Finite Group Databasebeta

← C32×#5593 #13178970

Subgroups — C32×#5593 #13178970

Order 1728.

2020 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#120C211yesmaximal, characteristic, complemented
2C32×#953C211yesmaximal, characteristic, complemented
3C2×C32×#217C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C32×#939C211yesmaximal, characteristic, complemented
6C32×#938C211yesmaximal, characteristic, complemented
7C32×#936C211yesmaximal, characteristic, complemented
8C32×#935C211yesmaximal, characteristic, complemented
9C32×D4×Dic3C211yesmaximal, characteristic, complemented
10C32×#885C211yesmaximal, characteristic, complemented
11C32×#883C211yesmaximal, characteristic, complemented
12C32×#67⋊C4C211yesmaximal, characteristic, complemented
13C32×#879C211yesmaximal, characteristic, complemented
14C32×#879C211yesmaximal, characteristic, complemented
15C32×#878C211yesmaximal, characteristic, complemented
16C32×#538—31nomaximal
17C3×#5593C314yesmaximal, direct product factor
18C24×C33C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic
28C22×C32×Dic3C2211yescharacteristic, complemented
29C2×C32×C4×D3C2211yescharacteristic, complemented
30C2×C32×Dic6C2211yescharacteristic, complemented
31C33×C22⋊C4C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic
33C33×C22⋊C4C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C32×#217C2211yescharacteristic
41C32×#217C2211yescharacteristic, complemented
42C32×#217C2211yescharacteristic, complemented
43C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×C4⋊Dic3C2211yescharacteristic, complemented
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—31no—
61C32×#121—31no—
62C32×#121—31no—
63C32×#120—24no—
64C32×#120—31no—
65C32×#120D311yescharacteristic, complemented
66C32×#120C2×C314yescomplemented
67C32×C4×D4—31no—
68C32×C4×D4—31no—
69C2×C32×C22⋊C4—31no—
70C3×#953C2×C314yescomplemented
71C2×C3×#217C2×C314yescomplemented
72C3×#939C2×C314yescomplemented
73C3×#939C2×C314yescomplemented
74C3×#938C2×C314yescomplemented
75C3×#936C2×C314yescomplemented
76C3×#935C2×C314yescomplemented
77C3×D4×Dic3C2×C314yescomplemented
78C3×#885C2×C314yescomplemented
79C3×#883C2×C314yescomplemented
80C3×#67⋊C4C2×C314yescomplemented
81C3×#879C2×C314yescomplemented
82C3×#879C2×C314yescomplemented
83C3×#878C2×C314yescomplemented
84C23×C33—22no—
85C23×C33—41no—
86C23×C33—41no—
87C23×C33C2311yescharacteristic
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C23×C33C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C33×D4—22no—
93C33×D4—41no—
94C33×D4—41no—
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C32×#67—22no—
99C32×#67—41no—
100C32×#67—41no—
101C32×#67—41no—
102C2×C32×Dic3—41no—
103C2×C32×Dic3—41no—
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C32×C4×D3—41no—
113C32×Dic6—41no—
114C3×#538—34no—
115#5593C3211yescharacteristic, direct product factor
116C24×C32—24no—
117C24×C32C2×D311yescharacteristic
118C24×C32C22×C314yes—
119C2×C32×Q8—31no—
120C2×C32×D4—24no—
121C2×C32×D4—24no—
122C2×C32×D4—24no—
123C2×C32×D4—31no—
124C2×C32×D4—31no—
125C2×C32×D4—31no—
126C2×C32×D4—31no—
127C2×C32×D4C2×D311yescharacteristic
128C2×C32×D4C2×D311yescharacteristic
