Finite Group Databasebeta

← C3×#10591277 #13158196

Subgroups — C3×#10591277 #13158196

Order 1728.

1394 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic
2C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#3724C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
6C3×#63658C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×#5210—31nomaximal
9C3×#4989—31nomaximal
10#10591277C311yesmaximal, characteristic, direct product factor
11C23×C32×D3C2211yescharacteristic
12C22×C33×C4C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C32×C4×D3—22no—
19C2×C32×C4×D3—22no—
20C2×C32×C4×D3—22no—
21C32×Dic3⋊C4—22no—
22C3×#3724—22no—
23C3×(C2×D3)⋊Dic3—22no—
24C3×(C2×D3)⋊Dic3C414yescomplemented
25C23×C32×C4—31no—
26C22×C3×C4×D3—21no—
27C22×C3×C4×D3D311yescharacteristic
28C22×C3×C4×D3C2×C311yescharacteristic
29C2×C32×C4⋊C4—31no—
30C2×C3×#217—31no—
31C2×C3×#217—31no—
32C2×C3×(C2×D3)⋊C4—31no—
33C2×C3×(C2×D3)⋊C4—31no—
34C2×C3×Dic3⋊C4—21no—
35C2×C3×Dic3⋊C4—31no—
36C2×C3×Dic3⋊C4—31no—
37C2×C3×Dic3⋊C4D311yescharacteristic, complemented
38C2×C3×Dic3⋊C4C2×C311yescharacteristic, complemented
39C2×#3724C2×C311yescharacteristic, complemented
40C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
41C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
42#63658C2×C311yescharacteristic, complemented
43C3×C3⋊#95—31no—
44C3×C3⋊#95—31no—
45C3×C3⋊#95—31no—
46C3×C3⋊#95—31no—
47C3×C3⋊#95—61no—
48#63579C2×C311yescharacteristic, complemented
49C23×C33C2311yescharacteristic
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3C2×C412yes—
55C22×C32×D3D412yes—
56C22×C32×D3Q812yes—
57C2×C33×C4—21no—
58C2×C33×C4—21no—
59C2×C33×C4D412yes—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3—21no—
65C2×C3×C3⋊Dic3C2×C412yescomplemented
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3—21no—
73C2×C32×Dic3C2×C412yescomplemented
74C2×C32×Dic3D412yes—
75C32×C4×D3—28no—
76C3×#385—91no—
77#5210—31no—
78#4989—31no—
79C24×C32—31no—
80C23×C3×D3—21no—
81C23×C3×D3C2×D311yescharacteristic
82C23×C3×D3C22×C311yescharacteristic
83C22×C32×C4—21no—
84C22×C32×C4—21no—
85C22×C32×C4—21no—
86C22×C32×C4—31no—
87C22×C32×C4—31no—
88C22×C32×C4—31no—
89C22×C32×C4—41no—
90C22×C32×C4—62no—
91C22×C32×C4—62no—
92C22×C32×C4—62no—
93C22×C32×C4C2×D311yescharacteristic
94C22×C32×C4C2×D311yescharacteristic
95C22×C32×C4C22×C311yescharacteristic
96C22×C3⋊Dic3C22×C311yescharacteristic
97C22×C3⋊Dic3C22×C311yescharacteristic
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C22×C3×Dic3—31no—
104C22×C3×Dic3—31no—
105C22×C3×Dic3—61no—
106C22×C3×Dic3—61no—
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C2×D311yescharacteristic
110C22×C3×Dic3C22×C311yescharacteristic
111C22×C3×Dic3C22×C311yescharacteristic
112C22×C3×Dic3C22×C311yescharacteristic
113C2×C3×C4×D3—24no—
114C2×C3×C4×D3—24no—
115C2×C3×C4×D3—24no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—22no—
122C32×C4⋊C4—62no—
123C3×#217—34no—
124C3×#217—62no—
125C3×(C2×D3)⋊C4—34no—
126C3×(C2×D3)⋊C4—62no—
127C3×Dic3⋊C4—24no—
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—62no—
131C3×Dic3⋊C4—62no—
132#3724—22no—
133(C2×D3)⋊Dic3—22no—
134(C2×D3)⋊Dic3C3×C414yescomplemented
135C22×C33C22×C411yescharacteristic
136C22×C33C2×D411yescharacteristic
137C22×C33C2×D411yescharacteristic
138C22×C33C2×D411yescharacteristic
139C22×C33C2×Q811yescharacteristic
