Finite Group Databasebeta

← C32×#5709 #13179087

Subgroups — C32×#5709 #13179087

Order 1728.

1668 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#126C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic, complemented
3C32×#895C211yesmaximal, characteristic, complemented
4C32×#894C211yesmaximal, characteristic, complemented
5C32×#893C211yesmaximal, characteristic, complemented
6C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
7C32×#889C211yesmaximal, characteristic, complemented
8C32×#886C211yesmaximal, characteristic, complemented
9C32×#884C211yesmaximal, characteristic, complemented
10C32×#884C211yesmaximal, characteristic, complemented
11C32×#884C211yesmaximal, characteristic, complemented
12C32×#67⋊C4C211yesmaximal, characteristic, complemented
13C32×#67⋊C4C211yesmaximal, characteristic, complemented
14C32×C4×D12C211yesmaximal, characteristic, complemented
15C32×#872C211yesmaximal, characteristic, complemented
16C32×#553—31nomaximal
17C3×#5709C314yesmaximal, direct product factor
18C2×C32×#67C2211yescharacteristic
19C2×C32×#67C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C2×C32×D12C2211yescharacteristic
23C2×C32×D12C2211yescharacteristic
24C2×C32×D12C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic
27C2×C32×C4×D3C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic
30C33×C4⋊C4C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic
32C33×C4⋊C4C2211yescharacteristic
33C33×C22⋊C4C2211yescharacteristic
34C33×C22⋊C4C2211yescharacteristic
35C33×C22⋊C4C2211yescharacteristic
36C33×C42C2211yescharacteristic
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
45C32×C4⋊Dic3C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×Dic3⋊C4C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#126—24no—
54C32×#126—31no—
55C32×#126D311yescharacteristic, complemented
56C32×#126C2×C314yescomplemented
57C32×#125—31no—
58C32×#123—31no—
59C32×#123—31no—
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×#898C2×C314yescomplemented
71C3×#895C2×C314yescomplemented
72C3×#894C2×C314yescomplemented
73C3×#893C2×C314yescomplemented
74C3×D3×C4⋊C4C2×C314yescomplemented
75C3×#889C2×C314yescomplemented
76C3×#886C2×C314yescomplemented
77C3×#884C2×C314yescomplemented
78C3×#884C2×C314yescomplemented
79C3×#884C2×C314yescomplemented
80C3×#67⋊C4C2×C314yescomplemented
81C3×#67⋊C4C2×C314yescomplemented
82C3×C4×D12C2×C314yescomplemented
83C3×#872C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C32×#67—22no—
95C32×#67—22no—
96C32×#67—41no—
97C2×C32×Dic3—41no—
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C32×D12—22no—
104C32×D12—22no—
105C32×D12—41no—
106C32×C4×D3—22no—
107C32×C4×D3—22no—
108C32×C4×D3—41no—
109C32×C4×D3—41no—
110C32×C4×D3—41no—
111C3×#553—34no—
112#5709C3211yescharacteristic, direct product factor
113C2×C32×D4—31no—
114C2×C32×D4—31no—
115C2×C32×D4—31no—
116C2×C32×D4—31no—
117C2×C32×D4—31no—
118C2×C32×D4—31no—
119C22×C32×C4—31no—
120C22×C32×C4—31no—
121C22×C32×C4—31no—
122C22×C32×C4—31no—
123C22×C32×C4—31no—
124C22×C32×C4—31no—
125C2×C3×#67C22×C314yes—
126C2×C3×#67C22×C314yes—
127C2×C3×#67C22×C314yes—
128C22×C3×Dic3C22×C314yes—
129C2×C3×D12C22×C314yes—
130C2×C3×D12C22×C314yes—
131C2×C3×D12C22×C314yes—
132C2×C3×C4×D3C22×C314yes—
133C2×C3×C4×D3C22×C314yes—
134C2×C3×C4×D3C22×C314yes—
135C2×C3×C4×D3C22×C314yes—
136C2×C3×C4×D3C22×C314yes—
137C32×C4⋊C4—24no—
138C32×C4⋊C4—24no—
139C32×C4⋊C4—24no—
140C32×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
148C32×C4⋊C4C2×D311yescharacteristic
149C32×C4⋊C4C2×D311yescharacteristic
150C32×C4⋊C4C22×C314yes—
