Finite Group Databasebeta

← C3×#82466 #11806923

Subgroups — C3×#82466 #11806923

Order 1152.

1413 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×Q8C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic
3C2×C3×#893C211yesmaximal, characteristic
4C3×#5229C211yesmaximal, characteristic, complemented
5C3×#4990C212yesmaximal, complemented
6C3×#4989C212yesmaximal, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C3×#4940C212yesmaximal, complemented
9C3×#4939C211yesmaximal, characteristic
10C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
11C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×#2367—31nomaximal
13#82466C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C32×C4×Q8—24no—
18C2×C32×C4⋊C4C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×C32×C42C2212yes—
22C3×#947C418yescomplemented
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#893—24no—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×#124—31no—
41C2×C3×C4×Q8—21no—
42C2×C3×C4×Q8D311yescharacteristic, complemented
43C2×C3×C4×Q8C2×C311yescharacteristic, complemented
44C2×C3×C4×D4—31no—
45C2×#947C2×C311yescharacteristic
46C2×#893C2×C311yescharacteristic
47C3×#391—31no—
48C3×#390—31no—
49C3×#388—32no—
50C3×#388—32no—
51C3×#385—32no—
52C3×C4×C4⋊C4—31no—
53C3×C4×C4⋊C4—31no—
54C3×C4×C22⋊C4—32no—
55#5229C2×C311yescharacteristic, complemented
56#4990C2×C312yescomplemented
57#4989C2×C312yescomplemented
58Dic3×C4⋊C4C2×C311yescharacteristic, complemented
59#4940C2×C312yescomplemented
60#4939C2×C311yescharacteristic
61C4×(C2×D3)⋊C4C2×C312yescomplemented
62C4×Dic3⋊C4C2×C311yescharacteristic, complemented
63C23×C3×D3C2312yes—
64C2×C32×Q8—22no—
65C2×C32×Q8—22no—
66C2×C32×Q8C2×C414yescomplemented
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2312yes—
69C22×C32×C4C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×D12—22no—
78C2×C3×D12—22no—
79C2×C3×D12C2×C414yes—
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3—24no—
82C2×C3×C4×D3—42no—
83C32×C4⋊C4—24no—
84C32×C4⋊C4D414yes—
85C32×C42—24no—
86C32×C42—22no—
87C3×(C2×D3)⋊C4—24no—
88C3×(C2×D3)⋊C4—24no—
89C3×(C2×D3)⋊C4—42no—
90C3×(C2×D3)⋊C4C2×C418yescomplemented
91C3×(C2×D3)⋊C4C2×C418yescomplemented
92C3×C4⋊Dic3—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3—42no—
97C3×C4×Dic3C2×C414yescomplemented
98#2367—31noSylow
99C22×C3×Q8—21no—
100C22×C3×Q8C2×D311yescharacteristic
101C22×C3×Q8C22×C311yescharacteristic
102C22×C3×D4—31no—
103C23×C3×C4—32no—
104C22×D12C22×C311yescharacteristic
105C22×C4×D3C22×C312yes—
106C3×#124—38no—
107C3×C4×Q8—28no—
108C3×C4×Q8—24no—
109C3×C4×Q8—24no—
110C3×C4×D4—64no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4C2×D312yes—
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C4⋊C4C22×C312yes—
119C2×C3×C4⋊C4C22×C311yescharacteristic
120C2×C3×C22⋊C4—32no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C42—22no—
126C2×C3×C42—21no—
127C2×C3×C42—31no—
128C2×C3×C42—31no—
129C2×C3×C42—32no—
130C2×C3×C42C2×D312yes—
131C2×C3×C42C2×D311yescharacteristic
132C2×C3×C42C22×C311yescharacteristic
133C2×C3×C42C22×C312yes—
134#947C3×C418yescomplemented
135C2×(C2×D3)⋊C4C22×C312yes—
136C2×(C2×D3)⋊C4C22×C312yes—
137C2×(C2×D3)⋊C4C22×C312yes—
138C2×(C2×D3)⋊C4C22×C312yes—
139C2×(C2×D3)⋊C4C22×C312yes—
140C2×C4⋊Dic3C22×C311yescharacteristic
141C2×Dic3⋊C4C22×C311yescharacteristic
142C2×Dic3⋊C4C22×C311yescharacteristic
