Finite Group Databasebeta

← C2×C3×#5600 #11900584

Subgroups — C2×C3×#5600 #11900584

Order 1152.

2677 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic, complemented
3C2×C3×#935C212yesmaximal, complemented
4C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
5C2×C3×D4×Dic3C212yesmaximal, complemented
6C2×C3×#924C211yesmaximal, characteristic, complemented
7C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
8C3×#5600C2116yesmaximal, direct product factor
9C2×C3×#890C211yesmaximal, characteristic, complemented
10C2×C3×#887C211yesmaximal, characteristic, complemented
11C2×C3×#879C212yesmaximal, complemented
12C2×C3×#877C212yesmaximal, complemented
13C2×C3×#529—31nomaximal
14C2×#5600C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2212yes—
16C22×C32×D4C2211yescharacteristic
17C23×C32×C4C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2212yes—
21C22×C3×Dic6C2211yescharacteristic
22C32×#121C2218yes—
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28C2×C3×#217C2212yes—
29C3×#936C2218yescomplemented
30C3×#935C22116yescomplemented
31C3×D4×Dic3C22116yescomplemented
32C3×D4×Dic3C2218yescomplemented
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2212yes—
35C3×#924C2218yescomplemented
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2212yes—
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2218yescomplemented
45C3×#890C2218yescomplemented
46C3×#887C2218yescomplemented
47C3×#879C22116yescomplemented
48C3×#877C22116yescomplemented
49C3×#529—316no—
50C2×C3×#126—32no—
51C2×C3×#125—31no—
52C2×C3×#124—31no—
53C2×C3×#123—32no—
54C2×C3×C22⋊Q8—31no—
55C2×C3×#121—21no—
56C2×C3×#121D311yescharacteristic
57C2×C3×#121C2×C311yescharacteristic
58C2×C3×C4×Q8—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—32no—
61C2×C3×#117—32no—
62C22×C3×C42—31no—
63C2×#936C2×C311yescharacteristic, complemented
64C2×#935C2×C312yescomplemented
65C2×D4×Dic3C2×C312yescomplemented
66C2×D4×Dic3C2×C311yescharacteristic, complemented
67C2×#924C2×C311yescharacteristic, complemented
68C22×C4×Dic3C2×C311yescharacteristic, complemented
69#5600C2×C3116yesdirect product factor
70C2×#890C2×C311yescharacteristic, complemented
71C2×#887C2×C311yescharacteristic, complemented
72C2×#879C2×C312yescomplemented
73C2×#877C2×C312yescomplemented
74C24×C32C2312yes—
75C24×C32C2311yescharacteristic
76C2×C32×D4—28no—
77C2×C32×D4—24no—
78C2×C32×D4C2318yes—
79C2×C32×D4C2314yes—
80C22×C32×C4—24no—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2312yes—
83C22×C32×C4C2314yes—
84C22×C32×C4C2311yescharacteristic
85C22×C3×Dic3—24no—
86C22×C3×Dic3—24no—
87C22×C3×Dic3—28no—
88C22×C3×Dic3C2318yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2314yes—
94C22×C3×Dic3C2314yes—
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C2×C3×Dic6—24no—
98C2×C3×Dic6C2314yes—
99C32×C4⋊C4C2314yes—
100C32×C22⋊C4C2318yes—
101C3×#217C2318yes—
102C3×#217C2318yes—
103C3×#217C2318yes—
104C3×#217C2318yes—
105C3×C4⋊Dic3C2318yes—
106C3×C4⋊Dic3C2314yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2318yes—
109C3×Dic3⋊C4C2318yes—
110C3×C4×Dic3C2314yes—
111C3×C4×Dic3C2318yes—
112C3×C4×Dic3C2314yes—
113C3×C4×Dic3C2314yes—
114C3×C4×Dic3C2314yes—
115C2×#529—31noSylow
