Finite Group Databasebeta

← C2×C3×#5690 #11903222

Subgroups — C2×C3×#5690 #11903222

Order 1152.

2513 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic, complemented
2C3×#5690C2116yesmaximal, direct product factor
3C2×C3×#897C212yesmaximal, complemented
4C2×C3×#896C212yesmaximal, complemented
5C2×C3×#896C212yesmaximal, complemented
6C2×C3×#893C211yesmaximal, characteristic
7C2×C3×#893C211yesmaximal, characteristic
8C2×C3×D3×C4⋊C4C212yesmaximal, complemented
9C2×C3×#890C211yesmaximal, characteristic, complemented
10C2×C3×#888C211yesmaximal, characteristic, complemented
11C2×C3×C4×D12C211yesmaximal, characteristic
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×#554—31nomaximal
14C2×#5690C311yesmaximal, characteristic, direct product factor
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2212yes—
18C22×C3×C4×D3C2212yes—
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2212yes—
21C32×#125C2218yescomplemented
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2212yes—
25C2×C32×C4⋊C4C2212yes—
26C2×C32×C42C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#897C22116yescomplemented
40C3×#896C22116yescomplemented
41C3×#896C22116yescomplemented
42C3×#893C2218yes—
43C3×#893C2218yes—
44C3×D3×C4⋊C4C22116yescomplemented
45C3×#890C2218yescomplemented
46C3×#888C2218yescomplemented
47C3×C4×D12C2218yes—
48C3×C4×Dic6C2218yescomplemented
49C3×#554—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#125—21no—
52C2×C3×#125—31no—
53C2×C3×#125D311yescharacteristic, complemented
54C2×C3×#125C2×C311yescharacteristic, complemented
55C2×C3×C22⋊Q8—32no—
56C2×C3×C22⋊Q8—32no—
57C2×C3×C22⋊Q8—32no—
58C2×C3×C4×Q8—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—31no—
61C2×C3×C4×D4—31no—
62C22×C3×C4⋊C4—32no—
63#5690C2×C3116yesdirect product factor
64C2×#897C2×C312yescomplemented
65C2×#896C2×C312yescomplemented
66C2×#896C2×C312yescomplemented
67C2×#893C2×C311yescharacteristic
68C2×#893C2×C311yescharacteristic
69C2×D3×C4⋊C4C2×C312yescomplemented
70C2×#890C2×C311yescharacteristic, complemented
71C2×#888C2×C311yescharacteristic, complemented
72C2×C4×D12C2×C311yescharacteristic
73C2×C4×Dic6C2×C311yescharacteristic, complemented
74C23×C3×D3C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2312yes—
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C2×C3×D12Q818yescomplemented
86C2×C3×D12C2314yes—
87C2×C3×C4×D3—28no—
88C2×C3×C4×D3—44no—
89C2×C3×C4×D3—44no—
90C2×C3×C4×D3C2318yes—
91C2×C3×C4×D3C2318yes—
92C2×C3×C4×D3C2318yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6—44no—
95C2×C3×Dic6C2314yes—
96C2×C3×Dic6C2318yes—
97C32×C4⋊C4C2314yes—
98C32×C4⋊C4C2314yes—
99C32×C4⋊C4C2318yes—
100C32×C4⋊C4C2318yes—
101C32×C42C2314yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×(C2×D3)⋊C4C2318yes—
105C3×C4⋊Dic3C2314yes—
106C3×C4⋊Dic3C2318yes—
107C3×C4⋊Dic3C2314yes—
108C3×Dic3⋊C4C2318yes—
109C3×Dic3⋊C4C2318yes—
110C3×Dic3⋊C4C2314yes—
111C3×Dic3⋊C4C2314yes—
112C3×C4×Dic3C2314yes—
113C3×C4×Dic3C2314yes—
114C2×#554—31noSylow
