Finite Group Databasebeta

← C32×#5660 #13179040

Subgroups — C32×#5660 #13179040

Order 1728.

1620 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#123C211yesmaximal, characteristic, complemented
2C32×#938C211yesmaximal, characteristic
3C32×#935C211yesmaximal, characteristic, complemented
4C32×C4×#67C211yesmaximal, characteristic, complemented
5C32×#924C211yesmaximal, characteristic, complemented
6C32×#896C211yesmaximal, characteristic, complemented
7C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
8C32×#890C211yesmaximal, characteristic, complemented
9C32×#889C211yesmaximal, characteristic, complemented
10C32×#883C211yesmaximal, characteristic, complemented
11C32×#883C211yesmaximal, characteristic, complemented
12C32×#67⋊C4C211yesmaximal, characteristic, complemented
13C32×#879C211yesmaximal, characteristic, complemented
14C32×#879C211yesmaximal, characteristic, complemented
15C32×#878C211yesmaximal, characteristic, complemented
16C32×#539—31nomaximal
17C3×#5660C314yesmaximal, direct product factor
18C2×C33×D4C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×Dic6C2211yescharacteristic
27C33×C4⋊C4C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C33×C22⋊C4C2211yescharacteristic
30C33×C22⋊C4C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×C4⋊Dic3C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic
41C32×C4⋊Dic3C2211yescharacteristic
42C32×C4⋊Dic3C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
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×#126—31no—
54C32×#126—31no—
55C32×#125—31no—
56C32×#125—31no—
57C32×#123—24no—
58C32×#123—31no—
59C32×#123—31no—
60C32×#123—31no—
61C32×#123D311yescharacteristic, complemented
62C32×#123C2×C314yescomplemented
63C32×C22⋊Q8—31no—
64C32×C22⋊Q8—31no—
65C32×C22⋊Q8—31no—
66C32×#121—31no—
67C32×C4×D4—31no—
68C32×C4×D4—31no—
69C2×C32×C4⋊C4—31no—
70C3×#938C2×C314yes—
71C3×#935C2×C314yescomplemented
72C3×C4×#67C2×C314yescomplemented
73C3×#924C2×C314yescomplemented
74C3×#896C2×C314yescomplemented
75C3×D3×C4⋊C4C2×C314yescomplemented
76C3×#890C2×C314yescomplemented
77C3×#889C2×C314yescomplemented
78C3×#883C2×C314yescomplemented
79C3×#883C2×C314yescomplemented
80C3×#67⋊C4C2×C314yescomplemented
81C3×#879C2×C314yescomplemented
82C3×#879C2×C314yescomplemented
83C3×#878C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C33×D4—41no—
88C2×C33×C4—41no—
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C32×#67—22no—
95C32×#67—22no—
96C2×C32×Dic3—41no—
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×C4×D3—22no—
105C32×C4×D3—41no—
106C32×C4×D3—41no—
107C32×Dic6—41no—
108C3×#539—34no—
109#5660C3211yescharacteristic, direct product factor
110C2×C32×Q8—31no—
111C2×C32×D4—24no—
112C2×C32×D4—31no—
