Finite Group Databasebeta

← C3×#10595076 #13174673

Subgroups — C3×#10595076 #13174673

Order 1728.

1726 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C3×C4×D32C211yesmaximal, characteristic, complemented
3C32×C4×#67C212yesmaximal, complemented
4C3×#63983C211yesmaximal, characteristic, complemented
5C3×#63975C211yesmaximal, characteristic, complemented
6C3×#63971C212yesmaximal, complemented
7C3×#63923C211yesmaximal, characteristic, complemented
8C3×C4×#626C212yesmaximal, complemented
9C3×#63897C211yesmaximal, characteristic, complemented
10C3×#63896C212yesmaximal, complemented
11C3×#63874C211yesmaximal, characteristic, complemented
12C3×#5547—32nomaximal
13#10595076C311yesmaximal, characteristic, direct product factor
14C22×C3×D32C2211yescharacteristic
15C22×C33×C4C2211yescharacteristic, complemented
16C2×C3×#638C2211yescharacteristic
17C2×C3×#638C2211yescharacteristic, complemented
18C3×#3828—24no—
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C3×#634C2211yescharacteristic, complemented
23C2×C32×#67C2212yes—
24C2×C32×C4×D3C2212yes—
25C2×C3×#626C2212yes—
26C2×C3×#624C2211yescharacteristic
27C2×C3×D3×Dic3C2212yes—
28C3×C4×D32—24no—
29C32×#217C2212yescomplemented
30C32×(C2×D3)⋊C4C2212yes—
31C32×Dic3⋊C4C2212yescomplemented
32C32×C4×Dic3C2212yescomplemented
33C3×#3724C2212yescomplemented
34C3×Dic3⋊Dic3C2212yescomplemented
35C3×#3722C2211yescharacteristic
36C3×#3722C2211yescharacteristic
37C3×#3722C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yes—
39C2×#3828C2×C311yescharacteristic, complemented
40C2×C3×#235—32no—
41C2×C3×#235—61no—
42C22×C3×C4×D3—32no—
43C2×C4×D32C2×C311yescharacteristic, complemented
44C32×C4×D4—32no—
45C3×#939—32no—
46C3×#937—32no—
47C3×C4×#67—22no—
48C3×C4×#67—32no—
49C3×C4×#67D312yescomplemented
50C3×C4×#67C2×C312yescomplemented
51C3×#896—32no—
52C3×#894—32no—
53C3×#884—32no—
54C3×#883—32no—
55C3×#882—32no—
56C3×#878—32no—
57C3×C4×D12—32no—
58C3×#872—32no—
59#63983C2×C311yescharacteristic, complemented
60#63975C2×C311yescharacteristic, complemented
61#63971C2×C312yescomplemented
62#63923C2×C311yescharacteristic, complemented
63C4×#626C2×C312yescomplemented
64#63897C2×C311yescharacteristic, complemented
65#63896C2×C312yescomplemented
66#63874C2×C311yescharacteristic, complemented
67C23×C33C2311yescharacteristic
68C22×C3×C3⋊D3C2311yescharacteristic
69C22×C3×C3⋊D3C2311yescharacteristic
70C22×C32×D3C2312yes—
71C2×C3×D32—22no—
72C2×C3×D32—24no—
73C2×C33×C4—22no—
74C2×C33×C4C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C3×#638—22no—
77C3×#638—22no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C3×C4⋊(C3⋊D3)—22no—
81C3×C4×C3⋊D3—22no—
82C3×C4×C3⋊D3D414yescomplemented
83C3×#634—22no—
84C32×#67—24no—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2312yes—
88C32×C4×D3—24no—
89C3×#626—24no—
90C3×#624—22no—
91C3×D3×Dic3—24no—
92C3×#525—91no—
93#5547—32no—
94C23×C3×D3—32no—
95C22×D32C22×C311yescharacteristic
