Finite Group Databasebeta

← C2×D32×#67 #13181345

Subgroups — C2×D32×#67 #13181345

Order 1728.

6210 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D32C211yesmaximal, characteristic, complemented
2C22×D33C211yesmaximal, characteristic, complemented
3C2×#89049C211yesmaximal, characteristic, complemented
4C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
5C2×D3×#638C212yesmaximal, complemented
6C2×C3×D3×#67C212yesmaximal, complemented
7D32×#67C2116yesmaximal, direct product factor
8C2×#88953C211yesmaximal, characteristic, complemented
9C2×#88952C211yesmaximal, characteristic, complemented
10C2×D3×#626C212yesmaximal, complemented
11C2×D3×#625C212yesmaximal, complemented
12C2×D32×Dic3C211yesmaximal, characteristic, complemented
13C22×D3×#67—32nomaximal
14C2×D32×D4—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic, complemented
16C23×C32×D3C2212yescomplemented
17C22×#1113C2211yescharacteristic, complemented
18C22×D3×C3⋊D3C2212yescomplemented
19C22×D3×C3⋊D3C2211yescharacteristic, complemented
20C22×C3×D32—28no—
21C22×C3×D32C2211yescharacteristic
22C22×C3×D32C2218yescomplemented
23C22×C3×D32C2212yescomplemented
24C22×C3×D32C2212yescomplemented
25C22×C3×D32C2211yescharacteristic, complemented
26C2×D33—28no—
27C2×D33C2218yescomplemented
28C2×#6312C2211yescharacteristic, complemented
29C2×C3×#638C2212yescomplemented
30C2×C32×#67C2211yescharacteristic, complemented
31#89049C2218yescomplemented
32C2×#6295C2212yescomplemented
33C2×#6294C2211yescharacteristic, complemented
34C3⋊D3×#67C2218yescomplemented
35D3×#638C22116yescomplemented
36C2×#6292C2211yescharacteristic, complemented
37C2×#6291C2212yescomplemented
38C2×#6290C2212yescomplemented
39C2×#6290C2211yescharacteristic, complemented
40C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
41C2×D3×C3⋊Dic3C2212yescomplemented
42C3×D3×#67C22116yescomplemented
43C2×C3×#626C2212yescomplemented
44C2×C3×#625C2212yescomplemented
45C2×C3×D3×Dic3C2212yescomplemented
46#88953C2218yescomplemented
47#88952C2218yescomplemented
48D3×#626C22116yescomplemented
49D3×#625C22116yescomplemented
50D32×Dic3C2218yescomplemented
51C24×C3×D3—32no—
52C23×D32—31no—
53C23×D32—32no—
54C23×D32D311yescharacteristic, complemented
55C22×#638—32no—
56C2×D4×C3⋊D3—31no—
57C22×C3×#67—32no—
58C2×C3×D3×D4—32no—
59C2×#3811—31no—
60C2×#3811—31no—
61C2×D3×#67—32no—
62C2×D3×#67—32no—
63C2×D3×#67—332no—
64C2×D3×#67—32no—
65C2×D3×#67—32no—
66C2×D3×#67—32no—
67C2×D3×#67—32no—
68C2×D3×#67—32no—
69C2×D3×#67—32no—
70C2×D3×#67—32no—
71C2×D3×#67—62no—
72C2×D3×#67—61no—
73C2×D3×#67D312yesdirect product factor
74C22×#626—32no—
75C22×#625—32no—
76C22×D3×Dic3—32no—
77D32×D4—316no—
78C2×#3802—31no—
79C2×D3×D12—32no—
80C2×C4×D32—31no—
81C23×C33C2311yescharacteristic, complemented
82C22×C3⋊(C3⋊D3)C2311yescharacteristic, complemented
83C22×C3×C3⋊D3—24no—
84C22×C3×C3⋊D3C2311yescharacteristic
85C22×C3×C3⋊D3C2314yescomplemented
86C22×C3×C3⋊D3C2311yescharacteristic, complemented
87C22×C3×C3⋊D3C2312yescomplemented
88C22×C32×D3—28no—
89C22×C32×D3C2312yes—
90C22×C32×D3C2318yescomplemented
91C22×C32×D3C2311yescharacteristic, complemented
92C22×C32×D3C2312yescomplemented
93C2×#1113—24no—
94C2×#1113C2314yescomplemented
95C2×D3×C3⋊D3—24no—
96C2×D3×C3⋊D3—28no—
97C2×D3×C3⋊D3C2318yescomplemented
98C2×D3×C3⋊D3C2314yescomplemented
99C2×C3×D32—24no—
100C2×C3×D32—28no—
101C2×C3×D32—28no—
102C2×C3×D32—232no—
103C2×C3×D32D418yescomplemented
104C2×C3×D32C2314yes—
105C2×C3×D32C2318yescomplemented
106C2×C3×D32C2318yescomplemented
107C2×C3×D32C2314yescomplemented
