Finite Group Databasebeta

← C2×C3×#63568 #13158139

Subgroups — C2×C3×#63568 #13158139

Order 1728.

1074 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic
2C2×C3×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C32×#208C211yesmaximal, characteristic, complemented
4C3×#63568C214yesmaximal, direct product factor
5C2×C3×#837—31nomaximal
6C2×C3×#825—31nomaximal
7C2×#63568C311yesmaximal, characteristic, direct product factor
8C22×C33×C4C2211yescharacteristic
9C22×C3×C3⋊Dic3—21no—
10C2×C32×#67—21no—
11C32×#235—21no—
12C32×#235—21no—
13C32×#235C412yescomplemented
14C32×#235C2212yes—
15C2×C32×D12C411yescharacteristic, complemented
16C2×C32×C4×D3—21no—
17C2×C32×Dic6C411yescharacteristic, complemented
18C3×C4×C3⋊Dic3—21no—
19C3×C4×C3⋊Dic3C2212yescomplemented
20C32×#208—21no—
21C32×#208C2212yescomplemented
22C2×C32×C3⋊C8—21no—
23C2×C32×#41—31no—
24C2×C3×#235—21no—
25C2×C3×#235D311yescharacteristic
26C2×C3×#235C2×C311yescharacteristic
27C2×C32×M16—31no—
28C2×C4×C3⋊Dic3C2×C311yescharacteristic, complemented
29C2×C3×C4×Dic3—31no—
30C2×C3×C4×Dic3—31no—
31C2×C3×C4×Dic3—61no—
32C2×C3×#208—21no—
33C2×C3×#208D311yescharacteristic, complemented
34C2×C3×#208C2×C311yescharacteristic, complemented
35C3×#837—34no—
36C3×#825—34no—
37#63568C2×C314yesdirect product factor
38C23×C33D411yescharacteristic
39C22×C32×D3—21no—
40C2×C33×C4C2×C411yescharacteristic
41C2×C33×C4C2×C411yescharacteristic
42C2×C33×C4D411yescharacteristic
43C2×C33×C4D411yescharacteristic
44C2×C33×C4D411yescharacteristic
45C2×C33×C4C2311yescharacteristic
46C2×C3×C3⋊Dic3—24no—
47C2×C3×C3⋊Dic3—22no—
48C32×#67—22no—
49C32×#67—22no—
50C2×C32×Dic3—21no—
51C32×D12—21no—
52C32×D12C2×C412yescomplemented
53C32×C4×D3—22no—
54C32×C4×D3—22no—
55C32×Dic6—21no—
56C32×Dic6C2×C412yescomplemented
57C32×C3⋊C8—22no—
58C2×C3×#104—91no—
59C2×#837—31no—
60C2×#825—31no—
61C32×#41—32no—
62C32×#41—32no—
63C32×#41—61no—
64C32×#41—61no—
65C2×C32×Q8—31no—
66C2×C32×D4—31no—
67C2×C32×D4—61no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4—41no—
72C22×C32×C4—61no—
73C22×C32×C4C2×D311yescharacteristic
74C22×C32×C4C2×D311yescharacteristic
75C22×C32×C4C22×C311yescharacteristic
76C22×C3⋊Dic3—21no—
77C2×C3×#67—22no—
78C2×C3×#67—21no—
79C2×C3×#67—21no—
80C22×C3×Dic3—62no—
81C22×C3×Dic3—61no—
82C22×C3×Dic3—61no—
83C3×#235—22no—
84C3×#235—22no—
85C3×#235—22no—
86C3×#235—22no—
87C3×#235—21no—
88C3×#235—21no—
89C3×#235—21no—
90C3×#235—21no—
91C3×#235Dic312yescomplemented
92C3×#235C3×C412yescomplemented
93C3×#235C2×D312yes—
94C3×#235C22×C312yes—
95C2×C3×D12—21no—
96C2×C3×D12Dic311yescharacteristic, complemented
97C2×C3×D12C3×C411yescharacteristic, complemented
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6Dic311yescharacteristic, complemented
