Finite Group Databasebeta

← C2×C3×#63971 #13175107

Subgroups — C2×C3×#63971 #13175107

Order 1728.

2442 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic, complemented
2C22×C32×#67C211yesmaximal, characteristic, complemented
3C22×C3×#626C211yesmaximal, characteristic, complemented
4C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
5C2×C32×#217C211yesmaximal, characteristic, complemented
6C3×#63971C218yesmaximal, direct product factor
7C2×C3×#3724C211yesmaximal, characteristic, complemented
8C2×C3×#3722C211yesmaximal, characteristic, complemented
9C2×C3×#939—31nomaximal
10C2×C3×#884—31nomaximal
11C2×#63971C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C2×C3×#638—24no—
16C2×C3×#638C2214yescomplemented
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C2×C32×#67—24no—
19C2×C32×#67C2214yescomplemented
20C22×C32×Dic3C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×C3×#626—24no—
24C2×C3×#626C2214yescomplemented
25C2×C3×D3×Dic3—24no—
26C2×C3×D3×Dic3C2214yescomplemented
27C32×#217C2214yescomplemented
28C3×#3724C2214yescomplemented
29C3×#3722C2214yescomplemented
30C22×C32×D4—31no—
31C22×#638C2×C311yescharacteristic, complemented
32C22×C3×#67—21no—
33C22×C3×#67—31no—
34C22×C3×#67—31no—
35C22×C3×#67—31no—
36C22×C3×#67—61no—
37C22×C3×#67D311yescharacteristic, complemented
38C22×C3×#67C2×C311yescharacteristic, complemented
39C23×C3×Dic3—31no—
40C22×C3×D12—31no—
41C22×C3×C4×D3—31no—
42C22×#626C2×C311yescharacteristic, complemented
43C22×D3×Dic3C2×C311yescharacteristic, complemented
44C2×C32×C22⋊C4—31no—
45C2×C3×#217—21no—
46C2×C3×#217D311yescharacteristic, complemented
47C2×C3×#217C2×C311yescharacteristic, complemented
48C3×#939—38no—
49C2×C3×(C2×D3)⋊C4—31no—
50C2×C3×(C2×D3)⋊C4—31no—
51C2×C3×Dic3⋊C4—31no—
52C2×C3×Dic3⋊C4—31no—
53C3×#884—38no—
54#63971C2×C318yesdirect product factor
55C2×#3724C2×C311yescharacteristic, complemented
56C2×#3722C2×C311yescharacteristic, complemented
57C23×C33—22no—
58C23×C33—22no—
59C23×C33—22no—
60C23×C33C2312yes—
61C23×C33C2311yescharacteristic
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3—22no—
64C22×C3×C3⋊D3—22no—
65C22×C3×C3⋊D3C2312yes—
66C22×C32×D3—22no—
67C22×C32×D3—22no—
68C22×C32×D3D414yescomplemented
69C22×C32×D3C2312yes—
70C3×#638—28no—
71C2×C3×C3⋊Dic3D414yescomplemented
72C2×C3×C3⋊Dic3C2312yes—
73C32×#67—28no—
74C2×C32×Dic3—22no—
75C2×C32×Dic3—22no—
76C2×C32×Dic3—22no—
77C2×C32×Dic3C2312yes—
78C2×C32×Dic3C2312yes—
79C2×C32×Dic3C2312yes—
80C3×#626—28no—
81C3×D3×Dic3—28no—
82C2×C3×#121—91no—
83C2×#939—31no—
84C2×#884—31no—
85C24×C32—21no—
86C24×C32—21no—
87C24×C32—21no—
88C24×C32—31no—
89C24×C32—41no—
90C24×C32C2×D311yescharacteristic
91C24×C32C2×D311yescharacteristic
92C24×C32C22×C311yescharacteristic
93C23×C3⋊D3C22×C311yescharacteristic
94C23×C3×D3—21no—
95C23×C3×D3—31no—
96C23×C3×D3—31no—
97C23×C3×D3—61no—
98C23×C3×D3C2×D311yescharacteristic
99C23×C3×D3C22×C311yescharacteristic
100C2×C32×D4—34no—
101C2×C32×D4—64no—
102C22×C32×C4—31no—
103C22×C32×C4—31no—
104C22×C32×C4—31no—
105C2×#638—24no—
106C2×#638C22×C314yescomplemented
107C22×C3⋊Dic3C22×C311yescharacteristic
108C2×C3×#67—28no—
109C2×C3×#67—24no—
110C2×C3×#67—24no—
