Finite Group Databasebeta

← C2×C3×D3×#208 #13174408

Subgroups — C2×C3×D3×#208 #13174408

Order 1728.

1618 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic
2C2×C3×#3748C211yesmaximal, characteristic, complemented
3C2×C32×#208C211yesmaximal, characteristic, complemented
4C2×C3×#3711C212yesmaximal, complemented
5C3×D3×#208C218yesmaximal, direct product factor
6C2×C3×D3×C3⋊C8C212yesmaximal, complemented
7C22×C3×#208—31nomaximal
8C2×C3×D3×M16—31nomaximal
9C2×D3×#208C311yesmaximal, characteristic, direct product factor
10C23×C32×D3C411yescharacteristic
11C22×C33×C4C2211yescharacteristic
12C22×C32×Dic3C411yescharacteristic
13C2×C32×C4×D3C411yescharacteristic
14C2×C32×C4×D3C414yes—
15C2×C32×C4×D3C411yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×C4×D3C2214yes—
18C2×C32×C4×D3C2211yescharacteristic
19C3×#3748C2214yescomplemented
20C2×C3×C3⋊(C3⋊C8)C2212yescomplemented
21C32×#208C2214yescomplemented
22C2×C32×C3⋊C8C2212yescomplemented
23C3×#3711C2218yescomplemented
24C3×D3×C3⋊C8C2218yescomplemented
25C23×C32×C4—31no—
26C22×C3×C4×D3—21no—
27C22×C3×C4×D3D311yescharacteristic
28C22×C3×C4×D3C2×C311yescharacteristic
29C2×C32×M16—31no—
30C2×#3748C2×C311yescharacteristic, complemented
31C2×C3×#208—21no—
32C2×C3×#208—31no—
33C2×C3×#208—31no—
34C2×C3×#208—38no—
35C2×C3×#208—32no—
36C2×C3×#208—61no—
37C2×C3×#208D311yescharacteristic, direct product factor
38C2×C3×#208C2×C311yescharacteristic, complemented
39C22×C3×C3⋊C8—32no—
40C3×D3×M16—38no—
41C2×C3×ΓL(1,𝔽25)—32no—
42C2×C3×D3×C8—32no—
43C2×#3711C2×C312yescomplemented
44D3×#208C2×C318yesdirect product factor
45C2×D3×C3⋊C8C2×C312yescomplemented
46C23×C33C2×C411yescharacteristic
47C22×C32×D3—24no—
48C22×C32×D3C2×C411yescharacteristic
49C22×C32×D3C2×C414yes—
50C22×C32×D3C2×C411yescharacteristic
51C2×C33×C4C2×C412yes—
52C2×C33×C4C2×C411yescharacteristic
53C2×C33×C4C2311yescharacteristic
54C2×C33×C4C2312yes—
55C2×C32×Dic3C2×C414yes—
56C2×C32×Dic3C2×C411yescharacteristic
57C2×C32×Dic3C2×C411yescharacteristic
58C32×C4×D3C2×C414yes—
59C32×C4×D3C2×C412yes—
60C32×C4×D3C2×C412yes—
61C32×C4×D3C2×C414yes—
62C32×C4×D3C2312yes—
63C32×C4×D3C2312yes—
64C3×C3⋊(C3⋊C8)C2314yescomplemented
65C32×C3⋊C8C2314yescomplemented
66C22×C3×M16—91no—
67C22×#208—31no—
68C2×D3×M16—31no—
69C24×C32—31no—
70C23×C3×D3—21no—
71C23×C3×D3Dic311yescharacteristic
72C23×C3×D3C3×C411yescharacteristic
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4—31no—
77C22×C32×C4—31no—
78C22×C32×C4—34no—
79C22×C32×C4—31no—
80C22×C32×C4—31no—
81C22×C32×C4—34no—
82C22×C32×C4—31no—
83C22×C32×C4—41no—
84C22×C32×C4C2×D311yescharacteristic
85C22×C32×C4C2×D311yescharacteristic
86C22×C32×C4C22×C311yescharacteristic
87C22×C3×Dic3—21no—
88C22×C3×Dic3Dic311yescharacteristic
89C22×C3×Dic3C3×C411yescharacteristic
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—21no—
92C2×C3×C4×D3—21no—
93C2×C3×C4×D3—21no—
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3Dic314yes—
97C2×C3×C4×D3Dic311yescharacteristic
98C2×C3×C4×D3Dic311yescharacteristic