103C2×C3×Dic6C3×C411yescharacteristic, complemented
104C32×M16—32no—
105C32×M16—61no—
106C2×C32×C8—61no—
107C4×C3⋊Dic3—21no—
108C4×C3⋊Dic3C22×C312yescomplemented
109C3×C4×Dic3—32no—
110C3×C4×Dic3—32no—
111C3×C4×Dic3—62no—
112C3×C4×Dic3—62no—
113C3×C4×Dic3—61no—
114C3×C4×Dic3—61no—
115C3×#208—22no—
116C3×#208—22no—
117C3×#208—21no—
118C3×#208—21no—
119C3×#208C2×D312yescomplemented
120C3×#208C22×C312yescomplemented
121C2×C3×C3⋊C8—22no—
122C2×C3×C3⋊C8—21no—
123C2×C3×C3⋊C8—21no—
124C22×C33—22no—
125C22×C33C22⋊C411yescharacteristic
126C22×C33C22⋊C411yescharacteristic
127C22×C33C2×D411yescharacteristic
128C2×C32×D3—22no—
129C2×C32×D3—42no—
130C33×C4C22⋊C411yescharacteristic
131C33×C4C22⋊C411yescharacteristic
132C33×C4C22×C411yescharacteristic
133C33×C4C2×D411yescharacteristic
134C3×C3⋊Dic3—24no—
135C32×Dic3—22no—
136C2×C3×#41—31no—
137C2×C3×#41—31no—
138C2×C3×#41—61no—
139C2×#235C3×D311yescharacteristic
140C2×C3×M16—31no—
141C2×C3×M16—31no—
142C2×C3×M16—61no—
143C2×C3×C42—91no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—31no—
146C2×C4×Dic3—61no—
147C2×#208C3×D311yescharacteristic, complemented
148C3×#104—94no—
149#837—34no—
150#825—34no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—41no—
155C23×C32—61no—
156C23×C32D1211yescharacteristic
157C23×C32#6711yescharacteristic
158C23×C32C3×D411yescharacteristic
159C22×C3×D3—22no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C32×Q8—32no—
163C32×Q8—61no—
164C32×D4—32no—
165C32×D4—62no—
166C32×D4—62no—
167C32×D4—61no—
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—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—41no—
187C2×C32×C4—41no—
188C2×C32×C4—41no—
189C2×C32×C4—41no—
190C2×C32×C4—41no—
191C2×C32×C4—41no—
192C2×C32×C4—61no—
193C2×C32×C4—62no—
194C2×C32×C4—62no—
195C2×C32×C4C4×D311yescharacteristic
196C2×C32×C4C4×D311yescharacteristic
197C2×C32×C4D1211yescharacteristic
198C2×C32×C4C2×Dic311yescharacteristic
199C2×C32×C4C2×Dic311yescharacteristic
200C2×C32×C4#6711yescharacteristic
201C2×C32×C4#6711yescharacteristic
202C2×C32×C4#6711yescharacteristic
203C2×C32×C4#6711yescharacteristic
204C2×C32×C4#6711yescharacteristic
205C2×C32×C4C2×C3×C411yescharacteristic
206C2×C32×C4C2×C3×C411yescharacteristic
207C2×C32×C4C3×D411yescharacteristic
208C2×C32×C4C3×D411yescharacteristic
209C2×C32×C4C3×D411yescharacteristic
210C2×C32×C4C22×D311yescharacteristic
211C2×C32×C4C22×D311yescharacteristic
212C2×C32×C4C23×C311yescharacteristic
213C2×C3⋊Dic3—24no—
214C2×C3⋊Dic3—22no—
215C3×#67—24no—
216C3×#67—24no—
217C3×#67—22no—
218C3×#67—22no—
219C3×#67—22no—
220C3×#67—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—64no—
225C2×C3×Dic3—68no—
226C2×C3×Dic3—64no—
227C2×C3×Dic3—64no—
