Finite Group Databasebeta

← C3×#10596011 #13179292

Subgroups — C3×#10596011 #13179292

Order 1728.

1804 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×C4×D4C211yesmaximal, characteristic, complemented
2C3×#64148C211yesmaximal, characteristic, complemented
3C3×#64148C211yesmaximal, characteristic, complemented
4C3×#64139C211yesmaximal, characteristic, complemented
5C3×#64138C211yesmaximal, characteristic, complemented
6C3×C4×#638C211yesmaximal, characteristic, complemented
7C2×C3×#3750C211yesmaximal, characteristic, complemented
8C3×#64103C211yesmaximal, characteristic, complemented
9C3×#64098C211yesmaximal, characteristic, complemented
10C3×#64093C211yesmaximal, characteristic, complemented
11C3×#64090C211yesmaximal, characteristic, complemented
12C3×#64090C211yesmaximal, characteristic, complemented
13C3×#64088C211yesmaximal, characteristic, complemented
14C3×#64085C211yesmaximal, characteristic, complemented
15C3×#64081C211yesmaximal, characteristic, complemented
16#10596011C311yesmaximal, characteristic, direct product factor
17C3×#5540—34nomaximal
18C2×C33×D4C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C22×C3×C3⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
28C2×C3×C4×C3⋊D3C2211yescharacteristic
29C2×C3×C4×C3⋊D3C2211yescharacteristic
30C33×C4⋊C4C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic
33C33×C42C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
43C3×#3750C2211yescharacteristic
44C3×#3750C2211yescharacteristic
45C3×#3750C2211yescharacteristic
46C3×#3750C2211yescharacteristic
47C3×#3750C2211yescharacteristic
48C3×#3750C2211yescharacteristic
49C3×#3750C2211yescharacteristic
50C3×#3750C2211yescharacteristic
51C3×C4×C3⋊Dic3C2211yescharacteristic
52C3×C4×C3⋊Dic3C2211yescharacteristic
53C32×C4×D4—24no—
54C32×C4×D4D314yescomplemented
55C32×C4×D4C2×C311yescharacteristic, complemented
56#64148C2×C311yescharacteristic, complemented
57#64148C2×C311yescharacteristic, complemented
58#64139C2×C311yescharacteristic, complemented
59#64138C2×C311yescharacteristic, complemented
60C4×#638C2×C311yescharacteristic, complemented
61C2×#3750C2×C311yescharacteristic, complemented
62#64103C2×C311yescharacteristic, complemented
63#64098C2×C311yescharacteristic, complemented
64#64093C2×C311yescharacteristic, complemented
65#64090C2×C311yescharacteristic, complemented
66#64090C2×C311yescharacteristic, complemented
67#64088C2×C311yescharacteristic, complemented
68#64085C2×C311yescharacteristic, complemented
69#64081C2×C311yescharacteristic, complemented
70C3×#939—34no—
71C3×#939—34no—
72C3×#930—34no—
73C3×#929—34no—
74C3×C4×#67—34no—
75C2×C3×Dic3⋊C4—34no—
76C3×#894—34no—
77C3×#889—34no—
78C3×#884—34no—
79C3×#67⋊C4—34no—
80C3×#67⋊C4—34no—
81C3×#879—34no—
82C3×#876—34no—
