Finite Group Databasebeta

← C32×#5613 #13178992

Subgroups — C32×#5613 #13178992

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#121C211yesmaximal, characteristic, complemented
2C32×#939C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic, complemented
4C32×#937C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6C32×#936C211yesmaximal, characteristic, complemented
7C32×#935C211yesmaximal, characteristic, complemented
8C32×#929C211yesmaximal, characteristic, complemented
9C32×C4×#67C211yesmaximal, characteristic, complemented
10C32×#898C211yesmaximal, characteristic, complemented
11C32×#896C211yesmaximal, characteristic, complemented
12C32×#885C211yesmaximal, characteristic, complemented
13C32×#67⋊C4C211yesmaximal, characteristic, complemented
14C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
15C32×#879C211yesmaximal, characteristic, complemented
16C32×#538—31nomaximal
17C3×#5613C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic, complemented
22C22×C33×C4C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic, complemented
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic
30C2×C32×Dic6C2211yescharacteristic, complemented
31C33×C4⋊C4C2211yescharacteristic, complemented
32C33×C22⋊C4C2211yescharacteristic
33C33×C22⋊C4C2211yescharacteristic, complemented
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic, complemented
38C32×#217C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48C32×Dic3⋊C4C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50C32×Dic3⋊C4C2211yescharacteristic, complemented
51C32×C4×Dic3C2211yescharacteristic, complemented
52C32×C4×Dic3C2211yescharacteristic, complemented
53C32×#126—31no—
54C32×#126—31no—
55C32×#124—31no—
56C32×#124—31no—
57C32×#123—31no—
58C32×#123—31no—
59C32×C22⋊Q8—31no—
60C32×#121—24no—
61C32×#121—31no—
62C32×#121—31no—
63C32×#121D311yescharacteristic, complemented
64C32×#121C2×C314yescomplemented
65C32×#120—31no—
66C32×#120—31no—
67C32×C4×D4—31no—
68C32×C4×D4—31no—
69C2×C32×C22⋊C4—31no—
70C3×#939C2×C314yescomplemented
71C3×#938C2×C314yescomplemented
72C3×#937C2×C314yescomplemented
73C3×#937C2×C314yescomplemented
74C3×#936C2×C314yescomplemented
75C3×#935C2×C314yescomplemented
76C3×#929C2×C314yescomplemented
77C3×C4×#67C2×C314yescomplemented
78C3×#898C2×C314yescomplemented
79C3×#896C2×C314yescomplemented
80C3×#885C2×C314yescomplemented
81C3×#67⋊C4C2×C314yescomplemented
82C3×D3×C22⋊C4C2×C314yescomplemented
83C3×#879C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C23×C33C2311yescharacteristic
87C22×C32×D3—22no—
88C22×C32×D3—41no—
89C22×C32×D3—41no—
90C22×C32×D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C33×D4—41no—
93C33×D4—41no—
94C33×D4—41no—
95C2×C33×C4—41no—
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100C32×#67—22no—
101C32×#67—22no—
102C32×#67—41no—
103C32×#67—41no—
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C32×C4×D3—41no—
