Finite Group Databasebeta

← C2×C3×#63853 #13174591

Subgroups — C2×C3×#63853 #13174591

Order 1728.

1882 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C3×#626C211yesmaximal, characteristic
3C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×#3722C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#63853C218yesmaximal, direct product factor
9C2×C3×#894—31nomaximal
10C2×C3×#883—31nomaximal
11C2×#63853C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C22×C33×C4C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4×C3⋊D3—24no—
17C2×C3×C4×C3⋊D3C2214yescomplemented
18C22×C32×Dic3C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic
21C2×C3×#626—24no—
22C2×C3×#626C2214yes—
23C32×(C2×D3)⋊C4C2214yescomplemented
24C32×Dic3⋊C4C2214yescomplemented
25C3×Dic3⋊Dic3C2214yescomplemented
26C3×#3722C2214yescomplemented
27C3×(C2×D3)⋊Dic3C2214yescomplemented
28C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
29C22×C3×#67—31no—
30C22×C3×D12—31no—
31C22×C3×C4×D3—31no—
32C22×C3×C4×D3—31no—
33C22×C3×C4×D3—61no—
34C22×#626C2×C311yescharacteristic
35C2×C32×C4⋊C4—31no—
36C2×C32×C22⋊C4—31no—
37C2×C3×#217—31no—
38C2×C3×(C2×D3)⋊C4—21no—
39C2×C3×(C2×D3)⋊C4—31no—
40C2×C3×(C2×D3)⋊C4—31no—
41C2×C3×(C2×D3)⋊C4—31no—
42C2×C3×(C2×D3)⋊C4D311yescharacteristic, complemented
43C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
44C2×C3×C4⋊Dic3—31no—
45C2×C3×Dic3⋊C4—21no—
46C2×C3×Dic3⋊C4—31no—
47C2×C3×Dic3⋊C4D311yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2×C311yescharacteristic, complemented
49C3×#894—38no—
50C3×#883—38no—
51C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
52C2×#3722C2×C311yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
54#63853C2×C318yesdirect product factor
55C23×C33C2311yescharacteristic
56C22×C3×C3⋊D3—22no—
57C22×C3×C3⋊D3—22no—
58C22×C3×C3⋊D3D414yes—
59C22×C3×C3⋊D3C2312yes—
60C22×C32×D3—22no—
61C22×C32×D3—22no—
62C22×C32×D3—22no—
63C22×C32×D3C2312yes—
64C2×C33×C4—22no—
65C2×C33×C4C2312yes—
66C2×C3×C3⋊Dic3—22no—
67C2×C3×C3⋊Dic3C2312yes—
68C3×C4×C3⋊D3—28no—
69C2×C32×Dic3—22no—
70C2×C32×Dic3—22no—
71C2×C32×Dic3—22no—
72C2×C32×Dic3C2312yes—
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C3×#626—28no—
76C2×C3×#123—91no—
77C2×#894—31no—
78C2×#883—31no—
79C24×C32—31no—
80C23×C3⋊D3C22×C311yescharacteristic
81C23×C3×D3—21no—
82C23×C3×D3—31no—
83C23×C3×D3—31no—
84C23×C3×D3—61no—
85C23×C3×D3C2×D311yescharacteristic
86C23×C3×D3C22×C311yescharacteristic
87C22×C32×C4—21no—
88C22×C32×C4—21no—
89C22×C32×C4—21no—
90C22×C32×C4—31no—
91C22×C32×C4—31no—
92C22×C32×C4—31no—
93C22×C32×C4—41no—
94C22×C32×C4C2×D311yescharacteristic
95C22×C32×C4C2×D311yescharacteristic
96C22×C32×C4C22×C311yescharacteristic
97C22×C3⋊Dic3C22×C311yescharacteristic
98C2×C4×C3⋊D3—24no—
99C2×C4×C3⋊D3C22×C314yescomplemented
100C2×C3×#67—34no—
101C2×C3×#67—64no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—31no—
106C22×C3×Dic3—31no—
107C22×C3×Dic3—61no—
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C2×D311yescharacteristic
110C22×C3×Dic3C2×D311yescharacteristic
111C22×C3×Dic3C22×C311yescharacteristic
112C22×C3×Dic3C22×C311yescharacteristic
113C22×C3×Dic3C22×C311yescharacteristic
114C2×C3×D12—34no—
115C2×C3×D12—64no—
116C2×C3×C4×D3—34no—
117C2×C3×C4×D3—34no—
118C2×C3×C4×D3—64no—
119C2×C3×C4×D3—64no—
120C2×C3×C4×D3—64no—
121C2×C3×C4×D3—68no—