143C2×C4×Dic3C22×C311yescharacteristic
144C2×C4×Dic3C22×C312yes—
145C2×C4×Dic3C22×C311yescharacteristic
146#893—24no—
147C3×#95—31no—
148C3×#95—32no—
149C3×#95—32no—
150C3×#95—31no—
151C3×#95—32no—
152C3⋊#95C22×C311yescharacteristic
153C3⋊#95C22×C311yescharacteristic
154C3⋊#95C22×C312yes—
155C3⋊#95C22×C312yes—
156C3⋊#95C22×C312yes—
157C23×C32C2411yescharacteristic
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3C22×C414yes—
165C32×Q8—28no—
166C2×C32×C4—21no—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C22×C414yes—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D414yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4#4112yes—
180C2×C32×C4#4112yes—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3C22×C412yes—
194C2×C3×Dic3C22×C412yes—
195C2×C3×Dic3#4112yes—
196C3×D12—28no—
197C3×C4×D3—48no—
198C2×#124—31no—
199C2×C4×Q8C3×D311yescharacteristic, complemented
200C2×C4×D4—31no—
201#391—31no—
202#390—31no—
203#388—32no—
204#388—32no—
205#385—32no—
206C4×C4⋊C4—31no—
207C4×C4⋊C4—31no—
208C4×C22⋊C4—32no—
209C24×C3—32no—
210C23×D3C23×C312yes—
211C2×C3×Q8—24no—
212C2×C3×Q8—24no—
213C2×C3×Q8—22no—
214C2×C3×Q8—22no—
215C2×C3×Q8—22no—
216C2×C3×Q8—22no—
217C2×C3×Q8—24no—
218C2×C3×Q8C4×D314yescomplemented
219C2×C3×Q8C2×C3×C414yescomplemented
220C2×C3×D4—34no—
221C2×C3×D4—62no—
222C2×C3×D4—62no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—32no—
232C22×C3×C4—31no—
233C22×C3×C4—64no—
234C22×C3×C4—64no—
235C22×C3×C4—122no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D312yes—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D312yes—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C23×C311yescharacteristic
242C22×C3×C4C23×C312yes—
243C22×C3×C4C23×C312yes—
244C22×C3×C4C23×C311yescharacteristic
245C22×C3×C4C23×C311yescharacteristic
246C22×Dic3C23×C311yescharacteristic
247C22×Dic3C23×C312yes—
248C22×Dic3C23×C311yescharacteristic
249C22×Dic3C23×C311yescharacteristic
250C22×Dic3C23×C311yescharacteristic
251C2×D12—22no—
252C2×D12—22no—
253C2×D12C2×C3×C414yes—
254C2×C4×D3—24no—
255C2×C4×D3—24no—
256C2×C4×D3—42no—
257C3×C4⋊C4—28no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—62no—
262C3×C4⋊C4—62no—
263C3×C4⋊C4—62no—
264C3×C4⋊C4#6714yes—
265C3×C4⋊C4C3×D414yes—
266C3×C22⋊C4—38no—
267C3×C22⋊C4—38no—
268C3×C22⋊C4—64no—
269C3×C22⋊C4—64no—
270C3×C22⋊C4—122no—
271C3×C42—28no—
272C3×C42—24no—
273C3×C42—24no—
274C3×C42—22no—
275C3×C42—24no—
276C3×C42—22no—
277C3×C42—34no—
278C3×C42—62no—
279C3×C42—122no—
280(C2×D3)⋊C4—24no—
281(C2×D3)⋊C4—24no—
282(C2×D3)⋊C4—42no—
283(C2×D3)⋊C4C2×C3×C418yescomplemented
284(C2×D3)⋊C4C2×C3×C418yescomplemented
285C4⋊Dic3—22no—
286Dic3⋊C4—22no—
287Dic3⋊C4—22no—
288C4×Dic3—22no—
289C4×Dic3—42no—
290C4×Dic3C2×C3×C414yescomplemented
291C22×C32C23×C411yescharacteristic
292C22×C32C22×D411yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C22×C32C2×#4111yescharacteristic
295C22×C32C2×#4111yescharacteristic
296C22×C32H(5,𝔽2)11yescharacteristic
297C22×C322−1+411yescharacteristic
298C2×C3×D3—24no—
299C2×C3×D3—24no—
300C2×C3×D3—24no—
301C2×C3×D3—42no—
302C2×C3×D3—42no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C32×C4—24no—
306C32×C4—22no—
307C32×C4—24no—
308C32×C4—41no—
309C32×C4C4×D414yes—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C3×Dic3—41no—
314C3×Dic3—42no—
315C22×Q8C2×C3×D311yescharacteristic
316C22×D4—31no—
317C23×C4—32no—
318#124—38no—