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C22×C3×D4—31no—
118C23×C3×C4—32no—
119C23×C3×C4—32no—
120C23×C3×C4—32no—
121C22×D12C22×C311yescharacteristic
122C22×C4×D3C22×C312yes—
123C22×C4×D3C22×C312yes—
124C22×C4×D3C22×C312yes—
125C22×Dic6C22×C311yescharacteristic
126C22×Dic6C22×C312yes—
127C3×C4⋊Q8—38no—
128C3×#125—28no—
129C3×#125—38no—
130C3×#125C2×D318yescomplemented
131C3×#125C22×C318yescomplemented
132C3×C22⋊Q8—316no—
133C3×C22⋊Q8—316no—
134C3×C22⋊Q8—316no—
135C3×C4×Q8—38no—
136C3×C4×D4—38no—
137C3×C4×D4—38no—
138C3×C4×D4—38no—
139C2×C3×C4⋊C4—22no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—22no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—32no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—32no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4—31no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—316no—
151C2×C3×C4⋊C4C2×D312yes—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C2×D312yes—
155C2×C3×C4⋊C4C22×C311yescharacteristic
156C2×C3×C4⋊C4C22×C311yescharacteristic
157C2×C3×C4⋊C4C22×C312yes—
158C2×C3×C4⋊C4C22×C312yes—
159C2×C3×C22⋊C4—32no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—32no—
162C2×C3×C42—21no—
163C2×C3×C42—31no—
164C2×C3×C42—31no—
165C2×C3×C42C2×D311yescharacteristic
166C2×C3×C42C22×C311yescharacteristic
167C2×(C2×D3)⋊C4C22×C312yes—
168C2×(C2×D3)⋊C4C22×C312yes—
169C2×(C2×D3)⋊C4C22×C312yes—
170C2×C4⋊Dic3C22×C311yescharacteristic
171C2×C4⋊Dic3C22×C311yescharacteristic
172C2×C4⋊Dic3C22×C312yes—
173C2×Dic3⋊C4C22×C311yescharacteristic
174C2×Dic3⋊C4C22×C311yescharacteristic
175C2×Dic3⋊C4C22×C312yes—
176C2×Dic3⋊C4C22×C312yes—
177C2×C4×Dic3C22×C311yescharacteristic
178C2×C4×Dic3C22×C311yescharacteristic
179#897C22×C3116yescomplemented
180#896C22×C3116yescomplemented
181#896C22×C3116yescomplemented
182#893C22×C318yes—
183#893C22×C318yes—
184D3×C4⋊C4C22×C3116yescomplemented
185#890C22×C318yescomplemented
186#888C22×C318yescomplemented
187C4×D12C22×C318yes—
188C4×Dic6C22×C318yescomplemented
189C23×C32C2411yescharacteristic
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2×Q818yes—
193C22×C3×D3C2414yes—
194C2×C32×C4—22no—
195C2×C32×C4—24no—
196C2×C32×C4—24no—
197C2×C32×C4—22no—
198C2×C32×C4C2×Q814yes—
199C2×C32×C4C2412yes—
200C2×C32×C4C2414yes—
201C2×C32×C4C2414yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2412yes—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3#4114yes—
209C2×C3×Dic3C2412yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2412yes—
214C3×D12C2×Q8116yescomplemented
215C3×C4×D3—216no—
216C3×C4×D3—48no—
217C3×C4×D3—48no—
218C3×Dic6—28no—
219C3×Dic6—48no—
220#554—316no—
221C2×C4⋊Q8—31no—
222C2×#125—31no—
223C2×#125C3×D311yescharacteristic, complemented
224C2×C22⋊Q8—32no—
225C2×C22⋊Q8—32no—
226C2×C22⋊Q8—32no—
227C2×C4×Q8—31no—
228C2×C4×D4—31no—
229C2×C4×D4—31no—
230C2×C4×D4—31no—
231C22×C4⋊C4—32no—
232C24×C3—32no—
233C23×D3C23×C312yes—
234C2×C3×Q8—34no—
235C2×C3×Q8—38no—
236C2×C3×Q8—64no—
237C2×C3×Q8—124no—
238C2×C3×D4—38no—
239C2×C3×D4—34no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—32no—
