Finite Group Databasebeta

← C32×#5661 #13179041

Subgroups — C32×#5661 #13179041

Order 1728.

1740 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#123C211yesmaximal, characteristic, complemented
2C32×#939C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic, complemented
4C32×C4×#67C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6C32×#898C211yesmaximal, characteristic, complemented
7C32×#893C211yesmaximal, characteristic, complemented
8C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
9C32×#889C211yesmaximal, characteristic, complemented
10C32×#884C211yesmaximal, characteristic, complemented
11C32×#884C211yesmaximal, characteristic, complemented
12C32×#883C211yesmaximal, characteristic, complemented
13C32×#67⋊C4C211yesmaximal, characteristic, complemented
14C32×#879C211yesmaximal, characteristic, complemented
15C32×#877C211yesmaximal, characteristic, complemented
16C32×#553—31nomaximal
17C3×#5661C314yesmaximal, direct product factor
18C2×C33×D4C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×C32×D12C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic
27C2×C32×C4×D3C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic
30C33×C4⋊C4C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic
33C33×C22⋊C4C2211yescharacteristic
34C33×C22⋊C4C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
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×C4×Dic3C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#126—31no—
54C32×#126—31no—
55C32×#125—31no—
56C32×#123—24no—
57C32×#123—31no—
58C32×#123D311yescharacteristic, complemented
59C32×#123C2×C314yescomplemented
60C32×#121—31no—
61C32×#121—31no—
62C32×#121—31no—
63C32×#121—31no—
64C32×C4×D4—31no—
65C32×C4×D4—31no—
66C32×C4×D4—31no—
67C32×C4×D4—31no—
68C32×#117—31no—
69C2×C32×C4⋊C4—31no—
70C3×#939C2×C314yescomplemented
71C3×#938C2×C314yescomplemented
72C3×C4×#67C2×C314yescomplemented
73C3×C4×#67C2×C314yescomplemented
74C3×#898C2×C314yescomplemented
75C3×#893C2×C314yescomplemented
76C3×D3×C4⋊C4C2×C314yescomplemented
77C3×#889C2×C314yescomplemented
78C3×#884C2×C314yescomplemented
79C3×#884C2×C314yescomplemented
80C3×#883C2×C314yescomplemented
81C3×#67⋊C4C2×C314yescomplemented
82C3×#879C2×C314yescomplemented
83C3×#877C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C33×D4—41no—
89C2×C33×C4—41no—
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C32×#67—22no—
96C32×#67—22no—
97C32×#67—22no—
98C32×#67—41no—
99C2×C32×Dic3—22no—
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×D12—22no—
107C32×C4×D3—22no—
108C32×C4×D3—41no—
109C32×C4×D3—41no—
110C32×C4×D3—41no—
111C3×#553—34no—
112#5661C3211yescharacteristic, direct product factor
113C2×C32×D4—24no—
114C2×C32×D4—31no—
115C2×C32×D4—31no—
116C2×C32×D4—31no—
117C2×C32×D4—31no—
118C2×C32×D4—31no—
119C2×C32×D4C2×D311yescharacteristic
120C2×C32×D4C22×C314yes—
121C22×C32×C4—24no—
122C22×C32×C4—31no—
123C22×C32×C4—31no—
124C22×C32×C4—31no—
125C22×C32×C4—31no—
126C22×C32×C4—31no—
127C22×C32×C4C2×D311yescharacteristic
128C22×C32×C4C22×C314yes—
129C2×C3×#67C22×C314yes—
130C2×C3×#67C22×C314yes—
131C2×C3×#67C22×C314yes—
132C2×C3×#67C22×C314yes—
133C22×C3×Dic3C22×C314yes—
134C2×C3×D12C22×C314yes—
135C2×C3×C4×D3C22×C314yes—
136C2×C3×C4×D3C22×C314yes—
137C2×C3×C4×D3C22×C314yes—
138C2×C3×C4×D3C22×C314yes—
139C32×C4⋊C4—24no—
140C32×C4⋊C4—24no—
141C32×C4⋊C4—31no—
142C32×C4⋊C4—31no—
143C32×C4⋊C4—31no—
