Finite Group Databasebeta

← C32×#5621 #13178998

Subgroups — C32×#5621 #13178998

Order 1728.

1696 conjugacy classes of subgroups.

The subgroup lattice has 740 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×#939C211yesmaximal, characteristic, complemented
4C32×#938C211yesmaximal, characteristic, complemented
5C32×#936C211yesmaximal, characteristic, complemented
6C32×#935C211yesmaximal, characteristic, complemented
7C32×#935C211yesmaximal, characteristic, complemented
8C32×#929C211yesmaximal, characteristic, complemented
9C32×#924C211yesmaximal, characteristic, complemented
10C32×#896C211yesmaximal, characteristic, complemented
11C32×#889C211yesmaximal, characteristic, complemented
12C32×#885C211yesmaximal, characteristic, complemented
13C32×#883C211yesmaximal, characteristic, complemented
14C32×#878C211yesmaximal, characteristic, complemented
15C32×#878C211yesmaximal, characteristic, complemented
16C32×#562—31nomaximal
17C3×#5621C314yesmaximal, direct product factor
18C2×C33×D4C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C22×C33×C4C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C2×C32×C4×D3C2211yescharacteristic
28C2×C32×Dic6C2211yescharacteristic
29C2×C32×Dic6C2211yescharacteristic
30C33×C4⋊C4C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×C4⋊Dic3C2211yescharacteristic
44C32×C4⋊Dic3C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×Dic3⋊C4C2211yescharacteristic
51C32×Dic3⋊C4C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#125—31no—
54C32×#124—31no—
55C32×#124—31no—
56C32×#123—31no—
57C32×#123—31no—
58C32×#123—31no—
59C32×#123—31no—
60C32×C22⋊Q8—31no—
61C32×C22⋊Q8—31no—
62C32×C22⋊Q8—31no—
63C32×C22⋊Q8—31no—
64C32×#121—24no—
65C32×#121—31no—
66C32×#121—31no—
67C32×#121—31no—
68C32×#121D311yescharacteristic, complemented
69C32×#121C2×C314yescomplemented
70C3×#939C2×C314yescomplemented
71C3×#939C2×C314yescomplemented
72C3×#938C2×C314yescomplemented
73C3×#936C2×C314yescomplemented
74C3×#935C2×C314yescomplemented
75C3×#935C2×C314yescomplemented
76C3×#929C2×C314yescomplemented
77C3×#924C2×C314yescomplemented
78C3×#896C2×C314yescomplemented
79C3×#889C2×C314yescomplemented
80C3×#885C2×C314yescomplemented
81C3×#883C2×C314yescomplemented
82C3×#878C2×C314yescomplemented
83C3×#878C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C23×C33C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C33×D4—41no—
89C33×D4—41no—
90C33×D4—41no—
91C2×C33×C4—41no—
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C32×#67—41no—
97C32×#67—41no—
98C32×#67—41no—
99C2×C32×Dic3—41no—
100C2×C32×Dic3—41no—
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C32×C4×D3—41no—
109C32×Dic6—41no—
110C32×Dic6—41no—
111C3×#562—34no—
112#5621C3211yescharacteristic, direct product factor
113C2×C32×Q8—31no—
114C2×C32×Q8—31no—
115C2×C32×D4—24no—
116C2×C32×D4—24no—
117C2×C32×D4—24no—
118C2×C32×D4—31no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4C2×D311yescharacteristic
122C2×C32×D4C2×D311yescharacteristic
123C2×C32×D4C2×D311yescharacteristic
124C2×C32×D4C22×C314yes—
125C2×C32×D4C22×C314yes—
126C2×C32×D4C22×C314yes—
127C22×C32×C4—24no—
128C22×C32×C4—31no—
129C22×C32×C4—31no—
130C22×C32×C4—31no—
131C22×C32×C4C2×D311yescharacteristic
132C22×C32×C4C22×C314yes—
133C2×C3×#67C22×C314yes—
134C2×C3×#67C22×C314yes—
135C2×C3×#67C22×C314yes—
136C22×C3×Dic3C22×C314yes—
137C22×C3×Dic3C22×C314yes—
138C2×C3×C4×D3C22×C314yes—
139C2×C3×Dic6C22×C314yes—
140C2×C3×Dic6C22×C314yes—
141C32×C4⋊C4—24no—
142C32×C4⋊C4—31no—
143C32×C4⋊C4—31no—
