Finite Group Databasebeta

← C32×#5658 #13179038

Subgroups — C32×#5658 #13179038

Order 1728.

1800 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#123C211yesmaximal, characteristic, complemented
2C32×#937C211yesmaximal, characteristic
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C32×#926C211yesmaximal, characteristic, complemented
6C32×#898C211yesmaximal, characteristic, complemented
7C32×#898C211yesmaximal, characteristic, complemented
8C32×#897C211yesmaximal, characteristic, complemented
9C32×#892C211yesmaximal, characteristic, complemented
10C32×#886C211yesmaximal, characteristic, complemented
11C32×#885C211yesmaximal, characteristic, complemented
12C32×#883C211yesmaximal, characteristic, complemented
13C32×#67⋊C4C211yesmaximal, characteristic, complemented
14C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
15C32×#878C211yesmaximal, characteristic, complemented
16C32×#551—31nomaximal
17C3×#5658C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic, complemented
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic
27C2×C32×Dic6C2211yescharacteristic, complemented
28C33×C4⋊C4C2211yescharacteristic, complemented
29C33×C4⋊C4C2211yescharacteristic, complemented
30C33×C22⋊C4C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic, complemented
32C33×C22⋊C4C2211yescharacteristic, complemented
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic, complemented
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×C4⋊Dic3C2211yescharacteristic, complemented
45C32×C4⋊Dic3C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47C32×C4⋊Dic3C2211yescharacteristic, complemented
48C32×Dic3⋊C4C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50C32×C4×Dic3C2211yescharacteristic, complemented
51C32×C4×Dic3C2211yescharacteristic, complemented
52C32×C4×Dic3C2211yescharacteristic, complemented
53C32×#126—31no—
54C32×#126—31no—
55C32×#124—31no—
56C32×#123—24no—
57C32×#123—31no—
58C32×#123—31no—
59C32×#123D311yescharacteristic, complemented
60C32×#123C2×C314yescomplemented
61C32×C22⋊Q8—31no—
62C32×C22⋊Q8—31no—
63C32×#120—31no—
64C32×C4×D4—31no—
65C32×C4×D4—31no—
66C32×#117—31no—
67C32×#117—31no—
68C2×C32×C22⋊C4—31no—
69C2×C32×C22⋊C4—31no—
70C3×#937C2×C314yes—
71C3×D4×Dic3C2×C314yescomplemented
72C2×C3×(C2×D3)⋊C4C2×C314yescomplemented
73C3×#926C2×C314yescomplemented
74C3×#898C2×C314yescomplemented
75C3×#898C2×C314yescomplemented
76C3×#897C2×C314yescomplemented
77C3×#892C2×C314yescomplemented
78C3×#886C2×C314yescomplemented
79C3×#885C2×C314yescomplemented
80C3×#883C2×C314yescomplemented
81C3×#67⋊C4C2×C314yescomplemented
82C3×D3×C22⋊C4C2×C314yescomplemented
83C3×#878C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C32×D3—22no—
87C22×C32×D3—22no—
88C22×C32×D3—41no—
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C33×D4—22no—
92C2×C33×C4—22no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C32×#67—22no—
99C32×#67—41no—
100C2×C32×Dic3—41no—
101C2×C32×Dic3—41no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C32×C4×D3—22no—
109C32×C4×D3—41no—
110C32×Dic6—41no—
111C3×#551—34no—
112#5658C3211yescharacteristic, direct product factor
113C24×C32—31no—
114C23×C3×D3C22×C314yes—
115C2×C32×Q8—31no—
116C2×C32×D4—24no—
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×C4C2×D311yescharacteristic