228C2×C3×Dic3—62no—
229C2×C3×Dic3—62no—
230C3×D12—22no—
231C3×D12—21no—
232C3×D12—21no—
233C3×D12—22no—
234C3×D12C2×Dic312yescomplemented
235C3×D12C2×C3×C412yescomplemented
236C3×C4×D3—24no—
237C3×C4×D3—24no—
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×C4×D3—22no—
241C3×C4×D3—22no—
242C3×Dic6—22no—
243C3×Dic6—21no—
244C3×Dic6—21no—
245C3×Dic6—22no—
246C3×Dic6C2×Dic312yescomplemented
247C3×Dic6C2×C3×C412yescomplemented
248C32×C8—62no—
249C3×C3⋊C8—24no—
250C3×C3⋊C8—22no—
251C3×C3⋊C8—22no—
252C2×#104—91noSylow
253C2×C33—21no—
254C2×C33—21no—
255C2×C33#10412yescomplemented
256C2×C33C2×C22⋊C411yescharacteristic
257C32×D3—42no—
258C3×#41—32no—
259C3×#41—32no—
260C3×#41—32no—
261C3×#41—32no—
262C3×#41—62no—
263C3×#41—62no—
264C3×#41—62no—
265C3×#41—62no—
266C3×#41—61no—
267C3×#41—61no—
268C3×#41—61no—
269C3×#41—61no—
270C2×C3×Q8—31no—
271C2×C3×Q8—31no—
272C2×C3×Q8—61no—
273C2×C3×D4—31no—
274C2×C3×D4—31no—
275C2×C3×D4—61no—
276C2×C3×D4—62no—
277C2×C3×D4—61no—
278C2×C3×D4—61no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—41no—
283C22×C3×C4—62no—
284C22×C3×C4—61no—
285C22×C3×C4—61no—
286C22×C3×C4—181no—
287C22×C3×C4D3211yescharacteristic
288C22×C3×C4C2×C3×D311yescharacteristic
289C22×C3×C4C2×C3×D311yescharacteristic
290C2×#67—21no—
291C22×Dic3—62no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294#235—21no—
295#235—21no—
296#235C3×Dic312yescomplemented
297#235C2×C3×D312yes—
298C2×D12C3×Dic311yescharacteristic, complemented
299C2×C4×D3—21no—
300C2×Dic6C3×Dic311yescharacteristic, complemented
301C3×M16—32no—
302C3×M16—32no—
303C3×M16—62no—
304C3×M16—62no—
305C3×M16—61no—
306C3×M16—61no—
307C2×C3×C8—62no—
308C2×C3×C8—61no—
309C2×C3×C8—61no—
310C3×C42—92no—
311C3×C42—181no—
312C4×Dic3—32no—
313C4×Dic3—32no—
314C4×Dic3—62no—
315C4×Dic3—62no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318#208—21no—
319#208C2×C3×D312yescomplemented
320C2×C3⋊C8—21no—
321C22×C32—22no—
322C22×C32—24no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—42no—
338C22×C32—42no—
339C22×C32—44no—
340C22×C32—62no—
341C22×C32—122no—
342C22×C32(C2×D3)⋊C411yescharacteristic
343C22×C32(C2×D3)⋊C411yescharacteristic
344C22×C32#21711yescharacteristic
345C22×C32#21711yescharacteristic
346C22×C32C3×C22⋊C411yescharacteristic
347C22×C32C3×C22⋊C411yescharacteristic
348C22×C32C2×D1211yescharacteristic
349C22×C32C2×#6711yescharacteristic
350C22×C32C2×C3×D411yescharacteristic
351C2×C3×D3—24no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—44no—
355C2×C3×D3—42no—
356C2×C3×D3—42no—
357C32×C4—21no—
358C32×C4—21no—
359C32×C4—21no—
360C32×C4—21no—
361C32×C4—21no—
362C32×C4—21no—
363C32×C4—21no—
364C32×C4—21no—
365C32×C4—21no—
366C32×C4—21no—
367C32×C4—21no—
368C32×C4—21no—
369C32×C4—41no—