140C22×C33#4111yescharacteristic
141C22×C33#4111yescharacteristic
142C2×C32×D3—22no—
143C2×C32×D3—22no—
144C2×C32×D3—22no—
145C2×C32×D3—22no—
146C2×C32×D3—22no—
147C2×C32×D3—22no—
148C2×C32×D3C4⋊C414yescomplemented
149C33×C4—22no—
150C3×C3⋊Dic3—22no—
151C3×C3⋊Dic3—41no—
152C32×Dic3—22no—
153C32×Dic3—22no—
154C32×Dic3—41no—
155C23×C3×C4—31no—
156C23×C3×C4—31no—
157C23×C3×C4—61no—
158C22×C4×D3C3×D311yescharacteristic
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—61no—
162C2×C3×C4⋊C4—91no—
163C2×C3×C22⋊C4—91no—
164C2×C3×C22⋊C4—91no—
165C2×#217—31no—
166C2×#217—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4C3×D311yescharacteristic, complemented
172C3×#95—91no—
173C3×#95—91no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—61no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—32no—
183C23×C32—32no—
184C23×C32—32no—
185C23×C32—41no—
186C23×C32—61no—
187C23×C32—61no—
188C23×C32—61no—
189C23×C32—61no—
190C23×C32C22×D311yescharacteristic
191C23×C32C22×D311yescharacteristic
192C23×C32C23×C311yescharacteristic
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3—21no—
198C22×C3×D3—21no—
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—21no—
202C22×C3×D3—21no—
203C22×C3×D3—21no—
204C22×C3×D3—21no—
205C22×C3×D3—22no—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3Dic612yes—
209C22×C3×D3C4×D312yes—
210C22×C3×D3#6712yes—
211C22×C3×D3C2×C3×C412yes—
212C22×C3×D3C3×D412yes—
213C22×C3×D3C3×Q812yes—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—22no—
217C2×C32×C4—22no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—22no—
223C2×C32×C4—22no—
224C2×C32×C4—22no—
225C2×C32×C4—32no—
226C2×C32×C4—32no—
227C2×C32×C4—42no—
228C2×C32×C4—41no—
229C2×C32×C4—41no—
230C2×C32×C4—41no—
231C2×C32×C4—41no—
232C2×C32×C4—42no—
233C2×C32×C4—42no—
234C2×C32×C4—68no—
235C2×C32×C4—61no—
236C2×C32×C4—61no—
237C2×C32×C4—61no—
238C2×C32×C4—61no—
239C2×C32×C4—61no—
240C2×C32×C4—61no—
241C2×C32×C4—61no—
242C2×C32×C4#6712yes—
243C2×C32×C4#6712yes—
244C2×C32×C4C3×D412yes—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×C3×C412yescomplemented
251C2×C3×Dic3—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—41no—
275C2×C3×Dic3—41no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—121no—
289C2×C3×Dic3—121no—
290C2×C3×Dic3—121no—
291C2×C3×Dic3—121no—
292C2×C3×Dic3C4×D312yescomplemented
293C2×C3×Dic3#6712yes—
294C2×C3×Dic3C2×C3×C412yescomplemented
295C2×C3×Dic3C3×D412yes—
296C3×C4×D3—216no—
297C3×C4×D3—28no—
298C3×C4×D3—28no—
299#385—91noSylow
300C2×C33C2×C4⋊C411yescharacteristic
301C2×C33C4×D411yescharacteristic
302C2×C33C4×D411yescharacteristic
303C2×C33#12011yescharacteristic
304C2×C33C22⋊Q811yescharacteristic
305C2×C33C22⋊Q811yescharacteristic
306C2×C33#12311yescharacteristic
307C32×D3—24no—
308C24×C3—31no—
309C24×C3—31no—
310C24×C3—61no—
311C23×D3C2×C3×D311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—41no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—62no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—64no—
330C22×C3×C4—64no—
331C22×C3×C4—64no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—91no—
335C22×C3×C4—91no—
336C22×C3×C4D3211yescharacteristic
337C22×C3×C4C2×C3×D311yescharacteristic
338C22×C3×C4C2×C3×D311yescharacteristic
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3C2×C3×D311yescharacteristic
