Finite Group Databasebeta

← C2×C3×#5733 #11901640

Subgroups — C2×C3×#5733 #11901640

Order 1152.

2409 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#947C212yesmaximal, complemented
3C2×C3×#946C212yesmaximal, complemented
4C3×#5733C2116yesmaximal, direct product factor
5C2×C3×#898C212yesmaximal, complemented
6C2×C3×#897C211yesmaximal, characteristic, complemented
7C2×C3×#895C211yesmaximal, characteristic
8C2×C3×#894C212yesmaximal, complemented
9C2×C3×#893C211yesmaximal, characteristic, complemented
10C2×C3×#887C211yesmaximal, characteristic, complemented
11C2×C3×#875C211yesmaximal, characteristic, complemented
12C2×C3×#872C211yesmaximal, characteristic, complemented
13C2×C3×#542—31nomaximal
14C2×#5733C311yesmaximal, characteristic, direct product factor
15C22×C32×Q8C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×D12C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×Dic6C2211yescharacteristic
21C32×C4⋊Q8C2218yescomplemented
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2212yes—
25C2×C32×C42C2211yescharacteristic
26C3×#947C22116yescomplemented
27C3×#946C22116yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2212yes—
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2212yes—
41C3×#898C22116yescomplemented
42C3×#897C2218yescomplemented
43C3×#895C2218yes—
44C3×#894C22116yescomplemented
45C3×#893C2218yescomplemented
46C3×#887C2218yescomplemented
47C3×#875C2218yescomplemented
48C3×#872C2218yescomplemented
49C3×#542—316no—
50C2×C3×C4⋊Q8—21no—
51C2×C3×C4⋊Q8D311yescharacteristic, complemented
52C2×C3×C4⋊Q8C2×C311yescharacteristic, complemented
53C2×C3×#126—32no—
54C2×C3×#124—32no—
55C2×C3×#124—31no—
56C2×C3×#123—32no—
57C2×C3×C22⋊Q8—32no—
58C2×C3×C22⋊Q8—31no—
59C2×C3×#121—31no—
60C2×C3×C4×Q8—31no—
61C2×C3×C4×D4—31no—
62C2×C3×#117—31no—
63C2×#947C2×C312yescomplemented
64C2×#946C2×C312yescomplemented
65#5733C2×C3116yesdirect product factor
66C2×#898C2×C312yescomplemented
67C2×#897C2×C311yescharacteristic, complemented
68C2×#895C2×C311yescharacteristic
69C2×#894C2×C312yescomplemented
70C2×#893C2×C311yescharacteristic, complemented
71C2×#887C2×C311yescharacteristic, complemented
72C2×#875C2×C311yescharacteristic, complemented
73C2×#872C2×C311yescharacteristic, complemented
74C23×C3×D3C2311yescharacteristic
75C23×C3×D3C2312yes—
76C2×C32×Q8—44no—
77C2×C32×Q8C2318yes—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2312yes—
82C22×C32×C4C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×D12—24no—
88C2×C3×D12—44no—
89C2×C3×D12C2314yes—
90C2×C3×D12C2318yes—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—44no—
93C2×C3×C4×D3C2314yes—
94C2×C3×C4×D3C2318yes—
95C2×C3×Dic6—24no—
96C2×C3×Dic6C2314yes—
97C32×C4⋊C4C2314yes—
98C32×C4⋊C4C2314yes—
99C32×C4⋊C4C2318yes—
100C32×C42C2314yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2314yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×(C2×D3)⋊C4C2318yes—
105C3×(C2×D3)⋊C4C2318yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×(C2×D3)⋊C4C2314yes—
108C3×C4⋊Dic3C2318yes—
109C3×Dic3⋊C4C2318yes—
110C3×Dic3⋊C4C2314yes—