116C22×C3×Q8—31no—
117C22×C3×D4—22no—
118C22×C3×D4—21no—
119C22×C3×D4C2×D312yes—
120C22×C3×D4C2×D311yescharacteristic
121C22×C3×D4C22×C312yes—
122C22×C3×D4C22×C311yescharacteristic
123C23×C3×C4—21no—
124C23×C3×C4—31no—
125C23×C3×C4—31no—
126C23×C3×C4—32no—
127C23×C3×C4C2×D311yescharacteristic
128C23×C3×C4C22×C311yescharacteristic
129C23×Dic3C22×C312yes—
130C23×Dic3C22×C311yescharacteristic
131C23×Dic3C22×C311yescharacteristic
132C22×Dic6C22×C311yescharacteristic
133C3×#126—316no—
134C3×#125—38no—
135C3×#124—38no—
136C3×#123—316no—
137C3×C22⋊Q8—38no—
138C3×#121—28no—
139C3×#121C2×D318yes—
140C3×#121C22×C318yes—
141C3×C4×Q8—38no—
142C3×C4×D4—38no—
143C3×C4×D4—316no—
144C3×#117—316no—
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4—32no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4—32no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4C2×D311yescharacteristic
152C2×C3×C4⋊C4C22×C311yescharacteristic
153C2×C3×C22⋊C4—22no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C22⋊C4—32no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C22⋊C4—32no—
158C2×C3×C22⋊C4C2×D312yes—
159C2×C3×C22⋊C4C22×C312yes—
160C2×C3×C42—31no—
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×C3×C42—31no—
164C2×C3×C42—32no—
165C2×C3×C42—38no—
166C2×#217C22×C312yes—
167C2×#217C22×C312yes—
168C2×#217C22×C312yes—
169C2×#217C22×C312yes—
170#936C22×C318yescomplemented
171#935C22×C3116yescomplemented
172D4×Dic3C22×C3116yescomplemented
173D4×Dic3C22×C318yescomplemented
174C2×C4⋊Dic3C22×C312yes—
175C2×C4⋊Dic3C22×C311yescharacteristic
176#924C22×C318yescomplemented
177C2×Dic3⋊C4C22×C312yes—
178C2×Dic3⋊C4C22×C312yes—
179C2×Dic3⋊C4C22×C312yes—
180C2×C4×Dic3C22×C311yescharacteristic
181C2×C4×Dic3C22×C312yes—
182C2×C4×Dic3C22×C311yescharacteristic
183C2×C4×Dic3C22×C311yescharacteristic
184C2×C4×Dic3C22×C311yescharacteristic
185C2×C4×Dic3C22×C318yescomplemented
186#890C22×C318yescomplemented
187#887C22×C318yescomplemented
188#879C22×C3116yescomplemented
189#877C22×C3116yescomplemented
190C23×C32—22no—
191C23×C32—22no—
192C23×C32—24no—
193C23×C32—24no—
194C23×C32—24no—
195C23×C32#4114yes—
196C23×C32C2414yes—
197C23×C32C2412yes—
198C23×C32C2411yescharacteristic
199C32×D4—216no—
200C32×D4—28no—
201C2×C32×C4—22no—
202C2×C32×C4—24no—
203C2×C32×C4—28no—
204C2×C32×C4#4114yes—
205C2×C32×C4C2412yes—
206C2×C32×C4C2414yes—
207C2×C32×C4C2412yes—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—28no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3—28no—
215C2×C3×Dic3—216no—
216C2×C3×Dic3#4114yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2412yes—
219C2×C3×Dic3C2412yes—
220C2×C3×Dic3C2414yes—
221C2×C3×Dic3C2414yes—
222C2×C3×Dic3C2412yes—
223C3×Dic6—28no—
224#529—316no—
225C2×#126—32no—
226C2×#125—31no—
227C2×#124—31no—
228C2×#123—32no—
229C2×C22⋊Q8—31no—
230C2×#121C3×D311yescharacteristic
231C2×C4×Q8—31no—
232C2×C4×D4—32no—
233C2×C4×D4—31no—
234C2×#117—32no—
235C22×C42—31no—
236C24×C3—21no—
237C24×C3—22no—
238C24×C3C22×D312yes—
239C24×C3C22×D311yescharacteristic
240C24×C3C23×C312yes—
241C24×C3C23×C311yescharacteristic
242C2×C3×Q8—34no—
243C2×C3×Q8—64no—
244C2×C3×D4—28no—
245C2×C3×D4—28no—
246C2×C3×D4—24no—
247C2×C3×D4—24no—