346C22×Dic3C2×C3×D311yescharacteristic
347C22×Dic3C2×C3×D311yescharacteristic
348C2×C4×D3—22no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C3×C4⋊C4—64no—
352C3×C4⋊C4—62no—
353C3×C4⋊C4—62no—
354C3×C4⋊C4—182no—
355C3×C22⋊C4—94no—
356C3×C22⋊C4—182no—
357#217—34no—
358#217—62no—
359(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—62no—
361Dic3⋊C4—22no—
362Dic3⋊C4—62no—
363Dic3⋊C4—62no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—34no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—62no—
394C22×C32—62no—
395C22×C32—62no—
396C22×C32—62no—
397C22×C32—62no—
398C22×C32—62no—
399C22×C32C2×Dic611yescharacteristic
400C22×C32C2×C4×D311yescharacteristic
401C22×C32C2×C4×D311yescharacteristic
402C22×C32#23511yescharacteristic
403C22×C32#23511yescharacteristic
404C22×C32#23511yescharacteristic
405C22×C32D3×D411yescharacteristic
406C22×C32D3×D411yescharacteristic
407C22×C32D3×Q811yescharacteristic
408C22×C32#23911yescharacteristic
409C22×C32C2×#6711yescharacteristic
410C22×C32C2×#6711yescharacteristic
411C22×C32C2×#6711yescharacteristic
412C22×C32C2×#6711yescharacteristic
413C22×C32C22×C3×C411yescharacteristic
414C22×C32C2×C3×D411yescharacteristic
415C22×C32C2×C3×D411yescharacteristic
416C22×C32C2×C3×D411yescharacteristic
417C22×C32C2×C3×Q811yescharacteristic
418C22×C32C3×#4111yescharacteristic
419C22×C32C3×#4111yescharacteristic
420C2×C3×D3—24no—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—24no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—24no—
439C2×C3×D3Dic3⋊C414yescomplemented
440C2×C3×D3C3×C4⋊C414yescomplemented
441C32×C4—22no—
442C32×C4—24no—
443C32×C4—22no—
444C32×C4—22no—
445C32×C4—42no—
446C32×C4—42no—
447C32×C4—44no—
448C32×C4—62no—
449C32×C4—62no—
450C32×C4—121no—
451C3⋊Dic3—22no—
452C3⋊Dic3—41no—
453C3×Dic3—24no—
454C3×Dic3—24no—
455C3×Dic3—22no—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—42no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—122no—
465C3×Dic3—122no—
466C3×Dic3—121no—
467C3×Dic3—121no—
468C23×C4—31no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—91no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473#95—91no—
474#95—91no—
475C33#38511yescharacteristic, complemented, Sylow
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—32no—
480C23×C3—32no—
481C23×C3—32no—
482C23×C3—32no—
483C23×C3—32no—
484C23×C3—32no—
485C23×C3—41no—
486C23×C3—62no—
487C23×C3—62no—
488C23×C3—62no—
489C23×C3—62no—
490C23×C3—62no—
491C23×C3—62no—
492C23×C3—62no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3C2×D3211yescharacteristic
502C23×C3C22×C3×D311yescharacteristic
503C23×C3C22×C3×D311yescharacteristic
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—21no—
508C22×D3C3×Dic612yes—
509C22×D3C3×C4×D312yes—
510C22×D3C3×#6712yes—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—32no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—42no—
531C2×C3×C4—42no—
532C2×C3×C4—42no—
533C2×C3×C4—62no—
534C2×C3×C4—62no—
535C2×C3×C4—616no—
536C2×C3×C4—68no—
537C2×C3×C4—68no—
538C2×C3×C4—62no—
539C2×C3×C4—62no—
540C2×C3×C4—62no—
541C2×C3×C4—62no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—62no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—92no—
558C2×C3×C4—121no—
559C2×C3×C4—121no—
560C2×C3×C4—181no—
561C2×C3×C4—181no—
562C2×C3×C4—181no—
563C2×C3×C4—181no—
564C2×C3×C4—181no—
565C2×C3×C4#62512yes—
