Finite Group Databasebeta

← C2×C3×#63877 #13174437

Subgroups — C2×C3×#63877 #13174437

Order 1728.

1706 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Dic3C211yesmaximal, characteristic
2C2×C3×#3750C211yesmaximal, characteristic, complemented
3C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×C32×C4×Dic3C211yesmaximal, characteristic, complemented
5C2×C3×#3724C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8C3×#63877C218yesmaximal, direct product factor
9C2×C3×#877—31nomaximal
10C2×C3×#872—31nomaximal
11C2×#63877C311yesmaximal, characteristic, direct product factor
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×C3×D3×Dic3C418yescomplemented
20C2×C3×D3×Dic3C2214yes—
21C3×#3750C2214yescomplemented
22C32×(C2×D3)⋊C4C2214yes—
23C32×C4×Dic3C2214yescomplemented
24C3×#3724C2214yescomplemented
25C3×(C2×D3)⋊Dic3C2214yes—
26C3×Dic32C2214yescomplemented
27C23×C3×Dic3—31no—
28C22×C3×C4×D3—31no—
29C22×D3×Dic3C2×C311yescharacteristic
30C2×C32×C22⋊C4—31no—
31C2×C32×C42—31no—
32C2×#3750C2×C311yescharacteristic, complemented
33C2×C3×#217—31no—
34C2×C3×(C2×D3)⋊C4—21no—
35C2×C3×(C2×D3)⋊C4—31no—
36C2×C3×(C2×D3)⋊C4D311yescharacteristic
37C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
38C2×C3×Dic3⋊C4—31no—
39C2×C3×Dic3⋊C4—31no—
40C2×C3×Dic3⋊C4—31no—
41C2×C3×Dic3⋊C4—31no—
42C2×C3×Dic3⋊C4—61no—
43C2×C3×C4×Dic3—21no—
44C2×C3×C4×Dic3—31no—
45C2×C3×C4×Dic3—31no—
46C2×C3×C4×Dic3D311yescharacteristic, complemented
47C2×C3×C4×Dic3C2×C311yescharacteristic, complemented
48C3×#877—38no—
49C3×#872—38no—
50C2×#3724C2×C311yescharacteristic, complemented
51C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
52C2×Dic32C2×C311yescharacteristic, complemented
53#63877C2×C318yesdirect product factor
54C23×C33C2311yescharacteristic
55C22×C32×D3—22no—
56C22×C32×D3—22no—
57C22×C32×D3C2×C414yes—
58C22×C32×D3C2312yes—
59C2×C33×C4—22no—
60C2×C33×C4C2312yes—
61C2×C3×C3⋊Dic3—22no—
62C2×C3×C3⋊Dic3C2×C414yes—
63C2×C3×C3⋊Dic3C2312yes—
64C2×C3×C3⋊Dic3C2312yes—
65C2×C32×Dic3—22no—
66C2×C32×Dic3—22no—
67C2×C32×Dic3C2×C414yes—
68C2×C32×Dic3C2312yes—
69C2×C32×Dic3C2312yes—
70C2×C32×Dic3C2312yes—
71C3×D3×Dic3C2×C4116yescomplemented
72C2×C3×#117—91no—
73C2×#877—31no—
74C2×#872—31no—
75C24×C32—31no—
76C23×C3×D3—21no—
77C23×C3×D3C2×D311yescharacteristic
78C23×C3×D3C22×C311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4—31no—
83C22×C32×C4—31no—
84C22×C32×C4—31no—
85C22×C32×C4—41no—
86C22×C32×C4C2×D311yescharacteristic
87C22×C32×C4C2×D311yescharacteristic
88C22×C32×C4C22×C311yescharacteristic
89C22×C3⋊Dic3C22×C311yescharacteristic
90C22×C3⋊Dic3C22×C311yescharacteristic
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—38no—
97C22×C3×Dic3—34no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—61no—
101C22×C3×Dic3—61no—
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C2×D311yescharacteristic
105C22×C3×Dic3C22×C311yescharacteristic
106C22×C3×Dic3C22×C311yescharacteristic
107C22×C3×Dic3C22×C311yescharacteristic
108C2×C3×C4×D3—38no—
109C2×C3×C4×D3—34no—
110C2×D3×Dic3C3×C418yescomplemented
111C2×D3×Dic3C22×C314yes—
