×C32×C4—41no—
278C2×C32×C4—41no—
279C2×C32×C4—41no—
280C2×C32×C4—42no—
281C2×C32×C4—42no—
282C2×C32×C4—42no—
283C2×C32×C4—44no—
284C2×C32×C4—121no—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C23×C311yescharacteristic
290C2×C32×C4C23×C311yescharacteristic
291#638—24no—
292C2×C3⋊Dic3C23×C312yes—
293C4⋊(C3⋊D3)—41no—
294C3×#67—24no—
295C3×#67—24no—
296C3×#67—44no—
297C3×#67—64no—
298C3×#67—64no—
299C3×#67—64no—
300C3×#67—64no—
301C3×#67—64no—
302C3×#67—124no—
303C3×#67—122no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—41no—
309C2×C3×Dic3—41no—
310C2×C3×Dic3—42no—
311C2×C3×Dic3—62no—
312C2×C3×Dic3—64no—
313C2×C3×Dic3C22×D312yes—
314C2×C3×Dic3C22×D312yes—
315C2×C3×Dic3C23×C312yes—
316C2×C3×Dic3C23×C312yes—
317C3×D12—41no—
318C3×D12—41no—
319C3×D12—42no—
320C3×D12—64no—
321C3×D12—121no—
322C3×D12—121no—
323C3×D12—122no—
324C3×D12—122no—
325C3×C4×D3—64no—
326#626—24no—
327#626—42no—
328#625—24no—
329D3×Dic3—24no—
330#534—91noSylow
331C2×C33—22no—
332C2×C33C22×D411yescharacteristic
333C2×C33H(5,𝔽2)11yescharacteristic
334C2×C33H(5,𝔽2)11yescharacteristic
335C3×C3⋊D3—42no—
336C32×D3—24no—
337C32×D3—42no—
338C24×C3—31no—
339C24×C3—31no—
340C24×C3—61no—
341C24×C3—92no—
342C23×D3—32no—
343C23×D3—32no—
344C23×D3C2×C3×D311yescharacteristic
345C2×C3×D4—32no—
346C2×C3×D4—32no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—61no—
350C2×C3×D4—62no—
351C2×C3×D4—92no—
352C2×C3×D4—92no—
353C2×C3×D4—92no—
354C2×C3×D4—92no—
355C2×C3×D4—91no—
356C2×C3×D4—188no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—41no—
363C22×C3×C4—61no—
364C22×C3×C4—92no—
365C22×C3×C4D3211yescharacteristic, complemented
366C22×C3×C4C2×C3×D311yescharacteristic, complemented
367C22×C3×C4C2×C3×D311yescharacteristic, complemented
368C2×#67—32no—
369C2×#67—32no—
370C2×#67—32no—
371C2×#67—32no—
372C2×#67—32no—
373C2×#67—32no—
374C2×#67—62no—
375C2×#67—68no—
376C2×#67C2×C3×D312yescomplemented
377C22×Dic3—32no—
378C22×Dic3C2×C3×D311yescharacteristic, complemented
379D3×D4—68no—
380C2×D12—32no—
381C2×D12—32no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—61no—
385C2×D12C2×C3×D311yescharacteristic, complemented
386C2×C4×D3—32no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—92no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—32no—
393C3×C22⋊C4—32no—
394C3×C22⋊C4—32no—
395C3×C22⋊C4—32no—
396C3×C22⋊C4—32no—
397C3×C22⋊C4—32no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C22⋊C4—92no—
402C3×C22⋊C4—92no—
403C3×C22⋊C4—92no—
404#217—32no—
405(C2×D3)⋊C4—32no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—32no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4C2×C3×D312yescomplemented
412(C2×D3)⋊C4C2×C3×D312yescomplemented
413(C2×D3)⋊C4C2×C3×D312yescomplemented
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416C4⋊Dic3—32no—
417C4⋊Dic3—61no—
418C4⋊Dic3C2×C3×D311yescharacteristic, complemented
419Dic3⋊C4—32no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—34no—
435C22×C32—42no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32—42no—
442C22×C32—42no—
443C22×C32—62no—
444C22×C32—62no—
445C22×C32—62no—
446C22×C32—62no—
447C22×C32—62no—
448C22×C32—124no—
449C22×C32C2×D1212yes—
450C22×C32D3×D412yes—
451C22×C32C2×C3×D412yes—
452C22×C32C23×D311yescharacteristic
453C22×C32C23×D311yescharacteristic