122C2×#626—24no—
123C2×#626C22×C314yes—
124C32×C4⋊C4—34no—
125C32×C22⋊C4—34no—
126C3×#217—34no—
127C3×(C2×D3)⋊C4—24no—
128C3×(C2×D3)⋊C4—34no—
129C3×(C2×D3)⋊C4—34no—
130C3×(C2×D3)⋊C4—34no—
131C3×(C2×D3)⋊C4C2×D314yescomplemented
132C3×(C2×D3)⋊C4C22×C314yescomplemented
133C3×C4⋊Dic3—34no—
134C3×Dic3⋊C4—24no—
135C3×Dic3⋊C4—34no—
136C3×Dic3⋊C4C2×D314yescomplemented
137C3×Dic3⋊C4C22×C314yescomplemented
138Dic3⋊Dic3C22×C314yescomplemented
139#3722C22×C314yescomplemented
140(C2×D3)⋊Dic3C22×C314yescomplemented
141C22×C33C2×D412yes—
142C22×C33#4112yes—
143C22×C33#4112yes—
144C22×C33C2411yescharacteristic
145C2×C3×C3⋊D3—28no—
146C2×C3×C3⋊D3—22no—
147C2×C3×C3⋊D3—22no—
148C2×C3×C3⋊D3C2×D414yes—
149C2×C32×D3—22no—
150C2×C32×D3—22no—
151C2×C32×D3—22no—
152C2×C32×D3—44no—
153C33×C4—22no—
154C3×C3⋊Dic3—22no—
155C32×Dic3—22no—
156C32×Dic3—22no—
157C32×Dic3—22no—
158C22×C3×D4—91no—
159C23×C3×C4—91no—
160C22×#67—31no—
161C22×D12—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—61no—
165C3×#123—98no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—61no—
169C2×C3×C4⋊C4—91no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—61no—
173C2×C3×C22⋊C4—91no—
174C2×C3×C22⋊C4—91no—
175C2×#217—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4C3×D311yescharacteristic, complemented
180C2×C4⋊Dic3—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4C3×D311yescharacteristic, complemented
183#894—38no—
184#883—38no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—32no—
189C23×C32—41no—
190C23×C32—62no—
191C23×C32—62no—
192C23×C32—62no—
193C23×C32C22×D311yescharacteristic
194C23×C32C22×D311yescharacteristic
195C23×C32C23×C311yescharacteristic
196C22×C3⋊D3—22no—
197C22×C3⋊D3—22no—
198C22×C3⋊D3C3×D414yes—
199C22×C3⋊D3C23×C312yes—
200C22×C3×D3—24no—
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3—22no—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3—34no—
209C22×C3×D3—34no—
210C22×C3×D3—32no—
211C22×C3×D3—32no—
212C22×C3×D3—42no—
213C22×C3×D3—42no—
214C22×C3×D3—64no—
215C22×C3×D3—62no—
216C22×C3×D3—64no—
217C22×C3×D3—64no—
218C22×C3×D3—62no—
219C22×C3×D3—62no—
220C22×C3×D3—62no—
221C22×C3×D3—62no—
222C22×C3×D3C22×D312yes—
223C22×C3×D3C23×C312yes—
224C2×C32×C4—22no—
225C2×C32×C4—24no—
226C2×C32×C4—22no—
227C2×C32×C4—22no—
228C2×C32×C4—22no—
229C2×C32×C4—22no—
230C2×C32×C4—22no—
231C2×C32×C4—32no—
232C2×C32×C4—32no—
233C2×C32×C4—32no—
234C2×C32×C4—42no—
235C2×C32×C4—42no—
236C2×C32×C4—42no—
237C2×C32×C4—44no—
238C2×C32×C4—62no—
239C2×C32×C4—62no—
240C2×C32×C4—62no—
241C2×C32×C4C22×D312yes—
242C2×C32×C4C22×D312yes—
243C2×C32×C4C23×C312yes—
244C2×C3⋊Dic3—22no—
245C2×C3⋊Dic3C23×C312yes—
246C4×C3⋊D3—28no—
247C3×#67—68no—
248C2×C3×Dic3—24no—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—22no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3—62no—
263C2×C3×Dic3—64no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3—62no—
266C2×C3×Dic3C22×D312yes—
267C2×C3×Dic3C22×D312yes—
268C2×C3×Dic3C22×D312yes—
269C2×C3×Dic3C23×C312yes—
270C2×C3×Dic3C23×C312yes—
271C2×C3×Dic3C23×C312yes—
272C3×D12—68no—
273C3×C4×D3—68no—
274C3×C4×D3—68no—
275C3×C4×D3—616no—
276#626—28no—
277C2×#123—91noSylow
278C2×C33#12314yescomplemented
279C2×C33C22×D411yescharacteristic
280C2×C33C2×#4111yescharacteristic
281C2×C33C2×#4111yescharacteristic
282C3×C3⋊D3—24no—
283C32×D3—42no—
