Finite Group Databasebeta

← C3×#10595058 #13174655

Subgroups — C3×#10595058 #13174655

Order 1728.

1726 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3811C211yesmaximal, characteristic
2C2×C3×#3752C211yesmaximal, characteristic, complemented
3C32×C4×#67C212yesmaximal, complemented
4C3×#63974C211yesmaximal, characteristic, complemented
5C3×#67⋊Dic3C212yesmaximal, complemented
6C3×D3×(C2×D3)⋊C4C212yesmaximal, complemented
7C3×#63904C212yesmaximal, complemented
8C3×#63880C212yesmaximal, complemented
9C3×#63836C212yesmaximal, complemented
10C3×#5545—32nomaximal
11#10595058C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C22×C3×D32C2211yescharacteristic
14C22×C33×C4C2211yescharacteristic, complemented
15C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
16C2×C32×#67C2212yes—
17C2×C32×C4×D3C2212yescomplemented
18C3×#3811C418yescomplemented
19C2×C3×#626C2212yes—
20C2×C3×#624C2211yescharacteristic
21C2×C3×#624C2211yescharacteristic, complemented
22C2×C3×#624C2211yescharacteristic, complemented
23C2×C3×D3×Dic3C2212yescomplemented
24C3×#3752C2212yes—
25C3×#3752C2212yescomplemented
26C32×#217C2212yescomplemented
27C32×(C2×D3)⋊C4C2212yescomplemented
28C32×Dic3⋊C4C2212yescomplemented
29C32×C4×Dic3C2212yescomplemented
30C3×Dic3⋊Dic3C2212yescomplemented
31C3×#3722C2212yes—
32C3×(C2×D3)⋊Dic3C2212yescomplemented
33C3×Dic32C2212yescomplemented
34C2×C3×D3×D4—32no—
35C2×#3811C2×C311yescharacteristic
36C32×C4×D4—32no—
37C2×#3752C2×C311yescharacteristic, complemented
38C3×D4×Dic3—32no—
39C3×C4×#67—22no—
40C3×C4×#67—32no—
41C3×C4×#67D312yescomplemented
42C3×C4×#67C2×C312yescomplemented
43C2×C3×(C2×D3)⋊C4—32no—
44C2×C3×(C2×D3)⋊C4—32no—
45C2×C3×(C2×D3)⋊C4—61no—
46C3×#893—32no—
47C3×#892—32no—
48C3×#67⋊C4—32no—
49C3×#67⋊C4—32no—
50C3×D3×C22⋊C4—32no—
51C3×D3×C22⋊C4—32no—
52C3×C4×D12—32no—
53C3×#872—32no—
54#63974C2×C311yescharacteristic, complemented
55#67⋊Dic3C2×C312yescomplemented
56D3×(C2×D3)⋊C4C2×C312yescomplemented
57#63904C2×C312yescomplemented
58#63880C2×C312yescomplemented
59#63836C2×C312yescomplemented
60C23×C33C2311yescharacteristic
61C22×C3×C3⋊D3—41no—
62C22×C3×C3⋊D3—41no—
63C22×C3×C3⋊D3C2×C414yescomplemented
64C22×C3×C3⋊D3C2311yescharacteristic
65C22×C3×C3⋊D3C2311yescharacteristic
66C22×C32×D3C2312yes—
67C2×C3×D32—41no—
68C2×C3×D32—41no—
69C2×C3×D32C2×C414yescomplemented
70C2×C33×C4—41no—
71C2×C33×C4C2312yes—
72C2×C3×C3⋊Dic3—41no—
73C2×C3×C3⋊Dic3C2312yes—
74C32×#67C2×C418yescomplemented
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78C32×C4×D3—42no—
79C3×#626C2×C418yescomplemented
80C3×#624—41no—
81C3×#624—41no—
82C3×#624C2×C414yescomplemented
83C3×D3×Dic3—42no—
84C3×#518—91no—
85#5545—32no—
86C23×C3⋊D3C22×C311yescharacteristic
87C23×C3×D3—32no—
88C23×C3×D3—32no—
89C23×C3×D3—61no—
90C22×D32C22×C311yescharacteristic
91C2×C32×D4—32no—
92C22×C32×C4—21no—
93C22×C32×C4—22no—
94C22×C32×C4—32no—
95C22×C32×C4—41no—
96C22×C32×C4C2×D312yescomplemented
97C22×C32×C4C22×C311yescharacteristic, complemented
98C22×C3⋊Dic3C22×C311yescharacteristic, complemented
