Finite Group Databasebeta

← C2×C3×#5557 #11900587

Subgroups — C2×C3×#5557 #11900587

Order 1152.

2677 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×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic
3C2×C3×#936C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C212yesmaximal, complemented
5C2×C3×#926C212yesmaximal, complemented
6C3×#5557C2116yesmaximal, direct product factor
7C2×C3×#897C211yesmaximal, characteristic, complemented
8C2×C3×#890C211yesmaximal, characteristic, complemented
9C2×C3×#883C212yesmaximal, complemented
10C2×C3×#879C212yesmaximal, complemented
11C2×C3×C42×D3C211yesmaximal, characteristic, complemented
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×#529—31nomaximal
14C2×#5557C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C32×C4×D4C2218yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2212yes—
25C2×C32×C42C2211yescharacteristic
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28C2×C3×#217C2212yes—
29C3×#938C2218yes—
30C3×#936C2218yescomplemented
31C3×C4×#67C22116yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yes—
33C3×#926C22116yescomplemented
34C2×C3×C4⋊Dic3C2212yes—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4⋊Dic3C2212yes—
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2212yes—
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#897C2218yescomplemented
44C3×#890C2218yescomplemented
45C3×#883C22116yescomplemented
46C3×#879C22116yescomplemented
47C3×C42×D3C2218yescomplemented
48C3×C4×Dic6C2218yescomplemented
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—31no—
56C2×C3×C4×Q8—31no—
57C2×C3×C4×D4—21no—
58C2×C3×C4×D4—32no—
59C2×C3×C4×D4D311yescharacteristic, complemented
60C2×C3×C4×D4C2×C311yescharacteristic, complemented
61C2×C3×#117—32no—
62C22×C3×C42—31no—
63C2×#938C2×C311yescharacteristic
64C2×#936C2×C311yescharacteristic, complemented
65C2×C4×#67C2×C312yescomplemented
66C2×#926C2×C312yescomplemented
67#5557C2×C3116yesdirect product factor
68C2×#897C2×C311yescharacteristic, complemented
69C2×#890C2×C311yescharacteristic, complemented
70C2×#883C2×C312yescomplemented
71C2×#879C2×C312yescomplemented
72C2×C42×D3C2×C311yescharacteristic, complemented
73C2×C4×Dic6C2×C311yescharacteristic, complemented
74C24×C32C2312yes—
75C23×C3×D3C2311yescharacteristic
76C2×C32×D4—24no—
77C2×C32×D4C2314yes—
78C22×C32×C4—28no—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2312yes—
81C22×C32×C4C2318yes—
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C2×C3×#67—28no—
85C2×C3×#67C2318yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3C2314yes—
95C2×C3×C4×D3C2314yes—
96C2×C3×C4×D3C2314yes—
97C2×C3×Dic6—24no—
98C2×C3×Dic6C2314yes—
99C32×C4⋊C4C2314yes—
100C32×C22⋊C4C2318yes—
101C32×C42C2314yes—
102C3×#217C2318yes—
103C3×#217C2318yes—
104C3×#217C2318yes—
105C3×(C2×D3)⋊C4C2318yes—
106C3×C4⋊Dic3C2318yes—
107C3×C4⋊Dic3C2318yes—
108C3×C4⋊Dic3C2314yes—
109C3×Dic3⋊C4C2318yes—
110C3×Dic3⋊C4C2318yes—
111C3×C4×Dic3C2314yes—
112C3×C4×Dic3C2314yes—
113C3×C4×Dic3C2314yes—
114C3×C4×Dic3C2318yes—
115C2×#529—31noSylow
116C22×C3×Q8—31no—
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×C4—31no—