108D33—232no—
109#6312C2314yescomplemented
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic, complemented
111C3×#638C2318yescomplemented
112C2×C3×C3⋊Dic3C2312yescomplemented
113C32×#67C2314yescomplemented
114C2×C32×Dic3C2311yescharacteristic, complemented
115#6295C2318yescomplemented
116#6294C2314yescomplemented
117#6292C2314yescomplemented
118#6291C2318yescomplemented
119#6290C2314yescomplemented
120#6290C2318yescomplemented
121Dic3×C3⋊D3C2314yescomplemented
122D3×C3⋊Dic3C2318yescomplemented
123C3×#626C2318yescomplemented
124C3×#625C2318yescomplemented
125C3×D3×Dic3C2318yescomplemented
126C23×#67—91no—
127C22×D3×D4—92no—
128C24×C32—32no—
129C23×C3⋊D3—31no—
130C23×C3⋊D3—32no—
131C23×C3⋊D3C2×D311yescharacteristic, complemented
132C23×C3×D3—22no—
133C23×C3×D3—32no—
134C23×C3×D3—32no—
135C23×C3×D3—32no—
136C23×C3×D3—32no—
137C23×C3×D3—32no—
138C23×C3×D3—32no—
139C23×C3×D3—32no—
140C23×C3×D3—316no—
141C23×C3×D3—616no—
142C23×C3×D3—61no—
143C23×C3×D3C2×D312yescomplemented
144C23×C3×D3C2×D312yescomplemented
145C22×D32—28no—
146C22×D32—31no—
147C22×D32—32no—
148C22×D32—32no—
149C22×D32—32no—
150C22×D32—32no—
151C22×D32—38no—
152C22×D32—316no—
153C22×D32—616no—
154C22×D32—68no—
155C22×D32—62no—
156C22×D32—61no—
157C22×D32C2×D311yescharacteristic
158C22×D32C2×D318yescomplemented
159C22×D32C2×D312yescomplemented
160C22×D32C2×D312yescomplemented
161C22×D32C2×D311yescharacteristic, complemented
162C2×C32×D4—31no—
163C2×#638—31no—
164C2×#638—32no—
165C2×#638—31no—
166C2×#638—32no—
167C2×#638—316no—
168C2×#638—32no—
169C2×#638—62no—
170C2×#638—61no—
171C2×#638—121no—
172C2×#638C2×D312yescomplemented
173C22×C3⋊Dic3—32no—
174D4×C3⋊D3—38no—
175C2×C4⋊(C3⋊D3)—31no—
176C2×C4×C3⋊D3—31no—
177C2×C3×#67—21no—
178C2×C3×#67—32no—
179C2×C3×#67—32no—
180C2×C3×#67—32no—
181C2×C3×#67—32no—
182C2×C3×#67—316no—
183C2×C3×#67—32no—
184C2×C3×#67—62no—
185C2×C3×#67C2×D312yescomplemented
186C22×C3×Dic3—32no—
187C3×D3×D4—316no—
188C2×C3×D12—32no—
189C2×C3×C4×D3—32no—
190#3811—38no—
191#3811—38no—
192D3×#67—316no—
193D3×#67—316no—
194D3×#67—316no—
195D3×#67—316no—
196D3×#67—316no—
197D3×#67—316no—
198D3×#67—316no—
199D3×#67—316no—
200D3×#67—316no—
201D3×#67—68no—
202D3×#67—616no—
203D3×#67C2×D3116yesdirect product factor
204C2×#626—32no—
205C2×#626—32no—
206C2×#626—32no—
207C2×#626—32no—
208C2×#626—32no—
209C2×#626—316no—
210C2×#626—61no—
211C2×#626—62no—
212C2×#626C2×D312yescomplemented
213C2×#625—32no—
214C2×#625—32no—
215C2×#625—32no—
216C2×#625—32no—
217C2×#625—316no—
218C2×#625—61no—
219C2×#625—62no—
220C2×#625C2×D312yescomplemented
221C2×#624—31no—
222C2×D3×Dic3—32no—
223C2×D3×Dic3—32no—
224C2×D3×Dic3—32no—
225C2×D3×Dic3—32no—
226C2×D3×Dic3—316no—
227C2×D3×Dic3—61no—
228C2×D3×Dic3—62no—
229C2×D3×Dic3C2×D312yescomplemented
230#3802—38no—
231D3×D12—316no—
232C4×D32—38no—
233C22×C33—22no—
234C22×C33C2411yescharacteristic
235C22×C33C2412yescomplemented
236C2×C3⋊(C3⋊D3)—22no—
237C2×C3⋊(C3⋊D3)C2412yescomplemented
238C2×C3×C3⋊D3—22no—
239C2×C3×C3⋊D3—24no—
240C2×C3×C3⋊D3—28no—
241C2×C3×C3⋊D3C2×D414yescomplemented
242C2×C3×C3⋊D3C2412yes—
243C2×C3×C3⋊D3C2414yescomplemented
244C2×C3×C3⋊D3C2412yescomplemented
245C2×C32×D3—22no—
246C2×C32×D3—24no—
247C2×C32×D3—216no—
248C2×C32×D3C2×D418yescomplemented
249C2×C32×D3C2414yes—
250C2×C32×D3C2412yescomplemented
251C2×C32×D3C2414yescomplemented
252#1113—28no—
253D3×C3⋊D3—28no—
254D3×C3⋊D3—216no—
255C3×D32—28no—
256C3×D32—216no—
257C3×D32—216no—
258C3×D32C2×D4116yescomplemented
259C3⋊(C3⋊Dic3)C2412yescomplemented
260C3×C3⋊Dic3C2414yescomplemented