112C32×C22⋊C4—34no—
113C32×C42—34no—
114#3750C22×C314yescomplemented
115C3×#217—34no—
116C3×(C2×D3)⋊C4—24no—
117C3×(C2×D3)⋊C4—34no—
118C3×(C2×D3)⋊C4C2×D314yes—
119C3×(C2×D3)⋊C4C22×C314yes—
120C3×Dic3⋊C4—34no—
121C3×Dic3⋊C4—34no—
122C3×Dic3⋊C4—34no—
123C3×Dic3⋊C4—34no—
124C3×Dic3⋊C4—64no—
125C3×C4×Dic3—24no—
126C3×C4×Dic3—34no—
127C3×C4×Dic3—34no—
128C3×C4×Dic3C2×D314yescomplemented
129C3×C4×Dic3C22×C314yescomplemented
130#3724C22×C314yescomplemented
131(C2×D3)⋊Dic3C22×C314yes—
132Dic32C22×C314yescomplemented
133C22×C33C22×C412yes—
134C22×C33#4112yes—
135C22×C33#4112yes—
136C22×C33C2411yescharacteristic
137C2×C32×D3—28no—
138C2×C32×D3—22no—
139C2×C32×D3—22no—
140C2×C32×D3C22×C414yes—
141C33×C4—22no—
142C3×C3⋊Dic3—22no—
143C3×C3⋊Dic3C22×C414yes—
144C32×Dic3—22no—
145C32×Dic3—22no—
146C32×Dic3C22×C414yes—
147C23×C3×C4—91no—
148C23×Dic3—31no—
149C22×C4×D3—31no—
150C3×#117—98no—
151C2×C3×C4⋊C4—91no—
152C2×C3×C4⋊C4—91no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—61no—
156C2×C3×C22⋊C4—91no—
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×C3×C42—61no—
160C2×C3×C42—91no—
161C2×#217—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4C3×D311yescharacteristic
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—61no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3C3×D311yescharacteristic, complemented
172#877—38no—
173#872—38no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—34no—
178C23×C32—32no—
179C23×C32—41no—
180C23×C32—62no—
181C23×C32—62no—
182C23×C32C22×D311yescharacteristic
183C23×C32C22×D311yescharacteristic
184C23×C32C23×C311yescharacteristic
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—24no—
190C22×C3×D3—22no—
191C22×C3×D3—42no—
192C22×C3×D3—42no—
193C22×C3×D3C4×D314yes—
194C22×C3×D3C2×C3×C414yes—
195C22×C3×D3C22×D312yes—
196C22×C3×D3C23×C312yes—
197C2×C32×C4—22no—
198C2×C32×C4—24no—
199C2×C32×C4—22no—
200C2×C32×C4—22no—
201C2×C32×C4—22no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—34no—
205C2×C32×C4—32no—
206C2×C32×C4—32no—
207C2×C32×C4—32no—
208C2×C32×C4—42no—
209C2×C32×C4—42no—
210C2×C32×C4—42no—
211C2×C32×C4—44no—
212C2×C32×C4—62no—
213C2×C32×C4—62no—
214C2×C32×C4C22×D312yes—
215C2×C32×C4C22×D312yes—
216C2×C32×C4C23×C312yes—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3C2×C3×C414yes—
219C2×C3⋊Dic3C23×C312yes—
220C2×C3⋊Dic3C23×C312yes—
221C2×C3×Dic3—24no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—24no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—34no—
231C2×C3×Dic3—34no—
232C2×C3×Dic3—32no—
233C2×C3×Dic3—32no—
234C2×C3×Dic3—316no—
235C2×C3×Dic3—32no—
236C2×C3×Dic3—32no—
237C2×C3×Dic3—42no—
238C2×C3×Dic3—62no—
239C2×C3×Dic3—64no—
240C2×C3×Dic3—62no—
241C2×C3×Dic3—62no—
242C2×C3×Dic3—62no—
243C2×C3×Dic3—122no—
244C2×C3×Dic3C4×D314yes—
245C2×C3×Dic3C2×C3×C414yes—
246C2×C3×Dic3C22×D312yes—
247C2×C3×Dic3C22×D312yes—
248C2×C3×Dic3C22×D312yes—
249C2×C3×Dic3C23×C312yes—
250C2×C3×Dic3C23×C312yes—
251C2×C3×Dic3C23×C312yes—
252C3×C4×D3—316no—
253D3×Dic3C2×C3×C4116yescomplemented
254C2×#117—91noSylow
255C2×C33#11714yescomplemented
