Finite Group Databasebeta

← C3×Dic3×#237 #13174742

Subgroups — C3×Dic3×#237 #13174742

Order 1728.

1646 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic
2C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#67⋊Dic3C212yesmaximal, complemented
5C3×Dic3×#67C212yesmaximal, complemented
6C3×#63955C212yesmaximal, complemented
7C2×C3×Dic32C212yesmaximal, complemented
8C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
9C3×#63843C211yesmaximal, characteristic, complemented
10C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
11C3×#63841C211yesmaximal, characteristic, complemented
12C3×Dic3×#41—31nomaximal
13C3×C4×#237—31nomaximal
14Dic3×#237C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C22×C3×C3⋊Dic3C2212yes—
17C2×C32×#67C2212yes—
18C22×C32×Dic3C2212yes—
19C22×C32×Dic3C2212yes—
20C32×#237C418yescomplemented
21C2×C32×C4×D3C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C3×#3757C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C32×#217C2212yes—
29C32×C4⋊Dic3C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31C3×Dic3⋊Dic3C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×(C2×D3)⋊Dic3C2212yes—
34C3×Dic32C2211yescharacteristic
35C3×Dic32C2212yes—
36C3×Dic32C2212yes—
37C3×Dic32C2212yes—
38C3×Dic32C2211yescharacteristic
39C2×C32×#41—31no—
40C2×C3×#237—21no—
41C2×C3×#237D311yescharacteristic
42C2×C3×#237C2×C311yescharacteristic
43C32×C4×D4—31no—
44D4×C3⋊Dic3C2×C311yescharacteristic, complemented
45C3×Q8×Dic3—31no—
46C3×Q8×Dic3—31no—
47C3×D4×Dic3—21no—
48C3×D4×Dic3—31no—
49C3×D4×Dic3—31no—
50C3×D4×Dic3—32no—
51C3×D4×Dic3—32no—
52C3×D4×Dic3—61no—
53C3×D4×Dic3D311yescharacteristic, complemented
54C3×D4×Dic3C2×C311yescharacteristic, complemented
55C3×C4×#67—32no—
56C3×#926—32no—
57C3×#926—31no—
58C2×C3×C4×Dic3—32no—
59C2×C3×C4×Dic3—32no—
60C2×C3×C4×Dic3—31no—
61C3×#892—31no—
62C3×#887—31no—
63C3×#67⋊C4—32no—
64C3×#877—32no—
65C3×C42×D3—31no—
66C3×C4×Dic6—31no—
67#67⋊Dic3C2×C312yescomplemented
68Dic3×#67C2×C312yescomplemented
69#63955C2×C312yescomplemented
70C2×Dic32C2×C312yescomplemented
71C4×D3×Dic3C2×C311yescharacteristic, complemented
72#63843C2×C311yescharacteristic, complemented
73Dic3×Dic6C2×C311yescharacteristic, complemented
74#63841C2×C311yescharacteristic, complemented
75C23×C33C2312yes—
76C22×C32×D3C2311yescharacteristic
77C33×D4C2×C414yescomplemented
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3—24no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C32×#67C2×C418yescomplemented
84C2×C32×Dic3—24no—
85C2×C32×Dic3C2×C418yescomplemented
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C32×C4×D3C2×C414yescomplemented
92C32×Dic6C2×C414yescomplemented
93C3×D3×Dic3—22no—
94C3×D3×Dic3—22no—
95C3×C4×#41—91no—
96Dic3×#41—31no—
97C4×#237—31no—
98C32×#41—38no—
99C2×C32×Q8—31no—