261C32×Dic3C2412yescomplemented
262C25×C3—91no—
263C24×D3—32no—
264C24×D3—92no—
265C24×D3—91no—
266C22×C3×D4—92no—
267C22×#67—32no—
268C22×#67—92no—
269C22×#67—91no—
270C22×#67—91no—
271C22×#67—916no—
272C22×#67—91no—
273C22×#67—92no—
274C22×#67—92no—
275C22×#67—92no—
276C22×#67—92no—
277C22×#67—91no—
278C22×#67—182no—
279C23×Dic3—91no—
280C2×D3×D4—32no—
281C2×D3×D4—92no—
282C2×D3×D4—92no—
283C2×D3×D4—932no—
284C2×D3×D4—92no—
285C2×D3×D4—92no—
286C2×D3×D4—92no—
287C2×D3×D4—92no—
288C2×D3×D4—92no—
289C2×D3×D4—181no—
290C22×D12—92no—
291C22×C4×D3—92no—
292C23×C32—22no—
293C23×C32—21no—
294C23×C32—32no—
295C23×C32—31no—
296C23×C32—32no—
297C23×C32—38no—
298C23×C32—41no—
299C23×C32—68no—
300C23×C32C22×D312yescomplemented
301C23×C32C22×D311yescharacteristic, complemented
302C22×C3⋊D3—24no—
303C22×C3⋊D3—31no—
304C22×C3⋊D3—32no—
305C22×C3⋊D3—34no—
306C22×C3⋊D3—38no—
307C22×C3⋊D3—62no—
308C22×C3⋊D3—61no—
309C22×C3⋊D3—68no—
310C22×C3⋊D3—64no—
311C22×C3⋊D3—121no—
312C22×C3⋊D3C22×D311yescharacteristic
313C22×C3⋊D3C22×D314yescomplemented
314C22×C3⋊D3C22×D312yescomplemented
315C22×C3⋊D3C22×D311yescharacteristic, complemented
316C22×C3×D3—28no—
317C22×C3×D3—28no—
318C22×C3×D3—22no—
319C22×C3×D3—21no—
320C22×C3×D3—22no—
321C22×C3×D3—28no—
322C22×C3×D3—32no—
323C22×C3×D3—316no—
324C22×C3×D3—38no—
325C22×C3×D3—32no—
326C22×C3×D3—32no—
327C22×C3×D3—32no—
328C22×C3×D3—38no—
329C22×C3×D3—38no—
330C22×C3×D3—38no—
331C22×C3×D3—38no—
332C22×C3×D3—38no—
333C22×C3×D3—38no—
334C22×C3×D3—48no—
335C22×C3×D3—61no—
336C22×C3×D3—62no—
337C22×C3×D3—61no—
338C22×C3×D3—64no—
339C22×C3×D3—68no—
340C22×C3×D3—664no—
341C22×C3×D3—68no—
342C22×C3×D3—68no—
343C22×C3×D3—68no—
344C22×C3×D3—68no—
345C22×C3×D3—68no—
346C22×C3×D3—124no—
347C22×C3×D3C22×D312yes—
348C22×C3×D3C22×D312yes—
349C22×C3×D3C22×D318yescomplemented
350C22×C3×D3C22×D318yescomplemented
351C22×C3×D3C22×D312yescomplemented
352C22×C3×D3C22×D312yescomplemented
353C22×C3×D3C22×D312yescomplemented
354C2×D32—24no—
355C2×D32—28no—
356C2×D32—28no—
357C2×D32—232no—
358C2×D32—34no—
359C2×D32—38no—
360C2×D32—38no—
361C2×D32—38no—
362C2×D32—38no—
363C2×D32—68no—
364C2×D32—64no—
365C2×D32—664no—
366C2×D32—68no—
367C2×D32—68no—
368C2×D32—64no—
369C2×D32—68no—
370C2×D32—68no—
371C2×D32—632no—
372C2×D32—128no—
373C2×D32—124no—
374C2×D32#6718yesdirect product factor
375C2×D32C22×D314yes—
376C2×D32C22×D318yescomplemented
377C2×D32C22×D318yescomplemented
378C2×D32C22×D314yescomplemented
379C32×D4—34no—
380C2×C32×C4—31no—
381#638—34no—
382#638—38no—
383#638—34no—
384#638—38no—
385#638—38no—
386#638—68no—
387#638—64no—
388#638—124no—
389#638C22×D318yescomplemented
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—32no—
392C2×C3⋊Dic3—38no—
393C2×C3⋊Dic3—62no—
394C2×C3⋊Dic3—61no—
395C2×C3⋊Dic3—121no—
396C2×C3⋊Dic3C22×D312yescomplemented
397C4⋊(C3⋊D3)—34no—
398C4×C3⋊D3—34no—
399C3×#67—24no—
400C3×#67—38no—
401C3×#67—38no—
402C3×#67—38no—
403C3×#67—38no—
404C3×#67—38no—
405C3×#67—68no—
406C3×#67C22×D318yescomplemented
407C2×C3×Dic3—21no—
408C2×C3×Dic3—32no—
409C2×C3×Dic3—32no—
410C2×C3×Dic3—38no—
411C2×C3×Dic3—62no—
412C2×C3×Dic3C22×D312yescomplemented
413C3×D12—38no—
414C3×C4×D3—38no—
415#626—38no—
416#626—38no—
417#626—38no—
418#626—38no—
419#626—38no—
420#626—68no—
421#626—64no—
422#626C22×D318yescomplemented
423#625—38no—
424#625—38no—
425#625—38no—
426#625—38no—
427#625—68no—
428#625—64no—
429#625C22×D318yescomplemented
430#624—34no—
431D3×Dic3—38no—
432D3×Dic3—38no—
433D3×Dic3—38no—
434D3×Dic3—38no—
435D3×Dic3—68no—
436D3×Dic3—64no—
