Finite Group Databasebeta

← C3×#11724611 #72220355

Subgroups — C3×#11724611 #72220355

Order 2592.

3466 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#6312C211yesmaximal, characteristic, complemented
2C2×C32×#638C211yesmaximal, characteristic, complemented
3C2×C33×#67C211yesmaximal, characteristic, complemented
4C3×#89039C212yesmaximal, complemented
5C3×D3×#638C212yesmaximal, complemented
6C3×C3⋊D3×#67C212yesmaximal, complemented
7C3×#89028C212yesmaximal, complemented
8C3×#89029C212yesmaximal, complemented
9C3×#89031C212yesmaximal, complemented
10C3×#64361—31nomaximal
11#11724611C311yesmaximal, characteristic, direct product factor
12C3×#64330—34nomaximal
13C23×C34C2211yescharacteristic, complemented
14C22×C3×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
15C22×C32×C3⋊D3C2211yescharacteristic, complemented
16C22×C33×D3C2211yescharacteristic, complemented
17C2×C3×D3×C3⋊D3C2212yescomplemented
18C3×#6312C2212yescomplemented
19C3×#6312C2212yescomplemented
20C2×C3×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
21C32×#638C2212yescomplemented
22C32×#638C2212yescomplemented
23C2×C32×C3⋊Dic3C2211yescharacteristic, complemented
24C33×#67C2212yescomplemented
25C33×#67C2212yescomplemented
26C2×C33×Dic3C2211yescharacteristic, complemented
27C3×#6293C2212yescomplemented
28C3×#6292C2212yescomplemented
29C3×#6291C2212yescomplemented
30C3×#6290C2212yescomplemented
31C3×#6289C2212yescomplemented
32C3×Dic3×C3⋊D3C2212yescomplemented
33C3×D3×C3⋊Dic3C2212yescomplemented
34C2×C33×D4—31no—
35C2×#6312C2×C311yescharacteristic, complemented
36C2×C3×#638—21no—
37C2×C3×#638—31no—
38C2×C3×#638—34no—
39C2×C3×#638—32no—
40C2×C3×#638—64no—
41C2×C3×#638D311yescharacteristic, complemented
42C2×C3×#638C2×C311yescharacteristic, complemented
43C3×#3830—32no—
44C3×#3830—32no—
45C3×D4×C3⋊D3—32no—
46C3×D4×C3⋊D3—32no—
47C3×#3828—32no—
48C2×C32×#67—24no—
49C2×C32×#67—34no—
50C2×C32×#67D314yescomplemented
51C2×C32×#67C2×C311yescharacteristic, complemented
52#89039C2×C312yescomplemented
53C3⋊D3×#67C2×C312yescomplemented
54D3×#638C2×C312yescomplemented
55#89031C2×C312yescomplemented
56#89029C2×C312yescomplemented
57#89028C2×C312yescomplemented
58C3×#3811—38no—
59C3×D3×#67—38no—
60C3×D3×#67—38no—
61C3×#3805—38no—
62C3×#3804—38no—
63C3×#3804—38no—
64C22×C34—41no—
65C22×C34C2311yescharacteristic
66C22×C34C2311yescharacteristic
67C22×C34C2311yescharacteristic
68C2×C3×C3⋊(C3⋊D3)—41no—
69C2×C3×C3⋊(C3⋊D3)C2312yes—
70C2×C32×C3⋊D3—41no—
71C2×C32×C3⋊D3C2312yes—
72C2×C33×D3—41no—
73C2×C33×D3C2312yes—
74C3×D3×C3⋊D3—42no—
75C3×C3⋊(C3⋊Dic3)C2312yes—
76C32×C3⋊Dic3C2312yes—
77C33×Dic3C2312yes—
78#64361—31no—
79C3×#1004—94no—
80C3×#1004—91no—
81#64330—34no—
82C23×C33—24no—
83C23×C33—24no—
84C23×C33—21no—
85C23×C33—31no—
86C23×C33—44no—
87C23×C33C2×D311yescharacteristic, complemented