96C2×C32×D4—32no—
97C22×C32×C4—21no—
98C22×C32×C4—22no—
99C22×C32×C4—32no—
100C22×C32×C4—41no—
101C22×C32×C4C2×D312yescomplemented
102C22×C32×C4C22×C311yescharacteristic, complemented
103C2×#638C22×C311yescharacteristic
104C2×#638C22×C311yescharacteristic, complemented
105#3828—24no—
106C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
107C2×C4×C3⋊D3C22×C311yescharacteristic
108C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
109C2×#634C22×C311yescharacteristic, complemented
110C2×C3×#67—22no—
111C2×C3×#67—32no—
112C2×C3×#67—32no—
113C2×C3×#67—32no—
114C2×C3×#67—61no—
115C2×C3×#67—61no—
116C2×C3×#67C2×D312yes—
117C2×C3×#67C22×C312yes—
118C22×C3×Dic3—32no—
119C3×#235—68no—
120C3×#235—68no—
121C2×C3×D12—32no—
122C2×C3×D12—32no—
123C2×C3×D12—61no—
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—32no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—68no—
130C2×C3×C4×D3—61no—
131C2×C3×C4×D3—61no—
132C2×C3×C4×D3C2×D312yes—
133C2×C3×C4×D3C22×C312yes—
134C2×C3×Dic6—32no—
135C2×C3×Dic6—61no—
136C2×#626C22×C312yes—
137C2×#624C22×C311yescharacteristic
138C2×D3×Dic3C22×C312yes—
139C4×D32—24no—
140C32×C4⋊C4—32no—
141C32×C22⋊C4—32no—
142C32×C22⋊C4—32no—
143C32×C42—32no—
144C3×#217—22no—
145C3×#217—32no—
146C3×#217C2×D312yescomplemented
147C3×#217C22×C312yescomplemented
148C3×(C2×D3)⋊C4—22no—
149C3×(C2×D3)⋊C4—32no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4C2×D312yes—
155C3×(C2×D3)⋊C4C22×C312yes—
156C3×C4⋊Dic3—32no—
157C3×Dic3⋊C4—22no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4—32no—
160C3×Dic3⋊C4—32no—
161C3×Dic3⋊C4C2×D312yescomplemented
162C3×Dic3⋊C4C22×C312yescomplemented
163C3×C4×Dic3—22no—
164C3×C4×Dic3C2×D312yescomplemented
165C3×C4×Dic3C22×C312yescomplemented
166#3724C22×C312yescomplemented
167Dic3⋊Dic3C22×C312yescomplemented
168#3722C22×C311yescharacteristic
169#3722C22×C311yescharacteristic
170#3722C22×C312yescomplemented
171(C2×D3)⋊Dic3C22×C312yes—
172C22×C33—21no—
173C22×C33—22no—
174C22×C33C2411yescharacteristic
175C2×C3×C3⋊D3—22no—
176C2×C3×C3⋊D3—21no—
177C2×C3×C3⋊D3—22no—
178C2×C3×C3⋊D3C2×D412yes—
179C2×C32×D3—22no—
180C2×C32×D3—22no—
181C2×C32×D3#4114yescomplemented
182C3×D32—28no—
183C33×C4—21no—
184C33×C4C2×D412yes—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3C2×D412yes—
187C32×Dic3—22no—
188C32×Dic3—22no—
189C32×Dic3—22no—
190C2×C3×#41—91no—
191C23×C3×C4—91no—
192C2×#235—32no—
193C2×#235—61no—
194C22×C4×D3—32no—
195C3×#123—91no—
196C3×#123—91no—
197C3×C22⋊Q8—92no—
198C3×#121—92no—
199C3×#120—91no—
200C3×#120—91no—
201C3×C4×D4—32no—
202C3×C4×D4—32no—
203C3×C4×D4—62no—
204C3×C4×D4—92no—
205C3×#117—91no—
206#939—32no—
207#937—32no—
208C4×#67—32no—
209C4×#67C3×D312yescomplemented
210#896—32no—
211#894—32no—
212#884—32no—
213#883—32no—
214#882—32no—
215#878—32no—
216C4×D12—32no—
217#872—32no—
218C23×C32—21no—
219C23×C32—22no—
220C23×C32—32no—
221C23×C32—41no—
222C23×C32C22×D312yes—
223C23×C32C23×C311yescharacteristic
