Finite Group Databasebeta

← #13177328

Subgroups — #13177328

Order 1728.

3512 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊(C3⋊D3))C211yesmaximal, characteristic, complemented
2C2×#89039C212yesmaximal, complemented
3C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×#64139C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6#11723639C212yesmaximal, complemented
7#11723542C212yesmaximal, complemented
8#11723517C211yesmaximal, characteristic, complemented
9#11723516C211yesmaximal, characteristic, complemented
10#11723486C212yesmaximal, complemented
11#11723484C211yesmaximal, characteristic, complemented
12D4×C4⋊(C3⋊D3)—31nomaximal
13#10595074—34nomaximal
14C23×C3⋊(C3⋊D3)C2212yescomplemented
15C22×D3×C3⋊D3C2212yescomplemented
16C22×C33×C4C2211yescharacteristic, complemented
17C2×C4⋊(C3⋊(C3⋊D3))—24no—
18C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2212yescomplemented
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
21C2×C3×#638C2212yescomplemented
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic, complemented
25#89039—28no—
26C2×#6292C2212yescomplemented
27C2×#6292C2212yescomplemented
28C2×#6292C2212yescomplemented
29C2×#6291C2212yescomplemented
30C2×#6289C2212yescomplemented
31D3×C4⋊(C3⋊D3)—24no—
32C3×#3752C2212yescomplemented
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C32×#217C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C32×Dic3⋊C4C2211yescharacteristic, complemented
37C32×C4×Dic3C2211yescharacteristic, complemented
38#88804C2212yescomplemented
39#88804C2212yescomplemented
40C2×D4×C3⋊D3—32no—
41C22×C4⋊(C3⋊D3)—31no—
42C22×C4⋊(C3⋊D3)—31no—
43C22×C4⋊(C3⋊D3)—34no—
44C22×C4⋊(C3⋊D3)—64no—
45C2×#3811—38no—
46C2×D3×D12—34no—
47C32×C4×D4—31no—
48#64139—31no—
49#64139D311yescharacteristic, complemented
50#64104—32no—
51#64091—32no—
52#64091—32no—
53#64083—31no—
54C4×C4⋊(C3⋊D3)—31no—
55C3×#930—34no—
56C3×C4×#67D314yescomplemented
57#63981—38no—
58#63923—38no—
59#63911—34no—
60#63910—38no—
61#63909—34no—
62#63894—34no—
63C23×C33C2311yescharacteristic
64C22×C3⋊(C3⋊D3)—24no—
65C22×C3⋊(C3⋊D3)—24no—
66C22×C3⋊(C3⋊D3)—42no—
67C22×C3⋊(C3⋊D3)C2312yes—
68C22×C3⋊(C3⋊D3)C2312yes—
69C22×C3×C3⋊D3C2312yes—
70C22×C32×D3C2311yescharacteristic
71C2×D3×C3⋊D3—24no—
72C2×D3×C3⋊D3—24no—
73C2×D3×C3⋊D3—42no—
74C2×C33×C4—22no—
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C4⋊(C3⋊(C3⋊D3))—24no—
78C4⋊(C3⋊(C3⋊D3))—22no—
79C4⋊(C3⋊(C3⋊D3))D414yescomplemented
80C3×#638—24no—
81C2×C3×C3⋊Dic3C2312yes—
82C3×C4⋊(C3⋊D3)—22no—
83C32×#67D414yescomplemented
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88#6292—24no—
89#6292—24no—
90#6292—42no—
91#6291—24no—
92#6289—24no—
93#5609—91no—
94D4×D12—94no—
95C23×C3⋊D3—32no—
96C23×C3⋊D3—38no—
97C23×C3⋊D3—32no—
98C23×C3⋊D3—68no—
99C22×D32—38no—
100C2×C32×D4—31no—
101C22×C32×C4—24no—
102C22×C32×C4—31no—