83C3×#872—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C33×D4—22no—
89C2×C33×C4—41no—
90C2×C33×C4—41no—
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C3×#638—22no—
97C3×#638—22no—
98C3×#638—22no—
99C3×#638—41no—
100C2×C3×C3⋊Dic3—22no—
101C2×C3×C3⋊Dic3—41no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C3×C4⋊(C3⋊D3)—41no—
109C3×C4×C3⋊D3—22no—
110C3×C4×C3⋊D3—41no—
111C3×#553—91no—
112#5540—34no—
113C2×C32×D4—24no—
114C2×C32×D4C2×D314yes—
115C2×C32×D4C22×C311yescharacteristic
116C22×C32×C4—24no—
117C22×C32×C4—24no—
118C22×C32×C4C2×D314yes—
119C22×C32×C4C2×D314yes—
120C22×C32×C4C22×C311yescharacteristic
121C22×C32×C4C22×C311yescharacteristic
122C2×#638C22×C311yescharacteristic
123C2×#638C22×C311yescharacteristic
124C2×#638C22×C311yescharacteristic
125C2×#638C22×C311yescharacteristic
126C22×C3⋊Dic3C22×C311yescharacteristic
127C22×C3⋊Dic3C22×C311yescharacteristic
128C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
129C2×C4×C3⋊D3C22×C311yescharacteristic
130C2×C4×C3⋊D3C22×C311yescharacteristic
131C2×C3×#67—34no—
132C2×C3×#67—34no—
133C2×C3×#67—34no—
134C2×C3×#67—34no—
135C22×C3×Dic3—34no—
136C22×C3×Dic3—34no—
137C2×C3×D12—34no—
138C2×C3×C4×D3—34no—
139C2×C3×C4×D3—34no—
140C32×C4⋊C4—24no—
141C32×C4⋊C4C2×D314yes—
142C32×C4⋊C4C22×C311yescharacteristic
143C32×C22⋊C4—24no—
144C32×C22⋊C4—24no—
145C32×C22⋊C4C2×D314yes—
146C32×C22⋊C4C2×D314yes—
147C32×C22⋊C4C22×C311yescharacteristic
148C32×C22⋊C4C22×C311yescharacteristic
149C32×C42—24no—
150C32×C42C2×D314yes—
151C32×C42C22×C311yescharacteristic
152#3757C22×C311yescharacteristic
153#3757C22×C311yescharacteristic
154#3752C22×C311yescharacteristic
155#3752C22×C311yescharacteristic
156#3752C22×C311yescharacteristic
157#3752C22×C311yescharacteristic
158#3752C22×C311yescharacteristic
159#3752C22×C311yescharacteristic
160C4⋊(C3⋊Dic3)C22×C311yescharacteristic
161#3750C22×C311yescharacteristic
162#3750C22×C311yescharacteristic
163#3750C22×C311yescharacteristic
164#3750C22×C311yescharacteristic
165#3750C22×C311yescharacteristic
166#3750C22×C311yescharacteristic
167#3750C22×C311yescharacteristic
168#3750C22×C311yescharacteristic
169C4×C3⋊Dic3C22×C311yescharacteristic
170C4×C3⋊Dic3C22×C311yescharacteristic
171C3×#217—34no—
172C3×#217—34no—
173C3×(C2×D3)⋊C4—34no—
174C3×(C2×D3)⋊C4—34no—
175C3×(C2×D3)⋊C4—34no—
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4—34no—
179C3×C4⋊Dic3—34no—
180C3×Dic3⋊C4—34no—
181C3×Dic3⋊C4—34no—
182C3×Dic3⋊C4—34no—
183C3×Dic3⋊C4—34no—
184C3×Dic3⋊C4—34no—
185C3×Dic3⋊C4—34no—
186C3×Dic3⋊C4—34no—
187C3×Dic3⋊C4—34no—
188C3×C4×Dic3—34no—
189C3×C4×Dic3—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33#4112yes—
196C22×C33C2411yescharacteristic
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C33×C4—21no—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C33×C4—21no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3#4112yes—
