Finite Group Databasebeta

← C2×C3×#63570 #13158143

Subgroups — C2×C3×#63570 #13158143

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×C3×#3828C211yesmaximal, characteristic
2C2×C32×C4×Dic3C211yesmaximal, characteristic, complemented
3C2×C32×#208C211yesmaximal, characteristic, complemented
4C3×#63570C214yesmaximal, direct product factor
5C2×C3×#825—31nomaximal
6C2×C3×#805—31nomaximal
7C2×#63570C311yesmaximal, characteristic, direct product factor
8C22×C33×C4C2211yescharacteristic
9C2×C3×#638—21no—
10C3×#3828—21no—
11C3×#3828—21no—
12C3×#3828C412yescomplemented
13C3×#3828C2212yes—
14C2×C3×C4⋊(C3⋊D3)C411yescharacteristic, complemented
15C2×C3×C4×C3⋊D3—21no—
16C2×C3×#634C411yescharacteristic, complemented
17C22×C32×Dic3—21no—
18C32×C4×Dic3—21no—
19C32×C4×Dic3C2212yescomplemented
20C32×#208—21no—
21C32×#208C2212yescomplemented
22C2×C32×C3⋊C8—21no—
23C2×#3828C2×C311yescharacteristic
24C2×C3×#235—31no—
25C2×C3×#235—31no—
26C2×C3×#235—61no—
27C2×C32×M16—31no—
28C2×C32×C42—31no—
29C2×C3×C4×Dic3—21no—
30C2×C3×C4×Dic3D311yescharacteristic, complemented
31C2×C3×C4×Dic3C2×C311yescharacteristic, complemented
32C2×C3×#208—21no—
33C2×C3×#208D311yescharacteristic, complemented
34C2×C3×#208C2×C311yescharacteristic, complemented
35C3×#825—34no—
36C3×#805—34no—
37#63570C2×C314yesdirect product factor
38C23×C33D411yescharacteristic
39C22×C3×C3⋊D3—21no—
40C2×C33×C4C2×C411yescharacteristic
41C2×C33×C4C2×C411yescharacteristic
42C2×C33×C4D411yescharacteristic
43C2×C33×C4D411yescharacteristic
44C2×C33×C4D411yescharacteristic
45C2×C33×C4C2311yescharacteristic
46C3×#638—22no—
47C3×#638—22no—
48C2×C3×C3⋊Dic3—21no—
49C3×C4⋊(C3⋊D3)—21no—
50C3×C4⋊(C3⋊D3)C2×C412yescomplemented
51C3×C4×C3⋊D3—22no—
52C3×C4×C3⋊D3—22no—
53C3×#634—21no—
54C3×#634C2×C412yescomplemented
55C2×C32×Dic3—24no—
56C2×C32×Dic3—22no—
57C32×C3⋊C8—22no—
58C2×C3×#104—91no—
59C2×#825—31no—
60C2×#805—31no—
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4—41no—
65C22×C32×C4—61no—
66C22×C32×C4C2×D311yescharacteristic
67C22×C32×C4C2×D311yescharacteristic
68C22×C32×C4C22×C311yescharacteristic
69C2×#638—21no—
70#3828—21no—
71#3828—21no—
72#3828C3×C412yescomplemented
73#3828C22×C312yes—
74C2×C4⋊(C3⋊D3)C3×C411yescharacteristic, complemented
75C2×C4×C3⋊D3—21no—
76C2×#634C3×C411yescharacteristic, complemented
77C2×C3×#67—62no—
78C2×C3×#67—61no—
79C2×C3×#67—61no—
80C22×C3×Dic3—22no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C3×#235—32no—
84C3×#235—32no—
85C3×#235—32no—
86C3×#235—32no—
87C3×#235—62no—
88C3×#235—62no—
89C3×#235—62no—
90C3×#235—62no—
91C3×#235—61no—
92C3×#235—61no—
93C3×#235—61no—
94C3×#235—61no—
95C2×C3×D12—31no—
96C2×C3×D12—31no—
97C2×C3×D12—61no—
98C2×C3×C4×D3—62no—
99C2×C3×C4×D3—61no—
100C2×C3×C4×D3—61no—
101C2×C3×Dic6—31no—
102C2×C3×Dic6—31no—
103C2×C3×Dic6—61no—
104C32×M16—32no—
105C32×M16—61no—
106C2×C32×C8—61no—
107C32×C42—32no—
108C32×C42—61no—
