Finite Group Databasebeta

← C3×#10591313 #13158233

Subgroups — C3×#10591313 #13158233

Order 1728.

1410 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic
2C2×C3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C2×C32×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊Dic3C212yesmaximal
5C3×#63579C212yesmaximal, complemented
6C3×#5212—31nomaximal
7C3×#4987—31nomaximal
8#10591313C311yesmaximal, characteristic, direct product factor
9C23×C32×D3C2211yescharacteristic
10C22×C33×C4C2211yescharacteristic
11C22×C3×C3⋊Dic3C2212yes—
12C22×C32×Dic3C2212yes—
13C22×C32×Dic3C2211yescharacteristic
14C2×C32×C4×D3—22no—
15C2×C32×C4×D3—22no—
16C2×C32×C4×D3C414yescomplemented
17C3×C4⋊(C3⋊Dic3)—22no—
18C32×C4⋊Dic3—22no—
19C3×(C2×D3)⋊Dic3—24no—
20C23×C32×C4—31no—
21C22×C3×C4×D3—21no—
22C22×C3×C4×D3D311yescharacteristic
23C22×C3×C4×D3C2×C311yescharacteristic
24C2×C32×C4⋊C4—31no—
25C2×C4⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
26C2×C3×#217—32no—
27C2×C3×(C2×D3)⋊C4—32no—
28C2×C3×C4⋊Dic3—21no—
29C2×C3×C4⋊Dic3—31no—
30C2×C3×C4⋊Dic3—31no—
31C2×C3×C4⋊Dic3—61no—
32C2×C3×C4⋊Dic3D311yescharacteristic, complemented
33C2×C3×C4⋊Dic3C2×C311yescharacteristic, complemented
34C2×(C2×D3)⋊Dic3C2×C312yes—
35C3×C3⋊#95—32no—
36C3×C3⋊#95—32no—
37#63579C2×C312yescomplemented
38C23×C33C2311yescharacteristic
39C22×C32×D3—21no—
40C22×C32×D3—21no—
41C22×C32×D3—21no—
42C22×C32×D3—21no—
43C22×C32×D3C2×C412yes—
44C22×C32×D3D412yes—
45C22×C32×D3Q812yes—
46C2×C33×C4C2×C412yes—
47C2×C33×C4D412yes—
48C2×C33×C4D412yes—
49C2×C3×C3⋊Dic3—22no—
50C2×C3×C3⋊Dic3—22no—
51C2×C3×C3⋊Dic3—22no—
52C2×C32×Dic3—21no—
53C2×C32×Dic3—21no—
54C2×C32×Dic3—22no—
55C2×C32×Dic3—22no—
56C2×C32×Dic3—22no—
57C2×C32×Dic3C2×C412yes—
58C32×C4×D3—28no—
59C3×#380—91no—
60#5212—31no—
61#4987—31no—
62C24×C32—31no—
63C23×C3×D3—21no—
64C23×C3×D3C2×D311yescharacteristic
65C23×C3×D3C22×C311yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4—31no—
70C22×C32×C4—34no—
71C22×C32×C4—32no—
72C22×C32×C4—41no—
73C22×C32×C4—62no—
74C22×C32×C4—62no—
75C22×C32×C4C2×D311yescharacteristic
76C22×C32×C4C2×D311yescharacteristic
77C22×C32×C4C22×C311yescharacteristic
78C22×C3⋊Dic3C22×C312yes—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—22no—
81C22×C3×Dic3—32no—
82C22×C3×Dic3—32no—
83C22×C3×Dic3—62no—
84C22×C3×Dic3C2×D312yes—
85C22×C3×Dic3C2×D311yescharacteristic
86C22×C3×Dic3C22×C312yes—
87C22×C3×Dic3C22×C311yescharacteristic
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3—22no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—22no—
95C2×C3×C4×D3Dic314yescomplemented
96C2×C3×C4×D3C3×C414yescomplemented
97C32×C4⋊C4—62no—
98C4⋊(C3⋊Dic3)—22no—
99C3×#217—64no—
100C3×(C2×D3)⋊C4—64no—
101C3×C4⋊Dic3—24no—
102C3×C4⋊Dic3—22no—
103C3×C4⋊Dic3—22no—
104C3×C4⋊Dic3—64no—
105C3×C4⋊Dic3—62no—
106C3×C4⋊Dic3—62no—
107(C2×D3)⋊Dic3—24no—
108C22×C33C22×C411yescharacteristic
109C22×C33C2×D411yescharacteristic
110C22×C33C2×D411yescharacteristic
111C22×C33C2×D411yescharacteristic
112C22×C33C2×Q811yescharacteristic
113C22×C33#4111yescharacteristic
114C22×C33#4111yescharacteristic
115C2×C32×D3—22no—
116C2×C32×D3—22no—
117C2×C32×D3—22no—
118C2×C32×D3—22no—
119C2×C32×D3—22no—
120C2×C32×D3—22no—
121C2×C32×D3C4⋊C414yescomplemented
