Finite Group Databasebeta

← C2×C3×#5561 #11901613

Subgroups — C2×C3×#5561 #11901613

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic
3C2×C3×#936C211yesmaximal, characteristic, complemented
4C2×C3×#929C212yesmaximal, complemented
5C2×C3×#924C212yesmaximal, complemented
6C3×#5561C2116yesmaximal, direct product factor
7C2×C3×#897C211yesmaximal, characteristic, complemented
8C2×C3×#888C211yesmaximal, characteristic, complemented
9C2×C3×#885C212yesmaximal, complemented
10C2×C3×#879C212yesmaximal, complemented
11C2×C3×#872C211yesmaximal, characteristic, complemented
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×#542—31nomaximal
14C2×#5561C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2212yes—
21C32×C4×D4C2218yescomplemented
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2212yes—
24C2×C32×C42C2211yescharacteristic
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28C3×#938C2218yes—
29C3×#936C2218yescomplemented
30C3×#929C22116yescomplemented
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4⋊Dic3C2212yes—
36C3×#924C22116yescomplemented
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2212yes—
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2212yes—
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#897C2218yescomplemented
44C3×#888C2218yescomplemented
45C3×#885C22116yescomplemented
46C3×#879C22116yescomplemented
47C3×#872C2218yescomplemented
48C3×C4×Dic6C2218yescomplemented
49C3×#542—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#126—32no—
52C2×C3×#124—31no—
53C2×C3×#124—32no—
54C2×C3×#123—32no—
55C2×C3×C22⋊Q8—32no—
56C2×C3×C22⋊Q8—31no—
57C2×C3×#121—31no—
58C2×C3×C4×Q8—31no—
59C2×C3×C4×D4—21no—
60C2×C3×C4×D4D311yescharacteristic, complemented
61C2×C3×C4×D4C2×C311yescharacteristic, complemented
62C2×C3×#117—31no—
63C2×#938C2×C311yescharacteristic
64C2×#936C2×C311yescharacteristic, complemented
65C2×#929C2×C312yescomplemented
66C2×#924C2×C312yescomplemented
67#5561C2×C3116yesdirect product factor
68C2×#897C2×C311yescharacteristic, complemented
69C2×#888C2×C311yescharacteristic, complemented
70C2×#885C2×C312yescomplemented
71C2×#879C2×C312yescomplemented
72C2×#872C2×C311yescharacteristic, complemented
73C2×C4×Dic6C2×C311yescharacteristic, complemented
74C24×C32C2312yes—
75C23×C3×D3C2311yescharacteristic
76C2×C32×D4—24no—
77C2×C32×D4C2314yes—
78C22×C32×C4—44no—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2312yes—
82C22×C32×C4C2318yes—
83C22×C32×C4C2311yescharacteristic
84C2×C3×#67—44no—
85C2×C3×#67C2318yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6—44no—
95C2×C3×Dic6C2314yes—
96C2×C3×Dic6C2318yes—
97C32×C4⋊C4C2314yes—
98C32×C22⋊C4C2318yes—
99C32×C42C2314yes—
100C3×#217C2318yes—
101C3×#217C2318yes—
102C3×#217C2318yes—
103C3×(C2×D3)⋊C4C2314yes—
104C3×(C2×D3)⋊C4C2318yes—
105C3×(C2×D3)⋊C4C2314yes—
106C3×C4⋊Dic3C2318yes—
107C3×C4⋊Dic3C2314yes—
108C3×Dic3⋊C4C2314yes—
109C3×Dic3⋊C4C2318yes—
110C3×Dic3⋊C4C2314yes—
111C3×Dic3⋊C4C2318yes—
112C3×C4×Dic3C2318yes—
113C3×C4×Dic3C2314yes—
114C2×#542—31noSylow