113C2×C32×D4—31no—
114C2×C32×D4C2×D311yescharacteristic
115C2×C32×D4C22×C314yes—
116C22×C32×C4—24no—
117C22×C32×C4—31no—
118C22×C32×C4—31no—
119C22×C32×C4—31no—
120C22×C32×C4—31no—
121C22×C32×C4C2×D311yescharacteristic
122C22×C32×C4C22×C314yes—
123C2×C3×#67C22×C314yes—
124C2×C3×#67C22×C314yes—
125C22×C3×Dic3C22×C314yes—
126C2×C3×C4×D3C22×C314yes—
127C2×C3×C4×D3C22×C314yes—
128C2×C3×C4×D3C22×C314yes—
129C2×C3×Dic6C22×C314yes—
130C32×C4⋊C4—24no—
131C32×C4⋊C4—24no—
132C32×C4⋊C4—31no—
133C32×C4⋊C4—31no—
134C32×C4⋊C4—31no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4—31no—
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⋊C4—31no—
144C32×C4⋊C4C2×D311yescharacteristic
145C32×C4⋊C4C2×D311yescharacteristic
146C32×C4⋊C4C22×C314yes—
147C32×C4⋊C4C22×C314yes—
148C32×C22⋊C4—24no—
149C32×C22⋊C4—24no—
150C32×C22⋊C4—24no—
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⋊C4C2×D311yescharacteristic
159C32×C22⋊C4C2×D311yescharacteristic
160C32×C22⋊C4C2×D311yescharacteristic
161C32×C22⋊C4C22×C314yes—
162C32×C22⋊C4C22×C314yes—
163C32×C22⋊C4C22×C314yes—
164C32×C42—31no—
165C32×C42—31no—
166C3×#217C22×C314yes—
167C3×#217C22×C314yes—
168C3×#217C22×C314yes—
169C3×#217C22×C314yes—
170C3×#217C22×C314yes—
171C3×(C2×D3)⋊C4C22×C314yes—
172C3×(C2×D3)⋊C4C22×C314yes—
173C3×C4⋊Dic3C22×C314yes—
174C3×C4⋊Dic3C22×C314yes—
175C3×C4⋊Dic3C22×C314yes—
176C3×C4⋊Dic3C22×C314yes—
177C3×Dic3⋊C4C22×C314yes—
178C3×Dic3⋊C4C22×C314yes—
179C3×Dic3⋊C4C22×C314yes—
180C3×Dic3⋊C4C22×C314yes—
181C3×Dic3⋊C4C22×C314yes—
182C3×Dic3⋊C4C22×C314yes—
183C3×Dic3⋊C4C22×C314yes—
184C3×Dic3⋊C4C22×C314yes—
185C3×C4×Dic3C22×C314yes—
186C3×C4×Dic3C22×C314yes—
187C22×C33—21no—
188C22×C33—21no—
189C22×C33—21no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33C2411yescharacteristic
194C2×C32×D3—21no—
195C2×C32×D3—21no—
196C2×C32×D3#4112yes—
197C33×C4—21no—
198C33×C4—21no—
199C33×C4—21no—
200C33×C4—21no—
201C33×C4—21no—
202C32×Dic3—21no—
203C32×Dic3—21no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C3×#126—34no—
210C3×#126—34no—
211C3×#125—34no—
212C3×#125—34no—
213C3×#123—24no—
214C3×#123—34no—
215C3×#123—34no—
216C3×#123—34no—
217C3×#123C3×D314yescomplemented
218C3×#123C2×C3211yescharacteristic, complemented
219C3×C22⋊Q8—34no—
220C3×C22⋊Q8—34no—
221C3×C22⋊Q8—34no—
222C3×#121—34no—
223C3×C4×D4—34no—
224C3×C4×D4—34no—
225C2×C3×C4⋊C4—34no—
226#938C2×C3211yescharacteristic
227#935C2×C3211yescharacteristic, complemented
228C4×#67C2×C3211yescharacteristic, complemented
229#924C2×C3211yescharacteristic, complemented
230#896C2×C3211yescharacteristic, complemented
231D3×C4⋊C4C2×C3211yescharacteristic, complemented
232#890C2×C3211yescharacteristic, complemented
233#889C2×C3211yescharacteristic, complemented
