Finite Group Databasebeta

← C32×#5693 #13179071

Subgroups — C32×#5693 #13179071

Order 1728.

1508 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#125C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic, complemented
3C32×#898C211yesmaximal, characteristic, complemented
4C32×#896C211yesmaximal, characteristic, complemented
5C32×#896C211yesmaximal, characteristic, complemented
6C32×#894C211yesmaximal, characteristic
7C32×#894C211yesmaximal, characteristic
8C32×#893C211yesmaximal, characteristic
9C32×#892C211yesmaximal, characteristic, complemented
10C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
11C32×#889C211yesmaximal, characteristic, complemented
12C32×#889C211yesmaximal, characteristic, complemented
13C32×#887C211yesmaximal, characteristic, complemented
14C32×#872C211yesmaximal, characteristic, complemented
15C32×#872C211yesmaximal, characteristic, complemented
16C32×#552—31nomaximal
17C3×#5693C314yesmaximal, direct product factor
18C2×C32×D12C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C33×C4⋊C4C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic
26C33×C4⋊C4C2211yescharacteristic
27C33×C4⋊C4C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C33×C4⋊C4C2211yescharacteristic
30C33×C42C2211yescharacteristic
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×C4⋊Dic3C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×C4×Dic3C2211yescharacteristic
50C32×C4×Dic3C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#126—31no—
54C32×#126—31no—
55C32×#125—24no—
56C32×#125—31no—
57C32×#125—31no—
58C32×#125D311yescharacteristic, complemented
59C32×#125C2×C314yescomplemented
60C32×#123—31no—
61C32×#123—31no—
62C32×C22⋊Q8—31no—
63C32×C22⋊Q8—31no—
64C32×C4×Q8—31no—
65C32×C4×D4—31no—
66C32×#117—31no—
67C32×#117—31no—
68C32×#117—31no—
69C2×C32×C4⋊C4—31no—
70C3×#898C2×C314yescomplemented
71C3×#898C2×C314yescomplemented
72C3×#896C2×C314yescomplemented
73C3×#896C2×C314yescomplemented
74C3×#894C2×C314yes—
75C3×#894C2×C314yes—
76C3×#893C2×C314yes—
77C3×#892C2×C314yescomplemented
78C3×D3×C4⋊C4C2×C314yescomplemented
79C3×#889C2×C314yescomplemented
80C3×#889C2×C314yescomplemented
81C3×#887C2×C314yescomplemented
82C3×#872C2×C314yescomplemented
83C3×#872C2×C314yescomplemented
84C22×C32×D3C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C33×C4C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C32×Dic3C2311yescharacteristic
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C32×D12—22no—
100C32×C4×D3—22no—
101C32×C4×D3—22no—
102C32×C4×D3—22no—
103C32×C4×D3—22no—
104C32×Dic6—22no—
105C3×#552—34no—
106#5693C3211yescharacteristic, direct product factor
107C2×C32×Q8—31no—
108C2×C32×D4—31no—
109C22×C32×C4—31no—
110C22×C32×C4—31no—
111C22×C32×C4—31no—
112C22×C32×C4—31no—
113C2×C3×D12C22×C314yes—
114C2×C3×C4×D3C22×C314yes—
115C2×C3×C4×D3C22×C314yes—
116C2×C3×C4×D3C22×C314yes—
117C2×C3×C4×D3C22×C314yes—
118C2×C3×Dic6C22×C314yes—
119C32×C4⋊C4—24no—
120C32×C4⋊C4—24no—
121C32×C4⋊C4—24no—
122C32×C4⋊C4—24no—
123C32×C4⋊C4—24no—
124C32×C4⋊C4—24no—
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⋊C4C2×D311yescharacteristic
139C32×C4⋊C4C2×D311yescharacteristic
140C32×C4⋊C4C2×D311yescharacteristic
141C32×C4⋊C4C22×C314yes—
142C32×C4⋊C4C22×C314yes—
143C32×C4⋊C4C22×C314yes—
144C32×C4⋊C4C22×C314yes—
145C32×C4⋊C4C22×C314yes—
146C32×C4⋊C4C22×C314yes—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151C32×C22⋊C4—31no—