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C22×C3×D4—21no—
118C22×C3×D4—32no—
119C22×C3×D4C2×D311yescharacteristic
120C22×C3×D4C22×C311yescharacteristic
121C23×C3×C4—22no—
122C23×C3×C4—31no—
123C23×C3×C4C2×D312yes—
124C23×C3×C4C22×C312yes—
125C22×#67C22×C312yes—
126C22×C4×D3C22×C311yescharacteristic
127C22×Dic6C22×C311yescharacteristic
128C22×Dic6C22×C312yes—
129C3×C4⋊Q8—38no—
130C3×#126—316no—
131C3×#124—38no—
132C3×#124—316no—
133C3×#123—316no—
134C3×C22⋊Q8—316no—
135C3×C22⋊Q8—38no—
136C3×#121—38no—
137C3×C4×Q8—38no—
138C3×C4×D4—28no—
139C3×C4×D4C2×D318yescomplemented
140C3×C4×D4C22×C318yescomplemented
141C3×#117—38no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4—32no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—32no—
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C22×C311yescharacteristic
151C2×C3×C22⋊C4—22no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—32no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—32no—
158C2×C3×C22⋊C4C2×D312yes—
159C2×C3×C22⋊C4C22×C312yes—
160C2×C3×C42—21no—
161C2×C3×C42—31no—
162C2×C3×C42—32no—
163C2×C3×C42C2×D311yescharacteristic
164C2×C3×C42C22×C311yescharacteristic
165C2×#217C22×C312yes—
166C2×#217C22×C312yes—
167C2×#217C22×C312yes—
168#938C22×C318yes—
169#936C22×C318yescomplemented
170#929C22×C3116yescomplemented
171C2×(C2×D3)⋊C4C22×C311yescharacteristic
172C2×(C2×D3)⋊C4C22×C311yescharacteristic
173C2×(C2×D3)⋊C4C22×C312yes—
174C2×C4⋊Dic3C22×C311yescharacteristic
175C2×C4⋊Dic3C22×C312yes—
176#924C22×C3116yescomplemented
177C2×Dic3⋊C4C22×C312yes—
178C2×Dic3⋊C4C22×C311yescharacteristic
179C2×Dic3⋊C4C22×C311yescharacteristic
180C2×Dic3⋊C4C22×C312yes—
181C2×C4×Dic3C22×C312yes—
182C2×C4×Dic3C22×C311yescharacteristic
183#897C22×C318yescomplemented
184#888C22×C318yescomplemented
185#885C22×C3116yescomplemented
186#879C22×C3116yescomplemented
187#872C22×C318yescomplemented
188C4×Dic6C22×C318yescomplemented
189C23×C32—24no—
190C23×C32—24no—
191C23×C32—24no—
192C23×C32C2414yes—
193C23×C32C2411yescharacteristic
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3C2412yes—
198C32×D4—28no—
199C2×C32×C4—22no—
200C2×C32×C4—24no—
201C2×C32×C4—22no—
202C2×C32×C4—48no—
203C2×C32×C4#4114yes—
204C2×C32×C4C2412yes—
205C2×C32×C4C2412yes—
206C2×C32×C4C2414yes—
207C2×C32×C4C2412yes—
208C3×#67—48no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2412yes—
219C3×C4×D3—28no—
220C3×Dic6—28no—
221C3×Dic6—48no—
222#542—316no—
223C2×C4⋊Q8—31no—
224C2×#126—32no—
225C2×#124—31no—
226C2×#124—32no—
227C2×#123—32no—
228C2×C22⋊Q8—32no—
229C2×C22⋊Q8—31no—
230C2×#121—31no—
231C2×C4×Q8—31no—
232C2×C4×D4C3×D311yescharacteristic, complemented
233C2×#117—31no—
234C24×C3—22no—
235C24×C3—31no—
236C24×C3C22×D312yes—
237C24×C3C23×C312yes—
238C23×D3C23×C311yescharacteristic
239C2×C3×Q8—34no—
240C2×C3×Q8—38no—
241C2×C3×Q8—64no—
242C2×C3×Q8—124no—
243C2×C3×D4—28no—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—24no—
247C2×C3×D4—38no—
248C2×C3×D4—124no—
249C2×C3×D4C22×D314yes—
250C2×C3×D4C23×C314yes—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4—28no—
256C22×C3×C4—31no—