99C2×C3×C4×D3C3×C411yescharacteristic
100C2×C3×C4×D3C3×C414yes—
101C2×C3×C4×D3C3×C411yescharacteristic
102C2×C3×C4×D3C2×D311yescharacteristic
103C2×C3×C4×D3C2×D311yescharacteristic
104C2×C3×C4×D3C2×D314yes—
105C2×C3×C4×D3C22×C311yescharacteristic
106C2×C3×C4×D3C22×C314yes—
107C2×C3×C4×D3C22×C311yescharacteristic
108C32×M16—34no—
109C2×C32×C8—32no—
110#3748C22×C314yescomplemented
111C2×C3⋊(C3⋊C8)C22×C312yescomplemented
112C3×#208—24no—
113C3×#208—34no—
114C3×#208—34no—
115C3×#208—38no—
116C3×#208—64no—
117C3×#208C2×D314yesdirect product factor
118C3×#208C22×C314yescomplemented
119C2×C3×C3⋊C8—22no—
120C2×C3×C3⋊C8—32no—
121C2×C3×C3⋊C8—32no—
122C2×C3×C3⋊C8—38no—
123C2×C3×C3⋊C8—62no—
124C2×C3×C3⋊C8C2×D312yescomplemented
125C2×C3×C3⋊C8C22×C312yescomplemented
126C3×ΓL(1,𝔽25)—38no—
127C3×D3×C8—38no—
128#3711C22×C318yescomplemented
129D3×C3⋊C8C22×C318yescomplemented
130C22×C33—22no—
131C22×C33C22×C412yes—
132C22×C33C22×C411yescharacteristic
133C2×C32×D3—22no—
134C2×C32×D3—28no—
135C2×C32×D3M1614yescomplemented
136C2×C32×D3C22×C412yes—
137C2×C32×D3C22×C412yes—
138C33×C4C22×C411yescharacteristic
139C33×C4C22×C412yes—
140C33×C4C2411yescharacteristic
141C32×Dic3C22×C412yes—
142C32×Dic3C22×C412yes—
143C23×C3×C4—31no—
144C23×C3×C4—31no—
145C23×C3×C4—61no—
146C22×C4×D3C3×D311yescharacteristic
147C2×C3×M16—31no—
148C2×C3×M16—31no—
149C2×C3×M16—61no—
150C2×C3×M16—92no—
151C2×C3×M16—98no—
152C2×C3×M16—91no—
153C22×C3×C8—92no—
154C2×#208—31no—
155C2×#208—31no—
156C2×#208—38no—
157C2×#208—32no—
158C2×#208—61no—
159C2×#208C3×D311yescharacteristic, direct product factor
160C22×C3⋊C8—32no—
161D3×M16—38no—
162C2×ΓL(1,𝔽25)—32no—
163C2×D3×C8—32no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—31no—
168C23×C32—34no—
169C23×C32—31no—
170C23×C32—41no—
171C23×C32—64no—
172C23×C32C4×D311yescharacteristic
173C23×C32C2×Dic311yescharacteristic
174C23×C32C2×C3×C411yescharacteristic
175C22×C3×D3—28no—
176C22×C3×D3—24no—
177C22×C3×D3—24no—
178C22×C3×D3—21no—
179C22×C3×D3—24no—
180C22×C3×D3—21no—
181C22×C3×D3C2×Dic311yescharacteristic
182C22×C3×D3C2×Dic314yes—
183C22×C3×D3C2×Dic311yescharacteristic
184C22×C3×D3C2×C3×C411yescharacteristic
185C22×C3×D3C2×C3×C414yes—
186C22×C3×D3C2×C3×C411yescharacteristic
187C2×C32×C4—21no—
188C2×C32×C4—22no—
189C2×C32×C4—21no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4—21no—
193C2×C32×C4—22no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—22no—
197C2×C32×C4—21no—
198C2×C32×C4—22no—
199C2×C32×C4—34no—
200C2×C32×C4—31no—
201C2×C32×C4—31no—
202C2×C32×C4—32no—
203C2×C32×C4—34no—
204C2×C32×C4—34no—
205C2×C32×C4—32no—
206C2×C32×C4—32no—
207C2×C32×C4—32no—
208C2×C32×C4—41no—
209C2×C32×C4—42no—
210C2×C32×C4—41no—
211C2×C32×C4—42no—
212C2×C32×C4C4×D312yes—
213C2×C32×C4C4×D311yescharacteristic
214C2×C32×C4C2×Dic312yes—
215C2×C32×C4C2×Dic311yescharacteristic
216C2×C32×C4C2×C3×C412yes—
217C2×C32×C4C2×C3×C411yescharacteristic
218C2×C32×C4C22×D312yes—
219C2×C32×C4C22×D312yes—
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C23×C311yescharacteristic