152C32×C22⋊C4—31no—
153C32×C22⋊C4—31no—
154C32×C22⋊C4—31no—
155C32×C42—24no—
156C32×C42—31no—
157C32×C42—31no—
158C32×C42—31no—
159C32×C42—31no—
160C32×C42C2×D311yescharacteristic
161C32×C42C22×C314yes—
162C3×(C2×D3)⋊C4C22×C314yes—
163C3×(C2×D3)⋊C4C22×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×(C2×D3)⋊C4C22×C314yes—
170C3×C4⋊Dic3C22×C314yes—
171C3×C4⋊Dic3C22×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×Dic3⋊C4C22×C314yes—
179C3×Dic3⋊C4C22×C314yes—
180C3×C4×Dic3C22×C314yes—
181C3×C4×Dic3C22×C314yes—
182C3×C4×Dic3C22×C314yes—
183C3×C4×Dic3C22×C314yes—
184C22×C33C2411yescharacteristic
185C2×C32×D3—21no—
186C2×C32×D3—21no—
187C2×C32×D3—21no—
188C2×C32×D3—21no—
189C2×C32×D3—21no—
190C2×C32×D3#4112yes—
191C33×C4—21no—
192C33×C4—21no—
193C33×C4—21no—
194C33×C4—21no—
195C33×C4—21no—
196C33×C4—21no—
197C33×C4—21no—
198C32×Dic3—21no—
199C32×Dic3—21no—
200C32×Dic3—21no—
201C32×Dic3—21no—
202C32×Dic3—21no—
203C32×Dic3#4112yes—
204C3×#126—34no—
205C3×#126—34no—
206C3×#125—24no—
207C3×#125—34no—
208C3×#125—34no—
209C3×#125C3×D314yescomplemented
210C3×#125C2×C3211yescharacteristic, complemented
211C3×#123—34no—
212C3×#123—34no—
213C3×C22⋊Q8—34no—
214C3×C22⋊Q8—34no—
215C3×C4×Q8—34no—
216C3×C4×D4—34no—
217C3×#117—34no—
218C3×#117—34no—
219C3×#117—34no—
220C2×C3×C4⋊C4—34no—
221#898C2×C3211yescharacteristic, complemented
222#898C2×C3211yescharacteristic, complemented
223#896C2×C3211yescharacteristic, complemented
224#896C2×C3211yescharacteristic, complemented
225#894C2×C3211yescharacteristic
226#894C2×C3211yescharacteristic
227#893C2×C3211yescharacteristic
228#892C2×C3211yescharacteristic, complemented
229D3×C4⋊C4C2×C3211yescharacteristic, complemented
230#889C2×C3211yescharacteristic, complemented
231#889C2×C3211yescharacteristic, complemented
232#887C2×C3211yescharacteristic, complemented
233#872C2×C3211yescharacteristic, complemented
234#872C2×C3211yescharacteristic, complemented
235C23×C32—31no—
236C23×C32—31no—
237C22×C3×D3C23×C314yes—
238C22×C3×D3C23×C314yes—
239C32×Q8—62no—
240C32×D4—62no—
241C2×C32×C4—24no—
242C2×C32×C4—24no—
243C2×C32×C4—24no—
244C2×C32×C4—24no—
245C2×C32×C4—24no—
246C2×C32×C4—24no—
247C2×C32×C4—24no—
248C2×C32×C4—31no—
249C2×C32×C4—31no—
250C2×C32×C4—31no—
251C2×C32×C4—31no—
252C2×C32×C4—31no—
253C2×C32×C4—31no—
254C2×C32×C4—62no—
255C2×C32×C4—62no—
256C2×C32×C4—62no—
257C2×C32×C4—62no—
258C2×C32×C4C22×D311yescharacteristic
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—
271C2×C32×C4C23×C314yes—
272C2×C3×Dic3C23×C314yes—
273C2×C3×Dic3C23×C314yes—
274C2×C3×Dic3C23×C314yes—
275C2×C3×Dic3C23×C314yes—
276C2×C3×Dic3C23×C314yes—
277C2×C3×Dic3C23×C314yes—
278C3×D12—28no—
279C3×C4×D3—28no—
280C3×C4×D3—28no—
281C3×C4×D3—28no—
282C3×C4×D3—28no—
283C3×Dic6—28no—
284#552—31noSylow
285C2×C33C2×#4111yescharacteristic
286C2×C33C2×#4111yescharacteristic
287C2×C332−1+411yescharacteristic
288C32×D3—22no—
289C32×D3—41no—
290C2×C3×Q8—34no—
291C2×C3×D4—34no—
292C22×C3×C4—34no—
293C22×C3×C4—34no—
294C22×C3×C4—34no—
295C22×C3×C4—34no—
296C2×D12C22×C3211yescharacteristic
297C2×C4×D3C22×C3211yescharacteristic
298C2×C4×D3C22×C3211yescharacteristic
299C2×C4×D3C22×C3211yescharacteristic
300C2×C4×D3C22×C3211yescharacteristic
301C2×Dic6C22×C3211yescharacteristic
302C3×C4⋊C4—24no—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—24no—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—24no—