127C22×C32×C4C22×C314yes—
128C2×C3×#67C22×C314yes—
129C2×C3×#67C22×C314yes—
130C22×C3×Dic3C22×C314yes—
131C22×C3×Dic3C22×C314yescomplemented
132C2×C3×C4×D3C22×C314yes—
133C2×C3×C4×D3C22×C314yes—
134C2×C3×Dic6C22×C314yescomplemented
135C32×C4⋊C4—24no—
136C32×C4⋊C4—24no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4—31no—
142C32×C4⋊C4—31no—
143C32×C4⋊C4C2×D311yescharacteristic, complemented
144C32×C4⋊C4C2×D311yescharacteristic, complemented
145C32×C4⋊C4C22×C314yescomplemented
146C32×C4⋊C4C22×C314yescomplemented
147C32×C22⋊C4—24no—
148C32×C22⋊C4—24no—
149C32×C22⋊C4—24no—
150C32×C22⋊C4—31no—
151C32×C22⋊C4—31no—
152C32×C22⋊C4—31no—
153C32×C22⋊C4—31no—
154C32×C22⋊C4—31no—
155C32×C22⋊C4—31no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4C2×D311yescharacteristic
162C32×C22⋊C4C2×D311yescharacteristic, complemented
163C32×C22⋊C4C2×D311yescharacteristic, complemented
164C32×C22⋊C4C22×C314yes—
165C32×C22⋊C4C22×C314yescomplemented
166C32×C22⋊C4C22×C314yescomplemented
167C32×C42—31no—
168C32×C42—31no—
169C32×C42—31no—
170C3×#217C22×C314yes—
171C3×#217C22×C314yes—
172C3×#217C22×C314yescomplemented
173C3×(C2×D3)⋊C4C22×C314yes—
174C3×(C2×D3)⋊C4C22×C314yes—
175C3×(C2×D3)⋊C4C22×C314yes—
176C3×(C2×D3)⋊C4C22×C314yes—
177C3×(C2×D3)⋊C4C22×C314yes—
178C3×(C2×D3)⋊C4C22×C314yes—
179C3×(C2×D3)⋊C4C22×C314yes—
180C3×(C2×D3)⋊C4C22×C314yes—
181C3×C4⋊Dic3C22×C314yescomplemented
182C3×C4⋊Dic3C22×C314yescomplemented
183C3×C4⋊Dic3C22×C314yescomplemented
184C3×C4⋊Dic3C22×C314yescomplemented
185C3×Dic3⋊C4C22×C314yescomplemented
186C3×Dic3⋊C4C22×C314yescomplemented
187C3×C4×Dic3C22×C314yescomplemented
188C3×C4×Dic3C22×C314yescomplemented
189C3×C4×Dic3C22×C314yescomplemented
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33#4112yes—
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—44no—
203C2×C32×D3#4112yes—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C33×C4—21no—
208C33×C4—21no—
209C32×Dic3—21no—
210C32×Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#126—34no—
216C3×#126—34no—
217C3×#124—34no—
218C3×#123—24no—
219C3×#123—34no—
220C3×#123—34no—
221C3×#123C3×D314yescomplemented
222C3×#123C2×C3211yescharacteristic, complemented
223C3×C22⋊Q8—34no—
224C3×C22⋊Q8—34no—
225C3×#120—34no—
226C3×C4×D4—34no—
227C3×C4×D4—34no—
228C3×#117—34no—
229C3×#117—34no—
230C2×C3×C22⋊C4—34no—
231C2×C3×C22⋊C4—34no—
232#937C2×C3211yescharacteristic
233D4×Dic3C2×C3211yescharacteristic, complemented
234C2×(C2×D3)⋊C4C2×C3211yescharacteristic, complemented
235#926C2×C3211yescharacteristic, complemented
236#898C2×C3211yescharacteristic, complemented
237#898C2×C3211yescharacteristic, complemented
238#897C2×C3211yescharacteristic, complemented
239#892C2×C3211yescharacteristic, complemented
240#886C2×C3211yescharacteristic, complemented
241#885C2×C3211yescharacteristic, complemented
242#883C2×C3211yescharacteristic, complemented
243#67⋊C4C2×C3211yescharacteristic, complemented
244D3×C22⋊C4C2×C3211yescharacteristic, complemented
245#878C2×C3211yescharacteristic, complemented
246C23×C32—24no—
247C23×C32—24no—
248C23×C32—31no—
249C23×C32—31no—
250C23×C32—62no—
251C23×C32—62no—
252C23×C32—121no—
253C23×C32C22×D311yescharacteristic
254C23×C32C22×D311yescharacteristic
255C23×C32C23×C314yes—
256C23×C32C23×C314yes—
257C22×C3×D3—28no—
258C22×C3×D3—28no—