144C32×C4⋊C4—31no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4C2×D311yescharacteristic
150C32×C4⋊C4C2×D311yescharacteristic
151C32×C4⋊C4C22×C314yes—
152C32×C4⋊C4C22×C314yes—
153C32×C22⋊C4—24no—
154C32×C22⋊C4—24no—
155C32×C22⋊C4—24no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4C2×D311yescharacteristic
164C32×C22⋊C4C2×D311yescharacteristic
165C32×C22⋊C4C2×D311yescharacteristic
166C32×C22⋊C4C22×C314yes—
167C32×C22⋊C4C22×C314yes—
168C32×C22⋊C4C22×C314yes—
169C32×C42—31no—
170C32×C42—31no—
171C32×C42—31no—
172C3×#217C22×C314yes—
173C3×#217C22×C314yes—
174C3×#217C22×C314yes—
175C3×(C2×D3)⋊C4C22×C314yes—
176C3×(C2×D3)⋊C4C22×C314yes—
177C3×(C2×D3)⋊C4C22×C314yes—
178C3×(C2×D3)⋊C4C22×C314yes—
179C3×C4⋊Dic3C22×C314yes—
180C3×C4⋊Dic3C22×C314yes—
181C3×Dic3⋊C4C22×C314yes—
182C3×Dic3⋊C4C22×C314yes—
183C3×Dic3⋊C4C22×C314yes—
184C3×Dic3⋊C4C22×C314yes—
185C3×Dic3⋊C4C22×C314yes—
186C3×Dic3⋊C4C22×C314yes—
187C3×C4×Dic3C22×C314yes—
188C3×C4×Dic3C22×C314yes—
189C3×C4×Dic3C22×C314yes—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C2411yescharacteristic
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3#4112yes—
203C33×C4—21no—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C33×C4—21no—
208C32×Dic3—21no—
209C32×Dic3—21no—
210C32×Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3#4112yes—
214C3×#126—34no—
215C3×#126—34no—
216C3×#125—34no—
217C3×#123—24no—
218C3×#123—34no—
219C3×#123C3×D314yescomplemented
220C3×#123C2×C3211yescharacteristic, complemented
221C3×#121—34no—
222C3×#121—34no—
223C3×#121—34no—
224C3×#121—34no—
225C3×C4×D4—34no—
226C3×C4×D4—34no—
227C3×C4×D4—34no—
228C3×C4×D4—34no—
229C3×#117—34no—
230C2×C3×C4⋊C4—34no—
231#939C2×C3211yescharacteristic, complemented
232#938C2×C3211yescharacteristic, complemented
233C4×#67C2×C3211yescharacteristic, complemented
234C4×#67C2×C3211yescharacteristic, complemented
235#898C2×C3211yescharacteristic, complemented
236#893C2×C3211yescharacteristic, complemented
237D3×C4⋊C4C2×C3211yescharacteristic, complemented
238#889C2×C3211yescharacteristic, complemented
239#884C2×C3211yescharacteristic, complemented
240#884C2×C3211yescharacteristic, complemented
241#883C2×C3211yescharacteristic, complemented
242#67⋊C4C2×C3211yescharacteristic, complemented
243#879C2×C3211yescharacteristic, complemented
244#877C2×C3211yescharacteristic, complemented
245C23×C32—24no—
246C23×C32—24no—
247C23×C32—31no—
248C23×C32—31no—
249C23×C32C22×D311yescharacteristic
250C23×C32C22×D311yescharacteristic
251C23×C32C23×C314yes—
252C23×C32C23×C314yes—
253C22×C3×D3C23×C314yes—
254C22×C3×D3C23×C314yes—
255C32×D4—41no—
256C32×D4—44no—
257C32×D4—48no—
258C32×D4—62no—
259C32×D4—62no—
260C32×D4—62no—
261C32×D4—62no—
262C32×D4—121no—
263C2×C32×C4—24no—
264C2×C32×C4—24no—
265C2×C32×C4—24no—
266C2×C32×C4—24no—
267C2×C32×C4—24no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—31no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—41no—
275C2×C32×C4—44no—
276C2×C32×C4—48no—
277C2×C32×C4—62no—
278C2×C32×C4—62no—
279C2×C32×C4—121no—
280C2×C32×C4—121no—
281C2×C32×C4—121no—
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C23×C314yes—
288C2×C32×C4C23×C314yes—
289C2×C32×C4C23×C314yes—
290C2×C32×C4C23×C314yes—
291C2×C32×C4C23×C314yes—
292C3×#67—28no—
293C3×#67—28no—
294C3×#67—28no—
295C3×#67—44no—
296C2×C3×Dic3—28no—
297C2×C3×Dic3C23×C314yes—
298C2×C3×Dic3C23×C314yes—