437D3×Dic3C22×D318yescomplemented
438C23×D4—271noSylow
439C2×C33—22no—
440C2×C33C22×D412yescomplemented
441C2×C33C2511yescharacteristic
442C3⋊(C3⋊D3)—22no—
443C3×C3⋊D3—22no—
444C3×C3⋊D3—24no—
445C3×C3⋊D3C22×D414yescomplemented
446C32×D3—22no—
447C32×D3—24no—
448C32×D3C22×D418yescomplemented
449C24×C3—32no—
450C24×C3—32no—
451C24×C3—62no—
452C24×C3—91no—
453C24×C3—92no—
454C24×C3—91no—
455C24×C3—98no—
456C24×C3—92no—
457C24×C3—91no—
458C24×C3—188no—
459C23×D3—32no—
460C23×D3—32no—
461C23×D3—32no—
462C23×D3—32no—
463C23×D3—32no—
464C23×D3—32no—
465C23×D3—316no—
466C23×D3—32no—
467C23×D3—61no—
468C23×D3—616no—
469C23×D3—92no—
470C23×D3—916no—
471C23×D3—91no—
472C23×D3—98no—
473C23×D3—92no—
474C23×D3—92no—
475C23×D3—92no—
476C23×D3—92no—
477C23×D3—91no—
478C23×D3—181no—
479C23×D3—182no—
480C23×D3—1816no—
481C23×D3—188no—
482C23×D3D3212yescomplemented
483C2×C3×D4—32no—
484C2×C3×D4—61no—
485C2×C3×D4—92no—
486C2×C3×D4—916no—
487C2×C3×D4—92no—
488C2×C3×D4—92no—
489C22×C3×C4—92no—
490C2×#67—32no—
491C2×#67—32no—
492C2×#67—32no—
493C2×#67—32no—
494C2×#67—316no—
495C2×#67—32no—
496C2×#67—62no—
497C2×#67—916no—
498C2×#67—92no—
499C2×#67—92no—
500C2×#67—92no—
501C2×#67—92no—
502C2×#67—98no—
503C2×#67—98no—
504C2×#67—98no—
505C2×#67—916no—
506C2×#67—916no—
507C2×#67—916no—
508C2×#67—916no—
509C2×#67—92no—
510C2×#67—92no—
511C2×#67—92no—
512C2×#67—92no—
513C2×#67—91no—
514C2×#67—92no—
515C2×#67—91no—
516C2×#67—98no—
517C2×#67—91no—
518C2×#67—182no—
519C2×#67—1816no—
520C2×#67—181no—
521C2×#67—182no—
522C2×#67—181no—
523C2×#67—182no—
524C2×#67—361no—
525C2×#67D3211yescharacteristic, direct product factor
526C22×Dic3—32no—
527C22×Dic3—91no—
528C22×Dic3—98no—
529C22×Dic3—92no—
530C22×Dic3—92no—
531C22×Dic3—91no—
532C22×Dic3—182no—
533D3×D4—316no—
534D3×D4—916no—
535D3×D4—916no—
536D3×D4—916no—
537D3×D4—916no—
538D3×D4—916no—
539D3×D4—916no—
540D3×D4—916no—
541D3×D4—188no—
542C2×D12—32no—
543C2×D12—916no—
544C2×D12—92no—
545C2×D12—92no—
546C2×D12—92no—
547C2×D12—181no—
548C2×C4×D3—32no—
549C2×C4×D3—916no—
550C2×C4×D3—92no—
551C2×C4×D3—92no—
552C2×C4×D3—92no—
553C2×C4×D3—181no—
554C22×C32—24no—
555C22×C32—22no—
556C22×C32—21no—
557C22×C32—22no—
558C22×C32—22no—
559C22×C32—24no—
560C22×C32—38no—
561C22×C32—34no—
562C22×C32—34no—
563C22×C32—32no—
564C22×C32—41no—
565C22×C32—42no—
566C22×C32—44no—
567C22×C32—42no—
568C22×C32—616no—
569C22×C32—64no—
570C22×C32—62no—
571C22×C32—82no—
572C22×C32C23×D312yes—
573C22×C32C23×D311yescharacteristic
574C22×C32C23×D312yescomplemented
575C22×C32C23×D314yescomplemented
576C2×C3⋊D3—24no—
577C2×C3⋊D3—22no—
578C2×C3⋊D3—28no—
579C2×C3⋊D3—32no—
580C2×C3⋊D3—34no—
581C2×C3⋊D3—64no—
582C2×C3⋊D3—62no—
583C2×C3⋊D3—616no—
584C2×C3⋊D3—64no—
585C2×C3⋊D3—62no—
586C2×C3⋊D3—68no—
587C2×C3⋊D3—122no—
588C2×C3⋊D3—122no—
589C2×C3⋊D3—124no—
590C2×C3⋊D3—242no—
591C2×C3⋊D3C2×#6714yescomplemented
592C2×C3⋊D3C23×D312yes—
593C2×C3⋊D3C23×D312yescomplemented
594C2×C3⋊D3C23×D314yescomplemented
595C2×C3×D3—24no—
596C2×C3×D3—24no—
597C2×C3×D3—24no—
598C2×C3×D3—216no—
599C2×C3×D3—216no—
600C2×C3×D3—24no—
601C2×C3×D3—24no—
602C2×C3×D3—22no—
603C2×C3×D3—28no—
604C2×C3×D3—38no—
605C2×C3×D3—34no—
606C2×C3×D3—332no—
607C2×C3×D3—34no—
608C2×C3×D3—34no—
609C2×C3×D3—34no—
610C2×C3×D3—416no—
611C2×C3×D3—42no—
612C2×C3×D3—44no—
613C2×C3×D3—64no—
614C2×C3×D3—62no—
615C2×C3×D3—62no—
616C2×C3×D3—64no—
617C2×C3×D3—616no—
618C2×C3×D3—616no—
619C2×C3×D3—616no—
620C2×C3×D3—616no—
621C2×C3×D3—64no—
622C2×C3×D3—64no—
623C2×C3×D3—64no—
624C2×C3×D3—616no—
625C2×C3×D3—616no—
626C2×C3×D3—128no—
