Finite Group Databasebeta

← C32×#5705 #13179083

Subgroups — C32×#5705 #13179083

Order 1728.

1728 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#126C211yesmaximal, characteristic, complemented
2C32×#897C211yesmaximal, characteristic, complemented
3C32×#896C211yesmaximal, characteristic, complemented
4C32×#894C211yesmaximal, characteristic, complemented
5C32×#894C211yesmaximal, characteristic, complemented
6C32×#893C211yesmaximal, characteristic, complemented
7C32×#892C211yesmaximal, characteristic, complemented
8C32×#885C211yesmaximal, characteristic, complemented
9C32×#883C211yesmaximal, characteristic, complemented
10C32×#882C211yesmaximal, characteristic
11C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
12C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
13C32×#879C211yesmaximal, characteristic, complemented
14C32×C4×D12C211yesmaximal, characteristic, complemented
15C32×#872C211yesmaximal, characteristic, complemented
16C32×#551—31nomaximal
17C3×#5705C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C32×#67C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×C32×D12C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic, complemented
27C2×C32×Dic6C2211yescharacteristic, complemented
28C33×C4⋊C4C2211yescharacteristic, complemented
29C33×C4⋊C4C2211yescharacteristic, complemented
30C33×C4⋊C4C2211yescharacteristic, complemented
31C33×C22⋊C4C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic
33C33×C22⋊C4C2211yescharacteristic
34C33×C42C2211yescharacteristic, complemented
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
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, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47C32×C4⋊Dic3C2211yescharacteristic, complemented
48C32×Dic3⋊C4C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50C32×Dic3⋊C4C2211yescharacteristic, complemented
51C32×C4×Dic3C2211yescharacteristic, complemented
52C32×C4×Dic3C2211yescharacteristic, complemented
53C32×#126—24no—
54C32×#126—31no—
55C32×#126D311yescharacteristic, complemented
56C32×#126C2×C314yescomplemented
57C32×#124—31no—
58C32×#123—31no—
59C32×#123—31no—
60C32×#123—31no—
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×#897C2×C314yescomplemented
71C3×#896C2×C314yescomplemented
72C3×#894C2×C314yescomplemented
73C3×#894C2×C314yescomplemented
74C3×#893C2×C314yescomplemented
75C3×#892C2×C314yescomplemented
76C3×#885C2×C314yescomplemented
77C3×#883C2×C314yescomplemented
78C3×#882C2×C314yes—
79C3×D3×C22⋊C4C2×C314yescomplemented
80C3×D3×C22⋊C4C2×C314yescomplemented
81C3×#879C2×C314yescomplemented
82C3×C4×D12C2×C314yescomplemented
83C3×#872C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3—22no—
86C22×C32×D3—22no—
87C22×C32×D3—41no—
88C22×C32×D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C32×#67—41no—
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C32×D12—22no—
104C32×D12—22no—
105C32×C4×D3—22no—
106C32×C4×D3—22no—
107C32×C4×D3—41no—
108C32×C4×D3—41no—
109C32×C4×D3—41no—
110C32×Dic6—41no—
