Finite Group Databasebeta

← C2×C3×#5644 #11901278

Subgroups — C2×C3×#5644 #11901278

Order 1152.

2833 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#947C212yesmaximal, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C3×#5644C2116yesmaximal, direct product factor
6C2×C3×#898C212yesmaximal, complemented
7C2×C3×#895C212yesmaximal, complemented
8C2×C3×#894C212yesmaximal, complemented
9C2×C3×#882C212yesmaximal, complemented
10C2×C3×#67⋊C4C212yesmaximal, complemented
11C2×C3×#538—31nomaximal
12C2×#5644C311yesmaximal, characteristic, direct product factor
13C24×C3×D3C2211yescharacteristic
14C22×C32×Q8C2211yescharacteristic, complemented
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×D12C2212yes—
19C22×C3×D12C2212yes—
20C22×C3×D12C2211yescharacteristic, complemented
21C22×C3×C4×D3C2212yescomplemented
22C32×C22⋊Q8C2218yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×C32×C4⋊C4C2212yescomplemented
25C2×C32×C22⋊C4C2212yes—
26C3×#947C22116yescomplemented
27C3×#930C2218yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yescomplemented
34C2×C3×(C2×D3)⋊C4C2212yescomplemented
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2212yescomplemented
37C2×C3×C4×Dic3C2212yescomplemented
38C3×#898C22116yescomplemented
39C3×#895C22116yescomplemented
40C3×#894C22116yescomplemented
41C3×#882C22116yescomplemented
42C3×#67⋊C4C22116yescomplemented
43C3×#538—316no—
44C2×C3×#126—32no—
45C2×C3×#124—32no—
46C2×C3×#123—32no—
47C2×C3×C22⋊Q8—21no—
48C2×C3×C22⋊Q8D311yescharacteristic, complemented
49C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
50C2×C3×#121—31no—
51C2×C3×#121—32no—
52C2×C3×#120—32no—
53C2×C3×C4×D4—32no—
54C22×C3×C22⋊C4—31no—
55C2×#947C2×C312yescomplemented
56C2×#930C2×C311yescharacteristic, complemented
57C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
58#5644C2×C3116yesdirect product factor
59C2×#898C2×C312yescomplemented
60C2×#895C2×C312yescomplemented
61C2×#894C2×C312yescomplemented
62C2×#882C2×C312yescomplemented
63C2×#67⋊C4C2×C312yescomplemented
64C24×C32C2311yescharacteristic
65C23×C3×D3—24no—
66C23×C3×D3—42no—
67C23×C3×D3—42no—
68C23×C3×D3C2312yes—
69C23×C3×D3C2312yes—
70C23×C3×D3C2314yes—
71C2×C32×Q8—42no—
72C2×C32×Q8C2314yescomplemented
73C22×C32×C4—42no—
74C22×C32×C4C2312yes—
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2314yes—
79C2×C3×#67—28no—
80C2×C3×#67C2318yes—
81C22×C3×Dic3—42no—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2314yes—
85C2×C3×D12—44no—
86C2×C3×D12—44no—
87C2×C3×D12—42no—
88C2×C3×D12C2318yes—
89C2×C3×D12C2318yes—
90C2×C3×D12C2314yescomplemented
91C2×C3×C4×D3—44no—
92C2×C3×C4×D3C2318yescomplemented
93C32×C4⋊C4C2314yescomplemented
94C32×C4⋊C4C2318yescomplemented
95C32×C22⋊C4C2318yes—
96C3×(C2×D3)⋊C4C2318yes—
97C3×(C2×D3)⋊C4C2318yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×(C2×D3)⋊C4C2318yes—
100C3×(C2×D3)⋊C4C2318yescomplemented
101C3×(C2×D3)⋊C4C2318yescomplemented