111C3×Dic3⋊C4C2314yes—
112C3×C4×Dic3C2314yes—
113C3×C4×Dic3C2318yes—
114C2×#542—31noSylow
115C22×C3×Q8—22no—
116C22×C3×Q8—31no—
117C22×C3×Q8C2×D312yes—
118C22×C3×Q8C22×C312yes—
119C22×C3×D4—31no—
120C22×C3×D4—32no—
121C23×C3×C4—31no—
122C23×C3×C4—32no—
123C22×D12C22×C311yescharacteristic
124C22×D12C22×C312yes—
125C22×C4×D3C22×C311yescharacteristic
126C22×C4×D3C22×C312yes—
127C22×Dic6C22×C311yescharacteristic
128C3×C4⋊Q8—28no—
129C3×C4⋊Q8C2×D318yescomplemented
130C3×C4⋊Q8C22×C318yescomplemented
131C3×#126—316no—
132C3×#124—316no—
133C3×#124—38no—
134C3×#123—316no—
135C3×C22⋊Q8—316no—
136C3×C22⋊Q8—38no—
137C3×#121—38no—
138C3×C4×Q8—38no—
139C3×C4×D4—38no—
140C3×#117—38no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—22no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—32no—
147C2×C3×C4⋊C4—32no—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C2×D312yes—
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C4⋊C4C22×C311yescharacteristic
153C2×C3×C4⋊C4C22×C312yes—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C22⋊C4—32no—
158C2×C3×C22⋊C4—32no—
159C2×C3×C22⋊C4—32no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C42—21no—
162C2×C3×C42—31no—
163C2×C3×C42—32no—
164C2×C3×C42C2×D311yescharacteristic
165C2×C3×C42C22×C311yescharacteristic
166#947C22×C3116yescomplemented
167#946C22×C3116yescomplemented
168C2×(C2×D3)⋊C4C22×C311yescharacteristic
169C2×(C2×D3)⋊C4C22×C311yescharacteristic
170C2×(C2×D3)⋊C4C22×C312yes—
171C2×(C2×D3)⋊C4C22×C312yes—
172C2×(C2×D3)⋊C4C22×C312yes—
173C2×(C2×D3)⋊C4C22×C312yes—
174C2×(C2×D3)⋊C4C22×C312yes—
175C2×C4⋊Dic3C22×C312yes—
176C2×Dic3⋊C4C22×C311yescharacteristic
177C2×Dic3⋊C4C22×C311yescharacteristic
178C2×Dic3⋊C4C22×C312yes—
179C2×C4×Dic3C22×C311yescharacteristic
180C2×C4×Dic3C22×C312yes—
181#898C22×C3116yescomplemented
182#897C22×C318yescomplemented
183#895C22×C318yes—
184#894C22×C3116yescomplemented
185#893C22×C318yescomplemented
186#887C22×C318yescomplemented
187#875C22×C318yescomplemented
188#872C22×C318yescomplemented
189C23×C32C2411yescharacteristic
190C22×C3×D3—22no—
191C22×C3×D3—24no—
192C22×C3×D3—24no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—24no—
196C22×C3×D3C2412yes—
197C22×C3×D3C2414yes—
198C32×Q8—48no—
199C2×C32×C4—22no—
200C2×C32×C4—22no—
201C2×C32×C4—24no—
202C2×C32×C4—24no—
203C2×C32×C4#4114yes—
204C2×C32×C4C2414yes—
205C2×C32×C4C2412yes—
206C2×C32×C4C2412yes—
207C2×C32×C4C2414yes—
208C2×C32×C4C2412yes—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C3×D12—28no—
218C3×D12—48no—
219C3×C4×D3—28no—
220C3×C4×D3—48no—
221C3×Dic6—28no—
222#542—316no—
223C2×C4⋊Q8C3×D311yescharacteristic, complemented
224C2×#126—32no—
225C2×#124—32no—
226C2×#124—31no—
227C2×#123—32no—
228C2×C22⋊Q8—32no—
229C2×C22⋊Q8—31no—
230C2×#121—31no—
231C2×C4×Q8—31no—
232C2×C4×D4—31no—
233C2×#117—31no—
234C24×C3—32no—
235C24×C3—31no—
236C23×D3C23×C311yescharacteristic
237C23×D3C23×C312yes—
238C2×C3×Q8—28no—
239C2×C3×Q8—34no—
240C2×C3×Q8—44no—
241C2×C3×Q8—44no—
242C2×C3×Q8—48no—
243C2×C3×Q8—64no—
244C2×C3×Q8C22×D318yes—