144C32×C4⋊C4—31no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C22×C314yes—
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⋊C4C2×D311yescharacteristic
166C32×C22⋊C4C2×D311yescharacteristic
167C32×C22⋊C4C22×C314yes—
168C32×C22⋊C4C22×C314yes—
169C32×C42—31no—
170C3×#217C22×C314yes—
171C3×#217C22×C314yes—
172C3×#217C22×C314yes—
173C3×#217C22×C314yes—
174C3×#217C22×C314yes—
175C3×#217C22×C314yes—
176C3×#217C22×C314yes—
177C3×(C2×D3)⋊C4C22×C314yes—
178C3×(C2×D3)⋊C4C22×C314yes—
179C3×(C2×D3)⋊C4C22×C314yes—
180C3×C4⋊Dic3C22×C314yes—
181C3×C4⋊Dic3C22×C314yes—
182C3×Dic3⋊C4C22×C314yes—
183C3×Dic3⋊C4C22×C314yes—
184C3×Dic3⋊C4C22×C314yes—
185C3×Dic3⋊C4C22×C314yes—
186C3×Dic3⋊C4C22×C314yes—
187C3×Dic3⋊C4C22×C314yes—
188C3×Dic3⋊C4C22×C314yes—
189C3×C4×Dic3C22×C314yes—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33C2411yescharacteristic
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C33×C4—21no—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C32×Dic3—21no—
210C32×Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C3×#125—34no—
215C3×#124—34no—
216C3×#124—34no—
217C3×#123—34no—
218C3×#123—34no—
219C3×#123—34no—
220C3×#123—34no—
221C3×C22⋊Q8—34no—
222C3×C22⋊Q8—34no—
223C3×C22⋊Q8—34no—
224C3×C22⋊Q8—34no—
225C3×#121—24no—
226C3×#121—34no—
227C3×#121—34no—
228C3×#121—34no—
229C3×#121C3×D314yescomplemented
230C3×#121C2×C3211yescharacteristic, complemented
231#939C2×C3211yescharacteristic, complemented
232#939C2×C3211yescharacteristic, complemented
233#938C2×C3211yescharacteristic, complemented
234#936C2×C3211yescharacteristic, complemented
235#935C2×C3211yescharacteristic, complemented
236#935C2×C3211yescharacteristic, complemented
237#929C2×C3211yescharacteristic, complemented
238#924C2×C3211yescharacteristic, complemented
239#896C2×C3211yescharacteristic, complemented
240#889C2×C3211yescharacteristic, complemented
241#885C2×C3211yescharacteristic, complemented
242#883C2×C3211yescharacteristic, complemented
243#878C2×C3211yescharacteristic, complemented
244#878C2×C3211yescharacteristic, complemented
245C23×C32—24no—
246C23×C32—24no—
247C23×C32—24no—
248C23×C32—31no—
249C23×C32C22×D311yescharacteristic
250C23×C32C22×D311yescharacteristic
251C23×C32C22×D311yescharacteristic
252C23×C32C23×C314yes—
253C23×C32C23×C314yes—
254C23×C32C23×C314yes—
255C22×C3×D3C23×C314yes—
256C32×Q8—121no—
257C32×Q8—121no—
258C32×D4—41no—
259C32×D4—41no—
260C32×D4—41no—
261C32×D4—44no—
262C32×D4—44no—
263C32×D4—44no—
264C32×D4—48no—
265C32×D4—48no—
266C32×D4—48no—
267C32×D4—121no—
268C32×D4—121no—
269C32×D4—121no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—24no—
273C2×C32×C4—24no—
274C2×C32×C4—31no—
275C2×C32×C4—31no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—41no—
282C2×C32×C4—44no—
283C2×C32×C4—48no—
284C2×C32×C4—121no—
285C2×C32×C4—121no—
286C2×C32×C4—121no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C23×C314yes—
292C2×C32×C4C23×C314yes—
293C2×C32×C4C23×C314yes—
294C2×C32×C4C23×C314yes—
295C3×#67—44no—
296C3×#67—44no—
297C3×#67—44no—
298C2×C3×Dic3—44no—
299C2×C3×Dic3—44no—
300C2×C3×Dic3C23×C314yes—
301C2×C3×Dic3C23×C314yes—
302C2×C3×Dic3C23×C314yes—
303C2×C3×Dic3C23×C314yes—
304C2×C3×Dic3C23×C314yes—
305C2×C3×Dic3C23×C314yes—
306C2×C3×Dic3C23×C314yes—
307C3×C4×D3—44no—
308C3×Dic6—44no—
309C3×Dic6—44no—
310#562—31noSylow
311C2×C33—41no—
312C2×C33—41no—
313C2×C33—41no—
314C2×C33H(5,𝔽2)11yescharacteristic
315C2×C33H(5,𝔽2)11yescharacteristic
316C2×C332−1+411yescharacteristic
317C32×D3—41no—
318C2×C3×Q8—34no—
319C2×C3×Q8—34no—
320C2×C3×D4—24no—
321C2×C3×D4—24no—