224C22×C3⋊D3C23×C311yescharacteristic
225C22×C3⋊D3C23×C311yescharacteristic
226C22×C3×D3—22no—
227C22×C3×D3—32no—
228C22×C3×D3—32no—
229C22×C3×D3—61no—
230C22×C3×D3—61no—
231C22×C3×D3—64no—
232C22×C3×D3—64no—
233C22×C3×D3—64no—
234C22×C3×D3C22×D312yes—
235C22×C3×D3C23×C312yes—
236C2×D32—22no—
237C2×D32—24no—
238C32×D4—64no—
239C2×C32×C4—22no—
240C2×C32×C4—24no—
241C2×C32×C4—24no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—22no—
245C2×C32×C4—22no—
246C2×C32×C4—32no—
247C2×C32×C4—32no—
248C2×C32×C4—32no—
249C2×C32×C4—41no—
250C2×C32×C4—41no—
251C2×C32×C4—44no—
252C2×C32×C4—44no—
253C2×C32×C4—64no—
254C2×C32×C4C22×D312yes—
255C2×C32×C4C22×D312yes—
256C2×C32×C4C23×C311yescharacteristic
257C2×C32×C4C23×C311yescharacteristic
258#638—22no—
259#638—22no—
260C2×C3⋊Dic3C23×C311yescharacteristic
261C2×C3⋊Dic3C23×C311yescharacteristic
262C4⋊(C3⋊D3)—22no—
263C4×C3⋊D3—22no—
264C4×C3⋊D3C3×D414yescomplemented
265#634—22no—
266C3×#67—28no—
267C3×#67—24no—
268C3×#67—24no—
269C3×#67—64no—
270C3×#67—64no—
271C3×#67—64no—
272C3×#67—64no—
273C3×#67—64no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—64no—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C23×C312yes—
286C2×C3×Dic3C23×C312yes—
287C2×C3×Dic3C23×C312yes—
288C3×D12—64no—
289C3×D12—64no—
290C3×D12—64no—
291C3×C4×D3—24no—
292C3×C4×D3—24no—
293C3×C4×D3—38no—
294C3×C4×D3—44no—
295C3×C4×D3—64no—
296C3×C4×D3—64no—
297C3×C4×D3—64no—
298C3×C4×D3—64no—
299C3×C4×D3—64no—
300C3×Dic6—64no—
301C3×Dic6—64no—
302#626—24no—
303#624—22no—
304D3×Dic3—24no—
305#525—91noSylow
306C2×C33—41no—
307C2×C33C22×D411yescharacteristic
308C2×C33C2×#4112yes—
309C3×C3⋊D3—22no—
310C3×C3⋊D3—41no—
311C32×D3—24no—
312C24×C3—91no—
313C23×D3—32no—
314C3×#41—184no—
315C2×C3×Q8—91no—
316C2×C3×D4—32no—
317C2×C3×D4—32no—
318C2×C3×D4—62no—
319C2×C3×D4—92no—
320C2×C3×D4—91no—
321C2×C3×D4—91no—
322C2×C3×D4—91no—
323C22×C3×C4—21no—
324C22×C3×C4—22no—
325C22×C3×C4—32no—
326C22×C3×C4—32no—
327C22×C3×C4—41no—
328C22×C3×C4—62no—
329C22×C3×C4—91no—
330C22×C3×C4—92no—
331C22×C3×C4—91no—
332C22×C3×C4—91no—
333C22×C3×C4—184no—
334C22×C3×C4D3211yescharacteristic, complemented
335C22×C3×C4C2×C3×D312yescomplemented
336C2×#67—32no—
337C2×#67—32no—
338C2×#67—32no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67C2×C3×D312yes—
342C22×Dic3—32no—
343#235—68no—
344#235—68no—
345C2×D12—32no—
346C2×D12—32no—
347C2×D12—61no—
348C2×C4×D3—32no—
349C2×C4×D3—32no—
350C2×C4×D3—32no—
351C2×C4×D3—32no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—68no—
355C2×C4×D3C2×C3×D312yes—
356C2×Dic6—32no—
357C2×Dic6—61no—
358C3×C4⋊C4—32no—
359C3×C4⋊C4—32no—
360C3×C4⋊C4—62no—
361C3×C4⋊C4—92no—
362C3×C4⋊C4—92no—
363C3×C22⋊C4—32no—
364C3×C22⋊C4—32no—
365C3×C22⋊C4—32no—
366C3×C22⋊C4—32no—
367C3×C22⋊C4—62no—
368C3×C22⋊C4—62no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4—91no—
371C3×C22⋊C4—92no—
372C3×C22⋊C4—92no—
373C3×C42—32no—
374C3×C42—32no—