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4—21no—
103C2×C32×D4—32no—
104C2×C32×D4—41no—
105C2×C32×D4C2×D311yescharacteristic
106C2×C32×D4C2×D311yescharacteristic
107C2×C32×D4C22×C311yescharacteristic
108C22×C32×C4—32no—
109C22×C32×C4—31no—
110C22×C32×C4—32no—
111C22×C3⋊Dic3C22×C312yes—
112C2×C3×#67—22no—
113C2×C3×#67C2×D312yes—
114C2×C3×#67C22×C312yes—
115C22×C3×Dic3—22no—
116C22×C3×Dic3—22no—
117C22×C3×Dic3—32no—
118C22×C3×Dic3—32no—
119C22×C3×Dic3—31no—
120C22×C3×Dic3—31no—
121C22×C3×Dic3—62no—
122C22×C3×Dic3C2×D312yes—
123C22×C3×Dic3C2×D312yes—
124C22×C3×Dic3C22×C312yes—
125C22×C3×Dic3C22×C312yes—
126C3×#237—28no—
127C3×#237Dic318yesdirect product factor
128C3×#237C3×C418yescomplemented
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×C4×D3C22×C311yescharacteristic
134C2×C3×Dic6—21no—
135C2×C3×Dic6C2×D311yescharacteristic
136C2×C3×Dic6C22×C311yescharacteristic
137C2×D3×Dic3C22×C311yescharacteristic
138C2×D3×Dic3C22×C311yescharacteristic
139C32×C4⋊C4—31no—
140C32×C22⋊C4—32no—
141C32×C42—31no—
142#3757C22×C312yes—
143C4⋊(C3⋊Dic3)C22×C311yescharacteristic
144C4×C3⋊Dic3C22×C311yescharacteristic
145C3×#217—22no—
146C3×#217—32no—
147C3×#217—32no—
148C3×#217—32no—
149C3×#217—62no—
150C3×#217C2×D312yes—
151C3×#217C22×C312yes—
152C3×(C2×D3)⋊C4—32no—
153C3×C4⋊Dic3—21no—
154C3×C4⋊Dic3—31no—
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—32no—
157C3×C4⋊Dic3—32no—
158C3×C4⋊Dic3—61no—
159C3×C4⋊Dic3C2×D311yescharacteristic
160C3×C4⋊Dic3C22×C311yescharacteristic
161C3×Dic3⋊C4—32no—
162C3×Dic3⋊C4—32no—
163C3×C4×Dic3—21no—
164C3×C4×Dic3—31no—
165C3×C4×Dic3—31no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—32no—
168C3×C4×Dic3—32no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—31no—
171C3×C4×Dic3—32no—
172C3×C4×Dic3—31no—
173C3×C4×Dic3—32no—
174C3×C4×Dic3—32no—
175C3×C4×Dic3—32no—
176C3×C4×Dic3—61no—
177C3×C4×Dic3C2×D311yescharacteristic
178C3×C4×Dic3C22×C311yescharacteristic
179Dic3⋊Dic3C22×C312yes—
180Dic3⋊Dic3C22×C312yes—
181(C2×D3)⋊Dic3C22×C312yes—
182Dic32C22×C312yes—
183Dic32C22×C312yes—
184Dic32C22×C312yes—
185Dic32C22×C311yescharacteristic
186Dic32C22×C311yescharacteristic
187C22×C33—22no—
188C22×C33—22no—
189C22×C33C22×C414yes—
190C22×C33C2411yescharacteristic
191C2×C32×D3—21no—
192C2×C32×D3—21no—
193C2×C32×D3C22×C412yes—
194C33×C4C22×C412yes—
195C3×C3⋊Dic3—21no—
196C3×C3⋊Dic3—22no—
197C3×C3⋊Dic3#4112yescomplemented
198C32×Dic3—21no—
199C32×Dic3—22no—
200C32×Dic3C22×C414yes—
201C32×Dic3C22×C412yes—
202C32×Dic3#4112yescomplemented
203C2×C3×#41—31no—
204C2×C3×#41—31no—
205C2×C3×#41—61no—
206C2×#237C3×D311yescharacteristic
207C3×C4×Q8—91no—
208C3×C4×Q8—91no—
209C3×C4×D4—31no—
210C3×C4×D4—31no—
211C3×C4×D4—61no—
212C3×C4×D4—92no—
213C3×C4×D4—92no—
214C3×C4×D4—91no—
215C3×#117—92no—
216C3×#117—91no—