109C3×C4×Dic3—22no—
110C3×C4×Dic3—22no—
111C3×C4×Dic3—21no—
112C3×C4×Dic3—21no—
113C3×C4×Dic3C2×D312yescomplemented
114C3×C4×Dic3C22×C312yescomplemented
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×C3×C3⋊D3—22no—
129C2×C3×C3⋊D3—42no—
130C33×C4C22⋊C411yescharacteristic
131C33×C4C22⋊C411yescharacteristic
132C33×C4C22×C411yescharacteristic
133C33×C4C2×D411yescharacteristic
134C3×C3⋊Dic3—22no—
135C32×Dic3—24no—
136C2×C3×#41—91no—
137C2×#235—31no—
138C2×#235—31no—
139C2×#235—61no—
140C2×C3×M16—31no—
141C2×C3×M16—31no—
142C2×C3×M16—61no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×C3×C42—61no—
146C2×C4×Dic3C3×D311yescharacteristic, complemented
147C2×#208C3×D311yescharacteristic, complemented
148C3×#104—94no—
149#825—34no—
150#805—34no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—41no—
155C23×C32D1211yescharacteristic
156C23×C32#6711yescharacteristic
157C23×C32C3×D411yescharacteristic
158C22×C3⋊D3—21no—
159C22×C3×D3—62no—
160C22×C3×D3—61no—
161C22×C3×D3—61no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
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—41no—
181C2×C32×C4—41no—
182C2×C32×C4—41no—
183C2×C32×C4—41no—
184C2×C32×C4—41no—
185C2×C32×C4—41no—
186C2×C32×C4—64no—
187C2×C32×C4—62no—
188C2×C32×C4C4×D311yescharacteristic
189C2×C32×C4C4×D311yescharacteristic
190C2×C32×C4C4×D311yescharacteristic
191C2×C32×C4C4×D311yescharacteristic
192C2×C32×C4D1211yescharacteristic
193C2×C32×C4D1211yescharacteristic
194C2×C32×C4D1211yescharacteristic
195C2×C32×C4#6711yescharacteristic
196C2×C32×C4#6711yescharacteristic
197C2×C32×C4#6711yescharacteristic
198C2×C32×C4C2×C3×C411yescharacteristic
199C2×C32×C4C2×C3×C411yescharacteristic
200C2×C32×C4C3×D411yescharacteristic
201C2×C32×C4C3×D411yescharacteristic
202C2×C32×C4C3×D411yescharacteristic
203C2×C32×C4C22×D311yescharacteristic
204C2×C32×C4C22×D311yescharacteristic
205C2×C32×C4C23×C311yescharacteristic
206#638—22no—
207#638—22no—
208C2×C3⋊Dic3—21no—
209C4⋊(C3⋊D3)—21no—
210C4⋊(C3⋊D3)C2×C3×C412yescomplemented
211C4×C3⋊D3—22no—
212C4×C3⋊D3—22no—
213#634—21no—
214#634C2×C3×C412yescomplemented
215C3×#67—64no—
216C3×#67—64no—
217C3×#67—62no—
218C3×#67—62no—
219C3×#67—62no—
220C3×#67—62no—
221C2×C3×Dic3—24no—
222C2×C3×Dic3—28no—
223C2×C3×Dic3—24no—
224C2×C3×Dic3—24no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—62no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—61no—
230C3×D12—32no—
231C3×D12—32no—
232C3×D12—62no—
233C3×D12—62no—
234C3×D12—61no—
235C3×D12—61no—
236C3×C4×D3—64no—
237C3×C4×D3—64no—
238C3×C4×D3—62no—
239C3×C4×D3—62no—
240C3×C4×D3—62no—
241C3×C4×D3—62no—
242C3×Dic6—32no—
243C3×Dic6—32no—
244C3×Dic6—62no—
245C3×Dic6—62no—
246C3×Dic6—61no—
247C3×Dic6—61no—
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
257C3×C3⋊D3—42no—
258C3×#41—92no—
259C3×#41—92no—
260C3×#41—181no—
261C3×#41—181no—
262C2×C3×Q8—91no—
263C2×C3×D4—91no—
