Finite Group Databasebeta

← C32×#5712 #13179089

Subgroups — C32×#5712 #13179089

Order 1728.

1416 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#126C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic, complemented
3C32×#897C211yesmaximal, characteristic, complemented
4C32×#896C211yesmaximal, characteristic, complemented
5C32×#890C211yesmaximal, characteristic, complemented
6C32×#889C211yesmaximal, characteristic, complemented
7C32×#888C211yesmaximal, characteristic, complemented
8C32×#886C211yesmaximal, characteristic
9C32×#885C211yesmaximal, characteristic
10C32×#883C211yesmaximal, characteristic
11C32×#879C211yesmaximal, characteristic, complemented
12C32×#878C211yesmaximal, characteristic, complemented
13C32×#878C211yesmaximal, characteristic, complemented
14C32×#876C211yesmaximal, characteristic, complemented
15C32×#869C211yesmaximal, characteristic, complemented
16C32×#563—31nomaximal
17C3×#5712C314yesmaximal, direct product factor
18C2×C32×#67C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C33×C4⋊C4C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic
26C33×C4⋊C4C2211yescharacteristic
27C33×C22⋊C4C2211yescharacteristic
28C33×C22⋊C4C2211yescharacteristic
29C33×C22⋊C4C2211yescharacteristic
30C33×C42C2211yescharacteristic
31C32×#217C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×C4⋊Dic3C2211yescharacteristic
39C32×C4⋊Dic3C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic
41C32×C4⋊Dic3C2211yescharacteristic
42C32×C4⋊Dic3C2211yescharacteristic
43C32×C4⋊Dic3C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×Dic3⋊C4C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×C4⋊Q8—31no—
54C32×C4⋊Q8—31no—
55C32×#126—24no—
56C32×#126—31no—
57C32×#126—31no—
58C32×#126—31no—
59C32×#126D311yescharacteristic, complemented
60C32×#126C2×C314yescomplemented
61C32×#125—31no—
62C32×#125—31no—
63C32×#124—31no—
64C32×#123—31no—
65C32×#123—31no—
66C32×C22⋊Q8—31no—
67C32×C22⋊Q8—31no—
68C32×C22⋊Q8—31no—
69C32×C22⋊Q8—31no—
70C3×#898C2×C314yescomplemented
71C3×#897C2×C314yescomplemented
72C3×#896C2×C314yescomplemented
73C3×#890C2×C314yescomplemented
74C3×#889C2×C314yescomplemented
75C3×#888C2×C314yescomplemented
76C3×#886C2×C314yes—
77C3×#885C2×C314yes—
78C3×#883C2×C314yes—
79C3×#879C2×C314yescomplemented
80C3×#878C2×C314yescomplemented
81C3×#878C2×C314yescomplemented
82C3×#876C2×C314yescomplemented
83C3×#869C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C33×C4C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C32×#67—41no—
93C2×C32×Dic3—41no—
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C32×C4×D3—41no—
102C32×Dic6—41no—
103C32×Dic6—41no—
104C32×Dic6—41no—
105C3×#563—34no—
