Finite Group Databasebeta

← C2×C3×D3×#213 #13174787

Subgroups — C2×C3×D3×#213 #13174787

Order 1728.

1794 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3C2×C3×#3753C211yesmaximal, characteristic, complemented
4C2×C32×#213C211yesmaximal, characteristic, complemented
5C3×D3×#213C218yesmaximal, direct product factor
6C2×C3×#3714C211yesmaximal, characteristic, complemented
7C2×C3×#3713C211yesmaximal, characteristic, complemented
8C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
9C22×C3×#213—31nomaximal
10C2×C3×D3×D8—31nomaximal
11C2×D3×#213C311yesmaximal, characteristic, direct product factor
12C23×C32×D3—21no—
13C22×C3×D32—21no—
14C2×C33×D4C2211yescharacteristic, complemented
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
16C2×C32×#67—21no—
17C32×D3×D4—22no—
18C32×D3×D4C2214yescomplemented
19C2×C32×D12C2211yescharacteristic, complemented
20C2×C32×D12C2211yescharacteristic, complemented
21C2×C32×C4×D3C2211yescharacteristic
22C2×C3×#626—21no—
23C3×D3×D12—22no—
24C3×D3×D12C2214yescomplemented
25C3×#3753C2214yescomplemented
26C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27C32×#213C2214yescomplemented
28C2×C32×C3⋊C8C2211yescharacteristic, complemented
29C3×#3714C2214yescomplemented
30C3×#3713C2214yescomplemented
31C3×D3×C3⋊C8C2214yescomplemented
32C22×C32×D4—31no—
33C2×C3×D3×D4—21no—
34C2×C3×D3×D4—31no—
35C2×C3×D3×D4D311yescharacteristic, complemented
36C2×C3×D3×D4C2×C311yescharacteristic, complemented
37C22×C3×D12—31no—
38C2×D3×D12C2×C311yescharacteristic, complemented
39C2×C32×D8—31no—
40C2×#3753C2×C311yescharacteristic, complemented
41C2×C3×#213—21no—
42C2×C3×#213—31no—
43C2×C3×#213—31no—
44C2×C3×#213—31no—
45C2×C3×#213—31no—
46C2×C3×#213—38no—
47C2×C3×#213—31no—
48C2×C3×#213—61no—
49C2×C3×#213D311yescharacteristic, direct product factor
50C2×C3×#213C2×C311yescharacteristic, complemented
51C22×C3×C3⋊C8—31no—
52C3×D3×D8—38no—
53C2×C3×D24—31no—
54C2×C3×D3×C8—31no—
55D3×#213C2×C318yesdirect product factor
56C2×#3714C2×C311yescharacteristic, complemented
57C2×#3713C2×C311yescharacteristic, complemented
58C2×D3×C3⋊C8C2×C311yescharacteristic, complemented
59C23×C33—21no—
60C22×C3×C3⋊D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3—24no—
64C22×C32×D3—44no—
65C22×C32×D3D411yescharacteristic
66C2×C3×D32—24no—
67C2×C3×D32—44no—
68C33×D4—21no—
69C33×D4C2312yescomplemented
70C2×C33×C4C2311yescharacteristic
71C3×C4⋊(C3⋊D3)—21no—
72C3×C4⋊(C3⋊D3)C2312yescomplemented
73C32×#67—24no—
74C2×C32×Dic3D411yescharacteristic
75C32×D12—21no—
76C32×D12—21no—
77C32×D12C2312yescomplemented
78C32×D12C2312yescomplemented
79C32×C4×D3D412yes—
80C32×C4×D3C2312yes—
81C3×#626—24no—
82C3×C3⋊(C3⋊C8)C2312yescomplemented
83C32×C3⋊C8C2312yescomplemented
84C22×C3×D8—91no—
85C22×#213—31no—
86C2×D3×D8—31no—
87C24×C32—61no—
88C23×C3×D3—22no—
89C23×C3×D3—21no—
90C23×C3×D3—21no—
91C23×C3×D3—61no—
92C23×C3×D3—61no—
93C22×D32—21no—
94C2×C32×D4—21no—
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4—34no—