99C2×C3×#67—22no—
100C2×C3×#67—32no—
101C2×C3×#67C2×D312yes—
102C2×C3×#67C22×C312yes—
103C22×C3×Dic3—32no—
104C22×C3×Dic3—32no—
105C22×C3×Dic3—61no—
106C3×D3×D4—316no—
107C2×C3×D12—32no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3C2×D312yescomplemented
114C2×C3×C4×D3C22×C312yescomplemented
115#3811C3×C418yescomplemented
116C2×#626C22×C312yes—
117C2×#624C22×C311yescharacteristic
118C2×#624C22×C311yescharacteristic, complemented
119C2×#624C22×C311yescharacteristic, complemented
120C2×D3×Dic3C22×C312yescomplemented
121C32×C4⋊C4—32no—
122C32×C22⋊C4—32no—
123C32×C22⋊C4—32no—
124C32×C42—32no—
125#3752C22×C312yes—
126#3752C22×C312yescomplemented
127C3×#217—22no—
128C3×#217—32no—
129C3×#217C2×D312yescomplemented
130C3×#217C22×C312yescomplemented
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—62no—
140C3×(C2×D3)⋊C4—62no—
141C3×(C2×D3)⋊C4C2×D312yescomplemented
142C3×(C2×D3)⋊C4C22×C312yescomplemented
143C3×C4⋊Dic3—32no—
144C3×Dic3⋊C4—22no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4C2×D312yescomplemented
147C3×Dic3⋊C4C22×C312yescomplemented
148C3×C4×Dic3—22no—
149C3×C4×Dic3—32no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3C2×D312yescomplemented
152C3×C4×Dic3C22×C312yescomplemented
153Dic3⋊Dic3C22×C312yescomplemented
154#3722C22×C312yes—
155(C2×D3)⋊Dic3C22×C312yescomplemented
156Dic32C22×C312yescomplemented
157C22×C33—21no—
158C22×C33—21no—
159C22×C33C22×C412yes—
160C22×C33C2411yescharacteristic
161C2×C3×C3⋊D3—21no—
162C2×C3×C3⋊D3—21no—
163C2×C3×C3⋊D3—21no—
164C2×C3×C3⋊D3—21no—
165C2×C3×C3⋊D3—44no—
166C2×C3×C3⋊D3C22×C412yes—
167C2×C3×C3⋊D3C22×C412yes—
168C2×C32×D3—22no—
169C2×C32×D3—22no—
170C2×C32×D3C22×C414yes—
171C3×D32—44no—
172C33×C4—22no—
173C3×C3⋊Dic3—22no—
174C32×Dic3—22no—
175C32×Dic3—22no—
176C32×Dic3C22×C414yes—
177C22×C3×D4—91no—
178C2×D3×D4—32no—
179C3×C4×D4—32no—
180C3×C4×D4—32no—
181C3×C4×D4—62no—
182C3×C4×D4—92no—
183C3×C4×D4—92no—
184C3×C4×D4—92no—
185C3×#117—92no—
186C2×C3×C22⋊C4—91no—
187C2×C3×C22⋊C4—92no—
188C2×C3×C22⋊C4—91no—
189D4×Dic3—32no—
190C4×#67—32no—
191C4×#67C3×D312yescomplemented
192C2×(C2×D3)⋊C4—32no—
193C2×(C2×D3)⋊C4—32no—
194C2×(C2×D3)⋊C4—61no—
195#893—32no—
196#892—32no—
197#67⋊C4—32no—
198#67⋊C4—32no—
199D3×C22⋊C4—32no—
200D3×C22⋊C4—32no—
201C4×D12—32no—
202#872—32no—
203C23×C32—21no—
204C23×C32—22no—
205C23×C32—32no—
206C23×C32—41no—
207C23×C32C22×D312yes—
208C23×C32C23×C311yescharacteristic
209C22×C3⋊D3—41no—
210C22×C3⋊D3—41no—
211C22×C3⋊D3C2×C3×C414yescomplemented
212C22×C3⋊D3C23×C311yescharacteristic
213C22×C3⋊D3C23×C311yescharacteristic
214C22×C3×D3—22no—
215C22×C3×D3—32no—
216C22×C3×D3—32no—
217C22×C3×D3—38no—
218C22×C3×D3—38no—
219C22×C3×D3—61no—
220C22×C3×D3—61no—
221C22×C3×D3—64no—
222C22×C3×D3—122no—
223C22×C3×D3—122no—
224C22×C3×D3—122no—
225C22×C3×D3—122no—
226C22×C3×D3—122no—
227C22×C3×D3—122no—
228C22×C3×D3C22×D312yes—
229C22×C3×D3C23×C312yes—
230C2×D32—41no—
231C2×D32—41no—
232C2×D32C2×C3×C414yescomplemented
233C32×D4—38no—
234C2×C32×C4—22no—
235C2×C32×C4—22no—