129C2×C32×D4C2×D311yescharacteristic
130C2×C32×D4C22×C314yes—
131C2×C32×D4C22×C314yes—
132C2×C32×D4C22×C314yes—
133C22×C32×C4—31no—
134C22×C32×C4—31no—
135C22×C32×C4—31no—
136C22×C32×C4—31no—
137C2×C3×#67C22×C314yes—
138C2×C3×#67C22×C314yes—
139C2×C3×#67C22×C314yes—
140C2×C3×#67C22×C314yescomplemented
141C22×C3×Dic3C22×C314yes—
142C22×C3×Dic3C22×C314yes—
143C22×C3×Dic3C22×C314yescomplemented
144C2×C3×C4×D3C22×C314yescomplemented
145C2×C3×Dic6C22×C314yescomplemented
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C22⋊C4—24no—
153C32×C22⋊C4—24no—
154C32×C22⋊C4—24no—
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⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4C2×D311yescharacteristic
167C32×C22⋊C4C2×D311yescharacteristic
168C32×C22⋊C4C2×D311yescharacteristic
169C32×C22⋊C4C22×C314yes—
170C32×C22⋊C4C22×C314yes—
171C32×C22⋊C4C22×C314yes—
172C32×C42—31no—
173C32×C42—31no—
174C3×#217C22×C314yes—
175C3×#217C22×C314yes—
176C3×#217C22×C314yes—
177C3×#217C22×C314yes—
178C3×#217C22×C314yes—
179C3×#217C22×C314yes—
180C3×#217C22×C314yes—
181C3×#217C22×C314yescomplemented
182C3×#217C22×C314yescomplemented
183C3×(C2×D3)⋊C4C22×C314yescomplemented
184C3×(C2×D3)⋊C4C22×C314yescomplemented
185C3×C4⋊Dic3C22×C314yescomplemented
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×C33—21no—
203C22×C33—21no—
204C22×C33—44no—
205C22×C33#4112yes—
206C22×C33C2411yescharacteristic
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C2×C32×D3—21no—
210C33×C4—21no—
211C33×C4—21no—
212C33×C4—21no—
213C32×Dic3—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—34no—
228C3×#121—34no—
229C3×#121—34no—
230C3×#120—24no—
231C3×#120—34no—
232C3×#120C3×D314yescomplemented
233C3×#120C2×C3211yescharacteristic, complemented
234C3×C4×D4—34no—
235C3×C4×D4—34no—
236C2×C3×C22⋊C4—34no—
237#953C2×C3211yescharacteristic, complemented
238C2×#217C2×C3211yescharacteristic, complemented
239#939C2×C3211yescharacteristic, complemented
240#939C2×C3211yescharacteristic, complemented
241#938C2×C3211yescharacteristic, complemented
242#936C2×C3211yescharacteristic, complemented
243#935C2×C3211yescharacteristic, complemented
244D4×Dic3C2×C3211yescharacteristic, complemented
245#885C2×C3211yescharacteristic, complemented
246#883C2×C3211yescharacteristic, complemented
247#67⋊C4C2×C3211yescharacteristic, complemented
248#879C2×C3211yescharacteristic, complemented
249#879C2×C3211yescharacteristic, complemented
250#878C2×C3211yescharacteristic, complemented
251C23×C32—22no—
252C23×C32—24no—
253C23×C32—24no—
254C23×C32—24no—
255C23×C32—24no—
256C23×C32—28no—
257C23×C32—31no—
258C23×C32—48no—
259C23×C32—41no—
260C23×C32—41no—
261C23×C32—44no—
262C23×C32—44no—
263C23×C32—48no—
264C23×C32—48no—
265C23×C32C22×D311yescharacteristic
266C23×C32C22×D311yescharacteristic
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C23×C32C23×C314yes—
270C23×C32C23×C314yes—
271C23×C32C23×C314yes—
272C23×C32C23×C314yes—
273C22×C3×D3C23×C314yes—
274C32×Q8—121no—
275C32×D4—22no—
276C32×D4—28no—
277C32×D4—48no—
278C32×D4—41no—
279C32×D4—41no—
280C32×D4—44no—
281C32×D4—44no—
282C32×D4—48no—
283C32×D4—48no—
284C32×D4—62no—
285C32×D4—121no—
286C32×D4—121no—
