Finite Group Databasebeta

← C2×C3×#63829 #13174427

Subgroups — C2×C3×#63829 #13174427

Order 1728.

1522 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C22×C32×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×C3×#3719C211yesmaximal, characteristic, complemented
5C2×C3×#3717C211yesmaximal, characteristic, complemented
6C3×#63829C218yesmaximal, direct product factor
7C2×C3×#3716C211yesmaximal, characteristic, complemented
8C2×C3×#3714C211yesmaximal, characteristic, complemented
9C2×C3×#950—31nomaximal
10C2×C3×#904—31nomaximal
11C2×#63829C311yesmaximal, characteristic, direct product factor
12C22×C33×C4C2211yescharacteristic
13C2×C3×#638—21no—
14C3×#3828—22no—
15C3×#3828C2214yescomplemented
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3—21no—
18C2×C3×#634C2211yescharacteristic
19C2×C32×#67—21no—
20C32×#235—22no—
21C32×#235C2214yescomplemented
22C2×C32×D12C2211yescharacteristic
23C2×C32×C4×D3—21no—
24C2×C32×Dic6C2211yescharacteristic
25C2×C32×C3⋊C8C2211yescharacteristic
26C2×C32×C3⋊C8C2211yescharacteristic
27C2×C32×C3⋊C8C2214yescomplemented
28C3×#3719C2214yescomplemented
29C3×#3717C2214yescomplemented
30C3×#3716C2214yescomplemented
31C3×#3714C2214yescomplemented
32C2×C32×#41—31no—
33C2×#3828C2×C311yescharacteristic, complemented
34C2×C3×#235—21no—
35C2×C3×#235—31no—
36C2×C3×#235—31no—
37C2×C3×#235—61no—
38C2×C3×#235D311yescharacteristic, complemented
39C2×C3×#235C2×C311yescharacteristic, complemented
40C22×C32×C8—31no—
41C3×#950—38no—
42C2×C3×#216—31no—
43C2×C3×#215—31no—
44C2×C3×#214—31no—
45C2×C3×#213—31no—
46C22×C3×C3⋊C8—21no—
47C22×C3×C3⋊C8D311yescharacteristic, complemented
48C22×C3×C3⋊C8C2×C311yescharacteristic, complemented
49C2×C3×Dic12—31no—
50C3×#904—38no—
51C2×C3×D24—31no—
52C2×C3×#204—31no—
53C2×C3×#204—31no—
54C2×#3719C2×C311yescharacteristic, complemented
55C2×#3717C2×C311yescharacteristic, complemented
56#63829C2×C318yesdirect product factor
57C2×#3716C2×C311yescharacteristic, complemented
58C2×#3714C2×C311yescharacteristic, complemented
59C23×C33D411yescharacteristic
60C22×C3×C3⋊D3—21no—
61C22×C32×D3—21no—
62C2×C33×C4D411yescharacteristic
63C2×C33×C4D412yes—
64C2×C33×C4C2311yescharacteristic
65C2×C33×C4C2312yes—
66C3×#638—24no—
67C2×C3×C3⋊Dic3—21no—
68C3×C4⋊(C3⋊D3)—21no—
69C3×C4⋊(C3⋊D3)C2312yes—
70C3×C4×C3⋊D3—24no—
71C3×#634—21no—
72C3×#634C2312yes—
73C32×#67—24no—
74C2×C32×Dic3—21no—
75C32×D12—21no—
76C32×D12C2312yes—
77C32×C4×D3—24no—
78C32×Dic6—21no—
79C32×Dic6C2312yes—
80C32×C3⋊C8C2312yes—
81C32×C3⋊C8C2312yes—
82C2×C3×#135—91no—
83C2×#950—31no—
84C2×#904—31no—
85C32×#41—34no—
86C32×#41—62no—
87C2×C32×Q8—31no—
88C2×C32×D4—31no—
89C2×C32×D4—61no—
90C22×C32×C4—21no—
91C22×C32×C4—21no—
92C22×C32×C4—21no—
93C22×C32×C4—41no—
94C22×C32×C4—61no—
95C22×C32×C4C2×D311yescharacteristic
96C22×C32×C4C2×D311yescharacteristic
97C22×C32×C4C22×C311yescharacteristic
98C2×#638—21no—
99#3828—22no—
100#3828C22×C314yescomplemented
101C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×#634C22×C311yescharacteristic