103C22×C32×C4C2×D314yescomplemented
104C22×C32×C4C2×D311yescharacteristic, complemented
105C2×#638—32no—
106C2×#638C2×D312yescomplemented
107D4×C3⋊D3—68no—
108C2×C4⋊(C3⋊D3)—31no—
109C2×C4⋊(C3⋊D3)—34no—
110C2×C4⋊(C3⋊D3)—32no—
111C2×C4⋊(C3⋊D3)—32no—
112C2×C4⋊(C3⋊D3)—31no—
113C2×C4⋊(C3⋊D3)—32no—
114C2×C4⋊(C3⋊D3)—34no—
115C2×C4⋊(C3⋊D3)—38no—
116C2×C4⋊(C3⋊D3)—32no—
117C2×C4⋊(C3⋊D3)—64no—
118C2×C4⋊(C3⋊D3)—64no—
119C2×C4⋊(C3⋊D3)—616no—
120C2×C4⋊(C3⋊D3)—64no—
121C2×C4⋊(C3⋊D3)—64no—
122C2×C4⋊(C3⋊D3)—68no—
123C2×C4⋊(C3⋊D3)—632no—
124C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
125C2×C4×C3⋊D3—32no—
126C2×C3×#67—38no—
127C2×C3×#67C2×D314yes—
128C2×C3×D12—34no—
129C2×C3×C4×D3C2×D314yescomplemented
130#3811—632no—
131C2×#626—38no—
132C2×#626—38no—
133C2×#626—38no—
134C2×#626—38no—
135C2×#624—38no—
136D3×D12—616no—
137C32×C4⋊C4—31no—
138C32×C22⋊C4—31no—
139C32×C22⋊C4—31no—
140C32×C42—31no—
141#3752—32no—
142#3752—32no—
143#3752C2×D312yescomplemented
144C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
145C3×#217C2×D314yescomplemented
146C3×(C2×D3)⋊C4—38no—
147C3×(C2×D3)⋊C4C2×D314yescomplemented
148C3×C4⋊Dic3—34no—
149C3×Dic3⋊C4C2×D314yescomplemented
150C3×C4×Dic3C2×D314yescomplemented
151#3722—38no—
152#3722—38no—
153C22×C33—21no—
154C22×C33—21no—
155C22×C33C2×D412yescomplemented
156C22×C33C2411yescharacteristic
157C2×C3⋊(C3⋊D3)—22no—
158C2×C3⋊(C3⋊D3)—22no—
159C2×C3⋊(C3⋊D3)—22no—
160C2×C3⋊(C3⋊D3)—22no—
161C2×C3⋊(C3⋊D3)—22no—
162C2×C3⋊(C3⋊D3)—48no—
163C2×C3⋊(C3⋊D3)C2×D414yescomplemented
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—22no—
167C2×C32×D3—21no—
168C2×C32×D3—21no—
169C2×C32×D3C2×D412yescomplemented
170D3×C3⋊D3—48no—
171C33×C4—21no—
172C33×C4C2×D412yescomplemented
173C3×C3⋊Dic3—22no—
174C32×Dic3—21no—
175C32×Dic3—21no—
176C32×Dic3C2×D412yescomplemented
177C2×D3×D4—98no—
178C2×D3×D4—92no—
179C2×D3×D4—91no—
180C22×D12—94no—
181C22×D12—94no—
182C22×D12—91no—
183C22×D12—184no—
184C3×#121—91no—
185C3×C4×D4—34no—
186#940—91no—
187#937—92no—
188#930—34no—
189#930—94no—
190C4×#67C3⋊D311yescharacteristic, complemented
191#895—98no—
192#895—91no—
193#893—91no—
194#884—92no—
195#882—98no—
196#882—98no—
197#882—92no—
198#874—94no—
199C4×D12—94no—
200C23×C32—24no—
201C23×C32—31no—
202C23×C32C22×D314yes—
203C23×C32C22×D311yescharacteristic
204C22×C3⋊D3—32no—
205C22×C3⋊D3—32no—
206C22×C3⋊D3—38no—
207C22×C3⋊D3—38no—
208C22×C3⋊D3—68no—
209C22×C3⋊D3—68no—
210C22×C3⋊D3—64no—
211C22×C3⋊D3—64no—
212C22×C3⋊D3—64no—
213C22×C3⋊D3—616no—
214C22×C3⋊D3—632no—
215C22×C3⋊D3—64no—
216C22×C3⋊D3—616no—
217C22×C3⋊D3—1216no—
218C22×C3⋊D3—122no—
219C22×C3⋊D3—122no—
220C22×C3⋊D3—128no—
221C22×C3⋊D3—1216no—
222C22×C3⋊D3C22×D312yes—
223C22×C3×D3—38no—
224C22×C3×D3C22×D314yes—
225C2×D32—616no—
226C2×D32—616no—
227C2×D32—128no—
228C32×D4—34no—
229C2×C32×C4—216no—
230C2×C32×C4—28no—
231C2×C32×C4—22no—
232C2×C32×C4—24no—