454C22×C32C24×C311yescharacteristic
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—24no—
469C2×C3×D3—42no—
470C2×C3×D3—42no—
471C2×C3×D3—42no—
472C2×C3×D3—42no—
473C2×C3×D3—42no—
474C2×C3×D3—44no—
475C2×C3×D3—44no—
476C2×C3×D3—48no—
477C2×C3×D3—62no—
478C2×C3×D3—62no—
479C2×C3×D3—62no—
480C2×C3×D3—62no—
481C2×C3×D3—62no—
482C2×C3×D3—62no—
483C2×C3×D3—122no—
484C2×C3×D3—122no—
485C2×C3×D3—122no—
486C2×C3×D3—128no—
487C2×C3×D3—128no—
488C2×C3×D3C2×D1214yes—
489C2×C3×D3C2×C3×D414yes—
490D32—48no—
491C32×C4—21no—
492C32×C4—21no—
493C32×C4—22no—
494C32×C4—22no—
495C32×C4—21no—
496C32×C4—21no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—41no—
500C32×C4—41no—
501C32×C4—41no—
502C32×C4—41no—
503C32×C4—42no—
504C32×C4—42no—
505C32×C4—62no—
506C32×C4—62no—
507C3⋊Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—42no—
513C3×Dic3—42no—
514C3×Dic3—62no—
515C3×Dic3—62no—
516C3×Dic3—122no—
517C22×D4—92no—
518#123—92no—
519#123—92no—
520#121—31no—
521#121—92no—
522#121—91no—
523#120—92no—
524#120—92no—
525C2×C22⋊C4—31no—
526C33#53411yescharacteristic, complemented, Sylow
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—32no—
531C23×C3—32no—
532C23×C3—34no—
533C23×C3—34no—
534C23×C3—32no—
535C23×C3—32no—
536C23×C3—41no—
537C23×C3—62no—
538C23×C3—64no—
539C23×C3—62no—
540C23×C3—92no—
541C23×C3—121no—
542C23×C3—121no—
543C23×C3—121no—
544C23×C3—121no—
545C23×C3—122no—
546C23×C3—122no—
547C23×C3—184no—
548C23×C3—362no—
549C23×C3—362no—
550C23×C3C2×D3211yescharacteristic
551C23×C3C22×C3×D311yescharacteristic
552C23×C3C22×C3×D311yescharacteristic
553C22×D3—32no—
554C22×D3—32no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—62no—
558C22×D3—64no—
559C22×D3—64no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3C3×D1214yescomplemented
565C22×D3C22×C3×D312yes—
566C22×D3C22×C3×D312yes—
567C3×D4—64no—
568C3×D4—64no—
569C3×D4—124no—
570C3×D4—121no—
571C3×D4—121no—
572C3×D4—122no—
573C3×D4—184no—
574C3×D4—184no—
575C3×D4—184no—
576C3×D4—361no—
577C3×D4—362no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—42no—
594C2×C3×C4—44no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—62no—
598C2×C3×C4—62no—
599C2×C3×C4—92no—
600C2×C3×C4—121no—
601C2×C3×C4—121no—
602C2×C3×C4—122no—
603C2×C3×C4—184no—
604C2×C3×C4C2×D3211yescharacteristic
605C2×C3×C4C2×D3211yescharacteristic
606C2×C3×C4C22×C3×D311yescharacteristic
607C2×C3×C4C22×C3×D311yescharacteristic
608C2×C3×C4C22×C3×D311yescharacteristic
609C2×C3×C4C22×C3×D311yescharacteristic
610#67—24no—
611#67—64no—
612#67—64no—
613#67—64no—
614#67—64no—
615#67—64no—
616#67—124no—
617#67—122no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—41no—
621C2×Dic3—62no—
622C2×Dic3—64no—
623C2×Dic3C22×C3×D312yes—
624C2×Dic3C22×C3×D312yes—
625D12—41no—
626D12—64no—
627D12—121no—
628D12—121no—
629D12—122no—
630D12—122no—
631C4×D3—64no—
632C2×C32—22no—
633C2×C32—24no—
634C2×C32—22no—
635C2×C32—22no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—21no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—21no—
645C2×C32—41no—
646C2×C32—41no—
647C2×C32—41no—
648C2×C32—42no—
649C2×C32—42no—
650C2×C32—44no—
651C2×C32—64no—
652C2×C32—122no—
653C2×C32C22×D1211yescharacteristic
654C2×C32C2×D3×D411yescharacteristic
655C2×C32#100411yescharacteristic
656C2×C32#100411yescharacteristic