111C2×C3×#67—24no—
112C2×C3×#67—34no—
113C2×C3×#67—34no—
114C2×C3×#67—34no—
115C2×C3×#67—64no—
116C2×C3×#67—64no—
117C2×C3×#67—64no—
118C2×C3×#67—64no—
119C2×C3×#67—68no—
120C2×C3×#67C2×D314yescomplemented
121C2×C3×#67C22×C314yescomplemented
122C22×C3×Dic3—21no—
123C22×C3×Dic3—21no—
124C22×C3×Dic3—21no—
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—34no—
128C22×C3×Dic3—64no—
129C22×C3×Dic3—61no—
130C22×C3×Dic3C2×D311yescharacteristic
131C22×C3×Dic3C2×D311yescharacteristic
132C22×C3×Dic3C2×D311yescharacteristic
133C22×C3×Dic3C22×C311yescharacteristic
134C22×C3×Dic3C22×C311yescharacteristic
135C22×C3×Dic3C22×C311yescharacteristic
136C2×C3×D12—34no—
137C2×C3×D12—64no—
138C2×C3×C4×D3—34no—
139C2×C3×C4×D3—64no—
140C2×#626—24no—
141C2×#626C22×C314yescomplemented
142C2×D3×Dic3—24no—
143C2×D3×Dic3C22×C314yescomplemented
144C32×C22⋊C4—34no—
145C3×#217—24no—
146C3×#217C2×D314yescomplemented
147C3×#217C22×C314yescomplemented
148C3×(C2×D3)⋊C4—34no—
149C3×(C2×D3)⋊C4—34no—
150C3×Dic3⋊C4—34no—
151C3×Dic3⋊C4—34no—
152#3724C22×C314yescomplemented
153#3722C22×C314yescomplemented
154C22×C33—22no—
155C22×C33—22no—
156C22×C33—22no—
157C22×C33—44no—
158C22×C33C2×D412yes—
159C22×C33C2×D412yes—
160C22×C33#4112yes—
161C22×C33C2411yescharacteristic
162C2×C3×C3⋊D3—22no—
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—44no—
166C2×C32×D3—28no—
167C2×C32×D3—22no—
168C2×C32×D3—22no—
169C2×C32×D3C2×D414yescomplemented
170C3×C3⋊Dic3C2×D414yescomplemented
171C32×Dic3—22no—
172C32×Dic3—22no—
173C32×Dic3—22no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—61no—
177C22×C3×D4—91no—
178C22×C3×D4—91no—
179C23×C3×C4—91no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—61no—
184C22×#67C3×D311yescharacteristic, complemented
185C23×Dic3—31no—
186C22×D12—31no—
187C22×C4×D3—31no—
188C3×#121—98no—
189C2×C3×C4⋊C4—91no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—61no—
193C2×C3×C22⋊C4—91no—
194C2×#217C3×D311yescharacteristic, complemented
195#939—38no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200#884—38no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—24no—
205C23×C32—24no—
206C23×C32—24no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32—22no—
211C23×C32—22no—
212C23×C32—22no—
213C23×C32—22no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—22no—
218C23×C32—22no—
219C23×C32—34no—
220C23×C32—32no—
221C23×C32—41no—
222C23×C32—42no—
223C23×C32—42no—
224C23×C32—42no—
225C23×C32—42no—
226C23×C32—42no—
227C23×C32—42no—
228C23×C32—42no—
229C23×C32—44no—
230C23×C32—44no—
231C23×C32—44no—
232C23×C32—62no—
233C23×C32—62no—
234C23×C32C22×D312yes—
235C23×C32C22×D312yes—
236C23×C32C22×D311yescharacteristic
237C23×C32C22×D311yescharacteristic
238C23×C32C23×C312yes—
239C23×C32C23×C311yescharacteristic
240C22×C3⋊D3—22no—
241C22×C3⋊D3—22no—
242C22×C3⋊D3—22no—
243C22×C3⋊D3C23×C312yes—
244C22×C3×D3—22no—
245C22×C3×D3—22no—
246C22×C3×D3—22no—
247C22×C3×D3—22no—
248C22×C3×D3—24no—
249C22×C3×D3—22no—
250C22×C3×D3—32no—
251C22×C3×D3—32no—
252C22×C3×D3—42no—
253C22×C3×D3—42no—
254C22×C3×D3—62no—
255C22×C3×D3—64no—
256C22×C3×D3—62no—
257C22×C3×D3—62no—
258C22×C3×D3—62no—
259C22×C3×D3—62no—
260C22×C3×D3—62no—
