Finite Group Databasebeta

← D3×#63981 #13172694

Subgroups — D3×#63981 #13172694

Order 1728.

3790 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C211yesmaximal, characteristic, complemented
3C2×D3×#626C212yesmaximal, complemented
4#11723727C211yesmaximal, characteristic, complemented
5#11723639C211yesmaximal, characteristic, complemented
6#11723638C211yesmaximal, characteristic, complemented
7C3×#63981C211yesmaximal, characteristic, complemented
8C3×D3×#217C211yesmaximal, characteristic, complemented
9#11722950C212yesmaximal, complemented
10#11722949C212yesmaximal, complemented
11D3×#3722C212yesmaximal, complemented
12C2×#63981—31nomaximal
13D3×#937—31nomaximal
14D3×#882—31nomaximal
15C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
16C23×C3×C3⋊D3C2211yescharacteristic, complemented
17C23×C32×D3C2211yescharacteristic
18C22×D3×C3⋊D3—24no—
19C22×D3×C3⋊D3—28no—
20C22×D3×C3⋊D3C2212yes—
21C22×D3×C3⋊D3C2212yescomplemented
22C22×C3×D32C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25C2×#6295C2212yescomplemented
26C2×#6292C2212yescomplemented
27C2×#6291C2212yescomplemented
28C3×D3×#67—24no—
29C2×C3×#626C2211yescharacteristic, complemented
30C2×C3×#626C2212yescomplemented
31C2×C3×#625C2211yescharacteristic, complemented
32C2×C3×D3×Dic3C2211yescharacteristic, complemented
33C2×C3×D3×Dic3C2212yescomplemented
34D3×#626—28no—
35C3×#3757C2211yescharacteristic, complemented
36C32×#217C2211yescharacteristic, complemented
37#88814C2212yescomplemented
38#88804C2212yescomplemented
39#88804C2212yescomplemented
40C3×#3722C2212yescomplemented
41C3×(C2×D3)⋊Dic3C2212yescomplemented
42C24×C3⋊D3—31no—
43C23×D32—31no—
44C23×D32—31no—
45C23×D32—61no—
46C22×C3×#67—31no—
47C2×C3×D3×D4—31no—
48C2×D3×#67—32no—
49C2×D3×#67D311yescharacteristic, complemented
50C22×#626—32no—
51C2×D3×D12—32no—
52#64146—31no—
53#64091—31no—
54C2×C3×#217—31no—
55C3×#937—31no—
56C3×#882—31no—
57C3×D3×C22⋊C4—31no—
58#63983—32no—
59#63981—31no—
60#63981—31no—
61#63981—32no—
62#63981—31no—
63#63981—31no—
64#63981—32no—
65#63981—31no—
66#63981—61no—
67#63981—61no—
68#63981D311yescharacteristic, direct product factor
69#63977—31no—
70#63976—31no—
71D3×#217D311yescharacteristic, complemented
72C2×#3722—32no—
73#63923—32no—
74#63922—32no—
75#63922—32no—
76D3×(C2×D3)⋊C4—32no—
77D3×(C2×D3)⋊C4—32no—
78C23×C33C2311yescharacteristic
79C22×C3⋊(C3⋊D3)—22no—
80C22×C3⋊(C3⋊D3)—24no—
81C22×C3⋊(C3⋊D3)C2312yes—
82C22×C3×C3⋊D3—22no—
83C22×C3×C3⋊D3—24no—
84C22×C3×C3⋊D3C2312yes—
85C22×C3×C3⋊D3C2311yescharacteristic, complemented
86C22×C32×D3—24no—
87C22×C32×D3D414yescomplemented
88C22×C32×D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic, complemented
91C2×D3×C3⋊D3—232no—
92C2×D3×C3⋊D3—24no—
93C2×D3×C3⋊D3—24no—
94C2×D3×C3⋊D3—24no—
95C2×D3×C3⋊D3—24no—
96C2×D3×C3⋊D3—24no—
97C2×D3×C3⋊D3D418yescomplemented
98C2×C3×D32—24no—
99C2×C3×D32—22no—
100C3×#638—22no—
101C2×C3×C3⋊Dic3C2312yescomplemented
102C2×C3×C3⋊Dic3C2311yescharacteristic, complemented
103C32×#67—22no—
104C2×C32×Dic3C2312yescomplemented
105C2×C32×Dic3C2311yescharacteristic, complemented
106#6295—24no—
107#6292—24no—
108#6291—24no—
109C3×#626—24no—
110C3×#626—22no—
111C3×#625—22no—
112C3×D3×Dic3—24no—
113C3×D3×Dic3—22no—
114C2×#937—91no—
115D3×#120—91no—
116C2×#882—91no—