104C2×C3×#67—22no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—62no—
108C2×C3×#67—61no—
109C2×C3×#67—61no—
110C3×#235—24no—
111C3×#235—24no—
112C3×#235—22no—
113C3×#235—22no—
114C3×#235—34no—
115C3×#235—34no—
116C3×#235—64no—
117C3×#235—64no—
118C3×#235—62no—
119C3×#235—62no—
120C3×#235C2×D314yescomplemented
121C3×#235C22×C314yescomplemented
122C2×C3×D12—21no—
123C2×C3×D12—31no—
124C2×C3×D12—31no—
125C2×C3×D12—61no—
126C2×C3×D12C2×D311yescharacteristic
127C2×C3×D12C22×C311yescharacteristic
128C2×C3×C4×D3—22no—
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—21no—
131C2×C3×C4×D3—62no—
132C2×C3×C4×D3—61no—
133C2×C3×C4×D3—61no—
134C2×C3×Dic6—21no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6—61no—
138C2×C3×Dic6C2×D311yescharacteristic
139C2×C3×Dic6C22×C311yescharacteristic
140C2×C32×C8—31no—
141C2×C32×C8—31no—
142C2×C32×C8—34no—
143C3×#216—34no—
144C3×#215—34no—
145C3×#214—34no—
146C3×#213—34no—
147C2×C3×C3⋊C8—21no—
148C2×C3×C3⋊C8—21no—
149C2×C3×C3⋊C8—24no—
150C2×C3×C3⋊C8C2×D311yescharacteristic
151C2×C3×C3⋊C8C2×D311yescharacteristic
152C2×C3×C3⋊C8C2×D314yescomplemented
153C2×C3×C3⋊C8C22×C311yescharacteristic
154C2×C3×C3⋊C8C22×C311yescharacteristic
155C2×C3×C3⋊C8C22×C314yescomplemented
156C3×Dic12—34no—
157C3×D24—34no—
158C3×#204—34no—
159C3×#204—34no—
160#3719C22×C314yescomplemented
161#3717C22×C314yescomplemented
162#3716C22×C314yescomplemented
163#3714C22×C314yescomplemented
164C22×C33—22no—
165C22×C33C2×D412yes—
166C22×C33C2×D411yescharacteristic
167C2×C3×C3⋊D3—22no—
168C2×C3×C3⋊D3—42no—
169C2×C32×D3—22no—
170C2×C32×D3—42no—
171C33×C4C2×D411yescharacteristic
172C33×C4C2×D412yes—
173C33×C4C2411yescharacteristic
174C3×C3⋊Dic3—22no—
175C32×Dic3—22no—
176C2×C3×#41—31no—
177C2×C3×#41—31no—
178C2×C3×#41—61no—
179C2×C3×#41—91no—
180C2×#235—31no—
181C2×#235—31no—
182C2×#235—61no—
183C2×#235C3×D311yescharacteristic, complemented
184C3×#135—98no—
185C2×C3×Q16—91no—
186C2×C3×SD16—91no—
187C2×C3×SD16—91no—
188C2×C3×D8—91no—
189C22×C3×C8—31no—
190C22×C3×C8—31no—
191C22×C3×C8—61no—
192#950—38no—
193C2×#216—31no—
194C2×#215—31no—
195C2×#214—31no—
196C2×#213—31no—
197C22×C3⋊C8C3×D311yescharacteristic, complemented
198C2×Dic12—31no—
199#904—38no—
200C2×D24—31no—
201C2×#204—31no—
202C2×#204—31no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—41no—
207C23×C32—61no—
208C23×C32D1211yescharacteristic
209C23×C32#6711yescharacteristic
210C23×C32C3×D411yescharacteristic
211C22×C3⋊D3—21no—
212C22×C3×D3—22no—
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—62no—
216C22×C3×D3—61no—
217C22×C3×D3—61no—
218C32×Q8—32no—
219C32×Q8—61no—
220C32×D4—32no—
221C32×D4—64no—
222C32×D4—61no—
223C2×C32×C4—22no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—22no—
227C2×C32×C4—21no—
228C2×C32×C4—22no—
229C2×C32×C4—21no—
230C2×C32×C4—22no—
231C2×C32×C4—21no—
232C2×C32×C4—22no—
233C2×C32×C4—21no—
234C2×C32×C4—22no—
235C2×C32×C4—41no—
236C2×C32×C4—42no—
237C2×C32×C4—41no—
238C2×C32×C4—42no—
239C2×C32×C4—61no—
240C2×C32×C4—64no—
