Finite Group Databasebeta

← C2×C3×#63922 #13174656

Subgroups — C2×C3×#63922 #13174656

Order 1728.

3202 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D32C211yesmaximal, characteristic, complemented
2C22×C32×D12C211yesmaximal, characteristic, complemented
3C22×C3×#626C211yesmaximal, characteristic, complemented
4C22×C3×#625C211yesmaximal, characteristic, complemented
5C2×C3×#3752C211yesmaximal, characteristic, complemented
6C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#63922C218yesmaximal, direct product factor
9C2×C3×#937—31nomaximal
10C2×C3×#882—31nomaximal
11C2×#63922C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C23×C32×D3C2211yescharacteristic, complemented
16C22×C3×D32—24no—
17C22×C3×D32—24no—
18C22×C3×D32—24no—
19C22×C3×D32C2214yescomplemented
20C22×C33×C4C2211yescharacteristic, complemented
21C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
22C22×C32×Dic3C2211yescharacteristic, complemented
23C2×C32×D12—24no—
24C2×C32×D12C2214yescomplemented
25C2×C3×#626—24no—
26C2×C3×#626C2214yescomplemented
27C2×C3×#625—24no—
28C2×C3×#625C2214yescomplemented
29C3×#3752C2214yescomplemented
30C32×(C2×D3)⋊C4C2214yescomplemented
31C3×(C2×D3)⋊Dic3C2214yescomplemented
32C24×C3×D3—31no—
33C24×C3×D3—31no—
34C23×D32C2×C311yescharacteristic, complemented
35C22×C32×D4—31no—
36C22×C3×#67—31no—
37C22×C3×#67—31no—
38C22×C3×#67—31no—
39C22×C3×D12—21no—
40C22×C3×D12—31no—
41C22×C3×D12D311yescharacteristic, complemented
42C22×C3×D12C2×C311yescharacteristic, complemented
43C22×#626C2×C311yescharacteristic, complemented
44C22×#625C2×C311yescharacteristic, complemented
45C2×C32×C22⋊C4—31no—
46C2×#3752C2×C311yescharacteristic, complemented
47C2×C3×#217—31no—
48C3×#937—38no—
49C2×C3×(C2×D3)⋊C4—21no—
50C2×C3×(C2×D3)⋊C4—31no—
51C2×C3×(C2×D3)⋊C4—31no—
52C2×C3×(C2×D3)⋊C4—31no—
53C2×C3×(C2×D3)⋊C4—61no—
54C2×C3×(C2×D3)⋊C4D311yescharacteristic, complemented
55C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
56C3×#882—38no—
57C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
58#63922C2×C318yesdirect product factor
59C23×C33C2311yescharacteristic
60C22×C3×C3⋊D3—22no—
61C22×C3×C3⋊D3—22no—
62C22×C3×C3⋊D3D414yescomplemented
63C22×C3×C3⋊D3C2312yes—
64C22×C32×D3—22no—
65C22×C32×D3—22no—
66C22×C32×D3—22no—
67C22×C32×D3—22no—
68C22×C32×D3—22no—
69C22×C32×D3—22no—
70C22×C32×D3—22no—
71C22×C32×D3D414yescomplemented
72C22×C32×D3D414yescomplemented
73C22×C32×D3C2312yes—
74C22×C32×D3C2312yes—
75C22×C32×D3C2312yescomplemented
76C2×C3×D32—232no—
77C2×C3×D32—28no—
78C2×C3×D32—28no—
79C2×C3×D32—28no—
80C2×C33×C4—22no—
81C2×C33×C4C2312yescomplemented
82C2×C3×C3⋊Dic3—22no—
83C2×C3×C3⋊Dic3C2312yescomplemented
84C2×C32×Dic3—22no—
85C2×C32×Dic3C2312yescomplemented
86C32×D12—28no—
87C3×#626—28no—
88C3×#625—28no—
89C2×C3×#120—91no—
90C2×#937—31no—
91C2×#882—31no—