117C24×C32—31no—
118C23×C3⋊D3—32no—
119C23×C3⋊D3—31no—
120C23×C3⋊D3—31no—
121C23×C3⋊D3—31no—
122C23×C3⋊D3—32no—
123C23×C3⋊D3—68no—
124C23×C3⋊D3—64no—
125C23×C3⋊D3—61no—
126C23×C3⋊D3—61no—
127C23×C3⋊D3—61no—
128C23×C3⋊D3—121no—
129C23×C3⋊D3C2×D311yescharacteristic, complemented
130C23×C3×D3—21no—
131C23×C3×D3—31no—
132C23×C3×D3—31no—
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C23×C3×D3C2×D311yescharacteristic
137C23×C3×D3C2×D311yescharacteristic
138C22×D32—32no—
139C22×D32—32no—
140C22×D32—32no—
141C22×D32—32no—
142C22×D32—68no—
143C22×D32—68no—
144C22×D32—62no—
145C22×D32—62no—
146C22×D32—616no—
147C22×D32—68no—
148C22×D32—64no—
149C22×D32—64no—
150C22×D32C2×D311yescharacteristic, complemented
151C2×C32×D4—31no—
152C2×#638—32no—
153C2×#638C2×D311yescharacteristic, complemented
154C2×C4⋊(C3⋊D3)—32no—
155C2×C3×#67—21no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—32no—
161C2×C3×#67—31no—
162C2×C3×#67—64no—
163C2×C3×#67—61no—
164C2×C3×#67C2×D311yescharacteristic, complemented
165C2×C3×#67C2×D311yescharacteristic, complemented
166C22×C3×Dic3—32no—
167C22×C3×Dic3—31no—
168C3×D3×D4—64no—
169C2×C3×D12—31no—
170C2×C3×D12—32no—
171C2×C3×C4×D3—32no—
172C2×C3×C4×D3—31no—
173D3×#67—24no—
174D3×#67—68no—
175C2×#626—32no—
176C2×#626—32no—
177C2×#626—32no—
178C2×#626—32no—
179C2×#626—32no—
180C2×#626—32no—
181C2×#626—68no—
182C2×#626—62no—
183C2×#626—62no—
184C2×#626C2×D311yescharacteristic, complemented
185C2×#626C2×D312yescomplemented
186C2×#625—32no—
187C2×#625C2×D311yescharacteristic, complemented
188C2×D3×Dic3C2×D312yescomplemented
189C2×D3×Dic3C2×D311yescharacteristic, complemented
190D3×D12—68no—
191C32×C22⋊C4—31no—
192#3757C2×D311yescharacteristic, complemented
193#3752—32no—
194#3752—32no—
195C3×#217—21no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—32no—
199C3×#217—61no—
200C3×#217C2×D311yescharacteristic, complemented
201C3×#217C2×D311yescharacteristic, complemented
202C3×(C2×D3)⋊C4—32no—
203C3×(C2×D3)⋊C4—32no—
204C3×(C2×D3)⋊C4—32no—
205#3722—32no—
206#3722—32no—
207#3722—32no—
208#3722—32no—
209#3722—32no—
210#3722—62no—
211#3722—62no—
212#3722C2×D312yescomplemented
213(C2×D3)⋊Dic3—32no—
214(C2×D3)⋊Dic3—32no—
215(C2×D3)⋊Dic3C2×D312yescomplemented
216C22×C33—22no—
217C22×C33C2×D412yescomplemented
218C22×C33C2411yescharacteristic
219C2×C3⋊(C3⋊D3)—28no—
220C2×C3⋊(C3⋊D3)—22no—
221C2×C3⋊(C3⋊D3)—22no—
222C2×C3⋊(C3⋊D3)C2×D414yescomplemented
223C2×C3×C3⋊D3—28no—
224C2×C3×C3⋊D3—22no—
225C2×C3×C3⋊D3—22no—
226C2×C3×C3⋊D3—21no—
227C2×C3×C3⋊D3—22no—
228C2×C3×C3⋊D3C2×D414yescomplemented
229C2×C32×D3—22no—
230C2×C32×D3—28no—
231C2×C32×D3—21no—
232C2×C32×D3—22no—
233C2×C32×D3C2×D412yes—
234C2×C32×D3C2×D414yes—
235C2×C32×D3C2×D412yescomplemented
236D3×C3⋊D3—216no—
237D3×C3⋊D3—216no—
238C3×D32—44no—
239C3×C3⋊Dic3—21no—
240C3×C3⋊Dic3—22no—
241C32×Dic3—22no—
242C32×Dic3—21no—
243C24×D3—91no—
244C24×D3—91no—
245C24×D3—91no—
246C24×D3—181no—
247C22×C3×D4—91no—
248C22×#67—31no—
249C22×#67—92no—
250C2×D3×D4—31no—
251C2×D3×D4—92no—
252C22×D12—92no—
253C3×#120—91no—
254C2×C3×C22⋊C4—91no—
255#953—91no—
256C2×#217—31no—
257#937—31no—
258#937—92no—
259#937—92no—
260#937—92no—
261#937—91no—
262#937—91no—
263#937—91no—
264#937—91no—
265#937—181no—
266C2×(C2×D3)⋊C4—92no—
267C2×(C2×D3)⋊C4—92no—
268#882—31no—