566C2×C3×C4C3×#6712yes—
567C2×C3×C4C3×#6712yes—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—32no—
576C2×Dic3—32no—
577C2×Dic3—62no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—62no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3C3×C4×D312yescomplemented
594C2×Dic3C3×#6712yes—
595C4×D3—28no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
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—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—41no—
618C2×C32—41no—
619C2×C32—41no—
620C2×C32—41no—
621C2×C32—41no—
622C2×C32—41no—
623C2×C32—41no—
624C2×C32—64no—
625C2×C32D3×C4⋊C411yescharacteristic
626C2×C32#89311yescharacteristic
627C2×C32#89411yescharacteristic
628C2×C32#89611yescharacteristic
629C2×C32C2×Dic3⋊C411yescharacteristic
630C2×C32#92411yescharacteristic
631C2×C32#92411yescharacteristic
632C2×C32C4×#6711yescharacteristic
633C2×C32C4×#6711yescharacteristic
634C2×C32C4×#6711yescharacteristic
635C2×C32#92911yescharacteristic
636C2×C32#93711yescharacteristic
637C2×C32#94611yescharacteristic
638C2×C32#95311yescharacteristic
639C2×C32C2×C3×C4⋊C411yescharacteristic
640C2×C32C3×C4×D411yescharacteristic
641C2×C32C3×C4×D411yescharacteristic
642C2×C32C3×#12011yescharacteristic
643C2×C32C3×C22⋊Q811yescharacteristic
644C2×C32C3×C22⋊Q811yescharacteristic
645C2×C32C3×#12311yescharacteristic
646C3×D3—28no—
647C3×D3—24no—
648C3×D3—24no—
649C24—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—91no—
657C22×C4—91no—
658C22×C4C3×D3211yescharacteristic
659C4⋊C4—62no—
660C4⋊C4—182no—
661C22⋊C4—94no—
662C22⋊C4—182no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—34no—
685C22×C3—34no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—64no—
694C22×C3—64no—
695C22×C3—64no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—64no—
699C22×C3—64no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3—62no—
703C22×C3—62no—
704C22×C3—62no—
705C22×C3—62no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3D3×Dic611yescharacteristic
713C22×C3#379811yescharacteristic
714C22×C3#379911yescharacteristic
715C22×C3C4×D3211yescharacteristic
716C22×C3C2×#62511yescharacteristic
717C22×C3D3×#6711yescharacteristic
718C22×C3D3×#6711yescharacteristic
719C22×C3C2×C3×Dic611yescharacteristic
720C22×C3C2×C3×C4×D311yescharacteristic
721C22×C3C2×C3×C4×D311yescharacteristic
722C22×C3C3×#23511yescharacteristic
723C22×C3C3×#23511yescharacteristic
724C22×C3C3×#23511yescharacteristic
725C22×C3C3×D3×D411yescharacteristic
726C22×C3C3×D3×D411yescharacteristic
727C22×C3C3×D3×Q811yescharacteristic
728C22×C3C3×#23911yescharacteristic
729C22×C3C2×C3×#6711yescharacteristic
730C22×C3C2×C3×#6711yescharacteristic
731C22×C3C2×C3×#6711yescharacteristic
732C22×C3C2×C3×#6711yescharacteristic
733C2×D3—22no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3C3×Dic3⋊C414yescomplemented
740C3×C4—24no—
741C3×C4—22no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—42no—
745C3×C4—42no—
746C3×C4—44no—
747C3×C4—64no—
748C3×C4—64no—
749C3×C4—62no—
750C3×C4—62no—
751C3×C4—62no—
752C3×C4—62no—
753C3×C4—122no—
754C3×C4—121no—
755C3×C4—121no—
756C3×C4—182no—
757C3×C4—361no—
758Dic3—22no—
759Dic3—22no—
760Dic3—41no—
761Dic3—62no—
762Dic3—62no—
763Dic3—122no—
764Dic3—122no—
765Dic3—121no—
766Dic3—121no—
767C32—21no—
768C32—21no—
769C32—21no—
770C32—41no—
771C32#498911yescharacteristic, complemented