261C22×C3×D3—62no—
262C22×C3×D3—122no—
263C22×C3×D3—122no—
264C22×C3×D3#6714yescomplemented
265C22×C3×D3C3×D414yescomplemented
266C22×C3×D3C22×D312yes—
267C22×C3×D3C23×C312yes—
268C32×D4—68no—
269C2×C32×C4—32no—
270C2×C32×C4—32no—
271C2×C32×C4—32no—
272C2×C32×C4—62no—
273C2×C32×C4—62no—
274C2×C32×C4—62no—
275#638—28no—
276C2×C3⋊Dic3C3×D414yescomplemented
277C2×C3⋊Dic3C23×C312yes—
278C3×#67—216no—
279C3×#67—28no—
280C3×#67—28no—
281C3×#67—68no—
282C3×#67—68no—
283C3×#67—68no—
284C3×#67—616no—
285C2×C3×Dic3—24no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—34no—
296C2×C3×Dic3—34no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—42no—
300C2×C3×Dic3—42no—
301C2×C3×Dic3—64no—
302C2×C3×Dic3—62no—
303C2×C3×Dic3—68no—
304C2×C3×Dic3C22×D312yes—
305C2×C3×Dic3C22×D312yes—
306C2×C3×Dic3C22×D312yes—
307C2×C3×Dic3C23×C312yes—
308C2×C3×Dic3C23×C312yes—
309C2×C3×Dic3C23×C312yes—
310C3×D12—68no—
311C3×C4×D3—68no—
312#626—28no—
313D3×Dic3—28no—
314C2×#121—91noSylow
315C2×C33—42no—
316C2×C33#12114yescomplemented
317C2×C33C22×D411yescharacteristic
318C2×C33C22×D411yescharacteristic
319C2×C33C2×#4111yescharacteristic
320C3×C3⋊D3—42no—
321C32×D3—24no—
322C24×C3—21no—
323C24×C3—21no—
324C24×C3—21no—
325C24×C3—31no—
326C24×C3—31no—
327C24×C3—41no—
328C24×C3—61no—
329C24×C3—91no—
330C24×C3D3211yescharacteristic
331C24×C3C2×C3×D311yescharacteristic
332C24×C3C2×C3×D311yescharacteristic
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—61no—
336C23×D3C2×C3×D311yescharacteristic
337C2×C3×D4—34no—
338C2×C3×D4—34no—
339C2×C3×D4—64no—
340C2×C3×D4—64no—
341C2×C3×D4—64no—
342C2×C3×D4—68no—
343C2×C3×D4—94no—
344C2×C3×D4—94no—
345C2×C3×D4—184no—
346C2×C3×D4—184no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—94no—
357C22×C3×C4—91no—
358C22×C3×C4—184no—
359C2×#67—24no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—64no—
364C2×#67—64no—
365C2×#67—64no—
366C2×#67—64no—
367C2×#67—68no—
368C2×#67C2×C3×D314yescomplemented
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—34no—
372C22×Dic3—61no—
373C22×Dic3—64no—
374C22×Dic3C2×C3×D311yescharacteristic
375C22×Dic3C2×C3×D311yescharacteristic
376C22×Dic3C2×C3×D311yescharacteristic
377C2×D12—34no—
378C2×D12—64no—
379C2×C4×D3—34no—
380C2×C4×D3—64no—
381C3×C4⋊C4—94no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—64no—
385C3×C22⋊C4—94no—
386#217C2×C3×D314yescomplemented
387(C2×D3)⋊C4—34no—
388(C2×D3)⋊C4—34no—
389Dic3⋊C4—34no—
390Dic3⋊C4—34no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—24no—
395C22×C32—24no—
396C22×C32—24no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—22no—
407C22×C32—22no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—22no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—34no—
416C22×C32—42no—
417C22×C32—42no—
418C22×C32—42no—
419C22×C32—41no—
420C22×C32—42no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—42no—
425C22×C32—42no—
426C22×C32—44no—
427C22×C32—44no—
428C22×C32—44no—
429C22×C32—48no—
430C22×C32—48no—
431C22×C32—48no—
432C22×C32—416no—
433C22×C32—44no—
434C22×C32—44no—
435C22×C32—44no—
436C22×C32—68no—
437C22×C32—62no—
438C22×C32—62no—
439C22×C32#23512yes—
440C22×C32D3×D412yes—
