Finite Group Databasebeta

← C32×#5663 #13179030

Subgroups — C32×#5663 #13179030

Order 1728.

1752 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#123C211yesmaximal, characteristic, complemented
2C32×#940C211yesmaximal, characteristic, complemented
3C32×#939C211yesmaximal, characteristic, complemented
4C32×#930C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6C32×#895C211yesmaximal, characteristic, complemented
7C32×#894C211yesmaximal, characteristic, complemented
8C32×#892C211yesmaximal, characteristic, complemented
9C32×#889C211yesmaximal, characteristic, complemented
10C32×#886C211yesmaximal, characteristic, complemented
11C32×#884C211yesmaximal, characteristic, complemented
12C32×#884C211yesmaximal, characteristic, complemented
13C32×#884C211yesmaximal, characteristic, complemented
14C32×#883C211yesmaximal, characteristic, complemented
15C32×#67⋊C4C211yesmaximal, characteristic, complemented
16C32×#540—31nomaximal
17C3×#5663C314yesmaximal, direct product factor
18C2×C33×D4C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C2×C32×D12C2211yescharacteristic
28C2×C32×D12C2211yescharacteristic
29C2×C32×D12C2211yescharacteristic
30C2×C32×C4×D3C2211yescharacteristic
31C2×C32×C4×D3C2211yescharacteristic
32C2×C32×C4×D3C2211yescharacteristic
33C33×C4⋊C4C2211yescharacteristic
34C33×C4⋊C4C2211yescharacteristic
35C33×C22⋊C4C2211yescharacteristic
36C33×C22⋊C4C2211yescharacteristic
37C33×C22⋊C4C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×C4⋊Dic3C2211yescharacteristic
46C32×C4⋊Dic3C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×Dic3⋊C4C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#127—31no—
54C32×#125—31no—
55C32×#123—24no—
56C32×#123—31no—
57C32×#123—31no—
58C32×#123—31no—
59C32×#123D311yescharacteristic, complemented
60C32×#123C2×C314yescomplemented
61C32×#121—31no—
62C32×#121—31no—
63C32×#121—31no—
64C32×#121—31no—
65C32×#121—31no—
66C32×#121—31no—
67C32×C4×D4—31no—
68C32×C4×D4—31no—
69C32×#117—31no—
70C3×#940C2×C314yescomplemented
71C3×#939C2×C314yescomplemented
72C3×#930C2×C314yescomplemented
73C3×C4×#67C2×C314yescomplemented
74C3×#895C2×C314yescomplemented
75C3×#894C2×C314yescomplemented
76C3×#892C2×C314yescomplemented
77C3×#889C2×C314yescomplemented
78C3×#886C2×C314yescomplemented
79C3×#884C2×C314yescomplemented
80C3×#884C2×C314yescomplemented
81C3×#884C2×C314yescomplemented
82C3×#883C2×C314yescomplemented
83C3×#67⋊C4C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C33×D4—41no—
90C2×C33×C4—41no—
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C32×#67—22no—
97C32×#67—22no—
98C32×#67—41no—
99C32×#67—41no—
100C32×#67—41no—
101C32×#67—41no—
102C2×C32×Dic3—41no—
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C32×D12—41no—
109C32×D12—41no—
110C32×D12—41no—
111C32×C4×D3—22no—
112C32×C4×D3—41no—
113C32×C4×D3—41no—
114C3×#540—34no—
115#5663C3211yescharacteristic, direct product factor