124C23×C3×C4—31no—
125C23×C3×C4C2×D312yes—
126C23×C3×C4C22×C312yes—
127C22×#67C22×C312yes—
128C22×C4×D3C22×C311yescharacteristic
129C22×C4×D3C22×C311yescharacteristic
130C22×C4×D3C22×C311yescharacteristic
131C22×Dic6C22×C311yescharacteristic
132C3×#126—316no—
133C3×#125—38no—
134C3×#124—38no—
135C3×#123—316no—
136C3×C22⋊Q8—38no—
137C3×#121—38no—
138C3×C4×Q8—38no—
139C3×C4×D4—28no—
140C3×C4×D4—316no—
141C3×C4×D4C2×D318yescomplemented
142C3×C4×D4C22×C318yescomplemented
143C3×#117—316no—
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4—32no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4—32no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4C2×D311yescharacteristic
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C22⋊C4—22no—
153C2×C3×C22⋊C4—32no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C22⋊C4—32no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C22⋊C4C2×D312yes—
158C2×C3×C22⋊C4C22×C312yes—
159C2×C3×C42—21no—
160C2×C3×C42—31no—
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×C3×C42—32no—
164C2×C3×C42—38no—
165C2×C3×C42C2×D311yescharacteristic
166C2×C3×C42C22×C311yescharacteristic
167C2×#217C22×C312yes—
168C2×#217C22×C312yes—
169C2×#217C22×C312yes—
170#938C22×C318yes—
171#936C22×C318yescomplemented
172C4×#67C22×C3116yescomplemented
173C2×(C2×D3)⋊C4C22×C312yes—
174#926C22×C3116yescomplemented
175C2×C4⋊Dic3C22×C311yescharacteristic
176C2×C4⋊Dic3C22×C312yes—
177C2×C4⋊Dic3C22×C312yes—
178C2×Dic3⋊C4C22×C312yes—
179C2×Dic3⋊C4C22×C312yes—
180C2×C4×Dic3C22×C312yes—
181C2×C4×Dic3C22×C311yescharacteristic
182C2×C4×Dic3C22×C311yescharacteristic
183C2×C4×Dic3C22×C311yescharacteristic
184#897C22×C318yescomplemented
185#890C22×C318yescomplemented
186#883C22×C3116yescomplemented
187#879C22×C3116yescomplemented
188C42×D3C22×C318yescomplemented
189C4×Dic6C22×C318yescomplemented
190C23×C32—24no—
191C23×C32—24no—
192C23×C32—24no—
193C23×C32C2414yes—
194C23×C32C2411yescharacteristic
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3#4114yes—
198C22×C3×D3C2412yes—
199C32×D4—28no—
200C2×C32×C4—22no—
201C2×C32×C4—24no—
202C2×C32×C4—216no—
203C2×C32×C4#4114yes—
204C2×C32×C4#4114yes—
205C2×C32×C4C2412yes—
206C2×C32×C4C2414yes—
207C2×C32×C4C2412yes—
208C2×C32×C4C2412yes—
209C3×#67—216no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2414yes—
219C2×C3×Dic3C2414yes—
220C3×C4×D3—28no—
221C3×C4×D3—28no—
222C3×C4×D3—28no—
223C3×Dic6—28no—
224#529—316no—
225C2×#126—32no—
226C2×#125—31no—
227C2×#124—31no—
228C2×#123—32no—
229C2×C22⋊Q8—31no—
230C2×#121—31no—
231C2×C4×Q8—31no—
232C2×C4×D4—32no—
233C2×C4×D4C3×D311yescharacteristic, complemented
234C2×#117—32no—
235C22×C42—31no—
236C24×C3—22no—
237C24×C3—31no—
238C24×C3C22×D312yes—
239C24×C3C23×C312yes—
240C23×D3C23×C311yescharacteristic
241C2×C3×Q8—34no—
242C2×C3×Q8—64no—
243C2×C3×D4—28no—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—24no—
247C2×C3×D4—38no—
248C2×C3×D4—68no—
249C2×C3×D4C22×D314yes—
250C2×C3×D4C23×C314yes—
251C22×C3×C4—28no—
252C22×C3×C4—28no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—22no—
257C22×C3×C4—28no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—31no—