92C24×C32—31no—
93C24×C32—31no—
94C24×C32—31no—
95C23×C3⋊D3C22×C311yescharacteristic
96C23×C3×D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C23×C3×D3—31no—
100C23×C3×D3—31no—
101C23×C3×D3—34no—
102C23×C3×D3—34no—
103C23×C3×D3—64no—
104C23×C3×D3—64no—
105C23×C3×D3—64no—
106C23×C3×D3—64no—
107C23×C3×D3—64no—
108C23×C3×D3—64no—
109C23×C3×D3—61no—
110C23×C3×D3C2×D311yescharacteristic
111C23×C3×D3C2×D311yescharacteristic
112C23×C3×D3C2×D311yescharacteristic, complemented
113C23×C3×D3C22×C311yescharacteristic
114C23×C3×D3C22×C311yescharacteristic
115C23×C3×D3C22×C311yescharacteristic, complemented
116C22×D32—24no—
117C22×D32—24no—
118C22×D32—24no—
119C22×D32C22×C314yescomplemented
120C2×C32×D4—34no—
121C2×C32×D4—64no—
122C22×C32×C4—21no—
123C22×C32×C4—21no—
124C22×C32×C4—21no—
125C22×C32×C4—31no—
126C22×C32×C4—41no—
127C22×C32×C4C2×D311yescharacteristic, complemented
128C22×C32×C4C2×D311yescharacteristic, complemented
129C22×C32×C4C22×C311yescharacteristic, complemented
130C22×C3⋊Dic3C22×C311yescharacteristic, complemented
131C2×C3×#67—34no—
132C2×C3×#67—34no—
133C2×C3×#67—34no—
134C2×C3×#67—64no—
135C2×C3×#67—64no—
136C2×C3×#67—64no—
137C22×C3×Dic3—21no—
138C22×C3×Dic3—31no—
139C22×C3×Dic3—31no—
140C22×C3×Dic3—61no—
141C22×C3×Dic3C2×D311yescharacteristic, complemented
142C22×C3×Dic3C22×C311yescharacteristic, complemented
143C2×C3×D12—28no—
144C2×C3×D12—24no—
145C2×C3×D12—24no—
146C2×C3×D12—24no—
147C2×C3×D12—34no—
148C2×C3×D12—64no—
149C2×C3×D12C2×D314yescomplemented
150C2×C3×D12C22×C314yescomplemented
151C2×#626—24no—
152C2×#626C22×C314yescomplemented
153C2×#625—24no—
154C2×#625C22×C314yescomplemented
155C32×C22⋊C4—34no—
156#3752C22×C314yescomplemented
157C3×#217—34no—
158C3×(C2×D3)⋊C4—24no—
159C3×(C2×D3)⋊C4—34no—
160C3×(C2×D3)⋊C4—34no—
161C3×(C2×D3)⋊C4—34no—
162C3×(C2×D3)⋊C4—64no—
163C3×(C2×D3)⋊C4C2×D314yescomplemented
164C3×(C2×D3)⋊C4C22×C314yescomplemented
165(C2×D3)⋊Dic3C22×C314yescomplemented
166C22×C33C2×D412yes—
167C22×C33C2×D412yes—
168C22×C33C2×D412yes—
169C22×C33C2411yescharacteristic
170C2×C3×C3⋊D3—28no—
171C2×C3×C3⋊D3—22no—
172C2×C3×C3⋊D3—22no—
173C2×C3×C3⋊D3C2×D414yescomplemented
174C2×C32×D3—28no—
175C2×C32×D3—28no—
176C2×C32×D3—22no—
177C2×C32×D3—22no—
178C2×C32×D3—22no—
179C2×C32×D3—22no—
180C2×C32×D3—22no—
181C2×C32×D3—22no—
182C2×C32×D3—22no—
183C2×C32×D3—44no—
184C2×C32×D3C2×D414yescomplemented
185C2×C32×D3C2×D414yescomplemented
186C3×D32—232no—
187C33×C4—22no—
188C3×C3⋊Dic3—22no—
189C32×Dic3—22no—
190C25×C3—91no—
191C24×D3—31no—
192C24×D3—31no—
193C22×C3×D4—31no—
194C22×C3×D4—31no—
195C22×C3×D4—61no—
196C22×C3×D4—91no—
197C22×C3×D4—91no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×D12—31no—
202C22×D12C3×D311yescharacteristic, complemented
203C3×#120—98no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—61no—
207C2×C3×C22⋊C4—91no—