88C23×C33C2×D314yescomplemented
89C23×C33C22×C311yescharacteristic, complemented
90C22×C3⋊(C3⋊D3)C22×C311yescharacteristic, complemented
91C22×C3×C3⋊D3—21no—
92C22×C3×C3⋊D3—31no—
93C22×C3×C3⋊D3—34no—
94C22×C3×C3⋊D3—32no—
95C22×C3×C3⋊D3—64no—
96C22×C3×C3⋊D3C2×D311yescharacteristic, complemented
97C22×C3×C3⋊D3C22×C311yescharacteristic, complemented
98C22×C32×D3—24no—
99C22×C32×D3—34no—
100C22×C32×D3C2×D314yescomplemented
101C22×C32×D3C22×C311yescharacteristic, complemented
102C2×D3×C3⋊D3C22×C312yescomplemented
103C2×C3×D32—38no—
104C33×D4—32no—
105C33×D4—32no—
106C2×C33×C4—31no—
107#6312C22×C312yescomplemented
108#6312C22×C312yescomplemented
109C2×C3⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
110C3×#638—22no—
111C3×#638—22no—
112C3×#638—32no—
113C3×#638—32no—
114C3×#638—38no—
115C3×#638—38no—
116C3×#638—32no—
117C3×#638—32no—
118C3×#638—68no—
119C3×#638—68no—
120C3×#638C2×D312yescomplemented
121C3×#638C2×D312yescomplemented
122C3×#638C22×C312yescomplemented
123C3×#638C22×C312yescomplemented
124C2×C3×C3⋊Dic3—21no—
125C2×C3×C3⋊Dic3—31no—
126C2×C3×C3⋊Dic3—34no—
127C2×C3×C3⋊Dic3—32no—
128C2×C3×C3⋊Dic3—64no—
129C2×C3×C3⋊Dic3C2×D311yescharacteristic, complemented
130C2×C3×C3⋊Dic3C22×C311yescharacteristic, complemented
131C3×C4⋊(C3⋊D3)—32no—
132C3×C4×C3⋊D3—32no—
133C3×C4×C3⋊D3—32no—
134C3×#634—32no—
135C32×#67—28no—
136C32×#67—28no—
137C32×#67—38no—
138C32×#67—38no—
139C32×#67C2×D318yescomplemented
140C32×#67C2×D318yescomplemented
141C32×#67C22×C312yescomplemented
142C32×#67C22×C312yescomplemented
143C2×C32×Dic3—24no—
144C2×C32×Dic3—34no—
145C2×C32×Dic3C2×D314yescomplemented
146C2×C32×Dic3C22×C311yescharacteristic, complemented
147#6293C22×C312yescomplemented
148#6292C22×C312yescomplemented
149#6291C22×C312yescomplemented
150#6290C22×C312yescomplemented
151#6289C22×C312yescomplemented
152Dic3×C3⋊D3C22×C312yescomplemented
153D3×C3⋊Dic3C22×C312yescomplemented
154C3×#627—38no—
155C3×#626—38no—
156C3×#626—38no—
157C3×#625—38no—
158C3×#624—38no—
159C3×D3×Dic3—38no—
160C3×D3×Dic3—38no—
161C2×C34—21no—
162C2×C34—21no—
163C2×C34—21no—
164C2×C34C2411yescharacteristic
165C3×C3⋊(C3⋊D3)—22no—
166C32×C3⋊D3—22no—
167C33×D3—22no—
168C2×C32×D4—34no—
169C2×C32×D4—31no—
170C2×C32×D4—64no—
171C2×C32×D4—91no—
172C2×#638—31no—
173C2×#638—34no—
174C2×#638—32no—
175C2×#638—64no—
176C2×#638C3×D311yescharacteristic, complemented
177#3830—32no—
178#3830—32no—
179D4×C3⋊D3—32no—
180D4×C3⋊D3—32no—
181#3828—32no—
182C2×C3×#67—24no—
183C2×C3×#67—34no—
184C2×C3×#67—34no—
185C2×C3×#67—64no—
186C2×C3×#67—98no—
187C2×C3×#67—94no—
188C2×C3×#67—91no—
189C2×C3×#67—92no—
190C2×C3×#67—184no—
191C2×C3×#67C3×D314yescomplemented
192C2×C3×#67C3⋊D311yescharacteristic, complemented
193C3×#237—98no—
194C3×#237—98no—
195C3×#237—92no—
196C3×#237—92no—
197C3×D3×D4—98no—
198C3×D3×D4—98no—
199C3×D3×D4—92no—
200C3×D3×D4—92no—
