Finite Group Databasebeta

← D3×#64104 #13176536

Subgroups — D3×#64104 #13176536

Order 1728.

2932 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊(C3⋊D3)C212yesmaximal, complemented
3C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
4#11723936C211yesmaximal, characteristic, complemented
5C3×#64104C211yesmaximal, characteristic, complemented
6C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
7D3×#3752C212yesmaximal, complemented
8#11723532C211yesmaximal, characteristic, complemented
9#11723526C211yesmaximal, characteristic, complemented
10#11723486C212yesmaximal, complemented
11#11723482C212yesmaximal, complemented
12C2×#64104—31nomaximal
13D3×#895—34nomaximal
14C22×D3×C3⋊D3C2212yes—
15C22×D3×C3⋊D3C2211yescharacteristic
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
17C2×C4⋊(C3⋊(C3⋊D3))C2212yescomplemented
18C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C32×C4×D3C2212yes—
23C2×C32×C4×D3C2211yescharacteristic
24C2×#6292C2212yescomplemented
25C2×#6292C2212yescomplemented
26C2×#6292C2212yescomplemented
27C2×#6289C2211yescharacteristic, complemented
28C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
29C2×D3×C3⋊Dic3C2211yescharacteristic
30D3×C4⋊(C3⋊D3)—28no—
31D3×C4⋊(C3⋊D3)—24no—
32C4×D3×C3⋊D3—24no—
33C33×C4⋊C4C2211yescharacteristic, complemented
34#88859C2212yescomplemented
35C3×#3752C2212yescomplemented
36C32×C4⋊Dic3C2211yescharacteristic, complemented
37C32×Dic3⋊C4C2212yescomplemented
38#88804C2212yescomplemented
39#88803C2212yescomplemented
40C22×C4⋊(C3⋊D3)—32no—
41C22×C4⋊(C3⋊D3)—31no—
42C22×C4×C3⋊D3—31no—
43C2×D3×D12—38no—
44C2×D3×D12—34no—
45C2×C4×D32—34no—
46C2×C32×C4⋊C4—31no—
47C2×#3752—32no—
48#64104—31no—
49#64104—32no—
50#64104—31no—
51#64104—31no—
52#64104—32no—
53#64104—34no—
54#64104—64no—
55#64104D311yescharacteristic, direct product factor
56C3×#895—34no—
57C3×D3×C4⋊C4D314yescomplemented
58D3×(C2×D3)⋊C4—38no—
59#63916—34no—
60#63910—38no—
61#63909—34no—
62#63886—38no—
63C22×C3⋊(C3⋊D3)C2312yes—
64C22×C3⋊(C3⋊D3)C2311yescharacteristic
65C22×C3×C3⋊D3C2312yes—
66C22×C3×C3⋊D3C2311yescharacteristic
67C22×C32×D3C2311yescharacteristic
68C2×D3×C3⋊D3—22no—
69C2×D3×C3⋊D3—22no—
70C2×D3×C3⋊D3—24no—
71C2×D3×C3⋊D3—24no—
72C2×D3×C3⋊D3—24no—
73C2×D3×C3⋊D3D414yescomplemented
74C2×C33×C4C2312yes—
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
77C4⋊(C3⋊(C3⋊D3))—24no—
78C4⋊(C3⋊(C3⋊D3))—22no—
79C4×C3⋊(C3⋊D3)—22no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4⋊(C3⋊D3)—24no—
82C3×C4⋊(C3⋊D3)—22no—
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—24no—
87C32×C4×D3D414yescomplemented
88#6292—24no—
89#6292—24no—
90#6292—24no—
91#6289—22no—
92Dic3×C3⋊D3—22no—
93D3×C3⋊Dic3—22no—
94D3×#121—91no—
95C2×#895—94no—