248C2×C3×D4—28no—
249C2×C3×D4—24no—
250C2×C3×D4—44no—
251C2×C3×D4—48no—
252C2×C3×D4C22×D318yes—
253C2×C3×D4C22×D314yes—
254C2×C3×D4C23×C318yes—
255C2×C3×D4C23×C314yes—
256C22×C3×C4—24no—
257C22×C3×C4—24no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—24no—
262C22×C3×C4—31no—
263C22×C3×C4—34no—
264C22×C3×C4—34no—
265C22×C3×C4—38no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—32no—
270C22×C3×C4—32no—
271C22×C3×C4—44no—
272C22×C3×C4—64no—
273C22×C3×C4—68no—
274C22×C3×C4—64no—
275C22×C3×C4C22×D314yes—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D312yes—
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C23×C311yescharacteristic
280C22×C3×C4C23×C312yes—
281C22×C3×C4C23×C314yes—
282C22×C3×C4C23×C311yescharacteristic
283C22×Dic3—24no—
284C22×Dic3—24no—
285C22×Dic3—28no—
286C22×Dic3C23×C318yes—
287C22×Dic3C23×C311yescharacteristic
288C22×Dic3C23×C311yescharacteristic
289C22×Dic3C23×C311yescharacteristic
290C22×Dic3C23×C312yes—
291C22×Dic3C23×C314yes—
292C22×Dic3C23×C314yes—
293C22×Dic3C23×C312yes—
294C22×Dic3C23×C311yescharacteristic
295C2×Dic6—24no—
296C2×Dic6C23×C314yes—
297C3×C4⋊C4—24no—
298C3×C4⋊C4—38no—
299C3×C4⋊C4—38no—
300C3×C4⋊C4—38no—
301C3×C4⋊C4—34no—
302C3×C4⋊C4—38no—
303C3×C4⋊C4C22×D314yes—
304C3×C4⋊C4C23×C314yes—
305C3×C22⋊C4—28no—
306C3×C22⋊C4—38no—
307C3×C22⋊C4—38no—
308C3×C22⋊C4—38no—
309C3×C22⋊C4—38no—
310C3×C22⋊C4C22×D318yes—
311C3×C22⋊C4C23×C318yes—
312C3×C42—34no—
313C3×C42—34no—
314C3×C42—34no—
315C3×C42—34no—
316C3×C42—38no—
317#217C23×C318yes—
318#217C23×C318yes—
319#217C23×C318yes—
320#217C23×C318yes—
321C4⋊Dic3C23×C318yes—
322C4⋊Dic3C23×C314yes—
323Dic3⋊C4C23×C318yes—
324Dic3⋊C4C23×C318yes—
325Dic3⋊C4C23×C318yes—
326C4×Dic3C23×C314yes—
327C4×Dic3C23×C318yes—
328C4×Dic3C23×C314yes—
329C4×Dic3C23×C314yes—
330C4×Dic3C23×C314yes—
331C22×C32—28no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—24no—
335C22×C32—24no—
336C22×C32—24no—
337C22×C32—48no—
338C22×C32C2×#4114yes—
339C22×C32C2×#4112yes—
340C22×C32C2×#4112yes—
341C22×C32C2×#4112yes—
342C22×C32C2511yescharacteristic
343C32×C4—22no—
344C32×C4—24no—
345C32×C4C2×#4114yes—
346C3×Dic3—24no—
347C3×Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—22no—
350C3×Dic3—24no—
351C3×Dic3C2×#4114yes—
352C22×Q8—31no—
353C22×D4C2×C3×D312yes—
354C22×D4C2×C3×D311yescharacteristic
355C23×C4—32no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4C2×C3×D311yescharacteristic
359#126—316no—
360#125—38no—
361#124—38no—
362#123—316no—
363C22⋊Q8—38no—
364#121C2×C3×D318yes—
365C4×Q8—38no—
366C4×D4—38no—
367C4×D4—316no—
368#117—316no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4C2×C3×D311yescharacteristic
375C2×C22⋊C4—32no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4C2×C3×D312yes—
380C2×C42—31no—
381C2×C42—32no—
382C2×C42—31no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—38no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—21no—
397C23×C3—22no—
398C23×C3—24no—
399C23×C3—24no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—44no—
403C23×C3—44no—
404C23×C3—44no—
405C23×C3#23714yes—
406C23×C3C3×#4114yes—
407C23×C3C23×D314yes—
408C23×C3C23×D312yes—
409C23×C3C23×D311yescharacteristic
410C23×C3C24×C314yes—