234#883C2×C3211yescharacteristic, complemented
235#883C2×C3211yescharacteristic, complemented
236#67⋊C4C2×C3211yescharacteristic, complemented
237#879C2×C3211yescharacteristic, complemented
238#879C2×C3211yescharacteristic, complemented
239#878C2×C3211yescharacteristic, complemented
240C23×C32—24no—
241C23×C32—24no—
242C23×C32—31no—
243C23×C32C22×D311yescharacteristic
244C23×C32C22×D311yescharacteristic
245C23×C32C23×C314yes—
246C23×C32C23×C314yes—
247C22×C3×D3C23×C314yes—
248C32×Q8—121no—
249C32×D4—41no—
250C32×D4—44no—
251C32×D4—48no—
252C32×D4—62no—
253C32×D4—62no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—24no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—31no—
264C2×C32×C4—31no—
265C2×C32×C4—31no—
266C2×C32×C4—41no—
267C2×C32×C4—44no—
268C2×C32×C4—48no—
269C2×C32×C4—62no—
270C2×C32×C4—121no—
271C2×C32×C4—121no—
272C2×C32×C4—121no—
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C23×C314yes—
279C2×C32×C4C23×C314yes—
280C2×C32×C4C23×C314yes—
281C2×C32×C4C23×C314yes—
282C2×C32×C4C23×C314yes—
283C3×#67—28no—
284C3×#67—28no—
285C2×C3×Dic3—44no—
286C2×C3×Dic3C23×C314yes—
287C2×C3×Dic3C23×C314yes—
288C2×C3×Dic3C23×C314yes—
289C2×C3×Dic3C23×C314yes—
290C2×C3×Dic3C23×C314yes—
291C2×C3×Dic3C23×C314yes—
292C2×C3×Dic3C23×C314yes—
293C3×C4×D3—28no—
294C3×C4×D3—44no—
295C3×C4×D3—44no—
296C3×Dic6—44no—
297#539—31noSylow
298C2×C33—41no—
299C2×C33—41no—
300C2×C33C2×#4111yescharacteristic
301C2×C33H(5,𝔽2)11yescharacteristic
302C2×C332−1+411yescharacteristic
303C32×D3—22no—
304C2×C3×Q8—34no—
305C2×C3×D4—24no—
306C2×C3×D4—34no—
307C2×C3×D4—34no—
308C2×C3×D4C2×C3×D314yes—
309C2×C3×D4C22×C3211yescharacteristic
310C22×C3×C4—24no—
311C22×C3×C4—34no—
312C22×C3×C4—34no—
313C22×C3×C4—34no—
314C22×C3×C4—34no—
315C22×C3×C4C2×C3×D314yes—
316C22×C3×C4C22×C3211yescharacteristic
317C2×#67C22×C3211yescharacteristic
318C2×#67C22×C3211yescharacteristic
319C22×Dic3C22×C3211yescharacteristic
320C2×C4×D3C22×C3211yescharacteristic
321C2×C4×D3C22×C3211yescharacteristic
322C2×C4×D3C22×C3211yescharacteristic
323C2×Dic6C22×C3211yescharacteristic
324C3×C4⋊C4—24no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—34no—
329C3×C4⋊C4—34no—
330C3×C4⋊C4—34no—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—34no—
333C3×C4⋊C4—34no—
334C3×C4⋊C4—34no—
335C3×C4⋊C4—34no—
336C3×C4⋊C4—34no—
337C3×C4⋊C4—34no—
338C3×C4⋊C4C2×C3×D314yes—
339C3×C4⋊C4C2×C3×D314yes—
340C3×C4⋊C4C22×C3211yescharacteristic
341C3×C4⋊C4C22×C3211yescharacteristic
342C3×C22⋊C4—24no—
343C3×C22⋊C4—24no—
344C3×C22⋊C4—24no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—34no—
350C3×C22⋊C4—34no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4C2×C3×D314yes—
353C3×C22⋊C4C2×C3×D314yes—
354C3×C22⋊C4C2×C3×D314yes—