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—24no—
170C32×C42—31no—
171C32×C42—31no—
172C32×C42C2×D311yescharacteristic
173C32×C42C22×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×C314yes—
182C3×C4⋊Dic3C22×C314yes—
183C3×Dic3⋊C4C22×C314yes—
184C3×Dic3⋊C4C22×C314yes—
185C3×Dic3⋊C4C22×C314yes—
186C3×Dic3⋊C4C22×C314yes—
187C3×Dic3⋊C4C22×C314yes—
188C3×C4×Dic3C22×C314yes—
189C3×C4×Dic3C22×C314yes—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33C2411yescharacteristic
194C2×C32×D3—21no—
195C2×C32×D3—21no—
196C2×C32×D3—21no—
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—
208C33×C4—21no—
209C32×Dic3—21no—
210C32×Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3#4112yes—
214C3×#126—24no—
215C3×#126—34no—
216C3×#126C3×D314yescomplemented
217C3×#126C2×C3211yescharacteristic, complemented
218C3×#125—34no—
219C3×#123—34no—
220C3×#123—34no—
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#898C2×C3211yescharacteristic, complemented
232#895C2×C3211yescharacteristic, complemented
233#894C2×C3211yescharacteristic, complemented
234#893C2×C3211yescharacteristic, complemented
235D3×C4⋊C4C2×C3211yescharacteristic, complemented
236#889C2×C3211yescharacteristic, complemented
237#886C2×C3211yescharacteristic, complemented
238#884C2×C3211yescharacteristic, complemented
239#884C2×C3211yescharacteristic, complemented
240#884C2×C3211yescharacteristic, complemented
241#67⋊C4C2×C3211yescharacteristic, complemented
242#67⋊C4C2×C3211yescharacteristic, complemented
243C4×D12C2×C3211yescharacteristic, complemented
244#872C2×C3211yescharacteristic, complemented
245C23×C32—24no—
246C23×C32—31no—
247C23×C32—31no—
248C23×C32—31no—
249C23×C32C22×D311yescharacteristic
250C23×C32C23×C314yes—
251C22×C3×D3C23×C314yes—
252C22×C3×D3C23×C314yes—
253C22×C3×D3C23×C314yes—
254C32×D4—62no—
255C32×D4—62no—
256C32×D4—62no—
257C32×D4—62no—
258C32×D4—121no—
259C32×D4—121no—
260C2×C32×C4—24no—
261C2×C32×C4—24no—
262C2×C32×C4—24no—
263C2×C32×C4—24no—
264C2×C32×C4—24no—
265C2×C32×C4—24no—
266C2×C32×C4—31no—
267C2×C32×C4—31no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—62no—
272C2×C32×C4—62no—
273C2×C32×C4—121no—
274C2×C32×C4—121no—
275C2×C32×C4—121no—
276C2×C32×C4—121no—
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C23×C314yes—
284C2×C32×C4C23×C314yes—
285C2×C32×C4C23×C314yes—
286C2×C32×C4C23×C314yes—
287C2×C32×C4C23×C314yes—
288C2×C32×C4C23×C314yes—
289C3×#67—28no—
290C3×#67—28no—
291C3×#67—44no—
292C2×C3×Dic3—44no—
293C2×C3×Dic3C23×C314yes—
294C2×C3×Dic3C23×C314yes—
295C2×C3×Dic3C23×C314yes—
296C2×C3×Dic3C23×C314yes—
297C2×C3×Dic3C23×C314yes—
298C3×D12—28no—
299C3×D12—28no—
300C3×D12—44no—
301C3×C4×D3—28no—
302C3×C4×D3—28no—
303C3×C4×D3—44no—
304C3×C4×D3—44no—
305C3×C4×D3—44no—
306#553—31noSylow
307C2×C33—41no—
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33H(5,𝔽2)11yescharacteristic
311C32×D3—22no—
312C32×D3—41no—
313C32×D3—41no—
314C2×C3×D4—34no—
315C2×C3×D4—34no—
316C2×C3×D4—34no—
317C2×C3×D4—34no—
318C2×C3×D4—34no—
319C2×C3×D4—34no—
320C22×C3×C4—34no—
321C22×C3×C4—34no—
322C22×C3×C4—34no—
323C22×C3×C4—34no—
324C22×C3×C4—34no—
325C22×C3×C4—34no—
326C2×#67C22×C3211yescharacteristic
327C2×#67C22×C3211yescharacteristic
328C2×#67C22×C3211yescharacteristic
329C22×Dic3C22×C3211yescharacteristic
330C2×D12C22×C3211yescharacteristic
331C2×D12C22×C3211yescharacteristic
332C2×D12C22×C3211yescharacteristic
333C2×C4×D3C22×C3211yescharacteristic
334C2×C4×D3C22×C3211yescharacteristic
335C2×C4×D3C22×C3211yescharacteristic
336C2×C4×D3C22×C3211yescharacteristic
337C2×C4×D3C22×C3211yescharacteristic