111C3×#551—34no—
112#5705C3211yescharacteristic, direct product factor
113C24×C32—31no—
114C23×C3×D3C22×C314yes—
115C2×C32×Q8—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—
124C2×C3×#67C22×C314yes—
125C2×C3×D12C22×C314yes—
126C2×C3×D12C22×C314yes—
127C2×C3×C4×D3C22×C314yes—
128C2×C3×C4×D3C22×C314yes—
129C2×C3×C4×D3C22×C314yes—
130C2×C3×C4×D3C22×C314yes—
131C2×C3×C4×D3C22×C314yescomplemented
132C2×C3×Dic6C22×C314yescomplemented
133C32×C4⋊C4—24no—
134C32×C4⋊C4—24no—
135C32×C4⋊C4—24no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4C2×D311yescharacteristic, complemented
142C32×C4⋊C4C2×D311yescharacteristic, complemented
143C32×C4⋊C4C2×D311yescharacteristic, complemented
144C32×C4⋊C4C22×C314yescomplemented
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
163C32×C22⋊C4C2×D311yescharacteristic
164C32×C22⋊C4C22×C314yes—
165C32×C22⋊C4C22×C314yes—
166C32×C22⋊C4C22×C314yes—
167C32×C42—24no—
168C32×C42—31no—
169C32×C42—31no—
170C32×C42C2×D311yescharacteristic, complemented
171C32×C42C22×C314yescomplemented
172C3×#217C22×C314yes—
173C3×#217C22×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×C314yescomplemented
181C3×(C2×D3)⋊C4C22×C314yescomplemented
182C3×(C2×D3)⋊C4C22×C314yescomplemented
183C3×C4⋊Dic3C22×C314yescomplemented
184C3×C4⋊Dic3C22×C314yescomplemented
185C3×Dic3⋊C4C22×C314yescomplemented
186C3×Dic3⋊C4C22×C314yescomplemented
187C3×Dic3⋊C4C22×C314yescomplemented
188C3×C4×Dic3C22×C314yescomplemented
189C3×C4×Dic3C22×C314yescomplemented
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—44no—
202C2×C32×D3#4112yes—
203C2×C32×D3#4112yes—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C33×C4—21no—
208C33×C4—21no—
209C33×C4—21no—
210C32×Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#126—24no—
216C3×#126—34no—
217C3×#126C3×D314yescomplemented
218C3×#126C2×C3211yescharacteristic, complemented
219C3×#124—34no—
220C3×#123—34no—
221C3×#123—34no—
222C3×#123—34no—
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#897C2×C3211yescharacteristic, complemented
233#896C2×C3211yescharacteristic, complemented
234#894C2×C3211yescharacteristic, complemented
235#894C2×C3211yescharacteristic, complemented
236#893C2×C3211yescharacteristic, complemented
237#892C2×C3211yescharacteristic, complemented
238#885C2×C3211yescharacteristic, complemented
239#883C2×C3211yescharacteristic, complemented
240#882C2×C3211yescharacteristic
241D3×C22⋊C4C2×C3211yescharacteristic, complemented
242D3×C22⋊C4C2×C3211yescharacteristic, complemented
243#879C2×C3211yescharacteristic, complemented
244C4×D12C2×C3211yescharacteristic, complemented
245#872C2×C3211yescharacteristic, complemented
246C23×C32—24no—
247C23×C32—31no—
248C23×C32—31no—
249C23×C32—31no—
250C23×C32—62no—
251C23×C32—62no—
252C23×C32—121no—
253C23×C32C22×D311yescharacteristic
254C23×C32C23×C314yes—
255C22×C3×D3—28no—
256C22×C3×D3—28no—
257C22×C3×D3—44no—
258C22×C3×D3C23×C314yes—
259C22×C3×D3C23×C314yes—
260C22×C3×D3C23×C314yes—
261C32×Q8—121no—
262C32×D4—62no—
263C32×D4—62no—