355C3×C22⋊C4C22×C3211yescharacteristic
356C3×C22⋊C4C22×C3211yescharacteristic
357C3×C22⋊C4C22×C3211yescharacteristic
358C3×C42—34no—
359C3×C42—34no—
360#217C22×C3211yescharacteristic
361#217C22×C3211yescharacteristic
362#217C22×C3211yescharacteristic
363#217C22×C3211yescharacteristic
364#217C22×C3211yescharacteristic
365(C2×D3)⋊C4C22×C3211yescharacteristic
366(C2×D3)⋊C4C22×C3211yescharacteristic
367C4⋊Dic3C22×C3211yescharacteristic
368C4⋊Dic3C22×C3211yescharacteristic
369C4⋊Dic3C22×C3211yescharacteristic
370C4⋊Dic3C22×C3211yescharacteristic
371Dic3⋊C4C22×C3211yescharacteristic
372Dic3⋊C4C22×C3211yescharacteristic
373Dic3⋊C4C22×C3211yescharacteristic
374Dic3⋊C4C22×C3211yescharacteristic
375Dic3⋊C4C22×C3211yescharacteristic
376Dic3⋊C4C22×C3211yescharacteristic
377Dic3⋊C4C22×C3211yescharacteristic
378Dic3⋊C4C22×C3211yescharacteristic
379C4×Dic3C22×C3211yescharacteristic
380C4×Dic3C22×C3211yescharacteristic
381C22×C32—28no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—24no—
389C22×C32—24no—
390C22×C32—24no—
391C22×C32—24no—
392C22×C32—24no—
393C22×C32—24no—
394C22×C32—24no—
395C22×C32—32no—
396C22×C32—44no—
397C22×C32—44no—
398C22×C32—44no—
399C22×C32—44no—
400C22×C32—44no—
401C22×C32—61no—
402C22×C32—61no—
403C22×C32C23×D311yescharacteristic
404C22×C32C24×C314yes—
405C2×C3×D3—24no—
406C2×C3×D3—24no—
407C2×C3×D3C3×#4118yes—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—24no—
414C32×C4—24no—
415C32×C4—24no—
416C32×C4—24no—
417C32×C4—24no—
418C32×C4—44no—
419C32×C4—44no—
420C32×C4—44no—
421C32×C4—44no—
422C32×C4—44no—
423C32×C4—61no—
424C32×C4—61no—
425C32×C4—61no—
426C32×C4—61no—
427C32×C4—61no—
428C32×C4—61no—
429C32×C4—61no—
430C3×Dic3—24no—
431C3×Dic3—24no—
432C3×Dic3—24no—
433C3×Dic3—24no—
434C3×Dic3—24no—
435C3×Dic3—24no—
436C3×Dic3—24no—
437#126—31no—
438#126—31no—
439#125—31no—
440#125—31no—
441#123—31no—
442#123—31no—
443#123—31no—
444#123C32×D311yescharacteristic, complemented
445C22⋊Q8—31no—
446C22⋊Q8—31no—
447C22⋊Q8—31no—
448#121—31no—
449C4×D4—31no—
450C4×D4—31no—
451C2×C4⋊C4—31no—
452C33#53911yescharacteristic, complemented, Sylow
453C23×C3—24no—
454C23×C3—24no—
455C23×C3—34no—
456C23×C3C22×C3×D314yes—
457C23×C3C22×C3×D314yes—
458C23×C3C23×C3211yescharacteristic
459C23×C3C23×C3211yescharacteristic
460C22×D3C23×C3211yescharacteristic
461C3×Q8—124no—
462C3×D4—44no—
463C3×D4—41no—
464C3×D4—48no—
465C3×D4—68no—
466C3×D4—68no—
467C2×C3×C4—24no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—24no—
472C2×C3×C4—34no—
473C2×C3×C4—34no—
474C2×C3×C4—34no—
475C2×C3×C4—34no—
476C2×C3×C4—34no—
477C2×C3×C4—34no—
478C2×C3×C4—34no—
479C2×C3×C4—44no—
480C2×C3×C4—41no—
481C2×C3×C4—48no—
482C2×C3×C4—68no—
483C2×C3×C4—124no—
484C2×C3×C4—124no—