102C3×C4⋊Dic3C2314yescomplemented
103C3×Dic3⋊C4C2318yescomplemented
104C3×C4×Dic3C2318yescomplemented
105C2×#538—31noSylow
106C25×C3—31no—
107C24×D3C22×C311yescharacteristic
108C22×C3×Q8—21no—
109C22×C3×Q8C2×D311yescharacteristic, complemented
110C22×C3×Q8C22×C311yescharacteristic, complemented
111C22×C3×D4—32no—
112C22×C3×D4—32no—
113C22×C3×D4—32no—
114C22×C3×D4—31no—
115C23×C3×C4—21no—
116C23×C3×C4—31no—
117C23×C3×C4—32no—
118C23×C3×C4C2×D311yescharacteristic
119C23×C3×C4C22×C311yescharacteristic
120C22×#67C22×C312yes—
121C23×Dic3C22×C311yescharacteristic
122C22×D12C22×C312yes—
123C22×D12C22×C312yes—
124C22×D12C22×C311yescharacteristic, complemented
125C22×C4×D3C22×C312yescomplemented
126C3×#126—316no—
127C3×#124—316no—
128C3×#123—316no—
129C3×C22⋊Q8—28no—
130C3×C22⋊Q8C2×D318yescomplemented
131C3×C22⋊Q8C22×C318yescomplemented
132C3×#121—38no—
133C3×#121—316no—
134C3×#120—316no—
135C3×C4×D4—316no—
136C2×C3×C4⋊C4—22no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—32no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4C2×D312yescomplemented
141C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
142C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
143C2×C3×C4⋊C4C22×C312yescomplemented
144C2×C3×C22⋊C4—22no—
145C2×C3×C22⋊C4—32no—
146C2×C3×C22⋊C4—32no—
147C2×C3×C22⋊C4—32no—
148C2×C3×C22⋊C4—32no—
149C2×C3×C22⋊C4—38no—
150C2×C3×C22⋊C4—32no—
151C2×C3×C22⋊C4—32no—
152C2×C3×C22⋊C4C2×D312yes—
153C2×C3×C22⋊C4C22×C312yes—
154C2×C3×C42—32no—
155#947C22×C3116yescomplemented
156#930C22×C318yescomplemented
157C2×(C2×D3)⋊C4C22×C312yes—
158C2×(C2×D3)⋊C4C22×C312yes—
159C2×(C2×D3)⋊C4C22×C312yes—
160C2×(C2×D3)⋊C4C22×C312yes—
161C2×(C2×D3)⋊C4C22×C318yescomplemented
162C2×(C2×D3)⋊C4C22×C312yescomplemented
163C2×(C2×D3)⋊C4C22×C312yescomplemented
164C2×C4⋊Dic3C22×C311yescharacteristic, complemented
165C2×Dic3⋊C4C22×C312yescomplemented
166C2×C4×Dic3C22×C312yescomplemented
167#898C22×C3116yescomplemented
168#895C22×C3116yescomplemented
169#894C22×C3116yescomplemented
170#882C22×C3116yescomplemented
171#67⋊C4C22×C3116yescomplemented
172C23×C32—22no—
173C23×C32—22no—
174C23×C32#4114yes—
175C23×C32C2412yes—
176C23×C32C2411yescharacteristic
177C22×C3×D3—28no—
178C22×C3×D3—24no—
179C22×C3×D3—24no—
180C22×C3×D3—24no—
181C22×C3×D3—24no—
182C22×C3×D3—24no—
183C22×C3×D3—24no—
184C22×C3×D3—44no—
185C22×C3×D3—44no—
186C22×C3×D3—416no—
187C22×C3×D3C2414yes—
188C22×C3×D3C2414yes—
189C32×Q8—44no—
190C2×C32×C4—22no—
191C2×C32×C4—24no—
192C2×C32×C4—22no—
193C2×C32×C4—24no—
194C2×C32×C4—44no—
195C2×C32×C4C2414yes—
196C2×C32×C4C2414yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199C3×#67—216no—
200C2×C3×Dic3—24no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—44no—
203C2×C3×Dic3C2414yes—
204C2×C3×Dic3C2414yes—
205C3×D12—48no—
206C3×D12—48no—
207C3×D12—44no—
208C3×C4×D3—48no—
209#538—316no—
210C2×#126—32no—
211C2×#124—32no—
212C2×#123—32no—