264C32×D4—121no—
265C2×C32×C4—24no—
266C2×C32×C4—24no—
267C2×C32×C4—24no—
268C2×C32×C4—24no—
269C2×C32×C4—24no—
270C2×C32×C4—24no—
271C2×C32×C4—31no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—31no—
276C2×C32×C4—62no—
277C2×C32×C4—62no—
278C2×C32×C4—121no—
279C2×C32×C4—121no—
280C2×C32×C4—121no—
281C2×C32×C4C22×D311yescharacteristic
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—
292C2×C32×C4C23×C314yes—
293C3×#67—44no—
294C2×C3×Dic3C23×C314yes—
295C2×C3×Dic3C23×C314yes—
296C2×C3×Dic3C23×C314yes—
297C2×C3×Dic3C23×C314yes—
298C2×C3×Dic3C23×C314yes—
299C3×D12—28no—
300C3×D12—28no—
301C3×C4×D3—28no—
302C3×C4×D3—28no—
303C3×C4×D3—44no—
304C3×C4×D3—44no—
305C3×C4×D3—44no—
306C3×Dic6—44no—
307#551—31noSylow
308C2×C33—41no—
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C2×C33H(5,𝔽2)11yescharacteristic
312C32×D3—22no—
313C32×D3—22no—
314C32×D3—41no—
315C24×C3—34no—
316C23×D3C22×C3211yescharacteristic
317C2×C3×Q8—34no—
318C2×C3×D4—34no—
319C2×C3×D4—34no—
320C2×C3×D4—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×D12C22×C3211yescharacteristic
328C2×D12C22×C3211yescharacteristic
329C2×C4×D3C22×C3211yescharacteristic
330C2×C4×D3C22×C3211yescharacteristic
331C2×C4×D3C22×C3211yescharacteristic
332C2×C4×D3C22×C3211yescharacteristic
333C2×C4×D3C22×C3211yescharacteristic, complemented
334C2×Dic6C22×C3211yescharacteristic, complemented
335C3×C4⋊C4—24no—
336C3×C4⋊C4—24no—
337C3×C4⋊C4—24no—
338C3×C4⋊C4—34no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4C2×C3×D314yescomplemented
344C3×C4⋊C4C2×C3×D314yescomplemented
345C3×C4⋊C4C2×C3×D314yescomplemented
346C3×C4⋊C4C22×C3211yescharacteristic, complemented
347C3×C4⋊C4C22×C3211yescharacteristic, complemented
348C3×C4⋊C4C22×C3211yescharacteristic, complemented
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—24no—
352C3×C22⋊C4—34no—
353C3×C22⋊C4—34no—
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⋊C4C2×C3×D314yes—
364C3×C22⋊C4C2×C3×D314yes—
365C3×C22⋊C4C2×C3×D314yes—
366C3×C22⋊C4C22×C3211yescharacteristic
367C3×C22⋊C4C22×C3211yescharacteristic
368C3×C22⋊C4C22×C3211yescharacteristic
369C3×C42—24no—
370C3×C42—34no—
371C3×C42—34no—
372C3×C42C2×C3×D314yescomplemented
373C3×C42C22×C3211yescharacteristic, complemented
374#217C22×C3211yescharacteristic
375#217C22×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
382(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
383(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
384(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
385C4⋊Dic3C22×C3211yescharacteristic, complemented
386C4⋊Dic3C22×C3211yescharacteristic, complemented
387Dic3⋊C4C22×C3211yescharacteristic, complemented
388Dic3⋊C4C22×C3211yescharacteristic, complemented
389Dic3⋊C4C22×C3211yescharacteristic, complemented
390C4×Dic3C22×C3211yescharacteristic, complemented
391C4×Dic3C22×C3211yescharacteristic, complemented
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—24no—
396C22×C32—24no—
397C22×C32—24no—
398C22×C32—24no—
399C22×C32—32no—
400C22×C32—32no—