208C2×C3×C22⋊C4—91no—
209C2×#217—31no—
210#937—38no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—61no—
215C2×(C2×D3)⋊C4C3×D311yescharacteristic, complemented
216#882—38no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—34no—
221C23×C32—34no—
222C23×C32—32no—
223C23×C32—32no—
224C23×C32—32no—
225C23×C32—41no—
226C23×C32—62no—
227C23×C32—62no—
228C23×C32—62no—
229C23×C32—62no—
230C23×C32—62no—
231C23×C32—62no—
232C23×C32—62no—
233C23×C32C22×D311yescharacteristic
234C23×C32C22×D311yescharacteristic
235C23×C32C23×C311yescharacteristic
236C22×C3⋊D3—22no—
237C22×C3⋊D3—22no—
238C22×C3⋊D3C3×D414yescomplemented
239C22×C3⋊D3C23×C312yes—
240C22×C3×D3—22no—
241C22×C3×D3—22no—
242C22×C3×D3—22no—
243C22×C3×D3—22no—
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—22no—
251C22×C3×D3—22no—
252C22×C3×D3—22no—
253C22×C3×D3—22no—
254C22×C3×D3—22no—
255C22×C3×D3—24no—
256C22×C3×D3—24no—
257C22×C3×D3—22no—
258C22×C3×D3—22no—
259C22×C3×D3—22no—
260C22×C3×D3—34no—
261C22×C3×D3—34no—
262C22×C3×D3—32no—
263C22×C3×D3—32no—
264C22×C3×D3—42no—
265C22×C3×D3—42no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3—42no—
269C22×C3×D3—42no—
270C22×C3×D3—62no—
271C22×C3×D3—64no—
272C22×C3×D3—68no—
273C22×C3×D3—68no—
274C22×C3×D3—68no—
275C22×C3×D3—68no—
276C22×C3×D3—632no—
277C22×C3×D3—632no—
278C22×C3×D3—62no—
279C22×C3×D3—62no—
280C22×C3×D3—62no—
281C22×C3×D3—62no—
282C22×C3×D3—68no—
283C22×C3×D3—68no—
284C22×C3×D3—122no—
285C22×C3×D3—122no—
286C22×C3×D3D1214yescomplemented
287C22×C3×D3#6714yescomplemented
288C22×C3×D3C3×D414yescomplemented
289C22×C3×D3C3×D414yescomplemented
290C22×C3×D3C22×D312yes—
291C22×C3×D3C22×D312yes—
292C22×C3×D3C22×D312yescomplemented
293C22×C3×D3C23×C312yes—
294C22×C3×D3C23×C312yes—
295C22×C3×D3C23×C312yescomplemented
296C2×D32—232no—
297C2×D32—28no—
298C2×D32—28no—
299C2×D32—28no—
300C32×D4—68no—
301C2×C32×C4—22no—
302C2×C32×C4—24no—
303C2×C32×C4—22no—
304C2×C32×C4—22no—
305C2×C32×C4—22no—
306C2×C32×C4—22no—
307C2×C32×C4—22no—
308C2×C32×C4—32no—
309C2×C32×C4—42no—
310C2×C32×C4—42no—
311C2×C32×C4—42no—
312C2×C32×C4—44no—
313C2×C32×C4—62no—
314C2×C32×C4C22×D312yescomplemented
315C2×C32×C4C22×D312yescomplemented
316C2×C32×C4C23×C312yescomplemented
317C2×C3⋊Dic3—22no—
318C2×C3⋊Dic3C23×C312yescomplemented
319C3×#67—68no—
320C3×#67—68no—
321C3×#67—68no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—32no—
326C2×C3×Dic3—32no—
327C2×C3×Dic3—42no—
328C2×C3×Dic3—62no—
329C2×C3×Dic3—62no—
330C2×C3×Dic3—62no—
331C2×C3×Dic3—122no—
332C2×C3×Dic3C22×D312yescomplemented
333C2×C3×Dic3C23×C312yescomplemented
334C3×D12—216no—
335C3×D12—28no—
336C3×D12—28no—
337C3×D12—68no—
338#626—28no—
339#625—28no—
340C2×#120—91noSylow
341C2×C33#12014yescomplemented
342C2×C33C22×D411yescharacteristic
343C2×C33C22×D411yescharacteristic
344C2×C33C22×D411yescharacteristic