96C23×C3⋊D3—31no—
97C23×C3⋊D3—32no—
98C22×D32—34no—
99C22×D32—38no—
100C22×C32×C4—31no—
101C22×C32×C4—32no—
102C22×C3⋊Dic3—31no—
103C2×C4⋊(C3⋊D3)—32no—
104C2×C4⋊(C3⋊D3)—32no—
105C2×C4⋊(C3⋊D3)—32no—
106C2×C4⋊(C3⋊D3)—32no—
107C2×C4⋊(C3⋊D3)—31no—
108C2×C4⋊(C3⋊D3)—34no—
109C2×C4⋊(C3⋊D3)—38no—
110C2×C4⋊(C3⋊D3)—64no—
111C2×C4⋊(C3⋊D3)—68no—
112C2×C4⋊(C3⋊D3)—64no—
113C2×C4⋊(C3⋊D3)—68no—
114C2×C4⋊(C3⋊D3)C2×D312yescomplemented
115C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
116C2×C4×C3⋊D3—31no—
117C2×C4×C3⋊D3—31no—
118C2×C4×C3⋊D3—34no—
119C2×C4×C3⋊D3—31no—
120C2×C4×C3⋊D3—64no—
121C2×C4×C3⋊D3—64no—
122C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
123C2×C3×D12—38no—
124C2×C3×D12—34no—
125C2×C3×C4×D3—34no—
126C2×C3×C4×D3C2×D318yes—
127C2×C3×C4×D3C2×D314yes—
128C2×#626—38no—
129C2×#626—38no—
130C2×#626—38no—
131C2×#624—34no—
132C2×D3×Dic3—34no—
133C2×D3×Dic3—34no—
134D3×D12—632no—
135D3×D12—616no—
136C4×D32—616no—
137C32×C4⋊C4—24no—
138C32×C4⋊C4—32no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4C2×D314yescomplemented
141C32×C4⋊C4C2×D311yescharacteristic, complemented
142#3752—32no—
143#3752—32no—
144#3752—38no—
145#3752—32no—
146#3752—68no—
147#3752C2×D312yescomplemented
148C3×(C2×D3)⋊C4—38no—
149C3×C4⋊Dic3C2×D314yescomplemented
150C3×Dic3⋊C4C2×D318yescomplemented
151#3722—38no—
152(C2×D3)⋊Dic3—38no—
153C22×C33C2411yescharacteristic
154C2×C3⋊(C3⋊D3)—21no—
155C2×C3⋊(C3⋊D3)—21no—
156C2×C3⋊(C3⋊D3)—22no—
157C2×C3⋊(C3⋊D3)—22no—
158C2×C3⋊(C3⋊D3)—22no—
159C2×C3⋊(C3⋊D3)C2×D412yescomplemented
160C2×C3×C3⋊D3—21no—
161C2×C3×C3⋊D3—21no—
162C2×C3×C3⋊D3—22no—
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3C2×D412yescomplemented
166C2×C32×D3C2×D412yes—
167C2×C32×D3C2×D412yes—
168C2×C32×D3#4112yes—
169D3×C3⋊D3—28no—
170D3×C3⋊D3—48no—
171C33×C4—22no—
172C33×C4C2×D412yescomplemented
173C3⋊(C3⋊Dic3)—21no—
174C3×C3⋊Dic3—21no—
175C32×Dic3—22no—
176C32×Dic3C2×D412yescomplemented
177C2×D3×D4—92no—
178C2×D3×D4—91no—
179C22×D12—94no—
180C22×D12—98no—
181C22×C4×D3—94no—
182C22×C4×D3—91no—
183C3×#121—91no—
184C2×C3×C4⋊C4—34no—
185#939—92no—
186#938—91no—
187#930—91no—
188C2×(C2×D3)⋊C4—98no—
189#895—34no—
190#895—98no—
191#895—94no—
192#895—98no—
193#895—94no—
194#895—94no—
195#895—91no—
196#895—184no—
197D3×C4⋊C4C3⋊D311yescharacteristic, complemented
198#884—92no—
199D3×C22⋊C4—92no—
200C23×C32—31no—
201C22×C3⋊D3—31no—
202C22×C3⋊D3—34no—
203C22×C3⋊D3—32no—
204C22×C3⋊D3—34no—
205C22×C3⋊D3—38no—
206C22×C3⋊D3—64no—
207C22×C3⋊D3—68no—
208C22×C3⋊D3—62no—
209C22×C3⋊D3—62no—
210C22×C3⋊D3—64no—
211C22×C3⋊D3—64no—
212C22×C3⋊D3—64no—
213C22×C3⋊D3C22×D312yes—
214C22×C3⋊D3C22×D311yescharacteristic
215C22×C3×D3—34no—
216C22×C3×D3—38no—
217C22×C3×D3C22×D314yes—
218C2×D32—316no—
219C2×D32—68no—
