Finite Group Databasebeta

← C2×C3×#63952 #13175089

Subgroups — C2×C3×#63952 #13175089

Order 1728.

2442 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic
2C23×C32×Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#624C211yesmaximal, characteristic, complemented
4C2×C32×#217C211yesmaximal, characteristic, complemented
5C2×C3×#3724C211yesmaximal, characteristic, complemented
6C2×C3×#3722C211yesmaximal, characteristic, complemented
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8C3×#63952C218yesmaximal, direct product factor
9C2×C3×C4×#67—31nomaximal
10C2×C3×#67⋊C4—31nomaximal
11C2×#63952C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C2×C3×#638C418yescomplemented
15C2×C3×#638C2214yes—
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C32×Dic3—24no—
18C22×C32×Dic3C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2214yescomplemented
23C2×C3×#624—24no—
24C2×C3×#624C2214yescomplemented
25C32×#217C2214yescomplemented
26C3×#3724C2214yescomplemented
27C3×#3722C2214yescomplemented
28C3×Dic32C2214yescomplemented
29C23×C32×C4—31no—
30C22×#638C2×C311yescharacteristic
31C22×C3×#67—31no—
32C22×C3×#67—31no—
33C22×C3×#67—61no—
34C23×C3×Dic3—21no—
35C23×C3×Dic3D311yescharacteristic, complemented
36C23×C3×Dic3C2×C311yescharacteristic, complemented
37C22×C3×C4×D3—31no—
38C22×C3×C4×D3—31no—
39C22×#624C2×C311yescharacteristic, complemented
40C2×C32×C22⋊C4—31no—
41C2×C3×#217—21no—
42C2×C3×#217D311yescharacteristic, complemented
43C2×C3×#217C2×C311yescharacteristic, complemented
44C3×C4×#67—38no—
45C2×C3×(C2×D3)⋊C4—31no—
46C2×C3×(C2×D3)⋊C4—31no—
47C2×C3×Dic3⋊C4—31no—
48C2×C3×Dic3⋊C4—31no—
49C2×C3×C4×Dic3—31no—
50C2×C3×C4×Dic3—31no—
51C3×#67⋊C4—38no—
52C2×#3724C2×C311yescharacteristic, complemented
53C2×#3722C2×C311yescharacteristic, complemented
54C2×Dic32C2×C311yescharacteristic, complemented
55#63952C2×C318yesdirect product factor
56C23×C33—22no—
57C23×C33—22no—
58C23×C33C2×C414yescomplemented
59C23×C33C2312yes—
60C23×C33C2311yescharacteristic
61C22×C3×C3⋊D3—22no—
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3C2×C414yescomplemented
64C22×C3×C3⋊D3C2312yes—
65C3×#638C2×C4116yescomplemented
66C2×C3×C3⋊Dic3C2×C414yescomplemented
67C2×C3×C3⋊Dic3C2312yes—
68C2×C32×Dic3—22no—
69C2×C32×Dic3—22no—
70C2×C32×Dic3—22no—
71C2×C32×Dic3—28no—
72C2×C32×Dic3D414yescomplemented
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C3×#624—28no—
78C2×C3×C4×D4—91no—
79C2×C4×#67—31no—
80C2×#67⋊C4—31no—
81C24×C32—21no—
82C24×C32—21no—
83C24×C32—21no—
84C24×C32—41no—
85C24×C32C2×D311yescharacteristic
86C24×C32C2×D311yescharacteristic
87C24×C32C22×C311yescharacteristic
88C23×C3⋊D3C22×C311yescharacteristic
89C23×C3×D3—31no—
90C23×C3×D3—31no—
91C23×C3×D3—61no—
92C22×C32×C4—31no—
93C22×C32×C4—31no—
94C22×C32×C4—31no—
95C22×C32×C4—31no—
96C22×C32×C4—34no—
97C22×C32×C4—64no—
98C2×#638C3×C418yescomplemented
99C2×#638C22×C314yes—
100C22×C3⋊Dic3C22×C311yescharacteristic
101C2×C3×#67—38no—
102C2×C3×#67—38no—
103C2×C3×#67—34no—
104C2×C3×#67—34no—
105C2×C3×#67—68no—
106C2×C3×#67—64no—
107C22×C3×Dic3—28no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—24no—
111C22×C3×Dic3—24no—
112C22×C3×Dic3—24no—
113C22×C3×Dic3—21no—
114C22×C3×Dic3—21no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—31no—