233C2×C32×C4—24no—
234C2×C32×C4—31no—
235C2×C32×C4—31no—
236C2×C32×C4—31no—
237C2×C32×C4—62no—
238C2×C32×C4C22×D314yes—
239C2×C32×C4C22×D314yes—
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D311yescharacteristic
242#638—24no—
243#638—64no—
244C2×C3⋊Dic3C22×D312yes—
245C4⋊(C3⋊D3)—22no—
246C4⋊(C3⋊D3)—34no—
247C4⋊(C3⋊D3)—316no—
248C4⋊(C3⋊D3)—616no—
249C4⋊(C3⋊D3)—64no—
250C4⋊(C3⋊D3)—616no—
251C4⋊(C3⋊D3)—632no—
252C4⋊(C3⋊D3)—616no—
253C4⋊(C3⋊D3)—64no—
254C4⋊(C3⋊D3)—64no—
255C4⋊(C3⋊D3)—68no—
256C4⋊(C3⋊D3)—62no—
257C4⋊(C3⋊D3)—122no—
258C4×C3⋊D3—64no—
259C3×#67—616no—
260C3×#67D12116yescomplemented
261C2×C3×Dic3—38no—
262C2×C3×Dic3C22×D314yes—
263C2×C3×Dic3C22×D314yes—
264C2×C3×Dic3C22×D314yes—
265C3×D12—68no—
266C3×C4×D3—28no—
267#626—616no—
268#626—616no—
269#626—616no—
270#626—128no—
271#624—616no—
272D42—271noSylow
273C2×C33—22no—
274C2×C33C22×D411yescharacteristic
275C2×C33C22×D411yescharacteristic
276C2×C33H(5,𝔽2)11yescharacteristic
277C3⋊(C3⋊D3)—24no—
278C3⋊(C3⋊D3)—42no—
279C3×C3⋊D3—42no—
280C32×D3—22no—
281C23×D3—98no—
282C23×D3—98no—
283C23×D3—92no—
284C23×D3—92no—
285C23×D3—188no—
286C2×C3×D4—34no—
287C2×C3×D4—92no—
288C2×C3×D4—91no—
289C22×C3×C4—24no—
290C22×C3×C4—34no—
291C22×C3×C4D3214yescomplemented
292C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
293C2×#67—38no—
294C2×#67—98no—
295C2×#67—92no—
296C2×#67—92no—
297C2×#67—92no—
298C2×#67C2×C3⋊D311yescharacteristic
299D3×D4—184no—
300D3×D4—1832no—
301D3×D4—188no—
302C2×D12—34no—
303C2×D12—94no—
304C2×D12—91no—
305C2×D12—98no—
306C2×D12—98no—
307C2×D12—92no—
308C2×D12—94no—
309C2×D12—98no—
310C2×D12—92no—
311C2×D12—91no—
312C2×D12—98no—
313C2×D12—184no—
314C2×D12—188no—
315C2×D12—184no—
316C2×D12—1816no—
317C2×D12—1816no—
318C2×D12—184no—
319C2×D12—1832no—
320C2×C4×D3—98no—
321C2×C4×D3—92no—
322C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
323C3×C4⋊C4—34no—
324C3×C4⋊C4—91no—
325C3×C22⋊C4—34no—
326C3×C22⋊C4—34no—
327C3×C22⋊C4—92no—
328C3×C42—34no—
329#217C2×C3⋊D311yescharacteristic, complemented
330(C2×D3)⋊C4—38no—
331(C2×D3)⋊C4—98no—
332(C2×D3)⋊C4—98no—
333(C2×D3)⋊C4—92no—
334(C2×D3)⋊C4—92no—
335(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
336C4⋊Dic3—34no—
337Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
338C4×Dic3C2×C3⋊D311yescharacteristic, complemented
339C22×C32—28no—
340C22×C32—28no—
341C22×C32—24no—
342C22×C32—21no—
343C22×C32—24no—
344C22×C32—21no—
345C22×C32—24no—
346C22×C32—28no—
347C22×C32—32no—
348C22×C32—61no—
349C22×C32—61no—
350C22×C32C2×D1218yescomplemented
351C22×C32D3×D412yescomplemented
352C22×C32C23×D314yes—
353C22×C32C23×D311yescharacteristic
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—34no—
358C2×C3⋊D3—316no—
359C2×C3⋊D3—616no—
360C2×C3⋊D3—62no—
361C2×C3⋊D3—62no—
362C2×C3⋊D3—616no—
363C2×C3⋊D3—68no—
364C2×C3⋊D3—62no—
365C2×C3⋊D3—62no—
366C2×C3⋊D3—62no—