236C2×C32×C4—22no—
237C2×C32×C4—32no—
238C2×C32×C4—32no—
239C2×C32×C4—32no—
240C2×C32×C4—42no—
241C2×C32×C4—42no—
242C2×C32×C4—41no—
243C2×C32×C4—44no—
244C2×C32×C4—42no—
245C2×C32×C4—44no—
246C2×C32×C4—122no—
247C2×C32×C4C22×D312yes—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C23×C312yes—
250C2×C3⋊Dic3—41no—
251C2×C3⋊Dic3C23×C312yes—
252C3×#67—28no—
253C3×#67—38no—
254C3×#67C4×D318yescomplemented
255C3×#67C2×C3×C418yescomplemented
256C2×C3×Dic3—22no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—62no—
262C2×C3×Dic3—122no—
263C2×C3×Dic3—122no—
264C2×C3×Dic3—122no—
265C2×C3×Dic3C22×D312yes—
266C2×C3×Dic3C22×D312yes—
267C2×C3×Dic3C22×D312yes—
268C2×C3×Dic3C23×C312yes—
269C2×C3×Dic3C23×C312yes—
270C2×C3×Dic3C23×C312yes—
271C3×D12—38no—
272C3×C4×D3—38no—
273C3×C4×D3—42no—
274C3×C4×D3—42no—
275C3×C4×D3—44no—
276C3×C4×D3—122no—
277C3×C4×D3—122no—
278C3×C4×D3—122no—
279#626C2×C3×C418yescomplemented
280#624—41no—
281#624—41no—
282#624C2×C3×C414yescomplemented
283D3×Dic3—42no—
284#518—91noSylow
285C2×C33—22no—
286C2×C33C23×C411yescharacteristic
287C2×C33H(5,𝔽2)11yescharacteristic
288C2×C33H(5,𝔽2)11yescharacteristic
289C3×C3⋊D3—22no—
290C3×C3⋊D3—22no—
291C32×D3—24no—
292C24×C3—91no—
293C24×C3—91no—
294C23×D3—32no—
295C23×D3—32no—
296C23×D3—61no—
297C2×C3×D4—32no—
298C2×C3×D4—32no—
299C2×C3×D4—62no—
300C2×C3×D4—92no—
301C2×C3×D4—98no—
302C22×C3×C4—21no—
303C22×C3×C4—22no—
304C22×C3×C4—32no—
305C22×C3×C4—32no—
306C22×C3×C4—41no—
307C22×C3×C4—62no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C22×C3×C4—91no—
311C22×C3×C4—92no—
312C22×C3×C4—91no—
313C22×C3×C4D3211yescharacteristic, complemented
314C22×C3×C4C2×C3×D312yescomplemented
315C2×#67—32no—
316C2×#67C2×C3×D312yes—
317C22×Dic3—32no—
318C22×Dic3—32no—
319C22×Dic3—61no—
320D3×D4—316no—
321C2×D12—32no—
322C2×C4×D3—32no—
323C2×C4×D3—32no—
324C2×C4×D3—32no—
325C2×C4×D3—32no—
326C2×C4×D3C2×C3×D312yescomplemented
327C3×C4⋊C4—32no—
328C3×C4⋊C4—32no—
329C3×C4⋊C4—62no—
330C3×C4⋊C4—92no—
331C3×C22⋊C4—32no—
332C3×C22⋊C4—32no—
333C3×C22⋊C4—32no—
334C3×C22⋊C4—32no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—62no—
337C3×C22⋊C4—92no—
338C3×C22⋊C4—92no—
339C3×C22⋊C4—92no—
340C3×C22⋊C4—92no—
341C3×C42—32no—
342C3×C42—32no—
343C3×C42—62no—
344C3×C42—92no—
345#217—32no—
346#217C2×C3×D312yescomplemented
347(C2×D3)⋊C4—32no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—32no—
351(C2×D3)⋊C4—32no—
352(C2×D3)⋊C4—32no—
353(C2×D3)⋊C4—32no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4C2×C3×D312yescomplemented
357C4⋊Dic3—32no—
358Dic3⋊C4—32no—
359Dic3⋊C4C2×C3×D312yescomplemented
360C4×Dic3—32no—
361C4×Dic3—32no—
362C4×Dic3C2×C3×D312yescomplemented
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—21no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—24no—
373C22×C32—34no—
374C22×C32—42no—
375C22×C32—41no—
376C22×C32—42no—
377C22×C32—42no—
378C22×C32—42no—
379C22×C32—42no—
380C22×C32—62no—
381C22×C32—62no—
382C22×C32C2×C4×D314yes—
383C22×C32C22×C3×C412yes—
384C22×C32C23×D312yes—