287C32×D4—121no—
288C2×C32×C4—24no—
289C2×C32×C4—24no—
290C2×C32×C4—24no—
291C2×C32×C4—31no—
292C2×C32×C4—31no—
293C2×C32×C4—31no—
294C2×C32×C4—31no—
295C2×C32×C4—31no—
296C2×C32×C4—31no—
297C2×C32×C4—31no—
298C2×C32×C4—121no—
299C2×C32×C4—121no—
300C2×C32×C4—121no—
301C2×C32×C4—121no—
302C2×C32×C4C22×D311yescharacteristic
303C2×C32×C4C22×D311yescharacteristic
304C2×C32×C4C22×D311yescharacteristic
305C2×C32×C4C23×C314yes—
306C2×C32×C4C23×C314yes—
307C2×C32×C4C23×C314yes—
308C3×#67—28no—
309C3×#67—44no—
310C3×#67—44no—
311C3×#67—44no—
312C2×C3×Dic3—44no—
313C2×C3×Dic3—44no—
314C2×C3×Dic3—44no—
315C2×C3×Dic3C23×C314yes—
316C2×C3×Dic3C23×C314yes—
317C2×C3×Dic3C23×C314yes—
318C2×C3×Dic3C23×C314yes—
319C2×C3×Dic3C23×C314yes—
320C2×C3×Dic3C23×C314yes—
321C2×C3×Dic3C23×C314yes—
322C3×C4×D3—44no—
323C3×Dic6—44no—
324#538—31noSylow
325C2×C33—22no—
326C2×C33—41no—
327C2×C33—41no—
328C2×C33—41no—
329C2×C33C2×#4111yescharacteristic
330C2×C33H(5,𝔽2)11yescharacteristic
331C2×C33H(5,𝔽2)11yescharacteristic
332C32×D3—41no—
333C24×C3—24no—
334C24×C3C2×C3×D314yes—
335C24×C3C22×C3211yescharacteristic
336C2×C3×Q8—34no—
337C2×C3×D4—24no—
338C2×C3×D4—24no—
339C2×C3×D4—24no—
340C2×C3×D4—34no—
341C2×C3×D4—34no—
342C2×C3×D4—34no—
343C2×C3×D4—34no—
344C2×C3×D4C2×C3×D314yes—
345C2×C3×D4C2×C3×D314yes—
346C2×C3×D4C2×C3×D314yes—
347C2×C3×D4C22×C3211yescharacteristic
348C2×C3×D4C22×C3211yescharacteristic
349C2×C3×D4C22×C3211yescharacteristic
350C22×C3×C4—34no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—34no—
354C2×#67C22×C3211yescharacteristic
355C2×#67C22×C3211yescharacteristic
356C2×#67C22×C3211yescharacteristic
357C2×#67C22×C3211yescharacteristic, complemented
358C22×Dic3C22×C3211yescharacteristic
359C22×Dic3C22×C3211yescharacteristic
360C22×Dic3C22×C3211yescharacteristic, complemented
361C2×C4×D3C22×C3211yescharacteristic, complemented
362C2×Dic6C22×C3211yescharacteristic, complemented
363C3×C4⋊C4—34no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4—34no—
368C3×C4⋊C4—34no—
369C3×C22⋊C4—24no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—24no—
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×D314yes—
385C3×C22⋊C4C2×C3×D314yes—
386C3×C22⋊C4C22×C3211yescharacteristic
387C3×C22⋊C4C22×C3211yescharacteristic
388C3×C22⋊C4C22×C3211yescharacteristic
389C3×C42—34no—
390C3×C42—34no—
391#217C22×C3211yescharacteristic
392#217C22×C3211yescharacteristic
393#217C22×C3211yescharacteristic
394#217C22×C3211yescharacteristic
395#217C22×C3211yescharacteristic
396#217C22×C3211yescharacteristic
397#217C22×C3211yescharacteristic
398#217C22×C3211yescharacteristic, complemented
399#217C22×C3211yescharacteristic, complemented
400(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
401(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
402C4⋊Dic3C22×C3211yescharacteristic, complemented
403C4⋊Dic3C22×C3211yescharacteristic, complemented
404Dic3⋊C4C22×C3211yescharacteristic, complemented
405Dic3⋊C4C22×C3211yescharacteristic, complemented
406Dic3⋊C4C22×C3211yescharacteristic, complemented
407Dic3⋊C4C22×C3211yescharacteristic, complemented
408C4×Dic3C22×C3211yescharacteristic, complemented
409C4×Dic3C22×C3211yescharacteristic, complemented