264C2×C3×D4—181no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—41no—
269C22×C3×C4—62no—
270C22×C3×C4—61no—
271C22×C3×C4—61no—
272C22×C3×C4—181no—
273C22×C3×C4D3211yescharacteristic
274C22×C3×C4C2×C3×D311yescharacteristic
275C22×C3×C4C2×C3×D311yescharacteristic
276C2×#67—62no—
277C2×#67—61no—
278C2×#67—61no—
279C22×Dic3—21no—
280#235—32no—
281#235—32no—
282#235—32no—
283#235—32no—
284#235—62no—
285#235—62no—
286#235—62no—
287#235—62no—
288#235—61no—
289#235—61no—
290#235—61no—
291#235—61no—
292C2×D12—31no—
293C2×D12—31no—
294C2×D12—61no—
295C2×C4×D3—62no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
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—32no—
311C3×C42—32no—
312C3×C42—62no—
313C3×C42—62no—
314C3×C42—61no—
315C3×C42—61no—
316C4×Dic3—21no—
317C4×Dic3C2×C3×D312yescomplemented
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(C2×D3)⋊C411yescharacteristic
341C22×C32(C2×D3)⋊C411yescharacteristic
342C22×C32(C2×D3)⋊C411yescharacteristic
343C22×C32(C2×D3)⋊C411yescharacteristic
344C22×C32C3×C22⋊C411yescharacteristic
345C22×C32C3×C22⋊C411yescharacteristic
346C22×C32C2×D1211yescharacteristic
347C22×C32C2×#6711yescharacteristic
348C22×C32C2×C3×D411yescharacteristic
349C2×C3⋊D3—22no—
350C2×C3⋊D3—42no—
351C2×C3×D3—64no—
352C2×C3×D3—62no—
353C2×C3×D3—62no—
354C2×C3×D3—124no—
355C2×C3×D3—122no—
356C2×C3×D3—122no—
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—64no—
374C32×C4(C2×D3)⋊C411yescharacteristic
375C32×C4(C2×D3)⋊C411yescharacteristic
376C32×C4(C2×D3)⋊C411yescharacteristic
377C32×C4(C2×D3)⋊C411yescharacteristic
378C32×C4C3×C22⋊C411yescharacteristic
379C32×C4C3×C22⋊C411yescharacteristic
380C32×C4C2×C4×D311yescharacteristic
381C32×C4C2×C4×D311yescharacteristic
382C32×C4C2×D1211yescharacteristic
383C32×C4C2×#6711yescharacteristic
384C32×C4C22×C3×C411yescharacteristic
385C32×C4C2×C3×D411yescharacteristic
386C3⋊Dic3—22no—
387C3×Dic3—28no—
388C3×Dic3—24no—
389C3×Dic3—24no—
390C3×Dic3—64no—
391C3×Dic3—62no—
392C3×Dic3—62no—
393C2×#41—91no—
394C2×M16—31no—
395C2×C42—31no—
396#104—94no—
397C33C2×#10411yescharacteristic, complemented, Sylow
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—41no—
402C23×C3—181no—
403C23×C3#62611yescharacteristic
404C23×C3C3×D1211yescharacteristic
405C23×C3C3×#6711yescharacteristic
406C22×D3—62no—
407C22×D3—61no—
408C22×D3—61no—
409C3×Q8—92no—
410C3×Q8—181no—
411C3×D4—92no—
412C3×D4—182no—
413C3×D4—182no—
414C3×D4—181no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
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—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—64no—
440C2×C3×C4—68no—
441C2×C3×C4—64no—
442C2×C3×C4—64no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—181no—
446C2×C3×C4—182no—
447C2×C3×C4—182no—
448C2×C3×C4#62411yescharacteristic
449C2×C3×C4#62411yescharacteristic
450C2×C3×C4#62611yescharacteristic
451C2×C3×C4#62611yescharacteristic