441C22×C32D3×D412yes—
442C22×C32D3×D412yes—
443C22×C32#23712yes—
444C22×C32C2×#6712yes—
445C22×C32C2×C3×D412yes—
446C22×C32C2×C3×D412yes—
447C22×C32C3×#4112yes—
448C22×C32C23×D311yescharacteristic
449C22×C32C23×D311yescharacteristic
450C22×C32C24×C311yescharacteristic
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—44no—
455C2×C3×D3—28no—
456C2×C3×D3—28no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—24no—
462C2×C3×D3—48no—
463C2×C3×D3—42no—
464C2×C3×D3—42no—
465C2×C3×D3—64no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—62no—
469C2×C3×D3—62no—
470C2×C3×D3—62no—
471C2×C3×D3—62no—
472C2×C3×D3—122no—
473C2×C3×D3—122no—
474C2×C3×D3—128no—
475C2×C3×D3—124no—
476C2×C3×D3—124no—
477C2×C3×D3C2×#6714yescomplemented
478C2×C3×D3C2×C3×D414yescomplemented
479C32×C4—62no—
480C32×C4—62no—
481C32×C4—62no—
482C3⋊Dic3C2×C3×D414yescomplemented
483C3×Dic3—24no—
484C3×Dic3—22no—
485C3×Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—34no—
491C3×Dic3—34no—
492C3×Dic3—42no—
493C3×Dic3—42no—
494C3×Dic3—64no—
495C22×D4—31no—
496C22×D4—91no—
497C22×D4—91no—
498C23×C4—91no—
499#121—98no—
500C2×C4⋊C4—91no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—91no—
503C33C2×#12111yescharacteristic, complemented, Sylow
504C23×C3—24no—
505C23×C3—24no—
506C23×C3—24no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—32no—
523C23×C3—32no—
524C23×C3—34no—
525C23×C3—34no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—44no—
533C23×C3—44no—
534C23×C3—44no—
535C23×C3—42no—
536C23×C3—41no—
537C23×C3—62no—
538C23×C3—64no—
539C23×C3—62no—
540C23×C3—62no—
541C23×C3—62no—
542C23×C3—62no—
543C23×C3—92no—
544C23×C3—122no—
545C23×C3—122no—
546C23×C3—182no—
547C23×C3—182no—
548C23×C3—182no—
549C23×C3C2×D3212yes—
550C23×C3C2×D3211yescharacteristic
551C23×C3C22×C3×D312yes—
552C23×C3C22×C3×D312yes—
553C23×C3C22×C3×D311yescharacteristic
554C23×C3C22×C3×D311yescharacteristic
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—32no—
558C22×D3—32no—
559C22×D3—62no—
560C22×D3—64no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3C3×#6714yescomplemented
570C22×D3C22×C3×D312yes—
571C3×D4—68no—
572C3×D4—68no—
573C3×D4—616no—
574C3×D4—188no—
575C3×D4—188no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—62no—
583C2×C3×C4—62no—
584C2×C3×C4—62no—
585C2×C3×C4—64no—
586C2×C3×C4—62no—
587C2×C3×C4—62no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—92no—
593C2×C3×C4—94no—
594C2×C3×C4—122no—
595C2×C3×C4—122no—
596C2×C3×C4—188no—
597#67—28no—
598#67—68no—
599#67—68no—
600#67—68no—
601#67—616no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—32no—
606C2×Dic3—32no—
607C2×Dic3—34no—
608C2×Dic3—34no—
609C2×Dic3—64no—
610C2×Dic3—62no—
611C2×Dic3—68no—
612C2×Dic3C22×C3×D312yes—
613C2×Dic3C22×C3×D312yes—
614C2×Dic3C22×C3×D312yes—
615D12—68no—
616C4×D3—68no—
617C2×C32—24no—
618C2×C32—24no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—24no—
629C2×C32—44no—
630C2×C32—41no—
631C2×C32—41no—
632C2×C32—41no—
633C2×C32—44no—
634C2×C32—44no—
635C2×C32—44no—
636C2×C32—48no—
637C2×C32—42no—
638C2×C32—42no—
639C2×C32—42no—
640C2×C32—64no—
641C2×C32#88414yescomplemented
642C2×C32#93914yescomplemented
643C2×C32C3×#12114yescomplemented
