Finite Group Databasebeta

← C3⋊D3×#930 #13177301

Subgroups — C3⋊D3×#930 #13177301

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
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C212yesmaximal, complemented
3C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
4#11723971C211yesmaximal, characteristic, complemented
5C32×#930C211yesmaximal, characteristic, complemented
6#11723635C212yesmaximal, complemented
7C3⋊D3×(C2×D3)⋊C4C212yesmaximal, complemented
8#11723526C211yesmaximal, characteristic, complemented
9#11723522C211yesmaximal, characteristic, complemented
10#11723520C212yesmaximal, complemented
11C3⋊D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12C3⋊D3×#121—31nomaximal
13D3×#930—34nomaximal
14C23×C3×C3⋊D3C2211yescharacteristic
15C22×D3×C3⋊D3C2212yes—
16C22×C33×C4C2211yescharacteristic, complemented
17C2×#6312C2212yescomplemented
18C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
19C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×C3×C4×C3⋊D3—24no—
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C32×#67C2212yescomplemented
26C2×C32×D12C2211yescharacteristic, complemented
27C3⋊D3×#67—28no—
28C2×#6292C2212yescomplemented
29C2×#6291C2212yescomplemented
30C2×#6290C2212yescomplemented
31C2×Dic3×C3⋊D3C2212yes—
32C3⋊D3×D12—24no—
33#88859C2212yescomplemented
34C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2212yescomplemented
36C32×C4⋊Dic3C2211yescharacteristic, complemented
37#88807C2212yescomplemented
38#88804C2212yescomplemented
39(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
40C2×D4×C3⋊D3—31no—
41C2×D4×C3⋊D3—32no—
42C22×C4×C3⋊D3D311yescharacteristic, complemented
43C22×C3×C4×D3—34no—
44C2×D3×#67—38no—
45C2×D3×D12—34no—
46C32×#121—31no—
47#64148—32no—
48#64147—31no—
49#64139—31no—
50#64139—34no—
51#64139—64no—
52#64104—31no—
53C4⋊C4×C3⋊D3—31no—
54#64093—32no—
55C22⋊C4×C3⋊D3—32no—
56C3×#930D314yescomplemented
57#63978—38no—
58D3×(C2×D3)⋊C4—38no—
59#63909—34no—
60#63908—34no—
61#63906—38no—
62D3×C4⋊Dic3—34no—
63C23×C33C2311yescharacteristic
64C22×C3⋊(C3⋊D3)C2312yes—
65C22×C3×C3⋊D3—22no—
66C22×C3×C3⋊D3—22no—
67C22×C3×C3⋊D3D414yescomplemented
68C22×C3×C3⋊D3C2311yescharacteristic
69C22×C3×C3⋊D3C2311yescharacteristic
70C22×C32×D3C2312yes—
71C2×D3×C3⋊D3—24no—
72C2×D3×C3⋊D3—24no—
73C2×D3×C3⋊D3—24no—
74C2×C33×C4—22no—
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77#6312—24no—
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C4⋊(C3⋊(C3⋊D3))—22no—
80C2×C3×C3⋊Dic3—22no—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—22no—
84C3×C4×C3⋊D3—22no—
85C3×C4×C3⋊D3—22no—
86C3×C4×C3⋊D3D414yescomplemented
87C32×#67—24no—
88C2×C32×Dic3C2312yes—
89C32×D12—22no—
90#6292—24no—
91#6291—24no—
92#6290—24no—