657C2×C32#100411yescharacteristic
658C2×C32#100911yescharacteristic
659C2×C32C22×C3×D411yescharacteristic
660C2×C32C3×H(5,𝔽2)11yescharacteristic
661C2×C32C3×H(5,𝔽2)11yescharacteristic
662C3⋊D3—42no—
663C3×D3—24no—
664C3×D3—24no—
665C3×D3—44no—
666C3×D3—42no—
667C3×D3—42no—
668C3×D3—82no—
669C3×D3—122no—
670C3×D3—122no—
671C3×D3—242no—
672C24—31no—
673C24—92no—
674C2×D4—32no—
675C2×D4—31no—
676C2×D4—92no—
677C2×D4—92no—
678C2×D4—92no—
679C2×D4—92no—
680C2×D4—91no—
681C2×D4—188no—
682C22×C4—31no—
683C22×C4—92no—
684C22×C4C3×D3211yescharacteristic, complemented
685C4⋊C4—31no—
686C4⋊C4—92no—
687C4⋊C4—91no—
688C22⋊C4—32no—
689C22⋊C4—32no—
690C22⋊C4—32no—
691C22⋊C4—92no—
692C22⋊C4—92no—
693C22⋊C4—92no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—34no—
709C22×C3—34no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—42no—
718C22×C3—64no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—122no—
730C22×C3—122no—
731C22×C3—122no—
732C22×C3—122no—
733C22×C3—122no—
734C22×C3—124no—
735C22×C3—124no—
736C22×C3—128no—
737C22×C3—182no—
738C22×C3—182no—
739C22×C3—182no—
740C22×C3—368no—
741C22×C3D3×D1212yes—
742C22×C3C2×C3×D1212yes—
743C22×C3C3×D3×D412yes—
744C22×C3C22×D3211yescharacteristic
745C22×C3C23×C3×D311yescharacteristic
746C22×C3C23×C3×D311yescharacteristic
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—44no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—128no—
763C2×D3—128no—
764C2×D3C2×C3×D1214yes—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—42no—
778C3×C4—42no—
779C3×C4—62no—
780C3×C4—62no—
781C3×C4—62no—
782C3×C4—62no—
783C3×C4—122no—
784C3×C4—122no—
785C3×C4—182no—
786Dic3—22no—
787Dic3—22no—
788Dic3—62no—
789Dic3—62no—
790Dic3—122no—
791C32—21no—
792C32—21no—
793C32—21no—
794C32—41no—
795C32#549311yescharacteristic, complemented
796C32#560511yescharacteristic, complemented
797C32C3×#53411yescharacteristic, complemented
798C23—32no—
799C23—34no—
800C23—32no—
801C23—92no—
802C23—121no—
803C23—121no—
804C23—184no—
805C23—362no—
806C23—362no—
807C23C2×C3×D3211yescharacteristic
808D4—64no—
809D4—121no—
810D4—184no—
811D4—184no—
812D4—184no—
813D4—361no—
814D4—362no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—41no—
818C2×C4—92no—
819C2×C4—121no—
820C2×C4—184no—
821C2×C4C2×C3×D3211yescharacteristic
822C2×C4C2×C3×D3211yescharacteristic
823C2×C3—24no—
824C2×C3—22no—
825C2×C3—22no—
826C2×C3—22no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—42no—
837C2×C3—42no—
838C2×C3—44no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—41no—
842C2×C3—64no—
843C2×C3—64no—
844C2×C3—124no—
845C2×C3—122no—
846C2×C3—122no—
847C2×C3—242no—
848C2×C3—362no—
849C2×C3C2×D3×D1211yescharacteristic
850C2×C3#6430711yescharacteristic
851C2×C3#6433011yescharacteristic
852C2×C3C22×C3×D1211yescharacteristic
853C2×C3C2×C3×D3×D411yescharacteristic
854C2×C3C3×#100411yescharacteristic
855C2×C3C3×#100411yescharacteristic
856C2×C3C3×#100411yescharacteristic
857C2×C3C3×#100911yescharacteristic
858D3—24no—
859D3—42no—
860D3—122no—
861D3—122no—
862D3—242no—
863C22—21no—
864C22—21no—
865C22—34no—
866C22—62no—
867C22—62no—
868C22—62no—
869C22—62no—
870C22—62no—
871C22—124no—
872C22—182no—
873C22—182no—
874C22—182no—
875C22—368no—
876C22C3×D3×D1212yes—
877C22C22×C3×D3211yescharacteristic