106#5712C3211yescharacteristic, direct product factor
107C2×C32×Q8—31no—
108C2×C32×Q8—31no—
109C2×C32×Q8—31no—
110C2×C32×D4—31no—
111C22×C32×C4—31no—
112C22×C32×C4—31no—
113C2×C3×#67C22×C314yes—
114C22×C3×Dic3C22×C314yes—
115C2×C3×C4×D3C22×C314yes—
116C2×C3×Dic6C22×C314yes—
117C2×C3×Dic6C22×C314yes—
118C2×C3×Dic6C22×C314yes—
119C32×C4⋊C4—24no—
120C32×C4⋊C4—24no—
121C32×C4⋊C4—24no—
122C32×C4⋊C4—31no—
123C32×C4⋊C4—31no—
124C32×C4⋊C4—31no—
125C32×C4⋊C4—31no—
126C32×C4⋊C4—31no—
127C32×C4⋊C4—31no—
128C32×C4⋊C4—31no—
129C32×C4⋊C4—31no—
130C32×C4⋊C4—31no—
131C32×C4⋊C4—31no—
132C32×C4⋊C4—31no—
133C32×C4⋊C4—31no—
134C32×C4⋊C4—31no—
135C32×C4⋊C4C2×D311yescharacteristic
136C32×C4⋊C4C2×D311yescharacteristic
137C32×C4⋊C4C2×D311yescharacteristic
138C32×C4⋊C4C22×C314yes—
139C32×C4⋊C4C22×C314yes—
140C32×C4⋊C4C22×C314yes—
141C32×C22⋊C4—24no—
142C32×C22⋊C4—24no—
143C32×C22⋊C4—24no—
144C32×C22⋊C4—31no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151C32×C22⋊C4C2×D311yescharacteristic
152C32×C22⋊C4C2×D311yescharacteristic
153C32×C22⋊C4C2×D311yescharacteristic
154C32×C22⋊C4C22×C314yes—
155C32×C22⋊C4C22×C314yes—
156C32×C22⋊C4C22×C314yes—
157C32×C42—24no—
158C32×C42—31no—
159C32×C42—31no—
160C32×C42C2×D311yescharacteristic
161C32×C42C22×C314yes—
162C3×#217C22×C314yes—
163C3×#217C22×C314yes—
164C3×(C2×D3)⋊C4C22×C314yes—
165C3×(C2×D3)⋊C4C22×C314yes—
166C3×(C2×D3)⋊C4C22×C314yes—
167C3×(C2×D3)⋊C4C22×C314yes—
168C3×(C2×D3)⋊C4C22×C314yes—
169C3×C4⋊Dic3C22×C314yes—
170C3×C4⋊Dic3C22×C314yes—
171C3×C4⋊Dic3C22×C314yes—
172C3×C4⋊Dic3C22×C314yes—
173C3×C4⋊Dic3C22×C314yes—
174C3×C4⋊Dic3C22×C314yes—
175C3×Dic3⋊C4C22×C314yes—
176C3×Dic3⋊C4C22×C314yes—
177C3×Dic3⋊C4C22×C314yes—
178C3×Dic3⋊C4C22×C314yes—
179C3×Dic3⋊C4C22×C314yes—
180C3×Dic3⋊C4C22×C314yes—
181C3×Dic3⋊C4C22×C314yes—
182C3×C4×Dic3C22×C314yes—
183C3×C4×Dic3C22×C314yes—
184C22×C33—21no—
185C22×C33—21no—
186C22×C33—21no—
187C22×C33C2411yescharacteristic
188C2×C32×D3—21no—
189C2×C32×D3—21no—
190C2×C32×D3—21no—
191C33×C4—21no—
192C33×C4—21no—
193C33×C4—21no—
194C33×C4—21no—
195C33×C4—21no—
196C33×C4—21no—
197C32×Dic3—21no—
198C32×Dic3—21no—
199C32×Dic3—21no—
200C32×Dic3—21no—
201C32×Dic3—21no—
202C32×Dic3—21no—
203C32×Dic3—21no—
204C3×C4⋊Q8—34no—
205C3×C4⋊Q8—34no—
206C3×#126—24no—
207C3×#126—34no—
208C3×#126—34no—
209C3×#126—34no—
210C3×#126C3×D314yescomplemented
211C3×#126C2×C3211yescharacteristic, complemented
212C3×#125—34no—
213C3×#125—34no—
214C3×#124—34no—
215C3×#123—34no—
216C3×#123—34no—
217C3×C22⋊Q8—34no—
218C3×C22⋊Q8—34no—
219C3×C22⋊Q8—34no—
220C3×C22⋊Q8—34no—
221#898C2×C3211yescharacteristic, complemented
222#897C2×C3211yescharacteristic, complemented
223#896C2×C3211yescharacteristic, complemented
