Finite Group Databasebeta

← C2×C3×#63851 #13174633

Subgroups — C2×C3×#63851 #13174633

Order 1728.

1762 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic
2C22×C3×#627C211yesmaximal, characteristic, complemented
3C2×C3×#3750C211yesmaximal, characteristic, complemented
4C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
8C3×#63851C218yesmaximal, direct product factor
9C2×C3×#924—31nomaximal
10C2×C3×#896—31nomaximal
11C2×#63851C311yesmaximal, characteristic, direct product factor
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×C32×C4×D3—24no—
20C2×C32×C4×D3C2214yes—
21C2×C3×#627—24no—
22C2×C3×#627C2214yescomplemented
23C3×#3750C2214yescomplemented
24C32×Dic3⋊C4C2214yescomplemented
25C3×Dic3⋊Dic3C2214yescomplemented
26C3×(C2×D3)⋊Dic3C2214yes—
27C3×(C2×D3)⋊Dic3C2214yes—
28C23×C32×C4—31no—
29C22×C3×C4×D3—21no—
30C22×C3×C4×D3D311yescharacteristic
31C22×C3×C4×D3C2×C311yescharacteristic
32C22×C3×Dic6—31no—
33C22×C3×Dic6—31no—
34C22×#627C2×C311yescharacteristic, complemented
35C2×C32×C4⋊C4—31no—
36C2×#3750C2×C311yescharacteristic, complemented
37C2×C3×#217—31no—
38C2×C3×#217—31no—
39C2×C3×(C2×D3)⋊C4—31no—
40C2×C3×(C2×D3)⋊C4—31no—
41C2×C3×C4⋊Dic3—31no—
42C3×#924—38no—
43C2×C3×Dic3⋊C4—21no—
44C2×C3×Dic3⋊C4—31no—
45C2×C3×Dic3⋊C4—31no—
46C2×C3×Dic3⋊C4—31no—
47C2×C3×Dic3⋊C4—61no—
48C2×C3×Dic3⋊C4D311yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2×C311yescharacteristic, complemented
50C3×#896—38no—
51C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
52C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
53C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
54#63851C2×C318yesdirect product factor
55C23×C33C2311yescharacteristic
56C22×C32×D3—22no—
57C22×C32×D3—22no—
58C22×C32×D3Q814yescomplemented
59C22×C32×D3C2312yes—
60C2×C33×C4—22no—
61C2×C33×C4C2312yes—
62C2×C3×C3⋊Dic3—22no—
63C2×C3×C3⋊Dic3—22no—
64C2×C3×C3⋊Dic3C2312yes—
65C2×C3×C3⋊Dic3C2312yes—
66C2×C32×Dic3—22no—
67C2×C32×Dic3—22no—
68C2×C32×Dic3D414yes—
69C2×C32×Dic3C2312yes—
70C2×C32×Dic3C2312yes—
71C2×C32×Dic3C2312yes—
72C32×C4×D3—28no—
73C3×#627—28no—
74C2×C3×C22⋊Q8—91no—
75C2×#924—31no—
76C2×#896—31no—
77C24×C32—31no—
78C23×C3×D3—21no—
79C23×C3×D3C2×D311yescharacteristic
80C23×C3×D3C22×C311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4—21no—
84C22×C32×C4—31no—
85C22×C32×C4—31no—
86C22×C32×C4—31no—
87C22×C32×C4—34no—
88C22×C32×C4—41no—
89C22×C32×C4—64no—
90C22×C32×C4C2×D311yescharacteristic
91C22×C32×C4C2×D311yescharacteristic
92C22×C32×C4C22×C311yescharacteristic
93C22×C3⋊Dic3C22×C311yescharacteristic
94C22×C3⋊Dic3C22×C311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—61no—
103C22×C3×Dic3—61no—
104C22×C3×Dic3C2×D311yescharacteristic
105C22×C3×Dic3C2×D311yescharacteristic
106C22×C3×Dic3C2×D311yescharacteristic
107C22×C3×Dic3C22×C311yescharacteristic
108C22×C3×Dic3C22×C311yescharacteristic
109C22×C3×Dic3C22×C311yescharacteristic
110C2×C3×C4×D3—28no—
111C2×C3×C4×D3—24no—
112C2×C3×C4×D3—24no—
113C2×C3×C4×D3—24no—
114C2×C3×C4×D3C2×D314yes—
115C2×C3×C4×D3C22×C314yes—
116C2×C3×Dic6—34no—
117C2×C3×Dic6—34no—
118C2×C3×Dic6—64no—
119C2×C3×Dic6—64no—
120C2×#627—24no—