269#882—92no—
270#882—92no—
271#882—91no—
272#882—91no—
273#882—92no—
274#882—91no—
275#882—91no—
276#882—181no—
277D3×C22⋊C4—31no—
278D3×C22⋊C4—92no—
279C23×C32—21no—
280C23×C32—21no—
281C23×C32—21no—
282C23×C32—31no—
283C23×C32—34no—
284C23×C32—31no—
285C23×C32—31no—
286C23×C32—41no—
287C23×C32—64no—
288C23×C32C22×D311yescharacteristic
289C23×C32C22×D311yescharacteristic
290C23×C32C22×D311yescharacteristic
291C22×C3⋊D3—22no—
292C22×C3⋊D3—24no—
293C22×C3⋊D3—32no—
294C22×C3⋊D3—32no—
295C22×C3⋊D3—32no—
296C22×C3⋊D3—38no—
297C22×C3⋊D3—62no—
298C22×C3⋊D3—62no—
299C22×C3⋊D3—62no—
300C22×C3⋊D3—64no—
301C22×C3⋊D3—64no—
302C22×C3⋊D3—64no—
303C22×C3⋊D3—64no—
304C22×C3⋊D3—632no—
305C22×C3⋊D3—64no—
306C22×C3⋊D3—62no—
307C22×C3⋊D3—64no—
308C22×C3⋊D3—64no—
309C22×C3⋊D3—64no—
310C22×C3⋊D3—68no—
311C22×C3⋊D3—64no—
312C22×C3⋊D3—62no—
313C22×C3⋊D3—62no—
314C22×C3⋊D3—122no—
315C22×C3⋊D3—124no—
316C22×C3⋊D3—124no—
317C22×C3⋊D3—122no—
318C22×C3⋊D3—122no—
319C22×C3⋊D3—128no—
320C22×C3⋊D3—124no—
321C22×C3⋊D3C22×D312yes—
322C22×C3⋊D3C22×D311yescharacteristic, complemented
323C22×C3×D3—28no—
324C22×C3×D3—24no—
325C22×C3×D3—24no—
326C22×C3×D3—24no—
327C22×C3×D3—21no—
328C22×C3×D3—21no—
329C22×C3×D3—21no—
330C22×C3×D3—32no—
331C22×C3×D3—32no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—62no—
335C22×C3×D3—61no—
336C22×C3×D3—64no—
337C22×C3×D3—62no—
338C22×C3×D3—64no—
339C22×C3×D3—64no—
340C22×C3×D3—68no—
341C22×C3×D3—64no—
342C22×C3×D3—62no—
343C22×C3×D3—62no—
344C22×C3×D3—62no—
345C22×C3×D3—64no—
346C22×C3×D3D1214yescomplemented
347C22×C3×D3#6714yescomplemented
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C22×C3×D3C22×D311yescharacteristic
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic, complemented
353C22×C3×D3C22×D311yescharacteristic, complemented
354C2×D32—24no—
355C2×D32—22no—
356C2×D32—38no—
357C2×D32—38no—
358C2×D32—68no—
359C2×D32—64no—
360C2×D32—64no—
361C2×D32—64no—
362C2×D32—64no—
363C2×D32—68no—
364C2×D32—68no—
365C2×D32—664no—
366C2×D32—632no—
367C2×D32—632no—
368C2×D32—68no—
369C2×D32—68no—
370C2×D32—68no—
371C2×D32—64no—
372C2×D32—64no—
373C2×D32—64no—
374C2×D32—64no—
375C2×D32—64no—
376C2×D32—64no—
377C32×D4—62no—
378C2×C32×C4—31no—
379C2×C32×C4—32no—
380#638—22no—
381#638—64no—
382C2×C3⋊Dic3C22×D311yescharacteristic, complemented
383C2×C3⋊Dic3C22×D312yescomplemented
384C4⋊(C3⋊D3)—64no—
385C3×#67—22no—
386C3×#67—22no—
387C3×#67—42no—
388C3×#67—64no—
389C3×#67—62no—
390C3×#67—62no—
391C3×#67—62no—
392C3×#67—62no—
393C3×#67—62no—
394C3×#67—122no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—22no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—32no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—32no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—62no—
403C2×C3×Dic3—64no—
404C2×C3×Dic3—62no—
405C2×C3×Dic3C22×D312yescomplemented
406C2×C3×Dic3C22×D311yescharacteristic, complemented
407C2×C3×Dic3C22×D311yescharacteristic, complemented
408C2×C3×Dic3C22×D312yescomplemented
409C3×D12—64no—
410C3×D12—62no—
411C3×C4×D3—62no—
412C3×C4×D3—64no—
413#626—24no—
414#626—22no—
415#626—64no—
416#626—64no—
417#626—64no—
418#626—64no—
419#626—64no—
420#626—64no—
421#626—124no—
422#626—124no—
423#625—22no—
424#625—64no—
425D3×Dic3—24no—
426D3×Dic3—22no—
427C2×#120—271noSylow