93Dic3×C3⋊D3—24no—
94C2×#930—91no—
95D3×#121—94no—
96C23×C3⋊D3—32no—
97C23×C3⋊D3C2×D311yescharacteristic
98C23×C3×D3—34no—
99C22×D32—38no—
100C2×C32×D4—32no—
101C2×C32×D4—31no—
102C22×C32×C4—24no—
103C22×C32×C4C2×D314yescomplemented
104C22×C32×C4C2×D311yescharacteristic, complemented
105C2×#638—32no—
106C2×#638—38no—
107C2×#638—32no—
108C2×#638—32no—
109C2×#638—68no—
110C22×C3⋊Dic3C2×D311yescharacteristic, complemented
111D4×C3⋊D3—68no—
112D4×C3⋊D3—64no—
113C2×C4⋊(C3⋊D3)—32no—
114C2×C4⋊(C3⋊D3)—31no—
115C2×C4⋊(C3⋊D3)—34no—
116C2×C4⋊(C3⋊D3)—64no—
117C2×C4×C3⋊D3—24no—
118C2×C4×C3⋊D3—32no—
119C2×C4×C3⋊D3C2×D311yescharacteristic
120C2×C4×C3⋊D3C2×D311yescharacteristic
121C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
122C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
123C2×C3×#67C2×D318yescomplemented
124C22×C3×Dic3—34no—
125C2×C3×D12C2×D314yescomplemented
126C2×C3×C4×D3—34no—
127C2×C3×C4×D3—34no—
128C2×C3×C4×D3—34no—
129C2×C3×C4×D3—34no—
130C2×C3×C4×D3—616no—
131D3×#67—632no—
132C2×#626—38no—
133C2×#626—38no—
134C2×#625—38no—
135C2×D3×Dic3—38no—
136D3×D12—616no—
137C32×C4⋊C4—31no—
138C32×C22⋊C4—32no—
139#3757—32no—
140#3752—32no—
141#3752—38no—
142#3752—32no—
143#3752—68no—
144C4⋊(C3⋊Dic3)—31no—
145C4⋊(C3⋊Dic3)—34no—
146C4⋊(C3⋊Dic3)—64no—
147#3750—32no—
148C3×(C2×D3)⋊C4C2×D318yescomplemented
149C3×C4⋊Dic3C2×D314yescomplemented
150Dic3⋊Dic3—38no—
151#3722—38no—
152(C2×D3)⋊Dic3—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—21no—
161C2×C3×C3⋊D3—21no—
162C2×C3×C3⋊D3—28no—
163C2×C3×C3⋊D3C2×D412yes—
164C2×C3×C3⋊D3C2×D412yes—
165C2×C3×C3⋊D3C2×D412yescomplemented
166C2×C3×C3⋊D3#4112yes—
167C2×C32×D3—22no—
168C2×C32×D3—22no—
169C2×C32×D3—22no—
170D3×C3⋊D3—48no—
171C33×C4—21no—
172C33×C4C2×D412yescomplemented
173C3⋊(C3⋊Dic3)—22no—
174C3×C3⋊Dic3—21no—
175C3×C3⋊Dic3C2×D412yescomplemented
176C32×Dic3—22no—
177C23×C3×C4—91no—
178C22×#67—92no—
179C2×D3×D4—94no—
180C2×D3×D4—98no—
181C22×D12—91no—
182C22×C4×D3—34no—
183C3×#121—34no—
184#939—98no—
185#938—94no—
186#930—94no—
187#930—91no—
188#930—92no—
189#930—91no—
190#930—92no—
191#930—91no—
192#930—184no—
193#930C3⋊D311yescharacteristic, direct product factor
194C2×(C2×D3)⋊C4—92no—
195C2×C4⋊Dic3—91no—
196#895—94no—
197D3×C4⋊C4—94no—
198#884—98no—
199D3×C22⋊C4—98no—
200C23×C32—24no—
201C23×C32—32no—
202C23×C32C22×D314yes—
203C23×C32C22×D311yescharacteristic
204C22×C3⋊D3—22no—
205C22×C3⋊D3—22no—
206C22×C3⋊D3—32no—
207C22×C3⋊D3—38no—
208C22×C3⋊D3—68no—
209C22×C3⋊D3—64no—
210C22×C3⋊D3—64no—
211C22×C3⋊D3—64no—
212C22×C3⋊D3D1214yescomplemented
213C22×C3⋊D3C22×D311yescharacteristic
214C22×C3⋊D3C22×D311yescharacteristic
215C22×C3×D3—34no—
216C22×C3×D3—316no—
217C22×C3×D3—34no—
218C22×C3×D3—68no—
219C22×C3×D3—68no—