112C32×C4×D3—41no—
113C32×Dic6—41no—
114C3×#538—34no—
115#5613C3211yescharacteristic, direct product factor
116C24×C32—31no—
117C23×C3×D3C22×C314yes—
118C2×C32×Q8—31no—
119C2×C32×D4—24no—
120C2×C32×D4—24no—
121C2×C32×D4—24no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C2×C32×D4—31no—
125C2×C32×D4—31no—
126C2×C32×D4C2×D311yescharacteristic
127C2×C32×D4C2×D311yescharacteristic
128C2×C32×D4C2×D311yescharacteristic, complemented
129C2×C32×D4C22×C314yes—
130C2×C32×D4C22×C314yes—
131C2×C32×D4C22×C314yescomplemented
132C22×C32×C4—24no—
133C22×C32×C4—31no—
134C22×C32×C4—31no—
135C22×C32×C4—31no—
136C22×C32×C4C2×D311yescharacteristic, complemented
137C22×C32×C4C22×C314yescomplemented
138C2×C3×#67C22×C314yes—
139C2×C3×#67C22×C314yes—
140C2×C3×#67C22×C314yes—
141C2×C3×#67C22×C314yes—
142C22×C3×Dic3C22×C314yescomplemented
143C2×C3×C4×D3C22×C314yes—
144C2×C3×C4×D3C22×C314yes—
145C2×C3×Dic6C22×C314yescomplemented
146C32×C4⋊C4—24no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C4⋊C4C2×D311yescharacteristic, complemented
153C32×C4⋊C4C22×C314yescomplemented
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⋊C4—31no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167C32×C22⋊C4—31no—
168C32×C22⋊C4C2×D311yescharacteristic
169C32×C22⋊C4C2×D311yescharacteristic, complemented
170C32×C22⋊C4C22×C314yes—
171C32×C22⋊C4C22×C314yescomplemented
172C32×C42—31no—
173C32×C42—31no—
174C3×#217C22×C314yes—
175C3×#217C22×C314yes—
176C3×#217C22×C314yes—
177C3×#217C22×C314yescomplemented
178C3×#217C22×C314yescomplemented
179C3×#217C22×C314yescomplemented
180C3×(C2×D3)⋊C4C22×C314yes—
181C3×(C2×D3)⋊C4C22×C314yes—
182C3×(C2×D3)⋊C4C22×C314yes—
183C3×(C2×D3)⋊C4C22×C314yes—
184C3×(C2×D3)⋊C4C22×C314yes—
185C3×(C2×D3)⋊C4C22×C314yes—
186C3×C4⋊Dic3C22×C314yescomplemented
187C3×Dic3⋊C4C22×C314yescomplemented
188C3×Dic3⋊C4C22×C314yescomplemented
189C3×Dic3⋊C4C22×C314yescomplemented
190C3×Dic3⋊C4C22×C314yescomplemented
191C3×C4×Dic3C22×C314yescomplemented
192C3×C4×Dic3C22×C314yescomplemented
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33—21no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33C2411yescharacteristic
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—44no—
209C2×C32×D3#4112yes—
210C33×C4—21no—
211C33×C4—21no—
212C33×C4—21no—
213C33×C4—21no—
214C32×Dic3—21no—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#126—34no—
221C3×#126—34no—
222C3×#124—34no—
223C3×#124—34no—
224C3×#123—34no—
225C3×#123—34no—
226C3×C22⋊Q8—34no—
227C3×#121—24no—
228C3×#121—34no—
229C3×#121—34no—
230C3×#121C3×D314yescomplemented
231C3×#121C2×C3211yescharacteristic, complemented
232C3×#120—34no—
233C3×#120—34no—
234C3×C4×D4—34no—
235C3×C4×D4—34no—
236C2×C3×C22⋊C4—34no—
237#939C2×C3211yescharacteristic, complemented
238#938C2×C3211yescharacteristic, complemented
239#937C2×C3211yescharacteristic, complemented
240#937C2×C3211yescharacteristic, complemented
241#936C2×C3211yescharacteristic, complemented