367C2×C3⋊D3—68no—
368C2×C3⋊D3—68no—
369C2×C3⋊D3—68no—
370C2×C3⋊D3—68no—
371C2×C3⋊D3—128no—
372C2×C3⋊D3—128no—
373C2×C3⋊D3—128no—
374C2×C3⋊D3—128no—
375C2×C3⋊D3—128no—
376C2×C3⋊D3—128no—
377C2×C3⋊D3—1232no—
378C2×C3⋊D3—1264no—
379C2×C3×D3—24no—
380C2×C3×D3—24no—
381C2×C3×D3—68no—
382C2×C3×D3—68no—
383C2×C3×D3—68no—
384C2×C3×D3C2×D1218yescomplemented
385D32—1232no—
386C32×C4—28no—
387C32×C4—24no—
388C32×C4—21no—
389C32×C4—28no—
390C32×C4—32no—
391C32×C4—61no—
392C32×C4—61no—
393C32×C4D3×D418yescomplemented
394C32×C4D3×D412yescomplemented
395C3⋊Dic3—22no—
396C3×Dic3—24no—
397C3×Dic3—24no—
398C3×Dic3—68no—
399C3×Dic3C2×D1218yescomplemented
400C22×D4—271no—
401C22×D4—272no—
402C22×D4—271no—
403#127—271no—
404#121—91no—
405#121—272no—
406#121—271no—
407#120—272no—
408#120—272no—
409C4×D4—31no—
410C4×D4—271no—
411C33D4211yescharacteristic, complemented, Sylow
412C23×C3—24no—
413C23×C3—34no—
414C23×C3—92no—
415C23×C3C2×D3214yes—
416C23×C3C22×C3⋊D311yescharacteristic
417C22×D3—38no—
418C22×D3—98no—
419C22×D3—92no—
420C22×D3—98no—
421C22×D3—92no—
422C22×D3—188no—
423C22×D3—188no—
424C22×D3—184no—
425C22×D3—1816no—
426C22×D3—1816no—
427C22×D3—1816no—
428C22×D3—184no—
429C22×D3—1832no—
430C22×D3—1816no—
431C22×D3—184no—
432C22×D3—184no—
433C22×D3—3616no—
434C22×D3—362no—
435C22×D3—368no—
436C22×D3—368no—
437C22×D3—362no—
438C22×D3—3616no—
439C22×D3C22×C3⋊D311yescharacteristic
440C3×D4—316no—
441C3×D4—184no—
442C3×D4—182no—
443C2×C3×C4—216no—
444C2×C3×C4—28no—
445C2×C3×C4—22no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—34no—
449C2×C3×C4—34no—
450C2×C3×C4—34no—
451C2×C3×C4—68no—
452C2×C3×C4—92no—
453C2×C3×C4C2×D3214yes—
454C2×C3×C4C2×D3214yes—
455C2×C3×C4C22×C3⋊D311yescharacteristic
456C2×C3×C4C22×C3⋊D311yescharacteristic
457#67—616no—
458#67—184no—
459#67—1816no—
460#67—184no—
461#67—362no—
462#67C4⋊(C3⋊D3)14yescomplemented
463C2×Dic3—38no—
464C2×Dic3C22×C3⋊D311yescharacteristic
465C2×Dic3C22×C3⋊D311yescharacteristic
466C2×Dic3C22×C3⋊D311yescharacteristic
467D12—68no—
468D12—916no—
469D12—94no—
470D12—1816no—
471D12—1816no—
472D12—184no—
473D12—1832no—
474D12—1816no—
475D12—1816no—
476D12—1816no—
477D12—184no—
478D12—188no—
479D12—182no—
480D12—368no—
481C4×D3—22no—
482C4×D3—1816no—
483C4×D3—184no—
484C2×C32—216no—
485C2×C32—28no—
486C2×C32—22no—
487C2×C32—24no—
488C2×C32—24no—
489C2×C32—24no—
490C2×C32—62no—
491C2×C32C22×D1214yes—
492C2×C32C2×D3×D414yes—
493C2×C32C2×D3×D411yescharacteristic
494C2×C32C2×D3×D411yescharacteristic
495C2×C32#100914yes—
496C2×C32#100911yescharacteristic
497C3⋊D3—42no—
498C3⋊D3—64no—
499C3⋊D3—616no—
500C3⋊D3—1216no—
501C3⋊D3—1216no—
502C3⋊D3—128no—
503C3⋊D3—122no—
504C3×D3—28no—
505C3×D3—128no—
506C24—272no—
507C24—272no—
508C2×D4—31no—
509C2×D4—92no—
510C2×D4—91no—
511C2×D4—272no—
512C2×D4—272no—
513C2×D4—272no—
514C2×D4—272no—
515C2×D4—271no—
516C2×D4—272no—