220C22×C3×D3C22×D318yes—
221C2×D32—616no—
222C2×D32—616no—
223C2×D32—616no—
224C32×D4—64no—
225C32×D4—62no—
226C2×C32×C4—22no—
227C2×C32×C4—24no—
228C2×C32×C4—24no—
229C2×C32×C4—28no—
230C2×C32×C4—32no—
231C2×C32×C4—48no—
232C2×C32×C4C22×D314yes—
233C2×C32×C4C22×D314yes—
234C2×C32×C4C22×D311yescharacteristic
235C2×C32×C4C22×D311yescharacteristic
236#638—64no—
237#638—64no—
238#638—64no—
239#638—616no—
240#638—1216no—
241C2×C3⋊Dic3—22no—
242C2×C3⋊Dic3—32no—
243C2×C3⋊Dic3—38no—
244C2×C3⋊Dic3—68no—
245C2×C3⋊Dic3C22×D311yescharacteristic
246C2×C3⋊Dic3C22×D311yescharacteristic
247C4⋊(C3⋊D3)—64no—
248C4⋊(C3⋊D3)—62no—
249C4⋊(C3⋊D3)—68no—
250C4⋊(C3⋊D3)—128no—
251C4×C3⋊D3—22no—
252C4×C3⋊D3—22no—
253C4×C3⋊D3—22no—
254C4×C3⋊D3—64no—
255C4×C3⋊D3#6714yescomplemented
256C3×#67—216no—
257C2×C3×Dic3—34no—
258C2×C3×Dic3—34no—
259C2×C3×Dic3—68no—
260C2×C3×Dic3C22×D318yes—
261C3×D12—28no—
262C3×C4×D3—316no—
263C3×C4×D3—68no—
264C3×C4×D3—68no—
265C3×C4×D3—68no—
266#626—616no—
267#626—616no—
268#625—616no—
269D3×Dic3—616no—
270C2×#121—271noSylow
271C2×C33—22no—
272C2×C33C22×D411yescharacteristic
273C2×C33C22×D411yescharacteristic
274C2×C33C2×#4111yescharacteristic
275C3⋊(C3⋊D3)—42no—
276C3×C3⋊D3—22no—
277C3×C3⋊D3#12114yescomplemented
278C32×D3—42no—
279C24×C3—91no—
280C23×D3—34no—
281C23×D3—98no—
282C23×D3—92no—
283C2×C3×D4—38no—
284C2×C3×D4—34no—
285C22×C3×C4—24no—
286C22×C3×C4—91no—
287C22×C3×C4—91no—
288C22×C3×C4—91no—
289C22×C3×C4—91no—
290C22×C3×C4—91no—
291C22×C3×C4—184no—
292C22×C3×C4D3214yescomplemented
293C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
294C2×#67—98no—
295C2×#67—98no—
296C2×#67—98no—
297C2×#67—92no—
298C2×#67—92no—
299C2×#67—92no—
300C2×#67—188no—
301C2×#67—188no—
302C2×#67C2×C3⋊D312yescomplemented
303C22×Dic3—34no—
304C22×Dic3—92no—
305D3×D4—1816no—
306D3×D4—1832no—
307C2×D12—98no—
308C2×D12—92no—
309C2×D12—94no—
310C2×D12—91no—
311C2×D12—184no—
312C2×D12—184no—
313C2×D12C2×C3⋊D311yescharacteristic, complemented
314C2×C4×D3—34no—
315C2×C4×D3—34no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—616no—
319C2×C4×D3—98no—
320C3×C4⋊C4—34no—
321C3×C22⋊C4—38no—
322#217—98no—
323(C2×D3)⋊C4—98no—
324(C2×D3)⋊C4—92no—
325(C2×D3)⋊C4—98no—
326(C2×D3)⋊C4—92no—
327(C2×D3)⋊C4—92no—
328(C2×D3)⋊C4—188no—
329(C2×D3)⋊C4C2×C3⋊D312yescomplemented
330C4⋊Dic3—94no—
331C4⋊Dic3—91no—
332C4⋊Dic3—92no—
333C4⋊Dic3—184no—
334C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
335Dic3⋊C4—98no—
336C22×C32—21no—
337C22×C32—21no—
338C22×C32—24no—
339C22×C32—28no—
340C22×C32—24no—
341C22×C32—24no—
342C22×C32—44no—
343C22×C32—44no—
344C22×C32—62no—
345C22×C32—62no—
346C22×C32—62no—
347C22×C32C2×D1212yescomplemented
348C22×C32D3×D418yescomplemented
349C22×C32C23×D314yes—