224#890C2×C3211yescharacteristic, complemented
225#889C2×C3211yescharacteristic, complemented
226#888C2×C3211yescharacteristic, complemented
227#886C2×C3211yescharacteristic
228#885C2×C3211yescharacteristic
229#883C2×C3211yescharacteristic
230#879C2×C3211yescharacteristic, complemented
231#878C2×C3211yescharacteristic, complemented
232#878C2×C3211yescharacteristic, complemented
233#876C2×C3211yescharacteristic, complemented
234#869C2×C3211yescharacteristic, complemented
235C23×C32—24no—
236C23×C32—31no—
237C23×C32C22×D311yescharacteristic
238C23×C32C23×C314yes—
239C22×C3×D3C23×C314yes—
240C32×Q8—121no—
241C32×Q8—121no—
242C32×Q8—121no—
243C32×D4—121no—
244C2×C32×C4—24no—
245C2×C32×C4—24no—
246C2×C32×C4—24no—
247C2×C32×C4—24no—
248C2×C32×C4—24no—
249C2×C32×C4—24no—
250C2×C32×C4—31no—
251C2×C32×C4—31no—
252C2×C32×C4—31no—
253C2×C32×C4—31no—
254C2×C32×C4—31no—
255C2×C32×C4—31no—
256C2×C32×C4—31no—
257C2×C32×C4—121no—
258C2×C32×C4—121no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C23×C314yes—
266C2×C32×C4C23×C314yes—
267C2×C32×C4C23×C314yes—
268C2×C32×C4C23×C314yes—
269C2×C32×C4C23×C314yes—
270C2×C32×C4C23×C314yes—
271C3×#67—44no—
272C2×C3×Dic3—44no—
273C2×C3×Dic3C23×C314yes—
274C2×C3×Dic3C23×C314yes—
275C2×C3×Dic3C23×C314yes—
276C2×C3×Dic3C23×C314yes—
277C2×C3×Dic3C23×C314yes—
278C2×C3×Dic3C23×C314yes—
279C2×C3×Dic3C23×C314yes—
280C3×C4×D3—44no—
281C3×Dic6—44no—
282C3×Dic6—44no—
283C3×Dic6—44no—
284#563—31noSylow
285C2×C33—41no—
286C2×C33H(5,𝔽2)11yescharacteristic
287C2×C332−1+411yescharacteristic
288C2×C332−1+411yescharacteristic
289C32×D3—41no—
290C2×C3×Q8—34no—
291C2×C3×Q8—34no—
292C2×C3×Q8—34no—
293C2×C3×D4—34no—
294C22×C3×C4—34no—
295C22×C3×C4—34no—
296C2×#67C22×C3211yescharacteristic
297C22×Dic3C22×C3211yescharacteristic
298C2×C4×D3C22×C3211yescharacteristic
299C2×Dic6C22×C3211yescharacteristic
300C2×Dic6C22×C3211yescharacteristic
301C2×Dic6C22×C3211yescharacteristic
302C3×C4⋊C4—24no—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—24no—
305C3×C4⋊C4—34no—
306C3×C4⋊C4—34no—
307C3×C4⋊C4—34no—
308C3×C4⋊C4—34no—
309C3×C4⋊C4—34no—
310C3×C4⋊C4—34no—
311C3×C4⋊C4—34no—
312C3×C4⋊C4—34no—
313C3×C4⋊C4—34no—
314C3×C4⋊C4—34no—
315C3×C4⋊C4—34no—
316C3×C4⋊C4—34no—
317C3×C4⋊C4—34no—
318C3×C4⋊C4C2×C3×D314yes—
319C3×C4⋊C4C2×C3×D314yes—
320C3×C4⋊C4C2×C3×D314yes—
321C3×C4⋊C4C22×C3211yescharacteristic
322C3×C4⋊C4C22×C3211yescharacteristic
323C3×C4⋊C4C22×C3211yescharacteristic
324C3×C22⋊C4—24no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—34no—
328C3×C22⋊C4—34no—
329C3×C22⋊C4—34no—
330C3×C22⋊C4—34no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4C2×C3×D314yes—
335C3×C22⋊C4C2×C3×D314yes—
336C3×C22⋊C4C2×C3×D314yes—
337C3×C22⋊C4C22×C3211yescharacteristic