375C3×C42—62no—
376#217—32no—
377#217C2×C3×D312yescomplemented
378(C2×D3)⋊C4—32no—
379(C2×D3)⋊C4—32no—
380(C2×D3)⋊C4—32no—
381(C2×D3)⋊C4—32no—
382(C2×D3)⋊C4—32no—
383(C2×D3)⋊C4C2×C3×D312yes—
384C4⋊Dic3—32no—
385Dic3⋊C4—32no—
386Dic3⋊C4—32no—
387Dic3⋊C4—32no—
388Dic3⋊C4C2×C3×D312yescomplemented
389C4×Dic3C2×C3×D312yescomplemented
390C22×C32—22no—
391C22×C32—21no—
392C22×C32—24no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—21no—
398C22×C32—22no—
399C22×C32—34no—
400C22×C32—41no—
401C22×C32—42no—
402C22×C32—42no—
403C22×C32—42no—
404C22×C32—42no—
405C22×C32—44no—
406C22×C32—62no—
407C22×C32—62no—
408C22×C32C23×D312yes—
409C22×C32C24×C311yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—22no—
412C2×C3⋊D3—22no—
413C2×C3⋊D3C2×C3×D412yes—
414C2×C3×D3—22no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—24no—
419C2×C3×D3—34no—
420C2×C3×D3—42no—
421C2×C3×D3—42no—
422C2×C3×D3—62no—
423C2×C3×D3—616no—
424C2×C3×D3—62no—
425C2×C3×D3—62no—
426C2×C3×D3—62no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—62no—
430C2×C3×D3—122no—
431C2×C3×D3—122no—
432C2×C3×D3#23514yescomplemented
433C2×C3×D3C3×#4114yescomplemented
434D32—28no—
435C32×C4—21no—
436C32×C4—22no—
437C32×C4—22no—
438C32×C4—22no—
439C32×C4—24no—
440C32×C4—42no—
441C32×C4—42no—
442C32×C4—42no—
443C32×C4—62no—
444C32×C4—62no—
445C32×C4—62no—
446C32×C4D3×D414yes—
447C32×C4C2×C3×D412yes—
448C3⋊Dic3—21no—
449C3⋊Dic3C2×C3×D412yes—
450C3×Dic3—24no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—22no—
457C3×Dic3—34no—
458C3×Dic3—42no—
459C3×Dic3—42no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C2×#41—91no—
464C23×C4—91no—
465#123—91no—
466#123—91no—
467C22⋊Q8—92no—
468#121—92no—
469#120—91no—
470#120—91no—
471C4×D4—32no—
472C4×D4—92no—
473#117—91no—
474C33#52511yescharacteristic, complemented, Sylow
475C23×C3—22no—
476C23×C3—21no—
477C23×C3—32no—
478C23×C3—32no—
479C23×C3—41no—
480C23×C3—62no—
481C23×C3—91no—
482C23×C3—91no—
483C23×C3—184no—
484C23×C3—182no—
485C23×C3C2×D3211yescharacteristic
486C23×C3C22×C3×D312yes—
487C22×D3—32no—
488C22×D3—32no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3—64no—
494C22×D3C22×C3×D312yes—
495C3×Q8—182no—
496C3×D4—64no—
497C3×D4—64no—
498C3×D4—68no—
499C3×D4—182no—
500C3×D4—184no—
501C3×D4—182no—
502C3×D4—182no—
503C2×C3×C4—24no—
504C2×C3×C4—22no—
505C2×C3×C4—24no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—44no—
517C2×C3×C4—44no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—62no—
521C2×C3×C4—62no—
522C2×C3×C4—62no—
523C2×C3×C4—64no—
524C2×C3×C4—64no—
525C2×C3×C4—91no—
526C2×C3×C4—94no—
527C2×C3×C4—91no—
528C2×C3×C4—124no—
529C2×C3×C4—182no—
530C2×C3×C4—184no—
531C2×C3×C4—182no—
532C2×C3×C4C2×D3211yescharacteristic
533C2×C3×C4C2×D3211yescharacteristic
534C2×C3×C4C22×C3×D312yes—
535C2×C3×C4C22×C3×D312yes—
536#67—24no—
537#67—64no—
538#67—64no—
539#67—64no—
540#67—64no—
541#67—64no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—64no—