98C2×C32×D4—31no—
99C2×C32×D4—31no—
100C2×C32×D4—41no—
101C2×C32×D4—62no—
102C2×C32×D4—61no—
103C2×C32×D4C2×D311yescharacteristic, complemented
104C2×C32×D4C2×D311yescharacteristic, complemented
105C2×C32×D4C22×C311yescharacteristic, complemented
106C22×C32×C4—31no—
107C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
108C2×C3×#67—22no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—61no—
112C3×D3×D4—24no—
113C3×D3×D4—24no—
114C3×D3×D4—22no—
115C3×D3×D4—22no—
116C3×D3×D4—34no—
117C3×D3×D4—62no—
118C3×D3×D4C2×D314yescomplemented
119C3×D3×D4C22×C314yescomplemented
120C2×C3×D12—21no—
121C2×C3×D12—21no—
122C2×C3×D12—31no—
123C2×C3×D12—31no—
124C2×C3×D12—34no—
125C2×C3×D12—62no—
126C2×C3×D12—61no—
127C2×C3×D12—61no—
128C2×C3×D12C2×D311yescharacteristic, complemented
129C2×C3×D12C2×D311yescharacteristic, complemented
130C2×C3×D12C22×C311yescharacteristic, complemented
131C2×C3×D12C22×C311yescharacteristic, complemented
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×C4×D3C22×C311yescharacteristic
135C2×#626—21no—
136D3×D12—22no—
137D3×D12C22×C314yescomplemented
138C32×D8—34no—
139C2×C32×C8—31no—
140#3753C22×C314yescomplemented
141C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
142C3×#213—24no—
143C3×#213—34no—
144C3×#213—34no—
145C3×#213—34no—
146C3×#213—34no—
147C3×#213—34no—
148C3×#213—64no—
149C3×#213C2×D314yesdirect product factor
150C3×#213C22×C314yescomplemented
151C2×C3×C3⋊C8—21no—
152C2×C3×C3⋊C8—31no—
153C2×C3×C3⋊C8—31no—
154C2×C3×C3⋊C8—34no—
155C2×C3×C3⋊C8—61no—
156C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
157C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
158C3×D24—34no—
159C3×D3×C8—34no—
160#3714C22×C314yescomplemented
161#3713C22×C314yescomplemented
162D3×C3⋊C8C22×C314yescomplemented
163C22×C33—22no—
164C22×C33—42no—
165C22×C33C2×D411yescharacteristic
166C2×C3×C3⋊D3—22no—
167C2×C3×C3⋊D3—42no—
168C2×C32×D3—22no—
169C2×C32×D3—22no—
170C2×C32×D3—42no—
171C2×C32×D3—42no—
172C2×C32×D3—48no—
173C2×C32×D3D814yescomplemented
174C2×C32×D3C2×D412yes—
175C3×D32—48no—
176C33×C4C2×D411yescharacteristic
177C33×C4C2411yescharacteristic
178C32×Dic3C2×D412yes—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—61no—
182C22×C3×D4—91no—
183C2×D3×D4—31no—
184C2×D3×D4C3×D311yescharacteristic, complemented
185C22×D12—31no—
186C2×C3×D8—31no—
187C2×C3×D8—31no—
188C2×C3×D8—61no—
189C2×C3×D8—91no—
190C2×C3×D8—98no—
191C2×C3×D8—91no—
192C2×C3×D8—91no—
193C22×C3×C8—91no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—38no—
199C2×#213—31no—
200C2×#213—61no—
201C2×#213C3×D311yescharacteristic, direct product factor
202C22×C3⋊C8—31no—
203D3×D8—38no—
204C2×D24—31no—
205C2×D3×C8—31no—
206C23×C32—21no—
207C23×C32—22no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—31no—
211C23×C32—41no—
212C23×C32—41no—
213C23×C32—42no—
214C23×C32—64no—
215C23×C32—61no—
216C23×C32—61no—
217C23×C32—124no—
218C22×C3⋊D3—21no—
219C22×C3×D3—22no—
220C22×C3×D3—28no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—24no—