385C22×C32C24×C311yescharacteristic
386C2×C3⋊D3—21no—
387C2×C3⋊D3—21no—
388C2×C3⋊D3—21no—
389C2×C3⋊D3—21no—
390C2×C3⋊D3—44no—
391C2×C3⋊D3C22×C3×C412yes—
392C2×C3⋊D3C22×C3×C412yes—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—24no—
398C2×C3×D3—34no—
399C2×C3×D3—34no—
400C2×C3×D3—42no—
401C2×C3×D3—42no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—62no—
408C2×C3×D3—121no—
409C2×C3×D3—121no—
410C2×C3×D3—121no—
411C2×C3×D3—121no—
412C2×C3×D3—128no—
413C2×C3×D3—128no—
414C2×C3×D3—128no—
415C2×C3×D3C2×C4×D314yes—
416C2×C3×D3C22×C3×C414yes—
417D32—44no—
418C32×C4—22no—
419C32×C4—24no—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—34no—
423C32×C4—42no—
424C32×C4—42no—
425C32×C4—44no—
426C32×C4—62no—
427C32×C4—62no—
428C3⋊Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—22no—
431C3×Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—24no—
434C3×Dic3—42no—
435C3×Dic3—42no—
436C3×Dic3—62no—
437C3×Dic3—62no—
438C3×Dic3—122no—
439C3×Dic3C2×C4×D314yes—
440C3×Dic3C22×C3×C414yes—
441C22×D4—91no—
442C4×D4—32no—
443C4×D4—92no—
444C4×D4—92no—
445C4×D4—92no—
446#117—92no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—92no—
449C2×C22⋊C4—91no—
450C33#51811yescharacteristic, complemented, Sylow
451C23×C3—21no—
452C23×C3—22no—
453C23×C3—32no—
454C23×C3—32no—
455C23×C3—41no—
456C23×C3—62no—
457C23×C3—94no—
458C23×C3—91no—
459C23×C3—91no—
460C23×C3—94no—
461C23×C3—361no—
462C23×C3—361no—
463C23×C3—361no—
464C23×C3—361no—
465C23×C3C2×D3211yescharacteristic
466C23×C3C22×C3×D312yes—
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—38no—
470C22×D3—38no—
471C22×D3—64no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—122no—
475C22×D3—122no—
476C22×D3—122no—
477C22×D3—122no—
478C22×D3—122no—
479C22×D3—122no—
480C22×D3C22×C3×D312yes—
481C3×D4—38no—
482C3×D4—38no—
483C3×D4—68no—
484C3×D4—98no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—41no—
495C2×C3×C4—42no—
496C2×C3×C4—44no—
497C2×C3×C4—42no—
498C2×C3×C4—44no—
499C2×C3×C4—42no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—94no—
504C2×C3×C4—92no—
505C2×C3×C4—122no—
506C2×C3×C4—122no—
507C2×C3×C4—124no—
508C2×C3×C4—361no—
509C2×C3×C4—361no—
510C2×C3×C4—362no—
511C2×C3×C4—361no—
512C2×C3×C4C2×D3212yes—
513C2×C3×C4C22×C3×D312yes—
514C2×C3×C4C22×C3×D312yes—
515#67—38no—
516#67C3×C4×D318yescomplemented
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—62no—
520C2×Dic3—122no—
521C2×Dic3—122no—
522C2×Dic3—122no—
523C2×Dic3C22×C3×D312yes—
524C2×Dic3C22×C3×D312yes—
525C2×Dic3C22×C3×D312yes—
526D12—38no—
527C4×D3—38no—
528C4×D3—42no—
529C4×D3—122no—
530C4×D3—122no—
531C4×D3—122no—
532C2×C32—22no—
533C2×C32—24no—
534C2×C32—24no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—22no—
539C2×C32—22no—
540C2×C32—22no—
541C2×C32—41no—
542C2×C32—41no—
543C2×C32—41no—
544C2×C32—44no—
545C2×C32—44no—
546C2×C32—64no—
547C2×C32C22×C4×D312yes—
548C2×C32#100412yes—
549C2×C32#100912yes—
550C2×C32C23×C3×C411yescharacteristic
551C2×C32C3×H(5,𝔽2)11yescharacteristic