250C22×C3×C4—38no—
251C22×C3×C4—38no—
252C22×C3×C4—38no—
253C22×C3×C4—68no—
254C22×C3×C4—124no—
255C22×C3×C4—124no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D312yes—
259C22×C3×C4C22×D312yes—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C23×C311yescharacteristic
262C22×C3×C4C23×C312yes—
263C22×C3×C4C23×C312yes—
264C22×C3×C4C23×C311yescharacteristic
265C22×C3×C4C23×C311yescharacteristic
266C22×Dic3C23×C311yescharacteristic
267C22×Dic3C23×C311yescharacteristic
268C22×Dic3C23×C311yescharacteristic
269C22×Dic3C23×C312yes—
270C22×Dic3C23×C311yescharacteristic
271C2×D12C3×Q818yescomplemented
272C2×D12C23×C314yes—
273C2×C4×D3—28no—
274C2×C4×D3—44no—
275C2×C4×D3—44no—
276C2×C4×D3C23×C318yes—
277C2×C4×D3C23×C318yes—
278C2×C4×D3C23×C318yes—
279C2×Dic6—24no—
280C2×Dic6—44no—
281C2×Dic6C23×C314yes—
282C2×Dic6C23×C318yes—
283C3×C4⋊C4—28no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—28no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4—38no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4—34no—
294C3×C4⋊C4C22×D318yes—
295C3×C4⋊C4C22×D314yes—
296C3×C4⋊C4C22×D314yes—
297C3×C4⋊C4C22×D318yes—
298C3×C4⋊C4C23×C314yes—
299C3×C4⋊C4C23×C314yes—
300C3×C4⋊C4C23×C318yes—
301C3×C4⋊C4C23×C318yes—
302C3×C22⋊C4—38no—
303C3×C22⋊C4—38no—
304C3×C22⋊C4—38no—
305C3×C42—24no—
306C3×C42—34no—
307C3×C42—34no—
308C3×C42C22×D314yes—
309C3×C42C23×C314yes—
310(C2×D3)⋊C4C23×C318yes—
311(C2×D3)⋊C4C23×C318yes—
312(C2×D3)⋊C4C23×C318yes—
313C4⋊Dic3C23×C314yes—
314C4⋊Dic3C23×C314yes—
315C4⋊Dic3C23×C318yes—
316Dic3⋊C4C23×C314yes—
317Dic3⋊C4C23×C314yes—
318Dic3⋊C4C23×C318yes—
319Dic3⋊C4C23×C318yes—
320C4×Dic3C23×C314yes—
321C4×Dic3C23×C314yes—
322C22×C32C22×Q812yes—
323C22×C32C2×#4112yes—
324C22×C32H(5,𝔽2)12yes—
325C22×C32C2511yescharacteristic
326C2×C3×D3—216no—
327C2×C3×D3—24no—
328C2×C3×D3—24no—
329C2×C3×D3C22×Q818yes—
330C32×C4—22no—
331C32×C4—24no—
332C32×C4—24no—
333C32×C4—22no—
334C32×C4C22×Q814yes—
335C3×Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3C2×#4114yes—
340C22×Q8—31no—
341C22×Q8—32no—
342C22×D4—31no—
343C23×C4—32no—
344C23×C4—32no—
345C23×C4—32no—
346C4⋊Q8—38no—
347#125—38no—
348#125C2×C3×D318yescomplemented
349C22⋊Q8—316no—
350C22⋊Q8—316no—
351C22⋊Q8—316no—
352C4×Q8—38no—
353C4×D4—38no—
354C4×D4—38no—
355C4×D4—38no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—316no—
364C2×C4⋊C4C2×C3×D312yes—
365C2×C4⋊C4C2×C3×D311yescharacteristic
366C2×C4⋊C4C2×C3×D311yescharacteristic
367C2×C4⋊C4C2×C3×D312yes—
368C2×C22⋊C4—32no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—32no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42C2×C3×D311yescharacteristic
374C23×C3—21no—
375C23×C3—38no—
376C23×C3—34no—
377C23×C3—64no—
378C23×C3—64no—
379C23×C3C23×D311yescharacteristic
380C23×C3C24×C311yescharacteristic
381C22×D3—24no—
382C22×D3—24no—
383C22×D3C2×C3×Q818yes—
384C22×D3C24×C314yes—
385C3×Q8—68no—
386C3×Q8—128no—
387C3×D4—316no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—24no—