259C22×C3×D3—44no—
260C22×C3×D3C23×C314yes—
261C22×C3×D3C23×C314yes—
262C32×Q8—121no—
263C32×D4—22no—
264C32×D4—28no—
265C32×D4—48no—
266C32×D4—62no—
267C32×D4—121no—
268C2×C32×C4—22no—
269C2×C32×C4—24no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—24no—
273C2×C32×C4—24no—
274C2×C32×C4—28no—
275C2×C32×C4—31no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—48no—
282C2×C32×C4—62no—
283C2×C32×C4—121no—
284C2×C32×C4—121no—
285C2×C32×C4—121no—
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C23×C314yes—
292C2×C32×C4C23×C314yes—
293C2×C32×C4C23×C314yes—
294C2×C32×C4C23×C314yes—
295C2×C32×C4C23×C314yes—
296C3×#67—28no—
297C3×#67—44no—
298C2×C3×Dic3—44no—
299C2×C3×Dic3—44no—
300C2×C3×Dic3C23×C314yes—
301C2×C3×Dic3C23×C314yes—
302C2×C3×Dic3C23×C314yes—
303C2×C3×Dic3C23×C314yes—
304C2×C3×Dic3C23×C314yes—
305C2×C3×Dic3C23×C314yes—
306C3×C4×D3—28no—
307C3×C4×D3—44no—
308C3×Dic6—44no—
309#551—31noSylow
310C2×C33—22no—
311C2×C33—41no—
312C2×C33C2×#4111yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33H(5,𝔽2)11yescharacteristic
315C32×D3—22no—
316C32×D3—41no—
317C24×C3—34no—
318C23×D3C22×C3211yescharacteristic
319C2×C3×Q8—34no—
320C2×C3×D4—24no—
321C2×C3×D4—34no—
322C2×C3×D4—34no—
323C2×C3×D4C2×C3×D314yes—
324C2×C3×D4C22×C3211yescharacteristic
325C22×C3×C4—24no—
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
334C22×Dic3C22×C3211yescharacteristic
335C22×Dic3C22×C3211yescharacteristic, complemented
336C2×C4×D3C22×C3211yescharacteristic
337C2×C4×D3C22×C3211yescharacteristic
338C2×Dic6C22×C3211yescharacteristic, complemented
339C3×C4⋊C4—24no—
340C3×C4⋊C4—24no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—34no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—34no—
347C3×C4⋊C4C2×C3×D314yescomplemented
348C3×C4⋊C4C2×C3×D314yescomplemented
349C3×C4⋊C4C22×C3211yescharacteristic, complemented
350C3×C4⋊C4C22×C3211yescharacteristic, complemented
351C3×C22⋊C4—24no—
352C3×C22⋊C4—24no—
353C3×C22⋊C4—24no—
354C3×C22⋊C4—34no—
355C3×C22⋊C4—34no—
356C3×C22⋊C4—34no—
357C3×C22⋊C4—34no—
358C3×C22⋊C4—34no—
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⋊C4C2×C3×D314yes—
366C3×C22⋊C4C2×C3×D314yescomplemented
367C3×C22⋊C4C2×C3×D314yescomplemented
368C3×C22⋊C4C22×C3211yescharacteristic
369C3×C22⋊C4C22×C3211yescharacteristic, complemented
370C3×C22⋊C4C22×C3211yescharacteristic, complemented
371C3×C42—34no—
372C3×C42—34no—
373C3×C42—34no—
374#217C22×C3211yescharacteristic
375#217C22×C3211yescharacteristic
376#217C22×C3211yescharacteristic, complemented
377(C2×D3)⋊C4C22×C3211yescharacteristic
378(C2×D3)⋊C4C22×C3211yescharacteristic
379(C2×D3)⋊C4C22×C3211yescharacteristic
380(C2×D3)⋊C4C22×C3211yescharacteristic
381(C2×D3)⋊C4C22×C3211yescharacteristic
382(C2×D3)⋊C4C22×C3211yescharacteristic
383(C2×D3)⋊C4C22×C3211yescharacteristic
384(C2×D3)⋊C4C22×C3211yescharacteristic
385C4⋊Dic3C22×C3211yescharacteristic, complemented
386C4⋊Dic3C22×C3211yescharacteristic, complemented
387C4⋊Dic3C22×C3211yescharacteristic, complemented
388C4⋊Dic3C22×C3211yescharacteristic, complemented
389Dic3⋊C4C22×C3211yescharacteristic, complemented
390Dic3⋊C4C22×C3211yescharacteristic, complemented
391C4×Dic3C22×C3211yescharacteristic, complemented
392C4×Dic3C22×C3211yescharacteristic, complemented
393C4×Dic3C22×C3211yescharacteristic, complemented