401C22×C32—44no—
402C22×C32—44no—
403C22×C32—44no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32—61no—
408C22×C32—61no—
409C22×C32—61no—
410C22×C32—61no—
411C22×C32—124no—
412C22×C32C23×D311yescharacteristic
413C22×C32C24×C314yes—
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×D3—24no—
421C2×C3×D3—416no—
422C2×C3×D3C3×#4118yes—
423C2×C3×D3C3×#4118yes—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—24no—
431C32×C4—24no—
432C32×C4—24no—
433C32×C4—24no—
434C32×C4—24no—
435C32×C4—24no—
436C32×C4—44no—
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—
452#126—31no—
453#126C32×D311yescharacteristic, complemented
454#124—31no—
455#123—31no—
456#123—31no—
457#123—31no—
458C22⋊Q8—31no—
459C22⋊Q8—31no—
460#120—31no—
461C4×D4—31no—
462C4×D4—31no—
463#117—31no—
464#117—31no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—31no—
467C33#55111yescharacteristic, complemented, Sylow
468C23×C3—24no—
469C23×C3—34no—
470C23×C3—34no—
471C23×C3—34no—
472C23×C3—68no—
473C23×C3—68no—
474C23×C3—124no—
475C23×C3C22×C3×D314yes—
476C23×C3C23×C3211yescharacteristic
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—41no—
480C22×D3C23×C3211yescharacteristic
481C22×D3C23×C3211yescharacteristic
482C22×D3C23×C3211yescharacteristic
483C3×Q8—124no—
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—24no—
493C2×C3×C4—34no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—34no—
497C2×C3×C4—34no—
498C2×C3×C4—68no—
499C2×C3×C4—68no—
500C2×C3×C4—124no—
501C2×C3×C4—124no—
502C2×C3×C4—124no—
503C2×C3×C4C22×C3×D314yes—
504C2×C3×C4C22×C3×D314yes—
505C2×C3×C4C22×C3×D314yes—
506C2×C3×C4C22×C3×D314yes—
507C2×C3×C4C22×C3×D314yes—
508C2×C3×C4C22×C3×D314yes—
509C2×C3×C4C23×C3211yescharacteristic
510C2×C3×C4C23×C3211yescharacteristic
511C2×C3×C4C23×C3211yescharacteristic
512C2×C3×C4C23×C3211yescharacteristic
513C2×C3×C4C23×C3211yescharacteristic
514C2×C3×C4C23×C3211yescharacteristic
515#67—41no—
516C2×Dic3C23×C3211yescharacteristic
517C2×Dic3C23×C3211yescharacteristic
518C2×Dic3C23×C3211yescharacteristic
519C2×Dic3C23×C3211yescharacteristic
520C2×Dic3C23×C3211yescharacteristic
521D12—22no—
522D12—22no—
523C4×D3—22no—
524C4×D3—22no—
525C4×D3—41no—
526C4×D3—41no—
527C4×D3—41no—
528Dic6—41no—
529C2×C32—24no—
530C2×C32—24no—
531C2×C32—24no—
532C2×C32—41no—
533C2×C32—44no—
534C2×C32—62no—
535C2×C32—62no—
536C2×C32—84no—
537C2×C32—121no—
538C2×C32D3×#4111yescharacteristic
539C2×C32D3×#4111yescharacteristic
540C2×C32#100911yescharacteristic
541C2×C32C2×C3×#4114yes—
542C2×C32C2×C3×#4114yes—
543C2×C32C3×H(5,𝔽2)14yes—
544C3×D3—28no—
545C3×D3—28no—
546C3×D3—44no—
547C24—31no—
548C2×Q8—31no—
549C2×D4—31no—
550C2×D4—31no—
551C2×D4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4C2×C32×D311yescharacteristic, complemented
563C4⋊C4C2×C32×D311yescharacteristic, complemented
564C4⋊C4C2×C32×D311yescharacteristic, complemented
565C22⋊C4—31no—
566C22⋊C4—31no—
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4C2×C32×D311yescharacteristic