226C22×C3×D3—24no—
227C22×C3×D3—21no—
228C22×C3×D3—41no—
229C22×C3×D3—48no—
230C22×C3×D3—44no—
231C22×C3×D3—44no—
232C22×C3×D3—64no—
233C22×C3×D3—61no—
234C22×C3×D3—61no—
235C22×C3×D3—64no—
236C22×C3×D3—121no—
237C22×C3×D3—124no—
238C22×C3×D3—124no—
239C22×C3×D3#6711yescharacteristic
240C22×C3×D3C3×D411yescharacteristic
241C2×D32—24no—
242C2×D32—44no—
243C32×D4—21no—
244C32×D4—22no—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—22no—
248C32×D4—22no—
249C32×D4—22no—
250C32×D4—32no—
251C32×D4—32no—
252C32×D4—42no—
253C32×D4—41no—
254C32×D4—41no—
255C32×D4—42no—
256C32×D4—64no—
257C32×D4—61no—
258C32×D4—61no—
259C32×D4C22×D312yescomplemented
260C32×D4C22×D312yescomplemented
261C32×D4C23×C312yescomplemented
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—31no—
266C2×C32×C4—32no—
267C2×C32×C4—32no—
268C2×C32×C4—41no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C23×C311yescharacteristic
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)C23×C312yescomplemented
274C3×#67—28no—
275C3×#67—24no—
276C3×#67—24no—
277C3×#67—64no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3#6711yescharacteristic
280C2×C3×Dic3C3×D411yescharacteristic
281C3×D12—22no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—22no—
287C3×D12—22no—
288C3×D12—32no—
289C3×D12—32no—
290C3×D12—41no—
291C3×D12—62no—
292C3×D12—64no—
293C3×D12—61no—
294C3×D12—61no—
295C3×D12—121no—
296C3×D12C22×D312yescomplemented
297C3×D12C22×D312yescomplemented
298C3×D12C23×C312yescomplemented
299C3×D12C23×C312yescomplemented
300C3×C4×D3—22no—
301C3×C4×D3—22no—
302C3×C4×D3#6712yes—
303C3×C4×D3C3×D412yes—
304C3×C4×D3C22×D312yes—
305C3×C4×D3C23×C312yes—
306#626—24no—
307C32×C8—32no—
308C3⋊(C3⋊C8)C23×C312yescomplemented
309C3×C3⋊C8—22no—
310C3×C3⋊C8—32no—
311C3×C3⋊C8—32no—
312C3×C3⋊C8—62no—
313C3×C3⋊C8C22×D312yescomplemented
314C3×C3⋊C8C23×C312yescomplemented
315C22×D8—91noSylow
316C2×C33—42no—
317C2×C33C2×D812yescomplemented
318C2×C33C22×D411yescharacteristic
319C3×C3⋊D3—42no—
320C32×D3—42no—
321C32×D3—42no—
322C32×D3C2×D814yescomplemented
323C24×C3—61no—
324C24×C3—61no—
325C24×C3—62no—
326C24×C3—181no—
327C23×D3—21no—
328C23×D3—61no—
329C23×D3—61no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—41no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—64no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—64no—
348C2×C3×D4—62no—
349C2×C3×D4—94no—
350C2×C3×D4—91no—
351C2×C3×D4—182no—
352C2×C3×D4—181no—
353C2×C3×D4D3211yescharacteristic, complemented
354C2×C3×D4C2×C3×D311yescharacteristic, complemented
355C2×C3×D4C2×C3×D311yescharacteristic, complemented
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—61no—
359C2×#67—21no—
360C2×#67—61no—
361D3×D4—22no—
362D3×D4—34no—
363D3×D4—62no—
364D3×D4C2×C3×D314yescomplemented
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—34no—
368C2×D12—61no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12C2×C3×D311yescharacteristic, complemented