370C32×C4—41no—
371C32×C4—41no—
372C32×C4—41no—
373C32×C4—62no—
374C32×C4(C2×D3)⋊C411yescharacteristic
375C32×C4(C2×D3)⋊C411yescharacteristic
376C32×C4#21711yescharacteristic
377C32×C4#21711yescharacteristic
378C32×C4C3×C22⋊C411yescharacteristic
379C32×C4C3×C22⋊C411yescharacteristic
380C32×C4C2×C4×D311yescharacteristic
381C32×C4C22×Dic311yescharacteristic
382C32×C4C2×#6711yescharacteristic
383C32×C4C2×#6711yescharacteristic
384C32×C4C22×C3×C411yescharacteristic
385C32×C4C2×C3×D411yescharacteristic
386C3⋊Dic3—24no—
387C3×Dic3—24no—
388C3×Dic3—22no—
389C3×Dic3—22no—
390C3×Dic3—68no—
391C3×Dic3—64no—
392C3×Dic3—64no—
393C2×#41—31no—
394C2×M16—31no—
395C2×C42—91no—
396#104—94no—
397C33C2×#10411yescharacteristic, complemented, Sylow
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—41no—
402C23×C3—62no—
403C23×C3—61no—
404C23×C3—61no—
405C23×C3#62611yescharacteristic
406C23×C3C3×D1211yescharacteristic
407C23×C3C3×#6711yescharacteristic
408C22×D3—21no—
409C3×Q8—32no—
410C3×Q8—32no—
411C3×Q8—62no—
412C3×Q8—62no—
413C3×Q8—61no—
414C3×Q8—61no—
415C3×D4—32no—
416C3×D4—32no—
417C3×D4—62no—
418C3×D4—62no—
419C3×D4—64no—
420C3×D4—64no—
421C3×D4—62no—
422C3×D4—62no—
423C3×D4—62no—
424C3×D4—62no—
425C3×D4—61no—
426C3×D4—61no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—64no—
452C2×C3×C4—64no—
453C2×C3×C4—62no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—184no—
461C2×C3×C4—182no—
462C2×C3×C4D3×Dic311yescharacteristic
463C2×C3×C4D3×Dic311yescharacteristic
464C2×C3×C4#62511yescharacteristic
465C2×C3×C4#62511yescharacteristic
466C2×C3×C4#62611yescharacteristic
467C2×C3×C4C3×C4×D311yescharacteristic
468C2×C3×C4C3×C4×D311yescharacteristic
469C2×C3×C4C3×D1211yescharacteristic
470C2×C3×C4C2×C3×Dic311yescharacteristic
471C2×C3×C4C2×C3×Dic311yescharacteristic
472C2×C3×C4C3×#6711yescharacteristic
473C2×C3×C4C3×#6711yescharacteristic
474C2×C3×C4C3×#6711yescharacteristic
475C2×C3×C4C3×#6711yescharacteristic
476C2×C3×C4C3×#6711yescharacteristic
477C2×C3×C4C2×D3211yescharacteristic
478C2×C3×C4C22×C3×D311yescharacteristic
479C2×C3×C4C22×C3×D311yescharacteristic
480#67—22no—
481#67—22no—
482C2×Dic3—21no—
483C2×Dic3—64no—
484C2×Dic3—68no—
485C2×Dic3—64no—
486C2×Dic3—64no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489D12—21no—
490D12C2×C3×Dic312yescomplemented
491C4×D3—22no—
492C4×D3—22no—
493Dic6—21no—
494Dic6C2×C3×Dic312yescomplemented
495C3×C8—64no—
496C3×C8—62no—
497C3×C8—62no—
498C3⋊C8—22no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—22no—
502C2×C32—22no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—22no—
510C2×C32—22no—
511C2×C32—22no—
512C2×C32—21no—
513C2×C32—42no—
514C2×C32—41no—
515C2×C32—41no—
516C2×C32—41no—
517C2×C32—41no—