217C2×C3×C42—91no—
218C2×C3×C42—92no—
219Q8×Dic3—31no—
220Q8×Dic3—31no—
221D4×Dic3—31no—
222D4×Dic3—31no—
223D4×Dic3—32no—
224D4×Dic3—32no—
225D4×Dic3—61no—
226D4×Dic3C3×D311yescharacteristic, complemented
227C4×#67—32no—
228#926—32no—
229#926—31no—
230C2×C4×Dic3—32no—
231C2×C4×Dic3—32no—
232C2×C4×Dic3—31no—
233#892—31no—
234#887—31no—
235#67⋊C4—32no—
236#877—32no—
237C42×D3—31no—
238C4×Dic6—31no—
239C23×C32—22no—
240C23×C32—22no—
241C23×C32—22no—
242C23×C32—31no—
243C23×C32—42no—
244C23×C32C22×D312yes—
245C23×C32C22×D312yes—
246C23×C32C23×C312yes—
247C22×C3×D3—21no—
248C22×C3×D3C22×D311yescharacteristic
249C22×C3×D3C23×C311yescharacteristic
250C32×Q8—34no—
251C32×D4—24no—
252C32×D4—24no—
253C32×D4—24no—
254C32×D4—38no—
255C32×D4—44no—
256C32×D4C4×D314yescomplemented
257C32×D4C2×Dic314yescomplemented
258C32×D4C2×C3×C414yescomplemented
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—38no—
263C2×C32×C4—31no—
264C2×C32×C4—31no—
265C2×C32×C4—32no—
266C2×C32×C4—34no—
267C2×C32×C4—32no—
268C2×C32×C4—31no—
269C2×C32×C4—41no—
270C2×C32×C4—64no—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C23×C311yescharacteristic
274C2×C3⋊Dic3—24no—
275C2×C3⋊Dic3C23×C312yes—
276C2×C3⋊Dic3C23×C311yescharacteristic
277C2×C3⋊Dic3C23×C311yescharacteristic
278C3×#67—28no—
279C3×#67C2×Dic318yescomplemented
280C3×#67C2×C3×C418yescomplemented
281C2×C3×Dic3—24no—
282C2×C3×Dic3—24no—
283C2×C3×Dic3—28no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—32no—
295C2×C3×Dic3—44no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—64no—
301C2×C3×Dic3—64no—
302C2×C3×Dic3—62no—
303C2×C3×Dic3—124no—
304C2×C3×Dic3C2×Dic318yescomplemented
305C2×C3×Dic3C2×C3×C418yescomplemented
306C2×C3×Dic3C22×D312yes—
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D311yescharacteristic
309C2×C3×Dic3C22×D311yescharacteristic
310C2×C3×Dic3C22×D312yes—
311C2×C3×Dic3C23×C312yes—
312C2×C3×Dic3C23×C311yescharacteristic
313C2×C3×Dic3C23×C311yescharacteristic
314C2×C3×Dic3C23×C312yes—
315C2×C3×Dic3C23×C311yescharacteristic
316C3×C4×D3—24no—
317C3×C4×D3—62no—
318C3×C4×D3—62no—
319C3×C4×D3C2×Dic314yescomplemented
320C3×C4×D3C2×C3×C414yescomplemented
321C3×Dic6—24no—
322C3×Dic6C2×Dic314yescomplemented
323C3×Dic6C2×C3×C414yescomplemented
324D3×Dic3—22no—
325D3×Dic3—22no—
326C4×#41—91noSylow
327C2×C33—24no—
328C2×C33C23×C411yescharacteristic
329C2×C33C2×#4111yescharacteristic
330C2×C33C2×#4111yescharacteristic
331C32×D3—22no—
332C3×#41—38no—
333C3×#41—38no—
334C3×#41—68no—
335C2×C3×Q8—31no—
336C2×C3×Q8—31no—
337C2×C3×Q8—61no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—32no—
342C2×C3×D4—32no—
343C2×C3×D4—41no—
344C2×C3×D4—62no—
345C2×C3×D4D3211yescharacteristic
346C2×C3×D4C2×C3×D311yescharacteristic
347C2×C3×D4C2×C3×D311yescharacteristic
348C22×C3×C4—32no—