772C32#521011yescharacteristic, complemented
773C32C3×#38511yescharacteristic, complemented
774C23—32no—
775C23—32no—
776C23—32no—
777C23—61no—
778C23—61no—
779C23—61no—
780C23—61no—
781C23C2×C3×D3211yescharacteristic
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—68no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—92no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4C3×#62512yes—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—41no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—41no—
826C2×C3—41no—
827C2×C3—41no—
828C2×C3—41no—
829C2×C3—68no—
830C2×C3—64no—
831C2×C3—64no—
832C2×C3#6385011yescharacteristic
833C2×C3#6385111yescharacteristic
834C2×C3#6385611yescharacteristic
835C2×C3D3×Dic3⋊C411yescharacteristic
836C2×C3C4×#62511yescharacteristic
837C2×C3#6390411yescharacteristic
838C2×C3#6397611yescharacteristic
839C2×C3C3×D3×C4⋊C411yescharacteristic
840C2×C3C3×#89311yescharacteristic
841C2×C3C3×#89411yescharacteristic
842C2×C3C3×#89611yescharacteristic
843C2×C3C2×C3×Dic3⋊C411yescharacteristic
844C2×C3C3×#92411yescharacteristic
845C2×C3C3×#92411yescharacteristic
846C2×C3C3×C4×#6711yescharacteristic
847C2×C3C3×C4×#6711yescharacteristic
848C2×C3C3×C4×#6711yescharacteristic
849C2×C3C3×#92911yescharacteristic
850C2×C3C3×#93711yescharacteristic
851C2×C3C3×#94611yescharacteristic
852C2×C3C3×#95311yescharacteristic
853D3—24no—
854C22—34no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22C3×D3×Dic611yescharacteristic
862C22C3×#379811yescharacteristic
863C22C3×#379911yescharacteristic
864C22C3×C4×D3211yescharacteristic
865C22C2×C3×#62511yescharacteristic
866C22C3×D3×#6711yescharacteristic
867C22C3×D3×#6711yescharacteristic
868C4—22no—
869C4—62no—
870C4—62no—
871C4—121no—
872C4—182no—
873C4—361no—
874C3—21no—
875C3—21no—
876C3—21no—
877C3—41no—
878C3#1059127711yescharacteristic, direct product factor
879C3C3×#498911yescharacteristic, complemented
880C3C3×#521011yescharacteristic, complemented
881C2—64no—
882C2C3×#6385011yescharacteristic
883C2C3×#6385111yescharacteristic
884C2C3×#6385611yescharacteristic
885C2C3×D3×Dic3⋊C411yescharacteristic
886C2C3×C4×#62511yescharacteristic
887C2C3×#6390411yescharacteristic
888C2C3×#6397611yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#385
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C32×Dic3⋊C4C2semidirect
3. C2×C3×#3724C2semidirect
6. C3×#63658C2semidirect
7. C3×#63579C2semidirect
10. #10591277C3direct (N × H)
24. C3×(C2×D3)⋊Dic3C4semidirect
37. C2×C3×Dic3⋊C4D3semidirect
38. C2×C3×Dic3⋊C4C2×C3semidirect
39. C2×#3724C2×C3semidirect
42. #63658C2×C3semidirect
48. #63579C2×C3semidirect
65. C2×C3×C3⋊Dic3C2×C4semidirect
73. C2×C32×Dic3C2×C4semidirect
134. (C2×D3)⋊Dic3C3×C4semidirect
148. C2×C32×D3C4⋊C4semidirect
171. C2×Dic3⋊C4C3×D3semidirect
250. C2×C3⋊Dic3C2×C3×C4semidirect
292. C2×C3×Dic3C4×D3semidirect
294. C2×C3×Dic3C2×C3×C4semidirect
439. C2×C3×D3Dic3⋊C4semidirect
440. C2×C3×D3C3×C4⋊C4semidirect
475. C33#385semidirect
593. C2×Dic3C3×C4×D3semidirect
739. C2×D3C3×Dic3⋊C4semidirect
771. C32#4989semidirect
772. C32#5210semidirect
773. C32C3×#385semidirect
878. C3#10591277direct (N × H)
879. C3C3×#4989semidirect
880. C3C3×#5210semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C2×C32×Dic3⋊C42
C2×C3×#37242
C2×C3×(C2×D3)⋊Dic32
C3×#636582
C3×#635792
C3×#52103
C3×#49893
#105912773