117C22×C3×Dic3—61no—
118C22×C3×Dic3C2×D311yescharacteristic
119C22×C3×Dic3C2×D311yescharacteristic
120C22×C3×Dic3C2×D311yescharacteristic
121C22×C3×Dic3C2×D311yescharacteristic
122C22×C3×Dic3C2×D314yescomplemented
123C22×C3×Dic3C22×C311yescharacteristic
124C22×C3×Dic3C22×C311yescharacteristic
125C22×C3×Dic3C22×C311yescharacteristic
126C22×C3×Dic3C22×C311yescharacteristic
127C22×C3×Dic3C22×C314yescomplemented
128C2×C3×C4×D3—34no—
129C2×C3×C4×D3—34no—
130C2×C3×C4×D3—64no—
131C2×C3×C4×D3—64no—
132C2×#624—24no—
133C2×#624C22×C314yescomplemented
134C32×C22⋊C4—34no—
135C3×#217—24no—
136C3×#217C2×D314yescomplemented
137C3×#217C22×C314yescomplemented
138C3×(C2×D3)⋊C4—34no—
139C3×(C2×D3)⋊C4—34no—
140C3×Dic3⋊C4—34no—
141C3×Dic3⋊C4—34no—
142C3×C4×Dic3—34no—
143C3×C4×Dic3—34no—
144#3724C22×C314yescomplemented
145#3722C22×C314yescomplemented
146Dic32C22×C314yescomplemented
147C22×C33—28no—
148C22×C33—22no—
149C22×C33—22no—
150C22×C33C22×C412yes—
151C22×C33C22×C414yescomplemented
152C22×C33C2×D412yes—
153C22×C33#4112yes—
154C22×C33C2411yescharacteristic
155C2×C3×C3⋊D3—28no—
156C2×C3×C3⋊D3—22no—
157C2×C3×C3⋊D3—22no—
158C2×C3×C3⋊D3C22×C414yescomplemented
159C3×C3⋊Dic3C22×C414yescomplemented
160C32×Dic3—22no—
161C32×Dic3—22no—
162C32×Dic3—22no—
163C32×Dic3C2×D414yescomplemented
164C22×C3×D4—91no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C23×C3×C4—61no—
168C23×C3×C4—91no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—61no—
172C23×Dic3C3×D311yescharacteristic, complemented
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C3×C4×D4—98no—
176C2×C3×C4⋊C4—91no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—61no—
180C2×C3×C22⋊C4—91no—
181C2×C3×C42—91no—
182C2×#217C3×D311yescharacteristic, complemented
183C4×#67—38no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190#67⋊C4—38no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—24no—
194C23×C32—24no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—24no—
200C23×C32—24no—
201C23×C32—24no—
202C23×C32—22no—
203C23×C32—21no—
204C23×C32—22no—
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—22no—
208C23×C32—44no—
209C23×C32—41no—
210C23×C32—42no—
211C23×C32—42no—
212C23×C32—42no—
213C23×C32—42no—
214C23×C32—42no—
215C23×C32—44no—
216C23×C32—44no—
217C23×C32C4×D314yescomplemented
218C23×C32C4×D314yescomplemented
219C23×C32C2×C3×C414yescomplemented
220C23×C32C22×D312yes—
221C23×C32C22×D312yes—
222C23×C32C22×D311yescharacteristic
223C23×C32C22×D311yescharacteristic
224C23×C32C23×C312yes—
225C23×C32C23×C311yescharacteristic
226C22×C3⋊D3—22no—
227C22×C3⋊D3—22no—
228C22×C3⋊D3C2×C3×C414yescomplemented
229C22×C3⋊D3C23×C312yes—
230C22×C3×D3—34no—
231C22×C3×D3—34no—
232C22×C3×D3—32no—
233C22×C3×D3—32no—
234C22×C3×D3—64no—
235C22×C3×D3—62no—
236C22×C3×D3—62no—
237C22×C3×D3—62no—
238C22×C3×D3—62no—
239C22×C3×D3—62no—
240C22×C3×D3—122no—
241C22×C3×D3—122no—
242C2×C32×C4—34no—
243C2×C32×C4—32no—
244C2×C32×C4—32no—
245C2×C32×C4—32no—
246C2×C32×C4—32no—
247C2×C32×C4—68no—
248C2×C32×C4—62no—
249C2×C32×C4—62no—
250C2×C32×C4—62no—
251#638C2×C3×C4116yescomplemented
252C2×C3⋊Dic3C2×C3×C414yescomplemented
253C2×C3⋊Dic3C23×C312yes—
254C3×#67—316no—
255C3×#67—316no—
256C3×#67—616no—
257C2×C3×Dic3—24no—