345C3×C3⋊D3—24no—
346C32×D3—24no—
347C32×D3—24no—
348C32×D3—42no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—31no—
353C24×C3—31no—
354C24×C3—31no—
355C24×C3—61no—
356C24×C3—61no—
357C24×C3—61no—
358C24×C3—94no—
359C24×C3—91no—
360C24×C3—184no—
361C24×C3—184no—
362C24×C3—184no—
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—34no—
366C23×D3—34no—
367C23×D3—61no—
368C23×D3—64no—
369C23×D3—64no—
370C23×D3—64no—
371C23×D3—64no—
372C23×D3—64no—
373C23×D3—64no—
374C23×D3C2×C3×D311yescharacteristic
375C23×D3C2×C3×D311yescharacteristic
376C23×D3C2×C3×D311yescharacteristic, complemented
377C2×C3×D4—34no—
378C2×C3×D4—34no—
379C2×C3×D4—64no—
380C2×C3×D4—64no—
381C2×C3×D4—64no—
382C2×C3×D4—68no—
383C2×C3×D4—94no—
384C2×C3×D4—94no—
385C2×C3×D4—184no—
386C2×C3×D4—184no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—41no—
393C22×C3×C4—61no—
394C22×C3×C4—91no—
395C22×C3×C4D3211yescharacteristic, complemented
396C22×C3×C4C2×C3×D311yescharacteristic, complemented
397C22×C3×C4C2×C3×D311yescharacteristic, complemented
398C2×#67—34no—
399C2×#67—34no—
400C2×#67—34no—
401C2×#67—64no—
402C2×#67—64no—
403C2×#67—64no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—61no—
407C22×Dic3C2×C3×D311yescharacteristic, complemented
408C2×D12—24no—
409C2×D12—34no—
410C2×D12—64no—
411C2×D12C2×C3×D314yescomplemented
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—64no—
415C3×C22⋊C4—94no—
416C3×C22⋊C4—94no—
417#217—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—64no—
422(C2×D3)⋊C4C2×C3×D314yescomplemented
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—22no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—34no—
436C22×C32—34no—
437C22×C32—42no—
438C22×C32—42no—
439C22×C32—42no—
440C22×C32—41no—
441C22×C32—62no—
442C22×C32—68no—
443C22×C32—68no—
444C22×C32—62no—
445C22×C32—62no—
446C22×C32—62no—
447C22×C32—62no—
448C22×C32—62no—
449C22×C32—62no—
450C22×C32—124no—
451C22×C32C2×D1212yes—
452C22×C32D3×D412yes—
453C22×C32D3×D412yes—
454C22×C32D3×D412yes—
455C22×C32D3×D412yes—
456C22×C32C2×#6712yes—
457C22×C32C2×C3×D412yes—
458C22×C32C2×C3×D412yes—
459C22×C32C2×C3×D412yes—
460C22×C32C23×D311yescharacteristic
461C22×C32C23×D311yescharacteristic
462C22×C32C24×C311yescharacteristic
463C2×C3⋊D3—28no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3C2×C3×D414yescomplemented
467C2×C3×D3—28no—
468C2×C3×D3—28no—
469C2×C3×D3—28no—
470C2×C3×D3—28no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—24no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—24no—
487C2×C3×D3—24no—
488C2×C3×D3—34no—
489C2×C3×D3—34no—
490C2×C3×D3—48no—
491C2×C3×D3—48no—
492C2×C3×D3—42no—
493C2×C3×D3—42no—
494C2×C3×D3—42no—
495C2×C3×D3—42no—
496C2×C3×D3—42no—
497C2×C3×D3—42no—
498C2×C3×D3—48no—
499C2×C3×D3—44no—
500C2×C3×D3—44no—
501C2×C3×D3—64no—
502C2×C3×D3—632no—