213C2×C22⋊Q8C3×D311yescharacteristic, complemented
214C2×#121—31no—
215C2×#121—32no—
216C2×#120—32no—
217C2×C4×D4—32no—
218C22×C22⋊C4—31no—
219C24×C3—21no—
220C24×C3—32no—
221C24×C3—32no—
222C24×C3—34no—
223C24×C3—64no—
224C24×C3—122no—
225C24×C3—122no—
226C24×C3C22×D311yescharacteristic
227C24×C3C23×C311yescharacteristic
228C23×D3—24no—
229C23×D3—42no—
230C23×D3—42no—
231C23×D3C23×C312yes—
232C23×D3C23×C312yes—
233C23×D3C23×C314yes—
234C2×C3×Q8—24no—
235C2×C3×Q8—42no—
236C2×C3×Q8—42no—
237C2×C3×Q8—44no—
238C2×C3×Q8C22×D314yescomplemented
239C2×C3×Q8C23×C314yescomplemented
240C2×C3×D4—38no—
241C2×C3×D4—38no—
242C2×C3×D4—38no—
243C2×C3×D4—34no—
244C2×C3×D4—68no—
245C2×C3×D4—122no—
246C2×C3×D4—124no—
247C2×C3×D4—124no—
248C22×C3×C4—21no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—21no—
252C22×C3×C4—24no—
253C22×C3×C4—32no—
254C22×C3×C4—32no—
255C22×C3×C4—34no—
256C22×C3×C4—38no—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4—44no—
260C22×C3×C4—124no—
261C22×C3×C4—122no—
262C22×C3×C4C22×D312yes—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D312yes—
266C22×C3×C4C22×D314yes—
267C22×C3×C4C23×C312yes—
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C311yescharacteristic
270C22×C3×C4C23×C311yescharacteristic
271C22×C3×C4C23×C314yes—
272C2×#67—28no—
273C2×#67C23×C318yes—
274C22×Dic3—42no—
275C22×Dic3C23×C312yes—
276C22×Dic3C23×C312yes—
277C22×Dic3C23×C314yes—
278C2×D12—44no—
279C2×D12—44no—
280C2×D12—42no—
281C2×D12C23×C318yes—
282C2×D12C23×C318yes—
283C2×D12C23×C314yescomplemented
284C2×C4×D3—44no—
285C2×C4×D3C23×C318yescomplemented
286C3×C4⋊C4—28no—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4C22×D318yescomplemented
291C3×C4⋊C4C22×D314yescomplemented
292C3×C4⋊C4C23×C314yescomplemented
293C3×C4⋊C4C23×C318yescomplemented
294C3×C22⋊C4—28no—
295C3×C22⋊C4—38no—
296C3×C22⋊C4—38no—
297C3×C22⋊C4—38no—
298C3×C22⋊C4—38no—
299C3×C22⋊C4—38no—
300C3×C22⋊C4—38no—
301C3×C22⋊C4C22×D318yes—
302C3×C22⋊C4C23×C318yes—
303C3×C42—38no—
304(C2×D3)⋊C4C23×C318yes—
305(C2×D3)⋊C4C23×C318yes—
306(C2×D3)⋊C4C23×C318yes—
307(C2×D3)⋊C4C23×C318yes—
308(C2×D3)⋊C4C23×C318yescomplemented
309(C2×D3)⋊C4C23×C318yescomplemented
310C4⋊Dic3C23×C314yescomplemented
311Dic3⋊C4C23×C318yescomplemented
312C4×Dic3C23×C318yescomplemented
313C22×C32—28no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32C2×#4114yes—
317C22×C32C2×#4112yes—
318C22×C32H(5,𝔽2)12yes—
319C22×C32H(5,𝔽2)12yes—
320C22×C32C2511yescharacteristic
321C2×C3×D3—24no—
322C2×C3×D3—24no—
323C2×C3×D3—24no—
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—24no—
327C2×C3×D3—416no—
328C2×C3×D3—48no—
329C2×C3×D3—48no—
330C32×C4—22no—
331C32×C4—24no—
332C32×C4—22no—
333C32×C4—24no—
334C3×Dic3—24no—
335C3×Dic3—24no—
336C25—31no—
337C22×Q8C2×C3×D311yescharacteristic, complemented
338C22×D4—32no—
339C22×D4—32no—
340C22×D4—32no—
341C22×D4—31no—
342C23×C4—31no—
343C23×C4—32no—
344C23×C4C2×C3×D311yescharacteristic
345#126—316no—