338C3×C4⋊C4—24no—
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⋊C4—34no—
348C3×C4⋊C4C2×C3×D314yes—
349C3×C4⋊C4C2×C3×D314yes—
350C3×C4⋊C4C2×C3×D314yes—
351C3×C4⋊C4C22×C3211yescharacteristic
352C3×C4⋊C4C22×C3211yescharacteristic
353C3×C4⋊C4C22×C3211yescharacteristic
354C3×C22⋊C4—24no—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—24no—
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⋊C4C2×C3×D314yes—
365C3×C22⋊C4C2×C3×D314yes—
366C3×C22⋊C4C2×C3×D314yes—
367C3×C22⋊C4C22×C3211yescharacteristic
368C3×C22⋊C4C22×C3211yescharacteristic
369C3×C22⋊C4C22×C3211yescharacteristic
370C3×C42—24no—
371C3×C42—34no—
372C3×C42—34no—
373C3×C42C2×C3×D314yes—
374C3×C42C22×C3211yescharacteristic
375(C2×D3)⋊C4C22×C3211yescharacteristic
376(C2×D3)⋊C4C22×C3211yescharacteristic
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
382C4⋊Dic3C22×C3211yescharacteristic
383C4⋊Dic3C22×C3211yescharacteristic
384Dic3⋊C4C22×C3211yescharacteristic
385Dic3⋊C4C22×C3211yescharacteristic
386Dic3⋊C4C22×C3211yescharacteristic
387Dic3⋊C4C22×C3211yescharacteristic
388Dic3⋊C4C22×C3211yescharacteristic
389C4×Dic3C22×C3211yescharacteristic
390C4×Dic3C22×C3211yescharacteristic
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—24no—
395C22×C32—24no—
396C22×C32—24no—
397C22×C32—24no—
398C22×C32—32no—
399C22×C32—44no—
400C22×C32—44no—
401C22×C32—44no—
402C22×C32—61no—
403C22×C32—61no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32—61no—
408C22×C32—61no—
409C22×C32—61no—
410C22×C32C23×D311yescharacteristic
411C22×C32C24×C314yes—
412C2×C3×D3—24no—
413C2×C3×D3—24no—
414C2×C3×D3—24no—
415C2×C3×D3—24no—
416C2×C3×D3—24no—
417C2×C3×D3—24no—
418C2×C3×D3—24no—
419C2×C3×D3—24no—
420C2×C3×D3C3×#4118yes—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—24no—
428C32×C4—24no—
429C32×C4—24no—
430C32×C4—24no—
431C32×C4—24no—
432C32×C4—24no—
433C32×C4—32no—
434C32×C4—44no—
435C32×C4—44no—
436C32×C4—44no—
437C32×C4—44no—
438C32×C4—44no—
439C32×C4—44no—
440C32×C4—61no—
441C32×C4—61no—
442C32×C4—61no—
443C32×C4—61no—
444C3×Dic3—24no—
445C3×Dic3—24no—
446C3×Dic3—24no—
447C3×Dic3—24no—
448C3×Dic3C3×#4118yes—
449#126—31no—
450#126C32×D311yescharacteristic, complemented
451#125—31no—
452#123—31no—
453#123—31no—
454#121—31no—
455#121—31no—
456#121—31no—
457#121—31no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—31no—
462#117—31no—
463C2×C4⋊C4—31no—
464C33#55311yescharacteristic, complemented, Sylow
465C23×C3—24no—
466C23×C3—34no—
467C23×C3—34no—
468C23×C3—34no—
469C23×C3C22×C3×D314yes—
470C23×C3C23×C3211yescharacteristic
471C22×D3C23×C3211yescharacteristic
472C22×D3C23×C3211yescharacteristic
473C22×D3C23×C3211yescharacteristic
474C3×D4—68no—
475C3×D4—68no—
476C3×D4—68no—
477C3×D4—68no—
478C3×D4—124no—
479C3×D4—124no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—34no—
487C2×C3×C4—34no—
488C2×C3×C4—34no—
489C2×C3×C4—34no—
490C2×C3×C4—34no—
491C2×C3×C4—68no—
492C2×C3×C4—68no—
493C2×C3×C4—124no—
494C2×C3×C4—124no—
495C2×C3×C4—124no—
496C2×C3×C4—124no—
497C2×C3×C4C22×C3×D314yes—
498C2×C3×C4C22×C3×D314yes—
499C2×C3×C4C22×C3×D314yes—
500C2×C3×C4C22×C3×D314yes—
501C2×C3×C4C22×C3×D314yes—
502C2×C3×C4C22×C3×D314yes—
503C2×C3×C4C23×C3211yescharacteristic
504C2×C3×C4C23×C3211yescharacteristic
505C2×C3×C4C23×C3211yescharacteristic
506C2×C3×C4C23×C3211yescharacteristic
507C2×C3×C4C23×C3211yescharacteristic
508C2×C3×C4C23×C3211yescharacteristic
509#67—22no—
510#67—22no—
511#67—41no—
512C2×Dic3—41no—
513C2×Dic3C23×C3211yescharacteristic
514C2×Dic3C23×C3211yescharacteristic
515C2×Dic3C23×C3211yescharacteristic