245C2×C3×Q8C23×C318yes—
246C2×C3×D4—34no—
247C2×C3×D4—38no—
248C2×C3×D4—64no—
249C2×C3×D4—124no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—31no—
256C22×C3×C4—32no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—34no—
260C22×C3×C4—38no—
261C22×C3×C4—64no—
262C22×C3×C4—124no—
263C22×C3×C4C22×D312yes—
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D312yes—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C311yescharacteristic
270C22×C3×C4C23×C311yescharacteristic
271C22×C3×C4C23×C312yes—
272C22×C3×C4C23×C311yescharacteristic
273C22×Dic3C23×C311yescharacteristic
274C22×Dic3C23×C311yescharacteristic
275C22×Dic3C23×C312yes—
276C22×Dic3C23×C311yescharacteristic
277C2×D12—24no—
278C2×D12—44no—
279C2×D12C23×C314yes—
280C2×D12C23×C318yes—
281C2×C4×D3—24no—
282C2×C4×D3—44no—
283C2×C4×D3C23×C314yes—
284C2×C4×D3C23×C318yes—
285C2×Dic6—24no—
286C2×Dic6C23×C314yes—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—28no—
290C3×C4⋊C4—34no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—38no—
293C3×C4⋊C4—38no—
294C3×C4⋊C4C22×D314yes—
295C3×C4⋊C4C22×D314yes—
296C3×C4⋊C4C22×D318yes—
297C3×C4⋊C4C23×C314yes—
298C3×C4⋊C4C23×C314yes—
299C3×C4⋊C4C23×C318yes—
300C3×C22⋊C4—34no—
301C3×C22⋊C4—34no—
302C3×C22⋊C4—38no—
303C3×C22⋊C4—38no—
304C3×C22⋊C4—38no—
305C3×C22⋊C4—38no—
306C3×C22⋊C4—38no—
307C3×C42—24no—
308C3×C42—34no—
309C3×C42—38no—
310C3×C42C22×D314yes—
311C3×C42C23×C314yes—
312(C2×D3)⋊C4C23×C314yes—
313(C2×D3)⋊C4C23×C314yes—
314(C2×D3)⋊C4C23×C318yes—
315(C2×D3)⋊C4C23×C318yes—
316(C2×D3)⋊C4C23×C318yes—
317(C2×D3)⋊C4C23×C318yes—
318(C2×D3)⋊C4C23×C318yes—
319C4⋊Dic3C23×C318yes—
320Dic3⋊C4C23×C314yes—
321Dic3⋊C4C23×C314yes—
322Dic3⋊C4C23×C318yes—
323C4×Dic3C23×C314yes—
324C4×Dic3C23×C318yes—
325C22×C32C2×#4112yes—
326C22×C32H(5,𝔽2)12yes—
327C22×C322−1+412yes—
328C22×C32C2511yescharacteristic
329C2×C3×D3—22no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3—24no—
335C2×C3×D3—44no—
336C2×C3×D3—48no—
337C32×C4—22no—
338C32×C4—22no—
339C32×C4—24no—
340C32×C4—24no—
341C32×C4C2×#4114yes—
342C3×Dic3—24no—
343C3×Dic3—22no—
344C3×Dic3—22no—
345C3×Dic3—22no—
346C22×Q8—31no—
347C22×Q8C2×C3×D312yes—
348C22×D4—31no—
349C22×D4—32no—
350C23×C4—31no—
351C23×C4—32no—
352C4⋊Q8C2×C3×D318yescomplemented
353#126—316no—
354#124—316no—
355#124—38no—
356#123—316no—
357C22⋊Q8—316no—
358C22⋊Q8—38no—
359#121—38no—
360C4×Q8—38no—
361C4×D4—38no—
362#117—38no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—32no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4C2×C3×D311yescharacteristic
368C2×C4⋊C4C2×C3×D311yescharacteristic
369C2×C4⋊C4C2×C3×D312yes—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4—32no—
377C2×C42—31no—
378C2×C42—32no—
379C2×C42C2×C3×D311yescharacteristic
380C23×C3—21no—
381C23×C3—34no—
382C23×C3—32no—
383C23×C3—64no—
384C23×C3—62no—
385C23×C3—62no—
386C23×C3—64no—
387C23×C3—64no—
388C23×C3—62no—
389C23×C3C23×D311yescharacteristic
390C23×C3C24×C311yescharacteristic
391C22×D3—22no—
392C22×D3—24no—
393C22×D3—24no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—24no—