223C2×C32×C4C23×C312yes—
224C2×C3×Dic3—24no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3C2×Dic314yes—
228C2×C3×Dic3C2×Dic311yescharacteristic
229C2×C3×Dic3C2×Dic311yescharacteristic
230C2×C3×Dic3C2×C3×C414yes—
231C2×C3×Dic3C2×C3×C411yescharacteristic
232C2×C3×Dic3C2×C3×C411yescharacteristic
233C3×C4×D3—22no—
234C3×C4×D3—24no—
235C3×C4×D3—22no—
236C3×C4×D3—24no—
237C3×C4×D3—22no—
238C3×C4×D3—22no—
239C3×C4×D3C2×Dic312yes—
240C3×C4×D3C2×Dic314yes—
241C3×C4×D3C2×Dic312yes—
242C3×C4×D3C2×Dic314yes—
243C3×C4×D3C2×C3×C414yes—
244C3×C4×D3C2×C3×C412yes—
245C3×C4×D3C2×C3×C412yes—
246C3×C4×D3C2×C3×C414yes—
247C3×C4×D3C22×D312yes—
248C3×C4×D3C22×D312yes—
249C3×C4×D3C23×C312yes—
250C3×C4×D3C23×C312yes—
251C32×C8—34no—
252C3⋊(C3⋊C8)C23×C314yescomplemented
253C3×C3⋊C8—24no—
254C3×C3⋊C8—34no—
255C3×C3⋊C8—34no—
256C3×C3⋊C8—64no—
257C3×C3⋊C8C22×D314yescomplemented
258C3×C3⋊C8C23×C314yescomplemented
259C22×M16—91noSylow
260C2×C33—22no—
261C2×C33C2×M1612yescomplemented
262C2×C33C23×C411yescharacteristic
263C32×D3—22no—
264C32×D3C2×M1614yescomplemented
265C24×C3—31no—
266C24×C3—31no—
267C24×C3—61no—
268C23×D3C3×Dic311yescharacteristic
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—34no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—34no—
279C22×C3×C4—31no—
280C22×C3×C4—34no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—34no—
285C22×C3×C4—31no—
286C22×C3×C4—41no—
287C22×C3×C4—61no—
288C22×C3×C4—64no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C22×C3×C4—64no—
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C22×C3×C4D3211yescharacteristic
295C22×C3×C4C2×C3×D311yescharacteristic
296C22×C3×C4C2×C3×D311yescharacteristic
297C22×Dic3C3×Dic311yescharacteristic
298C2×C4×D3C3×Dic314yes—
299C2×C4×D3C3×Dic311yescharacteristic
300C2×C4×D3C3×Dic311yescharacteristic
301C2×C4×D3C2×C3×D311yescharacteristic
302C2×C4×D3C2×C3×D311yescharacteristic
303C2×C4×D3C2×C3×D314yes—
304C3×M16—34no—
305C3×M16—34no—
306C3×M16—64no—
307C3×M16—98no—
308C3×M16—94no—
309C2×C3×C8—32no—
310C2×C3×C8—32no—
311C2×C3×C8—62no—
312C2×C3×C8—98no—
313C2×C3×C8—92no—
314#208—34no—
315#208—34no—
316#208—38no—
317#208—64no—
318#208C2×C3×D314yesdirect product factor
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—38no—
322C2×C3⋊C8—62no—
323C2×C3⋊C8C2×C3×D312yescomplemented
324ΓL(1,𝔽25)—38no—
325D3×C8—38no—
326C22×C32—22no—
327C22×C32—24no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—21no—
331C22×C32—22no—
332C22×C32—21no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—21no—
336C22×C32—34no—
337C22×C32—32no—
338C22×C32—32no—
339C22×C32—41no—
340C22×C32—42no—
341C22×C32—42no—
342C22×C32—42no—
343C22×C32—44no—
344C22×C32—68no—
345C22×C32—62no—
346C22×C32C2×C4×D312yes—
347C22×C32C2×C4×D311yescharacteristic
348C22×C32C22×Dic312yes—
349C22×C32C22×Dic311yescharacteristic
350C22×C32C22×C3×C412yes—
351C22×C32C22×C3×C411yescharacteristic
352C2×C3×D3—24no—
353C2×C3×D3—216no—
354C2×C3×D3—22no—
355C2×C3×D3—22no—
356C2×C3×D3—28no—
357C2×C3×D3—28no—
358C2×C3×D3—24no—