338C3×C22⋊C4C22×C3211yescharacteristic
339C3×C22⋊C4C22×C3211yescharacteristic
340C3×C42—24no—
341C3×C42—34no—
342C3×C42—34no—
343C3×C42C2×C3×D314yes—
344C3×C42C22×C3211yescharacteristic
345#217C22×C3211yescharacteristic
346#217C22×C3211yescharacteristic
347(C2×D3)⋊C4C22×C3211yescharacteristic
348(C2×D3)⋊C4C22×C3211yescharacteristic
349(C2×D3)⋊C4C22×C3211yescharacteristic
350(C2×D3)⋊C4C22×C3211yescharacteristic
351(C2×D3)⋊C4C22×C3211yescharacteristic
352C4⋊Dic3C22×C3211yescharacteristic
353C4⋊Dic3C22×C3211yescharacteristic
354C4⋊Dic3C22×C3211yescharacteristic
355C4⋊Dic3C22×C3211yescharacteristic
356C4⋊Dic3C22×C3211yescharacteristic
357C4⋊Dic3C22×C3211yescharacteristic
358Dic3⋊C4C22×C3211yescharacteristic
359Dic3⋊C4C22×C3211yescharacteristic
360Dic3⋊C4C22×C3211yescharacteristic
361Dic3⋊C4C22×C3211yescharacteristic
362Dic3⋊C4C22×C3211yescharacteristic
363Dic3⋊C4C22×C3211yescharacteristic
364Dic3⋊C4C22×C3211yescharacteristic
365C4×Dic3C22×C3211yescharacteristic
366C4×Dic3C22×C3211yescharacteristic
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—24no—
371C22×C32—24no—
372C22×C32—24no—
373C22×C32—24no—
374C22×C32—44no—
375C22×C32—44no—
376C22×C32—44no—
377C22×C32—61no—
378C22×C32—61no—
379C22×C32—61no—
380C22×C32C23×D311yescharacteristic
381C22×C32C24×C314yes—
382C2×C3×D3—24no—
383C2×C3×D3—24no—
384C2×C3×D3—24no—
385C32×C4—21no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—24no—
392C32×C4—24no—
393C32×C4—24no—
394C32×C4—24no—
395C32×C4—24no—
396C32×C4—24no—
397C32×C4—44no—
398C32×C4—44no—
399C32×C4—44no—
400C32×C4—44no—
401C32×C4—44no—
402C32×C4—44no—
403C32×C4—61no—
404C32×C4—61no—
405C32×C4—61no—
406C32×C4—61no—
407C32×C4—61no—
408C32×C4—61no—
409C32×C4—61no—
410C3×Dic3—24no—
411C3×Dic3—24no—
412C3×Dic3—24no—
413C3×Dic3—24no—
414C3×Dic3—24no—
415C3×Dic3—24no—
416C3×Dic3—24no—
417C4⋊Q8—31no—
418C4⋊Q8—31no—
419#126—31no—
420#126—31no—
421#126—31no—
422#126C32×D311yescharacteristic, complemented
423#125—31no—
424#125—31no—
425#124—31no—
426#123—31no—
427#123—31no—
428C22⋊Q8—31no—
429C22⋊Q8—31no—
430C22⋊Q8—31no—
431C22⋊Q8—31no—
432C33#56311yescharacteristic, complemented, Sylow
433C23×C3—24no—
434C23×C3—34no—
435C23×C3C22×C3×D314yes—
436C23×C3C23×C3211yescharacteristic
437C22×D3C23×C3211yescharacteristic
438C3×Q8—124no—
439C3×Q8—124no—
440C3×Q8—124no—
441C3×D4—124no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—24no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—34no—
449C2×C3×C4—34no—
450C2×C3×C4—34no—
451C2×C3×C4—34no—
452C2×C3×C4—34no—
453C2×C3×C4—34no—
454C2×C3×C4—34no—
455C2×C3×C4—124no—
456C2×C3×C4—124no—
457C2×C3×C4C22×C3×D314yes—
458C2×C3×C4C22×C3×D314yes—
459C2×C3×C4C22×C3×D314yes—