201C3×#235—98no—
202C3×#235—92no—
203#3811—38no—
204D3×#67—38no—
205D3×#67—38no—
206#3805—38no—
207#3804—38no—
208#3804—38no—
209C22×C33—24no—
210C22×C33—24no—
211C22×C33—21no—
212C22×C33—24no—
213C22×C33—24no—
214C22×C33—24no—
215C22×C33—24no—
216C22×C33—21no—
217C22×C33—21no—
218C22×C33—32no—
219C22×C33—41no—
220C22×C33—44no—
221C22×C33—41no—
222C22×C33—48no—
223C22×C33—42no—
224C22×C33—48no—
225C22×C33—44no—
226C22×C33—44no—
227C22×C33—44no—
228C22×C33—416no—
229C22×C33—121no—
230C22×C33C22×D311yescharacteristic
231C22×C33C22×D311yescharacteristic
232C22×C33C22×D311yescharacteristic
233C22×C33C22×D314yes—
234C22×C33C22×D314yes—
235C22×C33C22×D314yes—
236C22×C33C23×C311yescharacteristic
237C22×C33C23×C311yescharacteristic
238C22×C33C23×C311yescharacteristic
239C2×C3⋊(C3⋊D3)—41no—
240C2×C3⋊(C3⋊D3)C23×C312yes—
241C2×C3×C3⋊D3—22no—
242C2×C3×C3⋊D3—32no—
243C2×C3×C3⋊D3—38no—
244C2×C3×C3⋊D3—41no—
245C2×C3×C3⋊D3—41no—
246C2×C3×C3⋊D3—42no—
247C2×C3×C3⋊D3—68no—
248C2×C3×C3⋊D3—122no—
249C2×C3×C3⋊D3—121no—
250C2×C3×C3⋊D3—124no—
251C2×C3×C3⋊D3—128no—
252C2×C3×C3⋊D3C22×D312yes—
253C2×C3×C3⋊D3C23×C312yes—
254C2×C32×D3—28no—
255C2×C32×D3—38no—
256C2×C32×D3—44no—
257C2×C32×D3—41no—
258C2×C32×D3—48no—
259C2×C32×D3—124no—
260C2×C32×D3C22×D318yes—
261C2×C32×D3C23×C312yes—
262D3×C3⋊D3—42no—
263C3×D32—128no—
264C33×C4—32no—
265C3⋊(C3⋊Dic3)C23×C312yes—
266C3×C3⋊Dic3—22no—
267C3×C3⋊Dic3—32no—
268C3×C3⋊Dic3—38no—
269C3×C3⋊Dic3—68no—
270C3×C3⋊Dic3C22×D312yes—
271C3×C3⋊Dic3C23×C312yes—
272C32×Dic3—28no—
273C32×Dic3—38no—
274C32×Dic3C22×D318yes—
275C32×Dic3C23×C312yes—
276C3×H(5,𝔽2)—271no—
277#1004—94no—
278#1004—91no—
279C34H(5,𝔽2)11yescharacteristic, complemented, Sylow
280C23×C32—24no—
281C23×C32—24no—
282C23×C32—24no—
283C23×C32—24no—
284C23×C32—24no—
285C23×C32—31no—
286C23×C32—34no—
287C23×C32—44no—
288C23×C32—412no—
289C23×C32—44no—
290C23×C32—64no—
291C23×C32—91no—
292C23×C32D3214yescomplemented
293C23×C32C2×C3×D314yescomplemented
294C23×C32C2×C3×D311yescharacteristic, complemented
295C23×C32C2×C3⋊D311yescharacteristic, complemented
296C22×C3⋊D3—31no—
297C22×C3⋊D3—32no—
298C22×C3⋊D3—34no—
299C22×C3⋊D3—64no—
300C22×C3⋊D3C2×C3×D311yescharacteristic, complemented
301C22×C3×D3—24no—
302C22×C3×D3—34no—
303C22×C3×D3—34no—
304C22×C3×D3—64no—
305C22×C3×D3—98no—
306C22×C3×D3—94no—
307C22×C3×D3—91no—
308C22×C3×D3—92no—
309C22×C3×D3—184no—
310C22×C3×D3C2×C3×D314yescomplemented
311C22×C3×D3C2×C3⋊D311yescharacteristic, complemented
312C2×D32—38no—
313C32×D4—32no—
314C32×D4—32no—
315C32×D4—38no—
316C32×D4—38no—
317C32×D4—68no—
318C32×D4—68no—
319C32×D4—92no—
320C32×D4—92no—
321C2×C32×C4—31no—
322C2×C32×C4—34no—
323C2×C32×C4—64no—
324C2×C32×C4—91no—
325#638—32no—
326#638—32no—
327#638—32no—
328#638—32no—
329#638—38no—
330#638—38no—
331#638—68no—
332#638—68no—
333#638C2×C3×D312yescomplemented