116C2×C32×D4—24no—
117C2×C32×D4—31no—
118C2×C32×D4—31no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C2×C32×D4—31no—
125C2×C32×D4—31no—
126C2×C32×D4C2×D311yescharacteristic
127C2×C32×D4C22×C314yes—
128C22×C32×C4—24no—
129C22×C32×C4—31no—
130C22×C32×C4—31no—
131C22×C32×C4—31no—
132C22×C32×C4—31no—
133C22×C32×C4C2×D311yescharacteristic
134C22×C32×C4C22×C314yes—
135C2×C3×#67C22×C314yes—
136C2×C3×#67C22×C314yes—
137C2×C3×#67C22×C314yes—
138C2×C3×#67C22×C314yes—
139C2×C3×#67C22×C314yes—
140C2×C3×#67C22×C314yes—
141C22×C3×Dic3C22×C314yes—
142C2×C3×D12C22×C314yes—
143C2×C3×D12C22×C314yes—
144C2×C3×D12C22×C314yes—
145C2×C3×C4×D3C22×C314yes—
146C2×C3×C4×D3C22×C314yes—
147C2×C3×C4×D3C22×C314yes—
148C32×C4⋊C4—24no—
149C32×C4⋊C4—24no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154C32×C4⋊C4—31no—
155C32×C4⋊C4—31no—
156C32×C4⋊C4C2×D311yescharacteristic
157C32×C4⋊C4C2×D311yescharacteristic
158C32×C4⋊C4C22×C314yes—
159C32×C4⋊C4C22×C314yes—
160C32×C22⋊C4—24no—
161C32×C22⋊C4—24no—
162C32×C22⋊C4—24no—
163C32×C22⋊C4—31no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167C32×C22⋊C4—31no—
168C32×C22⋊C4—31no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4C2×D311yescharacteristic
171C32×C22⋊C4C2×D311yescharacteristic
172C32×C22⋊C4C2×D311yescharacteristic
173C32×C22⋊C4C22×C314yes—
174C32×C22⋊C4C22×C314yes—
175C32×C22⋊C4C22×C314yes—
176C32×C42—31no—
177C32×C42—31no—
178C3×#217C22×C314yes—
179C3×(C2×D3)⋊C4C22×C314yes—
180C3×(C2×D3)⋊C4C22×C314yes—
181C3×(C2×D3)⋊C4C22×C314yes—
182C3×(C2×D3)⋊C4C22×C314yes—
183C3×(C2×D3)⋊C4C22×C314yes—
184C3×(C2×D3)⋊C4C22×C314yes—
185C3×C4⋊Dic3C22×C314yes—
186C3×C4⋊Dic3C22×C314yes—
187C3×Dic3⋊C4C22×C314yes—
188C3×Dic3⋊C4C22×C314yes—
189C3×Dic3⋊C4C22×C314yes—
190C3×Dic3⋊C4C22×C314yes—
191C3×C4×Dic3C22×C314yes—
192C3×C4×Dic3C22×C314yes—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33C2411yescharacteristic
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C33×C4—21no—
210C33×C4—21no—
211C33×C4—21no—
212C33×C4—21no—
213C33×C4—21no—
214C32×Dic3—21no—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3#4112yes—
219C3×#127—34no—
220C3×#125—34no—
221C3×#123—24no—
222C3×#123—34no—
223C3×#123—34no—
224C3×#123—34no—
225C3×#123C3×D314yescomplemented
226C3×#123C2×C3211yescharacteristic, complemented
227C3×#121—34no—
228C3×#121—34no—
229C3×#121—34no—
230C3×#121—34no—
231C3×#121—34no—
232C3×#121—34no—
233C3×C4×D4—34no—
234C3×C4×D4—34no—
235C3×#117—34no—
236#940C2×C3211yescharacteristic, complemented
237#939C2×C3211yescharacteristic, complemented
238#930C2×C3211yescharacteristic, complemented
239C4×#67C2×C3211yescharacteristic, complemented
240#895C2×C3211yescharacteristic, complemented
241#894C2×C3211yescharacteristic, complemented
242#892C2×C3211yescharacteristic, complemented
243#889C2×C3211yescharacteristic, complemented
244#886C2×C3211yescharacteristic, complemented
245#884C2×C3211yescharacteristic, complemented