516C2×Dic3C23×C3211yescharacteristic
517C2×Dic3C23×C3211yescharacteristic
518D12—22no—
519D12—22no—
520D12—41no—
521C4×D3—22no—
522C4×D3—22no—
523C4×D3—41no—
524C4×D3—41no—
525C4×D3—41no—
526C2×C32—24no—
527C2×C32—24no—
528C2×C32—24no—
529C2×C32—41no—
530C2×C32—44no—
531C2×C32—62no—
532C2×C32—84no—
533C2×C32—121no—
534C2×C32—121no—
535C2×C32D3×#4111yescharacteristic
536C2×C32D3×#4111yescharacteristic
537C2×C32#100911yescharacteristic
538C2×C32C2×C3×#4114yes—
539C2×C32C2×C3×#4114yes—
540C2×C32C3×H(5,𝔽2)14yes—
541C3×D3—28no—
542C3×D3—44no—
543C3×D3—44no—
544C2×D4—31no—
545C2×D4—31no—
546C2×D4—31no—
547C2×D4—31no—
548C2×D4—31no—
549C2×D4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4C2×C32×D311yescharacteristic
564C4⋊C4C2×C32×D311yescharacteristic
565C4⋊C4C2×C32×D311yescharacteristic
566C22⋊C4—31no—
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—31no—
573C22⋊C4C2×C32×D311yescharacteristic
574C22⋊C4C2×C32×D311yescharacteristic
575C22⋊C4C2×C32×D311yescharacteristic
576C42—31no—
577C42—31no—
578C42C2×C32×D311yescharacteristic
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—24no—
586C22×C3—38no—
587C22×C3—44no—
588C22×C3—44no—
589C22×C3—44no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—64no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—64no—
597C22×C3—64no—
598C22×C3C23×C3×D314yes—
599C22×C3C24×C3211yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—21no—
603C2×D3—21no—
604C2×D3—21no—
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—21no—
608C2×D3C32×#4112yes—
609C3×C4—24no—
610C3×C4—24no—
611C3×C4—24no—
612C3×C4—24no—
613C3×C4—24no—
614C3×C4—24no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—38no—
622C3×C4—44no—
623C3×C4—44no—
624C3×C4—44no—
625C3×C4—44no—
626C3×C4—44no—
627C3×C4—44no—
628C3×C4—64no—
629C3×C4—64no—
630C3×C4—64no—
631C3×C4—64no—
632Dic3—21no—
633Dic3—21no—
634Dic3—21no—
635Dic3—21no—
636Dic3C32×#4112yes—
637C32—24no—
638C32#570911yescharacteristic, direct product factor
639C32C3×#55314yescomplemented
640C23—31no—
641C23—31no—
642C23—31no—
643C23C22×C32×D311yescharacteristic
644D4—62no—
645D4—62no—
646D4—62no—
647D4—62no—
648D4—121no—
649D4—121no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—121no—
660C2×C4—121no—
661C2×C4C22×C32×D311yescharacteristic
662C2×C4C22×C32×D311yescharacteristic
663C2×C4C22×C32×D311yescharacteristic
664C2×C4C22×C32×D311yescharacteristic
665C2×C4C22×C32×D311yescharacteristic
666C2×C4C22×C32×D311yescharacteristic
667C2×C3—24no—
668C2×C3—24no—
669C2×C3—24no—
670C2×C3—41no—
671C2×C3—44no—
672C2×C3—68no—
673C2×C3—84no—
674C2×C3—124no—
675C2×C3—124no—
676C2×C3C3×D3×#4114yes—
677C2×C3C3×D3×#4114yes—
678C2×C3C3×#100914yes—
679C2×C3C2×C32×#4111yescharacteristic
680C2×C3C2×C32×#4111yescharacteristic
681C2×C3C32×H(5,𝔽2)11yescharacteristic
682D3—22no—
683D3—41no—
684D3—41no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—32no—
689C22—61no—
690C22—61no—
691C22—61no—
692C22—61no—
693C22—61no—
694C22—61no—
695C22—61no—
696C22—61no—
697C22C23×C32×D311yescharacteristic
698C4—21no—
699C4—21no—
700C4—21no—
701C4—21no—
702C4—21no—
703C4—21no—
704C4—32no—
705C4—61no—
706C4—61no—
707C4—61no—
708C4—61no—
709C3—24no—
710C3C3×#570914yesdirect product factor
711C3C32×#55311yescharacteristic, complemented
712C2—41no—
713C2—62no—
714C2—121no—
715C2—121no—
716C2C32×D3×#4111yescharacteristic
717C2C32×D3×#4111yescharacteristic
718C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#126C2
socleC22×C33C24
hypercenterC32×#126D3
hypocenterC3C32×#553
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#126