334#638C2×C3×D312yescomplemented
335C2×C3⋊Dic3—31no—
336C2×C3⋊Dic3—32no—
337C2×C3⋊Dic3—34no—
338C2×C3⋊Dic3—64no—
339C2×C3⋊Dic3C2×C3×D311yescharacteristic, complemented
340C4⋊(C3⋊D3)—32no—
341C4×C3⋊D3—32no—
342C4×C3⋊D3—32no—
343#634—32no—
344C3×#67—28no—
345C3×#67—28no—
346C3×#67—38no—
347C3×#67—38no—
348C3×#67—38no—
349C3×#67—38no—
350C3×#67—68no—
351C3×#67—68no—
352C3×#67—98no—
353C3×#67—98no—
354C3×#67—98no—
355C3×#67—98no—
356C3×#67—92no—
357C3×#67—92no—
358C3×#67—92no—
359C3×#67—92no—
360C3×#67—188no—
361C3×#67—188no—
362C3×#67C2×C3×D318yescomplemented
363C3×#67C2×C3×D318yescomplemented
364C3×#67C2×C3⋊D312yescomplemented
365C3×#67C2×C3⋊D312yescomplemented
366C2×C3×Dic3—24no—
367C2×C3×Dic3—34no—
368C2×C3×Dic3—34no—
369C2×C3×Dic3—64no—
370C2×C3×Dic3—98no—
371C2×C3×Dic3—94no—
372C2×C3×Dic3—91no—
373C2×C3×Dic3—92no—
374C2×C3×Dic3—184no—
375C2×C3×Dic3C2×C3×D314yescomplemented
376C2×C3×Dic3C2×C3⋊D311yescharacteristic, complemented
377C3×D12—98no—
378C3×D12—92no—
379C3×C4×D3—98no—
380C3×C4×D3—98no—
381C3×C4×D3—92no—
382C3×C4×D3—92no—
383C3×Dic6—98no—
384C3×Dic6—92no—
385#627—38no—
386#626—38no—
387#626—38no—
388#625—38no—
389#624—38no—
390D3×Dic3—38no—
391D3×Dic3—38no—
392C2×C33—21no—
393C2×C33—21no—
394C2×C33—28no—
395C2×C33—22no—
396C2×C33—28no—
397C2×C33—24no—
398C2×C33—24no—
399C2×C33—21no—
400C2×C33—24no—
401C2×C33—21no—
402C2×C33—21no—
403C2×C33—21no—
404C2×C33—24no—
405C2×C33—24no—
406C2×C33—21no—
407C2×C33—44no—
408C2×C33—44no—
409C2×C33—44no—
410C2×C33—41no—
411C2×C33—41no—
412C2×C33—44no—
413C2×C33—44no—
414C2×C33—48no—
415C2×C33—48no—
416C2×C33—48no—
417C2×C33—62no—
418C2×C33C23×D311yescharacteristic
419C2×C33C23×D314yes—
420C2×C33C24×C311yescharacteristic
421C3⋊(C3⋊D3)—22no—
422C3×C3⋊D3—22no—
423C3×C3⋊D3—22no—
424C3×C3⋊D3—42no—
425C3×C3⋊D3—62no—
426C3×C3⋊D3—68no—
427C3×C3⋊D3—128no—
428C32×D3—22no—
429C32×D3—28no—
430C32×D3—48no—
431C32×D3—68no—
432C3×#41—272no—
433C3×#41—272no—
434C3×#41—272no—
435C2×C3×D4—34no—
436C2×C3×D4—31no—
437C2×C3×D4—64no—
438C2×C3×D4—91no—
439C2×C3×D4—91no—
440C2×C3×D4—181no—
441C2×C3×D4—272no—
442C2×C3×D4—272no—
443C2×C3×D4—272no—
444C2×C3×D4—271no—
445C2×#67—34no—
446C2×#67—98no—
447C2×#67—94no—
448C2×#67—91no—
449C2×#67—92no—
450C2×#67—184no—
451C2×#67C3×C3⋊D311yescharacteristic, complemented
452#237—98no—
453#237—98no—
454#237—92no—
455#237—92no—
456D3×D4—98no—
457D3×D4—98no—
458D3×D4—92no—
459D3×D4—92no—
460#235—98no—
461#235—92no—
462C22×C32—24no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—24no—
466C22×C32—24no—
467C22×C32—24no—
468C22×C32—24no—
469C22×C32—24no—
470C22×C32—24no—
471C22×C32—24no—
472C22×C32—24no—
473C22×C32—24no—
474C22×C32—24no—
475C22×C32—24no—
476C22×C32—24no—
477C22×C32—32no—
478C22×C32—38no—
479C22×C32—44no—
480C22×C32—44no—
481C22×C32—44no—
482C22×C32—412no—
483C22×C32—412no—