220C2×D32—68no—
221C2×D32—616no—
222C2×D32—616no—
223C2×D32—616no—
224C2×C32×C4—24no—
225C2×C32×C4—28no—
226C2×C32×C4—31no—
227C2×C32×C4—34no—
228C2×C32×C4—32no—
229C2×C32×C4—64no—
230C2×C32×C4C22×D318yes—
231C2×C32×C4C22×D314yes—
232C2×C32×C4C22×D312yes—
233C2×C32×C4C22×D311yescharacteristic
234C2×C3⋊Dic3—31no—
235C2×C3⋊Dic3—34no—
236C2×C3⋊Dic3—64no—
237C2×C3⋊Dic3—62no—
238C2×C3⋊Dic3C22×D311yescharacteristic
239C4⋊(C3⋊D3)—24no—
240C4⋊(C3⋊D3)—22no—
241C4⋊(C3⋊D3)—64no—
242C4⋊(C3⋊D3)—64no—
243C4⋊(C3⋊D3)—64no—
244C4⋊(C3⋊D3)—64no—
245C4⋊(C3⋊D3)—62no—
246C4⋊(C3⋊D3)—616no—
247C4⋊(C3⋊D3)—68no—
248C4⋊(C3⋊D3)—128no—
249C4⋊(C3⋊D3)—1216no—
250C4×C3⋊D3—22no—
251C4×C3⋊D3—62no—
252C4×C3⋊D3—62no—
253C4×C3⋊D3—62no—
254C4×C3⋊D3—68no—
255C4×C3⋊D3—128no—
256C2×C3×Dic3—34no—
257C2×C3×Dic3C22×D318yes—
258C2×C3×Dic3C22×D314yes—
259C3×D12—616no—
260C3×D12—68no—
261C3×C4×D3—216no—
262C3×C4×D3—68no—
263C3×C4×D3D12116yescomplemented
264#626—616no—
265#626—616no—
266#626—616no—
267#624—68no—
268D3×Dic3—68no—
269D3×Dic3—68no—
270C2×#121—271noSylow
271C2×C33C22×D411yescharacteristic
272C2×C33C22×D411yescharacteristic
273C2×C33C2×#4111yescharacteristic
274C3⋊(C3⋊D3)—22no—
275C3⋊(C3⋊D3)—42no—
276C3×C3⋊D3—22no—
277C3×C3⋊D3—42no—
278C32×D3#12114yescomplemented
279C23×D3—94no—
280C23×D3—98no—
281C23×D3—91no—
282C23×D3—92no—
283C2×C3×D4—91no—
284C2×C3×D4—92no—
285C22×C3×C4—34no—
286C22×C3×C4—38no—
287C22×C3×C4—91no—
288C2×#67—92no—
289C2×#67—92no—
290C2×#67—92no—
291C22×Dic3—94no—
292C22×Dic3—91no—
293D3×D4—188no—
294D3×D4—184no—
295C2×D12—38no—
296C2×D12—34no—
297C2×D12—98no—
298C2×D12—98no—
299C2×D12—98no—
300C2×D12—98no—
301C2×D12—94no—
302C2×D12—92no—
303C2×D12—91no—
304C2×D12—184no—
305C2×D12—188no—
306C2×D12—1816no—
307C2×D12—1832no—
308C2×C4×D3—34no—
309C2×C4×D3—94no—
310C2×C4×D3—94no—
311C2×C4×D3—91no—
312C2×C4×D3—94no—
313C2×C4×D3—91no—
314C2×C4×D3—91no—
315C2×C4×D3—184no—
316C2×C4×D3—1816no—
317C2×C4×D3—184no—
318C2×C4×D3C2×C3⋊D312yes—
319C2×C4×D3C2×C3⋊D311yescharacteristic
320C3×C4⋊C4—24no—
321C3×C4⋊C4—38no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4D3214yescomplemented
324C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
325C3×C22⋊C4—92no—
326#217—92no—
327(C2×D3)⋊C4—38no—
328(C2×D3)⋊C4—98no—
329(C2×D3)⋊C4—98no—
330(C2×D3)⋊C4—98no—
331(C2×D3)⋊C4—92no—
332(C2×D3)⋊C4—92no—
333(C2×D3)⋊C4—188no—
334C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
335Dic3⋊C4C2×C3⋊D312yescomplemented
336C22×C32—24no—
337C22×C32—32no—
338C22×C32—32no—
339C22×C32—32no—
340C22×C32C23×D314yes—
341C22×C32C23×D311yescharacteristic
342C2×C3⋊D3—21no—
343C2×C3⋊D3—21no—
344C2×C3⋊D3—22no—
345C2×C3⋊D3—22no—
346C2×C3⋊D3—22no—
347C2×C3⋊D3—32no—
348C2×C3⋊D3—38no—
349C2×C3⋊D3—68no—