518C2×C32—41no—
519C2×C32—42no—
520C2×C32—42no—
521C2×C32—122no—
522C2×C32#82512yescomplemented
523C2×C32#83712yescomplemented
524C2×C32C3×#10412yescomplemented
525C2×C32C2×(C2×D3)⋊C411yescharacteristic
526C2×C32C2×#21711yescharacteristic
527C2×C32C2×C3×C22⋊C411yescharacteristic
528C3×D3—44no—
529C3×D3—42no—
530C3×D3—42no—
531#41—32no—
532#41—32no—
533#41—61no—
534#41—61no—
535C2×Q8—31no—
536C2×D4—31no—
537C2×D4—61no—
538C22×C4—61no—
539C22×C4—181no—
540C22×C4C3×D3211yescharacteristic
541M16—32no—
542M16—61no—
543C2×C8—61no—
544C42—92no—
545C42—181no—
546C22×C3—24no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—44no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—64no—
566C22×C3—62no—
567C22×C3—62no—
568C22×C3—124no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3(C2×D3)⋊Dic311yescharacteristic
572C22×C3(C2×D3)⋊Dic311yescharacteristic
573C22×C3C3×(C2×D3)⋊C411yescharacteristic
574C22×C3C3×(C2×D3)⋊C411yescharacteristic
575C22×C3C3×#21711yescharacteristic
576C22×C3C3×#21711yescharacteristic
577C22×C3C2×#62611yescharacteristic
578C22×C3C2×C3×D1211yescharacteristic
579C22×C3C2×C3×#6711yescharacteristic
580C2×D3—22no—
581C2×D3—42no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—64no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4—184no—
602C3×C4(C2×D3)⋊Dic311yescharacteristic
603C3×C4(C2×D3)⋊Dic311yescharacteristic
604C3×C4C3×(C2×D3)⋊C411yescharacteristic
605C3×C4C3×(C2×D3)⋊C411yescharacteristic
606C3×C4C3×#21711yescharacteristic
607C3×C4C3×#21711yescharacteristic
608C3×C4C2×D3×Dic311yescharacteristic
609C3×C4C2×#62511yescharacteristic
610C3×C4C2×C3×C4×D311yescharacteristic
611C3×C4C22×C3×Dic311yescharacteristic
612C3×C4C2×C3×#6711yescharacteristic
613C3×C4C2×C3×#6711yescharacteristic
614Dic3—22no—
615Dic3—68no—
616Dic3—64no—
617Dic3—64no—
618C32—21no—
619C32—21no—
620C32—21no—
621C32—41no—
622C32C2×#82511yescharacteristic, complemented
623C32C2×#83711yescharacteristic, complemented
624C32C2×C3×#10411yescharacteristic, complemented
625C23—61no—
626C23C3×#62611yescharacteristic
627Q8—32no—
628Q8—61no—
629D4—32no—
630D4—62no—
631D4—62no—
632D4—61no—
633C2×C4—61no—
634C2×C4—62no—
635C2×C4—62no—
636C2×C4—184no—
637C2×C4—182no—
638C2×C4C3×D3×Dic311yescharacteristic
639C2×C4C3×D3×Dic311yescharacteristic
640C2×C4C3×#62511yescharacteristic
641C2×C4C3×#62511yescharacteristic
642C2×C4C3×#62611yescharacteristic
643C2×C4C2×C3×D3211yescharacteristic
644C8—62no—
645C2×C3—22no—
646C2×C3—22no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—22no—
654C2×C3—22no—
655C2×C3—22no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—41no—
660C2×C3—41no—
661C2×C3—41no—
662C2×C3—41no—
663C2×C3—42no—
664C2×C3—42no—
665C2×C3—42no—
666C2×C3—41no—