397C22×D3C24×C312yes—
398C22×D3C24×C314yes—
399C3×Q8—48no—
400C3×Q8—48no—
401C3×Q8—416no—
402C3×Q8—68no—
403C3×D4—68no—
404C3×D4—128no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—32no—
422C2×C3×C4—34no—
423C2×C3×C4—32no—
424C2×C3×C4—32no—
425C2×C3×C4—44no—
426C2×C3×C4—44no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—64no—
430C2×C3×C4—62no—
431C2×C3×C4—68no—
432C2×C3×C4—128no—
433C2×C3×C4#23914yes—
434C2×C3×C4C3×#4114yes—
435C2×C3×C4C23×D314yes—
436C2×C3×C4C23×D312yes—
437C2×C3×C4C23×D312yes—
438C2×C3×C4C23×D314yes—
439C2×C3×C4C23×D312yes—
440C2×C3×C4C24×C314yes—
441C2×C3×C4C24×C312yes—
442C2×C3×C4C24×C312yes—
443C2×C3×C4C24×C314yes—
444C2×C3×C4C24×C312yes—
445C2×Dic3—24no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3C24×C312yes—
450C2×Dic3C24×C312yes—
451C2×Dic3C24×C314yes—
452C2×Dic3C24×C312yes—
453D12—28no—
454D12—48no—
455C4×D3—28no—
456C4×D3—48no—
457Dic6—28no—
458C2×C32#54214yescomplemented
459C2×C32C22×#4111yescharacteristic
460C2×C32C2×H(5,𝔽2)11yescharacteristic
461C2×C32C2×2−1+411yescharacteristic
462C3×D3—42no—
463C3×D3—44no—
464C24—32no—
465C24—31no—
466C2×Q8—34no—
467C2×Q8—44no—
468C2×Q8—64no—
469C2×Q8C22×C3×D318yes—
470C2×D4—34no—
471C2×D4—38no—
472C2×D4—64no—
473C2×D4—124no—
474C22×C4—31no—
475C22×C4—32no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—38no—
480C22×C4—64no—
481C22×C4—124no—
482C22×C4C22×C3×D312yes—
483C22×C4C22×C3×D311yescharacteristic
484C22×C4C22×C3×D311yescharacteristic
485C22×C4C22×C3×D312yes—
486C22×C4C22×C3×D311yescharacteristic
487C4⋊C4—34no—
488C4⋊C4—34no—
489C4⋊C4—38no—
490C4⋊C4—38no—
491C4⋊C4C22×C3×D314yes—
492C4⋊C4C22×C3×D314yes—
493C4⋊C4C22×C3×D318yes—
494C22⋊C4—34no—
495C22⋊C4—34no—
496C22⋊C4—38no—
497C22⋊C4—38no—
498C22⋊C4—38no—
499C22⋊C4—38no—
500C22⋊C4—38no—
501C42—34no—
502C42—38no—
503C42C22×C3×D314yes—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—64no—
509C22×C3—62no—
510C22×C3—62no—
511C22×C3—64no—
512C22×C3—64no—
513C22×C3—62no—
514C22×C3—128no—
515C22×C3—124no—
516C22×C3#100412yes—
517C22×C3C2×#23912yes—
518C22×C3#100712yes—
519C22×C3C2×C3×#4112yes—
520C22×C3C3×H(5,𝔽2)12yes—
521C22×C3C3×2−1+412yes—
522C22×C3C24×D311yescharacteristic
523C22×C3C25×C311yescharacteristic
524C2×D3—22no—
525C2×D3—24no—
526C2×D3—24no—
527C2×D3—22no—
528C2×D3—22no—
529C2×D3—24no—
530C2×D3—44no—
531C2×D3—48no—
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—24no—
539C3×C4—24no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—24no—
543C3×C4—44no—
544C3×C4—44no—
545C3×C4—62no—
546C3×C4—62no—
547C3×C4—64no—
548C3×C4—62no—
549C3×C4C2×#23914yes—
550C3×C4C2×C3×#4114yes—
551Dic3—24no—
552Dic3—22no—
553Dic3—22no—
554Dic3—22no—
555C32C2×#54211yescharacteristic, complemented, Sylow
556C23—34no—
557C23—32no—
558C23—64no—
559C23—62no—
560C23—62no—
561C23—64no—
562C23—64no—
563C23—62no—
564C23C23×C3×D311yescharacteristic
565Q8—48no—
566Q8—68no—
567D4—68no—
568D4—128no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—32no—
574C2×C4—34no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—64no—
580C2×C4—62no—
581C2×C4—68no—