257C22×C3×C4—32no—
258C22×C3×C4—31no—
259C22×C3×C4—32no—
260C22×C3×C4—31no—
261C22×C3×C4—34no—
262C22×C3×C4—44no—
263C22×C3×C4—44no—
264C22×C3×C4—48no—
265C22×C3×C4—64no—
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C22×D312yes—
269C22×C3×C4C22×D318yes—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C23×C311yescharacteristic
272C22×C3×C4C23×C311yescharacteristic
273C22×C3×C4C23×C312yes—
274C22×C3×C4C23×C318yes—
275C22×C3×C4C23×C311yescharacteristic
276C2×#67—44no—
277C2×#67C23×C318yes—
278C22×Dic3C23×C311yescharacteristic
279C22×Dic3C23×C312yes—
280C22×Dic3C23×C312yes—
281C22×Dic3C23×C311yescharacteristic
282C22×Dic3C23×C311yescharacteristic
283C2×C4×D3—24no—
284C2×C4×D3C23×C314yes—
285C2×Dic6—24no—
286C2×Dic6—44no—
287C2×Dic6C23×C314yes—
288C2×Dic6C23×C318yes—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—34no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—38no—
293C3×C4⋊C4—38no—
294C3×C4⋊C4—34no—
295C3×C4⋊C4—38no—
296C3×C4⋊C4C22×D314yes—
297C3×C4⋊C4C23×C314yes—
298C3×C22⋊C4—28no—
299C3×C22⋊C4—38no—
300C3×C22⋊C4—38no—
301C3×C22⋊C4—38no—
302C3×C22⋊C4—34no—
303C3×C22⋊C4—34no—
304C3×C22⋊C4—38no—
305C3×C22⋊C4C22×D318yes—
306C3×C22⋊C4C23×C318yes—
307C3×C42—24no—
308C3×C42—34no—
309C3×C42—38no—
310C3×C42C22×D314yes—
311C3×C42C23×C314yes—
312#217C23×C318yes—
313#217C23×C318yes—
314#217C23×C318yes—
315(C2×D3)⋊C4C23×C314yes—
316(C2×D3)⋊C4C23×C314yes—
317(C2×D3)⋊C4C23×C318yes—
318C4⋊Dic3C23×C314yes—
319C4⋊Dic3C23×C318yes—
320Dic3⋊C4C23×C318yes—
321Dic3⋊C4C23×C314yes—
322Dic3⋊C4C23×C314yes—
323Dic3⋊C4C23×C318yes—
324C4×Dic3C23×C318yes—
325C4×Dic3C23×C314yes—
326C22×C32—24no—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—48no—
330C22×C32C2×#4112yes—
331C22×C32H(5,𝔽2)12yes—
332C22×C322−1+412yes—
333C22×C32C2511yescharacteristic
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3—22no—
337C2×C3×D3—44no—
338C32×C4—22no—
339C32×C4—24no—
340C32×C4—22no—
341C32×C4C2×#4114yes—
342C3×Dic3—24no—
343C3×Dic3—22no—
344C3×Dic3—22no—
345C3×Dic3—24no—
346C3×Dic3—22no—
347C22×Q8—31no—
348C22×Q8—32no—
349C22×D4—32no—
350C22×D4C2×C3×D311yescharacteristic
351C23×C4—31no—
352C23×C4C2×C3×D312yes—
353C4⋊Q8—38no—
354#126—316no—
355#124—38no—
356#124—316no—
357#123—316no—
358C22⋊Q8—316no—
359C22⋊Q8—38no—
360#121—38no—
361C4×Q8—38no—
362C4×D4C2×C3×D318yescomplemented
363#117—38no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4C2×C3×D311yescharacteristic
371C2×C22⋊C4—32no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—31no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4C2×C3×D312yes—
378C2×C42—31no—
379C2×C42—32no—
380C2×C42C2×C3×D311yescharacteristic
381C23×C3—28no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—21no—
389C23×C3—24no—
390C23×C3—32no—
391C23×C3—44no—
392C23×C3—44no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3C23×D314yes—
397C23×C3C23×D311yescharacteristic
398C23×C3C24×C314yes—
399C23×C3C24×C311yescharacteristic
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—22no—
403C22×D3C24×C312yes—
404C3×Q8—68no—
405C3×Q8—128no—
406C3×D4—216no—