517C2×D4—271no—
518C2×D4—544no—
519C2×D4—544no—
520C2×D4—548no—
521C22×C4—31no—
522C22×C4—272no—
523C22×C4D3×C3⋊D311yescharacteristic, complemented
524C4⋊C4—31no—
525C4⋊C4—91no—
526C22⋊C4—31no—
527C22⋊C4—31no—
528C22⋊C4—92no—
529C22⋊C4—272no—
530C22⋊C4—272no—
531C42—31no—
532C22×C3—28no—
533C22×C3—28no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—24no—
539C22×C3—28no—
540C22×C3—38no—
541C22×C3—64no—
542C22×C3—64no—
543C22×C3—182no—
544C22×C3—182no—
545C22×C3—182no—
546C22×C3D3×D1218yescomplemented
547C22×C3C2×C4⋊(C3⋊D3)12yescomplemented
548C22×C3C22×D3214yes—
549C22×C3C23×C3⋊D311yescharacteristic
550C2×D3—21no—
551C2×D3—21no—
552C2×D3—68no—
553C2×D3—68no—
554C2×D3—68no—
555C2×D3—916no—
556C2×D3—94no—
557C2×D3—1816no—
558C2×D3—188no—
559C2×D3—188no—
560C2×D3—182no—
561C2×D3—182no—
562C2×D3—1816no—
563C2×D3—188no—
564C2×D3—188no—
565C2×D3—188no—
566C2×D3—182no—
567C2×D3—182no—
568C2×D3—182no—
569C2×D3—368no—
570C2×D3—368no—
571C2×D3—368no—
572C2×D3—368no—
573C2×D3—368no—
574C2×D3—3632no—
575C2×D3—3632no—
576C2×D3—368no—
577C2×D3—3664no—
578C2×D3C2×C4⋊(C3⋊D3)12yescomplemented
579C3×C4—28no—
580C3×C4—24no—
581C3×C4—21no—
582C3×C4—28no—
583C3×C4—38no—
584C3×C4—64no—
585C3×C4—64no—
586C3×C4—182no—
587C3×C4#381118yescomplemented
588C3×C4D4×C3⋊D312yescomplemented
589Dic3—21no—
590Dic3—21no—
591Dic3—68no—
592Dic3C2×C4⋊(C3⋊D3)12yescomplemented
593C32—24no—
594C32D4×D1214yescomplemented
595C32#560911yescharacteristic, complemented
596C23—31no—
597C23—92no—
598C23—272no—
599C23—272no—
600C23—544no—
601C23—544no—
602C23—544no—
603C23—544no—
604C23—1082no—
605C23—1082no—
606C23C2×D3×C3⋊D311yescharacteristic
607D4—34no—
608D4—184no—
609D4—182no—
610D4—274no—
611D4—544no—
612D4—544no—
613D4—544no—
614D4—544no—
615D4—542no—
616D4—1082no—
617C2×C4—22no—
618C2×C4—31no—
619C2×C4—31no—
620C2×C4—31no—
621C2×C4—62no—
622C2×C4—92no—
623C2×C4—544no—
624C2×C4C2×D3×C3⋊D311yescharacteristic
625C2×C4C2×D3×C3⋊D311yescharacteristic
626C2×C3—216no—
627C2×C3—28no—
628C2×C3—22no—
629C2×C3—24no—
630C2×C3—24no—
631C2×C3—24no—
632C2×C3—68no—
633C2×C3—362no—
634C2×C3C2×D3×D1214yes—
635C2×C3#6430814yes—
636C2×C3C2×#381114yes—
637C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
638C2×C3C2×D4×C3⋊D311yescharacteristic
639C2×C3#6436611yescharacteristic
640D3—22no—
641D3—128no—
642D3—1816no—
643D3—184no—
644D3—3616no—
645D3—3616no—
646D3—368no—
647D3—362no—
648C22—21no—
649C22—21no—
650C22—32no—
651C22—61no—
652C22—61no—
653C22—182no—
654C22—182no—
655C22—182no—
656C22—274no—
657C22—542no—
658C22—542no—
659C22—542no—
660C22—542no—
661C22—542no—
662C22—1088no—
663C22—1088no—
664C22D3×C4⋊(C3⋊D3)12yescomplemented
665C22C22×D3×C3⋊D311yescharacteristic
666C4—21no—
667C4—32no—
668C4—61no—
669C4—61no—
670C4—182no—
671C4#8903912yescomplemented
672C3—24no—
673C3#1059507414yescomplemented
674C3D4×C4⋊(C3⋊D3)11yescharacteristic, complemented