503C2×C3×D3—632no—
504C2×C3×D3—68no—
505C2×C3×D3—68no—
506C2×C3×D3—62no—
507C2×C3×D3—62no—
508C2×C3×D3—62no—
509C2×C3×D3—62no—
510C2×C3×D3—122no—
511C2×C3×D3—122no—
512C2×C3×D3—128no—
513C2×C3×D3C2×D1214yescomplemented
514C2×C3×D3C2×#6714yescomplemented
515C2×C3×D3C2×C3×D414yescomplemented
516C2×C3×D3C2×C3×D414yescomplemented
517D32—232no—
518C32×C4—22no—
519C32×C4—24no—
520C32×C4—22no—
521C32×C4—22no—
522C32×C4—42no—
523C32×C4—42no—
524C32×C4—44no—
525C32×C4—62no—
526C3⋊Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—42no—
530C3×Dic3—62no—
531C3×Dic3—62no—
532C3×Dic3—122no—
533C25—91no—
534C22×D4—31no—
535C22×D4—91no—
536C22×D4—91no—
537#120—98no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C33C2×#12011yescharacteristic, complemented, Sylow
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—34no—
550C23×C3—34no—
551C23×C3—34no—
552C23×C3—34no—
553C23×C3—32no—
554C23×C3—32no—
555C23×C3—41no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3—64no—
559C23×C3—62no—
560C23×C3—64no—
561C23×C3—64no—
562C23×C3—62no—
563C23×C3—62no—
564C23×C3—62no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3—62no—
569C23×C3—62no—
570C23×C3—62no—
571C23×C3—62no—
572C23×C3—62no—
573C23×C3—62no—
574C23×C3—62no—
575C23×C3—62no—
576C23×C3—92no—
577C23×C3—94no—
578C23×C3—122no—
579C23×C3—122no—
580C23×C3—122no—
581C23×C3—122no—
582C23×C3—122no—
583C23×C3—122no—
584C23×C3—188no—
585C23×C3—188no—
586C23×C3—188no—
587C23×C3—1832no—
588C23×C3—182no—
589C23×C3—182no—
590C23×C3C2×D3211yescharacteristic
591C23×C3C22×C3×D311yescharacteristic
592C23×C3C22×C3×D311yescharacteristic
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—32no—
601C22×D3—32no—
602C22×D3—34no—
603C22×D3—34no—
604C22×D3—64no—
605C22×D3—62no—
606C22×D3—68no—
607C22×D3—68no—
608C22×D3—68no—
609C22×D3—68no—
610C22×D3—632no—
611C22×D3—632no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—68no—
617C22×D3—68no—
618C22×D3—122no—
619C22×D3—122no—
620C22×D3C3×D1214yescomplemented
621C22×D3C3×#6714yescomplemented
622C22×D3C22×C3×D312yes—
623C22×D3C22×C3×D312yes—
624C22×D3C22×C3×D312yescomplemented
625C3×D4—68no—
626C3×D4—68no—
627C3×D4—616no—
628C3×D4—188no—
629C3×D4—188no—
630C2×C3×C4—24no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—42no—
640C2×C3×C4—42no—
641C2×C3×C4—44no—
642C2×C3×C4—42no—
643C2×C3×C4—62no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—92no—
647C2×C3×C4—122no—
648C2×C3×C4—182no—
649C2×C3×C4C2×D3212yescomplemented
650C2×C3×C4C22×C3×D312yescomplemented
651C2×C3×C4C22×C3×D312yescomplemented
652#67—68no—
653#67—68no—
654#67—68no—
655C2×Dic3—22no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—122no—
662C2×Dic3C22×C3×D312yescomplemented
663D12—28no—
664D12—68no—
665C2×C32—24no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—24no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—24no—