407C3×D4—28no—
408C3×D4—28no—
409C3×D4—128no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—32no—
423C2×C3×C4—34no—
424C2×C3×C4—32no—
425C2×C3×C4—34no—
426C2×C3×C4—32no—
427C2×C3×C4—42no—
428C2×C3×C4—44no—
429C2×C3×C4—48no—
430C2×C3×C4—48no—
431C2×C3×C4—416no—
432C2×C3×C4—62no—
433C2×C3×C4—64no—
434C2×C3×C4—64no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—68no—
438C2×C3×C4#23514yes—
439C2×C3×C4C3×#4114yes—
440C2×C3×C4C23×D312yes—
441C2×C3×C4C23×D312yes—
442C2×C3×C4C23×D314yes—
443C2×C3×C4C23×D312yes—
444C2×C3×C4C24×C312yes—
445C2×C3×C4C24×C312yes—
446C2×C3×C4C24×C314yes—
447C2×C3×C4C24×C312yes—
448#67—48no—
449C2×Dic3—24no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—24no—
453C2×Dic3—22no—
454C2×Dic3C24×C312yes—
455C2×Dic3C24×C314yes—
456C2×Dic3C24×C314yes—
457C2×Dic3C24×C312yes—
458C2×Dic3C24×C312yes—
459C4×D3—28no—
460Dic6—28no—
461Dic6—48no—
462C2×C32—44no—
463C2×C32#54214yescomplemented
464C2×C32C22×#4111yescharacteristic
465C2×C32C2×H(5,𝔽2)11yescharacteristic
466C2×C32C2×2−1+411yescharacteristic
467C3×D3—42no—
468C24—31no—
469C24C22×C3×D312yes—
470C2×Q8—34no—
471C2×Q8—38no—
472C2×Q8—64no—
473C2×Q8—124no—
474C2×D4—24no—
475C2×D4—38no—
476C2×D4—124no—
477C2×D4C22×C3×D314yes—
478C22×C4—31no—
479C22×C4—32no—
480C22×C4—31no—
481C22×C4—32no—
482C22×C4—31no—
483C22×C4—34no—
484C22×C4—44no—
485C22×C4—64no—
486C22×C4C22×C3×D311yescharacteristic
487C22×C4C22×C3×D311yescharacteristic
488C22×C4C22×C3×D312yes—
489C22×C4C22×C3×D318yes—
490C22×C4C22×C3×D311yescharacteristic
491C4⋊C4—34no—
492C4⋊C4—34no—
493C4⋊C4—34no—
494C4⋊C4—38no—
495C4⋊C4—38no—
496C4⋊C4—38no—
497C4⋊C4C22×C3×D314yes—
498C22⋊C4—38no—
499C22⋊C4—38no—
500C22⋊C4—38no—
501C22⋊C4—34no—
502C22⋊C4—34no—
503C22⋊C4—38no—
504C22⋊C4C22×C3×D318yes—
505C42—34no—
506C42—38no—
507C42C22×C3×D314yes—
508C22×C3—28no—
509C22×C3—24no—
510C22×C3—24no—
511C22×C3—24no—
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—416no—
522C22×C3—48no—
523C22×C3—48no—
524C22×C3—62no—
525C22×C3—62no—
526C22×C3—62no—
527C22×C3—124no—
528C22×C3C2×#23512yes—
529C22×C3#100412yes—
530C22×C3#101012yes—
531C22×C3C2×C3×#4112yes—
532C22×C3C3×H(5,𝔽2)12yes—
533C22×C3C3×2−1+412yes—
534C22×C3C24×D311yescharacteristic
535C22×C3C25×C311yescharacteristic
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—22no—
539C2×D3—44no—
540C3×C4—24no—
541C3×C4—22no—
542C3×C4—24no—
543C3×C4—22no—
544C3×C4—24no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—24no—
548C3×C4—44no—
549C3×C4—42no—
550C3×C4—62no—
551C3×C4—64no—
552C3×C4—64no—
553C3×C4—62no—
554C3×C4—62no—
555C3×C4C2×#23514yes—
556C3×C4C2×C3×#4114yes—
557Dic3—24no—
558Dic3—22no—
559Dic3—22no—
560Dic3—24no—
561Dic3—22no—
562C32C2×#54211yescharacteristic, complemented, Sylow
563C23—24no—
564C23—24no—
565C23—24no—
566C23—32no—
567C23—62no—
568C23—62no—
569C23—62no—
570C23C23×C3×D314yes—
571C23C23×C3×D311yescharacteristic
572Q8—68no—
573Q8—128no—
574D4—28no—
575D4—128no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—32no—
580C2×C4—34no—
581C2×C4—32no—
582C2×C4—34no—
583C2×C4—32no—
584C2×C4—48no—