349C22×C3×C4—32no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—32no—
353C22×C3×C4—32no—
354C22×C3×C4—61no—
355C22×C3×C4—62no—
356C22×C3×C4—62no—
357C22×C3×C4—91no—
358C22×C3×C4—91no—
359C22×C3×C4—92no—
360C2×#67C2×C3×D312yes—
361C22×Dic3—32no—
362C22×Dic3—32no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—62no—
366C22×Dic3C2×C3×D312yes—
367C22×Dic3C2×C3×D312yes—
368#237C3×Dic318yesdirect product factor
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3C2×C3×D311yescharacteristic
372C2×Dic6C2×C3×D311yescharacteristic
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—92no—
377C3×C4⋊C4—92no—
378C3×C4⋊C4—91no—
379C3×C22⋊C4—32no—
380C3×C22⋊C4—32no—
381C3×C22⋊C4—62no—
382C3×C22⋊C4—92no—
383C3×C22⋊C4—92no—
384C3×C42—31no—
385C3×C42—31no—
386C3×C42—61no—
387C3×C42—91no—
388C3×C42—91no—
389C3×C42—92no—
390C3×C42—92no—
391C3×C42—92no—
392C3×C42—91no—
393#217—32no—
394#217—32no—
395#217—32no—
396#217—62no—
397#217C2×C3×D312yes—
398(C2×D3)⋊C4—32no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—32no—
402C4⋊Dic3—32no—
403C4⋊Dic3—61no—
404C4⋊Dic3C2×C3×D311yescharacteristic
405Dic3⋊C4—32no—
406Dic3⋊C4—32no—
407C4×Dic3—31no—
408C4×Dic3—31no—
409C4×Dic3—32no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—32no—
413C4×Dic3—32no—
414C4×Dic3—31no—
415C4×Dic3—32no—
416C4×Dic3—31no—
417C4×Dic3—32no—
418C4×Dic3—32no—
419C4×Dic3—61no—
420C4×Dic3C2×C3×D311yescharacteristic
421C22×C32—22no—
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—22no—
425C22×C32—22no—
426C22×C32—22no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—24no—
431C22×C32—24no—
432C22×C32—24no—
433C22×C32—32no—
434C22×C32—41no—
435C22×C32—44no—
436C22×C32—42no—
437C22×C32—42no—
438C22×C32—42no—
439C22×C32—42no—
440C22×C32—42no—
441C22×C32—42no—
442C22×C32—61no—
443C22×C32—61no—
444C22×C32—82no—
445C22×C32—82no—
446C22×C32C2×C4×D314yes—
447C22×C32C22×Dic314yes—
448C22×C32C22×C3×C414yes—
449C22×C32C23×D311yescharacteristic
450C22×C32C23×D311yescharacteristic
451C22×C32C24×C311yescharacteristic
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—22no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3C22×Dic312yes—
460C2×C3×D3C22×C3×C412yes—
461C32×C4—22no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—32no—
465C32×C4—34no—
466C32×C4—32no—
467C32×C4—42no—
468C32×C4—61no—
469C32×C4—62no—
470C32×C4C2×C4×D312yes—
471C32×C4C22×Dic312yes—
472C32×C4C22×C3×C412yes—
473C3⋊Dic3—21no—
474C3⋊Dic3—22no—
475C3⋊Dic3C3×#4112yescomplemented
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—22no—
480C3×Dic3—22no—
481C3×Dic3—24no—
482C3×Dic3—22no—
483C3×Dic3—32no—
484C3×Dic3—32no—
485C3×Dic3—41no—
486C3×Dic3—42no—
487C3×Dic3—62no—
488C3×Dic3—61no—
489C3×Dic3—61no—
490C3×Dic3—62no—
491C3×Dic3—62no—
492C3×Dic3—121no—
493C3×Dic3—122no—
494C3×Dic3#23712yesdirect product factor