258C2×C3×Dic3—216no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—28no—
266C2×C3×Dic3—28no—
267C2×C3×Dic3—24no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—34no—
273C2×C3×Dic3—34no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—42no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3—64no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3#6714yescomplemented
281C2×C3×Dic3C3×D414yescomplemented
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C23×C312yes—
287C2×C3×Dic3C23×C312yes—
288C2×C3×Dic3C23×C312yes—
289C2×C3×Dic3C23×C312yes—
290C3×C4×D3—68no—
291C3×C4×D3—68no—
292#624—28no—
293C2×C4×D4—91noSylow
294C2×C33—24no—
295C2×C33C4×D414yescomplemented
296C2×C33C23×C411yescharacteristic
297C2×C33C22×D411yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C3×C3⋊D3—24no—
300C24×C3—21no—
301C24×C3—21no—
302C24×C3—21no—
303C24×C3—41no—
304C24×C3—91no—
305C24×C3D3211yescharacteristic
306C24×C3C2×C3×D311yescharacteristic
307C24×C3C2×C3×D311yescharacteristic
308C23×D3—31no—
309C23×D3—31no—
310C23×D3—61no—
311C2×C3×D4—98no—
312C2×C3×D4—94no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—34no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—34no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—64no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—64no—
329C22×C3×C4—64no—
330C22×C3×C4—68no—
331C22×C3×C4—94no—
332C22×C3×C4—91no—
333C22×C3×C4—184no—
334C2×#67—38no—
335C2×#67—38no—
336C2×#67—34no—
337C2×#67—34no—
338C2×#67—68no—
339C2×#67—64no—
340C22×Dic3—24no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—61no—
344C22×Dic3C2×C3×D311yescharacteristic
345C22×Dic3C2×C3×D311yescharacteristic
346C22×Dic3C2×C3×D311yescharacteristic
347C22×Dic3C2×C3×D311yescharacteristic
348C22×Dic3C2×C3×D314yescomplemented
349C2×C4×D3—34no—
350C2×C4×D3—34no—
351C2×C4×D3—64no—
352C2×C4×D3—64no—
353C3×C4⋊C4—94no—
354C3×C22⋊C4—34no—
355C3×C22⋊C4—34no—
356C3×C22⋊C4—64no—
357C3×C22⋊C4—94no—
358C3×C42—94no—
359#217C2×C3×D314yescomplemented
360(C2×D3)⋊C4—34no—
361(C2×D3)⋊C4—34no—
362Dic3⋊C4—34no—
363Dic3⋊C4—34no—
364C4×Dic3—34no—
365C4×Dic3—34no—
366C22×C32—28no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—24no—
370C22×C32—216no—
371C22×C32—24no—
372C22×C32—28no—
373C22×C32—28no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—24no—
384C22×C32—22no—
385C22×C32—22no—
386C22×C32—22no—
387C22×C32—24no—
388C22×C32—24no—
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—42no—
394C22×C32—44no—
395C22×C32—42no—
396C22×C32—42no—
397C22×C32—41no—
398C22×C32—48no—
399C22×C32—42no—
400C22×C32—42no—
401C22×C32—42no—
402C22×C32—42no—
403C22×C32—48no—
404C22×C32—44no—
405C22×C32—416no—
406C22×C32—44no—
407C22×C32C2×C4×D312yes—
408C22×C32C2×C4×D312yes—
409C22×C32C2×C4×D314yescomplemented
410C22×C32C2×C4×D314yescomplemented
411C22×C32#23512yes—
412C22×C32D3×D412yes—
413C22×C32#23712yes—
414C22×C32C2×#6712yes—
415C22×C32C22×C3×C412yes—
416C22×C32C22×C3×C414yescomplemented
417C22×C32C2×C3×D412yes—
418C22×C32C3×#4112yes—
419C22×C32C23×D311yescharacteristic
420C22×C32C23×D311yescharacteristic
421C22×C32C24×C311yescharacteristic
422C2×C3⋊D3—28no—
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3C22×C3×C414yescomplemented
426C2×C3×D3—34no—
427C2×C3×D3—34no—
428C2×C3×D3—64no—
429C2×C3×D3—68no—