359C2×C3×D3—22no—
360C2×C3×D3—22no—
361C2×C3×D3#20814yesdirect product factor
362C2×C3×D3C3×M1614yescomplemented
363C2×C3×D3C22×Dic312yes—
364C2×C3×D3C22×Dic312yes—
365C2×C3×D3C22×C3×C412yes—
366C2×C3×D3C22×C3×C412yes—
367C32×C4—21no—
368C32×C4—21no—
369C32×C4—21no—
370C32×C4—22no—
371C32×C4—21no—
372C32×C4—21no—
373C32×C4—22no—
374C32×C4—21no—
375C32×C4—22no—
376C32×C4—32no—
377C32×C4—32no—
378C32×C4—41no—
379C32×C4—42no—
380C32×C4—41no—
381C32×C4C2×C4×D312yes—
382C32×C4C2×C4×D311yescharacteristic
383C32×C4C22×Dic312yes—
384C32×C4C22×Dic311yescharacteristic
385C32×C4C22×C3×C411yescharacteristic
386C32×C4C22×C3×C412yes—
387C32×C4C23×D311yescharacteristic
388C32×C4C23×D311yescharacteristic
389C32×C4C24×C311yescharacteristic
390C3×Dic3—22no—
391C3×Dic3—22no—
392C3×Dic3C22×Dic312yes—
393C3×Dic3C22×Dic312yes—
394C3×Dic3C22×C3×C412yes—
395C3×Dic3C22×C3×C412yes—
396C23×C4—31no—
397C2×M16—31no—
398C2×M16—92no—
399C2×M16—98no—
400C2×M16—91no—
401C22×C8—92no—
402C33C22×M1611yescharacteristic, complemented, Sylow
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—31no—
407C23×C3—31no—
408C23×C3—34no—
409C23×C3—31no—
410C23×C3—34no—
411C23×C3—31no—
412C23×C3—41no—
413C23×C3—61no—
414C23×C3—64no—
415C23×C3—61no—
416C23×C3—64no—
417C23×C3—64no—
418C23×C3—68no—
419C23×C3D3×Dic311yescharacteristic
420C23×C3C3×C4×D311yescharacteristic
421C23×C3C2×C3×Dic311yescharacteristic
422C22×D3—24no—
423C22×D3C2×C3×Dic311yescharacteristic
424C22×D3C2×C3×Dic314yes—
425C22×D3C2×C3×Dic311yescharacteristic
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—34no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—34no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—32no—
445C2×C3×C4—32no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—34no—
449C2×C3×C4—34no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—34no—
454C2×C3×C4—34no—
455C2×C3×C4—32no—
456C2×C3×C4—42no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—42no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—64no—
464C2×C3×C4—64no—
465C2×C3×C4—62no—
466C2×C3×C4—64no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4D3×Dic311yescharacteristic
470C2×C3×C4D3×Dic312yes—
471C2×C3×C4C3×C4×D312yes—
472C2×C3×C4C3×C4×D311yescharacteristic
473C2×C3×C4C2×C3×Dic312yes—
474C2×C3×C4C2×C3×Dic311yescharacteristic
475C2×C3×C4C2×D3212yes—
476C2×C3×C4C2×D3211yescharacteristic
477C2×C3×C4C22×C3×D311yescharacteristic
478C2×C3×C4C22×C3×D312yes—
479C2×C3×C4C22×C3×D311yescharacteristic
480C2×C3×C4C22×C3×D312yes—
481C2×Dic3C2×C3×Dic314yes—
482C2×Dic3C2×C3×Dic311yescharacteristic
483C2×Dic3C2×C3×Dic311yescharacteristic
484C4×D3C2×C3×Dic312yes—
485C4×D3C2×C3×Dic314yes—
486C4×D3C2×C3×Dic312yes—
487C4×D3C2×C3×Dic314yes—
488C4×D3C22×C3×D312yes—
489C4×D3C22×C3×D312yes—
490C3×C8—34no—
491C3×C8—34no—
492C3×C8—64no—
493C3×C8—94no—
494C3⋊C8—34no—
495C3⋊C8—34no—
496C3⋊C8—64no—
497C3⋊C8C22×C3×D314yescomplemented
498C2×C32—22no—
499C2×C32—24no—
500C2×C32—22no—
501C2×C32—22no—
502C2×C32—22no—
503C2×C32—22no—
504C2×C32—21no—