242#935C2×C3211yescharacteristic, complemented
243#929C2×C3211yescharacteristic, complemented
244C4×#67C2×C3211yescharacteristic, complemented
245#898C2×C3211yescharacteristic, complemented
246#896C2×C3211yescharacteristic, complemented
247#885C2×C3211yescharacteristic, complemented
248#67⋊C4C2×C3211yescharacteristic, complemented
249D3×C22⋊C4C2×C3211yescharacteristic, complemented
250#879C2×C3211yescharacteristic, complemented
251C23×C32—24no—
252C23×C32—24no—
253C23×C32—24no—
254C23×C32—31no—
255C23×C32—31no—
256C23×C32—62no—
257C23×C32—121no—
258C23×C32—121no—
259C23×C32C22×D311yescharacteristic
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C23×C32C23×C314yes—
263C23×C32C23×C314yes—
264C23×C32C23×C314yes—
265C22×C3×D3—28no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3C23×C314yes—
269C22×C3×D3C23×C314yes—
270C32×Q8—121no—
271C32×D4—41no—
272C32×D4—41no—
273C32×D4—41no—
274C32×D4—44no—
275C32×D4—44no—
276C32×D4—44no—
277C32×D4—48no—
278C32×D4—48no—
279C32×D4—48no—
280C32×D4—62no—
281C32×D4—62no—
282C32×D4—121no—
283C32×D4—121no—
284C2×C32×C4—24no—
285C2×C32×C4—24no—
286C2×C32×C4—24no—
287C2×C32×C4—24no—
288C2×C32×C4—31no—
289C2×C32×C4—31no—
290C2×C32×C4—31no—
291C2×C32×C4—31no—
292C2×C32×C4—31no—
293C2×C32×C4—31no—
294C2×C32×C4—41no—
295C2×C32×C4—44no—
296C2×C32×C4—48no—
297C2×C32×C4—121no—
298C2×C32×C4—121no—
299C2×C32×C4—121no—
300C2×C32×C4C22×D311yescharacteristic
301C2×C32×C4C22×D311yescharacteristic
302C2×C32×C4C22×D311yescharacteristic
303C2×C32×C4C22×D311yescharacteristic
304C2×C32×C4C23×C314yes—
305C2×C32×C4C23×C314yes—
306C2×C32×C4C23×C314yes—
307C2×C32×C4C23×C314yes—
308C3×#67—28no—
309C3×#67—28no—
310C3×#67—44no—
311C3×#67—44no—
312C2×C3×Dic3—44no—
313C2×C3×Dic3C23×C314yes—
314C2×C3×Dic3C23×C314yes—
315C2×C3×Dic3C23×C314yes—
316C2×C3×Dic3C23×C314yes—
317C2×C3×Dic3C23×C314yes—
318C2×C3×Dic3C23×C314yes—
319C3×C4×D3—44no—
320C3×C4×D3—44no—
321C3×Dic6—44no—
322#538—31noSylow
323C2×C33—41no—
324C2×C33—41no—
325C2×C33—41no—
326C2×C33C2×#4111yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C2×C33H(5,𝔽2)11yescharacteristic
329C32×D3—22no—
330C32×D3—41no—
331C24×C3—34no—
332C23×D3C22×C3211yescharacteristic
333C2×C3×Q8—34no—
334C2×C3×D4—24no—
335C2×C3×D4—24no—
336C2×C3×D4—24no—
337C2×C3×D4—34no—
338C2×C3×D4—34no—
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C2×C3×D4C2×C3×D314yes—
342C2×C3×D4C2×C3×D314yes—
343C2×C3×D4C2×C3×D314yescomplemented
344C2×C3×D4C22×C3211yescharacteristic
345C2×C3×D4C22×C3211yescharacteristic
346C2×C3×D4C22×C3211yescharacteristic, complemented
347C22×C3×C4—24no—
348C22×C3×C4—34no—
349C22×C3×C4—34no—
350C22×C3×C4—34no—
351C22×C3×C4C2×C3×D314yescomplemented
352C22×C3×C4C22×C3211yescharacteristic, complemented
353C2×#67C22×C3211yescharacteristic
354C2×#67C22×C3211yescharacteristic
355C2×#67C22×C3211yescharacteristic
356C2×#67C22×C3211yescharacteristic