122C33×C4C22⋊C414yescomplemented
123C3×C3⋊Dic3—42no—
124C32×Dic3—22no—
125C32×Dic3—42no—
126C23×C3×C4—31no—
127C23×C3×C4—31no—
128C23×C3×C4—61no—
129C22×C4×D3C3×D311yescharacteristic
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—61no—
133C2×C3×C4⋊C4—91no—
134C2×C3×C22⋊C4—92no—
135C2×#217—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—61no—
140C2×C4⋊Dic3C3×D311yescharacteristic, complemented
141C3×#95—92no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C23×C32—21no—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—32no—
148C23×C32—32no—
149C23×C32—32no—
150C23×C32—41no—
151C23×C32—61no—
152C23×C32—61no—
153C23×C32—61no—
154C23×C32—61no—
155C23×C32C22×D311yescharacteristic
156C23×C32C22×D311yescharacteristic
157C23×C32C23×C311yescharacteristic
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3Dic612yes—
174C22×C3×D3D1212yes—
175C22×C3×D3C2×Dic312yes—
176C22×C3×D3C2×C3×C412yes—
177C22×C3×D3C3×D412yes—
178C22×C3×D3C3×Q812yes—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—32no—
189C2×C32×C4—42no—
190C2×C32×C4—42no—
191C2×C32×C4—42no—
192C2×C32×C4—61no—
193C2×C32×C4—61no—
194C2×C32×C4—68no—
195C2×C32×C4—62no—
196C2×C32×C4—62no—
197C2×C32×C4—62no—
198C2×C32×C4C4×D312yes—
199C2×C32×C4D1212yes—
200C2×C32×C4C2×Dic312yes—
201C2×C32×C4#6712yes—
202C2×C32×C4#6712yes—
203C2×C32×C4#6712yes—
204C2×C32×C4C2×C3×C412yes—
205C2×C32×C4C3×D412yes—
206C2×C32×C4C3×D412yes—
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—24no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—42no—
225C2×C3×Dic3—42no—
226C2×C3×Dic3—64no—
227C2×C3×Dic3—62no—
228C2×C3×Dic3—62no—
229C2×C3×Dic3—62no—
230C2×C3×Dic3—62no—
231C2×C3×Dic3—62no—
232C2×C3×Dic3—62no—
233C2×C3×Dic3—122no—
234C2×C3×Dic3—122no—
235C2×C3×Dic3C2×Dic312yes—
236C2×C3×Dic3C2×C3×C412yes—
237C3×C4×D3—216no—
238C3×C4×D3—28no—
239C3×C4×D3—28no—
240#380—91noSylow
241C2×C33C2×C22⋊C411yescharacteristic
242C2×C33C2×C4⋊C411yescharacteristic
243C2×C33#11711yescharacteristic
244C2×C33#12111yescharacteristic
245C2×C33#12111yescharacteristic
246C2×C33C22⋊Q811yescharacteristic
247C2×C33C22⋊Q811yescharacteristic
248C32×D3—24no—
249C24×C3—31no—
250C24×C3—31no—
251C24×C3—61no—
252C23×D3C2×C3×D311yescharacteristic
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—34no—
259C22×C3×C4—34no—
260C22×C3×C4—32no—
261C22×C3×C4—32no—
262C22×C3×C4—41no—
263C22×C3×C4—64no—
264C22×C3×C4—61no—
265C22×C3×C4—62no—
266C22×C3×C4—64no—
267C22×C3×C4—64no—
268C22×C3×C4—62no—
269C22×C3×C4—62no—
270C22×C3×C4—62no—
271C22×C3×C4—62no—
272C22×C3×C4—92no—
273C22×C3×C4D3211yescharacteristic
274C22×C3×C4C2×C3×D311yescharacteristic
275C22×C3×C4C2×C3×D311yescharacteristic
276C22×Dic3—32no—
277C22×Dic3—32no—
278C22×Dic3—62no—
279C22×Dic3C2×C3×D312yes—
280C22×Dic3C2×C3×D311yescharacteristic
281C2×C4×D3—22no—
282C2×C4×D3—22no—
283C2×C4×D3C3×Dic314yescomplemented
284C3×C4⋊C4—64no—
285C3×C4⋊C4—62no—
286C3×C4⋊C4—62no—
287C3×C4⋊C4—182no—
288C3×C22⋊C4—184no—
289#217—64no—
290(C2×D3)⋊C4—64no—
291C4⋊Dic3—22no—
292C4⋊Dic3—64no—
293C4⋊Dic3—62no—
294C4⋊Dic3—62no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—34no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—62no—
325C22×C32—62no—
326C22×C32—62no—