261C22×C3×C4—32no—
262C22×C3×C4—32no—
263C22×C3×C4—34no—
264C22×C3×C4—34no—
265C22×C3×C4—34no—
266C22×C3×C4—48no—
267C22×C3×C4—64no—
268C22×C3×C4—64no—
269C22×C3×C4—64no—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D312yes—
272C22×C3×C4C22×D318yes—
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C23×C311yescharacteristic
276C22×C3×C4C23×C312yes—
277C22×C3×C4C23×C318yes—
278C22×C3×C4C23×C311yescharacteristic
279C22×C3×C4C23×C311yescharacteristic
280C2×#67—28no—
281C2×#67C23×C318yes—
282C22×Dic3C23×C311yescharacteristic
283C22×Dic3C23×C311yescharacteristic
284C22×Dic3C23×C311yescharacteristic
285C22×Dic3C23×C312yes—
286C22×Dic3C23×C312yes—
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—24no—
290C2×C4×D3C23×C314yes—
291C2×C4×D3C23×C314yes—
292C2×C4×D3C23×C314yes—
293C2×Dic6—24no—
294C2×Dic6C23×C314yes—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—38no—
297C3×C4⋊C4—38no—
298C3×C4⋊C4—38no—
299C3×C4⋊C4—38no—
300C3×C4⋊C4—34no—
301C3×C4⋊C4C22×D314yes—
302C3×C4⋊C4C23×C314yes—
303C3×C22⋊C4—28no—
304C3×C22⋊C4—38no—
305C3×C22⋊C4—38no—
306C3×C22⋊C4—38no—
307C3×C22⋊C4—38no—
308C3×C22⋊C4C22×D318yes—
309C3×C22⋊C4C23×C318yes—
310C3×C42—24no—
311C3×C42—34no—
312C3×C42—34no—
313C3×C42—34no—
314C3×C42—38no—
315C3×C42C22×D314yes—
316C3×C42C23×C314yes—
317#217C23×C318yes—
318#217C23×C318yes—
319#217C23×C318yes—
320(C2×D3)⋊C4C23×C318yes—
321C4⋊Dic3C23×C314yes—
322C4⋊Dic3C23×C318yes—
323C4⋊Dic3C23×C318yes—
324Dic3⋊C4C23×C318yes—
325Dic3⋊C4C23×C318yes—
326C4×Dic3C23×C318yes—
327C4×Dic3C23×C314yes—
328C4×Dic3C23×C314yes—
329C4×Dic3C23×C314yes—
330C22×C32—24no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—48no—
334C22×C32C2×#4112yes—
335C22×C32C2×#4112yes—
336C22×C32C2×#4112yes—
337C22×C32C2511yescharacteristic
338C2×C3×D3—28no—
339C2×C3×D3—22no—
340C2×C3×D3—22no—
341C2×C3×D3C2×#4114yes—
342C32×C4—22no—
343C32×C4—24no—
344C32×C4C2×#4114yes—
345C32×C4C2×#4114yes—
346C3×Dic3—24no—
347C3×Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—22no—
350C3×Dic3—24no—
351C22×Q8—31no—
352C22×D4—32no—
353C22×D4C2×C3×D311yescharacteristic
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4C2×C3×D312yes—
358#126—316no—
359#125—38no—
360#124—38no—
361#123—316no—
362C22⋊Q8—38no—
363#121—38no—
364C4×Q8—38no—
365C4×D4—316no—
366C4×D4C2×C3×D318yescomplemented
367#117—316no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4C2×C3×D311yescharacteristic
374C2×C22⋊C4—32no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4C2×C3×D312yes—
379C2×C42—31no—
380C2×C42—32no—
381C2×C42—31no—
382C2×C42—31no—
383C2×C42—38no—
384C2×C42C2×C3×D311yescharacteristic
385C23×C3—28no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—21no—
393C23×C3—24no—
394C23×C3—34no—
395C23×C3—32no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3C23×D314yes—
401C23×C3C23×D311yescharacteristic
402C23×C3C24×C314yes—
403C23×C3C24×C311yescharacteristic
404C22×D3—22no—
405C22×D3—22no—
406C22×D3C3×#4114yes—
407C22×D3C24×C312yes—
408C3×Q8—68no—
409C3×D4—216no—
410C3×D4—28no—
411C3×D4—28no—
412C3×D4—616no—
413C2×C3×C4—24no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—216no—