452C2×C3×C4#62611yescharacteristic
453C2×C3×C4C3×C4×D311yescharacteristic
454C2×C3×C4C3×C4×D311yescharacteristic
455C2×C3×C4C3×C4×D311yescharacteristic
456C2×C3×C4C3×C4×D311yescharacteristic
457C2×C3×C4C3×D1211yescharacteristic
458C2×C3×C4C3×D1211yescharacteristic
459C2×C3×C4C3×D1211yescharacteristic
460C2×C3×C4C3×#6711yescharacteristic
461C2×C3×C4C3×#6711yescharacteristic
462C2×C3×C4C3×#6711yescharacteristic
463C2×C3×C4C2×D3211yescharacteristic
464C2×C3×C4C22×C3×D311yescharacteristic
465C2×C3×C4C22×C3×D311yescharacteristic
466#67—64no—
467#67—64no—
468#67—62no—
469#67—62no—
470#67—62no—
471#67—62no—
472C2×Dic3—24no—
473C2×Dic3—22no—
474C2×Dic3—62no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477D12—32no—
478D12—32no—
479D12—62no—
480D12—62no—
481D12—61no—
482D12—61no—
483C4×D3—64no—
484C4×D3—64no—
485C4×D3—62no—
486C4×D3—62no—
487C4×D3—62no—
488C4×D3—62no—
489Dic6—32no—
490Dic6—32no—
491Dic6—62no—
492Dic6—62no—
493Dic6—61no—
494Dic6—61no—
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#80512yescomplemented
522C2×C32#82512yescomplemented
523C2×C32C3×#10412yescomplemented
524C2×C32C2×(C2×D3)⋊C411yescharacteristic
525C2×C32C2×(C2×D3)⋊C411yescharacteristic
526C2×C32C2×C3×C22⋊C411yescharacteristic
527C3⋊D3—42no—
528C3×D3—124no—
529C3×D3—122no—
530C3×D3—122no—
531#41—92no—
532#41—92no—
533#41—181no—
534#41—181no—
535C2×Q8—91no—
536C2×D4—91no—
537C2×D4—181no—
538C22×C4—61no—
539C22×C4—181no—
540C22×C4C3×D3211yescharacteristic
541M16—32no—
542M16—61no—
543C2×C8—61no—
544C42—32no—
545C42—61no—
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—182no—
566C22×C3—362no—
567C22×C3#372211yescharacteristic
568C22×C3#372211yescharacteristic
569C22×C3C3×(C2×D3)⋊C411yescharacteristic
570C22×C3C3×(C2×D3)⋊C411yescharacteristic
571C22×C3C3×(C2×D3)⋊C411yescharacteristic
572C22×C3C3×(C2×D3)⋊C411yescharacteristic
573C22×C3C2×#62611yescharacteristic
574C22×C3C2×C3×D1211yescharacteristic
575C22×C3C2×C3×#6711yescharacteristic
576C2×D3—64no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—124no—
580C2×D3—122no—
581C2×D3—122no—
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—68no—
599C3×C4—64no—
600C3×C4—64no—
601C3×C4—182no—
602C3×C4#372211yescharacteristic
603C3×C4#372211yescharacteristic
604C3×C4C3×(C2×D3)⋊C411yescharacteristic
605C3×C4C3×(C2×D3)⋊C411yescharacteristic
606C3×C4C3×(C2×D3)⋊C411yescharacteristic
607C3×C4C3×(C2×D3)⋊C411yescharacteristic
608C3×C4C2×#62411yescharacteristic
609C3×C4C2×#62611yescharacteristic
610C3×C4C2×C3×C4×D311yescharacteristic
611C3×C4C2×C3×C4×D311yescharacteristic
612C3×C4C2×C3×D1211yescharacteristic
613C3×C4C2×C3×#6711yescharacteristic
614Dic3—24no—
615Dic3—64no—
616Dic3—62no—
617Dic3—62no—
618C32—21no—
619C32—21no—
620C32—21no—
621C32—41no—
622C32C2×#80511yescharacteristic, complemented
623C32C2×#82511yescharacteristic, complemented
624C32C2×C3×#10411yescharacteristic, complemented
625C23—181no—