357C22×Dic3C22×C3211yescharacteristic, complemented
358C2×C4×D3C22×C3211yescharacteristic
359C2×C4×D3C22×C3211yescharacteristic
360C2×Dic6C22×C3211yescharacteristic, complemented
361C3×C4⋊C4—24no—
362C3×C4⋊C4—34no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4C2×C3×D314yescomplemented
368C3×C4⋊C4C22×C3211yescharacteristic, complemented
369C3×C22⋊C4—24no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—34no—
372C3×C22⋊C4—34no—
373C3×C22⋊C4—34no—
374C3×C22⋊C4—34no—
375C3×C22⋊C4—34no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4—34no—
378C3×C22⋊C4—34no—
379C3×C22⋊C4—34no—
380C3×C22⋊C4—34no—
381C3×C22⋊C4—34no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4C2×C3×D314yes—
384C3×C22⋊C4C2×C3×D314yescomplemented
385C3×C22⋊C4C22×C3211yescharacteristic
386C3×C22⋊C4C22×C3211yescharacteristic, complemented
387C3×C42—34no—
388C3×C42—34no—
389#217C22×C3211yescharacteristic
390#217C22×C3211yescharacteristic
391#217C22×C3211yescharacteristic
392#217C22×C3211yescharacteristic, complemented
393#217C22×C3211yescharacteristic, complemented
394#217C22×C3211yescharacteristic, complemented
395(C2×D3)⋊C4C22×C3211yescharacteristic
396(C2×D3)⋊C4C22×C3211yescharacteristic
397(C2×D3)⋊C4C22×C3211yescharacteristic
398(C2×D3)⋊C4C22×C3211yescharacteristic
399(C2×D3)⋊C4C22×C3211yescharacteristic
400(C2×D3)⋊C4C22×C3211yescharacteristic
401C4⋊Dic3C22×C3211yescharacteristic, complemented
402Dic3⋊C4C22×C3211yescharacteristic, complemented
403Dic3⋊C4C22×C3211yescharacteristic, complemented
404Dic3⋊C4C22×C3211yescharacteristic, complemented
405Dic3⋊C4C22×C3211yescharacteristic, complemented
406C4×Dic3C22×C3211yescharacteristic, complemented
407C4×Dic3C22×C3211yescharacteristic, complemented
408C22×C32—28no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—24no—
421C22×C32—24no—
422C22×C32—24no—
423C22×C32—24no—
424C22×C32—24no—
425C22×C32—24no—
426C22×C32—24no—
427C22×C32—24no—
428C22×C32—32no—
429C22×C32—44no—
430C22×C32—44no—
431C22×C32—44no—
432C22×C32—44no—
433C22×C32—44no—
434C22×C32—44no—
435C22×C32—44no—
436C22×C32—44no—
437C22×C32—61no—
438C22×C32—61no—
439C22×C32—61no—
440C22×C32—61no—
441C22×C32—61no—
442C22×C32—124no—
443C22×C32C23×D311yescharacteristic
444C22×C32C24×C314yes—
445C2×C3×D3—24no—
446C2×C3×D3—24no—
447C2×C3×D3—24no—
448C2×C3×D3—24no—
449C2×C3×D3—24no—
450C2×C3×D3—416no—
451C2×C3×D3C3×#4118yes—
452C32×C4—28no—
453C32×C4—21no—
454C32×C4—21no—
455C32×C4—21no—
456C32×C4—21no—
457C32×C4—24no—
458C32×C4—24no—
459C32×C4—24no—
460C32×C4—24no—
461C32×C4—44no—
462C32×C4—44no—
463C32×C4—44no—
464C32×C4—61no—
465C32×C4—61no—
466C32×C4—61no—
467C32×C4—61no—
468C32×C4—61no—
469C32×C4—61no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—24no—
473C3×Dic3—24no—
474C3×Dic3—24no—
475C3×Dic3—24no—
476#126—31no—
477#126—31no—
478#124—31no—
479#124—31no—
480#123—31no—
481#123—31no—
482C22⋊Q8—31no—
483#121—31no—
484#121—31no—
485#121C32×D311yescharacteristic, complemented