214C3×#126—91no—
215C3×#126—91no—
216C3×#125—91no—
217C3×#123—91no—
218C3×#123—91no—
219C3×#121—91no—
220C3×#121—91no—
221C3×#121—91no—
222C3×#121—91no—
223C3×C4×D4—24no—
224C3×C4×D4—91no—
225C3×C4×D4—91no—
226C3×C4×D4—91no—
227C3×C4×D4C3×D314yescomplemented
228C3×C4×D4C3⋊D311yescharacteristic, complemented
229C3×#117—91no—
230C2×C3×C4⋊C4—91no—
231#939—34no—
232#939—34no—
233#930—34no—
234#929—34no—
235C4×#67—34no—
236C2×Dic3⋊C4—34no—
237#894—34no—
238#889—34no—
239#884—34no—
240#67⋊C4—34no—
241#67⋊C4—34no—
242#879—34no—
243#876—34no—
244#872—34no—
245C23×C32—24no—
246C23×C32—24no—
247C23×C32C22×D314yes—
248C23×C32C22×D314yes—
249C23×C32C23×C311yescharacteristic
250C23×C32C23×C311yescharacteristic
251C22×C3⋊D3C23×C311yescharacteristic
252C22×C3⋊D3C23×C311yescharacteristic
253C22×C3×D3—34no—
254C22×C3×D3—34no—
255C32×D4—216no—
256C32×D4—28no—
257C32×D4—22no—
258C2×C32×C4—24no—
259C2×C32×C4—24no—
260C2×C32×C4—24no—
261C2×C32×C4—24no—
262C2×C32×C4—24no—
263C2×C32×C4—44no—
264C2×C32×C4—44no—
265C2×C32×C4—41no—
266C2×C32×C4—41no—
267C2×C32×C4—48no—
268C2×C32×C4—48no—
269C2×C32×C4C22×D314yes—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D314yes—
272C2×C32×C4C22×D314yes—
273C2×C32×C4C22×D314yes—
274C2×C32×C4C23×C311yescharacteristic
275C2×C32×C4C23×C311yescharacteristic
276C2×C32×C4C23×C311yescharacteristic
277C2×C32×C4C23×C311yescharacteristic
278C2×C32×C4C23×C311yescharacteristic
279#638—22no—
280#638—22no—
281#638—22no—
282#638—41no—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3—41no—
285C2×C3⋊Dic3C23×C311yescharacteristic
286C2×C3⋊Dic3C23×C311yescharacteristic
287C2×C3⋊Dic3C23×C311yescharacteristic
288C2×C3⋊Dic3C23×C311yescharacteristic
289C2×C3⋊Dic3C23×C311yescharacteristic
290C2×C3⋊Dic3C23×C311yescharacteristic
291C4⋊(C3⋊D3)—41no—
292C4×C3⋊D3—22no—
293C4×C3⋊D3—41no—
294C3×#67—68no—
295C3×#67—68no—
296C3×#67—68no—
297C3×#67—124no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—34no—
303C2×C3×Dic3—34no—
304C2×C3×Dic3—68no—
305C2×C3×Dic3—124no—
306C3×D12—124no—
307C3×C4×D3—68no—
308C3×C4×D3—124no—
309#553—91noSylow
310C2×C33—22no—
311C2×C33—41no—
312C2×C33C2×#4111yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33H(5,𝔽2)11yescharacteristic
315C3×C3⋊D3—41no—
316C3×C3⋊D3—41no—
317C2×C3×D4—24no—
318C2×C3×D4—91no—
319C2×C3×D4—91no—
320C2×C3×D4—91no—
321C2×C3×D4—91no—
322C2×C3×D4—91no—
323C2×C3×D4C2×C3×D314yes—
324C2×C3×D4C2×C3⋊D311yescharacteristic
325C22×C3×C4—24no—
326C22×C3×C4—24no—
327C22×C3×C4—91no—
328C22×C3×C4—91no—
329C22×C3×C4—91no—
330C22×C3×C4—91no—
331C22×C3×C4C2×C3×D314yes—
332C22×C3×C4C2×C3×D314yes—
333C22×C3×C4C2×C3⋊D311yescharacteristic
334C22×C3×C4C2×C3⋊D311yescharacteristic
335C2×#67—34no—
336C2×#67—34no—
337C2×#67—34no—
