Finite Group Databasebeta

← C32×#5702 #13179079

Subgroups — C32×#5702 #13179079

Order 1728.

1512 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×#898C211yesmaximal, characteristic, complemented
4C32×#896C211yesmaximal, characteristic, complemented
5C32×#888C211yesmaximal, characteristic, complemented
6C32×#887C211yesmaximal, characteristic, complemented
7C32×#887C211yesmaximal, characteristic, complemented
8C32×#885C211yesmaximal, characteristic
9C32×#885C211yesmaximal, characteristic
10C32×#67⋊C4C211yesmaximal, characteristic
11C32×#879C211yesmaximal, characteristic, complemented
12C32×#878C211yesmaximal, characteristic, complemented
13C32×#877C211yesmaximal, characteristic, complemented
14C32×#872C211yesmaximal, characteristic, complemented
15C32×C4×Dic6C211yesmaximal, characteristic, complemented
16C32×#556—31nomaximal
17C3×#5702C314yesmaximal, 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×Dic3⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×C4×Dic3C2211yescharacteristic
48C32×C4×Dic3C2211yescharacteristic
49C32×C4×Dic3C2211yescharacteristic
50C32×C4×Dic3C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×C4⋊Q8—31no—
54C32×#126—24no—
55C32×#126—31no—
56C32×#126—31no—
57C32×#126—31no—
58C32×#126D311yescharacteristic, complemented
59C32×#126C2×C314yescomplemented
60C32×#124—31no—
61C32×#124—31no—
62C32×C22⋊Q8—31no—
63C32×C22⋊Q8—31no—
64C32×C4×Q8—31no—
65C32×C4×Q8—31no—
66C32×C4×Q8—31no—
67C32×C4×D4—31no—
68C32×#117—31no—
69C32×#117—31no—
70C3×#898C2×C314yescomplemented
71C3×#898C2×C314yescomplemented
72C3×#896C2×C314yescomplemented
73C3×#888C2×C314yescomplemented
74C3×#887C2×C314yescomplemented
75C3×#887C2×C314yescomplemented
76C3×#885C2×C314yes—
77C3×#885C2×C314yes—
78C3×#67⋊C4C2×C314yes—
79C3×#879C2×C314yescomplemented
80C3×#878C2×C314yescomplemented
81C3×#877C2×C314yescomplemented
82C3×#872C2×C314yescomplemented
83C3×C4×Dic6C2×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—22no—
93C2×C32×Dic3—22no—
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C32×C4×D3—22no—
102C32×Dic6—22no—
103C32×Dic6—22no—
104C32×Dic6—22no—
105C3×#556—34no—
106#5702C3211yescharacteristic, 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⋊C4C2×D311yescharacteristic
132C32×C4⋊C4C2×D311yescharacteristic
133C32×C4⋊C4C2×D311yescharacteristic
134C32×C4⋊C4C22×C314yes—
135C32×C4⋊C4C22×C314yes—
136C32×C4⋊C4C22×C314yes—
137C32×C22⋊C4—24no—
138C32×C22⋊C4—24no—
139C32×C22⋊C4—24no—
140C32×C22⋊C4—31no—
141C32×C22⋊C4—31no—
142C32×C22⋊C4—31no—
143C32×C22⋊C4—31no—
144C32×C22⋊C4—31no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4C2×D311yescharacteristic
148C32×C22⋊C4C2×D311yescharacteristic
149C32×C22⋊C4C2×D311yescharacteristic
150C32×C22⋊C4C22×C314yes—
151C32×C22⋊C4C22×C314yes—
152C32×C22⋊C4C22×C314yes—
153C32×C42—24no—
154C32×C42—31no—
155C32×C42—31no—
156C32×C42—31no—
157C32×C42—31no—
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×Dic3⋊C4C22×C314yes—
172C3×Dic3⋊C4C22×C314yes—
173C3×Dic3⋊C4C22×C314yes—
174C3×Dic3⋊C4C22×C314yes—
175C3×Dic3⋊C4C22×C314yes—
176C3×Dic3⋊C4C22×C314yes—
177C3×Dic3⋊C4C22×C314yes—
178C3×C4×Dic3C22×C314yes—
179C3×C4×Dic3C22×C314yes—
180C3×C4×Dic3C22×C314yes—
181C3×C4×Dic3C22×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#4112yes—
203C32×Dic3#4112yes—
204C3×C4⋊Q8—34no—
205C3×#126—24no—
206C3×#126—34no—
207C3×#126—34no—
208C3×#126—34no—
209C3×#126C3×D314yescomplemented
210C3×#126C2×C3211yescharacteristic, complemented
211C3×#124—34no—