552C2×C32C3×H(5,𝔽2)11yescharacteristic
553C3⋊D3—22no—
554C3⋊D3—22no—
555C3×D3—24no—
556C3×D3—24no—
557C3×D3—44no—
558C3×D3—64no—
559C3×D3—64no—
560C3×D3—122no—
561C3×D3—122no—
562C24—91no—
563C24—91no—
564C2×D4—32no—
565C2×D4—92no—
566C2×D4—98no—
567C22×C4—32no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4—92no—
572C22×C4—91no—
573C22×C4C3×D3211yescharacteristic, complemented
574C4⋊C4—32no—
575C4⋊C4—92no—
576C22⋊C4—32no—
577C22⋊C4—32no—
578C22⋊C4—92no—
579C22⋊C4—92no—
580C22⋊C4—92no—
581C22⋊C4—92no—
582C42—32no—
583C42—92no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—21no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—24no—
594C22×C3—34no—
595C22×C3—34no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—41no—
601C22×C3—42no—
602C22×C3—64no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—92no—
608C22×C3—92no—
609C22×C3—122no—
610C22×C3—122no—
611C22×C3—181no—
612C22×C3—181no—
613C22×C3—181no—
614C22×C3—181no—
615C22×C3—364no—
616C22×C3—364no—
617C22×C3C4×D3212yes—
618C22×C3C2×C3×C4×D314yes—
619C22×C3C22×D3211yescharacteristic
620C22×C3C23×C3×D312yes—
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—34no—
624C2×D3—34no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—62no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—62no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—128no—
636C2×D3—128no—
637C2×D3—128no—
638C2×D3C2×C3×C4×D314yes—
639C3×C4—24no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—34no—
644C3×C4—34no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—44no—
648C3×C4—64no—
649C3×C4—62no—
650C3×C4—62no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—122no—
654C3×C4—122no—
655C3×C4—182no—
656Dic3—22no—
657Dic3—22no—
658Dic3—62no—
659Dic3—62no—
660Dic3—122no—
661Dic3C2×C3×C4×D314yes—
662C32—22no—
663C32—21no—
664C32—41no—
665C32#554512yescomplemented
666C32C3×#51811yescharacteristic, complemented
667C23—32no—
668C23—94no—
669C23—91no—
670C23—91no—
671C23—94no—
672C23—361no—
673C23—361no—
674C23—361no—
675C23—361no—
676C23C2×C3×D3211yescharacteristic
677D4—38no—
678D4—98no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—41no—
683C2×C4—94no—
684C2×C4—92no—
685C2×C4—122no—
686C2×C4—361no—
687C2×C4—361no—
688C2×C4—362no—
689C2×C4—361no—
690C2×C4C2×C3×D3212yes—
691C2×C3—24no—
692C2×C3—24no—
693C2×C3—22no—
694C2×C3—22no—
695C2×C3—21no—
696C2×C3—22no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—22no—
700C2×C3—44no—
701C2×C3—44no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—64no—
706C2×C3—64no—
707C2×C3—124no—
708C2×C3—182no—
709C2×C3—182no—
710C2×C3C2×C4×D3211yescharacteristic
711C2×C3#6430811yescharacteristic
712C2×C3#6433011yescharacteristic
713C2×C3C22×C3×C4×D312yes—
714C2×C3C3×#100412yes—
715C2×C3C3×#100912yes—
716D3—24no—
717D3—64no—
718D3—64no—
719D3—122no—
720D3—122no—
721C22—21no—
722C22—21no—
723C22—34no—
724C22—62no—
725C22—62no—
726C22—92no—
727C22—92no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22—364no—
733C22—364no—
734C22C3×C4×D3212yes—
735C22C22×C3×D3211yescharacteristic