372C2×D12C2×C3×D311yescharacteristic, complemented
373C2×C4×D3C2×C3×D311yescharacteristic
374C3×D8—34no—
375C3×D8—34no—
376C3×D8—64no—
377C3×D8—94no—
378C3×D8—94no—
379C3×D8—94no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—61no—
383C2×C3×C8—94no—
384C2×C3×C8—91no—
385#213—34no—
386#213—34no—
387#213—34no—
388#213—34no—
389#213—34no—
390#213—64no—
391#213C2×C3×D314yesdirect product factor
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—34no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
397D24—34no—
398D3×C8—34no—
399C22×C32—22no—
400C22×C32—24no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—34no—
407C22×C32—32no—
408C22×C32—41no—
409C22×C32—42no—
410C22×C32—42no—
411C22×C32—44no—
412C22×C32—42no—
413C22×C32—44no—
414C22×C32—42no—
415C22×C32—42no—
416C22×C32—62no—
417C22×C32—62no—
418C22×C32—82no—
419C22×C32—82no—
420C22×C32—84no—
421C22×C32—128no—
422C22×C32—122no—
423C22×C32—122no—
424C22×C32D3×D411yescharacteristic
425C22×C32C2×#6711yescharacteristic
426C22×C32C2×C3×D411yescharacteristic
427C2×C3⋊D3—22no—
428C2×C3⋊D3—42no—
429C2×C3×D3—24no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—24no—
435C2×C3×D3—22no—
436C2×C3×D3—42no—
437C2×C3×D3—416no—
438C2×C3×D3—44no—
439C2×C3×D3—42no—
440C2×C3×D3—42no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—48no—
444C2×C3×D3—48no—
445C2×C3×D3—62no—
446C2×C3×D3—62no—
447C2×C3×D3—82no—
448C2×C3×D3—122no—
449C2×C3×D3—128no—
450C2×C3×D3—122no—
451C2×C3×D3—122no—
452C2×C3×D3—128no—
453C2×C3×D3—242no—
454C2×C3×D3#21314yesdirect product factor
455C2×C3×D3C3×D814yescomplemented
456C2×C3×D3C2×#6712yes—
457C2×C3×D3C2×C3×D412yes—
458D32—48no—
459C32×C4—21no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C32×C4—32no—
466C32×C4—41no—
467C32×C4—41no—
468C32×C4D3×D411yescharacteristic
469C32×C4C2×#6711yescharacteristic
470C32×C4C2×C3×D411yescharacteristic
471C32×C4C23×D311yescharacteristic
472C32×C4C23×D311yescharacteristic
473C32×C4C24×C311yescharacteristic
474C3×Dic3—22no—
475C3×Dic3C2×#6712yes—
476C3×Dic3C2×C3×D412yes—
477C22×D4—31no—
478C22×D4—91no—
479C2×D8—31no—
480C2×D8—91no—
481C2×D8—98no—
482C2×D8—91no—
483C2×D8—91no—
484C22×C8—91no—
485C33C22×D811yescharacteristic, complemented, Sylow
486C23×C3—22no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—42no—
495C23×C3—61no—
496C23×C3—64no—
497C23×C3—64no—
498C23×C3—68no—
499C23×C3—62no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—121no—
505C23×C3—124no—
506C23×C3—124no—
507C23×C3—128no—
508C23×C3—184no—
509C23×C3—181no—
510C23×C3—364no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—24no—
514C22×D3—44no—
515C22×D3—64no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—64no—
519C22×D3—121no—
520C22×D3—124no—
521C22×D3—124no—
522C22×D3C3×#6711yescharacteristic
523C3×D4—22no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—22no—
528C3×D4—22no—
529C3×D4—22no—
530C3×D4—32no—
531C3×D4—32no—
532C3×D4—32no—
533C3×D4—32no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—42no—