307C3×C4⋊C4—24no—
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⋊C4C2×C3×D314yes—
322C3×C4⋊C4C2×C3×D314yes—
323C3×C4⋊C4C2×C3×D314yes—
324C3×C4⋊C4C22×C3211yescharacteristic
325C3×C4⋊C4C22×C3211yescharacteristic
326C3×C4⋊C4C22×C3211yescharacteristic
327C3×C4⋊C4C22×C3211yescharacteristic
328C3×C4⋊C4C22×C3211yescharacteristic
329C3×C4⋊C4C22×C3211yescharacteristic
330C3×C22⋊C4—34no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4—34no—
335C3×C22⋊C4—34no—
336C3×C22⋊C4—34no—
337C3×C22⋊C4—34no—
338C3×C42—24no—
339C3×C42—34no—
340C3×C42—34no—
341C3×C42—34no—
342C3×C42—34no—
343C3×C42C2×C3×D314yes—
344C3×C42C22×C3211yescharacteristic
345(C2×D3)⋊C4C22×C3211yescharacteristic
346(C2×D3)⋊C4C22×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
352(C2×D3)⋊C4C22×C3211yescharacteristic
353C4⋊Dic3C22×C3211yescharacteristic
354C4⋊Dic3C22×C3211yescharacteristic
355Dic3⋊C4C22×C3211yescharacteristic
356Dic3⋊C4C22×C3211yescharacteristic
357Dic3⋊C4C22×C3211yescharacteristic
358Dic3⋊C4C22×C3211yescharacteristic
359Dic3⋊C4C22×C3211yescharacteristic
360Dic3⋊C4C22×C3211yescharacteristic
361Dic3⋊C4C22×C3211yescharacteristic
362Dic3⋊C4C22×C3211yescharacteristic
363C4×Dic3C22×C3211yescharacteristic
364C4×Dic3C22×C3211yescharacteristic
365C4×Dic3C22×C3211yescharacteristic
366C4×Dic3C22×C3211yescharacteristic
367C22×C32—24no—
368C22×C32—32no—
369C22×C32—61no—
370C22×C32—61no—
371C22×C32—61no—
372C22×C32—61no—
373C22×C32—61no—
374C22×C32C23×D311yescharacteristic
375C22×C32C24×C314yes—
376C2×C3×D3—24no—
377C2×C3×D3—24no—
378C2×C3×D3—24no—
379C2×C3×D3—24no—
380C2×C3×D3—24no—
381C2×C3×D3C3×#4118yes—
382C32×C4—28no—
383C32×C4—21no—
384C32×C4—21no—
385C32×C4—21no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—24no—
391C32×C4—24no—
392C32×C4—24no—
393C32×C4—24no—
394C32×C4—24no—
395C32×C4—24no—
396C32×C4—24no—
397C32×C4—32no—
398C32×C4—44no—
399C32×C4—44no—
400C32×C4—44no—
401C32×C4—44no—
402C32×C4—44no—
403C32×C4—44no—
404C32×C4—61no—
405C32×C4—61no—
406C32×C4—61no—
407C32×C4—61no—
408C32×C4—61no—
409C3×Dic3—24no—
410C3×Dic3—24no—
411C3×Dic3—24no—
412C3×Dic3—24no—
413C3×Dic3—24no—
414C3×Dic3C3×#4118yes—
415#126—31no—
416#126—31no—
417#125—31no—
418#125—31no—
419#125C32×D311yescharacteristic, complemented
420#123—31no—
421#123—31no—
422C22⋊Q8—31no—
423C22⋊Q8—31no—
424C4×Q8—31no—
425C4×D4—31no—
426#117—31no—
427#117—31no—
428#117—31no—
429C2×C4⋊C4—31no—
430C33#55211yescharacteristic, complemented, Sylow
431C23×C3—34no—
432C23×C3—34no—
433C22×D3C23×C3211yescharacteristic
434C22×D3C23×C3211yescharacteristic
435C3×Q8—68no—
436C3×D4—68no—
437C2×C3×C4—24no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—34no—
445C2×C3×C4—34no—
446C2×C3×C4—34no—
447C2×C3×C4—34no—
448C2×C3×C4—34no—
449C2×C3×C4—34no—
450C2×C3×C4—68no—
451C2×C3×C4—68no—
452C2×C3×C4—68no—
453C2×C3×C4—68no—
454C2×C3×C4C22×C3×D314yes—
455C2×C3×C4C22×C3×D314yes—
456C2×C3×C4C22×C3×D314yes—
457C2×C3×C4C22×C3×D314yes—
458C2×C3×C4C22×C3×D314yes—
459C2×C3×C4C22×C3×D314yes—
460C2×C3×C4C22×C3×D314yes—
461C2×C3×C4C23×C3211yescharacteristic
462C2×C3×C4C23×C3211yescharacteristic
463C2×C3×C4C23×C3211yescharacteristic
464C2×C3×C4C23×C3211yescharacteristic
465C2×C3×C4C23×C3211yescharacteristic
466C2×C3×C4C23×C3211yescharacteristic
467C2×C3×C4C23×C3211yescharacteristic
468C2×Dic3C23×C3211yescharacteristic
469C2×Dic3C23×C3211yescharacteristic