319C4×Q8—24no—
320C4×D4—64no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4C2×C3×D312yes—
325C2×C4⋊C4C2×C3×D311yescharacteristic
326C2×C22⋊C4—32no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—32no—
331C2×C42—31no—
332C2×C42—31no—
333C2×C42—32no—
334C2×C42C2×C3×D312yes—
335C2×C42C2×C3×D311yescharacteristic
336#95—31no—
337#95—32no—
338#95—32no—
339#95—31no—
340#95—32no—
341C23×C3—21no—
342C23×C3—34no—
343C23×C3—62no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—62no—
349C23×C3C23×D311yescharacteristic
350C23×C3C24×C311yescharacteristic
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3C22×C3×C414yes—
358C3×Q8—216no—
359C3×Q8—28no—
360C3×Q8—28no—
361C3×D4—68no—
362C2×C3×C4—22no—
363C2×C3×C4—24no—
364C2×C3×C4—22no—
365C2×C3×C4—24no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—62no—
409C2×C3×C4—61no—
410C2×C3×C4—128no—
411C2×C3×C4C2×C4×D314yes—
412C2×C3×C4C2×C4×D312yes—
413C2×C3×C4#23512yes—
414C2×C3×C4#23912yes—
415C2×C3×C4C2×#6714yes—
416C2×C3×C4C2×#6712yes—
417C2×C3×C4C22×C3×C414yes—
418C2×C3×C4C22×C3×C412yes—
419C2×C3×C4C2×C3×D414yes—
420C2×C3×C4C2×C3×D412yes—
421C2×C3×C4C3×#4112yes—
422C2×C3×C4C3×#4112yes—
423C2×Dic3—21no—
424C2×Dic3—21no—
425C2×Dic3—21no—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—21no—
435C2×Dic3C22×C3×C412yes—
436C2×Dic3C22×C3×C412yes—
437C2×Dic3C3×#4112yes—
438D12—28no—
439C4×D3—48no—
440C2×C32C2×C4×D411yescharacteristic
441C2×C32C4×#4111yescharacteristic
442C2×C32#52011yescharacteristic
443C2×C32#54611yescharacteristic
444C2×C32#54811yescharacteristic
445C2×C32#55611yescharacteristic
446C2×C32#55911yescharacteristic
447C3×D3—44no—
448C24—32no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8C3×C4×D314yescomplemented
452C2×D4—34no—
453C2×D4—62no—
454C2×D4—62no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—31no—
458C22×C4—32no—
459C22×C4—31no—
460C22×C4—64no—
461C22×C4—64no—
462C22×C4—122no—
463C22×C4C22×C3×D311yescharacteristic
464C22×C4C22×C3×D312yes—
465C22×C4C22×C3×D311yescharacteristic
466C22×C4C22×C3×D312yes—
467C22×C4C22×C3×D311yescharacteristic
468C4⋊C4—24no—
469C4⋊C4—62no—
470C4⋊C4—62no—
471C4⋊C4—62no—
472C4⋊C4C3×#6714yes—
473C22⋊C4—38no—
474C22⋊C4—38no—
475C22⋊C4—64no—
476C22⋊C4—64no—
477C22⋊C4—122no—
478C42—24no—
479C42—22no—
480C42—34no—
481C42—62no—
482C42—122no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—64no—
491C22×C3—64no—
492C22×C3—64no—
493C22×C3—122no—
494C22×C3—122no—
495C22×C3—122no—
496C22×C3—122no—
497C22×C3C22×C4×D311yescharacteristic
498C22×C3C2×#23511yescharacteristic
499C22×C3C2×#23911yescharacteristic
500C22×C3#100711yescharacteristic
501C22×C3D3×#4111yescharacteristic
502C22×C3#100911yescharacteristic
503C22×C3C22×#6711yescharacteristic
504C22×C3C23×C3×C411yescharacteristic
505C22×C3C22×C3×D411yescharacteristic
506C22×C3C2×C3×#4111yescharacteristic
507C22×C3C2×C3×#4111yescharacteristic
508C22×C3C2×C3×#4111yescharacteristic
509C22×C3C3×H(5,𝔽2)11yescharacteristic
510C22×C3C3×2−1+411yescharacteristic
511C2×D3—24no—
512C2×D3—24no—
513C2×D3—24no—
514C2×D3—42no—
515C2×D3—42no—
516C2×D3—42no—
517C2×D3—42no—
518C3×C4—28no—
519C3×C4—24no—
520C3×C4—24no—
521C3×C4—22no—
522C3×C4—24no—
523C3×C4—24no—
524C3×C4—24no—
525C3×C4—22no—
526C3×C4—24no—
527C3×C4—44no—
528C3×C4—42no—
529C3×C4—41no—
530C3×C4—41no—
531C3×C4—62no—
532C3×C4—62no—
533C3×C4—62no—
534C3×C4—121no—
535C3×C4—122no—
536C3×C4C4×#6714yes—