485C2×C3×C4—124no—
486C2×C3×C4C22×C3×D314yes—
487C2×C3×C4C22×C3×D314yes—
488C2×C3×C4C22×C3×D314yes—
489C2×C3×C4C22×C3×D314yes—
490C2×C3×C4C22×C3×D314yes—
491C2×C3×C4C23×C3211yescharacteristic
492C2×C3×C4C23×C3211yescharacteristic
493C2×C3×C4C23×C3211yescharacteristic
494C2×C3×C4C23×C3211yescharacteristic
495C2×C3×C4C23×C3211yescharacteristic
496#67—22no—
497#67—22no—
498C2×Dic3—41no—
499C2×Dic3C23×C3211yescharacteristic
500C2×Dic3C23×C3211yescharacteristic
501C2×Dic3C23×C3211yescharacteristic
502C2×Dic3C23×C3211yescharacteristic
503C2×Dic3C23×C3211yescharacteristic
504C2×Dic3C23×C3211yescharacteristic
505C2×Dic3C23×C3211yescharacteristic
506C4×D3—22no—
507C4×D3—41no—
508C4×D3—41no—
509Dic6—41no—
510C2×C32—24no—
511C2×C32—24no—
512C2×C32—24no—
513C2×C32—48no—
514C2×C32—41no—
515C2×C32—41no—
516C2×C32—44no—
517C2×C32—44no—
518C2×C32—62no—
519C2×C32—84no—
520C2×C32#100411yescharacteristic
521C2×C32D3×#4111yescharacteristic
522C2×C32#101011yescharacteristic
523C2×C32C2×C3×#4114yes—
524C2×C32C3×H(5,𝔽2)14yes—
525C2×C32C3×2−1+414yes—
526C3×D3—28no—
527C2×Q8—31no—
528C2×D4—31no—
529C2×D4—31no—
530C2×D4C2×C32×D311yescharacteristic
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4C2×C32×D311yescharacteristic
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4C2×C32×D311yescharacteristic
549C4⋊C4C2×C32×D311yescharacteristic
550C22⋊C4—31no—
551C22⋊C4—31no—
552C22⋊C4—31no—
553C22⋊C4—31no—
554C22⋊C4—31no—
555C22⋊C4—31no—
556C22⋊C4—31no—
557C22⋊C4C2×C32×D311yescharacteristic
558C22⋊C4C2×C32×D311yescharacteristic
559C22⋊C4C2×C32×D311yescharacteristic
560C42—31no—
561C42—31no—
562C22×C3—28no—
563C22×C3—24no—
564C22×C3—24no—
565C22×C3—24no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—24no—
576C22×C3—38no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—64no—
583C22×C3—64no—
584C22×C3C23×C3×D314yes—
585C22×C3C24×C3211yescharacteristic
586C2×D3—21no—
587C2×D3—21no—
588C2×D3C32×#4112yes—
589C3×C4—24no—
590C3×C4—24no—
591C3×C4—24no—
592C3×C4—24no—
593C3×C4—24no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—44no—
600C3×C4—44no—
601C3×C4—44no—
602C3×C4—44no—
603C3×C4—44no—
604C3×C4—64no—
605C3×C4—64no—
606C3×C4—64no—
607C3×C4—64no—
608C3×C4—64no—
609C3×C4—64no—
610C3×C4—64no—
611Dic3—21no—
612Dic3—21no—
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—21no—
617Dic3—21no—
618C32—24no—
619C32#566011yescharacteristic, direct product factor
620C32C3×#53914yescomplemented
621C23—31no—
622C23C22×C32×D311yescharacteristic
623C23C22×C32×D311yescharacteristic
624Q8—121no—
625D4—41no—
626D4—62no—
627D4—62no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—41no—
636C2×C4—62no—
637C2×C4—121no—
638C2×C4—121no—
639C2×C4—121no—
640C2×C4C22×C32×D311yescharacteristic