212C3×#124—34no—
213C3×C22⋊Q8—34no—
214C3×C22⋊Q8—34no—
215C3×C4×Q8—34no—
216C3×C4×Q8—34no—
217C3×C4×Q8—34no—
218C3×C4×D4—34no—
219C3×#117—34no—
220C3×#117—34no—
221#898C2×C3211yescharacteristic, complemented
222#898C2×C3211yescharacteristic, complemented
223#896C2×C3211yescharacteristic, complemented
224#888C2×C3211yescharacteristic, complemented
225#887C2×C3211yescharacteristic, complemented
226#887C2×C3211yescharacteristic, complemented
227#885C2×C3211yescharacteristic
228#885C2×C3211yescharacteristic
229#67⋊C4C2×C3211yescharacteristic
230#879C2×C3211yescharacteristic, complemented
231#878C2×C3211yescharacteristic, complemented
232#877C2×C3211yescharacteristic, complemented
233#872C2×C3211yescharacteristic, complemented
234C4×Dic6C2×C3211yescharacteristic, complemented
235C23×C32—24no—
236C23×C32—31no—
237C23×C32C22×D311yescharacteristic
238C23×C32C23×C314yes—
239C22×C3×D3C23×C314yes—
240C32×Q8—62no—
241C32×Q8—62no—
242C32×Q8—62no—
243C32×D4—62no—
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—62no—
258C2×C32×C4—62no—
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—28no—
272C2×C3×Dic3—28no—
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—28no—
281C3×Dic6—28no—
282C3×Dic6—28no—
283C3×Dic6—28no—
284#556—31noSylow
285C2×C33—41no—
286C2×C33C2×#4111yescharacteristic
287C2×C33C2×#4111yescharacteristic
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⋊C4C2×C3×D314yes—
315C3×C4⋊C4C2×C3×D314yes—
316C3×C4⋊C4C2×C3×D314yes—
317C3×C4⋊C4C22×C3211yescharacteristic
318C3×C4⋊C4C22×C3211yescharacteristic
319C3×C4⋊C4C22×C3211yescharacteristic
320C3×C22⋊C4—24no—
321C3×C22⋊C4—24no—
322C3×C22⋊C4—24no—
323C3×C22⋊C4—34no—
324C3×C22⋊C4—34no—
325C3×C22⋊C4—34no—
326C3×C22⋊C4—34no—
327C3×C22⋊C4—34no—
328C3×C22⋊C4—34no—
329C3×C22⋊C4—34no—
330C3×C22⋊C4C2×C3×D314yes—
331C3×C22⋊C4C2×C3×D314yes—
332C3×C22⋊C4C2×C3×D314yes—
333C3×C22⋊C4C22×C3211yescharacteristic
334C3×C22⋊C4C22×C3211yescharacteristic
335C3×C22⋊C4C22×C3211yescharacteristic
336C3×C42—24no—
337C3×C42—34no—
338C3×C42—34no—
339C3×C42—34no—
340C3×C42—34no—
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
354Dic3⋊C4C22×C3211yescharacteristic
355Dic3⋊C4C22×C3211yescharacteristic
356Dic3⋊C4C22×C3211yescharacteristic
357Dic3⋊C4C22×C3211yescharacteristic
358Dic3⋊C4C22×C3211yescharacteristic
359Dic3⋊C4C22×C3211yescharacteristic
360Dic3⋊C4C22×C3211yescharacteristic
361C4×Dic3C22×C3211yescharacteristic
362C4×Dic3C22×C3211yescharacteristic
363C4×Dic3C22×C3211yescharacteristic
364C4×Dic3C22×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—32no—
398C32×C4—32no—
399C32×C4—44no—
400C32×C4—44no—
401C32×C4—44no—
402C32×C4—44no—
403C32×C4—44no—
404C32×C4—44no—
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×Dic3C3×#4118yes—
416C3×Dic3C3×#4118yes—
417C4⋊Q8—31no—
418#126—31no—
419#126—31no—
420#126—31no—
421#126C32×D311yescharacteristic, complemented
422#124—31no—
423#124—31no—
424C22⋊Q8—31no—
425C22⋊Q8—31no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×D4—31no—
430#117—31no—
431#117—31no—
432C33#55611yescharacteristic, complemented, Sylow
433C23×C3—24no—
434C23×C3—34no—
435C23×C3C22×C3×D314yes—
436C23×C3C23×C3211yescharacteristic
437C22×D3C23×C3211yescharacteristic
438C3×Q8—68no—
439C3×Q8—68no—
440C3×Q8—68no—
441C3×D4—68no—
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—68no—
456C2×C3×C4—68no—
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—22no—
470C2×Dic3—22no—
471C2×Dic3C23×C3211yescharacteristic
472C2×Dic3C23×C3211yescharacteristic