484C22×C32—412no—
485C22×C32—44no—
486C22×C32—41no—
487C22×C32—44no—
488C22×C32—41no—
489C22×C32—48no—
490C22×C32—48no—
491C22×C32—48no—
492C22×C32—48no—
493C22×C32—48no—
494C22×C32—416no—
495C22×C32—416no—
496C22×C32—448no—
497C22×C32—44no—
498C22×C32—44no—
499C22×C32—44no—
500C22×C32—68no—
501C22×C32—92no—
502C22×C32—121no—
503C22×C32—124no—
504C22×C32—128no—
505C22×C32—361no—
506C22×C32C2×D3214yes—
507C22×C32C2×D3214yes—
508C22×C32C2×D3214yes—
509C22×C32C22×C3×D314yes—
510C22×C32C22×C3×D314yes—
511C22×C32C22×C3×D314yes—
512C22×C32C22×C3×D311yescharacteristic
513C22×C32C22×C3×D311yescharacteristic
514C22×C32C22×C3×D311yescharacteristic
515C22×C32C22×C3⋊D311yescharacteristic
516C22×C32C22×C3⋊D311yescharacteristic
517C22×C32C22×C3⋊D311yescharacteristic
518C2×C3⋊D3—32no—
519C2×C3⋊D3—38no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—68no—
522C2×C3⋊D3—122no—
523C2×C3⋊D3—121no—
524C2×C3⋊D3—124no—
525C2×C3⋊D3—128no—
526C2×C3⋊D3C22×C3×D312yes—
527C2×C3×D3—28no—
528C2×C3×D3—38no—
529C2×C3×D3—38no—
530C2×C3×D3—44no—
531C2×C3×D3—41no—
532C2×C3×D3—48no—
533C2×C3×D3—68no—
534C2×C3×D3—98no—
535C2×C3×D3—92no—
536C2×C3×D3—124no—
537C2×C3×D3—124no—
538C2×C3×D3—128no—
539C2×C3×D3—188no—
540C2×C3×D3—362no—
541C2×C3×D3—368no—
542C2×C3×D3—364no—
543C2×C3×D3—361no—
544C2×C3×D3—368no—
545C2×C3×D3C22×C3×D318yes—
546C2×C3×D3C22×C3⋊D312yes—
547D32—128no—
548C32×C4—32no—
549C32×C4—38no—
550C32×C4—68no—
551C32×C4—92no—
552C3⋊Dic3—32no—
553C3⋊Dic3—38no—
554C3⋊Dic3—68no—
555C3⋊Dic3C22×C3×D312yes—
556C3×Dic3—28no—
557C3×Dic3—38no—
558C3×Dic3—38no—
559C3×Dic3—68no—
560C3×Dic3—98no—
561C3×Dic3—92no—
562C3×Dic3—188no—
563C3×Dic3C22×C3×D318yes—
564C3×Dic3C22×C3⋊D312yes—
565H(5,𝔽2)—271noSylow
566C33—24no—
567C33—24no—
568C33—21no—
569C33—44no—
570C33#100411yescharacteristic, complemented
571C33#100414yescomplemented
572C33C3×H(5,𝔽2)11yescharacteristic, complemented
573C23×C3—24no—
574C23×C3—24no—
575C23×C3—21no—
576C23×C3—34no—
577C23×C3—31no—
578C23×C3—44no—
579C23×C3—64no—
580C23×C3—91no—
581C23×C3—91no—
582C23×C3—181no—
583C23×C3—272no—
584C23×C3—271no—
585C23×C3C3×D3214yescomplemented
586C23×C3D3×C3⋊D311yescharacteristic, complemented
587C23×C3C2×C3×C3⋊D311yescharacteristic, complemented
588C22×D3—34no—
589C22×D3—98no—
590C22×D3—94no—
591C22×D3—91no—
592C22×D3—92no—
593C22×D3—184no—
594C22×D3C2×C3×C3⋊D311yescharacteristic, complemented
595C3×Q8—272no—
596C3×D4—38no—
597C3×D4—38no—
598C3×D4—32no—
599C3×D4—32no—
600C3×D4—68no—
601C3×D4—68no—
602C3×D4—92no—
603C3×D4—92no—
604C3×D4—92no—
605C3×D4—92no—
606C3×D4—182no—
607C3×D4—182no—
608C3×D4—272no—
609C3×D4—272no—
610C3×D4—272no—
611C3×D4—272no—
612C3×D4—272no—
613C2×C3×C4—34no—
614C2×C3×C4—31no—
615C2×C3×C4—64no—
616C2×C3×C4—91no—
617C2×C3×C4—91no—
618C2×C3×C4—181no—
619C2×C3×C4—272no—
620C2×C3×C4—272no—
621C2×C3×C4—272no—
622C2×C3×C4—271no—