284C24×C3—31no—
285C24×C3—31no—
286C24×C3—61no—
287C24×C3—91no—
288C23×D3—31no—
289C23×D3—31no—
290C23×D3—61no—
291C23×D3C2×C3×D311yescharacteristic
292C2×C3×D4—94no—
293C2×C3×D4—184no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—91no—
308C22×C3×C4—94no—
309C22×C3×C4—184no—
310C22×C3×C4D3211yescharacteristic
311C22×C3×C4C2×C3×D311yescharacteristic
312C22×C3×C4C2×C3×D311yescharacteristic
313C2×#67—34no—
314C2×#67—64no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—61no—
318C22×Dic3C2×C3×D311yescharacteristic
319C22×Dic3C2×C3×D311yescharacteristic
320C22×Dic3C2×C3×D311yescharacteristic
321C2×D12—34no—
322C2×D12—64no—
323C2×C4×D3—34no—
324C2×C4×D3—34no—
325C2×C4×D3—64no—
326C2×C4×D3—64no—
327C2×C4×D3—64no—
328C2×C4×D3—68no—
329C3×C4⋊C4—34no—
330C3×C4⋊C4—34no—
331C3×C4⋊C4—64no—
332C3×C4⋊C4—94no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4—34no—
335C3×C22⋊C4—64no—
336C3×C22⋊C4—94no—
337C3×C22⋊C4—94no—
338#217—34no—
339(C2×D3)⋊C4—34no—
340(C2×D3)⋊C4—34no—
341(C2×D3)⋊C4—34no—
342(C2×D3)⋊C4C2×C3×D314yescomplemented
343C4⋊Dic3—34no—
344Dic3⋊C4—34no—
345Dic3⋊C4C2×C3×D314yescomplemented
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—22no—
356C22×C32—22no—
357C22×C32—22no—
358C22×C32—42no—
359C22×C32—42no—
360C22×C32—42no—
361C22×C32—41no—
362C22×C32—62no—
363C22×C32—62no—
364C22×C32—62no—
365C22×C32—124no—
366C22×C32#23512yes—
367C22×C32#23512yes—
368C22×C32D3×D412yes—
369C22×C32D3×D412yes—
370C22×C32#23712yes—
371C22×C32#23912yes—
372C22×C32C2×C3×D412yes—
373C22×C32C3×#4112yes—
374C22×C32C3×#4112yes—
375C22×C32C23×D311yescharacteristic
376C22×C32C23×D311yescharacteristic
377C22×C32C24×C311yescharacteristic
378C2×C3⋊D3—28no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3—22no—
381C2×C3⋊D3C2×C3×D414yes—
382C2×C3×D3—24no—
383C2×C3×D3—22no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—34no—
390C2×C3×D3—34no—
391C2×C3×D3—42no—
392C2×C3×D3—42no—
393C2×C3×D3—48no—
394C2×C3×D3—44no—
395C2×C3×D3—44no—
396C2×C3×D3—64no—
397C2×C3×D3—64no—
398C2×C3×D3—64no—
399C2×C3×D3—616no—
400C2×C3×D3—68no—
401C2×C3×D3—68no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C32×C4—22no—
407C32×C4—24no—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—42no—
411C32×C4—42no—
412C32×C4—44no—
413C32×C4—62no—
414C32×C4—62no—
415C32×C4—62no—
416C3⋊Dic3—22no—
417C3×Dic3—24no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—22no—
424C3×Dic3—42no—
425C3×Dic3—42no—
426C3×Dic3—64no—
427C3×Dic3—62no—
428C3×Dic3—62no—
429C22×D4—91no—
430C23×C4—91no—
431#123—98no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—91no—
437C33C2×#12311yescharacteristic, complemented, Sylow
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—32no—
442C23×C3—32no—
443C23×C3—41no—
444C23×C3—62no—
445C23×C3—64no—
446C23×C3—62no—
447C23×C3—62no—
448C23×C3—62no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3—92no—
453C23×C3—94no—
454C23×C3—122no—
455C23×C3—122no—
456C23×C3—182no—
457C23×C3—182no—
458C23×C3C2×D3211yescharacteristic
459C23×C3C22×C3×D311yescharacteristic
460C23×C3C22×C3×D311yescharacteristic
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—32no—
465C22×D3—32no—
466C22×D3—34no—
467C22×D3—34no—
468C22×D3—64no—
469C22×D3—62no—
470C22×D3—64no—
471C22×D3—64no—
472C22×D3—62no—
473C22×D3—62no—
474C22×D3—62no—
475C22×D3—62no—
476C22×D3C22×C3×D312yes—