430C2×C3×D3—68no—
431C2×C3×D3—62no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—122no—
436C2×C3×D3—122no—
437C2×C3×D3—128no—
438C32×C4—34no—
439C32×C4—62no—
440C32×C4—62no—
441C32×C4—62no—
442C3⋊Dic3C22×C3×C414yescomplemented
443C3×Dic3—24no—
444C3×Dic3—22no—
445C3×Dic3—22no—
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—24no—
451C3×Dic3—34no—
452C3×Dic3—34no—
453C3×Dic3—42no—
454C3×Dic3—42no—
455C3×Dic3—64no—
456C3×Dic3C2×#6714yescomplemented
457C3×Dic3C2×C3×D414yescomplemented
458C22×D4—91no—
459C23×C4—31no—
460C23×C4—91no—
461C4×D4—98no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—31no—
464C2×C22⋊C4—91no—
465C2×C42—91no—
466C33C2×C4×D411yescharacteristic, complemented, Sylow
467C23×C3—24no—
468C23×C3—24no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—24no—
476C23×C3—24no—
477C23×C3—24no—
478C23×C3—22no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—42no—
485C23×C3—42no—
486C23×C3—42no—
487C23×C3—42no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3—42no—
492C23×C3—41no—
493C23×C3—92no—
494C23×C3—94no—
495C23×C3—182no—
496C23×C3—182no—
497C23×C3#62414yescomplemented
498C23×C3C3×C4×D314yescomplemented
499C23×C3C3×C4×D314yescomplemented
500C23×C3C2×D3212yes—
501C23×C3C2×D3211yescharacteristic
502C23×C3C22×C3×D312yes—
503C23×C3C22×C3×D312yes—
504C23×C3C22×C3×D311yescharacteristic
505C23×C3C22×C3×D311yescharacteristic
506C22×D3—32no—
507C22×D3—32no—
508C22×D3—34no—
509C22×D3—34no—
510C22×D3—64no—
511C22×D3—62no—
512C22×D3—62no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—122no—
517C22×D3—122no—
518C3×D4—916no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—34no—
522C2×C3×C4—34no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
529C2×C3×C4—62no—
530C2×C3×C4—64no—
531C2×C3×C4—62no—
532C2×C3×C4—62no—
533C2×C3×C4—62no—
534C2×C3×C4—68no—
535C2×C3×C4—68no—
536C2×C3×C4—616no—
537C2×C3×C4—64no—
538C2×C3×C4—62no—
539C2×C3×C4—62no—
540C2×C3×C4—62no—
541C2×C3×C4—62no—
542C2×C3×C4—62no—
543C2×C3×C4—62no—
544C2×C3×C4—92no—
545C2×C3×C4—94no—
546C2×C3×C4—122no—
547C2×C3×C4—122no—
548C2×C3×C4—188no—
549#67—316no—
550#67—316no—
551#67—616no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—28no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—34no—
559C2×Dic3—34no—
560C2×Dic3—64no—
561C2×Dic3—62no—
562C2×Dic3C3×#6714yescomplemented
563C2×Dic3C22×C3×D312yes—
564C2×Dic3C22×C3×D312yes—
565C2×Dic3C22×C3×D312yes—
566C2×Dic3C22×C3×D312yes—
567C4×D3—68no—
568C4×D3—68no—
569C2×C32—24no—
570C2×C32—28no—
571C2×C32—24no—
572C2×C32—24no—
573C2×C32—24no—
574C2×C32—24no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—24no—
585C2×C32—44no—
586C2×C32—41no—
587C2×C32—41no—
588C2×C32—41no—
589C2×C32—44no—
590C2×C32—44no—
591C2×C32—48no—
592C2×C32#67⋊C414yescomplemented
593C2×C32C4×#6714yescomplemented
594C2×C32C3×C4×D414yescomplemented
595C2×C32C22×C4×D311yescharacteristic
596C2×C32C22×C4×D311yescharacteristic
597C2×C32C2×#23511yescharacteristic
598C2×C32C2×D3×D411yescharacteristic
599C2×C32C2×#23711yescharacteristic
600C2×C32C22×#6711yescharacteristic
601C2×C32C23×C3×C411yescharacteristic
602C2×C32C22×C3×D411yescharacteristic
603C2×C32C2×C3×#4111yescharacteristic
604C3⋊D3—24no—
605C3×D3—64no—
606C3×D3—64no—
607C3×D3—124no—
608C24—91no—