241C2×C32×C4D1212yes—
242C2×C32×C4D1211yescharacteristic
243C2×C32×C4#6712yes—
244C2×C32×C4#6711yescharacteristic
245C2×C32×C4C3×D411yescharacteristic
246C2×C32×C4C3×D412yes—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D312yes—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D312yes—
251C2×C32×C4C23×C311yescharacteristic
252C2×C32×C4C23×C312yes—
253#638—24no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)C23×C312yes—
257C4×C3⋊D3—24no—
258#634—21no—
259#634C23×C312yes—
260C3×#67—28no—
261C3×#67—24no—
262C3×#67—24no—
263C3×#67—68no—
264C3×#67—64no—
265C3×#67—64no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—61no—
272C3×D12—22no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—22no—
276C3×D12—32no—
277C3×D12—32no—
278C3×D12—62no—
279C3×D12—62no—
280C3×D12—61no—
281C3×D12—61no—
282C3×D12C22×D312yes—
283C3×D12C23×C312yes—
284C3×C4×D3—28no—
285C3×C4×D3—24no—
286C3×C4×D3—24no—
287C3×C4×D3—68no—
288C3×C4×D3—64no—
289C3×C4×D3—64no—
290C3×Dic6—22no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—22no—
294C3×Dic6—32no—
295C3×Dic6—32no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—61no—
299C3×Dic6—61no—
300C3×Dic6C22×D312yes—
301C3×Dic6C23×C312yes—
302C32×C8—32no—
303C32×C8—32no—
304C3×C3⋊C8—22no—
305C3×C3⋊C8—22no—
306C3×C3⋊C8C22×D312yes—
307C3×C3⋊C8C22×D312yes—
308C3×C3⋊C8C23×C312yes—
309C3×C3⋊C8C23×C312yes—
310C2×#135—91noSylow
311C2×C33—22no—
312C2×C33#13512yescomplemented
313C2×C33C22×D411yescharacteristic
314C3×C3⋊D3—42no—
315C32×D3—42no—
316C3×#41—34no—
317C3×#41—34no—
318C3×#41—64no—
319C3×#41—64no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—94no—
323C3×#41—182no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×Q8—61no—
327C2×C3×Q8—91no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—62no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—91no—
335C2×C3×D4—181no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—41no—
340C22×C3×C4—62no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C22×C3×C4—181no—
344C22×C3×C4D3211yescharacteristic
345C22×C3×C4C2×C3×D311yescharacteristic
346C22×C3×C4C2×C3×D311yescharacteristic
347C2×#67—21no—
348C2×#67—62no—
349C2×#67—61no—
350C2×#67—61no—
351#235—22no—
352#235—34no—
353#235—34no—
354#235—64no—
355#235—64no—
356#235—62no—
357#235—62no—
358#235C2×C3×D314yescomplemented
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—61no—
362C2×D12C2×C3×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—62no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—61no—
370C2×Dic6C2×C3×D311yescharacteristic
371C3×Q16—94no—
372C3×SD16—94no—
373C3×SD16—94no—
374C3×D8—94no—
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C2×C3×C8—34no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8—34no—
381C2×C3×C8—61no—
382C2×C3×C8—61no—
383C2×C3×C8—64no—
384#216—34no—
385#215—34no—
386#214—34no—
387#213—34no—
388C2×C3⋊C8C2×C3×D311yescharacteristic
389C2×C3⋊C8C2×C3×D311yescharacteristic
390C2×C3⋊C8C2×C3×D314yescomplemented
391Dic12—34no—
392D24—34no—