627C2×C3×D3—124no—
628C2×C3×D3—122no—
629C2×C3×D3D3×D418yescomplemented
630C2×C3×D3C2×#6718yescomplemented
631C2×C3×D3C23×D314yes—
632C2×C3×D3C23×D314yes—
633C2×C3×D3C23×D314yescomplemented
634C2×C3×D3C23×D314yescomplemented
635C2×C3×D3C23×D314yescomplemented
636D32—28no—
637D32—216no—
638D32—216no—
639D32—616no—
640D32—616no—
641D32—68no—
642D32—616no—
643D32—616no—
644D32—1216no—
645D32—128no—
646D32C2×#67116yesdirect product factor
647C32×C4—32no—
648C3⋊Dic3—32no—
649C3⋊Dic3—34no—
650C3⋊Dic3—64no—
651C3⋊Dic3—62no—
652C3⋊Dic3—122no—
653C3⋊Dic3C23×D314yescomplemented
654C3×Dic3—22no—
655C3×Dic3—34no—
656C3×Dic3—34no—
657C3×Dic3—64no—
658C3×Dic3C23×D314yescomplemented
659C25—91no—
660C25—271no—
661C22×D4—92no—
662C22×D4—272no—
663C22×D4—271no—
664C22×D4—271no—
665C22×D4—2716no—
666C22×D4—271no—
667C22×D4—271no—
668C22×D4—272no—
669C22×D4—272no—
670C23×C4—271no—
671C33C23×D411yescharacteristic, complemented, Sylow
672C23×C3—22no—
673C23×C3—21no—
674C23×C3—32no—
675C23×C3—32no—
676C23×C3—32no—
677C23×C3—32no—
678C23×C3—32no—
679C23×C3—38no—
680C23×C3—38no—
681C23×C3—41no—
682C23×C3—62no—
683C23×C3—62no—
684C23×C3—68no—
685C23×C3—61no—
686C23×C3—68no—
687C23×C3—68no—
688C23×C3—94no—
689C23×C3—98no—
690C23×C3—98no—
691C23×C3—94no—
692C23×C3—98no—
693C23×C3—91no—
694C23×C3—91no—
695C23×C3—92no—
696C23×C3—94no—
697C23×C3—128no—
698C23×C3—184no—
699C23×C3—188no—
700C23×C3—188no—
701C23×C3—1832no—
702C23×C3—184no—
703C23×C3C2×D3211yescharacteristic, complemented
704C23×C3C2×D3212yescomplemented
705C22×D3—28no—
706C22×D3—32no—
707C22×D3—38no—
708C22×D3—316no—
709C22×D3—32no—
710C22×D3—32no—
711C22×D3—32no—
712C22×D3—38no—
713C22×D3—38no—
714C22×D3—38no—
715C22×D3—38no—
716C22×D3—38no—
717C22×D3—38no—
718C22×D3—61no—
719C22×D3—61no—
720C22×D3—64no—
721C22×D3—62no—
722C22×D3—68no—
723C22×D3—664no—
724C22×D3—68no—
725C22×D3—68no—
726C22×D3—68no—
727C22×D3—68no—
728C22×D3—68no—
729C22×D3—98no—
730C22×D3—94no—
731C22×D3—98no—
732C22×D3—98no—
733C22×D3—98no—
734C22×D3—92no—
735C22×D3—91no—
736C22×D3—98no—
737C22×D3—94no—
738C22×D3—124no—
739C22×D3—184no—
740C22×D3—188no—
741C22×D3—181no—
742C22×D3—182no—
743C22×D3—184no—
744C22×D3—188no—
745C22×D3—1864no—
746C22×D3—188no—
747C22×D3—1832no—
748C22×D3—184no—
749C22×D3—188no—
750C22×D3—188no—
751C22×D3—188no—
752C22×D3—361no—
753C22×D3—364no—
754C22×D3—368no—
755C22×D3C2×D3212yes—
756C22×D3C2×D3218yescomplemented
757C22×D3C2×D3212yescomplemented
758C22×D3C2×D3211yescharacteristic, complemented
759C3×D4—38no—
760C3×D4—64no—
761C3×D4—98no—
762C3×D4—98no—
763C3×D4—98no—
764C2×C3×C4—32no—
765C2×C3×C4—61no—
766C2×C3×C4—98no—
767C2×C3×C4—92no—
768#67—38no—
769#67—38no—
770#67—38no—
771#67—38no—
772#67—38no—
773#67—68no—
774#67—98no—
775#67—98no—
776#67—98no—
777#67—98no—
778#67—98no—
779#67—98no—
780#67—98no—
781#67—98no—
782#67—94no—
783#67—98no—
784#67—94no—
785#67—94no—
786#67—188no—
787#67—184no—
788#67—188no—
789#67—184no—
790#67—188no—
791#67—364no—
792#67C2×D3214yesdirect product factor
793C2×Dic3—32no—
794C2×Dic3—32no—
795C2×Dic3—38no—
796C2×Dic3—62no—
797C2×Dic3—94no—
798C2×Dic3—98no—
799C2×Dic3—98no—
800C2×Dic3—92no—
801C2×Dic3—91no—
802C2×Dic3—94no—
803C2×Dic3—188no—
804C2×Dic3—181no—
805C2×Dic3—182no—
806C2×Dic3—361no—
807C2×Dic3C2×D3211yescharacteristic, complemented
808D12—38no—
809D12—98no—
810D12—98no—
811D12—98no—
812D12—184no—
813C4×D3—38no—
814C4×D3—98no—
815C4×D3—98no—
816C4×D3—98no—
817C4×D3—184no—
818C2×C32—24no—
819C2×C32—22no—
820C2×C32—22no—
821C2×C32—24no—
822C2×C32—21no—
823C2×C32—22no—