Complements

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

NH ≅ G/Ntype
1. C33×#126C2semidirect
2. C32×#898C2semidirect
3. C32×#895C2semidirect
4. C32×#894C2semidirect
5. C32×#893C2semidirect
6. C32×D3×C4⋊C4C2semidirect
7. C32×#889C2semidirect
8. C32×#886C2semidirect
9. C32×#884C2semidirect
10. C32×#884C2semidirect
11. C32×#884C2semidirect
12. C32×#67⋊C4C2semidirect
13. C32×#67⋊C4C2semidirect
14. C32×C4×D12C2semidirect
15. C32×#872C2semidirect
17. C3×#5709C3direct (N × H)
55. C32×#126D3semidirect
56. C32×#126C2×C3semidirect
70. C3×#898C2×C3semidirect
71. C3×#895C2×C3semidirect
72. C3×#894C2×C3semidirect
73. C3×#893C2×C3semidirect
74. C3×D3×C4⋊C4C2×C3semidirect
75. C3×#889C2×C3semidirect
76. C3×#886C2×C3semidirect
77. C3×#884C2×C3semidirect
78. C3×#884C2×C3semidirect
79. C3×#884C2×C3semidirect
80. C3×#67⋊C4C2×C3semidirect
81. C3×#67⋊C4C2×C3semidirect
82. C3×C4×D12C2×C3semidirect
83. C3×#872C2×C3semidirect
112. #5709C32direct (N × H)
216. C3×#126C3×D3semidirect
217. C3×#126C2×C32semidirect
231. #898C2×C32semidirect
232. #895C2×C32semidirect
233. #894C2×C32semidirect
234. #893C2×C32semidirect
235. D3×C4⋊C4C2×C32semidirect
236. #889C2×C32semidirect
237. #886C2×C32semidirect
238. #884C2×C32semidirect
239. #884C2×C32semidirect
240. #884C2×C32semidirect
241. #67⋊C4C2×C32semidirect
242. #67⋊C4C2×C32semidirect
243. C4×D12C2×C32semidirect
244. #872C2×C32semidirect
450. #126C32×D3semidirect
464. C33#553semidirect
638. C32#5709direct (N × H)
639. C32C3×#553semidirect
710. C3C3×#5709direct (N × H)
711. C3C32×#553semidirect

Maximal subgroups

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

subgroupindex
C33×#1262
C32×#8982
C32×#8952
C32×#8942
C32×#8932
C32×D3×C4⋊C42
C32×#8892
C32×#8862
C32×#8842
C32×#67⋊C42
C32×C4×D122
C32×#8722
C32×#5533
C3×#57093