486#120—31no—
487#120—31no—
488C4×D4—31no—
489C4×D4—31no—
490C2×C22⋊C4—31no—
491C33#53811yescharacteristic, complemented, Sylow
492C23×C3—24no—
493C23×C3—24no—
494C23×C3—24no—
495C23×C3—34no—
496C23×C3—34no—
497C23×C3—68no—
498C23×C3—124no—
499C23×C3—124no—
500C23×C3C22×C3×D314yes—
501C23×C3C22×C3×D314yes—
502C23×C3C22×C3×D314yes—
503C23×C3C23×C3211yescharacteristic
504C23×C3C23×C3211yescharacteristic
505C23×C3C23×C3211yescharacteristic
506C22×D3—22no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3C23×C3211yescharacteristic
510C22×D3C23×C3211yescharacteristic
511C3×Q8—124no—
512C3×D4—44no—
513C3×D4—44no—
514C3×D4—44no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—48no—
519C3×D4—48no—
520C3×D4—48no—
521C3×D4—68no—
522C3×D4—68no—
523C3×D4—124no—
524C3×D4—124no—
525C2×C3×C4—24no—
526C2×C3×C4—24no—
527C2×C3×C4—24no—
528C2×C3×C4—24no—
529C2×C3×C4—34no—
530C2×C3×C4—34no—
531C2×C3×C4—34no—
532C2×C3×C4—34no—
533C2×C3×C4—34no—
534C2×C3×C4—34no—
535C2×C3×C4—44no—
536C2×C3×C4—41no—
537C2×C3×C4—48no—
538C2×C3×C4—124no—
539C2×C3×C4—124no—
540C2×C3×C4—124no—
541C2×C3×C4C22×C3×D314yes—
542C2×C3×C4C22×C3×D314yes—
543C2×C3×C4C22×C3×D314yes—
544C2×C3×C4C22×C3×D314yes—
545C2×C3×C4C23×C3211yescharacteristic
546C2×C3×C4C23×C3211yescharacteristic
547C2×C3×C4C23×C3211yescharacteristic
548C2×C3×C4C23×C3211yescharacteristic
549#67—22no—
550#67—22no—
551#67—41no—
552#67—41no—
553C2×Dic3—41no—
554C2×Dic3C23×C3211yescharacteristic
555C2×Dic3C23×C3211yescharacteristic
556C2×Dic3C23×C3211yescharacteristic
557C2×Dic3C23×C3211yescharacteristic
558C2×Dic3C23×C3211yescharacteristic
559C2×Dic3C23×C3211yescharacteristic
560C4×D3—41no—
561C4×D3—41no—
562Dic6—41no—
563C2×C32—24no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—48no—
567C2×C32—44no—
568C2×C32—41no—
569C2×C32—41no—
570C2×C32—41no—
571C2×C32—44no—
572C2×C32—44no—
573C2×C32—62no—
574C2×C32—84no—
575C2×C32—84no—
576C2×C32—121no—
577C2×C32#100411yescharacteristic
578C2×C32#100411yescharacteristic
579C2×C32D3×#4111yescharacteristic
580C2×C32C2×C3×#4114yes—
581C2×C32C3×H(5,𝔽2)14yes—
582C2×C32C3×H(5,𝔽2)14yes—
583C3×D3—28no—
584C3×D3—44no—
585C24—31no—
586C2×Q8—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4C2×C32×D311yescharacteristic
592C2×D4C2×C32×D311yescharacteristic
593C2×D4C2×C32×D311yescharacteristic, complemented
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4C2×C32×D311yescharacteristic, complemented
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4C2×C32×D311yescharacteristic, complemented
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4C2×C32×D311yescharacteristic
617C22⋊C4C2×C32×D311yescharacteristic, complemented
618C42—31no—
619C42—31no—
620C22×C3—28no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—24no—
640C22×C3—38no—
641C22×C3—44no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—44no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3—44no—