299C2×C3×Dic3C23×C314yes—
300C2×C3×Dic3C23×C314yes—
301C2×C3×Dic3C23×C314yes—
302C2×C3×Dic3C23×C314yes—
303C3×D12—28no—
304C3×C4×D3—28no—
305C3×C4×D3—44no—
306C3×C4×D3—44no—
307C3×C4×D3—44no—
308#553—31noSylow
309C2×C33—41no—
310C2×C33—41no—
311C2×C33C2×#4111yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C2×C33H(5,𝔽2)11yescharacteristic
314C32×D3—22no—
315C32×D3—41no—
316C2×C3×D4—24no—
317C2×C3×D4—34no—
318C2×C3×D4—34no—
319C2×C3×D4—34no—
320C2×C3×D4—34no—
321C2×C3×D4—34no—
322C2×C3×D4C2×C3×D314yes—
323C2×C3×D4C22×C3211yescharacteristic
324C22×C3×C4—24no—
325C22×C3×C4—34no—
326C22×C3×C4—34no—
327C22×C3×C4—34no—
328C22×C3×C4—34no—
329C22×C3×C4—34no—
330C22×C3×C4C2×C3×D314yes—
331C22×C3×C4C22×C3211yescharacteristic
332C2×#67C22×C3211yescharacteristic
333C2×#67C22×C3211yescharacteristic
334C2×#67C22×C3211yescharacteristic
335C2×#67C22×C3211yescharacteristic
336C22×Dic3C22×C3211yescharacteristic
337C2×D12C22×C3211yescharacteristic
338C2×C4×D3C22×C3211yescharacteristic
339C2×C4×D3C22×C3211yescharacteristic
340C2×C4×D3C22×C3211yescharacteristic
341C2×C4×D3C22×C3211yescharacteristic
342C3×C4⋊C4—24no—
343C3×C4⋊C4—24no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—34no—
347C3×C4⋊C4—34no—
348C3×C4⋊C4—34no—
349C3×C4⋊C4—34no—
350C3×C4⋊C4—34no—
351C3×C4⋊C4—34no—
352C3×C4⋊C4C2×C3×D314yes—
353C3×C4⋊C4C2×C3×D314yes—
354C3×C4⋊C4C22×C3211yescharacteristic
355C3×C4⋊C4C22×C3211yescharacteristic
356C3×C22⋊C4—24no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—24no—
359C3×C22⋊C4—34no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4C2×C3×D314yes—
367C3×C22⋊C4C2×C3×D314yes—
368C3×C22⋊C4C2×C3×D314yes—
369C3×C22⋊C4C22×C3211yescharacteristic
370C3×C22⋊C4C22×C3211yescharacteristic
371C3×C22⋊C4C22×C3211yescharacteristic
372C3×C42—34no—
373C3×C42—34no—
374C3×C42—34no—
375#217C22×C3211yescharacteristic
376#217C22×C3211yescharacteristic
377#217C22×C3211yescharacteristic
378(C2×D3)⋊C4C22×C3211yescharacteristic
379(C2×D3)⋊C4C22×C3211yescharacteristic
380(C2×D3)⋊C4C22×C3211yescharacteristic
381(C2×D3)⋊C4C22×C3211yescharacteristic
382C4⋊Dic3C22×C3211yescharacteristic
383C4⋊Dic3C22×C3211yescharacteristic
384Dic3⋊C4C22×C3211yescharacteristic
385Dic3⋊C4C22×C3211yescharacteristic
386Dic3⋊C4C22×C3211yescharacteristic
387Dic3⋊C4C22×C3211yescharacteristic
388Dic3⋊C4C22×C3211yescharacteristic
389Dic3⋊C4C22×C3211yescharacteristic
390C4×Dic3C22×C3211yescharacteristic
391C4×Dic3C22×C3211yescharacteristic
392C4×Dic3C22×C3211yescharacteristic
393C22×C32—28no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—24no—
401C22×C32—24no—
402C22×C32—24no—
403C22×C32—24no—
404C22×C32—24no—
405C22×C32—24no—
406C22×C32—24no—
407C22×C32—32no—
408C22×C32—44no—
409C22×C32—44no—
410C22×C32—44no—
411C22×C32—44no—
412C22×C32—44no—
413C22×C32—61no—
414C22×C32—61no—
415C22×C32—61no—
416C22×C32—61no—
417C22×C32—61no—
418C22×C32C23×D311yescharacteristic
419C22×C32C24×C314yes—
420C2×C3×D3—24no—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3C3×#4118yes—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—24no—
432C32×C4—24no—
433C32×C4—24no—
434C32×C4—24no—
435C32×C4—24no—
436C32×C4—32no—
437C32×C4—44no—
438C32×C4—44no—
439C32×C4—44no—
440C32×C4—44no—
441C32×C4—44no—
442C32×C4—61no—
443C32×C4—61no—
444C32×C4—61no—
445C32×C4—61no—
446C32×C4—61no—
447C3×Dic3—24no—
448C3×Dic3—24no—
449C3×Dic3—24no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3C3×#4118yes—