477C3×D4—188no—
478C2×C3×C4—24no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—44no—
494C2×C3×C4—42no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—64no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—92no—
506C2×C3×C4—122no—
507C2×C3×C4—122no—
508C2×C3×C4—188no—
509C2×C3×C4—182no—
510C2×C3×C4C2×D3212yes—
511C2×C3×C4C22×C3×D312yes—
512C2×C3×C4C22×C3×D312yes—
513#67—68no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—62no—
520C2×Dic3—64no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3C22×C3×D312yes—
524C2×Dic3C22×C3×D312yes—
525C2×Dic3C22×C3×D312yes—
526D12—68no—
527C4×D3—68no—
528C4×D3—68no—
529C4×D3—616no—
530C2×C32—24no—
531C2×C32—24no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—24no—
542C2×C32—44no—
543C2×C32—41no—
544C2×C32—41no—
545C2×C32—41no—
546C2×C32—122no—
547C2×C32#88314yescomplemented
548C2×C32#89414yescomplemented
549C2×C32C3×#12314yescomplemented
550C2×C32C2×#23511yescharacteristic
551C2×C32C2×#23511yescharacteristic
552C2×C32C2×D3×D411yescharacteristic
553C2×C32C2×D3×D411yescharacteristic
554C2×C32C2×#23711yescharacteristic
555C2×C32C2×#23911yescharacteristic
556C2×C32C22×C3×D411yescharacteristic
557C2×C32C2×C3×#4111yescharacteristic
558C2×C32C2×C3×#4111yescharacteristic
559C3⋊D3—24no—
560C3×D3—44no—
561C3×D3—42no—
562C3×D3—42no—
563C3×D3—68no—
564C3×D3—64no—
565C3×D3—64no—
566C24—31no—
567C24—91no—
568C2×D4—94no—
569C2×D4—184no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—91no—
574C22×C4—94no—
575C22×C4—184no—
576C22×C4C3×D3211yescharacteristic
577C4⋊C4—34no—
578C4⋊C4—94no—
579C22⋊C4—34no—
580C22⋊C4—94no—
581C22⋊C4—94no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—41no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—64no—
599C22×C3—62no—
600C22×C3—62no—
601C22×C3—62no—
602C22×C3—62no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—94no—
606C22×C3—122no—
607C22×C3—122no—
608C22×C3—128no—
609C22×C3—124no—
610C22×C3—124no—
611C22×C3—182no—
612C22×C3—182no—
613C22×C3—188no—
614C22×C3#379612yes—
615C22×C3#379812yes—
616C22×C3#381112yes—
617C22×C3C3×#23512yes—
618C22×C3C3×#23512yes—
619C22×C3C3×D3×D412yes—
620C22×C3C3×D3×D412yes—
621C22×C3C3×#23712yes—
622C22×C3C3×#23912yes—
623C22×C3C22×D3211yescharacteristic
624C22×C3C23×C3×D311yescharacteristic
625C22×C3C23×C3×D311yescharacteristic
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—34no—
630C2×D3—34no—
631C2×D3—44no—
632C2×D3—64no—
633C2×D3—616no—
634C2×D3—64no—
635C2×D3—64no—
636C2×D3—68no—
637C2×D3—68no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—62no—
641C2×D3—62no—
642C3×C4—24no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—44no—
649C3×C4—64no—
650C3×C4—62no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—122no—
657C3×C4—122no—
658C3×C4—182no—
659Dic3—22no—
660Dic3—22no—
661Dic3—22no—
662Dic3—64no—
663Dic3—62no—
664Dic3—62no—
665C32—21no—
666C32—21no—
667C32—21no—
668C32—41no—
669C32C2×#88311yescharacteristic, complemented
670C32C2×#89411yescharacteristic, complemented
671C32C2×C3×#12311yescharacteristic, complemented
672C23—32no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23—92no—
677C23—94no—
678C23—182no—
679C23—182no—
680C23C2×C3×D3211yescharacteristic
681D4—188no—
682C2×C4—22no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—92no—
690C2×C4—188no—
691C2×C4—182no—