346#124—316no—
347#123—316no—
348C22⋊Q8C2×C3×D318yescomplemented
349#121—38no—
350#121—316no—
351#120—316no—
352C4×D4—316no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4C2×C3×D312yescomplemented
356C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
357C2×C22⋊C4—32no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—38no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—32no—
364C2×C22⋊C4C2×C3×D312yes—
365C2×C42—32no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—22no—
372C23×C3—24no—
373C23×C3—34no—
374C23×C3—34no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—64no—
378C23×C3—64no—
379C23×C3—64no—
380C23×C3—68no—
381C23×C3—64no—
382C23×C3—64no—
383C23×C3—64no—
384C23×C3—124no—
385C23×C3—124no—
386C23×C3—1216no—
387C23×C3#23914yes—
388C23×C3C3×#4114yes—
389C23×C3C23×D312yes—
390C23×C3C23×D311yescharacteristic
391C23×C3C24×C312yes—
392C23×C3C24×C311yescharacteristic
393C22×D3—24no—
394C22×D3—28no—
395C22×D3—24no—
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—44no—
401C22×D3—44no—
402C22×D3—416no—
403C22×D3C24×C314yes—
404C22×D3C24×C314yes—
405C3×Q8—44no—
406C3×Q8—44no—
407C3×Q8—48no—
408C3×D4—616no—
409C3×D4—124no—
410C3×D4—128no—
411C3×D4—128no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—22no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—34no—
426C2×C3×C4—34no—
427C2×C3×C4—44no—
428C2×C3×C4—42no—
429C2×C3×C4—44no—
430C2×C3×C4—44no—
431C2×C3×C4—44no—
432C2×C3×C4—48no—
433C2×C3×C4—64no—
434C2×C3×C4—64no—
435C2×C3×C4—128no—
436C2×C3×C4—124no—
437C2×C3×C4C23×D314yes—
438C2×C3×C4C23×D312yes—
439C2×C3×C4C23×D312yes—
440C2×C3×C4C23×D314yes—
441C2×C3×C4C24×C314yes—
442C2×C3×C4C24×C314yes—
443C2×C3×C4C24×C312yes—
444C2×C3×C4C24×C312yes—
445#67—216no—
446C2×Dic3—24no—
447C2×Dic3—24no—
448C2×Dic3—44no—
449C2×Dic3C24×C314yes—
450C2×Dic3C24×C314yes—
451D12—48no—
452D12—48no—
453D12—44no—
454C4×D3—48no—
455C2×C32—24no—
456C2×C32#53814yescomplemented
457C2×C32C22×#4111yescharacteristic
458C2×C32C2×H(5,𝔽2)11yescharacteristic
459C2×C32C2×H(5,𝔽2)11yescharacteristic
460C3×D3—44no—
461C3×D3—44no—
462C24—32no—
463C24—32no—
464C24—34no—
465C24—64no—
466C24—122no—
467C24—122no—
468C24C22×C3×D311yescharacteristic
469C2×Q8—42no—
470C2×Q8C22×C3×D314yescomplemented
471C2×D4—38no—
472C2×D4—38no—
473C2×D4—38no—
474C2×D4—34no—
475C2×D4—68no—
476C2×D4—122no—
477C2×D4—124no—
478C2×D4—124no—
479C22×C4—32no—
480C22×C4—32no—
481C22×C4—34no—
482C22×C4—38no—
483C22×C4—42no—
484C22×C4—124no—
485C22×C4—122no—
486C22×C4C22×C3×D312yes—
487C22×C4C22×C3×D311yescharacteristic
488C22×C4C22×C3×D311yescharacteristic
489C22×C4C22×C3×D312yes—
490C22×C4C22×C3×D314yes—
491C4⋊C4—38no—
492C4⋊C4—34no—
493C4⋊C4C22×C3×D318yescomplemented
494C4⋊C4C22×C3×D314yescomplemented
495C22⋊C4—38no—
496C22⋊C4—38no—
497C22⋊C4—38no—
498C22⋊C4—38no—
499C22⋊C4—38no—
500C22⋊C4—38no—
501C22⋊C4C22×C3×D318yes—
502C42—38no—