623#67—38no—
624#67—38no—
625#67—98no—
626#67—98no—
627#67—98no—
628#67—98no—
629#67—92no—
630#67—92no—
631#67—92no—
632#67—92no—
633#67—188no—
634#67—188no—
635#67C2×C3×C3⋊D312yescomplemented
636#67C2×C3×C3⋊D312yescomplemented
637C2×Dic3—34no—
638C2×Dic3—98no—
639C2×Dic3—94no—
640C2×Dic3—91no—
641C2×Dic3—92no—
642C2×Dic3—184no—
643C2×Dic3C2×C3×C3⋊D311yescharacteristic, complemented
644D12—98no—
645D12—92no—
646C4×D3—98no—
647C4×D3—98no—
648C4×D3—92no—
649C4×D3—92no—
650Dic6—98no—
651Dic6—92no—
652C2×C32—28no—
653C2×C32—28no—
654C2×C32—24no—
655C2×C32—21no—
656C2×C32—24no—
657C2×C32—21no—
658C2×C32—21no—
659C2×C32—21no—
660C2×C32—24no—
661C2×C32—24no—
662C2×C32—28no—
663C2×C32—28no—
664C2×C32—28no—
665C2×C32—24no—
666C2×C32—24no—
667C2×C32—24no—
668C2×C32—24no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—24no—
672C2×C32—24no—
673C2×C32—24no—
674C2×C32—44no—
675C2×C32—412no—
676C2×C32—44no—
677C2×C32—44no—
678C2×C32—44no—
679C2×C32—44no—
680C2×C32—44no—
681C2×C32—44no—
682C2×C32—44no—
683C2×C32—44no—
684C2×C32—44no—
685C2×C32—44no—
686C2×C32—48no—
687C2×C32—424no—
688C2×C32—48no—
689C2×C32—424no—
690C2×C32—48no—
691C2×C32—48no—
692C2×C32—48no—
693C2×C32—48no—
694C2×C32—424no—
695C2×C32—44no—
696C2×C32—62no—
697C2×C32—68no—
698C2×C32—128no—
699C2×C32—182no—
700C2×C32C22×D3214yes—
701C2×C32C23×C3×D314yes—
702C2×C32C23×C3×D311yescharacteristic
703C2×C32C23×C3⋊D311yescharacteristic
704C3⋊D3—22no—
705C3⋊D3—62no—
706C3⋊D3—68no—
707C3⋊D3—128no—
708C3×D3—28no—
709C3×D3—22no—
710C3×D3—48no—
711C3×D3—68no—
712C3×D3—68no—
713C3×D3—128no—
714C3×D3—188no—
715C3×D3—182no—
716C3×D3—368no—
717#41—272no—
718#41—272no—
719#41—272no—
720C2×D4—31no—
721C2×D4—91no—
722C2×D4—272no—
723C2×D4—272no—
724C2×D4—272no—
725C2×D4—271no—
726C22×C3—24no—
727C22×C3—24no—
728C22×C3—21no—
729C22×C3—24no—
730C22×C3—24no—
731C22×C3—24no—
732C22×C3—24no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—38no—
736C22×C3—32no—
737C22×C3—44no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—48no—
741C22×C3—48no—
742C22×C3—42no—
743C22×C3—416no—
744C22×C3—44no—
745C22×C3—44no—
746C22×C3—44no—
747C22×C3—68no—
748C22×C3—92no—
749C22×C3—92no—
750C22×C3—124no—
751C22×C3—121no—
752C22×C3—128no—
753C22×C3—182no—
754C22×C3—272no—
755C22×C3—361no—
756C22×C3—361no—
757C22×C3—362no—
758C22×C3—1081no—
759C22×C3—1082no—
760C22×C3C2×C3×D3214yes—
761C22×C3C2×C3×D3214yes—
762C22×C3C2×C3×D3214yes—
763C22×C3C2×D3×C3⋊D311yescharacteristic
764C22×C3C2×D3×C3⋊D311yescharacteristic
765C22×C3C2×D3×C3⋊D311yescharacteristic
766C22×C3C22×C3×C3⋊D311yescharacteristic
767C22×C3C22×C3×C3⋊D311yescharacteristic
768C22×C3C22×C3×C3⋊D311yescharacteristic
769C2×D3—38no—
770C2×D3—41no—
771C2×D3—98no—
772C2×D3—92no—
773C2×D3—124no—
774C2×D3—188no—
775C2×D3—362no—
776C2×D3—368no—
777C2×D3—364no—
778C2×D3—361no—
779C2×D3—368no—