350C22×C32C23×D311yescharacteristic
351C2×C3⋊D3—21no—
352C2×C3⋊D3—21no—
353C2×C3⋊D3—28no—
354C2×C3⋊D3—62no—
355C2×C3⋊D3—62no—
356C2×C3⋊D3—62no—
357C2×C3⋊D3—68no—
358C2×C3⋊D3—68no—
359C2×C3⋊D3—68no—
360C2×C3⋊D3—128no—
361C2×C3⋊D3—128no—
362C2×C3⋊D3—128no—
363C2×C3⋊D3—128no—
364C2×C3⋊D3C2×D1212yes—
365C2×C3⋊D3C2×D1212yescomplemented
366C2×C3⋊D3#23512yes—
367C2×C3⋊D3C2×#6712yes—
368C2×C3×D3—28no—
369C2×C3×D3—28no—
370C2×C3×D3—28no—
371C2×C3×D3—38no—
372C2×C3×D3—38no—
373C2×C3×D3—38no—
374C2×C3×D3—38no—
375C2×C3×D3—632no—
376C2×C3×D3—64no—
377C2×C3×D3—64no—
378D32—1232no—
379C32×C4—21no—
380C32×C4—28no—
381C32×C4—24no—
382C32×C4—44no—
383C32×C4—62no—
384C32×C4D3×D418yescomplemented
385C32×C4C2×#6712yescomplemented
386C3⋊Dic3—21no—
387C3⋊Dic3—62no—
388C3⋊Dic3—68no—
389C3⋊Dic3—128no—
390C3⋊Dic3C2×#6712yescomplemented
391C3×Dic3—28no—
392C3×Dic3—38no—
393C3×Dic3—64no—
394C22×D4—271no—
395C22×D4—272no—
396C23×C4—91no—
397#121—31no—
398#121—272no—
399#121—271no—
400#121—271no—
401#121—272no—
402#121—271no—
403C2×C4⋊C4—271no—
404C2×C22⋊C4—272no—
405C33C2×#12111yescharacteristic, complemented, Sylow
406C23×C3—24no—
407C23×C3—38no—
408C23×C3—91no—
409C23×C3—91no—
410C23×C3—94no—
411C23×C3—182no—
412C23×C3—182no—
413C23×C3C2×D3214yes—
414C23×C3C22×C3⋊D311yescharacteristic
415C22×D3—34no—
416C22×D3—34no—
417C22×D3—316no—
418C22×D3—68no—
419C22×D3—68no—
420C22×D3—98no—
421C22×D3—92no—
422C22×D3—188no—
423C22×D3—184no—
424C22×D3—184no—
425C22×D3—184no—
426C22×D3—1816no—
427C22×D3—1816no—
428C22×D3—1816no—
429C22×D3C22×C3⋊D312yes—
430C3×D4—616no—
431C3×D4—68no—
432C2×C3×C4—28no—
433C2×C3×C4—22no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—38no—
437C2×C3×C4—48no—
438C2×C3×C4—91no—
439C2×C3×C4—94no—
440C2×C3×C4—91no—
441C2×C3×C4—182no—
442C2×C3×C4—182no—
443C2×C3×C4—182no—
444C2×C3×C4—182no—
445C2×C3×C4C2×D3214yes—
446C2×C3×C4C2×D3214yes—
447C2×C3×C4C22×C3⋊D311yescharacteristic
448C2×C3×C4C22×C3⋊D311yescharacteristic
449#67—24no—
450#67—184no—
451#67—1816no—
452#67—184no—
453#67—1816no—
454#67—1816no—
455#67—184no—
456#67—3616no—
457C2×Dic3—34no—
458C2×Dic3—34no—
459C2×Dic3—68no—
460C2×Dic3—98no—
461C2×Dic3—92no—
462C2×Dic3—188no—
463C2×Dic3—184no—
464C2×Dic3C22×C3⋊D312yes—
465D12—22no—
466D12—1816no—
467D12—184no—
468D12—188no—
469D12—182no—
470D12—368no—
471C4×D3—316no—
472C4×D3—68no—
473C4×D3—68no—
474C4×D3—68no—
475C4×D3—1816no—
476C2×C32—22no—
477C2×C32—24no—
478C2×C32—24no—
479C2×C32—24no—
480C2×C32—28no—
481C2×C32—48no—
482C2×C32—122no—
483C2×C32C22×D1211yescharacteristic
484C2×C32C2×#23511yescharacteristic
485C2×C32C2×D3×D414yes—
486C2×C32C2×D3×D414yes—
487C2×C32D3×#4114yes—
488C2×C32C22×#6711yescharacteristic
489C3⋊D3—22no—
490C3⋊D3—122no—
491C3⋊D3—128no—