418C2×C3×C4—216no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—32no—
426C2×C3×C4—32no—
427C2×C3×C4—32no—
428C2×C3×C4—34no—
429C2×C3×C4—34no—
430C2×C3×C4—416no—
431C2×C3×C4—42no—
432C2×C3×C4—44no—
433C2×C3×C4—68no—
434C2×C3×C4—62no—
435C2×C3×C4—64no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4—64no—
439C2×C3×C4—68no—
440C2×C3×C4—68no—
441C2×C3×C4#23514yes—
442C2×C3×C4#23714yes—
443C2×C3×C4C3×#4114yes—
444C2×C3×C4C3×#4114yes—
445C2×C3×C4C23×D312yes—
446C2×C3×C4C23×D314yes—
447C2×C3×C4C23×D312yes—
448C2×C3×C4C23×D312yes—
449C2×C3×C4C24×C312yes—
450C2×C3×C4C24×C314yes—
451C2×C3×C4C24×C312yes—
452C2×C3×C4C24×C312yes—
453#67—216no—
454C2×Dic3—24no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—24no—
459C2×Dic3C24×C312yes—
460C2×Dic3C24×C312yes—
461C2×Dic3C24×C312yes—
462C2×Dic3C24×C314yes—
463C2×Dic3C24×C314yes—
464C4×D3—28no—
465C4×D3—28no—
466C4×D3—28no—
467Dic6—28no—
468C2×C32—44no—
469C2×C32#52914yescomplemented
470C2×C32C22×#4111yescharacteristic
471C2×C32C22×#4111yescharacteristic
472C2×C32C22×#4111yescharacteristic
473C3×D3—24no—
474C24—31no—
475C24C22×C3×D312yes—
476C2×Q8—34no—
477C2×Q8—64no—
478C2×D4—24no—
479C2×D4—38no—
480C2×D4—68no—
481C2×D4C22×C3×D314yes—
482C22×C4—28no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—32no—
488C22×C4—34no—
489C22×C4—34no—
490C22×C4—34no—
491C22×C4—64no—
492C22×C4—64no—
493C22×C4—64no—
494C22×C4C22×C3×D311yescharacteristic
495C22×C4C22×C3×D312yes—
496C22×C4C22×C3×D318yes—
497C22×C4C22×C3×D311yescharacteristic
498C22×C4C22×C3×D311yescharacteristic
499C4⋊C4—38no—
500C4⋊C4—38no—
501C4⋊C4—38no—
502C4⋊C4—34no—
503C4⋊C4—38no—
504C4⋊C4C22×C3×D314yes—
505C22⋊C4—38no—
506C22⋊C4—38no—
507C22⋊C4—38no—
508C22⋊C4—38no—
509C22⋊C4C22×C3×D318yes—
510C42—34no—
511C42—34no—
512C42—34no—
513C42—38no—
514C42C22×C3×D314yes—
515C22×C3—28no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—34no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—416no—
530C22×C3—48no—
531C22×C3—48no—
532C22×C3—62no—
533C22×C3—62no—
534C22×C3—68no—
535C22×C3C2×#23512yes—
536C22×C3C2×#23712yes—
537C22×C3D3×#4112yes—
538C22×C3C2×C3×#4112yes—
539C22×C3C2×C3×#4112yes—
540C22×C3C2×C3×#4112yes—
541C22×C3C24×D311yescharacteristic
542C22×C3C25×C311yescharacteristic
543C2×D3—22no—
544C2×D3—22no—
545C2×D3—28no—
546C2×D3C2×C3×#4114yes—
547C3×C4—24no—
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—24no—
551C3×C4—24no—
552C3×C4—24no—
553C3×C4—44no—
554C3×C4—42no—
555C3×C4—62no—
556C3×C4—64no—
557C3×C4—62no—
558C3×C4—62no—
559C3×C4—64no—
560C3×C4C2×#23514yes—
561C3×C4C2×#23714yes—
562C3×C4C2×C3×#4114yes—
563C3×C4C2×C3×#4114yes—
564Dic3—24no—
565Dic3—22no—
566Dic3—22no—
567Dic3—22no—
568Dic3—24no—
569C32C2×#52911yescharacteristic, complemented, Sylow
570C23—24no—
571C23—24no—
572C23—24no—
573C23—34no—
574C23—32no—
575C23—62no—
576C23—62no—
577C23C23×C3×D314yes—
578C23C23×C3×D311yescharacteristic
579Q8—68no—
580D4—28no—
581D4—616no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—216no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—32no—
588C2×C4—34no—
589C2×C4—34no—
590C2×C4—68no—