736C4—22no—
737C4—34no—
738C4—62no—
739C4—62no—
740C4—182no—
741C3—21no—
742C3—22no—
743C3—41no—
744C3#1059505811yescharacteristic, direct product factor
745C3C3×#554512yescomplemented
746C2—22no—
747C2—64no—
748C2—182no—
749C2—182no—
750C2C2×C3×C4×D3211yescharacteristic
751C2C3×#6430811yescharacteristic
752C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC2×C3×#3811C2
cosocleC22×C32C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#518
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3752C2semidirect
3. C32×C4×#67C2semidirect
4. C3×#63974C2semidirect
5. C3×#67⋊Dic3C2semidirect
6. C3×D3×(C2×D3)⋊C4C2semidirect
7. C3×#63904C2semidirect
8. C3×#63880C2semidirect
9. C3×#63836C2semidirect
11. #10595058C3direct (N × H)
14. C22×C33×C4C22semidirect
15. C22×C3×C3⋊Dic3C22semidirect
17. C2×C32×C4×D3C22semidirect
18. C3×#3811C4semidirect
21. C2×C3×#624C22semidirect
22. C2×C3×#624C22semidirect
23. C2×C3×D3×Dic3C22semidirect
25. C3×#3752C22semidirect
26. C32×#217C22semidirect
27. C32×(C2×D3)⋊C4C22semidirect
28. C32×Dic3⋊C4C22semidirect
29. C32×C4×Dic3C22semidirect
30. C3×Dic3⋊Dic3C22semidirect
32. C3×(C2×D3)⋊Dic3C22semidirect
33. C3×Dic32C22semidirect
37. C2×#3752C2×C3semidirect
41. C3×C4×#67D3semidirect
42. C3×C4×#67C2×C3semidirect
54. #63974C2×C3semidirect
55. #67⋊Dic3C2×C3semidirect
56. D3×(C2×D3)⋊C4C2×C3semidirect
57. #63904C2×C3semidirect
58. #63880C2×C3semidirect
59. #63836C2×C3semidirect
63. C22×C3×C3⋊D3C2×C4semidirect
69. C2×C3×D32C2×C4semidirect
74. C32×#67C2×C4semidirect
79. C3×#626C2×C4semidirect
82. C3×#624C2×C4semidirect
96. C22×C32×C4C2×D3semidirect
97. C22×C32×C4C22×C3semidirect
98. C22×C3⋊Dic3C22×C3semidirect
113. C2×C3×C4×D3C2×D3semidirect
114. C2×C3×C4×D3C22×C3semidirect
115. #3811C3×C4semidirect
118. C2×#624C22×C3semidirect
119. C2×#624C22×C3semidirect
120. C2×D3×Dic3C22×C3semidirect
126. #3752C22×C3semidirect
129. C3×#217C2×D3semidirect
130. C3×#217C22×C3semidirect
141. C3×(C2×D3)⋊C4C2×D3semidirect
142. C3×(C2×D3)⋊C4C22×C3semidirect
146. C3×Dic3⋊C4C2×D3semidirect
147. C3×Dic3⋊C4C22×C3semidirect
151. C3×C4×Dic3C2×D3semidirect
152. C3×C4×Dic3C22×C3semidirect
153. Dic3⋊Dic3C22×C3semidirect
155. (C2×D3)⋊Dic3C22×C3semidirect
156. Dic32C22×C3semidirect
191. C4×#67C3×D3semidirect
211. C22×C3⋊D3C2×C3×C4semidirect
232. C2×D32C2×C3×C4semidirect
254. C3×#67C4×D3semidirect
255. C3×#67C2×C3×C4semidirect
279. #626C2×C3×C4semidirect
282. #624C2×C3×C4semidirect
313. C22×C3×C4D32semidirect
314. C22×C3×C4C2×C3×D3semidirect
326. C2×C4×D3C2×C3×D3semidirect
346. #217C2×C3×D3semidirect
356. (C2×D3)⋊C4C2×C3×D3semidirect
359. Dic3⋊C4C2×C3×D3semidirect
362. C4×Dic3C2×C3×D3semidirect
450. C33#518semidirect
516. #67C3×C4×D3semidirect
573. C22×C4C3×D32semidirect
665. C32#5545semidirect
666. C32C3×#518semidirect
744. C3#10595058direct (N × H)
745. C3C3×#5545semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38112
C2×C3×#37522
C32×C4×#672
C3×#639742
C3×#67⋊Dic32
C3×D3×(C2×D3)⋊C42
C3×#639042
C3×#638802
C3×#638362
C3×#55453
#105950583