648C22×C3—44no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—64no—
652C22×C3—64no—
653C22×C3—64no—
654C22×C3—1216no—
655C22×C3C23×C3×D314yes—
656C22×C3C24×C3211yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—44no—
663C2×D3C32×#4112yes—
664C3×C4—28no—
665C3×C4—24no—
666C3×C4—24no—
667C3×C4—24no—
668C3×C4—24no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—44no—
674C3×C4—44no—
675C3×C4—44no—
676C3×C4—64no—
677C3×C4—64no—
678C3×C4—64no—
679C3×C4—64no—
680C3×C4—64no—
681C3×C4—64no—
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688C32—24no—
689C32#561311yescharacteristic, direct product factor
690C32C3×#53814yescomplemented
691C23—31no—
692C23—31no—
693C23—62no—
694C23—121no—
695C23—121no—
696C23C22×C32×D311yescharacteristic
697C23C22×C32×D311yescharacteristic
698C23C22×C32×D311yescharacteristic
699Q8—121no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—62no—
704D4—62no—
705D4—121no—
706D4—121no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—41no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4C22×C32×D311yescharacteristic
718C2×C4C22×C32×D311yescharacteristic
719C2×C4C22×C32×D311yescharacteristic
720C2×C4C22×C32×D311yescharacteristic
721C2×C3—24no—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—48no—
725C2×C3—44no—
726C2×C3—44no—
727C2×C3—44no—
728C2×C3—41no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—68no—
732C2×C3—84no—
733C2×C3—84no—
734C2×C3—124no—
735C2×C3C3×#100414yes—
736C2×C3C3×#100414yes—
737C2×C3C3×D3×#4114yes—
738C2×C3C2×C32×#4111yescharacteristic
739C2×C3C32×H(5,𝔽2)11yescharacteristic
740C2×C3C32×H(5,𝔽2)11yescharacteristic
741D3—22no—
742D3—41no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—32no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—124no—
759C22C23×C32×D311yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—61no—
765C4—61no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—61no—
770C3—24no—
771C3C3×#561314yesdirect product factor
772C3C32×#53811yescharacteristic, complemented
773C2—41no—
774C2—41no—
775C2—41no—
776C2—62no—
777C2—121no—
778C2C32×#100411yescharacteristic
779C2C32×#100411yescharacteristic
780C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#121C2
socleC22×C33C24
hypercenterC32×#121D3
hypocenterC3C32×#538
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#121

Complements

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

NH ≅ G/Ntype
1. C33×#121C2semidirect
2. C32×#939C2semidirect
3. C32×#938C2semidirect
4. C32×#937C2semidirect
5. C32×#937C2semidirect
6. C32×#936C2semidirect
7. C32×#935C2semidirect
8. C32×#929C2semidirect
9. C32×C4×#67C2semidirect
10. C32×#898C2semidirect
11. C32×#896C2semidirect
12. C32×#885C2semidirect
13. C32×#67⋊C4C2semidirect
14. C32×D3×C22⋊C4C2semidirect
15. C32×#879C2semidirect
17. C3×#5613C3direct (N × H)
21. C2×C33×D4C22semidirect
22. C22×C33×C4C22semidirect
27. C22×C32×Dic3C22semidirect
30. C2×C32×Dic6C22semidirect