411C23×C3C24×C312yes—
412C23×C3C24×C311yescharacteristic
413C3×Q8—68no—
414C3×D4—216no—
415C3×D4—216no—
416C3×D4—28no—
417C3×D4—28no—
418C3×D4—48no—
419C3×D4—416no—
420C2×C3×C4—22no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—28no—
425C2×C3×C4—28no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—34no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—34no—
436C2×C3×C4—34no—
437C2×C3×C4—48no—
438C2×C3×C4—42no—
439C2×C3×C4—44no—
440C2×C3×C4—68no—
441C2×C3×C4—616no—
442C2×C3×C4—68no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—64no—
446C2×C3×C4—62no—
447C2×C3×C4—64no—
448C2×C3×C4#23714yes—
449C2×C3×C4C3×#4114yes—
450C2×C3×C4C23×D312yes—
451C2×C3×C4C23×D314yes—
452C2×C3×C4C23×D312yes—
453C2×C3×C4C24×C312yes—
454C2×C3×C4C24×C314yes—
455C2×C3×C4C24×C312yes—
456C2×Dic3—24no—
457C2×Dic3—28no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—24no—
462C2×Dic3—28no—
463C2×Dic3—216no—
464C2×Dic3C3×#4114yes—
465C2×Dic3C24×C312yes—
466C2×Dic3C24×C312yes—
467C2×Dic3C24×C312yes—
468C2×Dic3C24×C314yes—
469C2×Dic3C24×C314yes—
470C2×Dic3C24×C312yes—
471Dic6—28no—
472C2×C32—24no—
473C2×C32—44no—
474C2×C32#52914yescomplemented
475C2×C32C22×#4111yescharacteristic
476C2×C32C22×#4111yescharacteristic
477C2×C32C22×#4111yescharacteristic
478C24C22×C3×D312yes—
479C24C22×C3×D311yescharacteristic
480C2×Q8—34no—
481C2×Q8—64no—
482C2×D4—28no—
483C2×D4—24no—
484C2×D4C22×C3×D318yes—
485C2×D4C22×C3×D314yes—
486C22×C4—24no—
487C22×C4—31no—
488C22×C4—31no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—34no—
492C22×C4—34no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—38no—
496C22×C4—64no—
497C22×C4—68no—
498C22×C4—64no—
499C22×C4C22×C3×D311yescharacteristic
500C22×C4C22×C3×D314yes—
501C22×C4C22×C3×D312yes—
502C22×C4C22×C3×D311yescharacteristic
503C4⋊C4—38no—
504C4⋊C4—38no—
505C4⋊C4—34no—
506C4⋊C4—38no—
507C4⋊C4—38no—
508C4⋊C4C22×C3×D314yes—
509C22⋊C4—38no—
510C22⋊C4—38no—
511C22⋊C4—38no—
512C22⋊C4—38no—
513C22⋊C4C22×C3×D318yes—
514C42—34no—
515C42—34no—
516C42—34no—
517C42—34no—
518C42—38no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—28no—
524C22×C3—28no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3—24no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—24no—
534C22×C3—22no—
535C22×C3—21no—
536C22×C3—42no—
537C22×C3—48no—
538C22×C3—42no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—44no—
542C22×C3—48no—
543C22×C3—48no—
544C22×C3—88no—
545C22×C3C2×#23714yes—
546C22×C3C2×#23712yes—
547C22×C3C2×#23712yes—
548C22×C3D3×#4112yes—
549C22×C3C2×C3×#4114yes—
550C22×C3C2×C3×#4112yes—
551C22×C3C2×C3×#4112yes—
552C22×C3C2×C3×#4112yes—
553C22×C3C24×D311yescharacteristic
554C22×C3C25×C311yescharacteristic
555C3×C4—22no—
556C3×C4—24no—
557C3×C4—22no—
558C3×C4—24no—
559C3×C4—24no—
560C3×C4—34no—
561C3×C4—42no—
562C3×C4—44no—
563C3×C4—62no—
564C3×C4—62no—
565C3×C4—64no—
566C3×C4—62no—
567C3×C4—64no—
568C3×C4C2×#23714yes—
569C3×C4C2×C3×#4114yes—
570Dic3—24no—
571Dic3—22no—
572Dic3—22no—
573Dic3—22no—
574Dic3—24no—
575Dic3C2×C3×#4114yes—
576C32C2×#52911yescharacteristic, complemented, Sylow
577C23—22no—
578C23—22no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23C3×#23714yes—
583C23C23×C3×D314yes—