505C2×C32—22no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—34no—
509C2×C32—42no—
510C2×C32—41no—
511C2×C32—42no—
512C2×C32—42no—
513C2×C32—44no—
514C2×C32—62no—
515C2×C32D3×M1612yescomplemented
516C2×C32C2×#20812yescomplemented
517C2×C32C2×C3×M1612yescomplemented
518C2×C32C22×C4×D311yescharacteristic
519C2×C32C23×Dic311yescharacteristic
520C2×C32C23×C3×C411yescharacteristic
521C3×D3—24no—
522C3×D3—22no—
523C3×D3—22no—
524C3×D3—24no—
525C3×D3C2×#20814yesdirect product factor
526C3×D3C2×C3×M1614yescomplemented
527C24—31no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—34no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—34no—
534C22×C4—31no—
535C22×C4C3×D3211yescharacteristic
536M16—34no—
537M16—98no—
538M16—94no—
539C2×C8—32no—
540C2×C8—98no—
541C2×C8—92no—
542C22×C3—24no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—34no—
553C22×C3—32no—
554C22×C3—34no—
555C22×C3—32no—
556C22×C3—32no—
557C22×C3—32no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—44no—
561C22×C3—42no—
562C22×C3—41no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—64no—
566C22×C3—68no—
567C22×C3—68no—
568C22×C3—616no—
569C22×C3—64no—
570C22×C3—62no—
571C22×C3—62no—
572C22×C3C2×D3×Dic312yes—
573C22×C3C2×D3×Dic311yescharacteristic
574C22×C3C2×C3×C4×D312yes—
575C22×C3C2×C3×C4×D311yescharacteristic
576C22×C3C22×C3×Dic312yes—
577C22×C3C22×C3×Dic311yescharacteristic
578C2×D3—22no—
579C2×D3—28no—
580C2×D3C3×#20814yesdirect product factor
581C2×D3C22×C3×Dic312yes—
582C2×D3C22×C3×Dic312yes—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—22no—
588C3×C4—21no—
589C3×C4—22no—
590C3×C4—21no—
591C3×C4—22no—
592C3×C4—32no—
593C3×C4—32no—
594C3×C4—32no—
595C3×C4—32no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—42no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4C2×D3×Dic312yes—
602C3×C4C2×D3×Dic311yescharacteristic
603C3×C4C2×C3×C4×D311yescharacteristic
604C3×C4C2×C3×C4×D312yes—
605C3×C4C22×C3×Dic311yescharacteristic
606C3×C4C22×C3×Dic312yes—
607C3×C4C22×D3211yescharacteristic
608C3×C4C23×C3×D311yescharacteristic
609C3×C4C23×C3×D311yescharacteristic
610Dic3C22×C3×Dic312yes—
611Dic3C22×C3×Dic312yes—
612C32—21no—
613C32—21no—
614C32—21no—
615C32—41no—
616C32C2×D3×M1611yescharacteristic, complemented
617C32C22×#20811yescharacteristic, complemented
618C32C22×C3×M1611yescharacteristic, complemented
619C23—31no—
620C23—34no—
621C23—31no—
622C23—64no—
623C23C3×D3×Dic311yescharacteristic
624C2×C4—34no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—34no—
631C2×C4—34no—
632C2×C4—32no—
633C2×C4C3×D3×Dic312yes—
634C2×C4C3×D3×Dic311yescharacteristic
635C2×C4C2×C3×D3211yescharacteristic
636C2×C4C2×C3×D3212yes—
637C8—34no—
638C8—94no—
639C2×C3—24no—
640C2×C3—22no—
641C2×C3—22no—
642C2×C3—22no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—22no—
647C2×C3—22no—
648C2×C3—22no—
649C2×C3—34no—
650C2×C3—34no—
651C2×C3—42no—
652C2×C3—42no—
653C2×C3—44no—
654C2×C3—41no—
655C2×C3—42no—
656C2×C3—64no—
657C2×C3—64no—
658C2×C3—62no—
659C2×C3—62no—