338C2×#67—34no—
339C22×Dic3—34no—
340C22×Dic3—34no—
341C2×D12—34no—
342C2×C4×D3—34no—
343C2×C4×D3—34no—
344C3×C4⋊C4—24no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4—91no—
351C3×C4⋊C4—91no—
352C3×C4⋊C4—91no—
353C3×C4⋊C4—91no—
354C3×C4⋊C4C2×C3×D314yes—
355C3×C4⋊C4C2×C3⋊D311yescharacteristic
356C3×C22⋊C4—24no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4C2×C3×D314yes—
367C3×C22⋊C4C2×C3×D314yes—
368C3×C22⋊C4C2×C3⋊D311yescharacteristic
369C3×C22⋊C4C2×C3⋊D311yescharacteristic
370C3×C42—24no—
371C3×C42—91no—
372C3×C42—91no—
373C3×C42C2×C3×D314yes—
374C3×C42C2×C3⋊D311yescharacteristic
375#217—34no—
376#217—34no—
377(C2×D3)⋊C4—34no—
378(C2×D3)⋊C4—34no—
379(C2×D3)⋊C4—34no—
380(C2×D3)⋊C4—34no—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—34no—
383C4⋊Dic3—34no—
384Dic3⋊C4—34no—
385Dic3⋊C4—34no—
386Dic3⋊C4—34no—
387Dic3⋊C4—34no—
388Dic3⋊C4—34no—
389Dic3⋊C4—34no—
390Dic3⋊C4—34no—
391Dic3⋊C4—34no—
392C4×Dic3—34no—
393C4×Dic3—34no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—28no—
397C22×C32—24no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—24no—
402C22×C32—28no—
403C22×C32—24no—
404C22×C32—24no—
405C22×C32—24no—
406C22×C32—24no—
407C22×C32—44no—
408C22×C32—44no—
409C22×C32—44no—
410C22×C32—44no—
411C22×C32#23518yes—
412C22×C32C3×#4112yes—
413C22×C32C23×D314yes—
414C22×C32C24×C311yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3×D3—64no—
422C2×C3×D3—64no—
423C2×C3×D3—64no—
424C2×C3×D3—64no—
425C2×C3×D3—64no—
426C2×C3×D3—64no—
427C32×C4—28no—
428C32×C4—28no—
429C32×C4—24no—
430C32×C4—24no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—24no—
437C32×C4—24no—
438C32×C4—24no—
439C32×C4—44no—
440C32×C4—44no—
441C32×C4—44no—
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—21no—
445C3⋊Dic3—21no—
446C3⋊Dic3—21no—
447C3⋊Dic3C3×#4112yes—
448C3×Dic3—38no—
449C3×Dic3—64no—
450C3×Dic3—64no—
451C3×Dic3—64no—
452C3×Dic3—64no—
453C3×Dic3—64no—
454#126—91no—
455#126—91no—
456#125—91no—
457#123—91no—
458#123—91no—
459#121—91no—
460#121—91no—
461#121—91no—
462#121—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4C3×C3⋊D311yescharacteristic, complemented
467#117—91no—
468C2×C4⋊C4—91no—
469C33#55311yescharacteristic, complemented, Sylow
470C23×C3—24no—
471C23×C3—24no—
472C23×C3—91no—
473C23×C3—91no—
474C23×C3C22×C3×D314yes—
475C23×C3C22×C3×D314yes—
476C23×C3C22×C3⋊D311yescharacteristic
477C23×C3C22×C3⋊D311yescharacteristic
478C22×D3—34no—
479C22×D3—34no—
480C3×D4—216no—
481C3×D4—28no—
482C3×D4—22no—
483C3×D4—182no—
484C3×D4—182no—
485C3×D4—182no—
486C3×D4—361no—
487C3×D4—361no—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—24no—
493C2×C3×C4—44no—
494C2×C3×C4—44no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—48no—
498C2×C3×C4—48no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—182no—