246#884C2×C3211yescharacteristic, complemented
247#884C2×C3211yescharacteristic, complemented
248#883C2×C3211yescharacteristic, complemented
249#67⋊C4C2×C3211yescharacteristic, complemented
250C23×C32—24no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32—31no—
254C23×C32—31no—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C23×C32C23×C314yes—
258C23×C32C23×C314yes—
259C22×C3×D3C23×C314yes—
260C22×C3×D3C23×C314yes—
261C22×C3×D3C23×C314yes—
262C32×D4—41no—
263C32×D4—44no—
264C32×D4—48no—
265C32×D4—62no—
266C32×D4—62no—
267C32×D4—121no—
268C32×D4—121no—
269C32×D4—121no—
270C32×D4—121no—
271C32×D4—121no—
272C32×D4—121no—
273C32×D4—121no—
274C2×C32×C4—24no—
275C2×C32×C4—24no—
276C2×C32×C4—24no—
277C2×C32×C4—24no—
278C2×C32×C4—24no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4—31no—
284C2×C32×C4—41no—
285C2×C32×C4—44no—
286C2×C32×C4—48no—
287C2×C32×C4—62no—
288C2×C32×C4—121no—
289C2×C32×C4—121no—
290C2×C32×C4—121no—
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C23×C314yes—
297C2×C32×C4C23×C314yes—
298C2×C32×C4C23×C314yes—
299C2×C32×C4C23×C314yes—
300C2×C32×C4C23×C314yes—
301C3×#67—28no—
302C3×#67—28no—
303C3×#67—44no—
304C3×#67—44no—
305C3×#67—44no—
306C3×#67—44no—
307C2×C3×Dic3—44no—
308C2×C3×Dic3C23×C314yes—
309C2×C3×Dic3C23×C314yes—
310C2×C3×Dic3C23×C314yes—
311C2×C3×Dic3C23×C314yes—
312C2×C3×Dic3C23×C314yes—
313C3×D12—44no—
314C3×D12—44no—
315C3×D12—44no—
316C3×C4×D3—28no—
317C3×C4×D3—44no—
318C3×C4×D3—44no—
319#540—31noSylow
320C2×C33—41no—
321C2×C33—41no—
322C2×C33C2×#4111yescharacteristic
323C2×C33H(5,𝔽2)11yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C32×D3—41no—
326C32×D3—41no—
327C32×D3—41no—
328C2×C3×D4—24no—
329C2×C3×D4—34no—
330C2×C3×D4—34no—
331C2×C3×D4—34no—
332C2×C3×D4—34no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—34no—
338C2×C3×D4C2×C3×D314yes—
339C2×C3×D4C22×C3211yescharacteristic
340C22×C3×C4—24no—
341C22×C3×C4—34no—
342C22×C3×C4—34no—
343C22×C3×C4—34no—
344C22×C3×C4—34no—
345C22×C3×C4C2×C3×D314yes—
346C22×C3×C4C22×C3211yescharacteristic
347C2×#67C22×C3211yescharacteristic
348C2×#67C22×C3211yescharacteristic
349C2×#67C22×C3211yescharacteristic
350C2×#67C22×C3211yescharacteristic
351C2×#67C22×C3211yescharacteristic
352C2×#67C22×C3211yescharacteristic
353C22×Dic3C22×C3211yescharacteristic
354C2×D12C22×C3211yescharacteristic
355C2×D12C22×C3211yescharacteristic
356C2×D12C22×C3211yescharacteristic
357C2×C4×D3C22×C3211yescharacteristic
358C2×C4×D3C22×C3211yescharacteristic
359C2×C4×D3C22×C3211yescharacteristic
360C3×C4⋊C4—24no—
361C3×C4⋊C4—24no—
362C3×C4⋊C4—34no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4—34no—
368C3×C4⋊C4C2×C3×D314yes—
369C3×C4⋊C4C2×C3×D314yes—
370C3×C4⋊C4C22×C3211yescharacteristic
371C3×C4⋊C4C22×C3211yescharacteristic
372C3×C22⋊C4—24no—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—24no—
375C3×C22⋊C4—34no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4—34no—