537C3×C4C3×C4×D414yes—
538Dic3—22no—
539Dic3—22no—
540Dic3—22no—
541Dic3—42no—
542Dic3—41no—
543C32#236711yescharacteristic, complemented, Sylow
544C23—34no—
545C23—62no—
546C23—62no—
547C23—62no—
548C23—62no—
549C23—62no—
550C23—62no—
551C23C23×C3×D311yescharacteristic
552Q8—28no—
553D4—68no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—32no—
564C2×C4—32no—
565C2×C4—32no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—62no—
577C2×C4—61no—
578C2×C4—128no—
579C2×C4C2×C3×C4×D314yes—
580C2×C4C2×C3×C4×D312yes—
581C2×C4C3×#23512yes—
582C2×C4C3×#23912yes—
583C2×C4C2×C3×#6714yes—
584C2×C4C2×C3×#6712yes—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—124no—
593C2×C3#556811yescharacteristic
594C2×C3C4×#23911yescharacteristic
595C2×C3#557411yescharacteristic
596C2×C3#558511yescharacteristic
597C2×C3C2×C4×#6711yescharacteristic
598C2×C3#581711yescharacteristic
599C2×C3#582911yescharacteristic
600C2×C3C2×C3×C4×D411yescharacteristic
601C2×C3C3×C4×#4111yescharacteristic
602C2×C3C3×#52011yescharacteristic
603C2×C3C3×#54611yescharacteristic
604C2×C3C3×#54811yescharacteristic
605C2×C3C3×#55611yescharacteristic
606C2×C3C3×#55911yescharacteristic
607D3—44no—
608C22—64no—
609C22—64no—
610C22—64no—
611C22—122no—
612C22—122no—
613C22—122no—
614C22—122no—
615C22C22×C3×C4×D311yescharacteristic
616C22C2×C3×#23511yescharacteristic
617C22C2×C3×#23911yescharacteristic
618C22C3×#100711yescharacteristic
619C22C3×D3×#4111yescharacteristic
620C22C3×#100911yescharacteristic
621C22C22×C3×#6711yescharacteristic
622C4—24no—
623C4—22no—
624C4—24no—
625C4—41no—
626C4—62no—
627C4—62no—
628C4—62no—
629C4—121no—
630C4—122no—
631C4C3×C4×#6714yes—
632C3—21no—
633C3#8246611yescharacteristic, direct product factor
634C3C3×#236711yescharacteristic, complemented
635C2—124no—
636C2C3×#556811yescharacteristic
637C2C3×C4×#23911yescharacteristic
638C2C3×#557411yescharacteristic
639C2C3×#558511yescharacteristic
640C2C2×C3×C4×#6711yescharacteristic
641C2C3×#581711yescharacteristic
642C2C3×#582911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×Q8C2
socleC23×C32C24
prime radicalC22×C3×D12C22
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#2367
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
4. C3×#5229C2semidirect
5. C3×#4990C2semidirect
6. C3×#4989C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
8. C3×#4940C2semidirect
10. C3×C4×(C2×D3)⋊C4C2semidirect
11. C3×C4×Dic3⋊C4C2semidirect
13. #82466C3direct (N × H)
22. C3×#947C4semidirect
42. C2×C3×C4×Q8D3semidirect
43. C2×C3×C4×Q8C2×C3semidirect
55. #5229C2×C3semidirect
56. #4990C2×C3semidirect
57. #4989C2×C3semidirect
58. Dic3×C4⋊C4C2×C3semidirect
59. #4940C2×C3semidirect
61. C4×(C2×D3)⋊C4C2×C3semidirect
62. C4×Dic3⋊C4C2×C3semidirect
66. C2×C32×Q8C2×C4semidirect
90. C3×(C2×D3)⋊C4C2×C4semidirect
91. C3×(C2×D3)⋊C4C2×C4semidirect
97. C3×C4×Dic3C2×C4semidirect
134. #947C3×C4semidirect
199. C2×C4×Q8C3×D3semidirect
218. C2×C3×Q8C4×D3semidirect
219. C2×C3×Q8C2×C3×C4semidirect
283. (C2×D3)⋊C4C2×C3×C4semidirect
284. (C2×D3)⋊C4C2×C3×C4semidirect
290. C4×Dic3C2×C3×C4semidirect
451. C2×Q8C3×C4×D3semidirect
543. C32#2367semidirect
633. C3#82466direct (N × H)
634. C3C3×#2367semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×C3×#9472
C2×C3×#8932
C3×#52292
C3×#49902
C3×#49892
C3×Dic3×C4⋊C42
C3×#49402
C3×#49392
C3×C4×(C2×D3)⋊C42
C3×C4×Dic3⋊C42
C3×#23673
#824663