537C3×D4—42no—
538C3×D4—62no—
539C3×D4—62no—
540C3×D4—62no—
541C3×D4—64no—
542C3×D4—64no—
543C3×D4—68no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—61no—
547C3×D4—61no—
548C3×D4—92no—
549C3×D4—121no—
550C3×D4—184no—
551C3×D4—181no—
552C3×D4C2×D3212yescomplemented
553C3×D4C22×C3×D312yescomplemented
554C3×D4C22×C3×D312yescomplemented
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—41no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—61no—
568C2×C3×C4C2×D3211yescharacteristic
569C2×C3×C4C22×C3×D311yescharacteristic
570C2×C3×C4C22×C3×D311yescharacteristic
571#67—24no—
572#67—64no—
573C2×Dic3C3×#6711yescharacteristic
574D12—21no—
575D12—21no—
576D12—32no—
577D12—32no—
578D12—62no—
579D12—64no—
580D12—61no—
581D12—61no—
582D12—121no—
583D12C22×C3×D312yescomplemented
584D12C22×C3×D312yescomplemented
585C4×D3C3×#6712yes—
586C4×D3C22×C3×D312yes—
587C3×C8—32no—
588C3×C8—32no—
589C3×C8—62no—
590C3×C8—92no—
591C3⋊C8—32no—
592C3⋊C8—32no—
593C3⋊C8—62no—
594C3⋊C8C22×C3×D312yescomplemented
595C2×C32—22no—
596C2×C32—22no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—22no—
601C2×C32—34no—
602C2×C32—42no—
603C2×C32—41no—
604C2×C32—42no—
605C2×C32—44no—
606C2×C32—42no—
607C2×C32—42no—
608C2×C32—82no—
609C2×C32—82no—
610C2×C32—84no—
611C2×C32—122no—
612C2×C32—122no—
613C2×C32D3×D812yescomplemented
614C2×C32C2×#21312yescomplemented
615C2×C32C2×C3×D812yescomplemented
616C2×C32C2×D3×D411yescharacteristic
617C2×C32C22×#6711yescharacteristic
618C2×C32C22×C3×D411yescharacteristic
619C3⋊D3—42no—
620C3×D3—24no—
621C3×D3—44no—
622C3×D3—42no—
623C3×D3—42no—
624C3×D3—42no—
625C3×D3—42no—
626C3×D3—82no—
627C3×D3—122no—
628C3×D3—122no—
629C3×D3—242no—
630C3×D3C2×#21314yesdirect product factor
631C3×D3C2×C3×D814yescomplemented
632C24—61no—
633C24—181no—
634C2×D4—34no—
635C2×D4—31no—
636C2×D4—31no—
637C2×D4—62no—
638C2×D4—61no—
639C2×D4—94no—
640C2×D4—91no—
641C2×D4—182no—
642C2×D4—181no—
643C2×D4C3×D3211yescharacteristic, complemented
644C22×C4—31no—
645D8—34no—
646D8—94no—
647D8—94no—
648D8—94no—
649C2×C8—31no—
650C2×C8—94no—
651C2×C8—91no—
652C22×C3—24no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—34no—
660C22×C3—32no—
661C22×C3—32no—
662C22×C3—34no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—44no—
666C22×C3—44no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—41no—
671C22×C3—62no—
672C22×C3—64no—
673C22×C3—64no—
674C22×C3—62no—
675C22×C3—62no—
676C22×C3—62no—
677C22×C3—62no—
678C22×C3—82no—
679C22×C3—82no—
680C22×C3—84no—
681C22×C3—122no—
682C22×C3—124no—
683C22×C3—128no—
684C22×C3—128no—
685C22×C3—1216no—
686C22×C3—122no—
687C22×C3—122no—
688C22×C3—122no—
689C22×C3—122no—
690C22×C3—182no—
691C22×C3—242no—
692C22×C3—368no—
693C22×C3—362no—
694C22×C3D3×#6711yescharacteristic
695C22×C3C3×D3×D411yescharacteristic
696C22×C3C2×C3×#6711yescharacteristic
697C2×D3—22no—
698C2×D3—22no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—48no—
702C2×D3—62no—
703C2×D3—62no—