256C2×C33C23×C411yescharacteristic
257C2×C33C2×#4111yescharacteristic
258C2×C33C2×#4111yescharacteristic
259C32×D3—24no—
260C24×C3—31no—
261C24×C3—31no—
262C24×C3—61no—
263C23×D3C2×C3×D311yescharacteristic
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—41no—
274C22×C3×C4—61no—
275C22×C3×C4—61no—
276C22×C3×C4—61no—
277C22×C3×C4—94no—
278C22×C3×C4—98no—
279C22×C3×C4—91no—
280C22×C3×C4—91no—
281C22×C3×C4D3211yescharacteristic
282C22×C3×C4C2×C3×D311yescharacteristic
283C22×C3×C4C2×C3×D311yescharacteristic
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—38no—
287C22×Dic3—34no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3C2×C3×D311yescharacteristic
293C22×Dic3C2×C3×D311yescharacteristic
294C22×Dic3C2×C3×D311yescharacteristic
295C2×C4×D3—38no—
296C2×C4×D3—34no—
297C3×C4⋊C4—94no—
298C3×C4⋊C4—94no—
299C3×C22⋊C4—34no—
300C3×C22⋊C4—34no—
301C3×C22⋊C4—64no—
302C3×C22⋊C4—94no—
303C3×C42—34no—
304C3×C42—34no—
305C3×C42—64no—
306C3×C42—94no—
307#217—34no—
308(C2×D3)⋊C4—34no—
309(C2×D3)⋊C4C2×C3×D314yes—
310Dic3⋊C4—34no—
311Dic3⋊C4—34no—
312Dic3⋊C4—34no—
313Dic3⋊C4—34no—
314Dic3⋊C4—64no—
315C4×Dic3—34no—
316C4×Dic3—34no—
317C4×Dic3C2×C3×D314yescomplemented
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—34no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32—41no—
335C22×C32—68no—
336C22×C32—62no—
337C22×C32—62no—
338C22×C32C2×C4×D312yes—
339C22×C32C2×C4×D312yes—
340C22×C32#23512yes—
341C22×C32#23512yes—
342C22×C32#23712yes—
343C22×C32#23712yes—
344C22×C32C22×C3×C412yes—
345C22×C32C3×#4112yes—
346C22×C32C3×#4112yes—
347C22×C32C23×D311yescharacteristic
348C22×C32C23×D311yescharacteristic
349C22×C32C24×C311yescharacteristic
350C2×C3×D3—28no—
351C2×C3×D3—28no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—22no—
356C2×C3×D3—24no—
357C2×C3×D3—48no—
358C2×C3×D3—42no—
359C2×C3×D3—42no—
360C2×C3×D3C2×C4×D314yes—
361C2×C3×D3C22×C3×C414yes—
362C32×C4—22no—
363C32×C4—24no—
364C32×C4—22no—
365C32×C4—22no—
366C32×C4—34no—
367C32×C4—42no—
368C32×C4—42no—
369C32×C4—44no—
370C32×C4—62no—
371C32×C4—62no—
372C3⋊Dic3—22no—
373C3⋊Dic3C22×C3×C414yes—
374C3×Dic3—24no—
375C3×Dic3—22no—
376C3×Dic3—22no—
377C3×Dic3—22no—
378C3×Dic3—22no—
379C3×Dic3—24no—
380C3×Dic3—34no—
381C3×Dic3—34no—
382C3×Dic3—42no—
383C3×Dic3—64no—
384C3×Dic3—62no—
385C3×Dic3—62no—
386C3×Dic3—122no—
387C3×Dic3C2×C4×D314yes—
388C3×Dic3C22×C3×C414yes—
389C23×C4—91no—
390#117—98no—
391C2×C4⋊C4—91no—
392C2×C4⋊C4—91no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—91no—
395C2×C42—31no—
396C2×C42—91no—
397C33C2×#11711yescharacteristic, complemented, Sylow
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—32no—
402C23×C3—32no—
403C23×C3—34no—
404C23×C3—34no—
405C23×C3—41no—
406C23×C3—62no—
407C23×C3—64no—
408C23×C3—62no—
409C23×C3—62no—
410C23×C3—62no—
411C23×C3—62no—
412C23×C3—122no—
413C23×C3—122no—
414C23×C3C2×D3211yescharacteristic
415C23×C3C22×C3×D311yescharacteristic
416C23×C3C22×C3×D311yescharacteristic
417C22×D3—22no—
418C22×D3—22no—
419C22×D3C3×C4×D314yes—
420C22×D3C22×C3×D312yes—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—34no—