591C2×C4—62no—
592C2×C4—64no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—64no—
596C2×C4—68no—
597C2×C4—68no—
598C2×C4C3×#23514yes—
599C2×C4C3×#23714yes—
600C2×C4C23×C3×D312yes—
601C2×C4C23×C3×D314yes—
602C2×C4C23×C3×D312yes—
603C2×C4C23×C3×D312yes—
604C2×C3—24no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—48no—
609C2×C3—44no—
610C2×C3—44no—
611C2×C3—64no—
612C2×C3#555714yesdirect product factor
613C2×C3C3×#52914yescomplemented
614C2×C3C22×#23511yescharacteristic
615C2×C3C22×#23711yescharacteristic
616C2×C3C2×D3×#4111yescharacteristic
617C2×C3C22×C3×#4111yescharacteristic
618C2×C3C22×C3×#4111yescharacteristic
619C2×C3C22×C3×#4111yescharacteristic
620D3—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—34no—
625C22—48no—
626C22—68no—
627C22—62no—
628C22—62no—
629C22C2×C3×#23512yes—
630C22C2×C3×#23712yes—
631C22C3×D3×#4112yes—
632C22C24×C3×D311yescharacteristic
633C4—24no—
634C4—22no—
635C4—62no—
636C4—64no—
637C4—62no—
638C4—62no—
639C4—64no—
640C4C2×C3×#23514yes—
641C4C2×C3×#23714yes—
642C3—21no—
643C3C2×#555711yescharacteristic, direct product factor
644C3C2×C3×#52911yescharacteristic, complemented
645C2—44no—
646C2—64no—
647C2C3×#555714yesdirect product factor
648C2C22×C3×#23511yescharacteristic
649C2C22×C3×#23711yescharacteristic
650C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#938C2
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×#529
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ 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×C4×#67C2semidirect
5. C2×C3×#926C2semidirect
6. C3×#5557C2direct (N × H)
7. C2×C3×#897C2semidirect
8. C2×C3×#890C2semidirect
9. C2×C3×#883C2semidirect
10. C2×C3×#879C2semidirect
11. C2×C3×C42×D3C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5557C3direct (N × H)
22. C32×C4×D4C22semidirect
30. C3×#936C22semidirect
31. C3×C4×#67C22semidirect
33. C3×#926C22semidirect
43. C3×#897C22semidirect
44. C3×#890C22semidirect
45. C3×#883C22semidirect
46. C3×#879C22semidirect
47. C3×C42×D3C22semidirect
48. C3×C4×Dic6C22semidirect
59. C2×C3×C4×D4D3semidirect
60. C2×C3×C4×D4C2×C3semidirect
64. C2×#936C2×C3semidirect
65. C2×C4×#67C2×C3semidirect
66. C2×#926C2×C3semidirect
67. #5557C2×C3direct (N × H)
68. C2×#897C2×C3semidirect
69. C2×#890C2×C3semidirect
70. C2×#883C2×C3semidirect
71. C2×#879C2×C3semidirect
72. C2×C42×D3C2×C3semidirect
73. C2×C4×Dic6C2×C3semidirect
141. C3×C4×D4C2×D3semidirect
142. C3×C4×D4C22×C3semidirect
171. #936C22×C3semidirect
172. C4×#67C22×C3semidirect
174. #926C22×C3semidirect
184. #897C22×C3semidirect
185. #890C22×C3semidirect
186. #883C22×C3semidirect
187. #879C22×C3semidirect
188. C42×D3C22×C3semidirect
189. C4×Dic6C22×C3semidirect
233. C2×C4×D4C3×D3semidirect
366. C4×D4C2×C3×D3semidirect
469. C2×C32#529semidirect
569. C32C2×#529semidirect
612. C2×C3#5557direct (N × H)
613. C2×C3C3×#529semidirect
643. C3C2×#5557direct (N × H)
644. C3C2×C3×#529semidirect
647. C2C3×#5557direct (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×C4×#672
C2×C3×#9262
C3×#55572
C2×C3×#8972
C2×C3×#8902
C2×C3×#8832
C2×C3×#8792
C2×C3×C42×D32
C2×C3×C4×Dic62
C2×C3×#5293
C2×#55573