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—24no—
400C22×C32—28no—
401C22×C32—24no—
402C22×C32—24no—
403C22×C32—24no—
404C22×C32—24no—
405C22×C32—24no—
406C22×C32—32no—
407C22×C32—44no—
408C22×C32—44no—
409C22×C32—44no—
410C22×C32—44no—
411C22×C32—44no—
412C22×C32—61no—
413C22×C32—61no—
414C22×C32—61no—
415C22×C32—61no—
416C22×C32—61no—
417C22×C32—124no—
418C22×C32#23712yes—
419C22×C32C3×#4118yes—
420C22×C32C23×D311yescharacteristic
421C22×C32C24×C314yes—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—24no—
426C2×C3×D3—24no—
427C2×C3×D3—416no—
428C2×C3×D3C3×#4118yes—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—24no—
435C32×C4—24no—
436C32×C4—24no—
437C32×C4—24no—
438C32×C4—24no—
439C32×C4—44no—
440C32×C4—44no—
441C32×C4—44no—
442C32×C4—44no—
443C32×C4—44no—
444C32×C4—61no—
445C32×C4—61no—
446C32×C4—61no—
447C32×C4—61no—
448C32×C4—61no—
449C32×C4—61no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—24no—
453C3×Dic3—24no—
454C3×Dic3—24no—
455C3×Dic3—24no—
456#126—31no—
457#126—31no—
458#124—31no—
459#123—31no—
460#123—31no—
461#123C32×D311yescharacteristic, complemented
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464#120—31no—
465C4×D4—31no—
466C4×D4—31no—
467#117—31no—
468#117—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C33#55111yescharacteristic, complemented, Sylow
472C23×C3—24no—
473C23×C3—24no—
474C23×C3—34no—
475C23×C3—34no—
476C23×C3—68no—
477C23×C3—68no—
478C23×C3—124no—
479C23×C3C22×C3×D314yes—
480C23×C3C22×C3×D314yes—
481C23×C3C23×C3211yescharacteristic
482C23×C3C23×C3211yescharacteristic
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—41no—
486C22×D3C23×C3211yescharacteristic
487C22×D3C23×C3211yescharacteristic
488C3×Q8—124no—
489C3×D4—28no—
490C3×D4—22no—
491C3×D4—48no—
492C3×D4—68no—
493C3×D4—124no—
494C2×C3×C4—28no—
495C2×C3×C4—22no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—24no—
499C2×C3×C4—24no—
500C2×C3×C4—24no—
501C2×C3×C4—34no—
502C2×C3×C4—34no—
503C2×C3×C4—34no—
504C2×C3×C4—34no—
505C2×C3×C4—34no—
506C2×C3×C4—34no—
507C2×C3×C4—48no—
508C2×C3×C4—68no—
509C2×C3×C4—124no—
510C2×C3×C4—124no—
511C2×C3×C4—124no—
512C2×C3×C4C22×C3×D314yes—
513C2×C3×C4C22×C3×D314yes—
514C2×C3×C4C22×C3×D314yes—
515C2×C3×C4C22×C3×D314yes—
516C2×C3×C4C22×C3×D314yes—
517C2×C3×C4C23×C3211yescharacteristic
518C2×C3×C4C23×C3211yescharacteristic
519C2×C3×C4C23×C3211yescharacteristic
520C2×C3×C4C23×C3211yescharacteristic
521C2×C3×C4C23×C3211yescharacteristic
522#67—22no—
523#67—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3C23×C3211yescharacteristic
527C2×Dic3C23×C3211yescharacteristic
528C2×Dic3C23×C3211yescharacteristic
529C2×Dic3C23×C3211yescharacteristic
530C2×Dic3C23×C3211yescharacteristic
531C2×Dic3C23×C3211yescharacteristic
532C4×D3—22no—
533C4×D3—41no—
534Dic6—41no—
535C2×C32—22no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—24no—
539C2×C32—28no—
540C2×C32—48no—
541C2×C32—41no—
542C2×C32—44no—
543C2×C32—62no—
544C2×C32—84no—
545C2×C32—121no—
546C2×C32C2×#23711yescharacteristic
547C2×C32D3×#4111yescharacteristic
548C2×C32#100911yescharacteristic
549C2×C32C2×C3×#4114yes—
550C2×C32C2×C3×#4114yes—
551C2×C32C3×H(5,𝔽2)14yes—
552C3×D3—28no—
553C3×D3—44no—
554C24—31no—
555C2×Q8—31no—
556C2×D4—31no—
557C2×D4—31no—