506C2×C3×C4—182no—
507C2×C3×C4—361no—
508C2×C3×C4—361no—
509C2×C3×C4C22×C3×D314yes—
510C2×C3×C4C22×C3×D314yes—
511C2×C3×C4C22×C3×D314yes—
512C2×C3×C4C22×C3×D314yes—
513C2×C3×C4C22×C3×D314yes—
514C2×C3×C4C22×C3⋊D311yescharacteristic
515C2×C3×C4C22×C3⋊D311yescharacteristic
516C2×C3×C4C22×C3⋊D311yescharacteristic
517C2×C3×C4C22×C3⋊D311yescharacteristic
518C2×C3×C4C22×C3⋊D311yescharacteristic
519#67—68no—
520#67—68no—
521#67—68no—
522#67—124no—
523C2×Dic3—34no—
524C2×Dic3—34no—
525C2×Dic3—34no—
526C2×Dic3—34no—
527C2×Dic3—34no—
528C2×Dic3—34no—
529C2×Dic3—68no—
530C2×Dic3—124no—
531D12—124no—
532C4×D3—68no—
533C4×D3—124no—
534C2×C32—22no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—28no—
539C2×C32—48no—
540C2×C32—48no—
541C2×C32—44no—
542C2×C32—41no—
543C2×C32C2×#23514yes—
544C2×C32#100414yes—
545C2×C32D3×#4114yes—
546C2×C32C2×C3×#4111yescharacteristic
547C2×C32C2×C3×#4111yescharacteristic
548C2×C32C3×H(5,𝔽2)11yescharacteristic
549C3⋊D3—41no—
550C3⋊D3—41no—
551C3×D3—124no—
552C3×D3—124no—
553C2×D4—91no—
554C2×D4—91no—
555C2×D4—91no—
556C2×D4—91no—
557C2×D4—91no—
558C2×D4C2×C3×C3⋊D311yescharacteristic
559C22×C4—91no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4C2×C3×C3⋊D311yescharacteristic
564C22×C4C2×C3×C3⋊D311yescharacteristic
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—91no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4C2×C3×C3⋊D311yescharacteristic
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—91no—
581C22⋊C4—91no—
582C22⋊C4—91no—
583C22⋊C4C2×C3×C3⋊D311yescharacteristic
584C22⋊C4C2×C3×C3⋊D311yescharacteristic
585C42—91no—
586C42—91no—
587C42C2×C3×C3⋊D311yescharacteristic
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—28no—
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—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—181no—
606C22×C3—181no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3—181no—
611C22×C3C3×#23518yes—
612C22×C3#382812yes—
613C22×C3C23×C3×D314yes—
614C22×C3C23×C3⋊D311yescharacteristic
615C2×D3—64no—
616C2×D3—64no—
617C2×D3—64no—
618C2×D3—64no—
619C2×D3—64no—
620C2×D3—64no—
621C3×C4—28no—
622C3×C4—28no—
623C3×C4—24no—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—24no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—44no—
634C3×C4—44no—
635C3×C4—44no—
636C3×C4—92no—
637C3×C4—181no—
638C3×C4—181no—
639C3×C4—181no—
640C3×C4—181no—
641C3×C4—181no—
642Dic3—38no—
643Dic3—64no—
644Dic3—64no—
645Dic3—64no—
646Dic3—64no—
647Dic3—64no—
648C32—24no—
649C32#554014yescomplemented
650C32C3×#55311yescharacteristic, complemented
651C23—91no—
652C23—91no—
653C23C22×C3×C3⋊D311yescharacteristic
654C23C22×C3×C3⋊D311yescharacteristic
655D4—22no—
656D4—182no—
657D4—182no—
658D4—182no—
659D4—361no—
660D4—361no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—182no—