392C2×C3×C4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—34no—
403C2×C3×C4—32no—
404C2×C3×C4—32no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—34no—
408C2×C3×C4—44no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—44no—
412C2×C3×C4—616no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—64no—
416C2×C3×C4—62no—
417C2×C3×C4—128no—
418C2×C3×C4—128no—
419C2×C3×C4D3×Q814yes—
420C2×C3×C4C2×C3×Q814yes—
421C2×C3×C4C23×D312yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D314yes—
424C2×C3×C4C23×D314yes—
425C2×C3×C4C23×D312yes—
426C2×C3×C4C24×C312yes—
427C2×C3×C4C24×C314yes—
428C2×C3×C4C24×C314yes—
429C2×C3×C4C24×C312yes—
430C2×C3×C4C24×C312yes—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—24no—
434C2×Dic3—22no—
435C2×Dic3C3×#4114yes—
436C2×Dic3C24×C312yes—
437C2×Dic3C24×C312yes—
438C2×Dic3C24×C312yes—
439C2×Dic3C24×C314yes—
440C2×Dic3C24×C312yes—
441D12C2×C3×Q8116yescomplemented
442C4×D3—216no—
443C4×D3—48no—
444C4×D3—48no—
445Dic6—28no—
446Dic6—48no—
447C2×C32#55414yescomplemented
448C2×C32C23×Q811yescharacteristic
449C2×C32C22×#4111yescharacteristic
450C2×C32C2×H(5,𝔽2)11yescharacteristic
451C3×D3—28no—
452C24—32no—
453C2×Q8—34no—
454C2×Q8—38no—
455C2×Q8—64no—
456C2×Q8—124no—
457C2×D4—34no—
458C2×D4—38no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—32no—
464C22×C4—38no—
465C22×C4—38no—
466C22×C4—38no—
467C22×C4—68no—
468C22×C4—124no—
469C22×C4—124no—
470C22×C4C22×C3×D311yescharacteristic
471C22×C4C22×C3×D311yescharacteristic
472C22×C4C22×C3×D312yes—
473C22×C4C22×C3×D312yes—
474C22×C4C22×C3×D311yescharacteristic
475C4⋊C4—34no—
476C4⋊C4—38no—
477C4⋊C4—38no—
478C4⋊C4—34no—
479C4⋊C4—34no—
480C4⋊C4—34no—
481C4⋊C4—38no—
482C4⋊C4C22×C3×D318yes—
483C4⋊C4C22×C3×D314yes—
484C4⋊C4C22×C3×D314yes—
485C4⋊C4C22×C3×D318yes—
486C22⋊C4—38no—
487C22⋊C4—38no—
488C22⋊C4—38no—
489C42—34no—
490C42—34no—
491C42C22×C3×D314yes—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—21no—
496C22×C3—38no—
497C22×C3—616no—
498C22×C3—64no—
499C22×C3—64no—
500C22×C3C2×D3×Q812yes—
501C22×C3D3×#4112yes—
502C22×C3#100912yes—
503C22×C3C22×C3×Q812yes—
504C22×C3C2×C3×#4112yes—
505C22×C3C3×H(5,𝔽2)12yes—
506C22×C3C24×D311yescharacteristic
507C22×C3C25×C311yescharacteristic
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—216no—
511C2×D3C22×C3×Q818yes—
512C3×C4—24no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—24no—
516C3×C4—22no—
517C3×C4—24no—
518C3×C4—24no—
519C3×C4—22no—
520C3×C4—24no—
521C3×C4—34no—
522C3×C4—44no—
523C3×C4—42no—
524C3×C4—42no—
525C3×C4—44no—
526C3×C4—62no—
527C3×C4—62no—
528C3×C4—64no—
529C3×C4—62no—
530C3×C4C2×D3×Q814yes—
531C3×C4C22×C3×Q814yes—
532Dic3—22no—
533Dic3—22no—
534Dic3—24no—
535Dic3—22no—
536Dic3C2×C3×#4114yes—
537C32C2×#55411yescharacteristic, complemented, Sylow
538C23—38no—
539C23—34no—
540C23—64no—
541C23—64no—
542C23C23×C3×D311yescharacteristic
543Q8—68no—
544Q8—128no—
545D4—316no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—34no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—34no—