121C2×#627C22×C314yescomplemented
122C32×C4⋊C4—34no—
123#3750C22×C314yescomplemented
124C3×#217—34no—
125C3×#217—34no—
126C3×(C2×D3)⋊C4—34no—
127C3×(C2×D3)⋊C4—34no—
128C3×C4⋊Dic3—34no—
129C3×Dic3⋊C4—24no—
130C3×Dic3⋊C4—34no—
131C3×Dic3⋊C4—34no—
132C3×Dic3⋊C4—34no—
133C3×Dic3⋊C4—64no—
134C3×Dic3⋊C4C2×D314yescomplemented
135C3×Dic3⋊C4C22×C314yescomplemented
136Dic3⋊Dic3C22×C314yescomplemented
137(C2×D3)⋊Dic3C22×C314yes—
138(C2×D3)⋊Dic3C22×C314yes—
139C22×C33C2×D412yes—
140C22×C33C2×Q812yes—
141C22×C33#4112yes—
142C22×C33C2411yescharacteristic
143C2×C32×D3—28no—
144C2×C32×D3—22no—
145C2×C32×D3—22no—
146C2×C32×D3C2×Q814yescomplemented
147C33×C4—22no—
148C3×C3⋊Dic3—22no—
149C3×C3⋊Dic3—22no—
150C32×Dic3—22no—
151C32×Dic3—22no—
152C32×Dic3C2×D414yes—
153C22×C3×Q8—91no—
154C23×C3×C4—31no—
155C23×C3×C4—31no—
156C23×C3×C4—61no—
157C22×C4×D3C3×D311yescharacteristic
158C22×Dic6—31no—
159C22×Dic6—31no—
160C3×C22⋊Q8—98no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—61no—
164C2×C3×C4⋊C4—91no—
165C2×C3×C4⋊C4—91no—
166C2×C3×C22⋊C4—91no—
167C2×C3×C22⋊C4—91no—
168C2×#217—31no—
169C2×#217—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×C4⋊Dic3—31no—
173#924—38no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—61no—
178C2×Dic3⋊C4C3×D311yescharacteristic, complemented
179#896—38no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—34no—
184C23×C32—32no—
185C23×C32—41no—
186C23×C32—62no—
187C23×C32—62no—
188C23×C32C22×D311yescharacteristic
189C23×C32C22×D311yescharacteristic
190C23×C32C23×C311yescharacteristic
191C22×C3×D3—24no—
192C22×C3×D3—24no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3—24no—
198C22×C3×D3—22no—
199C22×C3×D3Dic614yescomplemented
200C22×C3×D3C3×Q814yescomplemented
201C22×C3×D3C22×D312yes—
202C22×C3×D3C23×C312yes—
203C2×C32×C4—22no—
204C2×C32×C4—24no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—34no—
211C2×C32×C4—32no—
212C2×C32×C4—32no—
213C2×C32×C4—32no—
214C2×C32×C4—42no—
215C2×C32×C4—42no—
216C2×C32×C4—42no—
217C2×C32×C4—44no—
218C2×C32×C4—68no—
219C2×C32×C4—62no—
220C2×C32×C4—62no—
221C2×C32×C4C22×D312yes—
222C2×C32×C4C22×D312yes—
223C2×C32×C4C23×C312yes—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3C23×C312yes—
227C2×C3⋊Dic3C23×C312yes—
228C2×C3×Dic3—24no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—32no—
238C2×C3×Dic3—32no—
239C2×C3×Dic3—32no—
240C2×C3×Dic3—32no—
241C2×C3×Dic3—42no—
242C2×C3×Dic3—62no—
243C2×C3×Dic3—62no—
244C2×C3×Dic3—64no—
245C2×C3×Dic3—62no—
246C2×C3×Dic3—62no—
247C2×C3×Dic3—62no—
248C2×C3×Dic3—62no—
249C2×C3×Dic3—122no—
250C2×C3×Dic3#6714yes—
251C2×C3×Dic3C3×D414yes—
252C2×C3×Dic3C22×D312yes—
253C2×C3×Dic3C22×D312yes—
254C2×C3×Dic3C22×D312yes—
255C2×C3×Dic3C23×C312yes—
256C2×C3×Dic3C23×C312yes—
257C2×C3×Dic3C23×C312yes—
258C3×C4×D3—216no—
259C3×C4×D3—28no—
260C3×C4×D3—28no—
261C3×Dic6—68no—
262C3×Dic6—68no—
263#627—28no—
264C2×C22⋊Q8—91noSylow
265C2×C33C22⋊Q814yescomplemented
266C2×C33C22×D411yescharacteristic
267C2×C33C22×Q811yescharacteristic
268C2×C33C2×#4111yescharacteristic
269C32×D3—24no—
270C24×C3—31no—
271C24×C3—31no—
272C24×C3—61no—
273C23×D3C2×C3×D311yescharacteristic