644C2×C32C2×#23511yescharacteristic
645C2×C32C2×D3×D411yescharacteristic
646C2×C32C2×D3×D411yescharacteristic
647C2×C32C2×D3×D411yescharacteristic
648C2×C32C2×#23711yescharacteristic
649C2×C32C22×#6711yescharacteristic
650C2×C32C22×C3×D411yescharacteristic
651C2×C32C22×C3×D411yescharacteristic
652C2×C32C2×C3×#4111yescharacteristic
653C3⋊D3—42no—
654C3×D3—24no—
655C3×D3—24no—
656C3×D3—44no—
657C3×D3—124no—
658C3×D3—122no—
659C3×D3—122no—
660C24—31no—
661C24—91no—
662C24C3×D3211yescharacteristic
663C2×D4—34no—
664C2×D4—64no—
665C2×D4—94no—
666C2×D4—94no—
667C2×D4—184no—
668C2×D4—184no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—94no—
673C22×C4—91no—
674C22×C4—184no—
675C4⋊C4—94no—
676C22⋊C4—34no—
677C22⋊C4—94no—
678C22×C3—24no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—34no—
703C22×C3—34no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—44no—
711C22×C3—44no—
712C22×C3—44no—
713C22×C3—48no—
714C22×C3—48no—
715C22×C3—48no—
716C22×C3—416no—
717C22×C3—44no—
718C22×C3—44no—
719C22×C3—44no—
720C22×C3—41no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—64no—
725C22×C3—68no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—68no—
731C22×C3—122no—
732C22×C3—122no—
733C22×C3—128no—
734C22×C3—182no—
735C22×C3—182no—
736C22×C3—182no—
737C22×C3—364no—
738C22×C3#380412yes—
739C22×C3D3×#6712yes—
740C22×C3#381112yes—
741C22×C3C3×#23512yes—
742C22×C3C3×D3×D412yes—
743C22×C3C3×D3×D412yes—
744C22×C3C3×D3×D412yes—
745C22×C3C3×#23712yes—
746C22×C3C2×C3×#6712yes—
747C22×C3C22×D3211yescharacteristic
748C22×C3C23×C3×D311yescharacteristic
749C22×C3C23×C3×D311yescharacteristic
750C2×D3—28no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—64no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—128no—
763C2×D3—124no—
764C2×D3—124no—
765C2×D3C2×C3×#6714yescomplemented
766C3×C4—64no—
767C3×C4—62no—
768C3×C4—62no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—62no—
773C3×C4—94no—
774C3×C4—122no—
775C3×C4—122no—
776Dic3—22no—
777Dic3—22no—
778Dic3—22no—
779Dic3—34no—
780Dic3—34no—
781Dic3—64no—
782C32—21no—
783C32—21no—
784C32—21no—
785C32—41no—
786C32C2×#88411yescharacteristic, complemented
787C32C2×#93911yescharacteristic, complemented
788C32C2×C3×#12111yescharacteristic, complemented
789C23—22no—
790C23—22no—
791C23—22no—
792C23—32no—
793C23—34no—
794C23—62no—
795C23—62no—
796C23—92no—
797C23—182no—
798C23—182no—
799C23—182no—
800C23C2×C3×D3212yes—
801C23C2×C3×D3211yescharacteristic
802D4—68no—
803D4—188no—
804D4—188no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—92no—
812C2×C4—94no—
813C2×C4—188no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—24no—
824C2×C3—24no—
825C2×C3—24no—
826C2×C3—44no—
827C2×C3—44no—
828C2×C3—44no—
829C2×C3—48no—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3—42no—
833C2×C3—41no—
834C2×C3—41no—
835C2×C3—41no—
836C2×C3—44no—
837C2×C3—64no—
838C2×C3—64no—
839C2×C3—124no—
840C2×C3—362no—
841C2×C3#6397114yesdirect product factor
842C2×C3C3×#88414yescomplemented
843C2×C3C3×#93914yescomplemented
844C2×C3C2×#380411yescharacteristic
845C2×C3C2×D3×#6711yescharacteristic
846C2×C3C2×#381111yescharacteristic