677C2×C32—44no—
678C2×C32—41no—
679C2×C32—41no—
680C2×C32—41no—
681C2×C32—64no—
682C2×C32—64no—
683C2×C32—122no—
684C2×C32#88214yescomplemented
685C2×C32#93714yescomplemented
686C2×C32C3×#12014yescomplemented
687C2×C32C22×D1211yescharacteristic
688C2×C32C2×D3×D411yescharacteristic
689C2×C32C2×D3×D411yescharacteristic
690C2×C32C2×D3×D411yescharacteristic
691C2×C32C2×D3×D411yescharacteristic
692C2×C32C22×#6711yescharacteristic
693C2×C32C22×C3×D411yescharacteristic
694C2×C32C22×C3×D411yescharacteristic
695C2×C32C22×C3×D411yescharacteristic
696C3⋊D3—24no—
697C3×D3—24no—
698C3×D3—24no—
699C3×D3—24no—
700C3×D3—24no—
701C3×D3—44no—
702C3×D3—44no—
703C3×D3—44no—
704C3×D3—42no—
705C3×D3—42no—
706C3×D3—64no—
707C3×D3—64no—
708C3×D3—124no—
709C24—31no—
710C24—31no—
711C24—31no—
712C24—94no—
713C24—91no—
714C24—184no—
715C24—184no—
716C24—184no—
717C2×D4—34no—
718C2×D4—64no—
719C2×D4—94no—
720C2×D4—94no—
721C2×D4—184no—
722C2×D4—184no—
723C22×C4—31no—
724C22×C4—91no—
725C22×C4C3×D3211yescharacteristic, complemented
726C22⋊C4—34no—
727C22⋊C4—94no—
728C22⋊C4—94no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—34no—
742C22×C3—34no—
743C22×C3—34no—
744C22×C3—34no—
745C22×C3—41no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—64no—
750C22×C3—64no—
751C22×C3—64no—
752C22×C3—68no—
753C22×C3—62no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—68no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—68no—
763C22×C3—68no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—94no—
771C22×C3—122no—
772C22×C3—128no—
773C22×C3—128no—
774C22×C3—122no—
775C22×C3—122no—
776C22×C3—122no—
777C22×C3—122no—
778C22×C3—122no—
779C22×C3—128no—
780C22×C3—124no—
781C22×C3—124no—
782C22×C3—1832no—
783C22×C3—182no—
784C22×C3—182no—
785C22×C3—188no—
786C22×C3D3×D1212yes—
787C22×C3#380212yes—
788C22×C3D3×#6712yes—
789C22×C3C2×C3×D1212yes—
790C22×C3C3×D3×D412yes—
791C22×C3C3×D3×D412yes—
792C22×C3C3×D3×D412yes—
793C22×C3C3×D3×D412yes—
794C22×C3C2×C3×#6712yes—
795C22×C3C22×D3211yescharacteristic
796C22×C3C23×C3×D311yescharacteristic
797C22×C3C23×C3×D311yescharacteristic
798C2×D3—28no—
799C2×D3—28no—
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—34no—
808C2×D3—34no—
809C2×D3—44no—
810C2×D3—64no—
811C2×D3—632no—
812C2×D3—632no—
813C2×D3—68no—
814C2×D3—68no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—122no—
820C2×D3—128no—
821C2×D3—122no—
822C2×D3C2×C3×D1214yescomplemented
823C2×D3C2×C3×#6714yescomplemented
824C3×C4—24no—
825C3×C4—22no—
826C3×C4—22no—
827C3×C4—22no—
828C3×C4—42no—
829C3×C4—42no—
830C3×C4—44no—
831C3×C4—62no—
832C3×C4—62no—
833C3×C4—122no—
834C3×C4—182no—
835Dic3—22no—
836Dic3—62no—
837Dic3—62no—
838Dic3—122no—
839C32—21no—
840C32—21no—
841C32—21no—
842C32—41no—
843C32C2×#88211yescharacteristic, complemented