878C4—21no—
879C4—21no—
880C4—62no—
881C4—62no—
882C4—182no—
883C3—21no—
884C3—21no—
885C3—21no—
886C3—41no—
887C3#1059507211yescharacteristic, direct product factor
888C3C3×#549311yescharacteristic, complemented
889C3C3×#560511yescharacteristic, complemented
890C2—22no—
891C2—64no—
892C2—122no—
893C2—362no—
894C2C2×C3×D3×D1211yescharacteristic
895C2C3×#6430711yescharacteristic
896C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#67C2semidirect
2. C3×#64139C2semidirect
3. C32×#930C2semidirect
4. C2×C32×(C2×D3)⋊C4C2semidirect
5. C3×#63978C2semidirect
6. C3×#63923C2semidirect
7. C3×#63922C2semidirect
8. C3×#63891C2semidirect
9. C3×#63890C2semidirect
12. #10595072C3direct (N × H)
14. C22×C3×D32C22semidirect
15. C22×C33×C4C22semidirect
16. C2×C3×#638C22semidirect
17. C2×C3×C4⋊(C3⋊D3)C22semidirect
18. C2×C32×#67C22semidirect
19. C22×C32×Dic3C22semidirect
20. C2×C32×D12C22semidirect
23. C2×C3×#626C22semidirect
25. C2×C3×D3×Dic3C22semidirect
26. C3×#3752C22semidirect
27. C3×C4⋊(C3⋊Dic3)C22semidirect
28. C32×(C2×D3)⋊C4C22semidirect
29. C32×(C2×D3)⋊C4C22semidirect
30. C32×(C2×D3)⋊C4C22semidirect
31. C32×C4⋊Dic3C22semidirect
32. C3×Dic3⋊Dic3C22semidirect
33. C3×#3722C22semidirect
34. C3×(C2×D3)⋊Dic3C22semidirect
37. C2×D3×#67C2×C3semidirect
40. #64139C2×C3semidirect
48. C3×#930D3semidirect
49. C3×#930C2×C3semidirect
51. C2×C3×(C2×D3)⋊C4D3semidirect
52. C2×C3×(C2×D3)⋊C4C2×C3semidirect
60. #63978C2×C3semidirect
61. #63923C2×C3semidirect
62. #63922C2×C3semidirect
63. #63891C2×C3semidirect
64. #63890C2×C3semidirect
69. C22×C32×D3D4semidirect
99. C22×D32C22×C3semidirect
107. C22×C32×C4C2×D3semidirect
108. C22×C32×C4C2×D3semidirect
109. C22×C32×C4C22×C3semidirect
110. C2×#638C22×C3semidirect
111. C2×C4⋊(C3⋊D3)C22×C3semidirect
121. C2×C3×#67C2×D3semidirect
122. C2×C3×#67C22×C3semidirect
125. C22×C3×Dic3C2×D3semidirect
126. C22×C3×Dic3C22×C3semidirect
134. C2×C3×D12C2×D3semidirect
135. C2×C3×D12C22×C3semidirect
139. C2×#626C22×C3semidirect
141. C2×D3×Dic3C22×C3semidirect
146. #3752C22×C3semidirect
147. C4⋊(C3⋊Dic3)C22×C3semidirect
158. C3×(C2×D3)⋊C4C2×D3semidirect
159. C3×(C2×D3)⋊C4C2×D3semidirect
160. C3×(C2×D3)⋊C4C2×D3semidirect
161. C3×(C2×D3)⋊C4C22×C3semidirect
162. C3×(C2×D3)⋊C4C22×C3semidirect
163. C3×(C2×D3)⋊C4C22×C3semidirect
169. C3×C4⋊Dic3C2×D3semidirect
170. C3×C4⋊Dic3C22×C3semidirect
172. Dic3⋊Dic3C22×C3semidirect
173. #3722C22×C3semidirect
174. (C2×D3)⋊Dic3C22×C3semidirect
216. #930C3×D3semidirect
217. C2×(C2×D3)⋊C4C3×D3semidirect
256. C22×C3×D3D12semidirect
257. C22×C3×D3C3×D4semidirect
365. C22×C3×C4D32semidirect
366. C22×C3×C4C2×C3×D3semidirect
367. C22×C3×C4C2×C3×D3semidirect
376. C2×#67C2×C3×D3semidirect
378. C22×Dic3C2×C3×D3semidirect
385. C2×D12C2×C3×D3semidirect
411. (C2×D3)⋊C4C2×C3×D3semidirect
412. (C2×D3)⋊C4C2×C3×D3semidirect
413. (C2×D3)⋊C4C2×C3×D3semidirect
418. C4⋊Dic3C2×C3×D3semidirect
526. C33#534semidirect
564. C22×D3C3×D12semidirect
684. C22×C4C3×D32semidirect
795. C32#5493semidirect
796. C32#5605semidirect
797. C32C3×#534semidirect
887. C3#10595072direct (N × H)
888. C3C3×#5493semidirect
889. C3C3×#5605semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#672
C3×#641392
C32×#9302
C2×C32×(C2×D3)⋊C42
C3×#639782
C3×#639232
C3×#639222
C3×#638912
C3×#638902
C3×#56053
C3×#54933
#105950723