393#204—34no—
394#204—34no—
395C22×C32—22no—
396C22×C32—24no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—21no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—22no—
405C22×C32—41no—
406C22×C32—42no—
407C22×C32—42no—
408C22×C32—42no—
409C22×C32—44no—
410C22×C32—62no—
411C22×C32—122no—
412C22×C32C2×D1212yes—
413C22×C32C2×D1211yescharacteristic
414C22×C32C2×#6712yes—
415C22×C32C2×#6711yescharacteristic
416C22×C32C2×C3×D412yes—
417C22×C32C2×C3×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—42no—
420C2×C3×D3—24no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—44no—
424C2×C3×D3—42no—
425C2×C3×D3—42no—
426C2×C3×D3—64no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—124no—
430C2×C3×D3—122no—
431C2×C3×D3—122no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—22no—
437C32×C4—21no—
438C32×C4—22no—
439C32×C4—21no—
440C32×C4—22no—
441C32×C4—41no—
442C32×C4—42no—
443C32×C4—41no—
444C32×C4—62no—
445C32×C4C2×D1211yescharacteristic
446C32×C4C2×D1212yes—
447C32×C4C2×#6711yescharacteristic
448C32×C4C2×#6712yes—
449C32×C4C2×C3×D411yescharacteristic
450C32×C4C2×C3×D412yes—
451C32×C4C23×D311yescharacteristic
452C32×C4C23×D311yescharacteristic
453C32×C4C24×C311yescharacteristic
454C3⋊Dic3—22no—
455C3×Dic3—24no—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—64no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C2×#41—31no—
462C2×#41—91no—
463#135—98no—
464C2×Q16—91no—
465C2×SD16—91no—
466C2×SD16—91no—
467C2×D8—91no—
468C22×C8—31no—
469C33C2×#13511yescharacteristic, complemented, Sylow
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—41no—
474C23×C3—62no—
475C23×C3—61no—
476C23×C3—61no—
477C23×C3—181no—
478C23×C3#62611yescharacteristic
479C23×C3C3×D1211yescharacteristic
480C23×C3C3×#6711yescharacteristic
481C22×D3—21no—
482C22×D3—62no—
483C22×D3—61no—
484C22×D3—61no—
485C3×Q8—32no—
486C3×Q8—32no—
487C3×Q8—62no—
488C3×Q8—62no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—92no—
492C3×Q8—181no—
493C3×D4—32no—
494C3×D4—32no—
495C3×D4—62no—
496C3×D4—62no—
497C3×D4—68no—
498C3×D4—64no—
499C3×D4—64no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—92no—
503C3×D4—184no—
504C3×D4—181no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—22no—
517C2×C3×C4—41no—
518C2×C3×C4—42no—
519C2×C3×C4—41no—
520C2×C3×C4—42no—
521C2×C3×C4—68no—
522C2×C3×C4—62no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—64no—
526C2×C3×C4—64no—
527C2×C3×C4—181no—
528C2×C3×C4—184no—
529C2×C3×C4#62612yes—
530C2×C3×C4#62611yescharacteristic
531C2×C3×C4C3×D1211yescharacteristic
532C2×C3×C4C3×D1212yes—
533C2×C3×C4C3×#6711yescharacteristic
534C2×C3×C4C3×#6712yes—
535C2×C3×C4C2×D3211yescharacteristic
536C2×C3×C4C2×D3212yes—
537C2×C3×C4C22×C3×D311yescharacteristic
538C2×C3×C4C22×C3×D312yes—
539C2×C3×C4C22×C3×D311yescharacteristic
540C2×C3×C4C22×C3×D312yes—
541#67—24no—
542#67—68no—
543#67—64no—
544#67—64no—
545C2×Dic3—21no—
546C2×Dic3—62no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549D12—21no—
550D12—32no—
551D12—32no—