460C2×C3×C4C22×C3×D314yes—
461C2×C3×C4C22×C3×D314yes—
462C2×C3×C4C22×C3×D314yes—
463C2×C3×C4C23×C3211yescharacteristic
464C2×C3×C4C23×C3211yescharacteristic
465C2×C3×C4C23×C3211yescharacteristic
466C2×C3×C4C23×C3211yescharacteristic
467C2×C3×C4C23×C3211yescharacteristic
468C2×C3×C4C23×C3211yescharacteristic
469#67—41no—
470C2×Dic3—41no—
471C2×Dic3C23×C3211yescharacteristic
472C2×Dic3C23×C3211yescharacteristic
473C2×Dic3C23×C3211yescharacteristic
474C2×Dic3C23×C3211yescharacteristic
475C2×Dic3C23×C3211yescharacteristic
476C2×Dic3C23×C3211yescharacteristic
477C2×Dic3C23×C3211yescharacteristic
478C4×D3—41no—
479Dic6—41no—
480Dic6—41no—
481Dic6—41no—
482C2×C32—24no—
483C2×C32—24no—
484C2×C32—24no—
485C2×C32—41no—
486C2×C32—44no—
487C2×C32—84no—
488C2×C32—121no—
489C2×C32#100911yescharacteristic
490C2×C32#101011yescharacteristic
491C2×C32#101011yescharacteristic
492C2×C32C3×H(5,𝔽2)14yes—
493C2×C32C3×2−1+414yes—
494C2×C32C3×2−1+414yes—
495C3×D3—44no—
496C2×Q8—31no—
497C2×Q8—31no—
498C2×Q8—31no—
499C2×D4—31no—
500C22×C4—31no—
501C22×C4—31no—
502C4⋊C4—31no—
503C4⋊C4—31no—
504C4⋊C4—31no—
505C4⋊C4—31no—
506C4⋊C4—31no—
507C4⋊C4—31no—
508C4⋊C4—31no—
509C4⋊C4—31no—
510C4⋊C4—31no—
511C4⋊C4—31no—
512C4⋊C4—31no—
513C4⋊C4—31no—
514C4⋊C4—31no—
515C4⋊C4C2×C32×D311yescharacteristic
516C4⋊C4C2×C32×D311yescharacteristic
517C4⋊C4C2×C32×D311yescharacteristic
518C22⋊C4—31no—
519C22⋊C4—31no—
520C22⋊C4—31no—
521C22⋊C4—31no—
522C22⋊C4—31no—
523C22⋊C4—31no—
524C22⋊C4—31no—
525C22⋊C4C2×C32×D311yescharacteristic
526C22⋊C4C2×C32×D311yescharacteristic
527C22⋊C4C2×C32×D311yescharacteristic
528C42—31no—
529C42—31no—
530C42C2×C32×D311yescharacteristic
531C22×C3—24no—
532C22×C3—24no—
533C22×C3—24no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—24no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—64no—
542C22×C3—64no—
543C22×C3—64no—
544C22×C3C23×C3×D314yes—
545C22×C3C24×C3211yescharacteristic
546C2×D3—21no—
547C2×D3—21no—
548C2×D3—21no—
549C3×C4—24no—
550C3×C4—24no—
551C3×C4—24no—
552C3×C4—24no—
553C3×C4—24no—
554C3×C4—24no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—44no—
562C3×C4—44no—
563C3×C4—44no—
564C3×C4—44no—
565C3×C4—44no—
566C3×C4—44no—
567C3×C4—64no—
568C3×C4—64no—
569C3×C4—64no—
570C3×C4—64no—
571C3×C4—64no—
572C3×C4—64no—
573C3×C4—64no—
574Dic3—21no—
575Dic3—21no—
576Dic3—21no—
577Dic3—21no—
578Dic3—21no—
579Dic3—21no—
580Dic3—21no—
581C32—24no—
582C32#571211yescharacteristic, direct product factor
583C32C3×#56314yescomplemented
584C23—31no—
585C23C22×C32×D311yescharacteristic
586Q8—121no—
587Q8—121no—
588Q8—121no—
589D4—121no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—121no—
598C2×C4—121no—
599C2×C4C22×C32×D311yescharacteristic