582C2×C4—128no—
583C2×C4C3×#23914yes—
584C2×C4C23×C3×D314yes—
585C2×C4C23×C3×D312yes—
586C2×C4C23×C3×D312yes—
587C2×C4C23×C3×D314yes—
588C2×C4C23×C3×D312yes—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—24no—
593C2×C3—124no—
594C2×C3—122no—
595C2×C3#573314yesdirect product factor
596C2×C3C3×#54214yescomplemented
597C2×C3C2×#100411yescharacteristic
598C2×C3C22×#23911yescharacteristic
599C2×C3C2×#100711yescharacteristic
600C2×C3C22×C3×#4111yescharacteristic
601C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
602C2×C3C2×C3×2−1+411yescharacteristic
603D3—42no—
604D3—44no—
605C22—64no—
606C22—62no—
607C22—62no—
608C22—64no—
609C22—64no—
610C22—62no—
611C22—128no—
612C22—124no—
613C22C3×#100412yes—
614C22C2×C3×#23912yes—
615C22C3×#100712yes—
616C22C24×C3×D311yescharacteristic
617C4—24no—
618C4—24no—
619C4—22no—
620C4—22no—
621C4—62no—
622C4—62no—
623C4—64no—
624C4—62no—
625C4C2×C3×#23914yes—
626C3—21no—
627C3C2×#573311yescharacteristic, direct product factor
628C3C2×C3×#54211yescharacteristic, complemented
629C2—124no—
630C2—122no—
631C2C3×#573314yesdirect product factor
632C2C2×C3×#100411yescharacteristic
633C2C22×C3×#23911yescharacteristic
634C2C2×C3×#100711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4⋊Q8C2
socleC23×C32C24
prime radicalC2×C3×#895C2
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C2×C3×#542
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
2. C2×C3×#947C2semidirect
3. C2×C3×#946C2semidirect
4. C3×#5733C2direct (N × H)
5. C2×C3×#898C2semidirect
6. C2×C3×#897C2semidirect
8. C2×C3×#894C2semidirect
9. C2×C3×#893C2semidirect
10. C2×C3×#887C2semidirect
11. C2×C3×#875C2semidirect
12. C2×C3×#872C2semidirect
14. C2×#5733C3direct (N × H)
21. C32×C4⋊Q8C22semidirect
26. C3×#947C22semidirect
27. C3×#946C22semidirect
41. C3×#898C22semidirect
42. C3×#897C22semidirect
44. C3×#894C22semidirect
45. C3×#893C22semidirect
46. C3×#887C22semidirect
47. C3×#875C22semidirect
48. C3×#872C22semidirect
51. C2×C3×C4⋊Q8D3semidirect
52. C2×C3×C4⋊Q8C2×C3semidirect
63. C2×#947C2×C3semidirect
64. C2×#946C2×C3semidirect
65. #5733C2×C3direct (N × H)
66. C2×#898C2×C3semidirect
67. C2×#897C2×C3semidirect
69. C2×#894C2×C3semidirect
70. C2×#893C2×C3semidirect
71. C2×#887C2×C3semidirect
72. C2×#875C2×C3semidirect
73. C2×#872C2×C3semidirect
129. C3×C4⋊Q8C2×D3semidirect
130. C3×C4⋊Q8C22×C3semidirect
166. #947C22×C3semidirect
167. #946C22×C3semidirect
181. #898C22×C3semidirect
182. #897C22×C3semidirect
184. #894C22×C3semidirect
185. #893C22×C3semidirect
186. #887C22×C3semidirect
187. #875C22×C3semidirect
188. #872C22×C3semidirect
223. C2×C4⋊Q8C3×D3semidirect
352. C4⋊Q8C2×C3×D3semidirect
458. C2×C32#542semidirect
555. C32C2×#542semidirect
595. C2×C3#5733direct (N × H)
596. C2×C3C3×#542semidirect
627. C3C2×#5733direct (N × H)
628. C3C2×C3×#542semidirect
631. C2C3×#5733direct (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⋊Q82
C2×C3×#9472
C2×C3×#9462
C3×#57332
C2×C3×#8982
C2×C3×#8972
C2×C3×#8952
C2×C3×#8942
C2×C3×#8932
C2×C3×#8872
C2×C3×#8752
C2×C3×#8722
C2×C3×#5423
C2×#57333