378C3×C22⋊C4—34no—
379C3×C22⋊C4—34no—
380C3×C22⋊C4—34no—
381C3×C22⋊C4—34no—
382C3×C22⋊C4C2×C3×D314yes—
383C3×C22⋊C4C2×C3×D314yes—
384C3×C22⋊C4C2×C3×D314yes—
385C3×C22⋊C4C22×C3211yescharacteristic
386C3×C22⋊C4C22×C3211yescharacteristic
387C3×C22⋊C4C22×C3211yescharacteristic
388C3×C42—34no—
389C3×C42—34no—
390#217C22×C3211yescharacteristic
391(C2×D3)⋊C4C22×C3211yescharacteristic
392(C2×D3)⋊C4C22×C3211yescharacteristic
393(C2×D3)⋊C4C22×C3211yescharacteristic
394(C2×D3)⋊C4C22×C3211yescharacteristic
395(C2×D3)⋊C4C22×C3211yescharacteristic
396(C2×D3)⋊C4C22×C3211yescharacteristic
397C4⋊Dic3C22×C3211yescharacteristic
398C4⋊Dic3C22×C3211yescharacteristic
399Dic3⋊C4C22×C3211yescharacteristic
400Dic3⋊C4C22×C3211yescharacteristic
401Dic3⋊C4C22×C3211yescharacteristic
402Dic3⋊C4C22×C3211yescharacteristic
403C4×Dic3C22×C3211yescharacteristic
404C4×Dic3C22×C3211yescharacteristic
405C22×C32—28no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—24no—
413C22×C32—24no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—44no—
420C22×C32—44no—
421C22×C32—44no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32—61no—
427C22×C32—61no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32C23×D311yescharacteristic
434C22×C32C24×C314yes—
435C2×C3×D3—24no—
436C2×C3×D3—24no—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—24no—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—24no—
450C32×C4—24no—
451C32×C4—24no—
452C32×C4—24no—
453C32×C4—24no—
454C32×C4—32no—
455C32×C4—44no—
456C32×C4—44no—
457C32×C4—44no—
458C32×C4—44no—
459C32×C4—44no—
460C32×C4—61no—
461C32×C4—61no—
462C32×C4—61no—
463C32×C4—61no—
464C3×Dic3—24no—
465C3×Dic3—24no—
466C3×Dic3—24no—
467C3×Dic3—24no—
468C3×Dic3C3×#4118yes—
469#127—31no—
470#125—31no—
471#123—31no—
472#123—31no—
473#123—31no—
474#123C32×D311yescharacteristic, complemented
475#121—31no—
476#121—31no—
477#121—31no—
478#121—31no—
479#121—31no—
480#121—31no—
481C4×D4—31no—
482C4×D4—31no—
483#117—31no—
484C33#54011yescharacteristic, complemented, Sylow
485C23×C3—24no—
486C23×C3—24no—
487C23×C3—34no—
488C23×C3—34no—
489C23×C3—34no—
490C23×C3C22×C3×D314yes—
491C23×C3C22×C3×D314yes—
492C23×C3C23×C3211yescharacteristic
493C23×C3C23×C3211yescharacteristic
494C22×D3C23×C3211yescharacteristic
495C22×D3C23×C3211yescharacteristic
496C22×D3C23×C3211yescharacteristic
497C3×D4—44no—
498C3×D4—41no—
499C3×D4—48no—
500C3×D4—68no—
501C3×D4—68no—
502C3×D4—124no—
503C3×D4—124no—
504C3×D4—124no—
505C3×D4—124no—
506C3×D4—124no—
507C3×D4—124no—
508C3×D4—124no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—24no—
512C2×C3×C4—24no—
513C2×C3×C4—24no—
514C2×C3×C4—34no—
515C2×C3×C4—34no—
516C2×C3×C4—34no—
517C2×C3×C4—34no—
518C2×C3×C4—34no—
519C2×C3×C4—44no—
520C2×C3×C4—41no—
521C2×C3×C4—48no—
522C2×C3×C4—68no—
523C2×C3×C4—124no—
524C2×C3×C4—124no—
525C2×C3×C4—124no—
526C2×C3×C4C22×C3×D314yes—
527C2×C3×C4C22×C3×D314yes—