274C2×C3×Q8—94no—
275C2×C3×Q8—184no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—34no—
286C22×C3×C4—34no—
287C22×C3×C4—41no—
288C22×C3×C4—64no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C22×C3×C4—64no—
293C22×C3×C4—64no—
294C22×C3×C4—68no—
295C22×C3×C4—91no—
296C22×C3×C4—91no—
297C22×C3×C4D3211yescharacteristic
298C22×C3×C4C2×C3×D311yescharacteristic
299C22×C3×C4C2×C3×D311yescharacteristic
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3C2×C3×D311yescharacteristic
307C22×Dic3C2×C3×D311yescharacteristic
308C22×Dic3C2×C3×D311yescharacteristic
309C2×C4×D3—24no—
310C2×C4×D3C2×C3×D314yes—
311C2×Dic6—34no—
312C2×Dic6—34no—
313C2×Dic6—64no—
314C2×Dic6—64no—
315C3×C4⋊C4—34no—
316C3×C4⋊C4—34no—
317C3×C4⋊C4—64no—
318C3×C4⋊C4—94no—
319C3×C4⋊C4—94no—
320C3×C22⋊C4—94no—
321C3×C22⋊C4—94no—
322#217—34no—
323#217—34no—
324(C2×D3)⋊C4—34no—
325(C2×D3)⋊C4—34no—
326C4⋊Dic3—34no—
327Dic3⋊C4—34no—
328Dic3⋊C4—34no—
329Dic3⋊C4—34no—
330Dic3⋊C4—64no—
331Dic3⋊C4C2×C3×D314yescomplemented
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—22no—
336C22×C32—22no—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—34no—
345C22×C32—42no—
346C22×C32—42no—
347C22×C32—42no—
348C22×C32—41no—
349C22×C32—68no—
350C22×C32—62no—
351C22×C32—62no—
352C22×C32C2×Dic612yes—
353C22×C32#23512yes—
354C22×C32#23512yes—
355C22×C32D3×D412yes—
356C22×C32D3×Q812yes—
357C22×C32C2×#6712yes—
358C22×C32C2×C3×D412yes—
359C22×C32C2×C3×Q812yes—
360C22×C32C3×#4112yes—
361C22×C32C23×D311yescharacteristic
362C22×C32C23×D311yescharacteristic
363C22×C32C24×C311yescharacteristic
364C2×C3×D3—24no—
365C2×C3×D3—216no—
366C2×C3×D3—24no—
367C2×C3×D3—28no—
368C2×C3×D3—28no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—24no—
374C2×C3×D3C2×Dic614yescomplemented
375C2×C3×D3C2×C3×Q814yescomplemented
376C32×C4—22no—
377C32×C4—24no—
378C32×C4—22no—
379C32×C4—22no—
380C32×C4—34no—
381C32×C4—42no—
382C32×C4—42no—
383C32×C4—44no—
384C32×C4—62no—
385C32×C4—62no—
386C3⋊Dic3—22no—
387C3⋊Dic3—22no—
388C3×Dic3—24no—
389C3×Dic3—22no—
390C3×Dic3—22no—
391C3×Dic3—22no—
392C3×Dic3—22no—
393C3×Dic3—24no—
394C3×Dic3—42no—
395C3×Dic3—64no—
396C3×Dic3—62no—
397C3×Dic3—62no—
398C3×Dic3—62no—
399C3×Dic3—62no—
400C3×Dic3—122no—
401C3×Dic3C2×#6714yes—
402C3×Dic3C2×C3×D414yes—
403C22×Q8—91no—
404C23×C4—31no—
405C22⋊Q8—98no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—91no—
408C2×C4⋊C4—91no—
409C2×C22⋊C4—91no—
410C2×C22⋊C4—91no—
411C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—32no—
416C23×C3—32no—
417C23×C3—34no—
418C23×C3—34no—
419C23×C3—41no—
420C23×C3—62no—
421C23×C3—64no—
422C23×C3—64no—
423C23×C3—64no—
424C23×C3—62no—
425C23×C3—62no—
426C23×C3—62no—
427C23×C3—62no—
428C23×C3C2×D3211yescharacteristic
429C23×C3C22×C3×D311yescharacteristic
430C23×C3C22×C3×D311yescharacteristic
431C22×D3—22no—
432C22×D3—22no—
433C22×D3C3×Dic614yescomplemented
434C22×D3C22×C3×D312yes—
435C3×Q8—188no—
436C2×C3×C4—24no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—34no—
446C2×C3×C4—34no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—44no—
454C2×C3×C4—42no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—64no—