609C24C3×D3211yescharacteristic
610C2×D4—98no—
611C2×D4—94no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—34no—
617C22×C4—64no—
618C22×C4—94no—
619C22×C4—91no—
620C22×C4—184no—
621C4⋊C4—94no—
622C22⋊C4—34no—
623C22⋊C4—94no—
624C42—94no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—216no—
628C22×C3—28no—
629C22×C3—28no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—28no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—48no—
657C22×C3—48no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—416no—
661C22×C3—41no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—44no—
665C22×C3—42no—
666C22×C3—94no—
667C22×C3—182no—
668C22×C3—182no—
669C22×C3—188no—
670C22×C3#380412yes—
671C22×C3C2×#62412yes—
672C22×C3C2×#62414yescomplemented
673C22×C3D3×#6712yes—
674C22×C3C2×C3×C4×D312yes—
675C22×C3C2×C3×C4×D312yes—
676C22×C3C2×C3×C4×D314yescomplemented
677C22×C3C2×C3×C4×D314yescomplemented
678C22×C3C3×#23512yes—
679C22×C3C3×D3×D412yes—
680C22×C3C3×#23712yes—
681C22×C3C2×C3×#6712yes—
682C22×C3C22×D3211yescharacteristic
683C22×C3C23×C3×D311yescharacteristic
684C22×C3C23×C3×D311yescharacteristic
685C2×D3—34no—
686C2×D3—34no—
687C2×D3—64no—
688C2×D3—68no—
689C2×D3—68no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—122no—
695C2×D3—122no—
696C2×D3—128no—
697C3×C4—34no—
698C3×C4—34no—
699C3×C4—64no—
700C3×C4—64no—
701C3×C4—62no—
702C3×C4—62no—
703C3×C4—62no—
704C3×C4—62no—
705C3×C4—62no—
706C3×C4—62no—
707C3×C4—94no—
708C3×C4—122no—
709C3×C4—122no—
710Dic3—22no—
711Dic3—22no—
712Dic3—22no—
713Dic3—34no—
714Dic3—34no—
715Dic3—64no—
716Dic3C2×C3×#6714yescomplemented
717C32—21no—
718C32—21no—
719C32—21no—
720C32—41no—
721C32C2×#67⋊C411yescharacteristic, complemented
722C32C2×C4×#6711yescharacteristic, complemented
723C32C2×C3×C4×D411yescharacteristic, complemented
724C23—22no—
725C23—22no—
726C23—92no—
727C23—94no—
728C23—182no—
729C23—182no—
730C23C3×#62414yescomplemented
731C23C2×C3×D3212yes—
732C23C2×C3×D3211yescharacteristic
733D4—916no—
734C2×C4—32no—
735C2×C4—34no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—68no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—92no—
744C2×C4—94no—
745C2×C4—188no—
746C2×C3—28no—
747C2×C3—24no—
748C2×C3—24no—
749C2×C3—24no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—24no—
760C2×C3—24no—
761C2×C3—24no—
762C2×C3—44no—
763C2×C3—44no—
764C2×C3—48no—
765C2×C3—41no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3—44no—
769C2×C3—184no—
770C2×C3#6395214yesdirect product factor
771C2×C3C3×#67⋊C414yescomplemented
772C2×C3C3×C4×#6714yescomplemented
773C2×C3C2×#380411yescharacteristic
774C2×C3C22×#62411yescharacteristic
775C2×C3C2×D3×#6711yescharacteristic
776C2×C3C22×C3×C4×D311yescharacteristic
777C2×C3C22×C3×C4×D311yescharacteristic
778C2×C3C2×C3×#23511yescharacteristic
779C2×C3C2×C3×D3×D411yescharacteristic
780C2×C3C2×C3×#23711yescharacteristic
781C2×C3C22×C3×#6711yescharacteristic
782D3—64no—
783D3—64no—
784D3—124no—
785C22—22no—
786C22—22no—
787C22—28no—
788C22—94no—
789C22—182no—
790C22—182no—
791C22—188no—
792C22C3×#380412yes—
793C22C2×C3×#62412yes—
794C22C2×C3×#62414yescomplemented
795C22C3×D3×#6712yes—
796C22C22×C3×D3211yescharacteristic
797C4—34no—
798C4—62no—
799C4—62no—
800C4—62no—
801C4—94no—