600C2×C4C22×C32×D311yescharacteristic
601C2×C4C22×C32×D311yescharacteristic
602C2×C4C22×C32×D311yescharacteristic
603C2×C4C22×C32×D311yescharacteristic
604C2×C4C22×C32×D311yescharacteristic
605C2×C3—24no—
606C2×C3—24no—
607C2×C3—24no—
608C2×C3—41no—
609C2×C3—44no—
610C2×C3—84no—
611C2×C3—124no—
612C2×C3C3×#100914yes—
613C2×C3C3×#101014yes—
614C2×C3C3×#101014yes—
615C2×C3C32×H(5,𝔽2)11yescharacteristic
616C2×C3C32×2−1+411yescharacteristic
617C2×C3C32×2−1+411yescharacteristic
618D3—41no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—61no—
623C22—61no—
624C22—61no—
625C22C23×C32×D311yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—61no—
633C4—61no—
634C4—61no—
635C4—61no—
636C4—61no—
637C4—61no—
638C4—61no—
639C3—24no—
640C3C3×#571214yesdirect product factor
641C3C32×#56311yescharacteristic, complemented
642C2—41no—
643C2—121no—
644C2C32×#100911yescharacteristic
645C2C32×#101011yescharacteristic
646C2C32×#101011yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#126C2
socleC22×C33C24
prime radicalC2×C32×#67C22
hypercenterC32×#126D3
hypocenterC3C32×#563
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#126

Complements

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

NH ≅ G/Ntype
1. C33×#126C2semidirect
2. C32×#898C2semidirect
3. C32×#897C2semidirect
4. C32×#896C2semidirect
5. C32×#890C2semidirect
6. C32×#889C2semidirect
7. C32×#888C2semidirect
11. C32×#879C2semidirect
12. C32×#878C2semidirect
13. C32×#878C2semidirect
14. C32×#876C2semidirect
15. C32×#869C2semidirect
17. C3×#5712C3direct (N × H)
59. C32×#126D3semidirect
60. C32×#126C2×C3semidirect
70. C3×#898C2×C3semidirect
71. C3×#897C2×C3semidirect
72. C3×#896C2×C3semidirect
73. C3×#890C2×C3semidirect
74. C3×#889C2×C3semidirect
75. C3×#888C2×C3semidirect
79. C3×#879C2×C3semidirect
80. C3×#878C2×C3semidirect
81. C3×#878C2×C3semidirect
82. C3×#876C2×C3semidirect
83. C3×#869C2×C3semidirect
106. #5712C32direct (N × H)
210. C3×#126C3×D3semidirect
211. C3×#126C2×C32semidirect
221. #898C2×C32semidirect
222. #897C2×C32semidirect
223. #896C2×C32semidirect
224. #890C2×C32semidirect
225. #889C2×C32semidirect
226. #888C2×C32semidirect
230. #879C2×C32semidirect
231. #878C2×C32semidirect
232. #878C2×C32semidirect
233. #876C2×C32semidirect
234. #869C2×C32semidirect
422. #126C32×D3semidirect
432. C33#563semidirect
582. C32#5712direct (N × H)
583. C32C3×#563semidirect
640. C3C3×#5712direct (N × H)
641. C3C32×#563semidirect

Maximal subgroups

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

subgroupindex
C33×#1262
C32×#8982
C32×#8972
C32×#8962
C32×#8902
C32×#8892
C32×#8882
C32×#8862
C32×#8852
C32×#8832
C32×#8792
C32×#8782
C32×#8762
C32×#8692
C32×#5633
C3×#57123