844C32C2×#93711yescharacteristic, complemented
845C32C2×C3×#12011yescharacteristic, complemented
846C23—32no—
847C23—32no—
848C23—34no—
849C23—34no—
850C23—32no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—92no—
859C23—94no—
860C23—188no—
861C23—188no—
862C23—188no—
863C23—1832no—
864C23—182no—
865C23—182no—
866C23C2×C3×D3211yescharacteristic
867D4—68no—
868D4—188no—
869D4—188no—
870C2×C4—22no—
871C2×C4—32no—
872C2×C4—62no—
873C2×C4—92no—
874C2×C4—182no—
875C2×C4C2×C3×D3212yescomplemented
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—24no—
880C2×C3—24no—
881C2×C3—24no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—41no—
889C2×C3—44no—
890C2×C3—41no—
891C2×C3—41no—
892C2×C3—64no—
893C2×C3—64no—
894C2×C3—64no—
895C2×C3—64no—
896C2×C3—124no—
897C2×C3—124no—
898C2×C3—124no—
899C2×C3—122no—
900C2×C3—122no—
901C2×C3—184no—
902C2×C3#6392214yesdirect product factor
903C2×C3C3×#88214yescomplemented
904C2×C3C3×#93714yescomplemented
905C2×C3C2×D3×D1211yescharacteristic
906C2×C3C2×#380211yescharacteristic
907C2×C3C2×D3×#6711yescharacteristic
908C2×C3C22×C3×D1211yescharacteristic
909C2×C3C2×C3×D3×D411yescharacteristic
910C2×C3C2×C3×D3×D411yescharacteristic
911C2×C3C2×C3×D3×D411yescharacteristic
912C2×C3C2×C3×D3×D411yescharacteristic
913C2×C3C22×C3×#6711yescharacteristic
914D3—24no—
915D3—24no—
916D3—42no—
917D3—64no—
918D3—64no—
919D3—124no—
920C22—34no—
921C22—34no—
922C22—62no—
923C22—68no—
924C22—68no—
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—94no—
932C22—124no—
933C22—1832no—
934C22—182no—
935C22—188no—
936C22—182no—
937C22C3×D3×D1212yes—
938C22C3×#380212yes—
939C22C3×D3×#6712yes—
940C22C22×C3×D3211yescharacteristic
941C4—22no—
942C4—62no—
943C4—182no—
944C3—21no—
945C3—21no—
946C3—21no—
947C3—41no—
948C3C2×#6392211yescharacteristic, direct product factor
949C3C2×C3×#88211yescharacteristic, complemented
950C3C2×C3×#93711yescharacteristic, complemented
951C2—64no—
952C2—64no—
953C2—122no—
954C2—184no—
955C2C3×#6392214yesdirect product factor
956C2C2×C3×D3×D1211yescharacteristic
957C2C2×C3×#380211yescharacteristic
958C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×D32C2semidirect
2. C22×C32×D12C2semidirect
3. C22×C3×#626C2semidirect
4. C22×C3×#625C2semidirect
5. C2×C3×#3752C2semidirect
6. C2×C32×(C2×D3)⋊C4C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. C3×#63922C2direct (N × H)
11. C2×#63922C3direct (N × H)
15. C23×C32×D3C22semidirect
19. C22×C3×D32C22semidirect
20. C22×C33×C4C22semidirect
21. C22×C3×C3⋊Dic3C22semidirect
22. C22×C32×Dic3C22semidirect
24. C2×C32×D12C22semidirect
26. C2×C3×#626C22semidirect
28. C2×C3×#625C22semidirect
29. C3×#3752C22semidirect
30. C32×(C2×D3)⋊C4C22semidirect
31. C3×(C2×D3)⋊Dic3C22semidirect
34. C23×D32C2×C3semidirect
41. C22×C3×D12D3semidirect
42. C22×C3×D12C2×C3semidirect