547C2×Dic3C22×C3×D312yes—
548C2×Dic3C22×C3×D312yes—
549C2×Dic3C22×C3×D312yes—
550D12—64no—
551D12—64no—
552D12—64no—
553C4×D3—24no—
554C4×D3—38no—
555C4×D3—64no—
556C4×D3—64no—
557C4×D3—64no—
558C4×D3—64no—
559C4×D3—64no—
560Dic6—64no—
561Dic6—64no—
562C2×C32—22no—
563C2×C32—21no—
564C2×C32—22no—
565C2×C32—22no—
566C2×C32—22no—
567C2×C32—41no—
568C2×C32—42no—
569C2×C32—42no—
570C2×C32—44no—
571C2×C32—44no—
572C2×C32—42no—
573C2×C32—41no—
574C2×C32—64no—
575C2×C32C2×#23512yes—
576C2×C32C2×D3×D412yes—
577C2×C32D3×#4112yes—
578C2×C32C22×C3×D411yescharacteristic
579C2×C32C2×C3×#4112yes—
580C3⋊D3—22no—
581C3⋊D3—41no—
582C3×D3—24no—
583C3×D3—24no—
584C3×D3—44no—
585C3×D3—64no—
586C3×D3—122no—
587C3×D3—122no—
588C3×D3—122no—
589C24—91no—
590#41—184no—
591C2×Q8—91no—
592C2×D4—32no—
593C2×D4—92no—
594C2×D4—91no—
595C2×D4—91no—
596C2×D4—91no—
597C22×C4—32no—
598C22×C4—91no—
599C22×C4—92no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4—184no—
603C22×C4C3×D3211yescharacteristic, complemented
604C4⋊C4—32no—
605C4⋊C4—92no—
606C4⋊C4—92no—
607C22⋊C4—32no—
608C22⋊C4—32no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—92no—
612C22⋊C4—92no—
613C42—32no—
614C22×C3—22no—
615C22×C3—24no—
616C22×C3—22no—
617C22×C3—21no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—22no—
623C22×C3—34no—
624C22×C3—34no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—44no—
630C22×C3—41no—
631C22×C3—64no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—92no—
637C22×C3—122no—
638C22×C3—122no—
639C22×C3—188no—
640C22×C3—182no—
641C22×C3—182no—
642C22×C3—181no—
643C22×C3C22×D3211yescharacteristic
644C22×C3C23×C3×D312yes—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—34no—
648C2×D3—62no—
649C2×D3—616no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—122no—
657C2×D3—122no—
658C2×D3C3×#23514yescomplemented
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—24no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—42no—
667C3×C4—64no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4—62no—
671C3×C4—62no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—92no—
675C3×C4—122no—
676C3×C4—122no—
677C3×C4—181no—
678C3×C4#381112yes—
679C3×C4C3×D3×D414yes—
680Dic3—22no—
681Dic3—22no—
682Dic3—22no—
683Dic3—34no—
684Dic3—62no—
685Dic3—62no—
686Dic3—62no—
687C32—21no—
688C32—22no—
689C32—41no—
690C32#554712yescomplemented
691C32C3×#52511yescharacteristic, complemented
692C23—32no—
693C23—91no—
694C23—91no—
695C23—184no—
696C23—182no—
697C23C2×C3×D3211yescharacteristic
698Q8—182no—
699D4—64no—
700D4—182no—
701D4—184no—
702D4—182no—
703D4—182no—
704C2×C4—22no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—64no—
709C2×C4—91no—
710C2×C4—94no—
711C2×C4—91no—
712C2×C4—182no—
713C2×C4—184no—
714C2×C4—182no—
715C2×C4C2×C3×D3211yescharacteristic
716C2×C4C2×C3×D3211yescharacteristic
717C2×C3—21no—
718C2×C3—22no—
719C2×C3—22no—
720C2×C3—22no—