802C3—21no—
803C3—21no—
804C3—21no—
805C3—41no—
806C3C2×#6395211yescharacteristic, direct product factor
807C3C2×C3×#67⋊C411yescharacteristic, complemented
808C3C2×C3×C4×#6711yescharacteristic, complemented
809C2—24no—
810C2—184no—
811C2C3×#6395214yesdirect product factor
812C2C2×C3×#380411yescharacteristic
813C2C22×C3×#62411yescharacteristic
814C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC23×C33C23
prime radicalC22×C3×#638C2
cosocleC22×C32C24×C3
hypercenterC24×C3D32
hypocenterC32C2×C3×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
2. C23×C32×Dic3C2semidirect
3. C22×C3×#624C2semidirect
4. C2×C32×#217C2semidirect
5. C2×C3×#3724C2semidirect
6. C2×C3×#3722C2semidirect
7. C2×C3×Dic32C2semidirect
8. C3×#63952C2direct (N × H)
11. C2×#63952C3direct (N × H)
14. C2×C3×#638C4semidirect
22. C22×C32×Dic3C22semidirect
24. C2×C3×#624C22semidirect
25. C32×#217C22semidirect
26. C3×#3724C22semidirect
27. C3×#3722C22semidirect
28. C3×Dic32C22semidirect
35. C23×C3×Dic3D3semidirect
36. C23×C3×Dic3C2×C3semidirect
39. C22×#624C2×C3semidirect
42. C2×C3×#217D3semidirect
43. C2×C3×#217C2×C3semidirect
52. C2×#3724C2×C3semidirect
53. C2×#3722C2×C3semidirect
54. C2×Dic32C2×C3semidirect
55. #63952C2×C3direct (N × H)
58. C23×C33C2×C4semidirect
63. C22×C3×C3⋊D3C2×C4semidirect
65. C3×#638C2×C4semidirect
66. C2×C3×C3⋊Dic3C2×C4semidirect
72. C2×C32×Dic3D4semidirect
98. C2×#638C3×C4semidirect
122. C22×C3×Dic3C2×D3semidirect
127. C22×C3×Dic3C22×C3semidirect
133. C2×#624C22×C3semidirect
136. C3×#217C2×D3semidirect
137. C3×#217C22×C3semidirect
144. #3724C22×C3semidirect
145. #3722C22×C3semidirect
146. Dic32C22×C3semidirect
151. C22×C33C22×C4semidirect
158. C2×C3×C3⋊D3C22×C4semidirect
159. C3×C3⋊Dic3C22×C4semidirect
163. C32×Dic3C2×D4semidirect
172. C23×Dic3C3×D3semidirect
182. C2×#217C3×D3semidirect
217. C23×C32C4×D3semidirect
218. C23×C32C4×D3semidirect
219. C23×C32C2×C3×C4semidirect
228. C22×C3⋊D3C2×C3×C4semidirect
251. #638C2×C3×C4semidirect
252. C2×C3⋊Dic3C2×C3×C4semidirect
280. C2×C3×Dic3#67semidirect
281. C2×C3×Dic3C3×D4semidirect
295. C2×C33C4×D4semidirect
348. C22×Dic3C2×C3×D3semidirect
359. #217C2×C3×D3semidirect
409. C22×C32C2×C4×D3semidirect
410. C22×C32C2×C4×D3semidirect
416. C22×C32C22×C3×C4semidirect
425. C2×C3⋊D3C22×C3×C4semidirect
442. C3⋊Dic3C22×C3×C4semidirect
456. C3×Dic3C2×#67semidirect
457. C3×Dic3C2×C3×D4semidirect
466. C33C2×C4×D4semidirect
497. C23×C3#624semidirect
498. C23×C3C3×C4×D3semidirect
499. C23×C3C3×C4×D3semidirect
562. C2×Dic3C3×#67semidirect
592. C2×C32#67⋊C4semidirect
593. C2×C32C4×#67semidirect
594. C2×C32C3×C4×D4semidirect
672. C22×C3C2×#624semidirect
676. C22×C3C2×C3×C4×D3semidirect
677. C22×C3C2×C3×C4×D3semidirect
716. Dic3C2×C3×#67semidirect
721. C32C2×#67⋊C4semidirect
722. C32C2×C4×#67semidirect
723. C32C2×C3×C4×D4semidirect
730. C23C3×#624semidirect
770. C2×C3#63952direct (N × H)
771. C2×C3C3×#67⋊C4semidirect
772. C2×C3C3×C4×#67semidirect
794. C22C2×C3×#624semidirect
806. C3C2×#63952direct (N × H)
807. C3C2×C3×#67⋊C4semidirect
808. C3C2×C3×C4×#67semidirect
811. C2C3×#63952direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C23×C32×Dic32
C22×C3×#6242
C2×C32×#2172
C2×C3×#37242
C2×C3×#37222
C2×C3×Dic322
C3×#639522
C2×C3×C4×#673
C2×C3×#67⋊C43
C2×#639523