495C3×Dic3C22×Dic314yes—
496C3×Dic3C22×Dic312yes—
497C3×Dic3C22×C3×C414yes—
498C3×Dic3C22×C3×C412yes—
499C3×Dic3C3×#4112yescomplemented
500C2×#41—31no—
501C4×Q8—91no—
502C4×Q8—91no—
503C4×D4—31no—
504C4×D4—92no—
505C4×D4—92no—
506C4×D4—91no—
507#117—92no—
508#117—91no—
509C2×C42—91no—
510C2×C42—92no—
511C33C4×#4111yescharacteristic, complemented, Sylow
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—31no—
516C23×C3—31no—
517C23×C3—42no—
518C23×C3—61no—
519C23×C3C2×D3212yes—
520C23×C3C22×C3×D312yes—
521C23×C3C22×C3×D312yes—
522C22×D3C22×C3×D311yescharacteristic
523C3×Q8—34no—
524C3×Q8—34no—
525C3×Q8—64no—
526C3×D4—24no—
527C3×D4—24no—
528C3×D4—24no—
529C3×D4—38no—
530C3×D4—38no—
531C3×D4—44no—
532C3×D4—68no—
533C3×D4D3×Dic314yescomplemented
534C3×D4C3×C4×D314yescomplemented
535C3×D4C2×C3×Dic314yescomplemented
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—32no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—32no—
545C2×C3×C4—38no—
546C2×C3×C4—38no—
547C2×C3×C4—34no—
548C2×C3×C4—34no—
549C2×C3×C4—31no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—31no—
553C2×C3×C4—41no—
554C2×C3×C4—64no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—62no—
558C2×C3×C4—68no—
559C2×C3×C4—61no—
560C2×C3×C4—62no—
561C2×C3×C4—64no—
562C2×C3×C4—64no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—92no—
566C2×C3×C4—124no—
567C2×C3×C4—182no—
568C2×C3×C4—182no—
569C2×C3×C4—184no—
570C2×C3×C4C2×D3211yescharacteristic
571C2×C3×C4C22×C3×D311yescharacteristic
572C2×C3×C4C22×C3×D311yescharacteristic
573#67C2×C3×Dic318yescomplemented
574C2×Dic3—24no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—32no—
579C2×Dic3—31no—
580C2×Dic3—32no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—62no—
584C2×Dic3—62no—
585C2×Dic3—64no—
586C2×Dic3—64no—
587C2×Dic3—62no—
588C2×Dic3—124no—
589C2×Dic3C2×C3×Dic318yescomplemented
590C2×Dic3C22×C3×D312yes—
591C2×Dic3C22×C3×D311yescharacteristic
592C2×Dic3C22×C3×D311yescharacteristic
593C2×Dic3C22×C3×D311yescharacteristic
594C2×Dic3C22×C3×D312yes—
595C4×D3—62no—
596C4×D3—62no—
597C4×D3C2×C3×Dic314yescomplemented
598Dic6C2×C3×Dic314yescomplemented
599C2×C32—24no—
600C2×C32—24no—
601C2×C32—24no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—41no—
612C2×C32—41no—
613C2×C32—41no—
614C2×C32—44no—
615C2×C32—44no—
616C2×C32—44no—
617C2×C32—62no—
618C2×C32—84no—
619C2×C32C22×C4×D311yescharacteristic
620C2×C32C2×#23711yescharacteristic
621C2×C32D3×#4111yescharacteristic
622C2×C32D3×#4111yescharacteristic
623C2×C32D3×#4111yescharacteristic
624C2×C32C23×Dic311yescharacteristic
625C2×C32C23×C3×C411yescharacteristic
626C2×C32C2×C3×#4111yescharacteristic
627C2×C32C2×C3×#4111yescharacteristic
628C3×D3—22no—
629C3×D3—22no—
630C3×D3—42no—
631#41—38no—
632C2×Q8—31no—
633C2×D4—32no—