660C2×C3D3×#20812yesdirect product factor
661C2×C3C3×D3×M1612yescomplemented
662C2×C3C2×C3×#20812yescomplemented
663C2×C3C22×D3×Dic311yescharacteristic
664C2×C3C22×C3×C4×D311yescharacteristic
665C2×C3C23×C3×Dic311yescharacteristic
666D3—22no—
667D3C2×C3×#20814yesdirect product factor
668C22—22no—
669C22—32no—
670C22—34no—
671C22—32no—
672C22—68no—
673C22—62no—
674C22C2×C3×D3×Dic312yes—
675C22C2×C3×D3×Dic311yescharacteristic
676C4—32no—
677C4—32no—
678C4C2×C3×D3×Dic311yescharacteristic
679C4C2×C3×D3×Dic312yes—
680C4C22×C3×D3211yescharacteristic
681C3—21no—
682C3—21no—
683C3—21no—
684C3—41no—
685C3C2×D3×#20811yescharacteristic, direct product factor
686C3C2×C3×D3×M1611yescharacteristic, complemented
687C3C22×C3×#20811yescharacteristic, complemented
688C2—22no—
689C2—34no—
690C2—62no—
691C2C3×D3×#20812yesdirect product factor
692C2C22×C3×D3×Dic311yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC4C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C22×C4
prime radicalC23×C32×D3C4
cosocleC32×C4C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C22×C3×M16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3748C2semidirect
3. C2×C32×#208C2semidirect
4. C2×C3×#3711C2semidirect
5. C3×D3×#208C2direct (N × H)
6. C2×C3×D3×C3⋊C8C2semidirect
9. C2×D3×#208C3direct (N × H)
19. C3×#3748C22semidirect
20. C2×C3×C3⋊(C3⋊C8)C22semidirect
21. C32×#208C22semidirect
22. C2×C32×C3⋊C8C22semidirect
23. C3×#3711C22semidirect
24. C3×D3×C3⋊C8C22semidirect
30. C2×#3748C2×C3semidirect
37. C2×C3×#208D3direct (N × H)
38. C2×C3×#208C2×C3semidirect
43. C2×#3711C2×C3semidirect
44. D3×#208C2×C3direct (N × H)
45. C2×D3×C3⋊C8C2×C3semidirect
64. C3×C3⋊(C3⋊C8)C23semidirect
65. C32×C3⋊C8C23semidirect
110. #3748C22×C3semidirect
111. C2×C3⋊(C3⋊C8)C22×C3semidirect
117. C3×#208C2×D3direct (N × H)
118. C3×#208C22×C3semidirect
124. C2×C3×C3⋊C8C2×D3semidirect
125. C2×C3×C3⋊C8C22×C3semidirect
128. #3711C22×C3semidirect
129. D3×C3⋊C8C22×C3semidirect
135. C2×C32×D3M16semidirect
159. C2×#208C3×D3direct (N × H)
252. C3⋊(C3⋊C8)C23×C3semidirect
257. C3×C3⋊C8C22×D3semidirect
258. C3×C3⋊C8C23×C3semidirect
261. C2×C33C2×M16semidirect
264. C32×D3C2×M16semidirect
318. #208C2×C3×D3direct (N × H)
323. C2×C3⋊C8C2×C3×D3semidirect
361. C2×C3×D3#208direct (N × H)
362. C2×C3×D3C3×M16semidirect
402. C33C22×M16semidirect
497. C3⋊C8C22×C3×D3semidirect
515. C2×C32D3×M16semidirect
516. C2×C32C2×#208semidirect
517. C2×C32C2×C3×M16semidirect
525. C3×D3C2×#208direct (N × H)
526. C3×D3C2×C3×M16semidirect
580. C2×D3C3×#208direct (N × H)
616. C32C2×D3×M16semidirect
617. C32C22×#208semidirect
618. C32C22×C3×M16semidirect
660. C2×C3D3×#208direct (N × H)
661. C2×C3C3×D3×M16semidirect
662. C2×C3C2×C3×#208semidirect
667. D3C2×C3×#208direct (N × H)
685. C3C2×D3×#208direct (N × H)
686. C3C2×C3×D3×M16semidirect
687. C3C22×C3×#208semidirect
691. C2C3×D3×#208direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C2×C3×#37482
C2×C32×#2082
C2×C3×#37112
C3×D3×#2082
C2×C3×D3×C3⋊C82
C22×C3×#2083
C2×C3×D3×M163
C2×D3×#2083