704C2×D3—122no—
705C2×D3—128no—
706C2×D3—122no—
707C2×D3—122no—
708C2×D3—128no—
709C2×D3—242no—
710C2×D3C3×#21314yesdirect product factor
711C2×D3C2×C3×#6712yes—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—32no—
719C3×C4—32no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—62no—
723C3×C4D3×#6711yescharacteristic
724C3×C4C3×D3×D411yescharacteristic
725C3×C4C2×C3×#6711yescharacteristic
726C3×C4C22×D3211yescharacteristic
727C3×C4C23×C3×D311yescharacteristic
728C3×C4C23×C3×D311yescharacteristic
729Dic3C2×C3×#6712yes—
730C32—21no—
731C32—21no—
732C32—21no—
733C32—41no—
734C32C2×D3×D811yescharacteristic, complemented
735C32C22×#21311yescharacteristic, complemented
736C32C22×C3×D811yescharacteristic, complemented
737C23—21no—
738C23—31no—
739C23—64no—
740C23—61no—
741C23—61no—
742C23—124no—
743C23—184no—
744C23—181no—
745C23—364no—
746D4—21no—
747D4—32no—
748D4—32no—
749D4—64no—
750D4—61no—
751D4—61no—
752D4—92no—
753D4—184no—
754D4—181no—
755D4C2×C3×D3212yescomplemented
756C2×C4—31no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4C2×C3×D3211yescharacteristic
760C8—32no—
761C8—92no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—22no—
766C2×C3—22no—
767C2×C3—22no—
768C2×C3—34no—
769C2×C3—34no—
770C2×C3—44no—
771C2×C3—42no—
772C2×C3—42no—
773C2×C3—42no—
774C2×C3—41no—
775C2×C3—42no—
776C2×C3—64no—
777C2×C3—82no—
778C2×C3—82no—
779C2×C3—84no—
780C2×C3—124no—
781C2×C3—122no—
782C2×C3—122no—
783C2×C3—122no—
784C2×C3—122no—
785C2×C3—242no—
786C2×C3—362no—
787C2×C3D3×#21312yesdirect product factor
788C2×C3C3×D3×D812yescomplemented
789C2×C3C2×C3×#21312yescomplemented
790C2×C3C2×D3×#6711yescharacteristic
791C2×C3C2×C3×D3×D411yescharacteristic
792C2×C3C22×C3×#6711yescharacteristic
793D3—42no—
794D3—42no—
795D3—122no—
796D3—122no—
797D3—242no—
798D3C2×C3×#21314yesdirect product factor
799C22—22no—
800C22—32no—
801C22—34no—
802C22—42no—
803C22—62no—
804C22—62no—
805C22—128no—
806C22—122no—
807C22—122no—
808C22—182no—
809C22—368no—
810C22—362no—
811C22C3×D3×#6711yescharacteristic
812C4—32no—
813C4C3×D3×#6711yescharacteristic
814C4C22×C3×D3211yescharacteristic
815C3—21no—
816C3—21no—
817C3—21no—
818C3—41no—
819C3C2×D3×#21311yescharacteristic, direct product factor
820C3C2×C3×D3×D811yescharacteristic, complemented
821C3C22×C3×#21311yescharacteristic, complemented
822C2—34no—
823C2—42no—
824C2—122no—
825C2—122no—
826C2—362no—
827C2C3×D3×#21312yesdirect product factor
828C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×C3×D4D32
hypocenterC32C22×C3×D8
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C2×C3×D3×D12C2semidirect
3. C2×C3×#3753C2semidirect
4. C2×C32×#213C2semidirect
5. C3×D3×#213C2direct (N × H)
6. C2×C3×#3714C2semidirect
7. C2×C3×#3713C2semidirect
8. C2×C3×D3×C3⋊C8C2semidirect
11. C2×D3×#213C3direct (N × H)
14. C2×C33×D4C22semidirect
15. C2×C3×C4⋊(C3⋊D3)C22semidirect
18. C32×D3×D4C22semidirect
19. C2×C32×D12C22semidirect
20. C2×C32×D12C22semidirect
24. C3×D3×D12C22semidirect