552D12—62no—
553D12—62no—
554D12—61no—
555D12—61no—
556D12C22×C3×D312yes—
557C4×D3—24no—
558C4×D3—68no—
559C4×D3—64no—
560C4×D3—64no—
561Dic6—21no—
562Dic6—32no—
563Dic6—32no—
564Dic6—62no—
565Dic6—62no—
566Dic6—61no—
567Dic6—61no—
568Dic6C22×C3×D312yes—
569C3×C8—32no—
570C3×C8—32no—
571C3×C8—32no—
572C3×C8—32no—
573C3×C8—62no—
574C3×C8—62no—
575C3⋊C8C22×C3×D312yes—
576C3⋊C8C22×C3×D312yes—
577C2×C32—22no—
578C2×C32—24no—
579C2×C32—22no—
580C2×C32—22no—
581C2×C32—22no—
582C2×C32—21no—
583C2×C32—22no—
584C2×C32—22no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—42no—
588C2×C32—41no—
589C2×C32—42no—
590C2×C32—42no—
591C2×C32—44no—
592C2×C32—122no—
593C2×C32#90412yescomplemented
594C2×C32#95012yescomplemented
595C2×C32C3×#13512yescomplemented
596C2×C32C22×D1211yescharacteristic
597C2×C32C22×#6711yescharacteristic
598C2×C32C22×C3×D411yescharacteristic
599C3⋊D3—42no—
600C3×D3—44no—
601C3×D3—42no—
602C3×D3—42no—
603C3×D3—124no—
604C3×D3—122no—
605C3×D3—122no—
606#41—34no—
607#41—62no—
608#41—94no—
609#41—182no—
610C2×Q8—31no—
611C2×Q8—91no—
612C2×D4—31no—
613C2×D4—61no—
614C2×D4—91no—
615C2×D4—181no—
616C22×C4—61no—
617C22×C4—181no—
618C22×C4C3×D3211yescharacteristic
619Q16—94no—
620SD16—94no—
621SD16—94no—
622D8—94no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—34no—
626C22×C3—24no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—44no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3—64no—
642C22×C3—62no—
643C22×C3—62no—
644C22×C3—124no—
645C22×C3—122no—
646C22×C3—122no—
647C22×C3—182no—
648C22×C3—362no—
649C22×C3C2×#62612yes—
650C22×C3C2×#62611yescharacteristic
651C22×C3C2×C3×D1212yes—
652C22×C3C2×C3×D1211yescharacteristic
653C22×C3C2×C3×#6712yes—
654C22×C3C2×C3×#6711yescharacteristic
655C2×D3—22no—
656C2×D3—42no—
657C2×D3—64no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—124no—
661C2×D3—122no—
662C2×D3—122no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—21no—
670C3×C4—22no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—42no—
674C3×C4—41no—
675C3×C4—64no—
676C3×C4—62no—
677C3×C4—62no—
678C3×C4—182no—
679C3×C4C2×#62612yes—
680C3×C4C2×#62611yescharacteristic
681C3×C4C2×C3×D1211yescharacteristic
682C3×C4C2×C3×D1212yes—
683C3×C4C2×C3×#6711yescharacteristic
684C3×C4C2×C3×#6712yes—
685C3×C4C22×D3211yescharacteristic
686C3×C4C23×C3×D311yescharacteristic
687C3×C4C23×C3×D311yescharacteristic
688Dic3—22no—
689Dic3—64no—
690Dic3—62no—
691Dic3—62no—
692C32—21no—
693C32—21no—
694C32—21no—
695C32—41no—
696C32C2×#90411yescharacteristic, complemented
697C32C2×#95011yescharacteristic, complemented
698C32C2×C3×#13511yescharacteristic, complemented
699C23—61no—
700C23—181no—
701C23C3×#62611yescharacteristic
702Q8—32no—
703Q8—61no—
704Q8—92no—
705Q8—181no—
706D4—32no—
707D4—64no—
708D4—61no—
709D4—92no—
710D4—184no—
711D4—181no—
712C2×C4—61no—
713C2×C4—64no—
714C2×C4—181no—
715C2×C4—184no—
716C2×C4C3×#62611yescharacteristic
717C2×C4C3×#62612yes—
718C2×C4C2×C3×D3211yescharacteristic
719C2×C4C2×C3×D3212yes—