350C2×C3⋊D3—68no—
351C2×C3⋊D3—61no—
352C2×C3⋊D3—61no—
353C2×C3⋊D3—62no—
354C2×C3⋊D3—62no—
355C2×C3⋊D3—62no—
356C2×C3⋊D3—64no—
357C2×C3⋊D3—64no—
358C2×C3⋊D3—68no—
359C2×C3⋊D3—68no—
360C2×C3⋊D3—68no—
361C2×C3⋊D3—124no—
362C2×C3⋊D3—124no—
363C2×C3⋊D3—128no—
364C2×C3⋊D3—128no—
365C2×C3⋊D3—128no—
366C2×C3⋊D3—128no—
367C2×C3⋊D3D3×D412yescomplemented
368C2×C3×D3—38no—
369C2×C3×D3—64no—
370C2×C3×D3—64no—
371C2×C3×D3—68no—
372C2×C3×D3—68no—
373C2×C3×D3—68no—
374C2×C3×D3C2×D1218yes—
375C2×C3×D3D3×D418yes—
376C2×C3×D3#23918yes—
377D32—632no—
378D32—1232no—
379C32×C4—22no—
380C32×C4—28no—
381C32×C4—28no—
382C32×C4—32no—
383C32×C4—48no—
384C32×C4—62no—
385C32×C4C2×D1218yescomplemented
386C32×C4D3×D412yescomplemented
387C3⋊Dic3—21no—
388C3⋊Dic3—61no—
389C3⋊Dic3—64no—
390C3⋊Dic3—124no—
391C3×Dic3—28no—
392C3×Dic3—64no—
393C3×Dic3C2×D1218yescomplemented
394C22×D4—271no—
395C22×D4—272no—
396C23×C4—271no—
397#121—91no—
398#121—272no—
399#121—271no—
400#121—271no—
401#121—272no—
402#121—271no—
403C2×C4⋊C4—31no—
404C2×C22⋊C4—272no—
405C33C2×#12111yescharacteristic, complemented, Sylow
406C23×C3—34no—
407C23×C3—91no—
408C23×C3—92no—
409C22×D3—34no—
410C22×D3—38no—
411C22×D3—916no—
412C22×D3—94no—
413C22×D3—91no—
414C22×D3—94no—
415C22×D3—98no—
416C22×D3—92no—
417C22×D3—184no—
418C22×D3—188no—
419C22×D3—188no—
420C22×D3—188no—
421C22×D3—1816no—
422C22×D3—1816no—
423C22×D3—1816no—
424C22×D3—182no—
425C22×D3—182no—
426C22×D3—184no—
427C22×D3—184no—
428C22×D3—184no—
429C22×D3C22×C3⋊D311yescharacteristic
430C3×D4—184no—
431C3×D4—182no—
432C2×C3×C4—24no—
433C2×C3×C4—28no—
434C2×C3×C4—34no—
435C2×C3×C4—316no—
436C2×C3×C4—38no—
437C2×C3×C4—616no—
438C2×C3×C4—91no—
439C2×C3×C4—182no—
440C2×C3×C4C2×D3218yes—
441C2×C3×C4C2×D3214yes—
442C2×C3×C4C22×C3⋊D312yes—
443C2×C3×C4C22×C3⋊D311yescharacteristic
444#67—184no—
445#67—184no—
446#67—184no—
447C2×Dic3—34no—
448C2×Dic3—94no—
449C2×Dic3—91no—
450C2×Dic3—184no—
451C2×Dic3—188no—
452C2×Dic3—182no—
453C2×Dic3C22×C3⋊D312yes—
454C2×Dic3C22×C3⋊D311yescharacteristic
455D12—616no—
456D12—68no—
457D12—184no—
458D12—1816no—
459D12—1816no—
460D12—1816no—
461D12—1816no—
462D12—188no—
463D12—182no—
464D12—368no—
465D12—3616no—
466C4×D3—24no—
467C4×D3—68no—
468C4×D3—188no—
469C4×D3—188no—
470C4×D3—182no—
471C4×D3—188no—
472C4×D3—182no—
473C4×D3—182no—
474C4×D3—368no—
475C4×D3C4⋊(C3⋊D3)14yescomplemented
476C2×C32—24no—
477C2×C32—24no—
478C2×C32—24no—
479C2×C32—34no—
480C2×C32C22×D1214yes—
481C2×C32C2×D3×D414yes—
482C2×C32C2×D3×D411yescharacteristic
483C2×C32C2×D3×D411yescharacteristic
484C2×C32C2×#23914yes—
485C2×C32D3×#4111yescharacteristic
486C3⋊D3—22no—
487C3⋊D3—42no—
488C3⋊D3—62no—
489C3⋊D3—68no—
490C3⋊D3—128no—
491C3⋊D3—122no—
492C3⋊D3—128no—
493C3⋊D3—248no—