634C2×D4C3×D3211yescharacteristic
635C22×C4—32no—
636C22×C4—31no—
637C22×C4—32no—
638C22×C4—91no—
639C22×C4—91no—
640C22×C4—92no—
641C4⋊C4—31no—
642C4⋊C4—92no—
643C4⋊C4—92no—
644C4⋊C4—91no—
645C22⋊C4—32no—
646C22⋊C4—92no—
647C22⋊C4—92no—
648C42—31no—
649C42—91no—
650C42—91no—
651C42—92no—
652C42—92no—
653C42—92no—
654C42—91no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—24no—
665C22×C3—24no—
666C22×C3—24no—
667C22×C3—32no—
668C22×C3—32no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—41no—
676C22×C3—44no—
677C22×C3—62no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—82no—
683C22×C3—82no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3C2×D3×Dic314yes—
687C22×C3C2×C3×C4×D314yes—
688C22×C3C22×C3×Dic314yes—
689C22×C3C22×D3211yescharacteristic
690C22×C3C23×C3×D311yescharacteristic
691C22×C3C23×C3×D311yescharacteristic
692C2×D3—21no—
693C2×D3—21no—
694C2×D3C22×C3×Dic312yes—
695C3×C4—22no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—32no—
699C3×C4—32no—
700C3×C4—34no—
701C3×C4—32no—
702C3×C4—34no—
703C3×C4—32no—
704C3×C4—42no—
705C3×C4—62no—
706C3×C4—64no—
707C3×C4—62no—
708C3×C4—62no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—62no—
712C3×C4—92no—
713C3×C4—122no—
714C3×C4—121no—
715C3×C4—181no—
716C3×C4—182no—
717C3×C4C2×D3×Dic312yes—
718C3×C4C2×C3×C4×D312yes—
719C3×C4C22×C3×Dic312yes—
720Dic3—22no—
721Dic3—21no—
722Dic3—32no—
723Dic3—32no—
724Dic3—62no—
725Dic3—61no—
726Dic3—61no—
727Dic3—62no—
728Dic3—62no—
729Dic3—122no—
730Dic3—121no—
731Dic3C3×#23712yesdirect product factor
732Dic3C22×C3×Dic314yes—
733Dic3C22×C3×Dic312yes—
734C32—21no—
735C32—21no—
736C32—21no—
737C32—41no—
738C32C4×#23711yescharacteristic, complemented
739C32Dic3×#4111yescharacteristic, complemented
740C32C3×C4×#4111yescharacteristic, complemented
741C23—31no—
742C23C2×C3×D3212yes—
743Q8—34no—
744D4—38no—
745D4C3×D3×Dic314yescomplemented
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—32no—
749C2×C4—38no—
750C2×C4—34no—
751C2×C4—31no—
752C2×C4—32no—
753C2×C4—64no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—92no—
757C2×C4—182no—
758C2×C4—182no—
759C2×C4—184no—
760C2×C4C2×C3×D3211yescharacteristic
761C2×C3—24no—
762C2×C3—24no—
763C2×C3—24no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—44no—
774C2×C3—44no—
775C2×C3—44no—
776C2×C3—41no—
777C2×C3—41no—
778C2×C3—41no—
779C2×C3—62no—
780C2×C3—62no—
781C2×C3—84no—
782C2×C3—122no—
783C2×C3D3×#23711yescharacteristic
784C2×C3#6431211yescharacteristic
785C2×C3C22×D3×Dic311yescharacteristic
786C2×C3C22×C3×C4×D311yescharacteristic
787C2×C3C2×C3×#23711yescharacteristic
788C2×C3C3×D3×#4111yescharacteristic
789C2×C3C3×D3×#4111yescharacteristic
790C2×C3C3×D3×#4111yescharacteristic
791C2×C3C23×C3×Dic311yescharacteristic
792D3—22no—
793C22—22no—
794C22—22no—
795C22—32no—