721C2×C3—22no—
722C2×C3—42no—
723C2×C3—44no—
724C2×C3—44no—
725C2×C3—41no—
726C2×C3—42no—
727C2×C3—41no—
728C2×C3—42no—
729C2×C3—64no—
730C2×C3—64no—
731C2×C3—124no—
732C2×C3—182no—
733C2×C3—361no—
734C2×C3D3×#23512yes—
735C2×C3C2×#381111yescharacteristic
736C2×C3C2×C3×#23512yes—
737C2×C3C2×C3×D3×D412yes—
738C2×C3C3×D3×#4112yes—
739D3—24no—
740D3—64no—
741D3—122no—
742D3—122no—
743D3—122no—
744C22—21no—
745C22—22no—
746C22—34no—
747C22—62no—
748C22—62no—
749C22—92no—
750C22—188no—
751C22—182no—
752C22—181no—
753C22—182no—
754C22C22×C3×D3211yescharacteristic
755C4—21no—
756C4—62no—
757C4—62no—
758C4—62no—
759C4—92no—
760C4—181no—
761C4C3×#381112yes—
762C3—21no—
763C3—22no—
764C3—41no—
765C3#1059507611yescharacteristic, direct product factor
766C3C3×#554712yescomplemented
767C2—41no—
768C2—64no—
769C2—182no—
770C2—361no—
771C2C3×D3×#23512yes—
772C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×C3×C4×D32C2semidirect
3. C32×C4×#67C2semidirect
4. C3×#63983C2semidirect
5. C3×#63975C2semidirect
6. C3×#63971C2semidirect
7. C3×#63923C2semidirect
8. C3×C4×#626C2semidirect
9. C3×#63897C2semidirect
10. C3×#63896C2semidirect
11. C3×#63874C2semidirect
13. #10595076C3direct (N × H)
15. C22×C33×C4C22semidirect
17. C2×C3×#638C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C2×C3×#634C22semidirect
29. C32×#217C22semidirect
31. C32×Dic3⋊C4C22semidirect
32. C32×C4×Dic3C22semidirect
33. C3×#3724C22semidirect
34. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
39. C2×#3828C2×C3semidirect
43. C2×C4×D32C2×C3semidirect
49. C3×C4×#67D3semidirect
50. C3×C4×#67C2×C3semidirect
59. #63983C2×C3semidirect
60. #63975C2×C3semidirect
61. #63971C2×C3semidirect
62. #63923C2×C3semidirect
63. C4×#626C2×C3semidirect
64. #63897C2×C3semidirect
65. #63896C2×C3semidirect
66. #63874C2×C3semidirect
82. C3×C4×C3⋊D3D4semidirect
101. C22×C32×C4C2×D3semidirect
102. C22×C32×C4C22×C3semidirect
104. C2×#638C22×C3semidirect
108. C2×C4×C3⋊D3C22×C3semidirect
109. C2×#634C22×C3semidirect
146. C3×#217C2×D3semidirect
147. C3×#217C22×C3semidirect
161. C3×Dic3⋊C4C2×D3semidirect
162. C3×Dic3⋊C4C22×C3semidirect
164. C3×C4×Dic3C2×D3semidirect
165. C3×C4×Dic3C22×C3semidirect
166. #3724C22×C3semidirect
167. Dic3⋊Dic3C22×C3semidirect
170. #3722C22×C3semidirect
181. C2×C32×D3#41semidirect
209. C4×#67C3×D3semidirect
264. C4×C3⋊D3C3×D4semidirect
334. C22×C3×C4D32semidirect
335. C22×C3×C4C2×C3×D3semidirect
377. #217C2×C3×D3semidirect
388. Dic3⋊C4C2×C3×D3semidirect
389. C4×Dic3C2×C3×D3semidirect
432. C2×C3×D3#235semidirect
433. C2×C3×D3C3×#41semidirect
474. C33#525semidirect
603. C22×C4C3×D32semidirect
658. C2×D3C3×#235semidirect
690. C32#5547semidirect
691. C32C3×#525semidirect
765. C3#10595076direct (N × H)
766. C3C3×#5547semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C3×C4×D322
C32×C4×#672
C3×#639832
C3×#639752
C3×#639712
C3×#639232
C3×C4×#6262
C3×#638972
C3×#638962
C3×#638742
C3×#55473
#105950763