428C2×C33—22no—
429C2×C33C22×D411yescharacteristic
430C2×C33C22×D412yes—
431C3⋊(C3⋊D3)—24no—
432C3×C3⋊D3—24no—
433C3×C3⋊D3—41no—
434C32×D3—22no—
435C32×D3—41no—
436C32×D3#12014yescomplemented
437C24×C3—31no—
438C24×C3—31no—
439C24×C3—61no—
440C24×C3—91no—
441C24×C3—91no—
442C23×D3—31no—
443C23×D3—31no—
444C23×D3—31no—
445C23×D3—31no—
446C23×D3—61no—
447C23×D3—92no—
448C23×D3—92no—
449C23×D3—92no—
450C23×D3—92no—
451C23×D3—92no—
452C23×D3—91no—
453C23×D3—91no—
454C23×D3—91no—
455C23×D3—92no—
456C23×D3—182no—
457C23×D3—182no—
458C23×D3—181no—
459C23×D3—181no—
460C23×D3—181no—
461C23×D3—188no—
462C23×D3—188no—
463C23×D3—188no—
464C23×D3—184no—
465C23×D3—184no—
466C23×D3—188no—
467C23×D3—1816no—
468C23×D3—184no—
469C23×D3—361no—
470C23×D3D3211yescharacteristic
471C2×C3×D4—31no—
472C2×C3×D4—31no—
473C2×C3×D4—61no—
474C2×C3×D4—91no—
475C2×C3×D4—92no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C2×C3×D4—184no—
479C22×C3×C4—91no—
480C22×C3×C4—92no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—32no—
487C2×#67—61no—
488C2×#67—64no—
489C2×#67—92no—
490C2×#67—92no—
491C2×#67—92no—
492C2×#67—92no—
493C2×#67—92no—
494C2×#67—182no—
495C2×#67—188no—
496C2×#67D3211yescharacteristic, complemented
497C22×Dic3—31no—
498C22×Dic3—32no—
499D3×D4—64no—
500D3×D4—188no—
501C2×D12—31no—
502C2×D12—32no—
503C2×D12—92no—
504C2×D12—92no—
505C2×D12—92no—
506C2×D12—92no—
507C2×D12—182no—
508C2×D12—188no—
509C2×C4×D3—32no—
510C2×C4×D3—31no—
511C3×C22⋊C4—31no—
512C3×C22⋊C4—31no—
513C3×C22⋊C4—61no—
514C3×C22⋊C4—92no—
515C3×C22⋊C4—92no—
516C3×C22⋊C4—91no—
517#217—31no—
518#217—31no—
519#217—32no—
520#217—61no—
521#217—92no—
522#217D3211yescharacteristic, complemented
523(C2×D3)⋊C4—32no—
524(C2×D3)⋊C4—32no—
525(C2×D3)⋊C4—32no—
526(C2×D3)⋊C4—92no—
527(C2×D3)⋊C4—92no—
528(C2×D3)⋊C4—92no—
529(C2×D3)⋊C4—92no—
530(C2×D3)⋊C4—92no—
531(C2×D3)⋊C4—92no—
532(C2×D3)⋊C4—92no—
533(C2×D3)⋊C4—92no—
534(C2×D3)⋊C4—182no—
535(C2×D3)⋊C4—182no—
536C22×C32—22no—
537C22×C32—24no—
538C22×C32—22no—
539C22×C32—22no—
540C22×C32—21no—
541C22×C32—21no—
542C22×C32—21no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32—34no—
547C22×C32—32no—
548C22×C32—32no—
549C22×C32—42no—
550C22×C32—41no—
551C22×C32—42no—
552C22×C32—42no—
553C22×C32—44no—
554C22×C32—68no—
555C22×C32—62no—
556C22×C32—61no—
557C22×C32—62no—
558C22×C32C2×D1212yescomplemented
559C22×C32D3×D412yescomplemented
560C22×C32C2×#6712yescomplemented
561C22×C32C23×D311yescharacteristic
562C22×C32C23×D311yescharacteristic
563C22×C32C23×D311yescharacteristic
564C2×C3⋊D3—28no—
565C2×C3⋊D3—22no—
566C2×C3⋊D3—22no—
567C2×C3⋊D3—22no—
568C2×C3⋊D3—21no—
569C2×C3⋊D3—34no—
570C2×C3⋊D3—34no—
571C2×C3⋊D3—34no—
572C2×C3⋊D3—64no—
573C2×C3⋊D3—64no—
574C2×C3⋊D3—64no—
575C2×C3⋊D3—616no—
576C2×C3⋊D3—616no—
577C2×C3⋊D3—68no—
578C2×C3⋊D3—62no—
579C2×C3⋊D3—62no—
580C2×C3⋊D3—616no—
581C2×C3⋊D3—68no—
582C2×C3⋊D3—68no—
583C2×C3⋊D3—64no—
584C2×C3⋊D3—64no—
585C2×C3⋊D3—62no—
586C2×C3⋊D3—62no—
587C2×C3⋊D3—62no—
588C2×C3⋊D3—62no—
589C2×C3⋊D3—124no—
590C2×C3⋊D3—122no—
591C2×C3⋊D3—122no—
592C2×C3⋊D3—122no—
593C2×C3⋊D3—122no—
594C2×C3⋊D3—124no—
595C2×C3⋊D3—124no—
596C2×C3⋊D3—128no—
597C2×C3⋊D3—128no—
598C2×C3⋊D3—1216no—
599C2×C3⋊D3D3×D414yescomplemented
600C2×C3×D3—24no—
601C2×C3×D3—216no—
602C2×C3×D3—22no—