453#126—31no—
454#126—31no—
455#125—31no—
456#123—31no—
457#123C32×D311yescharacteristic, complemented
458#121—31no—
459#121—31no—
460#121—31no—
461#121—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—31no—
465C4×D4—31no—
466#117—31no—
467C2×C4⋊C4—31no—
468C33#55311yescharacteristic, complemented, Sylow
469C23×C3—24no—
470C23×C3—24no—
471C23×C3—34no—
472C23×C3—34no—
473C23×C3C22×C3×D314yes—
474C23×C3C22×C3×D314yes—
475C23×C3C23×C3211yescharacteristic
476C23×C3C23×C3211yescharacteristic
477C22×D3C23×C3211yescharacteristic
478C22×D3C23×C3211yescharacteristic
479C3×D4—44no—
480C3×D4—41no—
481C3×D4—48no—
482C3×D4—68no—
483C3×D4—68no—
484C3×D4—68no—
485C3×D4—68no—
486C3×D4—124no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—34no—
493C2×C3×C4—34no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—34no—
497C2×C3×C4—34no—
498C2×C3×C4—44no—
499C2×C3×C4—41no—
500C2×C3×C4—48no—
501C2×C3×C4—68no—
502C2×C3×C4—68no—
503C2×C3×C4—124no—
504C2×C3×C4—124no—
505C2×C3×C4—124no—
506C2×C3×C4C22×C3×D314yes—
507C2×C3×C4C22×C3×D314yes—
508C2×C3×C4C22×C3×D314yes—
509C2×C3×C4C22×C3×D314yes—
510C2×C3×C4C22×C3×D314yes—
511C2×C3×C4C23×C3211yescharacteristic
512C2×C3×C4C23×C3211yescharacteristic
513C2×C3×C4C23×C3211yescharacteristic
514C2×C3×C4C23×C3211yescharacteristic
515C2×C3×C4C23×C3211yescharacteristic
516#67—22no—
517#67—22no—
518#67—22no—
519#67—41no—
520C2×Dic3—22no—
521C2×Dic3C23×C3211yescharacteristic
522C2×Dic3C23×C3211yescharacteristic
523C2×Dic3C23×C3211yescharacteristic
524C2×Dic3C23×C3211yescharacteristic
525C2×Dic3C23×C3211yescharacteristic
526C2×Dic3C23×C3211yescharacteristic
527D12—22no—
528C4×D3—22no—
529C4×D3—41no—
530C4×D3—41no—
531C4×D3—41no—
532C2×C32—24no—
533C2×C32—24no—
534C2×C32—24no—
535C2×C32—48no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—44no—
539C2×C32—44no—
540C2×C32—62no—
541C2×C32—84no—
542C2×C32—121no—
543C2×C32#100411yescharacteristic
544C2×C32D3×#4111yescharacteristic
545C2×C32D3×#4111yescharacteristic
546C2×C32C2×C3×#4114yes—
547C2×C32C2×C3×#4114yes—
548C2×C32C3×H(5,𝔽2)14yes—
549C3×D3—28no—
550C3×D3—44no—
551C2×D4—31no—
552C2×D4—31no—
553C2×D4—31no—
554C2×D4—31no—
555C2×D4—31no—
556C2×D4C2×C32×D311yescharacteristic
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4C2×C32×D311yescharacteristic
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4C2×C32×D311yescharacteristic
572C4⋊C4C2×C32×D311yescharacteristic
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—31no—
579C22⋊C4—31no—
580C22⋊C4C2×C32×D311yescharacteristic
581C22⋊C4C2×C32×D311yescharacteristic
582C22⋊C4C2×C32×D311yescharacteristic
583C42—31no—
584C42—31no—
585C42—31no—
586C22×C3—28no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—24no—
600C22×C3—38no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—44no—
606C22×C3—64no—
607C22×C3—64no—
608C22×C3—64no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3C23×C3×D314yes—
612C22×C3C24×C3211yescharacteristic
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—21no—
617C2×D3—21no—
618C2×D3C32×#4112yes—
619C3×C4—24no—
620C3×C4—24no—
621C3×C4—24no—
622C3×C4—24no—
623C3×C4—24no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—38no—
630C3×C4—44no—
631C3×C4—44no—
632C3×C4—44no—
633C3×C4—44no—
634C3×C4—44no—
635C3×C4—64no—
636C3×C4—64no—
637C3×C4—64no—
638C3×C4—64no—
639C3×C4—64no—
640Dic3—21no—
641Dic3—21no—
642Dic3—21no—