503C22×C3—28no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—28no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—24no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—48no—
517C22×C3—64no—
518C22×C3—64no—
519C22×C3—64no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—64no—
523C22×C3—1216no—
524C22×C3—128no—
525C22×C3—128no—
526C22×C3#100412yes—
527C22×C3C2×#23914yes—
528C22×C3C2×#23912yes—
529C22×C3#100912yes—
530C22×C3C2×C3×#4114yes—
531C22×C3C2×C3×#4112yes—
532C22×C3C3×H(5,𝔽2)12yes—
533C22×C3C3×H(5,𝔽2)12yes—
534C22×C3C24×D311yescharacteristic
535C22×C3C25×C311yescharacteristic
536C2×D3—24no—
537C2×D3—24no—
538C2×D3—24no—
539C2×D3—24no—
540C2×D3—24no—
541C2×D3—24no—
542C2×D3—416no—
543C2×D3—48no—
544C2×D3—48no—
545C3×C4—24no—
546C3×C4—22no—
547C3×C4—22no—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—24no—
551C3×C4—22no—
552C3×C4—24no—
553C3×C4—22no—
554C3×C4—42no—
555C3×C4—44no—
556C3×C4—44no—
557C3×C4—64no—
558C3×C4—64no—
559Dic3—24no—
560Dic3—24no—
561C32C2×#53811yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—34no—
565C23—34no—
566C23—64no—
567C23—64no—
568C23—64no—
569C23—68no—
570C23—64no—
571C23—64no—
572C23—64no—
573C23—124no—
574C23—124no—
575C23—1216no—
576C23C3×#23914yes—
577C23C23×C3×D312yes—
578C23C23×C3×D311yescharacteristic
579Q8—44no—
580D4—616no—
581D4—124no—
582D4—128no—
583D4—128no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—34no—
589C2×C4—34no—
590C2×C4—44no—
591C2×C4—64no—
592C2×C4—64no—
593C2×C4—128no—
594C2×C4—124no—
595C2×C4C23×C3×D314yes—
596C2×C4C23×C3×D312yes—
597C2×C4C23×C3×D312yes—
598C2×C4C23×C3×D314yes—
599C2×C3—24no—
600C2×C3—24no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—24no—
605C2×C3—44no—
606C2×C3—124no—
607C2×C3—124no—
608C2×C3#564414yesdirect product factor
609C2×C3C3×#53814yescomplemented
610C2×C3C2×#100411yescharacteristic
611C2×C3C22×#23911yescharacteristic
612C2×C3C2×#100911yescharacteristic
613C2×C3C22×C3×#4111yescharacteristic
614C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
615C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
616D3—44no—
617D3—44no—
618C22—22no—
619C22—22no—
620C22—28no—
621C22—64no—
622C22—64no—
623C22—64no—
624C22—64no—
625C22—64no—
626C22—64no—
627C22—1216no—
628C22—128no—
629C22—128no—
630C22C3×#100412yes—
631C22C2×C3×#23914yes—
632C22C2×C3×#23912yes—
633C22C3×#100912yes—
634C22C24×C3×D311yescharacteristic
635C4—22no—
636C4—22no—
637C4—24no—
638C4—24no—
639C4—64no—
640C4—64no—
641C3—21no—
642C3C2×#564411yescharacteristic, direct product factor
643C3C2×C3×#53811yescharacteristic, complemented
644C2—24no—
645C2—124no—
646C2—124no—
647C2C3×#564414yesdirect product factor
648C2C2×C3×#100411yescharacteristic
649C2C22×C3×#23911yescharacteristic
650C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C2×C3×#538
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C22⋊Q8C2semidirect
2. C2×C3×#947C2semidirect
3. C2×C3×#930C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C3×#5644C2direct (N × H)