31. C33×C4⋊C4C22semidirect
33. C33×C22⋊C4C22semidirect
37. C32×#217C22semidirect
38. C32×#217C22semidirect
39. C32×#217C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. C32×C4×Dic3C22semidirect
52. C32×C4×Dic3C22semidirect
63. C32×#121D3semidirect
64. C32×#121C2×C3semidirect
70. C3×#939C2×C3semidirect
71. C3×#938C2×C3semidirect
72. C3×#937C2×C3semidirect
73. C3×#937C2×C3semidirect
74. C3×#936C2×C3semidirect
75. C3×#935C2×C3semidirect
76. C3×#929C2×C3semidirect
77. C3×C4×#67C2×C3semidirect
78. C3×#898C2×C3semidirect
79. C3×#896C2×C3semidirect
80. C3×#885C2×C3semidirect
81. C3×#67⋊C4C2×C3semidirect
82. C3×D3×C22⋊C4C2×C3semidirect
83. C3×#879C2×C3semidirect
115. #5613C32direct (N × H)
128. C2×C32×D4C2×D3semidirect
131. C2×C32×D4C22×C3semidirect
136. C22×C32×C4C2×D3semidirect
137. C22×C32×C4C22×C3semidirect
142. C22×C3×Dic3C22×C3semidirect
145. C2×C3×Dic6C22×C3semidirect
152. C32×C4⋊C4C2×D3semidirect
153. C32×C4⋊C4C22×C3semidirect
169. C32×C22⋊C4C2×D3semidirect
171. C32×C22⋊C4C22×C3semidirect
177. C3×#217C22×C3semidirect
178. C3×#217C22×C3semidirect
179. C3×#217C22×C3semidirect
186. C3×C4⋊Dic3C22×C3semidirect
187. C3×Dic3⋊C4C22×C3semidirect
188. C3×Dic3⋊C4C22×C3semidirect
189. C3×Dic3⋊C4C22×C3semidirect
190. C3×Dic3⋊C4C22×C3semidirect
191. C3×C4×Dic3C22×C3semidirect
192. C3×C4×Dic3C22×C3semidirect
230. C3×#121C3×D3semidirect
231. C3×#121C2×C32semidirect
237. #939C2×C32semidirect
238. #938C2×C32semidirect
239. #937C2×C32semidirect
240. #937C2×C32semidirect
241. #936C2×C32semidirect
242. #935C2×C32semidirect
243. #929C2×C32semidirect
244. C4×#67C2×C32semidirect
245. #898C2×C32semidirect
246. #896C2×C32semidirect
247. #885C2×C32semidirect
248. #67⋊C4C2×C32semidirect
249. D3×C22⋊C4C2×C32semidirect
250. #879C2×C32semidirect
343. C2×C3×D4C2×C3×D3semidirect
346. C2×C3×D4C22×C32semidirect
351. C22×C3×C4C2×C3×D3semidirect
352. C22×C3×C4C22×C32semidirect
357. C22×Dic3C22×C32semidirect
360. C2×Dic6C22×C32semidirect
367. C3×C4⋊C4C2×C3×D3semidirect
368. C3×C4⋊C4C22×C32semidirect
384. C3×C22⋊C4C2×C3×D3semidirect
386. C3×C22⋊C4C22×C32semidirect
392. #217C22×C32semidirect
393. #217C22×C32semidirect
394. #217C22×C32semidirect
401. C4⋊Dic3C22×C32semidirect
402. Dic3⋊C4C22×C32semidirect
403. Dic3⋊C4C22×C32semidirect
404. Dic3⋊C4C22×C32semidirect
405. Dic3⋊C4C22×C32semidirect
406. C4×Dic3C22×C32semidirect
407. C4×Dic3C22×C32semidirect
485. #121C32×D3semidirect
491. C33#538semidirect
593. C2×D4C2×C32×D3semidirect
597. C22×C4C2×C32×D3semidirect
603. C4⋊C4C2×C32×D3semidirect
617. C22⋊C4C2×C32×D3semidirect
689. C32#5613direct (N × H)
690. C32C3×#538semidirect
771. C3C3×#5613direct (N × H)
772. C3C32×#538semidirect

Maximal subgroups

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

subgroupindex
C33×#1212
C32×#9392
C32×#9382
C32×#9372
C32×#9362
C32×#9352
C32×#9292
C32×C4×#672
C32×#8982
C32×#8962
C32×#8852
C32×#67⋊C42
C32×D3×C22⋊C42
C32×#8792
C32×#5383
C3×#56133