528C2×C3×C4C22×C3×D314yes—
529C2×C3×C4C22×C3×D314yes—
530C2×C3×C4C22×C3×D314yes—
531C2×C3×C4C23×C3211yescharacteristic
532C2×C3×C4C23×C3211yescharacteristic
533C2×C3×C4C23×C3211yescharacteristic
534C2×C3×C4C23×C3211yescharacteristic
535C2×C3×C4C23×C3211yescharacteristic
536#67—22no—
537#67—22no—
538#67—41no—
539#67—41no—
540#67—41no—
541#67—41no—
542C2×Dic3—41no—
543C2×Dic3C23×C3211yescharacteristic
544C2×Dic3C23×C3211yescharacteristic
545C2×Dic3C23×C3211yescharacteristic
546C2×Dic3C23×C3211yescharacteristic
547C2×Dic3C23×C3211yescharacteristic
548D12—41no—
549D12—41no—
550D12—41no—
551C4×D3—22no—
552C4×D3—41no—
553C4×D3—41no—
554C2×C32—24no—
555C2×C32—24no—
556C2×C32—24no—
557C2×C32—48no—
558C2×C32—41no—
559C2×C32—41no—
560C2×C32—44no—
561C2×C32—44no—
562C2×C32—84no—
563C2×C32—121no—
564C2×C32—121no—
565C2×C32—121no—
566C2×C32#100411yescharacteristic
567C2×C32D3×#4111yescharacteristic
568C2×C32#100911yescharacteristic
569C2×C32C2×C3×#4114yes—
570C2×C32C3×H(5,𝔽2)14yes—
571C2×C32C3×H(5,𝔽2)14yes—
572C3×D3—44no—
573C3×D3—44no—
574C3×D3—44no—
575C2×D4—31no—
576C2×D4—31no—
577C2×D4—31no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4C2×C32×D311yescharacteristic
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4C2×C32×D311yescharacteristic
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4C2×C32×D311yescharacteristic
597C4⋊C4C2×C32×D311yescharacteristic
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4C2×C32×D311yescharacteristic
606C22⋊C4C2×C32×D311yescharacteristic
607C22⋊C4C2×C32×D311yescharacteristic
608C42—31no—
609C42—31no—
610C22×C3—28no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—24no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—44no—
627C22×C3—44no—
628C22×C3—44no—
629C22×C3—64no—
630C22×C3—64no—
631C22×C3—64no—
632C22×C3—64no—
633C22×C3—64no—
634C22×C3—64no—
635C22×C3—64no—
636C22×C3—64no—
637C22×C3—64no—
638C22×C3C23×C3×D314yes—
639C22×C3C24×C3211yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C3×C4—24no—
650C3×C4—24no—
651C3×C4—24no—
652C3×C4—24no—
653C3×C4—24no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—38no—
660C3×C4—44no—
661C3×C4—44no—
662C3×C4—44no—
663C3×C4—44no—
664C3×C4—44no—
665C3×C4—64no—
666C3×C4—64no—
667C3×C4—64no—
668C3×C4—64no—
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3C32×#4112yes—
674C32—24no—
675C32#566311yescharacteristic, direct product factor
676C32C3×#54014yescomplemented
677C23—31no—
678C23—31no—
679C23—31no—
680C23C22×C32×D311yescharacteristic
681C23C22×C32×D311yescharacteristic
682D4—41no—
683D4—62no—
684D4—62no—
685D4—121no—
686D4—121no—
687D4—121no—
688D4—121no—
689D4—121no—
690D4—121no—
691D4—121no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—41no—
698C2×C4—62no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4C22×C32×D311yescharacteristic
703C2×C4C22×C32×D311yescharacteristic
704C2×C4C22×C32×D311yescharacteristic