603C2×C3×D3—22no—
604C2×C3×D3—28no—
605C2×C3×D3—28no—
606C2×C3×D3—22no—
607C2×C3×D3—22no—
608C2×C3×D3—21no—
609C2×C3×D3—21no—
610C2×C3×D3—22no—
611C2×C3×D3—22no—
612C2×C3×D3—24no—
613C2×C3×D3—34no—
614C2×C3×D3—34no—
615C2×C3×D3—42no—
616C2×C3×D3—41no—
617C2×C3×D3—64no—
618C2×C3×D3—616no—
619C2×C3×D3—68no—
620C2×C3×D3—68no—
621C2×C3×D3—64no—
622C2×C3×D3—64no—
623C2×C3×D3—62no—
624C2×C3×D3—62no—
625C2×C3×D3—62no—
626C2×C3×D3—62no—
627C2×C3×D3—61no—
628C2×C3×D3—62no—
629C2×C3×D3—62no—
630C2×C3×D3—61no—
631C2×C3×D3—122no—
632C2×C3×D3—121no—
633C2×C3×D3—124no—
634C2×C3×D3—124no—
635C2×C3×D3C2×D1212yes—
636C2×C3×D3C2×D1212yescomplemented
637C2×C3×D3D3×D414yes—
638C2×C3×D3D3×D414yes—
639C2×C3×D3C2×#6712yes—
640C2×C3×D3C2×#6712yescomplemented
641D32—44no—
642D32—632no—
643D32—616no—
644D32—616no—
645D32—632no—
646D32—616no—
647D32—616no—
648C32×C4—61no—
649C32×C4—62no—
650C3⋊Dic3—22no—
651C3⋊Dic3—21no—
652C3×Dic3—22no—
653C3×Dic3—22no—
654C3×Dic3—21no—
655C3×Dic3—21no—
656C3×Dic3—42no—
657C3×Dic3—41no—
658C3×Dic3—61no—
659C3×Dic3—62no—
660C3×Dic3—62no—
661C3×Dic3—61no—
662C3×Dic3—122no—
663C3×Dic3—121no—
664C25—271no—
665C22×D4—91no—
666C22×D4—272no—
667#120—91no—
668#120—271no—
669#120—272no—
670#120—271no—
671#120—272no—
672#120—271no—
673C2×C22⋊C4—91no—
674C2×C22⋊C4—272no—
675C33C2×#12011yescharacteristic, complemented, Sylow
676C23×C3—21no—
677C23×C3—21no—
678C23×C3—21no—
679C23×C3—31no—
680C23×C3—31no—
681C23×C3—31no—
682C23×C3—31no—
683C23×C3—34no—
684C23×C3—34no—
685C23×C3—31no—
686C23×C3—31no—
687C23×C3—41no—
688C23×C3—61no—
689C23×C3—61no—
690C23×C3—64no—
691C23×C3—61no—
692C23×C3—64no—
693C23×C3—64no—
694C23×C3—68no—
695C23×C3—92no—
696C23×C3—91no—
697C23×C3—184no—
698C23×C3—184no—
699C23×C3—182no—
700C23×C3—182no—
701C23×C3C2×D3211yescharacteristic
702C23×C3C2×D3211yescharacteristic
703C23×C3C2×D3211yescharacteristic
704C22×D3—24no—
705C22×D3—32no—
706C22×D3—32no—
707C22×D3—31no—
708C22×D3—31no—
709C22×D3—62no—
710C22×D3—61no—
711C22×D3—64no—
712C22×D3—62no—
713C22×D3—64no—
714C22×D3—64no—
715C22×D3—68no—
716C22×D3—64no—
717C22×D3—62no—
718C22×D3—62no—
719C22×D3—62no—
720C22×D3—64no—
721C22×D3—98no—
722C22×D3—98no—
723C22×D3—92no—
724C22×D3—92no—
725C22×D3—92no—
726C22×D3—98no—
727C22×D3—188no—
728C22×D3—182no—
729C22×D3—182no—
730C22×D3—182no—
731C22×D3—184no—
732C22×D3—184no—
733C22×D3—1832no—
734C22×D3—184no—
735C22×D3—184no—
736C22×D3—184no—
737C22×D3—184no—
738C22×D3—184no—
739C22×D3—184no—
740C22×D3—184no—
741C22×D3—184no—
742C22×D3—184no—
743C22×D3—184no—
744C22×D3—188no—
745C22×D3—188no—
746C22×D3—188no—
747C22×D3—188no—
748C22×D3—188no—
749C22×D3—1832no—
750C22×D3—1832no—
751C22×D3—1864no—
752C22×D3—184no—
753C22×D3—184no—
754C22×D3—184no—
755C22×D3—188no—
756C22×D3—184no—
757C22×D3—182no—
758C22×D3—182no—
759C22×D3—182no—
760C22×D3—184no—
761C22×D3—184no—
762C22×D3—184no—
763C22×D3—362no—
764C22×D3—364no—
765C22×D3—364no—
766C22×D3—362no—
767C22×D3—362no—
768C22×D3—368no—
769C22×D3—364no—
770C22×D3#62614yescomplemented
771C22×D3C2×D3211yescharacteristic
772C22×D3C2×D3211yescharacteristic
773C22×D3C2×D3211yescharacteristic, complemented
774C3×D4—62no—
775C3×D4—62no—
776C3×D4—122no—
777C3×D4—182no—
778C3×D4—184no—
779C3×D4—182no—
780C3×D4—182no—