796C22—61no—
797C22—61no—
798C22C2×C3×D3×Dic314yes—
799C22C22×C3×D3211yescharacteristic
800C4—32no—
801C4—34no—
802C4—32no—
803C4—62no—
804C4—61no—
805C4—92no—
806C4—181no—
807C4—182no—
808C4C2×C3×D3×Dic312yes—
809C3—21no—
810C3—21no—
811C3—21no—
812C3—41no—
813C3Dic3×#23711yescharacteristic, direct product factor
814C3C3×C4×#23711yescharacteristic, complemented
815C3C3×Dic3×#4111yescharacteristic, complemented
816C2—24no—
817C2—62no—
818C2C3×D3×#23711yescharacteristic
819C2C3×#6431211yescharacteristic
820C2C22×C3×D3×Dic311yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC2×C32×#237C2
cosocleC22×C32C24×C3
hypercenterC2×C3×D4D32
hypocenterC32C3×C4×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×C3⋊Dic3C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#67⋊Dic3C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×#63955C2semidirect
7. C2×C3×Dic32C2semidirect
8. C3×C4×D3×Dic3C2semidirect
9. C3×#63843C2semidirect
10. C3×Dic3×Dic6C2semidirect
11. C3×#63841C2semidirect
14. Dic3×#237C3direct (N × H)
20. C32×#237C4semidirect
44. D4×C3⋊Dic3C2×C3semidirect
53. C3×D4×Dic3D3semidirect
54. C3×D4×Dic3C2×C3semidirect
67. #67⋊Dic3C2×C3semidirect
68. Dic3×#67C2×C3semidirect
69. #63955C2×C3semidirect
70. C2×Dic32C2×C3semidirect
71. C4×D3×Dic3C2×C3semidirect
72. #63843C2×C3semidirect
73. Dic3×Dic6C2×C3semidirect
74. #63841C2×C3semidirect
77. C33×D4C2×C4semidirect
83. C32×#67C2×C4semidirect
85. C2×C32×Dic3C2×C4semidirect
91. C32×C4×D3C2×C4semidirect
92. C32×Dic6C2×C4semidirect
127. C3×#237Dic3direct (N × H)
128. C3×#237C3×C4semidirect
197. C3×C3⋊Dic3#41semidirect
202. C32×Dic3#41semidirect
226. D4×Dic3C3×D3semidirect
256. C32×D4C4×D3semidirect
257. C32×D4C2×Dic3semidirect
258. C32×D4C2×C3×C4semidirect
279. C3×#67C2×Dic3semidirect
280. C3×#67C2×C3×C4semidirect
304. C2×C3×Dic3C2×Dic3semidirect
305. C2×C3×Dic3C2×C3×C4semidirect
319. C3×C4×D3C2×Dic3semidirect
320. C3×C4×D3C2×C3×C4semidirect
322. C3×Dic6C2×Dic3semidirect
323. C3×Dic6C2×C3×C4semidirect
368. #237C3×Dic3direct (N × H)
475. C3⋊Dic3C3×#41semidirect
494. C3×Dic3#237direct (N × H)
499. C3×Dic3C3×#41semidirect
511. C33C4×#41semidirect
533. C3×D4D3×Dic3semidirect
534. C3×D4C3×C4×D3semidirect
535. C3×D4C2×C3×Dic3semidirect
573. #67C2×C3×Dic3semidirect
589. C2×Dic3C2×C3×Dic3semidirect
597. C4×D3C2×C3×Dic3semidirect
598. Dic6C2×C3×Dic3semidirect
731. Dic3C3×#237direct (N × H)
738. C32C4×#237semidirect
739. C32Dic3×#41semidirect
740. C32C3×C4×#41semidirect
745. D4C3×D3×Dic3semidirect
813. C3Dic3×#237direct (N × H)
814. C3C3×C4×#237semidirect
815. C3C3×Dic3×#41semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C3×D4×C3⋊Dic32
C32×D4×Dic32
C3×#67⋊Dic32
C3×Dic3×#672
C3×#639552
C2×C3×Dic322
C3×C4×D3×Dic32
C3×#638432
C3×Dic3×Dic62
C3×#638412
C3×Dic3×#413
C3×C4×#2373
Dic3×#2373