327C22×C32—62no—
328C22×C32—62no—
329C22×C32—62no—
330C22×C32C2×Dic611yescharacteristic
331C22×C32C2×C4×D311yescharacteristic
332C22×C32C2×D1211yescharacteristic
333C22×C32C2×D1211yescharacteristic
334C22×C32#23511yescharacteristic
335C22×C32#23511yescharacteristic
336C22×C32D3×D411yescharacteristic
337C22×C32#23711yescharacteristic
338C22×C32D3×Q811yescharacteristic
339C22×C32#23911yescharacteristic
340C22×C32C22×Dic311yescharacteristic
341C22×C32C2×#6711yescharacteristic
342C22×C32C2×#6711yescharacteristic
343C22×C32C2×#6711yescharacteristic
344C22×C32C22×C3×C411yescharacteristic
345C22×C32C2×C3×D411yescharacteristic
346C22×C32C2×C3×D411yescharacteristic
347C22×C32C2×C3×D411yescharacteristic
348C22×C32C2×C3×Q811yescharacteristic
349C22×C32C3×#4111yescharacteristic
350C22×C32C3×#4111yescharacteristic
351C2×C3×D3—24no—
352C2×C3×D3—24no—
353C2×C3×D3—24no—
354C2×C3×D3—24no—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—22no—
358C2×C3×D3—22no—
359C2×C3×D3—22no—
360C2×C3×D3—22no—
361C2×C3×D3—22no—
362C2×C3×D3—22no—
363C2×C3×D3—22no—
364C2×C3×D3—22no—
365C2×C3×D3—22no—
366C2×C3×D3—22no—
367C2×C3×D3—22no—
368C2×C3×D3—22no—
369C2×C3×D3—24no—
370C2×C3×D3C4⋊Dic314yescomplemented
371C2×C3×D3C3×C4⋊C414yescomplemented
372C32×C4—24no—
373C32×C4—24no—
374C32×C4—24no—
375C32×C4—44no—
376C32×C4—62no—
377C32×C4—122no—
378C32×C4(C2×D3)⋊C414yescomplemented
379C32×C4#21714yescomplemented
380C32×C4C3×C22⋊C414yescomplemented
381C3⋊Dic3—42no—
382C3×Dic3—24no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—44no—
386C3×Dic3—42no—
387C3×Dic3—42no—
388C3×Dic3—124no—
389C3×Dic3—122no—
390C3×Dic3—122no—
391C23×C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—91no—
394C2×C22⋊C4—92no—
395#95—92no—
396C33#38011yescharacteristic, complemented, Sylow
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—32no—
401C23×C3—32no—
402C23×C3—32no—
403C23×C3—32no—
404C23×C3—32no—
405C23×C3—32no—
406C23×C3—41no—
407C23×C3—62no—
408C23×C3—62no—
409C23×C3—62no—
410C23×C3—62no—
411C23×C3—62no—
412C23×C3—62no—
413C23×C3—62no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—61no—
417C23×C3—61no—
418C23×C3—61no—
419C23×C3—61no—
420C23×C3—61no—
421C23×C3—61no—
422C23×C3C2×D3211yescharacteristic
423C23×C3C22×C3×D311yescharacteristic
424C23×C3C22×C3×D311yescharacteristic
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3C3×Dic612yes—
430C22×D3C3×D1212yes—
431C22×D3C2×C3×Dic312yes—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—32no—
442C2×C3×C4—32no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—62no—
447C2×C3×C4—616no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—68no—
455C2×C3×C4—68no—
456C2×C3×C4—64no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—122no—
464C2×C3×C4—122no—
465C2×C3×C4—182no—
466C2×C3×C4—182no—
467C2×C3×C4—182no—
468C2×C3×C4D3×Dic312yes—
469C2×C3×C4#62512yes—
470C2×C3×C4#62612yes—
471C2×C3×C4C3×C4×D312yes—
472C2×C3×C4C3×D1212yes—
473C2×C3×C4C2×C3×Dic312yes—
474C2×C3×C4C3×#6712yes—
475C2×C3×C4C3×#6712yes—
476C2×C3×C4C3×#6712yes—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—64no—
483C2×Dic3—62no—
484C2×Dic3—62no—
485C2×Dic3—62no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—122no—
490C2×Dic3—122no—