494C3×D3—68no—
495C3×D3—128no—
496C3×D3#895116yescomplemented
497C24—271no—
498C24—272no—
499C2×D4—92no—
500C2×D4—91no—
501C2×D4—272no—
502C2×D4—272no—
503C2×D4—272no—
504C2×D4—272no—
505C2×D4—271no—
506C2×D4—544no—
507C2×D4—548no—
508C22×C4—31no—
509C22×C4—32no—
510C22×C4—91no—
511C22×C4—271no—
512C22×C4—271no—
513C22×C4—271no—
514C22×C4—271no—
515C22×C4—544no—
516C4⋊C4—32no—
517C4⋊C4—31no—
518C4⋊C4D3×C3⋊D311yescharacteristic, complemented
519C22⋊C4—92no—
520C22⋊C4—272no—
521C22⋊C4—272no—
522C22⋊C4—272no—
523C22×C3—24no—
524C22×C3—38no—
525C22×C3—38no—
526C22×C3—38no—
527C22×C3—92no—
528C22×C3—181no—
529C22×C3—181no—
530C22×C3—182no—
531C22×C3—182no—
532C22×C3—182no—
533C22×C3C22×D3214yes—
534C22×C3C23×C3⋊D311yescharacteristic
535C2×D3—38no—
536C2×D3—64no—
537C2×D3—64no—
538C2×D3—68no—
539C2×D3—68no—
540C2×D3—68no—
541C2×D3—98no—
542C2×D3—92no—
543C2×D3—188no—
544C2×D3—1832no—
545C2×D3—184no—
546C2×D3—184no—
547C2×D3—181no—
548C2×D3—181no—
549C2×D3—188no—
550C2×D3—188no—
551C2×D3—188no—
552C2×D3—188no—
553C2×D3—182no—
554C2×D3—182no—
555C2×D3—182no—
556C2×D3—364no—
557C2×D3—364no—
558C2×D3—368no—
559C2×D3—368no—
560C2×D3—368no—
561C2×D3—3632no—
562C2×D3—368no—
563C2×D3C2×C4⋊(C3⋊D3)12yes—
564C2×D3D4×C3⋊D312yes—
565C2×D3#383212yes—
566C3×C4—28no—
567C3×C4—22no—
568C3×C4—28no—
569C3×C4—38no—
570C3×C4—48no—
571C3×C4—68no—
572C3×C4—181no—
573C3×C4D3×D1218yescomplemented
574C3×C4C2×C4⋊(C3⋊D3)12yescomplemented
575Dic3—22no—
576Dic3—64no—
577Dic3—184no—
578Dic3—181no—
579Dic3—364no—
580Dic3C2×C4⋊(C3⋊D3)12yescomplemented
581C32—24no—
582C32C2×#89514yescomplemented
583C32D3×#12111yescharacteristic, complemented
584C23—31no—
585C23—91no—
586C23—92no—
587C23—274no—
588C23—271no—
589C23—272no—
590C23—542no—
591C23—542no—
592C23—544no—
593C23—544no—
594C23—544no—
595D4—184no—
596D4—182no—
597D4—544no—
598D4—544no—
599D4—544no—
600D4—544no—
601D4—542no—
602C2×C4—31no—
603C2×C4—34no—
604C2×C4—32no—
605C2×C4—64no—
606C2×C4—91no—
607C2×C4—182no—
608C2×C4—271no—
609C2×C4—542no—
610C2×C4—542no—
611C2×C4—542no—
612C2×C4—542no—
613C2×C4C2×D3×C3⋊D312yes—
614C2×C4C2×D3×C3⋊D311yescharacteristic
615C2×C3—24no—
616C2×C3—24no—
617C2×C3—24no—
618C2×C3—316no—
619C2×C3—182no—
620C2×C3—362no—
621C2×C3C2×D3×D1214yes—
622C2×C3D32×D414yes—
623C2×C3D3×#23914yes—
624C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
625C2×C3C2×D4×C3⋊D311yescharacteristic
626C2×C3C2×#383211yescharacteristic
627D3—68no—
628D3—128no—
629D3—188no—
630D3—182no—
631D3—368no—
632D3—368no—
633D3—362no—
634D3—728no—
635D3#6410414yesdirect product factor
636C22—32no—
637C22—32no—
638C22—32no—
639C22—92no—
640C22—181no—
641C22—181no—
642C22—182no—
643C22—182no—
644C22—182no—
645C22—272no—
646C22—548no—
647C22—541no—