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—28no—
413C22×C32—28no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—24no—
424C22×C32—24no—
425C22×C32—24no—
426C22×C32—28no—
427C22×C32—24no—
428C22×C32—24no—
429C22×C32—24no—
430C22×C32—24no—
431C22×C32—24no—
432C22×C32—24no—
433C22×C32—24no—
434C22×C32—24no—
435C22×C32—24no—
436C22×C32—44no—
437C22×C32—44no—
438C22×C32—44no—
439C22×C32—44no—
440C22×C32—44no—
441C22×C32—44no—
442C22×C32—44no—
443C22×C32—44no—
444C22×C32—44no—
445C22×C32—44no—
446C22×C32—416no—
447C22×C32—432no—
448C22×C32—61no—
449C22×C32—61no—
450C22×C32—61no—
451C22×C32#23712yes—
452C22×C32C3×#4118yes—
453C22×C32C23×D311yescharacteristic
454C22×C32C24×C314yes—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—24no—
458C32×C4—21no—
459C32×C4—21no—
460C32×C4—21no—
461C32×C4—24no—
462C32×C4—24no—
463C32×C4—24no—
464C32×C4—44no—
465C32×C4—44no—
466C32×C4—44no—
467C32×C4—61no—
468C32×C4—61no—
469C32×C4—61no—
470C32×C4—61no—
471C32×C4—61no—
472C32×C4—61no—
473C32×C4—61no—
474C3×Dic3—24no—
475C3×Dic3—24no—
476C3×Dic3—24no—
477C3×Dic3—24no—
478C3×Dic3—24no—
479C3×Dic3—24no—
480C3×Dic3—24no—
481#126—31no—
482#126—31no—
483#124—31no—
484#124—31no—
485#123—31no—
486#123—31no—
487C22⋊Q8—31no—
488#121—31no—
489#121—31no—
490#121—31no—
491#120—31no—
492#120C32×D311yescharacteristic, complemented
493C4×D4—31no—
494C4×D4—31no—
495C2×C22⋊C4—31no—
496C33#53811yescharacteristic, complemented, Sylow
497C23×C3—28no—
498C23×C3—22no—
499C23×C3—24no—
500C23×C3—24no—
501C23×C3—24no—
502C23×C3—24no—
503C23×C3—34no—
504C23×C3—48no—
505C23×C3—44no—
506C23×C3—44no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—48no—
510C23×C3—48no—
511C23×C3C22×C3×D314yes—
512C23×C3C22×C3×D314yes—
513C23×C3C22×C3×D314yes—
514C23×C3C22×C3×D314yes—
515C23×C3C23×C3211yescharacteristic
516C23×C3C23×C3211yescharacteristic
517C23×C3C23×C3211yescharacteristic
518C23×C3C23×C3211yescharacteristic
519C22×D3C23×C3211yescharacteristic
520C3×Q8—124no—
521C3×D4—28no—
522C3×D4—22no—
523C3×D4—48no—
524C3×D4—44no—
525C3×D4—44no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—48no—
529C3×D4—48no—
530C3×D4—68no—
531C3×D4—124no—
532C3×D4—124no—
533C3×D4—124no—
534C2×C3×C4—24no—
535C2×C3×C4—24no—
536C2×C3×C4—24no—
537C2×C3×C4—34no—
538C2×C3×C4—34no—
539C2×C3×C4—34no—
540C2×C3×C4—34no—
541C2×C3×C4—34no—
542C2×C3×C4—34no—
543C2×C3×C4—34no—
544C2×C3×C4—124no—
545C2×C3×C4—124no—
546C2×C3×C4—124no—
547C2×C3×C4—124no—
548C2×C3×C4C22×C3×D314yes—
549C2×C3×C4C22×C3×D314yes—
550C2×C3×C4C22×C3×D314yes—
551C2×C3×C4C23×C3211yescharacteristic
552C2×C3×C4C23×C3211yescharacteristic
553C2×C3×C4C23×C3211yescharacteristic
554#67—22no—
555#67—41no—
556#67—41no—
557#67—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3C23×C3211yescharacteristic
562C2×Dic3C23×C3211yescharacteristic
563C2×Dic3C23×C3211yescharacteristic
564C2×Dic3C23×C3211yescharacteristic
565C2×Dic3C23×C3211yescharacteristic
566C2×Dic3C23×C3211yescharacteristic
567C2×Dic3C23×C3211yescharacteristic
568C4×D3—41no—
569Dic6—41no—
570C2×C32—22no—
571C2×C32—24no—
572C2×C32—24no—
573C2×C32—24no—
574C2×C32—28no—
575C2×C32—48no—
576C2×C32—48no—
577C2×C32—48no—