43. C22×#626C2×C3semidirect
44. C22×#625C2×C3semidirect
46. C2×#3752C2×C3semidirect
54. C2×C3×(C2×D3)⋊C4D3semidirect
55. C2×C3×(C2×D3)⋊C4C2×C3semidirect
57. C2×(C2×D3)⋊Dic3C2×C3semidirect
58. #63922C2×C3direct (N × H)
62. C22×C3×C3⋊D3D4semidirect
71. C22×C32×D3D4semidirect
72. C22×C32×D3D4semidirect
75. C22×C32×D3C23semidirect
81. C2×C33×C4C23semidirect
83. C2×C3×C3⋊Dic3C23semidirect
85. C2×C32×Dic3C23semidirect
112. C23×C3×D3C2×D3semidirect
115. C23×C3×D3C22×C3semidirect
119. C22×D32C22×C3semidirect
127. C22×C32×C4C2×D3semidirect
128. C22×C32×C4C2×D3semidirect
129. C22×C32×C4C22×C3semidirect
130. C22×C3⋊Dic3C22×C3semidirect
141. C22×C3×Dic3C2×D3semidirect
142. C22×C3×Dic3C22×C3semidirect
149. C2×C3×D12C2×D3semidirect
150. C2×C3×D12C22×C3semidirect
152. C2×#626C22×C3semidirect
154. C2×#625C22×C3semidirect
156. #3752C22×C3semidirect
163. C3×(C2×D3)⋊C4C2×D3semidirect
164. C3×(C2×D3)⋊C4C22×C3semidirect
165. (C2×D3)⋊Dic3C22×C3semidirect
173. C2×C3×C3⋊D3C2×D4semidirect
184. C2×C32×D3C2×D4semidirect
185. C2×C32×D3C2×D4semidirect
202. C22×D12C3×D3semidirect
215. C2×(C2×D3)⋊C4C3×D3semidirect
238. C22×C3⋊D3C3×D4semidirect
286. C22×C3×D3D12semidirect
287. C22×C3×D3#67semidirect
288. C22×C3×D3C3×D4semidirect
289. C22×C3×D3C3×D4semidirect
292. C22×C3×D3C22×D3semidirect
295. C22×C3×D3C23×C3semidirect
314. C2×C32×C4C22×D3semidirect
315. C2×C32×C4C22×D3semidirect
316. C2×C32×C4C23×C3semidirect
318. C2×C3⋊Dic3C23×C3semidirect
332. C2×C3×Dic3C22×D3semidirect
333. C2×C3×Dic3C23×C3semidirect
341. C2×C33#120semidirect
376. C23×D3C2×C3×D3semidirect
395. C22×C3×C4D32semidirect
396. C22×C3×C4C2×C3×D3semidirect
397. C22×C3×C4C2×C3×D3semidirect
407. C22×Dic3C2×C3×D3semidirect
411. C2×D12C2×C3×D3semidirect
422. (C2×D3)⋊C4C2×C3×D3semidirect
466. C2×C3⋊D3C2×C3×D4semidirect
513. C2×C3×D3C2×D12semidirect
514. C2×C3×D3C2×#67semidirect
515. C2×C3×D3C2×C3×D4semidirect
516. C2×C3×D3C2×C3×D4semidirect
541. C33C2×#120semidirect
620. C22×D3C3×D12semidirect
621. C22×D3C3×#67semidirect
624. C22×D3C22×C3×D3semidirect
649. C2×C3×C4C2×D32semidirect
650. C2×C3×C4C22×C3×D3semidirect
651. C2×C3×C4C22×C3×D3semidirect
662. C2×Dic3C22×C3×D3semidirect
684. C2×C32#882semidirect
685. C2×C32#937semidirect
686. C2×C32C3×#120semidirect
725. C22×C4C3×D32semidirect
822. C2×D3C2×C3×D12semidirect
823. C2×D3C2×C3×#67semidirect
843. C32C2×#882semidirect
844. C32C2×#937semidirect
845. C32C2×C3×#120semidirect
875. C2×C4C2×C3×D32semidirect
902. C2×C3#63922direct (N × H)
903. C2×C3C3×#882semidirect
904. C2×C3C3×#937semidirect
948. C3C2×#63922direct (N × H)
949. C3C2×C3×#882semidirect
950. C3C2×C3×#937semidirect
955. C2C3×#63922direct (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×C32×D122
C22×C3×#6262
C22×C3×#6252
C2×C3×#37522
C2×C32×(C2×D3)⋊C42
C2×C3×(C2×D3)⋊Dic32
C3×#639222
C2×C3×#9373
C2×C3×#8823
C2×#639223