824C2×C32—38no—
825C2×C32—42no—
826C2×C32—41no—
827C2×C32—44no—
828C2×C32—42no—
829C2×C32—64no—
830C2×C32—62no—
831C2×C32—82no—
832C2×C32C2×D3×D414yescomplemented
833C2×C32C22×#6712yescomplemented
834C2×C32C24×D312yes—
835C2×C32C24×D311yescharacteristic
836C3⋊D3—24no—
837C3⋊D3—22no—
838C3⋊D3—64no—
839C3⋊D3—62no—
840C3⋊D3—122no—
841C3⋊D3—124no—
842C3⋊D3—242no—
843C3⋊D3C22×#6714yescomplemented
844C3×D3—24no—
845C3×D3—24no—
846C3×D3—24no—
847C3×D3—28no—
848C3×D3—38no—
849C3×D3—42no—
850C3×D3—44no—
851C3×D3—64no—
852C3×D3—64no—
853C3×D3—64no—
854C3×D3—64no—
855C3×D3—124no—
856C3×D3—122no—
857C3×D3C2×D3×D418yescomplemented
858C3×D3C22×#6718yescomplemented
859C24—32no—
860C24—91no—
861C24—92no—
862C24—92no—
863C24—91no—
864C24—98no—
865C24—91no—
866C24—188no—
867C24—272no—
868C24—271no—
869C24—278no—
870C24—271no—
871C24—548no—
872C2×D4—31no—
873C2×D4—92no—
874C2×D4—916no—
875C2×D4—92no—
876C2×D4—92no—
877C2×D4—271no—
878C2×D4—2716no—
879C2×D4—272no—
880C2×D4—272no—
881C2×D4—278no—
882C2×D4—278no—
883C2×D4—278no—
884C2×D4—278no—
885C2×D4—2716no—
886C2×D4—2716no—
887C2×D4—271no—
888C2×D4—272no—
889C2×D4—271no—
890C22×C4—92no—
891C22×C4—271no—
892C22×C4—278no—
893C22×C4—271no—
894C22×C4—272no—
895C22×C3—22no—
896C22×C3—24no—
897C22×C3—22no—
898C22×C3—21no—
899C22×C3—24no—
900C22×C3—22no—
901C22×C3—38no—
902C22×C3—38no—
903C22×C3—34no—
904C22×C3—34no—
905C22×C3—34no—
906C22×C3—34no—
907C22×C3—34no—
908C22×C3—42no—
909C22×C3—44no—
910C22×C3—41no—
911C22×C3—42no—
912C22×C3—64no—
913C22×C3—68no—
914C22×C3—64no—
915C22×C3—62no—
916C22×C3—616no—
917C22×C3—616no—
918C22×C3—64no—
919C22×C3—64no—
920C22×C3—64no—
921C22×C3—82no—
922C22×C3—916no—
923C22×C3—94no—
924C22×C3—92no—
925C22×C3—92no—
926C22×C3—94no—
927C22×C3—122no—
928C22×C3—124no—
929C22×C3—1216no—
930C22×C3—188no—
931C22×C3—1816no—
932C22×C3—1816no—
933C22×C3—188no—
934C22×C3—182no—
935C22×C3—184no—
936C22×C3C22×D3211yescharacteristic
937C22×C3C22×D3212yes—
938C22×C3C22×D3212yescomplemented
939C22×C3C22×D3214yescomplemented
940C2×D3—22no—
941C2×D3—24no—
942C2×D3—216no—
943C2×D3—38no—
944C2×D3—34no—
945C2×D3—332no—
946C2×D3—34no—
947C2×D3—34no—
948C2×D3—34no—
949C2×D3—62no—
950C2×D3—64no—
951C2×D3—62no—
952C2×D3—64no—
953C2×D3—616no—
954C2×D3—616no—
955C2×D3—616no—
956C2×D3—616no—
957C2×D3—64no—
958C2×D3—64no—
959C2×D3—64no—
960C2×D3—616no—
961C2×D3—616no—
962C2×D3—94no—
963C2×D3—92no—
964C2×D3—128no—
965C2×D3—122no—
966C2×D3—124no—
967C2×D3—182no—
968C2×D3—184no—
969C2×D3—188no—
970C2×D3—1816no—
971C2×D3—1816no—
972C2×D3—188no—
973C2×D3—1816no—
974C2×D3—1816no—
975C2×D3—182no—
976C2×D3—184no—
977C2×D3—1816no—
978C2×D3—362no—
979C2×D3—368no—
980C2×D3—3616no—
981C2×D3—362no—
982C2×D3—364no—
983C2×D3—722no—
984C2×D3D3×#6718yesdirect product factor
985C2×D3C22×D3214yes—
986C2×D3C22×D3214yescomplemented
987C2×D3C22×D3212yescomplemented
988C3×C4—34no—
989C3×C4—62no—
990C3×C4—94no—
991Dic3—34no—
992Dic3—34no—
993Dic3—64no—
994Dic3—94no—
995Dic3—92no—
996Dic3—182no—
997Dic3—184no—
998Dic3—362no—
999Dic3C22×D3212yescomplemented
1000C32—21no—
1001C32—22no—
1002C32—41no—
1003C32C22×D3×D412yescomplemented
1004C32C23×#6711yescharacteristic, complemented
1005C23—32no—
1006C23—31no—
1007C23—32no—
1008C23—38no—
1009C23—68no—
1010C23—94no—
1011C23—98no—
1012C23—98no—
1013C23—98no—
1014C23—94no—
1015C23—91no—
1016C23—92no—
1017C23—91no—
1018C23—94no—
1019C23—184no—
1020C23—188no—
1021C23—188no—
1022C23—1832no—
1023C23—184no—
1024C23—278no—
1025C23—274no—
1026C23—274no—
1027C23—271no—
1028C23—548no—
1029C23—544no—