578C2×C32—41no—
579C2×C32—41no—
580C2×C32—41no—
581C2×C32—44no—
582C2×C32—44no—
583C2×C32—44no—
584C2×C32—84no—
585C2×C32—121no—
586C2×C32C2×#23711yescharacteristic
587C2×C32#100411yescharacteristic
588C2×C32#100411yescharacteristic
589C2×C32C2×C3×#4114yes—
590C2×C32C3×H(5,𝔽2)14yes—
591C2×C32C3×H(5,𝔽2)14yes—
592C3×D3—44no—
593C24C2×C32×D311yescharacteristic
594C2×Q8—31no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4C2×C32×D311yescharacteristic
600C2×D4C2×C32×D311yescharacteristic
601C2×D4C2×C32×D311yescharacteristic
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—31no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4C2×C32×D311yescharacteristic
624C22⋊C4C2×C32×D311yescharacteristic
625C22⋊C4C2×C32×D311yescharacteristic
626C42—31no—
627C42—31no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—28no—
633C22×C3—28no—
634C22×C3—24no—
635C22×C3—24no—
636C22×C3—24no—
637C22×C3—24no—
638C22×C3—24no—
639C22×C3—24no—
640C22×C3—24no—
641C22×C3—24no—
642C22×C3—24no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—24no—
653C22×C3—28no—
654C22×C3—44no—
655C22×C3—44no—
656C22×C3—44no—
657C22×C3—44no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—44no—
663C22×C3—416no—
664C22×C3—44no—
665C22×C3—432no—
666C22×C3—64no—
667C22×C3—64no—
668C22×C3—64no—
669C22×C3C3×#23718yes—
670C22×C3C32×#4112yes—
671C22×C3C23×C3×D314yes—
672C22×C3C24×C3211yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C3×C4—24no—
677C3×C4—24no—
678C3×C4—24no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—44no—
683C3×C4—44no—
684C3×C4—44no—
685C3×C4—64no—
686C3×C4—64no—
687C3×C4—64no—
688C3×C4—64no—
689C3×C4—64no—
690C3×C4—64no—
691C3×C4—64no—
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699C32—24no—
700C32#559311yescharacteristic, direct product factor
701C32C3×#53814yescomplemented
702C23—22no—
703C23—31no—
704C23—41no—
705C23—41no—
706C23C22×C32×D311yescharacteristic
707C23C22×C32×D311yescharacteristic
708C23C22×C32×D311yescharacteristic
709C23C22×C32×D311yescharacteristic
710Q8—121no—
711D4—22no—
712D4—41no—
713D4—41no—
714D4—62no—
715D4—121no—
716D4—121no—
717D4—121no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4C22×C32×D311yescharacteristic
730C2×C4C22×C32×D311yescharacteristic
731C2×C4C22×C32×D311yescharacteristic
732C2×C3—28no—
733C2×C3—22no—
734C2×C3—24no—
735C2×C3—24no—
736C2×C3—24no—
737C2×C3—48no—
738C2×C3—48no—
739C2×C3—48no—
740C2×C3—44no—
741C2×C3—44no—
742C2×C3—44no—
743C2×C3—41no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—84no—
747C2×C3—124no—
748C2×C3C2×C3×#23714yes—
749C2×C3C3×#100414yes—
750C2×C3C3×#100414yes—
751C2×C3C2×C32×#4111yescharacteristic
752C2×C3C32×H(5,𝔽2)11yescharacteristic
753C2×C3C32×H(5,𝔽2)11yescharacteristic
754D3—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—44no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22C32×#23712yes—
771C22C23×C32×D311yescharacteristic
772C4—21no—
773C4—21no—
774C4—21no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—61no—
782C3—24no—
783C3C3×#559314yesdirect product factor
784C3C32×#53811yescharacteristic, complemented
785C2—22no—
786C2—41no—
787C2—41no—
788C2—41no—
789C2—121no—
790C2C2×C32×#23711yescharacteristic