780C2×D3C22×C3×C3⋊D312yes—
781C3×C4—38no—
782C3×C4—32no—
783C3×C4—68no—
784C3×C4—92no—
785C3×C4—92no—
786C3×C4—182no—
787C3×C4—272no—
788Dic3—38no—
789Dic3—98no—
790Dic3—92no—
791Dic3—188no—
792Dic3C22×C3×C3⋊D312yes—
793C32—24no—
794C32—24no—
795C32—24no—
796C32—24no—
797C32—24no—
798C32—44no—
799C32—412no—
800C32—44no—
801C32#6433014yescomplemented
802C32C3×#100414yescomplemented
803C32C3×#100411yescharacteristic, complemented
804C32#6436111yescharacteristic, complemented
805C23—31no—
806C23—91no—
807C23—272no—
808C23—271no—
809C23C3×D3×C3⋊D311yescharacteristic, complemented
810Q8—272no—
811D4—32no—
812D4—32no—
813D4—92no—
814D4—92no—
815D4—272no—
816D4—272no—
817D4—272no—
818D4—272no—
819D4—272no—
820C2×C4—31no—
821C2×C4—91no—
822C2×C4—272no—
823C2×C4—272no—
824C2×C4—272no—
825C2×C4—271no—
826C2×C3—28no—
827C2×C3—28no—
828C2×C3—22no—
829C2×C3—24no—
830C2×C3—24no—
831C2×C3—24no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—24no—
839C2×C3—24no—
840C2×C3—21no—
841C2×C3—44no—
842C2×C3—41no—
843C2×C3—44no—
844C2×C3—44no—
845C2×C3—44no—
846C2×C3—41no—
847C2×C3—48no—
848C2×C3—48no—
849C2×C3—48no—
850C2×C3—44no—
851C2×C3—68no—
852C2×C3—62no—
853C2×C3—128no—
854C2×C3—182no—
855C2×C3—182no—
856C2×C3—362no—
857C2×C3—542no—
858C2×C3C22×C3×D3214yes—
859C2×C3C22×D3×C3⋊D311yescharacteristic
860C2×C3C23×C3×C3⋊D311yescharacteristic
861D3—22no—
862D3—68no—
863D3—188no—
864D3—182no—
865D3—368no—
866C22—32no—
867C22—41no—
868C22—92no—
869C22—121no—
870C22—272no—
871C22—361no—
872C22—1081no—
873C22—1082no—
874C22C2×C3×D3×C3⋊D311yescharacteristic
875C22C2×C3×D3×C3⋊D311yescharacteristic
876C22C2×C3×D3×C3⋊D311yescharacteristic
877C4—32no—
878C4—92no—
879C4—272no—
880C3—24no—
881C3—24no—
882C3—21no—
883C3—44no—
884C3C3×#6433014yescomplemented
885C3#1172461111yescharacteristic, direct product factor
886C3C3×#6436111yescharacteristic, complemented
887C2—21no—
888C2—21no—
889C2—21no—
890C2—62no—
891C2—182no—
892C2—542no—
893C2C22×C3×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C3C22×D3×C3⋊D3
commutator, cosocleC2×C33C24×C3
FrattiniC2C22×C3×D3×C3⋊D3
FittingC23×C34C22
socleC2×C34C24
hypercenterC23×C3D3×C3⋊D3
hypocenterC33C3×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#6312C2semidirect
2. C2×C32×#638C2semidirect
3. C2×C33×#67C2semidirect
4. C3×#89039C2semidirect
5. C3×D3×#638C2semidirect
6. C3×C3⋊D3×#67C2semidirect
7. C3×#89028C2semidirect
8. C3×#89029C2semidirect
9. C3×#89031C2semidirect
11. #11724611C3direct (N × H)
13. C23×C34C22semidirect
14. C22×C3×C3⋊(C3⋊D3)C22semidirect
15. C22×C32×C3⋊D3C22semidirect
16. C22×C33×D3C22semidirect
17. C2×C3×D3×C3⋊D3C22semidirect
18. C3×#6312C22semidirect
19. C3×#6312C22semidirect
20. C2×C3×C3⋊(C3⋊Dic3)C22semidirect
21. C32×#638C22semidirect
22. C32×#638C22semidirect
23. C2×C32×C3⋊Dic3C22semidirect
24. C33×#67C22semidirect