431C2×C3×C4—34no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—44no—
439C2×C3×C4—42no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—64no—
443C2×C3×C4—62no—
444C2×C3×C4—64no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—916no—
450C2×C3×C4—92no—
451C2×C3×C4—94no—
452C2×C3×C4—92no—
453C2×C3×C4—122no—
454C2×C3×C4—182no—
455C2×C3×C4C2×D3212yes—
456C2×C3×C4C22×C3×D312yes—
457C2×C3×C4C22×C3×D312yes—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—32no—
461C2×Dic3—32no—
462C2×Dic3—34no—
463C2×Dic3—34no—
464C2×Dic3—316no—
465C2×Dic3—32no—
466C2×Dic3—32no—
467C2×Dic3—64no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—122no—
473C2×Dic3C3×C4×D314yes—
474C2×Dic3C22×C3×D312yes—
475C2×Dic3C22×C3×D312yes—
476C2×Dic3C22×C3×D312yes—
477C4×D3—316no—
478C2×C32—24no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—24no—
489C2×C32—24no—
490C2×C32—44no—
491C2×C32—41no—
492C2×C32—41no—
493C2×C32—41no—
494C2×C32—64no—
495C2×C32#87214yescomplemented
496C2×C32#87714yescomplemented
497C2×C32C3×#11714yescomplemented
498C2×C32C22×C4×D311yescharacteristic
499C2×C32C22×C4×D311yescharacteristic
500C2×C32C2×#23511yescharacteristic
501C2×C32C2×#23511yescharacteristic
502C2×C32C2×#23711yescharacteristic
503C2×C32C2×#23711yescharacteristic
504C2×C32C23×C3×C411yescharacteristic
505C2×C32C2×C3×#4111yescharacteristic
506C2×C32C2×C3×#4111yescharacteristic
507C3×D3—24no—
508C3×D3—24no—
509C3×D3—44no—
510C24—31no—
511C22×C4—31no—
512C22×C4—31no—
513C22×C4—31no—
514C22×C4—94no—
515C22×C4—98no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4C3×D3211yescharacteristic
519C4⋊C4—94no—
520C4⋊C4—94no—
521C22⋊C4—34no—
522C22⋊C4—94no—
523C42—34no—
524C42—94no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—34no—
538C22×C3—34no—
539C22×C3—41no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—64no—
544C22×C3—62no—
545C22×C3—62no—
546C22×C3—62no—
547C22×C3—62no—
548C22×C3—68no—
549C22×C3—68no—
550C22×C3—122no—
551C22×C3—128no—
552C22×C3—122no—
553C22×C3#379512yes—
554C22×C3C4×D3212yes—
555C22×C3#380412yes—
556C22×C3C2×C3×C4×D312yes—
557C22×C3C2×C3×C4×D312yes—
558C22×C3C3×#23512yes—
559C22×C3C3×#23512yes—
560C22×C3C3×#23712yes—
561C22×C3C3×#23712yes—
562C22×C3C22×D3211yescharacteristic
563C22×C3C23×C3×D311yescharacteristic
564C22×C3C23×C3×D311yescharacteristic
565C2×D3—28no—
566C2×D3—22no—
567C2×D3—22no—
568C2×D3C2×C3×C4×D314yes—
569C3×C4—24no—
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—34no—
574C3×C4—34no—
575C3×C4—42no—
576C3×C4—42no—
577C3×C4—44no—
578C3×C4—64no—
579C3×C4—64no—
580C3×C4—62no—
581C3×C4—62no—
582C3×C4—62no—
583C3×C4—62no—
584C3×C4—94no—
585C3×C4—122no—
586C3×C4—182no—
587Dic3—22no—
588Dic3—22no—
589Dic3—34no—
590Dic3—34no—
591Dic3—64no—
592Dic3—62no—
593Dic3—62no—
594Dic3—122no—
595Dic3C2×C3×C4×D314yes—
596C32—21no—
597C32—21no—
598C32—21no—
599C32—41no—
600C32C2×#87211yescharacteristic, complemented
601C32C2×#87711yescharacteristic, complemented
602C32C2×C3×#11711yescharacteristic, complemented
603C23—32no—
604C23—34no—
605C23—62no—
606C23—62no—