692C2×C4C2×C3×D3212yes—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—24no—
697C2×C3—24no—
698C2×C3—24no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—41no—
706C2×C3—44no—
707C2×C3—41no—
708C2×C3—41no—
709C2×C3—124no—
710C2×C3—122no—
711C2×C3—122no—
712C2×C3—184no—
713C2×C3#6385314yesdirect product factor
714C2×C3C3×#88314yescomplemented
715C2×C3C3×#89414yescomplemented
716C2×C3C2×#379611yescharacteristic
717C2×C3C2×#379811yescharacteristic
718C2×C3C2×#381111yescharacteristic
719C2×C3C2×C3×#23511yescharacteristic
720C2×C3C2×C3×#23511yescharacteristic
721C2×C3C2×C3×D3×D411yescharacteristic
722C2×C3C2×C3×D3×D411yescharacteristic
723C2×C3C2×C3×#23711yescharacteristic
724C2×C3C2×C3×#23911yescharacteristic
725D3—42no—
726D3—68no—
727D3—64no—
728D3—64no—
729C22—62no—
730C22—62no—
731C22—62no—
732C22—94no—
733C22—124no—
734C22—188no—
735C22—182no—
736C22—182no—
737C22C3×#379612yes—
738C22C3×#379812yes—
739C22C3×#381112yes—
740C22C22×C3×D3211yescharacteristic
741C4—22no—
742C4—62no—
743C4—62no—
744C4—62no—
745C4—182no—
746C3—21no—
747C3—21no—
748C3—21no—
749C3—41no—
750C3C2×#6385311yescharacteristic, direct product factor
751C3C2×C3×#88311yescharacteristic, complemented
752C3C2×C3×#89411yescharacteristic, complemented
753C2—122no—
754C2—184no—
755C2C3×#6385314yesdirect product factor
756C2C2×C3×#379611yescharacteristic
757C2C2×C3×#379811yescharacteristic
758C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC22×C3×#626C2
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#123
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. C22×C3×C4×C3⋊D3C2semidirect
3. C2×C32×(C2×D3)⋊C4C2semidirect
4. C2×C32×Dic3⋊C4C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
6. C2×C3×#3722C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. C3×#63853C2direct (N × H)
11. C2×#63853C3direct (N × H)
17. C2×C3×C4×C3⋊D3C22semidirect
23. C32×(C2×D3)⋊C4C22semidirect
24. C32×Dic3⋊C4C22semidirect
25. C3×Dic3⋊Dic3C22semidirect
26. C3×#3722C22semidirect
27. C3×(C2×D3)⋊Dic3C22semidirect
28. C22×C4×C3⋊D3C2×C3semidirect
42. C2×C3×(C2×D3)⋊C4D3semidirect
43. C2×C3×(C2×D3)⋊C4C2×C3semidirect
47. C2×C3×Dic3⋊C4D3semidirect
48. C2×C3×Dic3⋊C4C2×C3semidirect
51. C2×Dic3⋊Dic3C2×C3semidirect
52. C2×#3722C2×C3semidirect
53. C2×(C2×D3)⋊Dic3C2×C3semidirect
54. #63853C2×C3direct (N × H)
99. C2×C4×C3⋊D3C22×C3semidirect
131. C3×(C2×D3)⋊C4C2×D3semidirect
132. C3×(C2×D3)⋊C4C22×C3semidirect
136. C3×Dic3⋊C4C2×D3semidirect
137. C3×Dic3⋊C4C22×C3semidirect
138. Dic3⋊Dic3C22×C3semidirect
139. #3722C22×C3semidirect
140. (C2×D3)⋊Dic3C22×C3semidirect
179. C2×(C2×D3)⋊C4C3×D3semidirect
182. C2×Dic3⋊C4C3×D3semidirect
278. C2×C33#123semidirect
342. (C2×D3)⋊C4C2×C3×D3semidirect
345. Dic3⋊C4C2×C3×D3semidirect
437. C33C2×#123semidirect
547. C2×C32#883semidirect
548. C2×C32#894semidirect
549. C2×C32C3×#123semidirect
669. C32C2×#883semidirect
670. C32C2×#894semidirect
671. C32C2×C3×#123semidirect
713. C2×C3#63853direct (N × H)
714. C2×C3C3×#883semidirect
715. C2×C3C3×#894semidirect
750. C3C2×#63853direct (N × H)
751. C3C2×C3×#883semidirect
752. C3C2×C3×#894semidirect
755. C2C3×#63853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C22×C3×#6262
C2×C32×(C2×D3)⋊C42
C2×C32×Dic3⋊C42
C2×C3×Dic3⋊Dic32
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
C3×#638532
C2×C3×#8943
C2×C3×#8833
C2×#638533