1030C23—5432no—
1031C23—544no—
1032C23D3311yescharacteristic, complemented
1033D4—34no—
1034D4—98no—
1035D4—98no—
1036D4—98no—
1037D4—274no—
1038D4—278no—
1039D4—278no—
1040D4—274no—
1041D4—278no—
1042D4—274no—
1043C2×C4—31no—
1044C2×C4—98no—
1045C2×C4—92no—
1046C2×C4—274no—
1047C2×C4—274no—
1048C2×C4—278no—
1049C2×C4—271no—
1050C2×C3—22no—
1051C2×C3—24no—
1052C2×C3—22no—
1053C2×C3—24no—
1054C2×C3—22no—
1055C2×C3—21no—
1056C2×C3—38no—
1057C2×C3—38no—
1058C2×C3—42no—
1059C2×C3—44no—
1060C2×C3—42no—
1061C2×C3—41no—
1062C2×C3—68no—
1063C2×C3—64no—
1064C2×C3—64no—
1065C2×C3—64no—
1066C2×C3—82no—
1067C2×C3—94no—
1068C2×C3—122no—
1069C2×C3—124no—
1070C2×C3—182no—
1071C2×C3—184no—
1072C2×C3D32×D412yescomplemented
1073C2×C3C2×D3×#6714yescomplemented
1074C2×C3C23×D3211yescharacteristic
1075C2×C3C23×D3212yes—
1076D3—22no—
1077D3—24no—
1078D3—38no—
1079D3—64no—
1080D3—64no—
1081D3—64no—
1082D3—64no—
1083D3—122no—
1084D3—124no—
1085D3—182no—
1086D3—184no—
1087D3—362no—
1088D3—364no—
1089D3—722no—
1090D3C2×D3×#6718yesdirect product factor
1091C22—22no—
1092C22—38no—
1093C22—34no—
1094C22—32no—
1095C22—34no—
1096C22—616no—
1097C22—64no—
1098C22—62no—
1099C22—916no—
1100C22—94no—
1101C22—92no—
1102C22—94no—
1103C22—92no—
1104C22—188no—
1105C22—1816no—
1106C22—1816no—
1107C22—188no—
1108C22—182no—
1109C22—184no—
1110C22—272no—
1111C22—5416no—
1112C22—548no—
1113C22—548no—
1114C22—542no—
1115C22C2×D3311yescharacteristic
1116C22C2×D3312yescomplemented
1117C4—32no—
1118C4—94no—
1119C4—272no—
1120C3—21no—
1121C3—22no—
1122C3—41no—
1123C3C2×D32×D411yescharacteristic, complemented
1124C3C22×D3×#6712yescomplemented
1125C2—22no—
1126C2—38no—
1127C2—64no—
1128C2—62no—
1129C2—94no—
1130C2—182no—
1131C2—184no—
1132C2—542no—
1133C2D32×#6712yesdirect product factor
1134C2C22×D3311yescharacteristic
subgroupG/H
centerC22C2×D33
commutator, cosocleC2×C33C25
FrattiniC2C22×D33
FittingC23×C33C23
socleC22×C33C24
hypercenterC23D33
hypocenterC33C23×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×C3×D32C2semidirect
2. C22×D33C2semidirect
3. C2×#89049C2semidirect
4. C2×C3⋊D3×#67C2semidirect
5. C2×D3×#638C2semidirect
6. C2×C3×D3×#67C2semidirect
7. D32×#67C2direct (N × H)
8. C2×#88953C2semidirect
9. C2×#88952C2semidirect
10. C2×D3×#626C2semidirect
11. C2×D3×#625C2semidirect
12. C2×D32×Dic3C2semidirect
15. C23×C3×C3⋊D3C22semidirect
16. C23×C32×D3C22semidirect
17. C22×#1113C22semidirect
18. C22×D3×C3⋊D3C22semidirect
19. C22×D3×C3⋊D3C22semidirect
22. C22×C3×D32C22semidirect
23. C22×C3×D32C22semidirect
24. C22×C3×D32C22semidirect
25. C22×C3×D32C22semidirect
27. C2×D33C22semidirect
28. C2×#6312C22semidirect
29. C2×C3×#638C22semidirect
30. C2×C32×#67C22semidirect
31. #89049C22semidirect
32. C2×#6295C22semidirect
33. C2×#6294C22semidirect
34. C3⋊D3×#67C22semidirect
35. D3×#638C22semidirect
36. C2×#6292C22semidirect
37. C2×#6291C22semidirect
38. C2×#6290C22semidirect
39. C2×#6290C22semidirect
40. C2×Dic3×C3⋊D3C22semidirect
41. C2×D3×C3⋊Dic3C22semidirect
42. C3×D3×#67C22semidirect
43. C2×C3×#626C22semidirect
44. C2×C3×#625C22semidirect
45. C2×C3×D3×Dic3C22semidirect
46. #88953C22semidirect
47. #88952C22semidirect
48. D3×#626C22semidirect
49. D3×#625C22semidirect
50. D32×Dic3C22semidirect
54. C23×D32D3semidirect
73. C2×D3×#67D3direct (N × H)
81. C23×C33C23semidirect
82. C22×C3⋊(C3⋊D3)C23semidirect
85. C22×C3×C3⋊D3C23semidirect
86. C22×C3×C3⋊D3C23semidirect
87. C22×C3×C3⋊D3C23semidirect
90. C22×C32×D3C23semidirect
91. C22×C32×D3C23semidirect
92. C22×C32×D3C23semidirect
94. C2×#1113C23semidirect