720C8—32no—
721C8—32no—
722C2×C3—24no—
723C2×C3—22no—
724C2×C3—22no—
725C2×C3—22no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—42no—
733C2×C3—42no—
734C2×C3—44no—
735C2×C3—41no—
736C2×C3—42no—
737C2×C3—124no—
738C2×C3—122no—
739C2×C3—122no—
740C2×C3—362no—
741C2×C3#6382912yesdirect product factor
742C2×C3C3×#90412yescomplemented
743C2×C3C3×#95012yescomplemented
744C2×C3C22×#62611yescharacteristic
745C2×C3C22×C3×D1211yescharacteristic
746C2×C3C22×C3×#6711yescharacteristic
747D3—42no—
748D3—124no—
749D3—122no—
750D3—122no—
751C22—22no—
752C22—62no—
753C22—122no—
754C22—182no—
755C22—362no—
756C22C2×C3×#62612yes—
757C22C2×C3×#62611yescharacteristic
758C4—62no—
759C4—182no—
760C4C2×C3×#62612yes—
761C4C2×C3×#62611yescharacteristic
762C4C22×C3×D3211yescharacteristic
763C3—21no—
764C3—21no—
765C3—21no—
766C3—41no—
767C3C2×#6382911yescharacteristic, direct product factor
768C3C2×C3×#90411yescharacteristic, complemented
769C3C2×C3×#95011yescharacteristic, complemented
770C2—22no—
771C2—122no—
772C2—362no—
773C2C3×#6382912yesdirect product factor
774C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC2×C3×C4#626
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C2×D4
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#135
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
1. C2×C3×#3828C2semidirect
2. C2×C32×#235C2semidirect
3. C22×C32×C3⋊C8C2semidirect
4. C2×C3×#3719C2semidirect
5. C2×C3×#3717C2semidirect
6. C3×#63829C2direct (N × H)
7. C2×C3×#3716C2semidirect
8. C2×C3×#3714C2semidirect
11. C2×#63829C3direct (N × H)
15. C3×#3828C22semidirect
21. C32×#235C22semidirect
27. C2×C32×C3⋊C8C22semidirect
28. C3×#3719C22semidirect
29. C3×#3717C22semidirect
30. C3×#3716C22semidirect
31. C3×#3714C22semidirect
33. C2×#3828C2×C3semidirect
38. C2×C3×#235D3semidirect
39. C2×C3×#235C2×C3semidirect
47. C22×C3×C3⋊C8D3semidirect
48. C22×C3×C3⋊C8C2×C3semidirect
54. C2×#3719C2×C3semidirect
55. C2×#3717C2×C3semidirect
56. #63829C2×C3direct (N × H)
57. C2×#3716C2×C3semidirect
58. C2×#3714C2×C3semidirect
100. #3828C22×C3semidirect
120. C3×#235C2×D3semidirect
121. C3×#235C22×C3semidirect
152. C2×C3×C3⋊C8C2×D3semidirect
155. C2×C3×C3⋊C8C22×C3semidirect
160. #3719C22×C3semidirect
161. #3717C22×C3semidirect
162. #3716C22×C3semidirect
163. #3714C22×C3semidirect
183. C2×#235C3×D3semidirect
197. C22×C3⋊C8C3×D3semidirect
312. C2×C33#135semidirect
358. #235C2×C3×D3semidirect
390. C2×C3⋊C8C2×C3×D3semidirect
469. C33C2×#135semidirect
593. C2×C32#904semidirect
594. C2×C32#950semidirect
595. C2×C32C3×#135semidirect
696. C32C2×#904semidirect
697. C32C2×#950semidirect
698. C32C2×C3×#135semidirect
741. C2×C3#63829direct (N × H)
742. C2×C3C3×#904semidirect
743. C2×C3C3×#950semidirect
767. C3C2×#63829direct (N × H)
768. C3C2×C3×#904semidirect
769. C3C2×C3×#950semidirect
773. C2C3×#63829direct (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×#2352
C22×C32×C3⋊C82
C2×C3×#37192
C2×C3×#37172
C3×#638292
C2×C3×#37162
C2×C3×#37142
C2×C3×#9503
C2×C3×#9043
C2×#638293