458C2×C3×C4—62no—
459C2×C3×C4—68no—
460C2×C3×C4—68no—
461C2×C3×C4—616no—
462C2×C3×C4—64no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—92no—
468C2×C3×C4—92no—
469C2×C3×C4—122no—
470C2×C3×C4—182no—
471C2×C3×C4—182no—
472C2×C3×C4C2×D3212yes—
473C2×C3×C4C22×C3×D312yes—
474C2×C3×C4C22×C3×D312yes—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—32no—
478C2×Dic3—32no—
479C2×Dic3—32no—
480C2×Dic3—32no—
481C2×Dic3—62no—
482C2×Dic3—62no—
483C2×Dic3—64no—
484C2×Dic3—62no—
485C2×Dic3—62no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—122no—
489C2×Dic3C3×#6714yes—
490C2×Dic3C22×C3×D312yes—
491C2×Dic3C22×C3×D312yes—
492C2×Dic3C22×C3×D312yes—
493C4×D3—28no—
494Dic6—68no—
495Dic6—68no—
496C2×C32—24no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—24no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—24no—
508C2×C32—44no—
509C2×C32—41no—
510C2×C32—41no—
511C2×C32—41no—
512C2×C32—64no—
513C2×C32#89614yescomplemented
514C2×C32#92414yescomplemented
515C2×C32C3×C22⋊Q814yescomplemented
516C2×C32C22×Dic611yescharacteristic
517C2×C32C2×#23511yescharacteristic
518C2×C32C2×#23511yescharacteristic
519C2×C32C2×D3×D411yescharacteristic
520C2×C32C2×D3×Q811yescharacteristic
521C2×C32C22×#6711yescharacteristic
522C2×C32C22×C3×D411yescharacteristic
523C2×C32C22×C3×Q811yescharacteristic
524C2×C32C2×C3×#4111yescharacteristic
525C3×D3—28no—
526C3×D3—24no—
527C3×D3—24no—
528C24—31no—
529C2×Q8—94no—
530C2×Q8—184no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—34no—
535C22×C4—64no—
536C22×C4—91no—
537C22×C4—91no—
538C22×C4C3×D3211yescharacteristic
539C4⋊C4—34no—
540C4⋊C4—94no—
541C4⋊C4—94no—
542C22⋊C4—94no—
543C22⋊C4—94no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—22no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—34no—
557C22×C3—34no—
558C22×C3—41no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—64no—
563C22×C3—64no—
564C22×C3—616no—
565C22×C3—64no—
566C22×C3—68no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—62no—
570C22×C3—62no—
571C22×C3—68no—
572C22×C3D3×Dic612yes—
573C22×C3#379812yes—
574C22×C3D3×#6712yes—
575C22×C3C2×C3×Dic612yes—
576C22×C3C3×#23512yes—
577C22×C3C3×#23512yes—
578C22×C3C3×D3×D412yes—
579C22×C3C3×D3×Q812yes—
580C22×C3C2×C3×#6712yes—
581C22×C3C22×D3211yescharacteristic
582C22×C3C23×C3×D311yescharacteristic
583C22×C3C23×C3×D311yescharacteristic
584C2×D3—28no—
585C2×D3—22no—
586C2×D3—22no—
587C2×D3C2×C3×Dic614yescomplemented
588C3×C4—24no—
589C3×C4—22no—
590C3×C4—22no—
591C3×C4—22no—
592C3×C4—34no—
593C3×C4—34no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—44no—
597C3×C4—64no—
598C3×C4—64no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4—122no—
604C3×C4—182no—
605C3×C4—182no—
606Dic3—22no—
607Dic3—22no—
608Dic3—64no—
609Dic3—62no—
610Dic3—62no—
611Dic3—62no—
612Dic3—62no—
613Dic3—122no—
614Dic3C2×C3×#6714yes—
615C32—21no—
616C32—21no—
617C32—21no—
618C32—41no—
619C32C2×#89611yescharacteristic, complemented
620C32C2×#92411yescharacteristic, complemented
621C32C2×C3×C22⋊Q811yescharacteristic, complemented
622C23—32no—
623C23—34no—
624C23—62no—
625C23—62no—