705C2×C4C22×C32×D311yescharacteristic
706C2×C4C22×C32×D311yescharacteristic
707C2×C3—24no—
708C2×C3—24no—
709C2×C3—24no—
710C2×C3—48no—
711C2×C3—44no—
712C2×C3—44no—
713C2×C3—41no—
714C2×C3—41no—
715C2×C3—84no—
716C2×C3—124no—
717C2×C3—124no—
718C2×C3—124no—
719C2×C3C3×#100414yes—
720C2×C3C3×D3×#4114yes—
721C2×C3C3×#100914yes—
722C2×C3C2×C32×#4111yescharacteristic
723C2×C3C32×H(5,𝔽2)11yescharacteristic
724C2×C3C32×H(5,𝔽2)11yescharacteristic
725D3—41no—
726D3—41no—
727D3—41no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—61no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22C23×C32×D311yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—32no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—61no—
754C3—24no—
755C3C3×#566314yesdirect product factor
756C3C32×#54011yescharacteristic, complemented
757C2—41no—
758C2—41no—
759C2—121no—
760C2—121no—
761C2—121no—
762C2C32×#100411yescharacteristic
763C2C32×D3×#4111yescharacteristic
764C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#123C2
socleC22×C33C24
hypercenterC32×#123D3
hypocenterC3C32×#540
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#123

Complements

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

NH ≅ G/Ntype
1. C33×#123C2semidirect
2. C32×#940C2semidirect
3. C32×#939C2semidirect
4. C32×#930C2semidirect
5. C32×C4×#67C2semidirect
6. C32×#895C2semidirect
7. C32×#894C2semidirect
8. C32×#892C2semidirect
9. C32×#889C2semidirect
10. C32×#886C2semidirect
11. C32×#884C2semidirect
12. C32×#884C2semidirect
13. C32×#884C2semidirect
14. C32×#883C2semidirect
15. C32×#67⋊C4C2semidirect
17. C3×#5663C3direct (N × H)
59. C32×#123D3semidirect
60. C32×#123C2×C3semidirect
70. C3×#940C2×C3semidirect
71. C3×#939C2×C3semidirect
72. C3×#930C2×C3semidirect
73. C3×C4×#67C2×C3semidirect
74. C3×#895C2×C3semidirect
75. C3×#894C2×C3semidirect
76. C3×#892C2×C3semidirect
77. C3×#889C2×C3semidirect
78. C3×#886C2×C3semidirect
79. C3×#884C2×C3semidirect
80. C3×#884C2×C3semidirect
81. C3×#884C2×C3semidirect
82. C3×#883C2×C3semidirect
83. C3×#67⋊C4C2×C3semidirect
115. #5663C32direct (N × H)
225. C3×#123C3×D3semidirect
226. C3×#123C2×C32semidirect
236. #940C2×C32semidirect
237. #939C2×C32semidirect
238. #930C2×C32semidirect
239. C4×#67C2×C32semidirect
240. #895C2×C32semidirect
241. #894C2×C32semidirect
242. #892C2×C32semidirect
243. #889C2×C32semidirect
244. #886C2×C32semidirect
245. #884C2×C32semidirect
246. #884C2×C32semidirect
247. #884C2×C32semidirect
248. #883C2×C32semidirect
249. #67⋊C4C2×C32semidirect
474. #123C32×D3semidirect
484. C33#540semidirect
675. C32#5663direct (N × H)
676. C32C3×#540semidirect
755. C3C3×#5663direct (N × H)
756. C3C32×#540semidirect

Maximal subgroups

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

subgroupindex
C33×#1232
C32×#9402
C32×#9392
C32×#9302
C32×C4×#672
C32×#8952
C32×#8942
C32×#8922
C32×#8892
C32×#8862
C32×#8842
C32×#8832
C32×#67⋊C42
C32×#5403
C3×#56633