648C22—541no—
649C22—542no—
650C22—542no—
651C22—542no—
652C22—1088no—
653C22C22×D3×C3⋊D311yescharacteristic
654C4—22no—
655C4—32no—
656C4—62no—
657C4—181no—
658C4—541no—
659C4D3×C4⋊(C3⋊D3)12yescomplemented
660C3—24no—
661C3D3×#89514yescomplemented
662C3C2×#6410411yescharacteristic, complemented
663C2—34no—
664C2—182no—
665C2—362no—
666C2—542no—
667C2—1082no—
668C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
669C2D3×D4×C3⋊D311yescharacteristic
670C2D3×#383211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×C4⋊(C3⋊D3)C2semidirect
2. C2×D3×C4⋊(C3⋊D3)C2semidirect
3. C2×C4×D3×C3⋊D3C2semidirect
4. #11723936C2semidirect
5. C3×#64104C2semidirect
6. C32×D3×C4⋊C4C2semidirect
7. D3×#3752C2semidirect
8. #11723532C2semidirect
9. #11723526C2semidirect
10. #11723486C2semidirect
11. #11723482C2semidirect
16. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
17. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
18. C2×C4×C3⋊(C3⋊D3)C22semidirect
19. C2×C3×C4⋊(C3⋊D3)C22semidirect
20. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
24. C2×#6292C22semidirect
25. C2×#6292C22semidirect
26. C2×#6292C22semidirect
27. C2×#6289C22semidirect
28. C2×Dic3×C3⋊D3C22semidirect
33. C33×C4⋊C4C22semidirect
34. #88859C22semidirect
35. C3×#3752C22semidirect
36. C32×C4⋊Dic3C22semidirect
37. C32×Dic3⋊C4C22semidirect
38. #88804C22semidirect
39. #88803C22semidirect
55. #64104D3direct (N × H)
57. C3×D3×C4⋊C4D3semidirect
73. C2×D3×C3⋊D3D4semidirect
87. C32×C4×D3D4semidirect
114. C2×C4⋊(C3⋊D3)C2×D3semidirect
115. C2×C4⋊(C3⋊D3)C2×D3semidirect
122. C2×C4×C3⋊D3C2×D3semidirect
140. C32×C4⋊C4C2×D3semidirect
141. C32×C4⋊C4C2×D3semidirect
147. #3752C2×D3semidirect
149. C3×C4⋊Dic3C2×D3semidirect
150. C3×Dic3⋊C4C2×D3semidirect
159. C2×C3⋊(C3⋊D3)C2×D4semidirect
165. C2×C3×C3⋊D3C2×D4semidirect
172. C33×C4C2×D4semidirect
176. C32×Dic3C2×D4semidirect
197. D3×C4⋊C4C3⋊D3semidirect
263. C3×C4×D3D12semidirect
278. C32×D3#121semidirect
323. C3×C4⋊C4D32semidirect
324. C3×C4⋊C4C2×C3⋊D3semidirect
334. C4⋊Dic3C2×C3⋊D3semidirect
335. Dic3⋊C4C2×C3⋊D3semidirect
367. C2×C3⋊D3D3×D4semidirect
385. C32×C4C2×D12semidirect
386. C32×C4D3×D4semidirect
393. C3×Dic3C2×D12semidirect
405. C33C2×#121semidirect
475. C4×D3C4⋊(C3⋊D3)semidirect
496. C3×D3#895semidirect
518. C4⋊C4D3×C3⋊D3semidirect
573. C3×C4D3×D12semidirect
574. C3×C4C2×C4⋊(C3⋊D3)semidirect
580. Dic3C2×C4⋊(C3⋊D3)semidirect
582. C32C2×#895semidirect
583. C32D3×#121semidirect
635. D3#64104direct (N × H)
659. C4D3×C4⋊(C3⋊D3)semidirect
661. C3D3×#895semidirect
662. C3C2×#64104semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C2×C4×D3×C3⋊D32
#117239362
C3×#641042
C32×D3×C4⋊C42
D3×#37522
#117235322
#117235262
#117234862
#117234822
C2×#641043
D3×#8953