577C22⋊C4C2×C32×D311yescharacteristic
578C22⋊C4C2×C32×D311yescharacteristic
579C42—31no—
580C42—31no—
581C42C2×C32×D311yescharacteristic, complemented
582C22×C3—24no—
583C22×C3—24no—
584C22×C3—24no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—24no—
589C22×C3—38no—
590C22×C3—38no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—64no—
597C22×C3—64no—
598C22×C3—64no—
599C22×C3—64no—
600C22×C3—64no—
601C22×C3—1216no—
602C22×C3C23×C3×D314yes—
603C22×C3C24×C3211yescharacteristic
604C2×D3—21no—
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—44no—
612C2×D3C32×#4112yes—
613C2×D3C32×#4112yes—
614C3×C4—24no—
615C3×C4—24no—
616C3×C4—24no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—24no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—44no—
627C3×C4—44no—
628C3×C4—44no—
629C3×C4—44no—
630C3×C4—44no—
631C3×C4—44no—
632C3×C4—64no—
633C3×C4—64no—
634C3×C4—64no—
635C3×C4—64no—
636C3×C4—64no—
637Dic3—21no—
638Dic3—21no—
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642C32—24no—
643C32#570511yescharacteristic, direct product factor
644C32C3×#55114yescomplemented
645C23—31no—
646C23—31no—
647C23—31no—
648C23—62no—
649C23—62no—
650C23—121no—
651C23C22×C32×D311yescharacteristic
652Q8—121no—
653D4—62no—
654D4—62no—
655D4—121no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4C22×C32×D311yescharacteristic
667C2×C4C22×C32×D311yescharacteristic
668C2×C4C22×C32×D311yescharacteristic
669C2×C4C22×C32×D311yescharacteristic
670C2×C4C22×C32×D311yescharacteristic
671C2×C4C22×C32×D311yescharacteristic
672C2×C3—24no—
673C2×C3—24no—
674C2×C3—24no—
675C2×C3—41no—
676C2×C3—44no—
677C2×C3—68no—
678C2×C3—68no—
679C2×C3—84no—
680C2×C3—124no—
681C2×C3C3×D3×#4114yes—
682C2×C3C3×D3×#4114yes—
683C2×C3C3×#100914yes—
684C2×C3C2×C32×#4111yescharacteristic
685C2×C3C2×C32×#4111yescharacteristic
686C2×C3C32×H(5,𝔽2)11yescharacteristic
687D3—22no—
688D3—22no—
689D3—41no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—32no—
694C22—32no—
695C22—61no—
696C22—61no—
697C22—61no—
698C22—61no—
699C22—61no—
700C22—61no—
701C22—61no—
702C22—124no—
703C22C23×C32×D311yescharacteristic
704C4—21no—
705C4—21no—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—61no—
711C4—61no—
712C4—61no—
713C4—61no—
714C4—61no—
715C3—24no—
716C3C3×#570514yesdirect product factor
717C3C32×#55111yescharacteristic, complemented
718C2—41no—
719C2—62no—
720C2—62no—
721C2—121no—
722C2C32×D3×#4111yescharacteristic
723C2C32×D3×#4111yescharacteristic
724C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#126C2
socleC22×C33C24
prime radicalC32×#882C2
hypercenterC32×#126D3
hypocenterC3C32×#551
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×#897C2semidirect
3. C32×#896C2semidirect
4. C32×#894C2semidirect
5. C32×#894C2semidirect
6. C32×#893C2semidirect
7. C32×#892C2semidirect
8. C32×#885C2semidirect
9. C32×#883C2semidirect
11. C32×D3×C22⋊C4C2semidirect
12. C32×D3×C22⋊C4C2semidirect
13. C32×#879C2semidirect
14. C32×C4×D12C2semidirect
15. C32×#872C2semidirect
17. C3×#5705C3direct (N × H)