585C2×C4—62no—
586C2×C4—64no—
587C2×C4—64no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—68no—
591C2×C4C3×#23514yes—
592C2×C4C23×C3×D312yes—
593C2×C4C23×C3×D312yes—
594C2×C4C23×C3×D314yes—
595C2×C4C23×C3×D312yes—
596C2×C3—24no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—48no—
601C2×C3—44no—
602C2×C3—44no—
603C2×C3—122no—
604C2×C3#556114yesdirect product factor
605C2×C3C3×#54214yescomplemented
606C2×C3C22×#23511yescharacteristic
607C2×C3C2×#100411yescharacteristic
608C2×C3C2×#101011yescharacteristic
609C2×C3C22×C3×#4111yescharacteristic
610C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
611C2×C3C2×C3×2−1+411yescharacteristic
612D3—42no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—48no—
617C22—62no—
618C22—62no—
619C22—62no—
620C22—124no—
621C22C2×C3×#23512yes—
622C22C3×#100412yes—
623C22C3×#101012yes—
624C22C24×C3×D311yescharacteristic
625C4—22no—
626C4—24no—
627C4—22no—
628C4—62no—
629C4—64no—
630C4—64no—
631C4—62no—
632C4—62no—
633C4C2×C3×#23514yes—
634C3—21no—
635C3C2×#556111yescharacteristic, direct product factor
636C3C2×C3×#54211yescharacteristic, complemented
637C2—44no—
638C2—122no—
639C2C3×#556114yesdirect product factor
640C2C22×C3×#23511yescharacteristic
641C2C2×C3×#100411yescharacteristic
642C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#938C2
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×#542
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C3×#936C2semidirect
4. C2×C3×#929C2semidirect
5. C2×C3×#924C2semidirect
6. C3×#5561C2direct (N × H)
7. C2×C3×#897C2semidirect
8. C2×C3×#888C2semidirect
9. C2×C3×#885C2semidirect
10. C2×C3×#879C2semidirect
11. C2×C3×#872C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5561C3direct (N × H)
21. C32×C4×D4C22semidirect
29. C3×#936C22semidirect
30. C3×#929C22semidirect
36. C3×#924C22semidirect
43. C3×#897C22semidirect
44. C3×#888C22semidirect
45. C3×#885C22semidirect
46. C3×#879C22semidirect
47. C3×#872C22semidirect
48. C3×C4×Dic6C22semidirect
60. C2×C3×C4×D4D3semidirect
61. C2×C3×C4×D4C2×C3semidirect
64. C2×#936C2×C3semidirect
65. C2×#929C2×C3semidirect
66. C2×#924C2×C3semidirect
67. #5561C2×C3direct (N × H)
68. C2×#897C2×C3semidirect
69. C2×#888C2×C3semidirect
70. C2×#885C2×C3semidirect
71. C2×#879C2×C3semidirect
72. C2×#872C2×C3semidirect
73. C2×C4×Dic6C2×C3semidirect
139. C3×C4×D4C2×D3semidirect
140. C3×C4×D4C22×C3semidirect
169. #936C22×C3semidirect
170. #929C22×C3semidirect
176. #924C22×C3semidirect
183. #897C22×C3semidirect
184. #888C22×C3semidirect
185. #885C22×C3semidirect
186. #879C22×C3semidirect
187. #872C22×C3semidirect
188. C4×Dic6C22×C3semidirect
232. C2×C4×D4C3×D3semidirect
362. C4×D4C2×C3×D3semidirect
463. C2×C32#542semidirect
562. C32C2×#542semidirect
604. C2×C3#5561direct (N × H)
605. C2×C3C3×#542semidirect
635. C3C2×#5561direct (N × H)
636. C3C2×C3×#542semidirect
639. C2C3×#5561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9382
C2×C3×#9362
C2×C3×#9292
C2×C3×#9242
C3×#55612
C2×C3×#8972
C2×C3×#8882
C2×C3×#8852
C2×C3×#8792
C2×C3×#8722
C2×C3×C4×Dic62
C2×C3×#5423
C2×#55613