670C2×C4—182no—
671C2×C4—361no—
672C2×C4—361no—
673C2×C4C22×C3×C3⋊D311yescharacteristic
674C2×C4C22×C3×C3⋊D311yescharacteristic
675C2×C4C22×C3×C3⋊D311yescharacteristic
676C2×C4C22×C3×C3⋊D311yescharacteristic
677C2×C4C22×C3×C3⋊D311yescharacteristic
678C2×C3—28no—
679C2×C3—22no—
680C2×C3—24no—
681C2×C3—24no—
682C2×C3—24no—
683C2×C3—48no—
684C2×C3—48no—
685C2×C3—44no—
686C2×C3—41no—
687C2×C3—361no—
688C2×C3—361no—
689C2×C3C2×C3×#23514yes—
690C2×C3C3×#100414yes—
691C2×C3C3×D3×#4114yes—
692C2×C3C2×#382811yescharacteristic
693C2×C3#6436111yescharacteristic
694C2×C3#41×C3⋊D311yescharacteristic
695D3—124no—
696D3—124no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—181no—
703C22—181no—
704C22—181no—
705C22—181no—
706C22—181no—
707C22—181no—
708C22C3×#382812yes—
709C22C23×C3×C3⋊D311yescharacteristic
710C4—21no—
711C4—21no—
712C4—21no—
713C4—21no—
714C4—21no—
715C4—92no—
716C4—181no—
717C4—181no—
718C4—181no—
719C4—181no—
720C4—181no—
721C3—24no—
722C3C3×#554014yescomplemented
723C3#1059601111yescharacteristic, direct product factor
724C2—22no—
725C2—41no—
726C2—361no—
727C2—361no—
728C2C2×C3×#382811yescharacteristic
729C2C3×#6436111yescharacteristic
730C2C3×#41×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C3C23×C3⋊D3
commutator, cosocleC22×C32C24×C3
FrattiniC22C23×C3×C3⋊D3
FittingC33×C4×D4C2
socleC22×C33C24
hypercenterC3×C4×D4C3⋊D3
hypocenterC32C3×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C33×C4×D4C2semidirect
2. C3×#64148C2semidirect
3. C3×#64148C2semidirect
4. C3×#64139C2semidirect
5. C3×#64138C2semidirect
6. C3×C4×#638C2semidirect
7. C2×C3×#3750C2semidirect
8. C3×#64103C2semidirect
9. C3×#64098C2semidirect
10. C3×#64093C2semidirect
11. C3×#64090C2semidirect
12. C3×#64090C2semidirect
13. C3×#64088C2semidirect
14. C3×#64085C2semidirect
15. C3×#64081C2semidirect
16. #10596011C3direct (N × H)
54. C32×C4×D4D3semidirect
55. C32×C4×D4C2×C3semidirect
56. #64148C2×C3semidirect
57. #64148C2×C3semidirect
58. #64139C2×C3semidirect
59. #64138C2×C3semidirect
60. C4×#638C2×C3semidirect
61. C2×#3750C2×C3semidirect
62. #64103C2×C3semidirect
63. #64098C2×C3semidirect
64. #64093C2×C3semidirect
65. #64090C2×C3semidirect
66. #64090C2×C3semidirect
67. #64088C2×C3semidirect
68. #64085C2×C3semidirect
69. #64081C2×C3semidirect
227. C3×C4×D4C3×D3semidirect
228. C3×C4×D4C3⋊D3semidirect
466. C4×D4C3×C3⋊D3semidirect
469. C33#553semidirect
649. C32#5540semidirect
650. C32C3×#553semidirect
722. C3C3×#5540semidirect
723. C3#10596011direct (N × H)

Maximal subgroups

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

subgroupindex
C33×C4×D42
C3×#641482
C3×#641392
C3×#641382
C3×C4×#6382
C2×C3×#37502
C3×#641032
C3×#640982
C3×#640932
C3×#640902
C3×#640882
C3×#640852
C3×#640812
#105960113
C3×#55403