781C2×C3×C4—31no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—31no—
785C2×C3×C4—61no—
786C2×C3×C4—62no—
787C2×C3×C4—91no—
788C2×C3×C4—92no—
789C2×C3×C4—184no—
790C2×C3×C4—182no—
791#67—22no—
792#67—64no—
793#67—62no—
794#67—62no—
795#67—62no—
796#67—62no—
797#67—62no—
798#67—122no—
799#67—184no—
800#67—184no—
801#67—184no—
802#67—184no—
803#67—184no—
804#67—364no—
805C2×Dic3—32no—
806C2×Dic3—31no—
807C2×Dic3—32no—
808C2×Dic3—31no—
809C2×Dic3—61no—
810C2×Dic3—62no—
811C2×Dic3—62no—
812C2×Dic3—64no—
813C2×Dic3C2×D3211yescharacteristic, complemented
814C2×Dic3C2×D3212yescomplemented
815D12—64no—
816D12—62no—
817D12—184no—
818D12—184no—
819D12—184no—
820D12—184no—
821D12—364no—
822C4×D3—62no—
823C4×D3—64no—
824C2×C32—22no—
825C2×C32—24no—
826C2×C32—22no—
827C2×C32—22no—
828C2×C32—21no—
829C2×C32—22no—
830C2×C32—22no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—22no—
834C2×C32—34no—
835C2×C32—41no—
836C2×C32—42no—
837C2×C32—42no—
838C2×C32—42no—
839C2×C32—44no—
840C2×C32—62no—
841C2×C32—121no—
842C2×C32C22×D1211yescharacteristic
843C2×C32C2×D3×D411yescharacteristic
844C2×C32C2×D3×D412yes—
845C2×C32C2×D3×D412yes—
846C2×C32C2×D3×D412yes—
847C2×C32C22×#6711yescharacteristic
848C3⋊D3—24no—
849C3⋊D3—41no—
850C3⋊D3—64no—
851C3⋊D3—68no—
852C3⋊D3—64no—
853C3⋊D3—64no—
854C3⋊D3—124no—
855C3⋊D3—124no—
856C3⋊D3—128no—
857C3×D3—24no—
858C3×D3—22no—
859C3×D3—22no—
860C3×D3—24no—
861C3×D3—41no—
862C3×D3—41no—
863C3×D3—68no—
864C3×D3—64no—
865C3×D3—64no—
866C3×D3—81no—
867C3×D3—121no—
868C3×D3—121no—
869C3×D3—241no—
870C3×D3#88214yescomplemented
871C3×D3#93714yescomplemented
872C24—31no—
873C24—91no—
874C24—91no—
875C24—272no—
876C24—272no—
877C24—271no—
878C24—544no—
879C24—548no—
880C2×D4—31no—
881C2×D4—92no—
882C2×D4—91no—
883C2×D4—91no—
884C2×D4—91no—
885C2×D4—184no—
886C2×D4—272no—
887C2×D4—272no—
888C2×D4—272no—
889C2×D4—548no—
890C22×C4—92no—
891C22×C4—91no—
892C22⋊C4—31no—
893C22⋊C4—92no—
894C22⋊C4—92no—
895C22⋊C4—91no—
896C22⋊C4—272no—
897C22⋊C4—272no—
898C22⋊C4—272no—
899C22×C3—24no—
900C22×C3—22no—
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—22no—
907C22×C3—22no—
908C22×C3—22no—
909C22×C3—32no—
910C22×C3—34no—
911C22×C3—34no—
912C22×C3—32no—
913C22×C3—32no—
914C22×C3—32no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—44no—
918C22×C3—41no—
919C22×C3—42no—
920C22×C3—62no—
921C22×C3—64no—
922C22×C3—62no—
923C22×C3—68no—
924C22×C3—68no—
925C22×C3—616no—
926C22×C3—64no—
927C22×C3—62no—
928C22×C3—62no—
929C22×C3—61no—
930C22×C3—62no—
931C22×C3—61no—
932C22×C3—62no—
933C22×C3—94no—
934C22×C3—122no—
935C22×C3—121no—
936C22×C3—188no—
937C22×C3—182no—
938C22×C3—182no—
939C22×C3—181no—
940C22×C3—182no—
941C22×C3—364no—
942C22×C3D3×D1212yescomplemented
943C22×C3C2×#62612yescomplemented
944C22×C3D3×#6712yescomplemented
945C22×C3C22×D3211yescharacteristic
946C22×C3C22×D3211yescharacteristic
947C22×C3C22×D3211yescharacteristic
948C2×D3—22no—
949C2×D3—28no—
950C2×D3—22no—
951C2×D3—21no—
952C2×D3—34no—
953C2×D3—34no—
954C2×D3—64no—
955C2×D3—616no—
956C2×D3—68no—
957C2×D3—68no—
958C2×D3—64no—
959C2×D3—64no—
960C2×D3—62no—
961C2×D3—62no—
962C2×D3—62no—
963C2×D3—62no—
964C2×D3—62no—
965C2×D3—61no—
966C2×D3—61no—
967C2×D3—62no—
968C2×D3—94no—
969C2×D3—94no—
970C2×D3—94no—
971C2×D3—122no—
972C2×D3—121no—
973C2×D3—124no—