607C23C2×C3×D3211yescharacteristic
608C2×C4—22no—
609C2×C4—32no—
610C2×C4—34no—
611C2×C4—32no—
612C2×C4—32no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—916no—
616C2×C4—92no—
617C2×C4—94no—
618C2×C4—92no—
619C2×C4—182no—
620C2×C4C2×C3×D3212yes—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—24no—
625C2×C3—24no—
626C2×C3—24no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—41no—
634C2×C3—44no—
635C2×C3—41no—
636C2×C3—41no—
637C2×C3—64no—
638C2×C3—64no—
639C2×C3—124no—
640C2×C3#6387714yesdirect product factor
641C2×C3C3×#87214yescomplemented
642C2×C3C3×#87714yescomplemented
643C2×C3C2×#379511yescharacteristic
644C2×C3C2×C4×D3211yescharacteristic
645C2×C3C2×#380411yescharacteristic
646C2×C3C22×C3×C4×D311yescharacteristic
647C2×C3C22×C3×C4×D311yescharacteristic
648C2×C3C2×C3×#23511yescharacteristic
649C2×C3C2×C3×#23511yescharacteristic
650C2×C3C2×C3×#23711yescharacteristic
651C2×C3C2×C3×#23711yescharacteristic
652D3—24no—
653C22—34no—
654C22—62no—
655C22—68no—
656C22—62no—
657C22C3×#379512yes—
658C22C3×C4×D3212yes—
659C22C3×#380412yes—
660C22C22×C3×D3211yescharacteristic
661C4—22no—
662C4—34no—
663C4—62no—
664C4—62no—
665C4—94no—
666C4—182no—
667C3—21no—
668C3—21no—
669C3—21no—
670C3—41no—
671C3C2×#6387711yescharacteristic, direct product factor
672C3C2×C3×#87211yescharacteristic, complemented
673C3C2×C3×#87711yescharacteristic, complemented
674C2—64no—
675C2C3×#6387714yesdirect product factor
676C2C2×C3×#379511yescharacteristic
677C2C2×C3×C4×D3211yescharacteristic
678C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC22×C32C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#117
LCSG ▷ C2×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×#3750C2semidirect
4. C2×C32×C4×Dic3C2semidirect
5. C2×C3×#3724C2semidirect
7. C2×C3×Dic32C2semidirect
8. C3×#63877C2direct (N × H)
11. C2×#63877C3direct (N × H)
19. C2×C3×D3×Dic3C4semidirect
21. C3×#3750C22semidirect
23. C32×C4×Dic3C22semidirect
24. C3×#3724C22semidirect
26. C3×Dic32C22semidirect
32. C2×#3750C2×C3semidirect
46. C2×C3×C4×Dic3D3semidirect
47. C2×C3×C4×Dic3C2×C3semidirect
50. C2×#3724C2×C3semidirect
52. C2×Dic32C2×C3semidirect
53. #63877C2×C3direct (N × H)
71. C3×D3×Dic3C2×C4semidirect
110. C2×D3×Dic3C3×C4semidirect
114. #3750C22×C3semidirect
128. C3×C4×Dic3C2×D3semidirect
129. C3×C4×Dic3C22×C3semidirect
130. #3724C22×C3semidirect
132. Dic32C22×C3semidirect
171. C2×C4×Dic3C3×D3semidirect
253. D3×Dic3C2×C3×C4semidirect
255. C2×C33#117semidirect
317. C4×Dic3C2×C3×D3semidirect
397. C33C2×#117semidirect
495. C2×C32#872semidirect
496. C2×C32#877semidirect
497. C2×C32C3×#117semidirect
600. C32C2×#872semidirect
601. C32C2×#877semidirect
602. C32C2×C3×#117semidirect
640. C2×C3#63877direct (N × H)
641. C2×C3C3×#872semidirect
642. C2×C3C3×#877semidirect
671. C3C2×#63877direct (N × H)
672. C3C2×C3×#872semidirect
673. C3C2×C3×#877semidirect
675. C2C3×#63877direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Dic32
C2×C3×#37502
C2×C32×(C2×D3)⋊C42
C2×C32×C4×Dic32
C2×C3×#37242
C2×C3×(C2×D3)⋊Dic32
C2×C3×Dic322
C3×#638772
C2×C3×#8773
C2×C3×#8723
C2×#638773