26. C2×C32×C4×D3C22semidirect
27. C2×C32×Dic6C22semidirect
28. C33×C4⋊C4C22semidirect
29. C33×C4⋊C4C22semidirect
30. C33×C4⋊C4C22semidirect
34. C33×C42C22semidirect
43. C32×(C2×D3)⋊C4C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. C32×C4⋊Dic3C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. C32×C4×Dic3C22semidirect
52. C32×C4×Dic3C22semidirect
55. C32×#126D3semidirect
56. C32×#126C2×C3semidirect
70. C3×#897C2×C3semidirect
71. C3×#896C2×C3semidirect
72. C3×#894C2×C3semidirect
73. C3×#894C2×C3semidirect
74. C3×#893C2×C3semidirect
75. C3×#892C2×C3semidirect
76. C3×#885C2×C3semidirect
77. C3×#883C2×C3semidirect
79. C3×D3×C22⋊C4C2×C3semidirect
80. C3×D3×C22⋊C4C2×C3semidirect
81. C3×#879C2×C3semidirect
82. C3×C4×D12C2×C3semidirect
83. C3×#872C2×C3semidirect
112. #5705C32direct (N × H)
131. C2×C3×C4×D3C22×C3semidirect
132. C2×C3×Dic6C22×C3semidirect
141. C32×C4⋊C4C2×D3semidirect
142. C32×C4⋊C4C2×D3semidirect
143. C32×C4⋊C4C2×D3semidirect
144. C32×C4⋊C4C22×C3semidirect
145. C32×C4⋊C4C22×C3semidirect
146. C32×C4⋊C4C22×C3semidirect
170. C32×C42C2×D3semidirect
171. C32×C42C22×C3semidirect
180. C3×(C2×D3)⋊C4C22×C3semidirect
181. C3×(C2×D3)⋊C4C22×C3semidirect
182. C3×(C2×D3)⋊C4C22×C3semidirect
183. C3×C4⋊Dic3C22×C3semidirect
184. C3×C4⋊Dic3C22×C3semidirect
185. C3×Dic3⋊C4C22×C3semidirect
186. C3×Dic3⋊C4C22×C3semidirect
187. C3×Dic3⋊C4C22×C3semidirect
188. C3×C4×Dic3C22×C3semidirect
189. C3×C4×Dic3C22×C3semidirect
217. C3×#126C3×D3semidirect
218. C3×#126C2×C32semidirect
232. #897C2×C32semidirect
233. #896C2×C32semidirect
234. #894C2×C32semidirect
235. #894C2×C32semidirect
236. #893C2×C32semidirect
237. #892C2×C32semidirect
238. #885C2×C32semidirect
239. #883C2×C32semidirect
241. D3×C22⋊C4C2×C32semidirect
242. D3×C22⋊C4C2×C32semidirect
243. #879C2×C32semidirect
244. C4×D12C2×C32semidirect
245. #872C2×C32semidirect
333. C2×C4×D3C22×C32semidirect
334. C2×Dic6C22×C32semidirect
343. C3×C4⋊C4C2×C3×D3semidirect
344. C3×C4⋊C4C2×C3×D3semidirect
345. C3×C4⋊C4C2×C3×D3semidirect
346. C3×C4⋊C4C22×C32semidirect
347. C3×C4⋊C4C22×C32semidirect
348. C3×C4⋊C4C22×C32semidirect
372. C3×C42C2×C3×D3semidirect
373. C3×C42C22×C32semidirect
382. (C2×D3)⋊C4C22×C32semidirect
383. (C2×D3)⋊C4C22×C32semidirect
384. (C2×D3)⋊C4C22×C32semidirect
385. C4⋊Dic3C22×C32semidirect
386. C4⋊Dic3C22×C32semidirect
387. Dic3⋊C4C22×C32semidirect
388. Dic3⋊C4C22×C32semidirect
389. Dic3⋊C4C22×C32semidirect
390. C4×Dic3C22×C32semidirect
391. C4×Dic3C22×C32semidirect
453. #126C32×D3semidirect
467. C33#551semidirect
562. C4⋊C4C2×C32×D3semidirect
563. C4⋊C4C2×C32×D3semidirect
564. C4⋊C4C2×C32×D3semidirect
581. C42C2×C32×D3semidirect
643. C32#5705direct (N × H)
644. C32C3×#551semidirect
716. C3C3×#5705direct (N × H)
717. C3C32×#551semidirect

Maximal subgroups

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

subgroupindex
C33×#1262
C32×#8972
C32×#8962
C32×#8942
C32×#8932
C32×#8922
C32×#8852
C32×#8832
C32×#8822
C32×D3×C22⋊C42
C32×#8792
C32×C4×D122
C32×#8722
C32×#5513
C3×#57053