491C2×Dic3C2×C3×Dic312yes—
492C4×D3—28no—
493C2×C32—21no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—41no—
515C2×C32—41no—
516C2×C32—41no—
517C2×C32—41no—
518C2×C32—41no—
519C2×C32—41no—
520C2×C32—41no—
521C2×C32—64no—
522C2×C32D3×C4⋊C411yescharacteristic
523C2×C32#89211yescharacteristic
524C2×C32#89511yescharacteristic
525C2×C32#89711yescharacteristic
526C2×C32#92411yescharacteristic
527C2×C32#92411yescharacteristic
528C2×C32C2×C4⋊Dic311yescharacteristic
529C2×C32#92611yescharacteristic
530C2×C32C2×(C2×D3)⋊C411yescharacteristic
531C2×C32#93011yescharacteristic
532C2×C32#93011yescharacteristic
533C2×C32#93811yescharacteristic
534C2×C32#94611yescharacteristic
535C2×C32C2×#21711yescharacteristic
536C2×C32C2×C3×C22⋊C411yescharacteristic
537C2×C32C2×C3×C4⋊C411yescharacteristic
538C2×C32C3×#11711yescharacteristic
539C2×C32C3×#12111yescharacteristic
540C2×C32C3×#12111yescharacteristic
541C2×C32C3×C22⋊Q811yescharacteristic
542C2×C32C3×C22⋊Q811yescharacteristic
543C3×D3—28no—
544C3×D3—24no—
545C3×D3—24no—
546C24—31no—
547C22×C4—31no—
548C22×C4—34no—
549C22×C4—32no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—92no—
553C22×C4C3×D3211yescharacteristic
554C4⋊C4—62no—
555C4⋊C4—182no—
556C22⋊C4—184no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—34no—
579C22×C3—34no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—64no—
588C22×C3—64no—
589C22×C3—64no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—64no—
594C22×C3—62no—
595C22×C3—62no—
596C22×C3—62no—
597C22×C3—62no—
598C22×C3—62no—
599C22×C3—62no—
600C22×C3—62no—
601C22×C3—62no—
602C22×C3—62no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—62no—
606C22×C3D3×Dic611yescharacteristic
607C22×C3#379511yescharacteristic
608C22×C3#379911yescharacteristic
609C22×C3D3×D1211yescharacteristic
610C22×C3C2×D3×Dic311yescharacteristic
611C22×C3C2×#62511yescharacteristic
612C22×C3C2×#62611yescharacteristic
613C22×C3C2×C3×Dic611yescharacteristic
614C22×C3C2×C3×C4×D311yescharacteristic
615C22×C3C2×C3×D1211yescharacteristic
616C22×C3C2×C3×D1211yescharacteristic
617C22×C3C3×#23511yescharacteristic
618C22×C3C3×#23511yescharacteristic
619C22×C3C3×D3×D411yescharacteristic
620C22×C3C3×#23711yescharacteristic
621C22×C3C3×D3×Q811yescharacteristic
622C22×C3C3×#23911yescharacteristic
623C22×C3C22×C3×Dic311yescharacteristic
624C22×C3C2×C3×#6711yescharacteristic
625C22×C3C2×C3×#6711yescharacteristic
626C22×C3C2×C3×#6711yescharacteristic
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—22no—
632C2×D3—22no—
633C2×D3C3×C4⋊Dic314yescomplemented
634C3×C4—24no—
635C3×C4—24no—
636C3×C4—24no—
637C3×C4—44no—
638C3×C4—64no—
639C3×C4—62no—
640C3×C4—62no—
641C3×C4—124no—
642C3×C4—122no—
643C3×C4—122no—
644C3×C4—362no—
645C3×C4(C2×D3)⋊Dic314yescomplemented
646C3×C4C3×(C2×D3)⋊C414yescomplemented
647C3×C4C3×#21714yescomplemented
648Dic3—22no—
649Dic3—42no—
650Dic3—124no—
651Dic3—122no—
652Dic3—122no—
653C32—21no—
654C32—21no—
655C32—21no—
656C32—41no—
657C32#498711yescharacteristic, complemented
658C32#521211yescharacteristic, complemented
659C32C3×#38011yescharacteristic, complemented
660C23—32no—
661C23—32no—
662C23—32no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23C2×C3×D3211yescharacteristic