558C2×D4C2×C32×D311yescharacteristic
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4C2×C32×D311yescharacteristic
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4C2×C32×D311yescharacteristic, complemented
571C4⋊C4C2×C32×D311yescharacteristic, complemented
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—31no—
579C22⋊C4—31no—
580C22⋊C4—31no—
581C22⋊C4—31no—
582C22⋊C4—31no—
583C22⋊C4C2×C32×D311yescharacteristic
584C22⋊C4C2×C32×D311yescharacteristic, complemented
585C22⋊C4C2×C32×D311yescharacteristic, complemented
586C42—31no—
587C42—31no—
588C42—31no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—24no—
600C22×C3—28no—
601C22×C3—38no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3—64no—
608C22×C3—64no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—1216no—
613C22×C3C3×#23718yes—
614C22×C3C32×#4112yes—
615C22×C3C23×C3×D314yes—
616C22×C3C24×C3211yescharacteristic
617C2×D3—21no—
618C2×D3—21no—
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—44no—
623C2×D3C32×#4112yes—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—24no—
628C3×C4—24no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—44no—
635C3×C4—44no—
636C3×C4—44no—
637C3×C4—44no—
638C3×C4—44no—
639C3×C4—64no—
640C3×C4—64no—
641C3×C4—64no—
642C3×C4—64no—
643C3×C4—64no—
644C3×C4—64no—
645Dic3—21no—
646Dic3—21no—
647Dic3—21no—
648Dic3—21no—
649Dic3—21no—
650Dic3—21no—
651C32—24no—
652C32#565811yescharacteristic, direct product factor
653C32C3×#55114yescomplemented
654C23—31no—
655C23—31no—
656C23—62no—
657C23—62no—
658C23—121no—
659C23C22×C32×D311yescharacteristic
660C23C22×C32×D311yescharacteristic
661Q8—121no—
662D4—22no—
663D4—62no—
664D4—121no—
665C2×C4—22no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—62no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4C22×C32×D311yescharacteristic
677C2×C4C22×C32×D311yescharacteristic
678C2×C4C22×C32×D311yescharacteristic
679C2×C4C22×C32×D311yescharacteristic
680C2×C4C22×C32×D311yescharacteristic
681C2×C3—22no—
682C2×C3—28no—
683C2×C3—24no—
684C2×C3—24no—
685C2×C3—24no—
686C2×C3—48no—
687C2×C3—41no—
688C2×C3—44no—
689C2×C3—68no—
690C2×C3—84no—
691C2×C3—124no—
692C2×C3C2×C3×#23714yes—
693C2×C3C3×D3×#4114yes—
694C2×C3C3×#100914yes—
695C2×C3C2×C32×#4111yescharacteristic
696C2×C3C2×C32×#4111yescharacteristic
697C2×C3C32×H(5,𝔽2)11yescharacteristic
698D3—22no—
699D3—41no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—32no—
706C22—61no—
707C22—61no—
708C22—61no—
709C22—61no—
710C22—61no—
711C22—124no—
712C22C32×#23712yes—
713C22C23×C32×D311yescharacteristic
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—61no—
720C4—61no—
721C4—61no—
722C4—61no—
723C4—61no—
724C4—61no—
725C3—24no—
726C3C3×#565814yesdirect product factor
727C3C32×#55111yescharacteristic, complemented
728C2—22no—
729C2—41no—
730C2—62no—
731C2—121no—
732C2C2×C32×#23711yescharacteristic
733C2C32×D3×#4111yescharacteristic
734C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#123C2
socleC22×C33C24
prime radicalC32×#937C2
hypercenterC32×#123D3
hypocenterC3C32×#551
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
3. C32×D4×Dic3C2semidirect
4. C2×C32×(C2×D3)⋊C4C2semidirect
5. C32×#926C2semidirect
6. C32×#898C2semidirect
7. C32×#898C2semidirect
8. C32×#897C2semidirect
9. C32×#892C2semidirect
10. C32×#886C2semidirect