667C2×C3—124no—
668C2×C3—122no—
669C2×C3—122no—
670C2×C3#6356812yesdirect product factor
671C2×C3C3×#82512yescomplemented
672C2×C3C3×#83712yescomplemented
673C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
674C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
675C2×C3C2×C3×#21711yescharacteristic
676D3—42no—
677C22—22no—
678C22—62no—
679C22—122no—
680C22C3×(C2×D3)⋊Dic311yescharacteristic
681C22C3×(C2×D3)⋊Dic311yescharacteristic
682C22C2×C3×#62611yescharacteristic
683C4—62no—
684C4—184no—
685C4C3×(C2×D3)⋊Dic311yescharacteristic
686C4C3×(C2×D3)⋊Dic311yescharacteristic
687C4C2×C3×D3×Dic311yescharacteristic
688C4C2×C3×#62511yescharacteristic
689C3—21no—
690C3—21no—
691C3—21no—
692C3—41no—
693C3C2×#6356811yescharacteristic, direct product factor
694C3C2×C3×#82511yescharacteristic, complemented
695C3C2×C3×#83711yescharacteristic, complemented
696C2—21no—
697C2—21no—
698C2—122no—
699C2C3×#6356812yesdirect product factor
700C2C2×C3×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC2×C3×C4#625
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC22×C33C22⋊C4
prime radicalC2×C32×#235C2
cosocleC2×C32×C4C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C3⋊Dic3C2semidirect
3. C2×C32×#208C2semidirect
4. C3×#63568C2direct (N × H)
7. C2×#63568C3direct (N × H)
13. C32×#235C4semidirect
15. C2×C32×D12C4semidirect
17. C2×C32×Dic6C4semidirect
19. C3×C4×C3⋊Dic3C22semidirect
21. C32×#208C22semidirect
28. C2×C4×C3⋊Dic3C2×C3semidirect
33. C2×C3×#208D3semidirect
34. C2×C3×#208C2×C3semidirect
37. #63568C2×C3direct (N × H)
52. C32×D12C2×C4semidirect
56. C32×Dic6C2×C4semidirect
91. C3×#235Dic3semidirect
92. C3×#235C3×C4semidirect
96. C2×C3×D12Dic3semidirect
97. C2×C3×D12C3×C4semidirect
102. C2×C3×Dic6Dic3semidirect
103. C2×C3×Dic6C3×C4semidirect
108. C4×C3⋊Dic3C22×C3semidirect
119. C3×#208C2×D3semidirect
120. C3×#208C22×C3semidirect
147. C2×#208C3×D3semidirect
234. C3×D12C2×Dic3semidirect
235. C3×D12C2×C3×C4semidirect
246. C3×Dic6C2×Dic3semidirect
247. C3×Dic6C2×C3×C4semidirect
255. C2×C33#104semidirect
296. #235C3×Dic3semidirect
298. C2×D12C3×Dic3semidirect
300. C2×Dic6C3×Dic3semidirect
319. #208C2×C3×D3semidirect
397. C33C2×#104semidirect
490. D12C2×C3×Dic3semidirect
494. Dic6C2×C3×Dic3semidirect
522. C2×C32#825semidirect
523. C2×C32#837semidirect
524. C2×C32C3×#104semidirect
622. C32C2×#825semidirect
623. C32C2×#837semidirect
624. C32C2×C3×#104semidirect
670. C2×C3#63568direct (N × H)
671. C2×C3C3×#825semidirect
672. C2×C3C3×#837semidirect
693. C3C2×#63568direct (N × H)
694. C3C2×C3×#825semidirect
695. C3C2×C3×#837semidirect
699. C2C3×#63568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C2×C3×C4×C3⋊Dic32
C2×C32×#2082
C3×#635682
C2×C3×#8373
C2×C3×#8253
C2×#635683