25. C3×#3753C22semidirect
26. C2×C3×C3⋊(C3⋊C8)C22semidirect
27. C32×#213C22semidirect
28. C2×C32×C3⋊C8C22semidirect
29. C3×#3714C22semidirect
30. C3×#3713C22semidirect
31. C3×D3×C3⋊C8C22semidirect
35. C2×C3×D3×D4D3semidirect
36. C2×C3×D3×D4C2×C3semidirect
38. C2×D3×D12C2×C3semidirect
40. C2×#3753C2×C3semidirect
49. C2×C3×#213D3direct (N × H)
50. C2×C3×#213C2×C3semidirect
55. D3×#213C2×C3direct (N × H)
56. C2×#3714C2×C3semidirect
57. C2×#3713C2×C3semidirect
58. C2×D3×C3⋊C8C2×C3semidirect
69. C33×D4C23semidirect
72. C3×C4⋊(C3⋊D3)C23semidirect
77. C32×D12C23semidirect
78. C32×D12C23semidirect
82. C3×C3⋊(C3⋊C8)C23semidirect
83. C32×C3⋊C8C23semidirect
103. C2×C32×D4C2×D3semidirect
104. C2×C32×D4C2×D3semidirect
105. C2×C32×D4C22×C3semidirect
107. C2×C4⋊(C3⋊D3)C22×C3semidirect
118. C3×D3×D4C2×D3semidirect
119. C3×D3×D4C22×C3semidirect
128. C2×C3×D12C2×D3semidirect
129. C2×C3×D12C2×D3semidirect
130. C2×C3×D12C22×C3semidirect
131. C2×C3×D12C22×C3semidirect
137. D3×D12C22×C3semidirect
140. #3753C22×C3semidirect
141. C2×C3⋊(C3⋊C8)C22×C3semidirect
149. C3×#213C2×D3direct (N × H)
150. C3×#213C22×C3semidirect
156. C2×C3×C3⋊C8C2×D3semidirect
157. C2×C3×C3⋊C8C22×C3semidirect
160. #3714C22×C3semidirect
161. #3713C22×C3semidirect
162. D3×C3⋊C8C22×C3semidirect
173. C2×C32×D3D8semidirect
184. C2×D3×D4C3×D3semidirect
201. C2×#213C3×D3direct (N × H)
259. C32×D4C22×D3semidirect
260. C32×D4C22×D3semidirect
261. C32×D4C23×C3semidirect
273. C4⋊(C3⋊D3)C23×C3semidirect
296. C3×D12C22×D3semidirect
297. C3×D12C22×D3semidirect
298. C3×D12C23×C3semidirect
299. C3×D12C23×C3semidirect
308. C3⋊(C3⋊C8)C23×C3semidirect
313. C3×C3⋊C8C22×D3semidirect
314. C3×C3⋊C8C23×C3semidirect
317. C2×C33C2×D8semidirect
322. C32×D3C2×D8semidirect
353. C2×C3×D4D32semidirect
354. C2×C3×D4C2×C3×D3semidirect
355. C2×C3×D4C2×C3×D3semidirect
364. D3×D4C2×C3×D3semidirect
371. C2×D12C2×C3×D3semidirect
372. C2×D12C2×C3×D3semidirect
391. #213C2×C3×D3direct (N × H)
396. C2×C3⋊C8C2×C3×D3semidirect
454. C2×C3×D3#213direct (N × H)
455. C2×C3×D3C3×D8semidirect
485. C33C22×D8semidirect
552. C3×D4C2×D32semidirect
553. C3×D4C22×C3×D3semidirect
554. C3×D4C22×C3×D3semidirect
583. D12C22×C3×D3semidirect
584. D12C22×C3×D3semidirect
594. C3⋊C8C22×C3×D3semidirect
613. C2×C32D3×D8semidirect
614. C2×C32C2×#213semidirect
615. C2×C32C2×C3×D8semidirect
630. C3×D3C2×#213direct (N × H)
631. C3×D3C2×C3×D8semidirect
643. C2×D4C3×D32semidirect
710. C2×D3C3×#213direct (N × H)
734. C32C2×D3×D8semidirect
735. C32C22×#213semidirect
736. C32C22×C3×D8semidirect
755. D4C2×C3×D32semidirect
787. C2×C3D3×#213direct (N × H)
788. C2×C3C3×D3×D8semidirect
789. C2×C3C2×C3×#213semidirect
798. D3C2×C3×#213direct (N × H)
819. C3C2×D3×#213direct (N × H)
820. C3C2×C3×D3×D8semidirect
821. C3C22×C3×#213semidirect
827. C2C3×D3×#213direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×C3×D3×D122
C2×C3×#37532
C2×C32×#2132
C3×D3×#2132
C2×C3×#37142
C2×C3×#37132
C2×C3×D3×C3⋊C82
C22×C3×#2133
C2×C3×D3×D83
C2×D3×#2133