974C2×D3—124no—
975C2×D3—184no—
976C2×D3—184no—
977C2×D3—184no—
978C2×D3—1816no—
979C2×D3—1816no—
980C2×D3—1816no—
981C2×D3—1832no—
982C2×D3—1832no—
983C2×D3—1816no—
984C2×D3—1816no—
985C2×D3—188no—
986C2×D3—1816no—
987C2×D3—188no—
988C2×D3—188no—
989C2×D3—184no—
990C2×D3—184no—
991C2×D3—182no—
992C2×D3—182no—
993C2×D3—182no—
994C2×D3—182no—
995C2×D3—182no—
996C2×D3—182no—
997C2×D3—1816no—
998C2×D3—364no—
999C2×D3—362no—
1000C2×D3—362no—
1001C2×D3—362no—
1002C2×D3—362no—
1003C2×D3—368no—
1004C2×D3—368no—
1005C2×D3—3616no—
1006C2×D3—364no—
1007C2×D3—364no—
1008C2×D3C2×#62612yes—
1009C2×D3C2×#62612yescomplemented
1010C2×D3#381114yes—
1011C3×C4—61no—
1012C3×C4—62no—
1013C3×C4—61no—
1014C3×C4—62no—
1015C3×C4—122no—
1016C3×C4—121no—
1017C3×C4—181no—
1018C3×C4—182no—
1019Dic3—22no—
1020Dic3—21no—
1021Dic3—62no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—62no—
1025Dic3—121no—
1026Dic3—122no—
1027C32—21no—
1028C32—21no—
1029C32—21no—
1030C32—41no—
1031C32C2×#88211yescharacteristic, complemented
1032C32D3×#12011yescharacteristic, complemented
1033C32C2×#93711yescharacteristic, complemented
1034C23—31no—
1035C23—31no—
1036C23—34no—
1037C23—31no—
1038C23—64no—
1039C23—92no—
1040C23—91no—
1041C23—184no—
1042C23—182no—
1043C23—184no—
1044C23—182no—
1045C23—278no—
1046C23—272no—
1047C23—544no—
1048C23—544no—
1049C23—544no—
1050C23—544no—
1051C23—544no—
1052C23—544no—
1053C23—5432no—
1054C23—542no—
1055C23D3311yescharacteristic
1056D4—62no—
1057D4—182no—
1058D4—184no—
1059D4—182no—
1060D4—182no—
1061D4—544no—
1062D4—544no—
1063D4—544no—
1064C2×C4—32no—
1065C2×C4—31no—
1066C2×C4—92no—
1067C2×C4—91no—
1068C2×C4—182no—
1069C2×C4—184no—
1070C2×C3—24no—
1071C2×C3—22no—
1072C2×C3—22no—
1073C2×C3—22no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—22no—
1078C2×C3—22no—
1079C2×C3—22no—
1080C2×C3—34no—
1081C2×C3—34no—
1082C2×C3—42no—
1083C2×C3—42no—
1084C2×C3—44no—
1085C2×C3—41no—
1086C2×C3—42no—
1087C2×C3—64no—
1088C2×C3—64no—
1089C2×C3—62no—
1090C2×C3—62no—
1091C2×C3—121no—
1092C2×C3—121no—
1093C2×C3—184no—
1094C2×C3—241no—
1095C2×C3—361no—
1096C2×C3C2×D3×D1211yescharacteristic
1097C2×C3D32×D412yes—
1098C2×C3D32×D412yes—
1099C2×C3C22×#62611yescharacteristic
1100C2×C3C2×D3×#6711yescharacteristic
1101C2×C3C2×#381112yes—
1102D3—22no—
1103D3—41no—
1104D3—68no—
1105D3—64no—
1106D3—64no—
1107D3—121no—
1108D3—121no—
1109D3—188no—
1110D3—184no—
1111D3—184no—
1112D3—184no—
1113D3—241no—
1114D3—364no—
1115D3—364no—
1116D3—368no—
1117D3#6398114yesdirect product factor
1118C22—22no—
1119C22—32no—
1120C22—34no—
1121C22—32no—
1122C22—68no—
1123C22—62no—
1124C22—61no—
1125C22—62no—
1126C22—94no—
1127C22—188no—
1128C22—182no—
1129C22—182no—
1130C22—181no—
1131C22—182no—
1132C22—274no—
1133C22—364no—
1134C22—548no—
1135C22—5416no—
1136C22—5416no—
1137C22—542no—
1138C22—542no—
1139C22D3×#62612yescomplemented
1140C22C2×D3311yescharacteristic
1141C4—61no—
1142C4—62no—
1143C4—181no—
1144C4—182no—
1145C3—21no—
1146C3—21no—
1147C3—21no—
1148C3—41no—
1149C3D3×#88211yescharacteristic, complemented
1150C3D3×#93711yescharacteristic, complemented
1151C3C2×#6398111yescharacteristic, complemented
1152C2—22no—
1153C2—34no—
1154C2—62no—
1155C2—121no—
1156C2—184no—
1157C2—361no—
1158C2—544no—
1159C2C2×D3×#62611yescharacteristic