492C3⋊D3—248no—
493C3⋊D3#93014yesdirect product factor
494C3×D3—316no—
495C3×D3—48no—
496C3×D3—68no—
497C24—91no—
498C24—272no—
499C2×D4—32no—
500C2×D4—31no—
501C2×D4—272no—
502C2×D4—272no—
503C2×D4—272no—
504C2×D4—272no—
505C2×D4—271no—
506C2×D4—544no—
507C2×D4—548no—
508C22×C4—91no—
509C22×C4—91no—
510C22×C4—91no—
511C22×C4—91no—
512C22×C4—91no—
513C22×C4—184no—
514C22×C4—272no—
515C22×C4D3×C3⋊D311yescharacteristic, complemented
516C4⋊C4—31no—
517C4⋊C4—272no—
518C4⋊C4—271no—
519C22⋊C4—32no—
520C22⋊C4—272no—
521C22⋊C4—272no—
522C22⋊C4—272no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—24no—
528C22×C3—28no—
529C22×C3—44no—
530C22×C3—44no—
531C22×C3—68no—
532C22×C3—68no—
533C22×C3—68no—
534C22×C3—92no—
535C22×C3—92no—
536C22×C3—92no—
537C22×C3—92no—
538C22×C3—188no—
539C22×C3—181no—
540C22×C3—181no—
541C22×C3D3×D1218yescomplemented
542C22×C3D4×C3⋊D312yescomplemented
543C22×C3C22×D3214yes—
544C22×C3C23×C3⋊D311yescharacteristic
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—22no—
548C2×D3—38no—
549C2×D3—38no—
550C2×D3—38no—
551C2×D3—38no—
552C2×D3—632no—
553C2×D3—64no—
554C2×D3—64no—
555C2×D3—188no—
556C2×D3—188no—
557C2×D3—188no—
558C2×D3—182no—
559C2×D3—182no—
560C2×D3—182no—
561C2×D3—368no—
562C2×D3—368no—
563C2×D3—368no—
564C2×D3—3632no—
565C2×D3—368no—
566C3×C4—24no—
567C3×C4—21no—
568C3×C4—28no—
569C3×C4—44no—
570C3×C4—68no—
571C3×C4—92no—
572C3×C4—181no—
573C3×C4D3×#6718yescomplemented
574C3×C4D4×C3⋊D312yescomplemented
575Dic3—22no—
576Dic3—38no—
577Dic3—64no—
578Dic3—188no—
579Dic3—182no—
580Dic3—368no—
581C32—24no—
582C32D3×#12114yescomplemented
583C32C2×#93011yescharacteristic, complemented
584C23—32no—
585C23—91no—
586C23—91no—
587C23—94no—
588C23—182no—
589C23—182no—
590C23—272no—
591C23—544no—
592C23—544no—
593C23—544no—
594C23C2×D3×C3⋊D311yescharacteristic
595D4—64no—
596D4—62no—
597D4—544no—
598D4—544no—
599D4—544no—
600D4—544no—
601D4—542no—
602C2×C4—22no—
603C2×C4—32no—
604C2×C4—91no—
605C2×C4—94no—
606C2×C4—91no—
607C2×C4—182no—
608C2×C4—182no—
609C2×C4—182no—
610C2×C4—182no—
611C2×C4—272no—
612C2×C4—544no—
613C2×C4C2×D3×C3⋊D311yescharacteristic
614C2×C4C2×D3×C3⋊D311yescharacteristic
615C2×C3—22no—
616C2×C3—28no—
617C2×C3—24no—
618C2×C3—24no—
619C2×C3—24no—
620C2×C3—48no—
621C2×C3—94no—
622C2×C3—128no—
623C2×C3—182no—
624C2×C3C2×D3×D1214yes—
625C2×C3D3×#23514yes—
626C2×C3C2×D3×#6714yes—
627C2×C3C2×D4×C3⋊D311yescharacteristic
628C2×C3C2×D4×C3⋊D311yescharacteristic
629C2×C3#41×C3⋊D311yescharacteristic
630D3—316no—
631D3—42no—
632D3—68no—
633D3—362no—
634D3—368no—
635D3—728no—
636C22—21no—
637C22—21no—
638C22—62no—
639C22—62no—
640C22—62no—
641C22—92no—
642C22—92no—
643C22—92no—
644C22—92no—
645C22—188no—
646C22—181no—