6. C2×C3×#898C2semidirect
7. C2×C3×#895C2semidirect
8. C2×C3×#894C2semidirect
9. C2×C3×#882C2semidirect
10. C2×C3×#67⋊C4C2semidirect
12. C2×#5644C3direct (N × H)
14. C22×C32×Q8C22semidirect
20. C22×C3×D12C22semidirect
21. C22×C3×C4×D3C22semidirect
22. C32×C22⋊Q8C22semidirect
23. C2×C32×C4⋊C4C22semidirect
24. C2×C32×C4⋊C4C22semidirect
26. C3×#947C22semidirect
27. C3×#930C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. C3×#898C22semidirect
39. C3×#895C22semidirect
40. C3×#894C22semidirect
41. C3×#882C22semidirect
42. C3×#67⋊C4C22semidirect
48. C2×C3×C22⋊Q8D3semidirect
49. C2×C3×C22⋊Q8C2×C3semidirect
55. C2×#947C2×C3semidirect
56. C2×#930C2×C3semidirect
57. C22×(C2×D3)⋊C4C2×C3semidirect
58. #5644C2×C3direct (N × H)
59. C2×#898C2×C3semidirect
60. C2×#895C2×C3semidirect
61. C2×#894C2×C3semidirect
62. C2×#882C2×C3semidirect
63. C2×#67⋊C4C2×C3semidirect
72. C2×C32×Q8C23semidirect
90. C2×C3×D12C23semidirect
92. C2×C3×C4×D3C23semidirect
93. C32×C4⋊C4C23semidirect
94. C32×C4⋊C4C23semidirect
100. C3×(C2×D3)⋊C4C23semidirect
101. C3×(C2×D3)⋊C4C23semidirect
102. C3×C4⋊Dic3C23semidirect
103. C3×Dic3⋊C4C23semidirect
104. C3×C4×Dic3C23semidirect
109. C22×C3×Q8C2×D3semidirect
110. C22×C3×Q8C22×C3semidirect
124. C22×D12C22×C3semidirect
125. C22×C4×D3C22×C3semidirect
130. C3×C22⋊Q8C2×D3semidirect
131. C3×C22⋊Q8C22×C3semidirect
140. C2×C3×C4⋊C4C2×D3semidirect
141. C2×C3×C4⋊C4C2×D3semidirect
142. C2×C3×C4⋊C4C22×C3semidirect
143. C2×C3×C4⋊C4C22×C3semidirect
155. #947C22×C3semidirect
156. #930C22×C3semidirect
161. C2×(C2×D3)⋊C4C22×C3semidirect
162. C2×(C2×D3)⋊C4C22×C3semidirect
163. C2×(C2×D3)⋊C4C22×C3semidirect
164. C2×C4⋊Dic3C22×C3semidirect
165. C2×Dic3⋊C4C22×C3semidirect
166. C2×C4×Dic3C22×C3semidirect
167. #898C22×C3semidirect
168. #895C22×C3semidirect
169. #894C22×C3semidirect
170. #882C22×C3semidirect
171. #67⋊C4C22×C3semidirect
213. C2×C22⋊Q8C3×D3semidirect
238. C2×C3×Q8C22×D3semidirect
239. C2×C3×Q8C23×C3semidirect
283. C2×D12C23×C3semidirect
285. C2×C4×D3C23×C3semidirect
290. C3×C4⋊C4C22×D3semidirect
291. C3×C4⋊C4C22×D3semidirect
292. C3×C4⋊C4C23×C3semidirect
293. C3×C4⋊C4C23×C3semidirect
308. (C2×D3)⋊C4C23×C3semidirect
309. (C2×D3)⋊C4C23×C3semidirect
310. C4⋊Dic3C23×C3semidirect
311. Dic3⋊C4C23×C3semidirect
312. C4×Dic3C23×C3semidirect
337. C22×Q8C2×C3×D3semidirect
348. C22⋊Q8C2×C3×D3semidirect
355. C2×C4⋊C4C2×C3×D3semidirect
356. C2×C4⋊C4C2×C3×D3semidirect
456. C2×C32#538semidirect
470. C2×Q8C22×C3×D3semidirect
493. C4⋊C4C22×C3×D3semidirect
494. C4⋊C4C22×C3×D3semidirect
561. C32C2×#538semidirect
608. C2×C3#5644direct (N × H)
609. C2×C3C3×#538semidirect
642. C3C2×#5644direct (N × H)
643. C3C2×C3×#538semidirect
647. C2C3×#5644direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×C3×#9472
C2×C3×#9302
C22×C3×(C2×D3)⋊C42
C3×#56442
C2×C3×#8982
C2×C3×#8952
C2×C3×#8942
C2×C3×#8822
C2×C3×#67⋊C42
C2×C3×#5383
C2×#56443