470C2×Dic3C23×C3211yescharacteristic
471C2×Dic3C23×C3211yescharacteristic
472C2×Dic3C23×C3211yescharacteristic
473C2×Dic3C23×C3211yescharacteristic
474D12—22no—
475C4×D3—22no—
476C4×D3—22no—
477C4×D3—22no—
478C4×D3—22no—
479Dic6—22no—
480C2×C32—24no—
481C2×C32—24no—
482C2×C32—24no—
483C2×C32—62no—
484C2×C32—121no—
485C2×C32#100711yescharacteristic
486C2×C32D3×#4111yescharacteristic
487C2×C32D3×#4111yescharacteristic
488C2×C32C2×C3×#4114yes—
489C2×C32C2×C3×#4114yes—
490C2×C32C3×2−1+414yes—
491C3×D3—28no—
492C3×D3—44no—
493C2×Q8—31no—
494C2×D4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—31no—
499C4⋊C4—31no—
500C4⋊C4—31no—
501C4⋊C4—31no—
502C4⋊C4—31no—
503C4⋊C4—31no—
504C4⋊C4—31no—
505C4⋊C4—31no—
506C4⋊C4—31no—
507C4⋊C4—31no—
508C4⋊C4—31no—
509C4⋊C4C2×C32×D311yescharacteristic
510C4⋊C4C2×C32×D311yescharacteristic
511C4⋊C4C2×C32×D311yescharacteristic
512C4⋊C4C2×C32×D311yescharacteristic
513C4⋊C4C2×C32×D311yescharacteristic
514C4⋊C4C2×C32×D311yescharacteristic
515C22⋊C4—31no—
516C22⋊C4—31no—
517C22⋊C4—31no—
518C22⋊C4—31no—
519C22⋊C4—31no—
520C22⋊C4—31no—
521C22⋊C4—31no—
522C22⋊C4—31no—
523C42—31no—
524C42—31no—
525C42—31no—
526C42—31no—
527C42C2×C32×D311yescharacteristic
528C22×C3—24no—
529C22×C3—38no—
530C22×C3—64no—
531C22×C3—64no—
532C22×C3—64no—
533C22×C3—64no—
534C22×C3—64no—
535C22×C3C23×C3×D314yes—
536C22×C3C24×C3211yescharacteristic
537C2×D3—21no—
538C2×D3—21no—
539C2×D3—21no—
540C2×D3—21no—
541C2×D3—21no—
542C2×D3C32×#4112yes—
543C3×C4—28no—
544C3×C4—24no—
545C3×C4—24no—
546C3×C4—24no—
547C3×C4—24no—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—24no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—38no—
559C3×C4—44no—
560C3×C4—44no—
561C3×C4—44no—
562C3×C4—44no—
563C3×C4—44no—
564C3×C4—44no—
565C3×C4—64no—
566C3×C4—64no—
567C3×C4—64no—
568C3×C4—64no—
569C3×C4—64no—
570Dic3—21no—
571Dic3—21no—
572Dic3—21no—
573Dic3—21no—
574Dic3—21no—
575Dic3C32×#4112yes—
576C32—24no—
577C32#569311yescharacteristic, direct product factor
578C32C3×#55214yescomplemented
579C23—31no—
580C23—31no—
581Q8—62no—
582D4—62no—
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—31no—
588C2×C4—31no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4C22×C32×D311yescharacteristic
594C2×C4C22×C32×D311yescharacteristic
595C2×C4C22×C32×D311yescharacteristic
596C2×C4C22×C32×D311yescharacteristic
597C2×C4C22×C32×D311yescharacteristic
598C2×C4C22×C32×D311yescharacteristic
599C2×C4C22×C32×D311yescharacteristic
600C2×C3—24no—
601C2×C3—24no—
602C2×C3—24no—
603C2×C3—68no—
604C2×C3—124no—
605C2×C3C3×#100714yes—
606C2×C3C3×D3×#4114yes—
607C2×C3C3×D3×#4114yes—
608C2×C3C2×C32×#4111yescharacteristic
609C2×C3C2×C32×#4111yescharacteristic
610C2×C3C32×2−1+411yescharacteristic
611D3—22no—
612D3—41no—
613C22—32no—
614C22—61no—
615C22—61no—
616C22—61no—
617C22—61no—
618C22—61no—
619C22C23×C32×D311yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—32no—
628C4—61no—
629C4—61no—
630C4—61no—
631C4—61no—
632C4—61no—
633C3—24no—
634C3C3×#569314yesdirect product factor
635C3C32×#55211yescharacteristic, complemented
636C2—62no—
637C2—121no—
638C2C32×#100711yescharacteristic
639C2C32×D3×#4111yescharacteristic
640C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#125C2
socleC22×C33C24
prime radicalC2×C32×D12C22
hypercenterC32×#125D3
hypocenterC3C32×#552
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#125