11. C32×#885C2semidirect
12. C32×#883C2semidirect
13. C32×#67⋊C4C2semidirect
14. C32×D3×C22⋊C4C2semidirect
15. C32×#878C2semidirect
17. C3×#5658C3direct (N × H)
24. C22×C32×Dic3C22semidirect
27. C2×C32×Dic6C22semidirect
28. C33×C4⋊C4C22semidirect
29. C33×C4⋊C4C22semidirect
31. C33×C22⋊C4C22semidirect
32. C33×C22⋊C4C22semidirect
35. C32×#217C22semidirect
44. C32×C4⋊Dic3C22semidirect
45. C32×C4⋊Dic3C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. C32×C4⋊Dic3C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. C32×C4×Dic3C22semidirect
51. C32×C4×Dic3C22semidirect
52. C32×C4×Dic3C22semidirect
59. C32×#123D3semidirect
60. C32×#123C2×C3semidirect
71. C3×D4×Dic3C2×C3semidirect
72. C2×C3×(C2×D3)⋊C4C2×C3semidirect
73. C3×#926C2×C3semidirect
74. C3×#898C2×C3semidirect
75. C3×#898C2×C3semidirect
76. C3×#897C2×C3semidirect
77. C3×#892C2×C3semidirect
78. C3×#886C2×C3semidirect
79. C3×#885C2×C3semidirect
80. C3×#883C2×C3semidirect
81. C3×#67⋊C4C2×C3semidirect
82. C3×D3×C22⋊C4C2×C3semidirect
83. C3×#878C2×C3semidirect
112. #5658C32direct (N × H)
131. C22×C3×Dic3C22×C3semidirect
134. C2×C3×Dic6C22×C3semidirect
143. C32×C4⋊C4C2×D3semidirect
144. C32×C4⋊C4C2×D3semidirect
145. C32×C4⋊C4C22×C3semidirect
146. C32×C4⋊C4C22×C3semidirect
162. C32×C22⋊C4C2×D3semidirect
163. C32×C22⋊C4C2×D3semidirect
165. C32×C22⋊C4C22×C3semidirect
166. C32×C22⋊C4C22×C3semidirect
172. C3×#217C22×C3semidirect
181. C3×C4⋊Dic3C22×C3semidirect
182. C3×C4⋊Dic3C22×C3semidirect
183. C3×C4⋊Dic3C22×C3semidirect
184. C3×C4⋊Dic3C22×C3semidirect
185. C3×Dic3⋊C4C22×C3semidirect
186. C3×Dic3⋊C4C22×C3semidirect
187. C3×C4×Dic3C22×C3semidirect
188. C3×C4×Dic3C22×C3semidirect
189. C3×C4×Dic3C22×C3semidirect
221. C3×#123C3×D3semidirect
222. C3×#123C2×C32semidirect
233. D4×Dic3C2×C32semidirect
234. C2×(C2×D3)⋊C4C2×C32semidirect
235. #926C2×C32semidirect
236. #898C2×C32semidirect
237. #898C2×C32semidirect
238. #897C2×C32semidirect
239. #892C2×C32semidirect
240. #886C2×C32semidirect
241. #885C2×C32semidirect
242. #883C2×C32semidirect
243. #67⋊C4C2×C32semidirect
244. D3×C22⋊C4C2×C32semidirect
245. #878C2×C32semidirect
335. C22×Dic3C22×C32semidirect
338. C2×Dic6C22×C32semidirect
347. C3×C4⋊C4C2×C3×D3semidirect
348. C3×C4⋊C4C2×C3×D3semidirect
349. C3×C4⋊C4C22×C32semidirect
350. C3×C4⋊C4C22×C32semidirect
366. C3×C22⋊C4C2×C3×D3semidirect
367. C3×C22⋊C4C2×C3×D3semidirect
369. C3×C22⋊C4C22×C32semidirect
370. C3×C22⋊C4C22×C32semidirect
376. #217C22×C32semidirect
385. C4⋊Dic3C22×C32semidirect
386. C4⋊Dic3C22×C32semidirect
387. C4⋊Dic3C22×C32semidirect
388. C4⋊Dic3C22×C32semidirect
389. Dic3⋊C4C22×C32semidirect
390. Dic3⋊C4C22×C32semidirect
391. C4×Dic3C22×C32semidirect
392. C4×Dic3C22×C32semidirect
393. C4×Dic3C22×C32semidirect
461. #123C32×D3semidirect
471. C33#551semidirect
570. C4⋊C4C2×C32×D3semidirect
571. C4⋊C4C2×C32×D3semidirect
584. C22⋊C4C2×C32×D3semidirect
585. C22⋊C4C2×C32×D3semidirect
652. C32#5658direct (N × H)
653. C32C3×#551semidirect
726. C3C3×#5658direct (N × H)
727. C3C32×#551semidirect

Maximal subgroups

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

subgroupindex
C33×#1232
C32×#9372
C32×D4×Dic32
C2×C32×(C2×D3)⋊C42
C32×#9262
C32×#8982
C32×#8972
C32×#8922
C32×#8862
C32×#8852
C32×#8832
C32×#67⋊C42
C32×D3×C22⋊C42
C32×#8782
C32×#5513
C3×#56583