643Dic3—21no—
644Dic3—21no—
645Dic3C32×#4112yes—
646C32—24no—
647C32#566111yescharacteristic, direct product factor
648C32C3×#55314yescomplemented
649C23—31no—
650C23—31no—
651C23C22×C32×D311yescharacteristic
652C23C22×C32×D311yescharacteristic
653D4—41no—
654D4—62no—
655D4—62no—
656D4—62no—
657D4—62no—
658D4—121no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—41no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4C22×C32×D311yescharacteristic
672C2×C4C22×C32×D311yescharacteristic
673C2×C4C22×C32×D311yescharacteristic
674C2×C4C22×C32×D311yescharacteristic
675C2×C4C22×C32×D311yescharacteristic
676C2×C3—24no—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—48no—
680C2×C3—41no—
681C2×C3—41no—
682C2×C3—44no—
683C2×C3—44no—
684C2×C3—68no—
685C2×C3—84no—
686C2×C3—124no—
687C2×C3C3×#100414yes—
688C2×C3C3×D3×#4114yes—
689C2×C3C3×D3×#4114yes—
690C2×C3C2×C32×#4111yescharacteristic
691C2×C3C2×C32×#4111yescharacteristic
692C2×C3C32×H(5,𝔽2)11yescharacteristic
693D3—22no—
694D3—41no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—32no—
702C22—61no—
703C22—61no—
704C22—61no—
705C22—61no—
706C22—61no—
707C22C23×C32×D311yescharacteristic
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—21no—
713C4—32no—
714C4—61no—
715C4—61no—
716C4—61no—
717C4—61no—
718C4—61no—
719C3—24no—
720C3C3×#566114yesdirect product factor
721C3C32×#55311yescharacteristic, complemented
722C2—41no—
723C2—41no—
724C2—62no—
725C2—121no—
726C2C32×#100411yescharacteristic
727C2C32×D3×#4111yescharacteristic
728C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#123C2
socleC22×C33C24
hypercenterC32×#123D3
hypocenterC3C32×#553
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×#939C2semidirect
3. C32×#938C2semidirect
4. C32×C4×#67C2semidirect
5. C32×C4×#67C2semidirect
6. C32×#898C2semidirect
7. C32×#893C2semidirect
8. C32×D3×C4⋊C4C2semidirect
9. C32×#889C2semidirect
10. C32×#884C2semidirect
11. C32×#884C2semidirect
12. C32×#883C2semidirect
13. C32×#67⋊C4C2semidirect
14. C32×#879C2semidirect
15. C32×#877C2semidirect
17. C3×#5661C3direct (N × H)
58. C32×#123D3semidirect
59. C32×#123C2×C3semidirect
70. C3×#939C2×C3semidirect
71. C3×#938C2×C3semidirect
72. C3×C4×#67C2×C3semidirect
73. C3×C4×#67C2×C3semidirect
74. C3×#898C2×C3semidirect
75. C3×#893C2×C3semidirect
76. C3×D3×C4⋊C4C2×C3semidirect
77. C3×#889C2×C3semidirect
78. C3×#884C2×C3semidirect
79. C3×#884C2×C3semidirect
80. C3×#883C2×C3semidirect
81. C3×#67⋊C4C2×C3semidirect
82. C3×#879C2×C3semidirect
83. C3×#877C2×C3semidirect
112. #5661C32direct (N × H)
219. C3×#123C3×D3semidirect
220. C3×#123C2×C32semidirect
231. #939C2×C32semidirect
232. #938C2×C32semidirect
233. C4×#67C2×C32semidirect
234. C4×#67C2×C32semidirect
235. #898C2×C32semidirect
236. #893C2×C32semidirect
237. D3×C4⋊C4C2×C32semidirect
238. #889C2×C32semidirect
239. #884C2×C32semidirect
240. #884C2×C32semidirect
241. #883C2×C32semidirect
242. #67⋊C4C2×C32semidirect
243. #879C2×C32semidirect
244. #877C2×C32semidirect
457. #123C32×D3semidirect
468. C33#553semidirect
647. C32#5661direct (N × H)
648. C32C3×#553semidirect
720. C3C3×#5661direct (N × H)
721. C3C32×#553semidirect

Maximal subgroups

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

subgroupindex
C33×#1232
C32×#9392
C32×#9382
C32×C4×#672
C32×#8982
C32×#8932
C32×D3×C4⋊C42
C32×#8892
C32×#8842
C32×#8832
C32×#67⋊C42
C32×#8792
C32×#8772
C32×#5533
C3×#56613