668C2×C4—32no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—68no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—182no—
676C2×C4—182no—
677C2×C4—182no—
678C2×C4C3×D3×Dic312yes—
679C2×C4C3×#62512yes—
680C2×C4C3×#62612yes—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—41no—
709C2×C3—68no—
710C2×C3—64no—
711C2×C3—64no—
712C2×C3#6384111yescharacteristic
713C2×C3#6385611yescharacteristic
714C2×C3#6385711yescharacteristic
715C2×C3D3×C4⋊Dic311yescharacteristic
716C2×C3#6390811yescharacteristic
717C2×C3#6390911yescharacteristic
718C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
719C2×C3C3×D3×C4⋊C411yescharacteristic
720C2×C3C3×#89211yescharacteristic
721C2×C3C3×#89511yescharacteristic
722C2×C3C3×#89711yescharacteristic
723C2×C3C3×#92411yescharacteristic
724C2×C3C3×#92411yescharacteristic
725C2×C3C2×C3×C4⋊Dic311yescharacteristic
726C2×C3C3×#92611yescharacteristic
727C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
728C2×C3C3×#93011yescharacteristic
729C2×C3C3×#93011yescharacteristic
730C2×C3C3×#93811yescharacteristic
731C2×C3C3×#94611yescharacteristic
732C2×C3C2×C3×#21711yescharacteristic
733D3—24no—
734C22—34no—
735C22—62no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—62no—
741C22C3×D3×Dic611yescharacteristic
742C22C3×#379511yescharacteristic
743C22C3×#379911yescharacteristic
744C22C3×D3×D1211yescharacteristic
745C22C2×C3×D3×Dic311yescharacteristic
746C22C2×C3×#62511yescharacteristic
747C22C2×C3×#62611yescharacteristic
748C4—62no—
749C4—122no—
750C4—362no—
751C4C3×(C2×D3)⋊Dic314yescomplemented
752C3—21no—
753C3—21no—
754C3—21no—
755C3—41no—
756C3#1059131311yescharacteristic, direct product factor
757C3C3×#498711yescharacteristic, complemented
758C3C3×#521211yescharacteristic, complemented
759C2—64no—
760C2C3×#6384111yescharacteristic
761C2C3×#6385611yescharacteristic
762C2C3×#6385711yescharacteristic
763C2C3×D3×C4⋊Dic311yescharacteristic
764C2C3×#6390811yescharacteristic
765C2C3×#6390911yescharacteristic
766C2C2×C3×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#380
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. C2×C3×C4⋊(C3⋊Dic3)C2semidirect
3. C2×C32×C4⋊Dic3C2semidirect
5. C3×#63579C2semidirect
8. #10591313C3direct (N × H)
16. C2×C32×C4×D3C4semidirect
25. C2×C4⋊(C3⋊Dic3)C2×C3semidirect
32. C2×C3×C4⋊Dic3D3semidirect
33. C2×C3×C4⋊Dic3C2×C3semidirect
37. #63579C2×C3semidirect
95. C2×C3×C4×D3Dic3semidirect
96. C2×C3×C4×D3C3×C4semidirect
121. C2×C32×D3C4⋊C4semidirect
122. C33×C4C22⋊C4semidirect
140. C2×C4⋊Dic3C3×D3semidirect
283. C2×C4×D3C3×Dic3semidirect
370. C2×C3×D3C4⋊Dic3semidirect
371. C2×C3×D3C3×C4⋊C4semidirect
378. C32×C4(C2×D3)⋊C4semidirect
379. C32×C4#217semidirect
380. C32×C4C3×C22⋊C4semidirect
396. C33#380semidirect
633. C2×D3C3×C4⋊Dic3semidirect
645. C3×C4(C2×D3)⋊Dic3semidirect
646. C3×C4C3×(C2×D3)⋊C4semidirect
647. C3×C4C3×#217semidirect
657. C32#4987semidirect
658. C32#5212semidirect
659. C32C3×#380semidirect
751. C4C3×(C2×D3)⋊Dic3semidirect
756. C3#10591313direct (N × H)
757. C3C3×#4987semidirect
758. C3C3×#5212semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C2×C3×C4⋊(C3⋊Dic3)2
C2×C32×C4⋊Dic32
C2×C3×(C2×D3)⋊Dic32
C3×#635792
C3×#52123
C3×#49873
#105913133