Complements

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

NH ≅ G/Ntype
1. C33×#125C2semidirect
2. C32×#898C2semidirect
3. C32×#898C2semidirect
4. C32×#896C2semidirect
5. C32×#896C2semidirect
9. C32×#892C2semidirect
10. C32×D3×C4⋊C4C2semidirect
11. C32×#889C2semidirect
12. C32×#889C2semidirect
13. C32×#887C2semidirect
14. C32×#872C2semidirect
15. C32×#872C2semidirect
17. C3×#5693C3direct (N × H)
58. C32×#125D3semidirect
59. C32×#125C2×C3semidirect
70. C3×#898C2×C3semidirect
71. C3×#898C2×C3semidirect
72. C3×#896C2×C3semidirect
73. C3×#896C2×C3semidirect
77. C3×#892C2×C3semidirect
78. C3×D3×C4⋊C4C2×C3semidirect
79. C3×#889C2×C3semidirect
80. C3×#889C2×C3semidirect
81. C3×#887C2×C3semidirect
82. C3×#872C2×C3semidirect
83. C3×#872C2×C3semidirect
106. #5693C32direct (N × H)
209. C3×#125C3×D3semidirect
210. C3×#125C2×C32semidirect
221. #898C2×C32semidirect
222. #898C2×C32semidirect
223. #896C2×C32semidirect
224. #896C2×C32semidirect
228. #892C2×C32semidirect
229. D3×C4⋊C4C2×C32semidirect
230. #889C2×C32semidirect
231. #889C2×C32semidirect
232. #887C2×C32semidirect
233. #872C2×C32semidirect
234. #872C2×C32semidirect
419. #125C32×D3semidirect
430. C33#552semidirect
577. C32#5693direct (N × H)
578. C32C3×#552semidirect
634. C3C3×#5693direct (N × H)
635. C3C32×#552semidirect

Maximal subgroups

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

subgroupindex
C33×#1252
C32×#8982
C32×#8962
C32×#8942
C32×#8932
C32×#8922
C32×D3×C4⋊C42
C32×#8892
C32×#8872
C32×#8722
C32×#5523
C3×#56933