647C22—181no—
648C22—542no—
649C22—542no—
650C22—542no—
651C22—1088no—
652C22C3⋊D3×D1212yescomplemented
653C22C22×D3×C3⋊D311yescharacteristic
654C4—21no—
655C4—62no—
656C4—92no—
657C4—181no—
658C4—542no—
659C4C3⋊D3×#6712yescomplemented
660C3—24no—
661C3D3×#93014yescomplemented
662C3C3⋊D3×#12111yescharacteristic, complemented
663C2—22no—
664C2—94no—
665C2—122no—
666C2—182no—
667C2—1082no—
668C2C2×C3⋊D3×D1211yescharacteristic
669C2C3⋊D3×#23511yescharacteristic
670C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×C3⋊D3C2semidirect
2. C2×C3⋊D3×#67C2semidirect
3. C2×C3⋊D3×D12C2semidirect
4. #11723971C2semidirect
5. C32×#930C2semidirect
6. #11723635C2semidirect
7. C3⋊D3×(C2×D3)⋊C4C2semidirect
8. #11723526C2semidirect
9. #11723522C2semidirect
10. #11723520C2semidirect
11. C3⋊D3×C4⋊Dic3C2semidirect
16. C22×C33×C4C22semidirect
17. C2×#6312C22semidirect
18. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×D12C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6290C22semidirect
33. #88859C22semidirect
34. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C32×C4⋊Dic3C22semidirect
37. #88807C22semidirect
38. #88804C22semidirect
39. (C2×D3)⋊(C3⋊Dic3)C22semidirect
42. C22×C4×C3⋊D3D3semidirect
56. C3×#930D3semidirect
67. C22×C3×C3⋊D3D4semidirect
86. C3×C4×C3⋊D3D4semidirect
103. C22×C32×C4C2×D3semidirect
104. C22×C32×C4C2×D3semidirect
110. C22×C3⋊Dic3C2×D3semidirect
121. C2×C4×C3⋊D3C2×D3semidirect
122. C2×C4×C3⋊D3C2×D3semidirect
123. C2×C3×#67C2×D3semidirect
125. C2×C3×D12C2×D3semidirect
148. C3×(C2×D3)⋊C4C2×D3semidirect
149. C3×C4⋊Dic3C2×D3semidirect
155. C22×C33C2×D4semidirect
165. C2×C3×C3⋊D3C2×D4semidirect
172. C33×C4C2×D4semidirect
175. C3×C3⋊Dic3C2×D4semidirect
193. #930C3⋊D3direct (N × H)
212. C22×C3⋊D3D12semidirect
255. C4×C3⋊D3#67semidirect
277. C3×C3⋊D3#121semidirect
292. C22×C3×C4D32semidirect
293. C22×C3×C4C2×C3⋊D3semidirect
302. C2×#67C2×C3⋊D3semidirect
313. C2×D12C2×C3⋊D3semidirect
329. (C2×D3)⋊C4C2×C3⋊D3semidirect
334. C4⋊Dic3C2×C3⋊D3semidirect
347. C22×C32C2×D12semidirect
348. C22×C32D3×D4semidirect
365. C2×C3⋊D3C2×D12semidirect
384. C32×C4D3×D4semidirect
385. C32×C4C2×#67semidirect
390. C3⋊Dic3C2×#67semidirect
405. C33C2×#121semidirect
493. C3⋊D3#930direct (N × H)
515. C22×C4D3×C3⋊D3semidirect
541. C22×C3D3×D12semidirect
542. C22×C3D4×C3⋊D3semidirect
573. C3×C4D3×#67semidirect
574. C3×C4D4×C3⋊D3semidirect
582. C32D3×#121semidirect
583. C32C2×#930semidirect
652. C22C3⋊D3×D12semidirect
659. C4C3⋊D3×#67semidirect
661. C3D3×#930semidirect
662. C3C3⋊D3×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C2×C3⋊D3×#672
C2×C3⋊D3×D122
#117239712
C32×#9302
#117236352
C3⋊D3×(C2×D3)⋊C42
#117235262
#117235222
#117235202
C3⋊D3×C4⋊Dic32
C3⋊D3×#1213
D3×#9303