675C2—22no—
676C2—62no—
677C2—362no—
678C2—544no—
679C2—1082no—
680C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
681C2#1172458111yescharacteristic
682C2C2×#8903911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊(C3⋊(C3⋊D3))C2semidirect
2. C2×#89039C2semidirect
3. C2×D3×C4⋊(C3⋊D3)C2semidirect
4. C3×#64139C2semidirect
5. C32×C4×#67C2semidirect
6. #11723639C2semidirect
7. #11723542C2semidirect
8. #11723517C2semidirect
9. #11723516C2semidirect
10. #11723486C2semidirect
11. #11723484C2semidirect
14. C23×C3⋊(C3⋊D3)C22semidirect
15. C22×D3×C3⋊D3C22semidirect
16. C22×C33×C4C22semidirect
19. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
20. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
21. C2×C3×#638C22semidirect
22. C2×C3×C4⋊(C3⋊D3)C22semidirect
24. C2×C32×C4×D3C22semidirect
26. C2×#6292C22semidirect
27. C2×#6292C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6289C22semidirect
32. C3×#3752C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C32×#217C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C32×Dic3⋊C4C22semidirect
37. C32×C4×Dic3C22semidirect
38. #88804C22semidirect
39. #88804C22semidirect
49. #64139D3semidirect
56. C3×C4×#67D3semidirect
79. C4⋊(C3⋊(C3⋊D3))D4semidirect
83. C32×#67D4semidirect
103. C22×C32×C4C2×D3semidirect
104. C22×C32×C4C2×D3semidirect
106. C2×#638C2×D3semidirect
124. C2×C4⋊(C3⋊D3)C2×D3semidirect
129. C2×C3×C4×D3C2×D3semidirect
143. #3752C2×D3semidirect
144. C4⋊(C3⋊Dic3)C2×D3semidirect
145. C3×#217C2×D3semidirect
147. C3×(C2×D3)⋊C4C2×D3semidirect
149. C3×Dic3⋊C4C2×D3semidirect
150. C3×C4×Dic3C2×D3semidirect
155. C22×C33C2×D4semidirect
163. C2×C3⋊(C3⋊D3)C2×D4semidirect
169. C2×C32×D3C2×D4semidirect
172. C33×C4C2×D4semidirect
176. C32×Dic3C2×D4semidirect
190. C4×#67C3⋊D3semidirect
260. C3×#67D12semidirect
291. C22×C3×C4D32semidirect
292. C22×C3×C4C2×C3⋊D3semidirect
322. C2×C4×D3C2×C3⋊D3semidirect
329. #217C2×C3⋊D3semidirect
335. (C2×D3)⋊C4C2×C3⋊D3semidirect
337. Dic3⋊C4C2×C3⋊D3semidirect
338. C4×Dic3C2×C3⋊D3semidirect
350. C22×C32C2×D12semidirect
351. C22×C32D3×D4semidirect
384. C2×C3×D3C2×D12semidirect
393. C32×C4D3×D4semidirect
394. C32×C4D3×D4semidirect
399. C3×Dic3C2×D12semidirect
411. C33D42semidirect
462. #67C4⋊(C3⋊D3)semidirect
523. C22×C4D3×C3⋊D3semidirect
546. C22×C3D3×D12semidirect
547. C22×C3C2×C4⋊(C3⋊D3)semidirect
578. C2×D3C2×C4⋊(C3⋊D3)semidirect
587. C3×C4#3811semidirect
588. C3×C4D4×C3⋊D3semidirect
592. Dic3C2×C4⋊(C3⋊D3)semidirect
594. C32D4×D12semidirect
595. C32#5609semidirect
664. C22D3×C4⋊(C3⋊D3)semidirect
671. C4#89039semidirect
673. C3#10595074semidirect
674. C3D4×C4⋊(C3⋊D3)semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊(C3⋊D3))2
C2×#890392
C2×D3×C4⋊(C3⋊D3)2
C3×#641392
C32×C4×#672
#117236392
#117235422
#117235172
#117235162
#117234862
#117234842
D4×C4⋊(C3⋊D3)3
#105950743