791C2C32×#100411yescharacteristic
792C2C32×#100411yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#120C2
socleC22×C33C24
hypercenterC32×#120D3
hypocenterC3C32×#538
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#120

Complements

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

NH ≅ G/Ntype
1. C33×#120C2semidirect
2. C32×#953C2semidirect
3. C2×C32×#217C2semidirect
4. C32×#939C2semidirect
5. C32×#939C2semidirect
6. C32×#938C2semidirect
7. C32×#936C2semidirect
8. C32×#935C2semidirect
9. C32×D4×Dic3C2semidirect
10. C32×#885C2semidirect
11. C32×#883C2semidirect
12. C32×#67⋊C4C2semidirect
13. C32×#879C2semidirect
14. C32×#879C2semidirect
15. C32×#878C2semidirect
17. C3×#5593C3direct (N × H)
25. C2×C32×#67C22semidirect
28. C22×C32×Dic3C22semidirect
29. C2×C32×C4×D3C22semidirect
30. C2×C32×Dic6C22semidirect
41. C32×#217C22semidirect
42. C32×#217C22semidirect
43. C32×(C2×D3)⋊C4C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×C4⋊Dic3C22semidirect
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
65. C32×#120D3semidirect
66. C32×#120C2×C3semidirect
70. C3×#953C2×C3semidirect
71. C2×C3×#217C2×C3semidirect
72. C3×#939C2×C3semidirect
73. C3×#939C2×C3semidirect
74. C3×#938C2×C3semidirect
75. C3×#936C2×C3semidirect
76. C3×#935C2×C3semidirect
77. C3×D4×Dic3C2×C3semidirect
78. C3×#885C2×C3semidirect
79. C3×#883C2×C3semidirect
80. C3×#67⋊C4C2×C3semidirect
81. C3×#879C2×C3semidirect
82. C3×#879C2×C3semidirect
83. C3×#878C2×C3semidirect
115. #5593C32direct (N × H)
140. C2×C3×#67C22×C3semidirect
143. C22×C3×Dic3C22×C3semidirect
144. C2×C3×C4×D3C22×C3semidirect
145. C2×C3×Dic6C22×C3semidirect
181. C3×#217C22×C3semidirect
182. C3×#217C22×C3semidirect
183. C3×(C2×D3)⋊C4C22×C3semidirect
184. C3×(C2×D3)⋊C4C22×C3semidirect
185. C3×C4⋊Dic3C22×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
232. C3×#120C3×D3semidirect
233. C3×#120C2×C32semidirect
237. #953C2×C32semidirect
238. C2×#217C2×C32semidirect
239. #939C2×C32semidirect
240. #939C2×C32semidirect
241. #938C2×C32semidirect
242. #936C2×C32semidirect
243. #935C2×C32semidirect
244. D4×Dic3C2×C32semidirect
245. #885C2×C32semidirect
246. #883C2×C32semidirect
247. #67⋊C4C2×C32semidirect
248. #879C2×C32semidirect
249. #879C2×C32semidirect
250. #878C2×C32semidirect
357. C2×#67C22×C32semidirect
360. C22×Dic3C22×C32semidirect
361. C2×C4×D3C22×C32semidirect
362. C2×Dic6C22×C32semidirect
398. #217C22×C32semidirect
399. #217C22×C32semidirect
400. (C2×D3)⋊C4C22×C32semidirect
401. (C2×D3)⋊C4C22×C32semidirect
402. C4⋊Dic3C22×C32semidirect
403. C4⋊Dic3C22×C32semidirect
404. Dic3⋊C4C22×C32semidirect
405. Dic3⋊C4C22×C32semidirect
406. Dic3⋊C4C22×C32semidirect
407. Dic3⋊C4C22×C32semidirect
408. C4×Dic3C22×C32semidirect
409. C4×Dic3C22×C32semidirect
492. #120C32×D3semidirect
496. C33#538semidirect
700. C32#5593direct (N × H)
701. C32C3×#538semidirect
783. C3C3×#5593direct (N × H)
784. C3C32×#538semidirect

Maximal subgroups

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

subgroupindex
C33×#1202
C32×#9532
C2×C32×#2172
C32×#9392
C32×#9382
C32×#9362
C32×#9352
C32×D4×Dic32
C32×#8852
C32×#8832
C32×#67⋊C42
C32×#8792
C32×#8782
C32×#5383
C3×#55933