626C23C3×#62611yescharacteristic
627Q8—92no—
628Q8—181no—
629D4—92no—
630D4—182no—
631D4—182no—
632D4—181no—
633C2×C4—64no—
634C2×C4—62no—
635C2×C4—181no—
636C2×C4—182no—
637C2×C4—182no—
638C2×C4C3×#62411yescharacteristic
639C2×C4C3×#62411yescharacteristic
640C2×C4C3×#62611yescharacteristic
641C2×C4C3×#62611yescharacteristic
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—362no—
668C2×C3#6357012yesdirect product factor
669C2×C3C3×#80512yescomplemented
670C2×C3C3×#82512yescomplemented
671C2×C3C2×#372211yescharacteristic
672C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
673C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
674D3—124no—
675D3—122no—
676D3—122no—
677C22—22no—
678C22—182no—
679C22—362no—
680C22C3×#372211yescharacteristic
681C22C3×#372211yescharacteristic
682C22C2×C3×#62611yescharacteristic
683C4—64no—
684C4—182no—
685C4C3×#372211yescharacteristic
686C4C3×#372211yescharacteristic
687C4C2×C3×#62411yescharacteristic
688C4C2×C3×#62611yescharacteristic
689C3—21no—
690C3—21no—
691C3—21no—
692C3—41no—
693C3C2×#6357011yescharacteristic, direct product factor
694C3C2×C3×#80511yescharacteristic, complemented
695C3C2×C3×#82511yescharacteristic, complemented
696C2—21no—
697C2—21no—
698C2—362no—
699C2C3×#6357012yesdirect product factor
700C2C2×C3×#372211yescharacteristic
subgroupG/H
centerC2×C3×C4#626
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC22×C33C22⋊C4
prime radicalC2×C3×#3828C2
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×C32×C4×Dic3C2semidirect
3. C2×C32×#208C2semidirect
4. C3×#63570C2direct (N × H)
7. C2×#63570C3direct (N × H)
12. C3×#3828C4semidirect
14. C2×C3×C4⋊(C3⋊D3)C4semidirect
16. C2×C3×#634C4semidirect
19. C32×C4×Dic3C22semidirect
21. C32×#208C22semidirect
30. C2×C3×C4×Dic3D3semidirect
31. C2×C3×C4×Dic3C2×C3semidirect
33. C2×C3×#208D3semidirect
34. C2×C3×#208C2×C3semidirect
37. #63570C2×C3direct (N × H)
50. C3×C4⋊(C3⋊D3)C2×C4semidirect
54. C3×#634C2×C4semidirect
72. #3828C3×C4semidirect
74. C2×C4⋊(C3⋊D3)C3×C4semidirect
76. C2×#634C3×C4semidirect
113. C3×C4×Dic3C2×D3semidirect
114. C3×C4×Dic3C22×C3semidirect
119. C3×#208C2×D3semidirect
120. C3×#208C22×C3semidirect
146. C2×C4×Dic3C3×D3semidirect
147. C2×#208C3×D3semidirect
210. C4⋊(C3⋊D3)C2×C3×C4semidirect
214. #634C2×C3×C4semidirect
255. C2×C33#104semidirect
317. C4×Dic3C2×C3×D3semidirect
319. #208C2×C3×D3semidirect
397. C33C2×#104semidirect
521. C2×C32#805semidirect
522. C2×C32#825semidirect
523. C2×C32C3×#104semidirect
622. C32C2×#805semidirect
623. C32C2×#825semidirect
624. C32C2×C3×#104semidirect
668. C2×C3#63570direct (N × H)
669. C2×C3C3×#805semidirect
670. C2×C3C3×#825semidirect
693. C3C2×#63570direct (N × H)
694. C3C2×C3×#805semidirect
695. C3C2×C3×#825semidirect
699. C2C3×#63570direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C32×C4×Dic32
C2×C32×#2082
C3×#635702
C2×C3×#8253
C2×C3×#8053
C2×#635703