1160C2D3×#381112yes—
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33C2×#120
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×D3×C3⋊D3C2semidirect
2. C2×C3×D3×#67C2semidirect
3. C2×D3×#626C2semidirect
4. #11723727C2semidirect
5. #11723639C2semidirect
6. #11723638C2semidirect
7. C3×#63981C2semidirect
8. C3×D3×#217C2semidirect
9. #11722950C2semidirect
10. #11722949C2semidirect
11. D3×#3722C2semidirect
15. C23×C3⋊(C3⋊D3)C22semidirect
16. C23×C3×C3⋊D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
22. C22×C3×D32C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C32×#67C22semidirect
25. C2×#6295C22semidirect
26. C2×#6292C22semidirect
27. C2×#6291C22semidirect
29. C2×C3×#626C22semidirect
30. C2×C3×#626C22semidirect
31. C2×C3×#625C22semidirect
32. C2×C3×D3×Dic3C22semidirect
33. C2×C3×D3×Dic3C22semidirect
35. C3×#3757C22semidirect
36. C32×#217C22semidirect
37. #88814C22semidirect
38. #88804C22semidirect
39. #88804C22semidirect
40. C3×#3722C22semidirect
41. C3×(C2×D3)⋊Dic3C22semidirect
49. C2×D3×#67D3semidirect
68. #63981D3direct (N × H)
71. D3×#217D3semidirect
85. C22×C3×C3⋊D3C23semidirect
87. C22×C32×D3D4semidirect
90. C22×C32×D3C23semidirect
97. C2×D3×C3⋊D3D4semidirect
101. C2×C3×C3⋊Dic3C23semidirect
102. C2×C3×C3⋊Dic3C23semidirect
104. C2×C32×Dic3C23semidirect
105. C2×C32×Dic3C23semidirect
129. C23×C3⋊D3C2×D3semidirect
150. C22×D32C2×D3semidirect
153. C2×#638C2×D3semidirect
164. C2×C3×#67C2×D3semidirect
165. C2×C3×#67C2×D3semidirect
184. C2×#626C2×D3semidirect
185. C2×#626C2×D3semidirect
187. C2×#625C2×D3semidirect
188. C2×D3×Dic3C2×D3semidirect
189. C2×D3×Dic3C2×D3semidirect
192. #3757C2×D3semidirect
200. C3×#217C2×D3semidirect
201. C3×#217C2×D3semidirect
212. #3722C2×D3semidirect
215. (C2×D3)⋊Dic3C2×D3semidirect
217. C22×C33C2×D4semidirect
222. C2×C3⋊(C3⋊D3)C2×D4semidirect
228. C2×C3×C3⋊D3C2×D4semidirect
235. C2×C32×D3C2×D4semidirect
322. C22×C3⋊D3C22×D3semidirect
346. C22×C3×D3D12semidirect
347. C22×C3×D3#67semidirect
352. C22×C3×D3C22×D3semidirect
353. C22×C3×D3C22×D3semidirect
382. C2×C3⋊Dic3C22×D3semidirect
383. C2×C3⋊Dic3C22×D3semidirect
405. C2×C3×Dic3C22×D3semidirect
406. C2×C3×Dic3C22×D3semidirect
407. C2×C3×Dic3C22×D3semidirect
408. C2×C3×Dic3C22×D3semidirect
436. C32×D3#120semidirect
496. C2×#67D32semidirect
522. #217D32semidirect
558. C22×C32C2×D12semidirect
559. C22×C32D3×D4semidirect
560. C22×C32C2×#67semidirect
599. C2×C3⋊D3D3×D4semidirect
636. C2×C3×D3C2×D12semidirect
640. C2×C3×D3C2×#67semidirect
675. C33C2×#120semidirect
770. C22×D3#626semidirect
773. C22×D3C2×D32semidirect
813. C2×Dic3C2×D32semidirect
814. C2×Dic3C2×D32semidirect
870. C3×D3#882semidirect
871. C3×D3#937semidirect
942. C22×C3D3×D12semidirect
943. C22×C3C2×#626semidirect
944. C22×C3D3×#67semidirect
1009. C2×D3C2×#626semidirect
1031. C32C2×#882semidirect
1032. C32D3×#120semidirect
1033. C32C2×#937semidirect
1117. D3#63981direct (N × H)
1139. C22D3×#626semidirect
1149. C3D3×#882semidirect
1150. C3D3×#937semidirect
1151. C3C2×#63981semidirect

Maximal subgroups

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

subgroupindex
C23×D3×C3⋊D32
C2×C3×D3×#672
C2×D3×#6262
#117237272
#117236392
#117236382
C3×#639812
C3×D3×#2172
#117229502
#117229492
D3×#37222
C2×#639813
D3×#9373
D3×#8823