97. C2×D3×C3⋊D3C23semidirect
98. C2×D3×C3⋊D3C23semidirect
103. C2×C3×D32D4semidirect
105. C2×C3×D32C23semidirect
106. C2×C3×D32C23semidirect
107. C2×C3×D32C23semidirect
109. #6312C23semidirect
110. C2×C3⋊(C3⋊Dic3)C23semidirect
111. C3×#638C23semidirect
112. C2×C3×C3⋊Dic3C23semidirect
113. C32×#67C23semidirect
114. C2×C32×Dic3C23semidirect
115. #6295C23semidirect
116. #6294C23semidirect
117. #6292C23semidirect
118. #6291C23semidirect
119. #6290C23semidirect
120. #6290C23semidirect
121. Dic3×C3⋊D3C23semidirect
122. D3×C3⋊Dic3C23semidirect
123. C3×#626C23semidirect
124. C3×#625C23semidirect
125. C3×D3×Dic3C23semidirect
131. C23×C3⋊D3C2×D3semidirect
143. C23×C3×D3C2×D3semidirect
144. C23×C3×D3C2×D3semidirect
158. C22×D32C2×D3semidirect
159. C22×D32C2×D3semidirect
160. C22×D32C2×D3semidirect
161. C22×D32C2×D3semidirect
172. C2×#638C2×D3semidirect
185. C2×C3×#67C2×D3semidirect
203. D3×#67C2×D3direct (N × H)
212. C2×#626C2×D3semidirect
220. C2×#625C2×D3semidirect
229. C2×D3×Dic3C2×D3semidirect
235. C22×C33C24semidirect
237. C2×C3⋊(C3⋊D3)C24semidirect
241. C2×C3×C3⋊D3C2×D4semidirect
243. C2×C3×C3⋊D3C24semidirect
244. C2×C3×C3⋊D3C24semidirect
248. C2×C32×D3C2×D4semidirect
250. C2×C32×D3C24semidirect
251. C2×C32×D3C24semidirect
258. C3×D32C2×D4semidirect
259. C3⋊(C3⋊Dic3)C24semidirect
260. C3×C3⋊Dic3C24semidirect
261. C32×Dic3C24semidirect
300. C23×C32C22×D3semidirect
301. C23×C32C22×D3semidirect
313. C22×C3⋊D3C22×D3semidirect
314. C22×C3⋊D3C22×D3semidirect
315. C22×C3⋊D3C22×D3semidirect
349. C22×C3×D3C22×D3semidirect
350. C22×C3×D3C22×D3semidirect
351. C22×C3×D3C22×D3semidirect
352. C22×C3×D3C22×D3semidirect
353. C22×C3×D3C22×D3semidirect
374. C2×D32#67direct (N × H)
376. C2×D32C22×D3semidirect
377. C2×D32C22×D3semidirect
378. C2×D32C22×D3semidirect
389. #638C22×D3semidirect
396. C2×C3⋊Dic3C22×D3semidirect
406. C3×#67C22×D3semidirect
412. C2×C3×Dic3C22×D3semidirect
422. #626C22×D3semidirect
429. #625C22×D3semidirect
437. D3×Dic3C22×D3semidirect
440. C2×C33C22×D4semidirect
445. C3×C3⋊D3C22×D4semidirect
448. C32×D3C22×D4semidirect
482. C23×D3D32semidirect
525. C2×#67D32direct (N × H)
574. C22×C32C23×D3semidirect
575. C22×C32C23×D3semidirect
591. C2×C3⋊D3C2×#67semidirect
593. C2×C3⋊D3C23×D3semidirect
594. C2×C3⋊D3C23×D3semidirect
629. C2×C3×D3D3×D4semidirect
630. C2×C3×D3C2×#67semidirect
633. C2×C3×D3C23×D3semidirect
634. C2×C3×D3C23×D3semidirect
635. C2×C3×D3C23×D3semidirect
646. D32C2×#67direct (N × H)
653. C3⋊Dic3C23×D3semidirect
658. C3×Dic3C23×D3semidirect
671. C33C23×D4semidirect
703. C23×C3C2×D32semidirect
704. C23×C3C2×D32semidirect
756. C22×D3C2×D32semidirect
757. C22×D3C2×D32semidirect
758. C22×D3C2×D32semidirect
792. #67C2×D32direct (N × H)
807. C2×Dic3C2×D32semidirect
832. C2×C32C2×D3×D4semidirect
833. C2×C32C22×#67semidirect
843. C3⋊D3C22×#67semidirect
857. C3×D3C2×D3×D4semidirect
858. C3×D3C22×#67semidirect
938. C22×C3C22×D32semidirect
939. C22×C3C22×D32semidirect
984. C2×D3D3×#67direct (N × H)
986. C2×D3C22×D32semidirect
987. C2×D3C22×D32semidirect
999. Dic3C22×D32semidirect
1003. C32C22×D3×D4semidirect
1004. C32C23×#67semidirect
1032. C23D33semidirect
1072. C2×C3D32×D4semidirect
1073. C2×C3C2×D3×#67semidirect
1090. D3C2×D3×#67direct (N × H)
1116. C22C2×D33semidirect
1123. C3C2×D32×D4semidirect
1124. C3C22×D3×#67semidirect
1133. C2D32×#67direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D322
C22×D332
C2×#890492
C2×C3⋊D3×#672
C2×D3×#6382
C2×C3×D3×#672
D32×#672
C2×#889532
C2×#889522
C2×D3×#6262
C2×D3×#6252
C2×D32×Dic32
C22×D3×#673
C2×D32×D43