847C2×C3C2×C3×#23511yescharacteristic
848C2×C3C2×C3×D3×D411yescharacteristic
849C2×C3C2×C3×D3×D411yescharacteristic
850C2×C3C2×C3×D3×D411yescharacteristic
851C2×C3C2×C3×#23711yescharacteristic
852C2×C3C22×C3×#6711yescharacteristic
853D3—24no—
854D3—124no—
855D3—122no—
856D3—122no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—34no—
861C22—44no—
862C22—62no—
863C22—62no—
864C22—68no—
865C22—182no—
866C22—182no—
867C22—182no—
868C22—364no—
869C22C3×#380412yes—
870C22C3×D3×#6712yes—
871C22C3×#381112yes—
872C22C22×C3×D3211yescharacteristic
873C4—62no—
874C4—62no—
875C4—62no—
876C4—94no—
877C3—21no—
878C3—21no—
879C3—21no—
880C3—41no—
881C3C2×#6397111yescharacteristic, direct product factor
882C3C2×C3×#88411yescharacteristic, complemented
883C3C2×C3×#93911yescharacteristic, complemented
884C2—42no—
885C2—64no—
886C2—362no—
887C2C3×#6397114yesdirect product factor
888C2C2×C3×#380411yescharacteristic
889C2C2×C3×D3×#6711yescharacteristic
890C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC23×C33C23
hypercenterC24×C3D32
hypocenterC32C2×C3×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×#638C2semidirect
2. C22×C32×#67C2semidirect
3. C22×C3×#626C2semidirect
4. C22×C3×D3×Dic3C2semidirect
5. C2×C32×#217C2semidirect
6. C3×#63971C2direct (N × H)
7. C2×C3×#3724C2semidirect
8. C2×C3×#3722C2semidirect
11. C2×#63971C3direct (N × H)
16. C2×C3×#638C22semidirect
19. C2×C32×#67C22semidirect
24. C2×C3×#626C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. C32×#217C22semidirect
28. C3×#3724C22semidirect
29. C3×#3722C22semidirect
31. C22×#638C2×C3semidirect
37. C22×C3×#67D3semidirect
38. C22×C3×#67C2×C3semidirect
42. C22×#626C2×C3semidirect
43. C22×D3×Dic3C2×C3semidirect
46. C2×C3×#217D3semidirect
47. C2×C3×#217C2×C3semidirect
54. #63971C2×C3direct (N × H)
55. C2×#3724C2×C3semidirect
56. C2×#3722C2×C3semidirect
68. C22×C32×D3D4semidirect
71. C2×C3×C3⋊Dic3D4semidirect
106. C2×#638C22×C3semidirect
120. C2×C3×#67C2×D3semidirect
121. C2×C3×#67C22×C3semidirect
141. C2×#626C22×C3semidirect
143. C2×D3×Dic3C22×C3semidirect
146. C3×#217C2×D3semidirect
147. C3×#217C22×C3semidirect
152. #3724C22×C3semidirect
153. #3722C22×C3semidirect
169. C2×C32×D3C2×D4semidirect
170. C3×C3⋊Dic3C2×D4semidirect
184. C22×#67C3×D3semidirect
194. C2×#217C3×D3semidirect
264. C22×C3×D3#67semidirect
265. C22×C3×D3C3×D4semidirect
276. C2×C3⋊Dic3C3×D4semidirect
316. C2×C33#121semidirect
368. C2×#67C2×C3×D3semidirect
386. #217C2×C3×D3semidirect
477. C2×C3×D3C2×#67semidirect
478. C2×C3×D3C2×C3×D4semidirect
482. C3⋊Dic3C2×C3×D4semidirect
503. C33C2×#121semidirect
569. C22×D3C3×#67semidirect
641. C2×C32#884semidirect
642. C2×C32#939semidirect
643. C2×C32C3×#121semidirect
765. C2×D3C2×C3×#67semidirect
786. C32C2×#884semidirect
787. C32C2×#939semidirect
788. C32C2×C3×#121semidirect
841. C2×C3#63971direct (N × H)
842. C2×C3C3×#884semidirect
843. C2×C3C3×#939semidirect
881. C3C2×#63971direct (N × H)
882. C3C2×C3×#884semidirect
883. C3C2×C3×#939semidirect
887. C2C3×#63971direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C22×C32×#672
C22×C3×#6262
C22×C3×D3×Dic32
C2×C32×#2172
C3×#639712
C2×C3×#37242
C2×C3×#37222
C2×C3×#9393
C2×C3×#8843
C2×#639713