626C23C2×C3×D3211yescharacteristic
627Q8—188no—
628C2×C4—22no—
629C2×C4—32no—
630C2×C4—34no—
631C2×C4—32no—
632C2×C4—32no—
633C2×C4—68no—
634C2×C4—62no—
635C2×C4—62no—
636C2×C4—92no—
637C2×C4—92no—
638C2×C4—182no—
639C2×C4—182no—
640C2×C4C2×C3×D3212yes—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—24no—
645C2×C3—24no—
646C2×C3—24no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—41no—
654C2×C3—44no—
655C2×C3—41no—
656C2×C3—41no—
657C2×C3—68no—
658C2×C3—64no—
659C2×C3—64no—
660C2×C3#6385114yesdirect product factor
661C2×C3C3×#89614yescomplemented
662C2×C3C3×#92414yescomplemented
663C2×C3C2×D3×Dic611yescharacteristic
664C2×C3C2×#379811yescharacteristic
665C2×C3C2×D3×#6711yescharacteristic
666C2×C3C22×C3×Dic611yescharacteristic
667C2×C3C2×C3×#23511yescharacteristic
668C2×C3C2×C3×#23511yescharacteristic
669C2×C3C2×C3×D3×D411yescharacteristic
670C2×C3C2×C3×D3×Q811yescharacteristic
671C2×C3C22×C3×#6711yescharacteristic
672D3—24no—
673C22—34no—
674C22—62no—
675C22—68no—
676C22—62no—
677C22C3×D3×Dic612yes—
678C22C3×#379812yes—
679C22C3×D3×#6712yes—
680C22C22×C3×D3211yescharacteristic
681C4—22no—
682C4—34no—
683C4—62no—
684C4—62no—
685C4—182no—
686C4—182no—
687C3—21no—
688C3—21no—
689C3—21no—
690C3—41no—
691C3C2×#6385111yescharacteristic, direct product factor
692C3C2×C3×#89611yescharacteristic, complemented
693C3C2×C3×#92411yescharacteristic, complemented
694C2—64no—
695C2C3×#6385114yesdirect product factor
696C2C2×C3×D3×Dic611yescharacteristic
697C2C2×C3×#379811yescharacteristic
698C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#627C2semidirect
3. C2×C3×#3750C2semidirect
4. C2×C32×Dic3⋊C4C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
8. C3×#63851C2direct (N × H)
11. C2×#63851C3direct (N × H)
22. C2×C3×#627C22semidirect
23. C3×#3750C22semidirect
24. C32×Dic3⋊C4C22semidirect
25. C3×Dic3⋊Dic3C22semidirect
34. C22×#627C2×C3semidirect
36. C2×#3750C2×C3semidirect
48. C2×C3×Dic3⋊C4D3semidirect
49. C2×C3×Dic3⋊C4C2×C3semidirect
51. C2×Dic3⋊Dic3C2×C3semidirect
54. #63851C2×C3direct (N × H)
58. C22×C32×D3Q8semidirect
121. C2×#627C22×C3semidirect
123. #3750C22×C3semidirect
134. C3×Dic3⋊C4C2×D3semidirect
135. C3×Dic3⋊C4C22×C3semidirect
136. Dic3⋊Dic3C22×C3semidirect
146. C2×C32×D3C2×Q8semidirect
178. C2×Dic3⋊C4C3×D3semidirect
199. C22×C3×D3Dic6semidirect
200. C22×C3×D3C3×Q8semidirect
265. C2×C33C22⋊Q8semidirect
331. Dic3⋊C4C2×C3×D3semidirect
374. C2×C3×D3C2×Dic6semidirect
375. C2×C3×D3C2×C3×Q8semidirect
411. C33C2×C22⋊Q8semidirect
433. C22×D3C3×Dic6semidirect
513. C2×C32#896semidirect
514. C2×C32#924semidirect
515. C2×C32C3×C22⋊Q8semidirect
587. C2×D3C2×C3×Dic6semidirect
619. C32C2×#896semidirect
620. C32C2×#924semidirect
621. C32C2×C3×C22⋊Q8semidirect
660. C2×C3#63851direct (N × H)
661. C2×C3C3×#896semidirect
662. C2×C3C3×#924semidirect
691. C3C2×#63851direct (N × H)
692. C3C2×C3×#896semidirect
693. C3C2×C3×#924semidirect
695. C2C3×#63851direct (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
C22×C3×#6272
C2×C3×#37502
C2×C32×Dic3⋊C42
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
C3×#638512
C2×C3×#9243
C2×C3×#8963
C2×#638513