584C23C23×C3×D312yes—
585C23C23×C3×D311yescharacteristic
586Q8—68no—
587D4—216no—
588D4—28no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—28no—
592C2×C4—34no—
593C2×C4—32no—
594C2×C4—32no—
595C2×C4—32no—
596C2×C4—32no—
597C2×C4—34no—
598C2×C4—34no—
599C2×C4—68no—
600C2×C4—616no—
601C2×C4—68no—
602C2×C4—62no—
603C2×C4—62no—
604C2×C4—64no—
605C2×C4—62no—
606C2×C4—64no—
607C2×C4C3×#23714yes—
608C2×C4C23×C3×D312yes—
609C2×C4C23×C3×D314yes—
610C2×C4C23×C3×D312yes—
611C2×C3—24no—
612C2×C3—24no—
613C2×C3—24no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—44no—
618C2×C3—44no—
619C2×C3—44no—
620C2×C3—84no—
621C2×C3#560014yesdirect product factor
622C2×C3C3×#52914yescomplemented
623C2×C3C22×#23711yescharacteristic
624C2×C3C22×#23711yescharacteristic
625C2×C3C2×D3×#4111yescharacteristic
626C2×C3C22×C3×#4111yescharacteristic
627C2×C3C22×C3×#4111yescharacteristic
628C2×C3C22×C3×#4111yescharacteristic
629C22—28no—
630C22—22no—
631C22—22no—
632C22—24no—
633C22—24no—
634C22—24no—
635C22—48no—
636C22C2×C3×#23714yes—
637C22C2×C3×#23712yes—
638C22C2×C3×#23712yes—
639C22C3×D3×#4112yes—
640C22C24×C3×D311yescharacteristic
641C4—22no—
642C4—24no—
643C4—34no—
644C4—62no—
645C4—62no—
646C4—64no—
647C4—62no—
648C4—64no—
649C4C2×C3×#23714yes—
650C3—21no—
651C3C2×#560011yescharacteristic, direct product factor
652C3C2×C3×#52911yescharacteristic, complemented
653C2—24no—
654C2—44no—
655C2C3×#560014yesdirect product factor
656C2C22×C3×#23711yescharacteristic
657C2C22×C3×#23711yescharacteristic
658C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#529
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C2×C3×#936C2semidirect
3. C2×C3×#935C2semidirect
4. C2×C3×D4×Dic3C2semidirect
5. C2×C3×D4×Dic3C2semidirect
6. C2×C3×#924C2semidirect
7. C22×C3×C4×Dic3C2semidirect
8. C3×#5600C2direct (N × H)
9. C2×C3×#890C2semidirect
10. C2×C3×#887C2semidirect
11. C2×C3×#879C2semidirect
12. C2×C3×#877C2semidirect
14. C2×#5600C3direct (N × H)
29. C3×#936C22semidirect
30. C3×#935C22semidirect
31. C3×D4×Dic3C22semidirect
32. C3×D4×Dic3C22semidirect
35. C3×#924C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. C3×#890C22semidirect
46. C3×#887C22semidirect
47. C3×#879C22semidirect
48. C3×#877C22semidirect
63. C2×#936C2×C3semidirect
64. C2×#935C2×C3semidirect
65. C2×D4×Dic3C2×C3semidirect
66. C2×D4×Dic3C2×C3semidirect
67. C2×#924C2×C3semidirect
68. C22×C4×Dic3C2×C3semidirect
69. #5600C2×C3direct (N × H)
70. C2×#890C2×C3semidirect
71. C2×#887C2×C3semidirect
72. C2×#879C2×C3semidirect
73. C2×#877C2×C3semidirect
170. #936C22×C3semidirect
171. #935C22×C3semidirect
172. D4×Dic3C22×C3semidirect
173. D4×Dic3C22×C3semidirect
176. #924C22×C3semidirect
185. C2×C4×Dic3C22×C3semidirect
186. #890C22×C3semidirect
187. #887C22×C3semidirect
188. #879C22×C3semidirect
189. #877C22×C3semidirect
474. C2×C32#529semidirect
576. C32C2×#529semidirect
621. C2×C3#5600direct (N × H)
622. C2×C3C3×#529semidirect
651. C3C2×#5600direct (N × H)
652. C3C2×C3×#529semidirect
655. C2C3×#5600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×#9362
C2×C3×#9352
C2×C3×D4×Dic32
C2×C3×#9242
C22×C3×C4×Dic32
C3×#56002
C2×C3×#8902
C2×C3×#8872
C2×C3×#8792
C2×C3×#8772
C2×C3×#5293
C2×#56003