473C2×Dic3C23×C3211yescharacteristic
474C2×Dic3C23×C3211yescharacteristic
475C2×Dic3C23×C3211yescharacteristic
476C2×Dic3C23×C3211yescharacteristic
477C2×Dic3C23×C3211yescharacteristic
478C4×D3—22no—
479Dic6—22no—
480Dic6—22no—
481Dic6—22no—
482C2×C32—24no—
483C2×C32—24no—
484C2×C32—24no—
485C2×C32—41no—
486C2×C32—44no—
487C2×C32—84no—
488C2×C32—121no—
489C2×C32D3×#4111yescharacteristic
490C2×C32D3×#4111yescharacteristic
491C2×C32#101011yescharacteristic
492C2×C32C2×C3×#4114yes—
493C2×C32C2×C3×#4114yes—
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⋊C4C2×C32×D311yescharacteristic
512C4⋊C4C2×C32×D311yescharacteristic
513C4⋊C4C2×C32×D311yescharacteristic
514C22⋊C4—31no—
515C22⋊C4—31no—
516C22⋊C4—31no—
517C22⋊C4—31no—
518C22⋊C4—31no—
519C22⋊C4—31no—
520C22⋊C4—31no—
521C22⋊C4C2×C32×D311yescharacteristic
522C22⋊C4C2×C32×D311yescharacteristic
523C22⋊C4C2×C32×D311yescharacteristic
524C42—31no—
525C42—31no—
526C42—31no—
527C42—31no—
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—38no—
562C3×C4—38no—
563C3×C4—44no—
564C3×C4—44no—
565C3×C4—44no—
566C3×C4—44no—
567C3×C4—44no—
568C3×C4—44no—
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—
579Dic3C32×#4112yes—
580Dic3C32×#4112yes—
581C32—24no—
582C32#570211yescharacteristic, direct product factor
583C32C3×#55614yescomplemented
584C23—31no—
585C23C22×C32×D311yescharacteristic
586Q8—62no—
587Q8—62no—
588Q8—62no—
589D4—62no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—62no—
598C2×C4—62no—
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×D3×#4114yes—
613C2×C3C3×D3×#4114yes—
614C2×C3C3×#101014yes—
615C2×C3C2×C32×#4111yescharacteristic
616C2×C3C2×C32×#4111yescharacteristic
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—32no—
633C4—32no—
634C4—61no—
635C4—61no—
636C4—61no—
637C4—61no—
638C4—61no—
639C3—24no—
640C3C3×#570214yesdirect product factor
641C3C32×#55611yescharacteristic, complemented
642C2—41no—
643C2—121no—
644C2C32×D3×#4111yescharacteristic
645C2C32×D3×#4111yescharacteristic
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×#556
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×#898C2semidirect
4. C32×#896C2semidirect
5. C32×#888C2semidirect
6. C32×#887C2semidirect
7. C32×#887C2semidirect
11. C32×#879C2semidirect
12. C32×#878C2semidirect
13. C32×#877C2semidirect
14. C32×#872C2semidirect
15. C32×C4×Dic6C2semidirect
17. C3×#5702C3direct (N × H)
58. C32×#126D3semidirect
59. C32×#126C2×C3semidirect
70. C3×#898C2×C3semidirect
71. C3×#898C2×C3semidirect
72. C3×#896C2×C3semidirect
73. C3×#888C2×C3semidirect
74. C3×#887C2×C3semidirect
75. C3×#887C2×C3semidirect
79. C3×#879C2×C3semidirect
80. C3×#878C2×C3semidirect
81. C3×#877C2×C3semidirect
82. C3×#872C2×C3semidirect
83. C3×C4×Dic6C2×C3semidirect
106. #5702C32direct (N × H)
209. C3×#126C3×D3semidirect
210. C3×#126C2×C32semidirect
221. #898C2×C32semidirect
222. #898C2×C32semidirect
223. #896C2×C32semidirect
224. #888C2×C32semidirect
225. #887C2×C32semidirect
226. #887C2×C32semidirect
230. #879C2×C32semidirect
231. #878C2×C32semidirect
232. #877C2×C32semidirect
233. #872C2×C32semidirect
234. C4×Dic6C2×C32semidirect
421. #126C32×D3semidirect
432. C33#556semidirect
582. C32#5702direct (N × H)
583. C32C3×#556semidirect
640. C3C3×#5702direct (N × H)
641. C3C32×#556semidirect

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×#8962
C32×#8882
C32×#8872
C32×#8852
C32×#67⋊C42
C32×#8792
C32×#8782
C32×#8772
C32×#8722
C32×C4×Dic62
C32×#5563
C3×#57023