25. C33×#67C22semidirect
26. C2×C33×Dic3C22semidirect
27. C3×#6293C22semidirect
28. C3×#6292C22semidirect
29. C3×#6291C22semidirect
30. C3×#6290C22semidirect
31. C3×#6289C22semidirect
32. C3×Dic3×C3⋊D3C22semidirect
33. C3×D3×C3⋊Dic3C22semidirect
35. C2×#6312C2×C3semidirect
41. C2×C3×#638D3semidirect
42. C2×C3×#638C2×C3semidirect
50. C2×C32×#67D3semidirect
51. C2×C32×#67C2×C3semidirect
52. #89039C2×C3semidirect
53. C3⋊D3×#67C2×C3semidirect
54. D3×#638C2×C3semidirect
55. #89031C2×C3semidirect
56. #89029C2×C3semidirect
57. #89028C2×C3semidirect
87. C23×C33C2×D3semidirect
88. C23×C33C2×D3semidirect
89. C23×C33C22×C3semidirect
90. C22×C3⋊(C3⋊D3)C22×C3semidirect
96. C22×C3×C3⋊D3C2×D3semidirect
97. C22×C3×C3⋊D3C22×C3semidirect
100. C22×C32×D3C2×D3semidirect
101. C22×C32×D3C22×C3semidirect
102. C2×D3×C3⋊D3C22×C3semidirect
107. #6312C22×C3semidirect
108. #6312C22×C3semidirect
109. C2×C3⋊(C3⋊Dic3)C22×C3semidirect
120. C3×#638C2×D3semidirect
121. C3×#638C2×D3semidirect
122. C3×#638C22×C3semidirect
123. C3×#638C22×C3semidirect
129. C2×C3×C3⋊Dic3C2×D3semidirect
130. C2×C3×C3⋊Dic3C22×C3semidirect
139. C32×#67C2×D3semidirect
140. C32×#67C2×D3semidirect
141. C32×#67C22×C3semidirect
142. C32×#67C22×C3semidirect
145. C2×C32×Dic3C2×D3semidirect
146. C2×C32×Dic3C22×C3semidirect
147. #6293C22×C3semidirect
148. #6292C22×C3semidirect
149. #6291C22×C3semidirect
150. #6290C22×C3semidirect
151. #6289C22×C3semidirect
152. Dic3×C3⋊D3C22×C3semidirect
153. D3×C3⋊Dic3C22×C3semidirect
176. C2×#638C3×D3semidirect
191. C2×C3×#67C3×D3semidirect
192. C2×C3×#67C3⋊D3semidirect
279. C34H(5,𝔽2)semidirect
292. C23×C32D32semidirect
293. C23×C32C2×C3×D3semidirect
294. C23×C32C2×C3×D3semidirect
295. C23×C32C2×C3⋊D3semidirect
300. C22×C3⋊D3C2×C3×D3semidirect
310. C22×C3×D3C2×C3×D3semidirect
311. C22×C3×D3C2×C3⋊D3semidirect
333. #638C2×C3×D3semidirect
334. #638C2×C3×D3semidirect
339. C2×C3⋊Dic3C2×C3×D3semidirect
362. C3×#67C2×C3×D3semidirect
363. C3×#67C2×C3×D3semidirect
364. C3×#67C2×C3⋊D3semidirect
365. C3×#67C2×C3⋊D3semidirect
375. C2×C3×Dic3C2×C3×D3semidirect
376. C2×C3×Dic3C2×C3⋊D3semidirect
451. C2×#67C3×C3⋊D3semidirect
570. C33#1004semidirect
571. C33#1004semidirect
572. C33C3×H(5,𝔽2)semidirect
585. C23×C3C3×D32semidirect
586. C23×C3D3×C3⋊D3semidirect
587. C23×C3C2×C3×C3⋊D3semidirect
594. C22×D3C2×C3×C3⋊D3semidirect
635. #67C2×C3×C3⋊D3semidirect
636. #67C2×C3×C3⋊D3semidirect
643. C2×Dic3C2×C3×C3⋊D3semidirect
801. C32#64330semidirect
802. C32C3×#1004semidirect
803. C32C3×#1004semidirect
804. C32#64361semidirect
809. C23C3×D3×C3⋊D3semidirect
884. C3C3×#64330semidirect
885. C3#11724611direct (N × H)
886. C3C3×#64361semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#63122
C2×C32×#6382
C2×C33×#672
C3×#890392
C3×D3×#6382
C3×C3⋊D3×#672
C3×#890282
C3×#890292
C3×#890312
C3×#643613
#117246113
C3×#643303