641C2×C4C22×C32×D311yescharacteristic
642C2×C4C22×C32×D311yescharacteristic
643C2×C4C22×C32×D311yescharacteristic
644C2×C4C22×C32×D311yescharacteristic
645C2×C3—24no—
646C2×C3—24no—
647C2×C3—24no—
648C2×C3—48no—
649C2×C3—44no—
650C2×C3—44no—
651C2×C3—41no—
652C2×C3—41no—
653C2×C3—68no—
654C2×C3—84no—
655C2×C3C3×#100414yes—
656C2×C3C3×D3×#4114yes—
657C2×C3C3×#101014yes—
658C2×C3C2×C32×#4111yescharacteristic
659C2×C3C32×H(5,𝔽2)11yescharacteristic
660C2×C3C32×2−1+411yescharacteristic
661D3—22no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—32no—
669C22—61no—
670C22—61no—
671C22C23×C32×D311yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—61no—
681C4—61no—
682C4—61no—
683C4—61no—
684C3—24no—
685C3C3×#566014yesdirect product factor
686C3C32×#53911yescharacteristic, complemented
687C2—41no—
688C2—41no—
689C2—62no—
690C2C32×#100411yescharacteristic
691C2C32×D3×#4111yescharacteristic
692C2C32×#101011yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#123C2
socleC22×C33C24
prime radicalC32×#938C2
hypercenterC32×#123D3
hypocenterC3C32×#539
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×#935C2semidirect
4. C32×C4×#67C2semidirect
5. C32×#924C2semidirect
6. C32×#896C2semidirect
7. C32×D3×C4⋊C4C2semidirect
8. C32×#890C2semidirect
9. C32×#889C2semidirect
10. C32×#883C2semidirect
11. C32×#883C2semidirect
12. C32×#67⋊C4C2semidirect
13. C32×#879C2semidirect
14. C32×#879C2semidirect
15. C32×#878C2semidirect
17. C3×#5660C3direct (N × H)
61. C32×#123D3semidirect
62. C32×#123C2×C3semidirect
71. C3×#935C2×C3semidirect
72. C3×C4×#67C2×C3semidirect
73. C3×#924C2×C3semidirect
74. C3×#896C2×C3semidirect
75. C3×D3×C4⋊C4C2×C3semidirect
76. C3×#890C2×C3semidirect
77. C3×#889C2×C3semidirect
78. C3×#883C2×C3semidirect
79. C3×#883C2×C3semidirect
80. C3×#67⋊C4C2×C3semidirect
81. C3×#879C2×C3semidirect
82. C3×#879C2×C3semidirect
83. C3×#878C2×C3semidirect
109. #5660C32direct (N × H)
217. C3×#123C3×D3semidirect
218. C3×#123C2×C32semidirect
227. #935C2×C32semidirect
228. C4×#67C2×C32semidirect
229. #924C2×C32semidirect
230. #896C2×C32semidirect
231. D3×C4⋊C4C2×C32semidirect
232. #890C2×C32semidirect
233. #889C2×C32semidirect
234. #883C2×C32semidirect
235. #883C2×C32semidirect
236. #67⋊C4C2×C32semidirect
237. #879C2×C32semidirect
238. #879C2×C32semidirect
239. #878C2×C32semidirect
444. #123C32×D3semidirect
452. C33#539semidirect
619. C32#5660direct (N × H)
620. C32C3×#539semidirect
685. C3C3×#5660direct (N × H)
686. C3C32×#539semidirect

Maximal subgroups

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

subgroupindex
C33×#1232
C32×#9382
C32×#9352
C32×C4×#672
C32×#9242
C32×#8962
C32×D3×C4⋊C42
C32×#8902
C32×#8892
C32×#8832
C32×#67⋊C42
C32×#8792
C32×#8782
C32×#5393
C3×#56603