556C2×C4—616no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—64no—
560C2×C4—62no—
561C2×C4—128no—
562C2×C4—128no—
563C2×C4C3×D3×Q814yes—
564C2×C4C23×C3×D312yes—
565C2×C4C23×C3×D312yes—
566C2×C4C23×C3×D314yes—
567C2×C4C23×C3×D314yes—
568C2×C4C23×C3×D312yes—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—24no—
573C2×C3—68no—
574C2×C3#569014yesdirect product factor
575C2×C3C3×#55414yescomplemented
576C2×C3C22×D3×Q811yescharacteristic
577C2×C3C2×D3×#4111yescharacteristic
578C2×C3C2×#100911yescharacteristic
579C2×C3C23×C3×Q811yescharacteristic
580C2×C3C22×C3×#4111yescharacteristic
581C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
582D3—28no—
583C22—38no—
584C22—64no—
585C22—64no—
586C22—616no—
587C22C2×C3×D3×Q812yes—
588C22C3×D3×#4112yes—
589C22C3×#100912yes—
590C22C24×C3×D311yescharacteristic
591C4—24no—
592C4—22no—
593C4—22no—
594C4—24no—
595C4—34no—
596C4—62no—
597C4—62no—
598C4—64no—
599C4—62no—
600C4C2×C3×D3×Q814yes—
601C3—21no—
602C3C2×#569011yescharacteristic, direct product factor
603C3C2×C3×#55411yescharacteristic, complemented
604C2—68no—
605C2C3×#569014yesdirect product factor
606C2C22×C3×D3×Q811yescharacteristic
607C2C2×C3×D3×#4111yescharacteristic
608C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#125C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C3×#125D3
hypocenterC3C2×C3×#554
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#125

Complements

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

NH ≅ G/Ntype
1. C2×C32×#125C2semidirect
2. C3×#5690C2direct (N × H)
3. C2×C3×#897C2semidirect
4. C2×C3×#896C2semidirect
5. C2×C3×#896C2semidirect
8. C2×C3×D3×C4⋊C4C2semidirect
9. C2×C3×#890C2semidirect
10. C2×C3×#888C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5690C3direct (N × H)
21. C32×#125C22semidirect
39. C3×#897C22semidirect
40. C3×#896C22semidirect
41. C3×#896C22semidirect
44. C3×D3×C4⋊C4C22semidirect
45. C3×#890C22semidirect
46. C3×#888C22semidirect
48. C3×C4×Dic6C22semidirect
53. C2×C3×#125D3semidirect
54. C2×C3×#125C2×C3semidirect
63. #5690C2×C3direct (N × H)
64. C2×#897C2×C3semidirect
65. C2×#896C2×C3semidirect
66. C2×#896C2×C3semidirect
69. C2×D3×C4⋊C4C2×C3semidirect
70. C2×#890C2×C3semidirect
71. C2×#888C2×C3semidirect
73. C2×C4×Dic6C2×C3semidirect
85. C2×C3×D12Q8semidirect
130. C3×#125C2×D3semidirect
131. C3×#125C22×C3semidirect
179. #897C22×C3semidirect
180. #896C22×C3semidirect
181. #896C22×C3semidirect
184. D3×C4⋊C4C22×C3semidirect
185. #890C22×C3semidirect
186. #888C22×C3semidirect
188. C4×Dic6C22×C3semidirect
214. C3×D12C2×Q8semidirect
223. C2×#125C3×D3semidirect
271. C2×D12C3×Q8semidirect
348. #125C2×C3×D3semidirect
441. D12C2×C3×Q8semidirect
447. C2×C32#554semidirect
537. C32C2×#554semidirect
574. C2×C3#5690direct (N × H)
575. C2×C3C3×#554semidirect
602. C3C2×#5690direct (N × H)
603. C3C2×C3×#554semidirect
605. C2C3×#5690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1252
C3×#56902
C2×C3×#8972
C2×C3×#8962
C2×C3×#8932
C2×C3×D3×C4⋊C42
C2×C3×#8902
C2×C3×#8882
C2×C3×C4×D122
C2×C3×C4×Dic62
C2×C3×#5543
C2×#56903