322C2×C3×D4—24no—
323C2×C3×D4—34no—
324C2×C3×D4—34no—
325C2×C3×D4—34no—
326C2×C3×D4C2×C3×D314yes—
327C2×C3×D4C2×C3×D314yes—
328C2×C3×D4C2×C3×D314yes—
329C2×C3×D4C22×C3211yescharacteristic
330C2×C3×D4C22×C3211yescharacteristic
331C2×C3×D4C22×C3211yescharacteristic
332C22×C3×C4—24no—
333C22×C3×C4—34no—
334C22×C3×C4—34no—
335C22×C3×C4—34no—
336C22×C3×C4C2×C3×D314yes—
337C22×C3×C4C22×C3211yescharacteristic
338C2×#67C22×C3211yescharacteristic
339C2×#67C22×C3211yescharacteristic
340C2×#67C22×C3211yescharacteristic
341C22×Dic3C22×C3211yescharacteristic
342C22×Dic3C22×C3211yescharacteristic
343C2×C4×D3C22×C3211yescharacteristic
344C2×Dic6C22×C3211yescharacteristic
345C2×Dic6C22×C3211yescharacteristic
346C3×C4⋊C4—24no—
347C3×C4⋊C4—34no—
348C3×C4⋊C4—34no—
349C3×C4⋊C4—34no—
350C3×C4⋊C4—34no—
351C3×C4⋊C4—34no—
352C3×C4⋊C4—34no—
353C3×C4⋊C4—34no—
354C3×C4⋊C4—34no—
355C3×C4⋊C4—34no—
356C3×C4⋊C4C2×C3×D314yes—
357C3×C4⋊C4C22×C3211yescharacteristic
358C3×C22⋊C4—24no—
359C3×C22⋊C4—24no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—34no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—34no—
370C3×C22⋊C4C2×C3×D314yes—
371C3×C22⋊C4C2×C3×D314yes—
372C3×C22⋊C4C22×C3211yescharacteristic
373C3×C22⋊C4C22×C3211yescharacteristic
374C3×C42—34no—
375#217C22×C3211yescharacteristic
376#217C22×C3211yescharacteristic
377#217C22×C3211yescharacteristic
378#217C22×C3211yescharacteristic
379#217C22×C3211yescharacteristic
380#217C22×C3211yescharacteristic
381#217C22×C3211yescharacteristic
382(C2×D3)⋊C4C22×C3211yescharacteristic
383(C2×D3)⋊C4C22×C3211yescharacteristic
384(C2×D3)⋊C4C22×C3211yescharacteristic
385C4⋊Dic3C22×C3211yescharacteristic
386C4⋊Dic3C22×C3211yescharacteristic
387Dic3⋊C4C22×C3211yescharacteristic
388Dic3⋊C4C22×C3211yescharacteristic
389Dic3⋊C4C22×C3211yescharacteristic
390Dic3⋊C4C22×C3211yescharacteristic
391Dic3⋊C4C22×C3211yescharacteristic
392Dic3⋊C4C22×C3211yescharacteristic
393Dic3⋊C4C22×C3211yescharacteristic
394C4×Dic3C22×C3211yescharacteristic
395C22×C32—28no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—24no—
406C22×C32—24no—
407C22×C32—24no—
408C22×C32—24no—
409C22×C32—24no—
410C22×C32—24no—
411C22×C32—24no—
412C22×C32—24no—
413C22×C32—24no—
414C22×C32—24no—
415C22×C32—44no—
416C22×C32—44no—
417C22×C32—44no—
418C22×C32—44no—
419C22×C32—44no—
420C22×C32—44no—
421C22×C32—44no—
422C22×C32—44no—
423C22×C32—61no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32C23×D311yescharacteristic
427C22×C32C24×C314yes—
428C2×C3×D3—24no—
429C2×C3×D3—24no—
430C2×C3×D3—24no—
431C32×C4—28no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—24no—
437C32×C4—24no—
438C32×C4—24no—
439C32×C4—24no—
440C32×C4—44no—
441C32×C4—44no—
442C32×C4—44no—
443C32×C4—61no—
444C32×C4—61no—
445C32×C4—61no—
446C32×C4—61no—
447C32×C4—61no—
448C32×C4—61no—
449C32×C4—61no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—24no—
453C3×Dic3—24no—
454C3×Dic3—24no—
455C3×Dic3—24no—
456C3×Dic3—24no—
457#125—31no—
458#124—31no—
459#124—31no—
460#123—31no—
461#123—31no—
462#123—31no—
463#123—31no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—31no—
467C22⋊Q8—31no—
468#121—31no—
469#121—31no—
470#121—31no—
471#121C32×D311yescharacteristic, complemented
472C33#56211yescharacteristic, complemented, Sylow
473C23×C3—24no—
474C23×C3—24no—
475C23×C3—24no—
476C23×C3—34no—
477C23×C3C22×C3×D314yes—
478C23×C3C22×C3×D314yes—
479C23×C3C22×C3×D314yes—
480C23×C3C23×C3211yescharacteristic
481C23×C3C23×C3211yescharacteristic
482C23×C3C23×C3211yescharacteristic
483C22×D3C23×C3211yescharacteristic
484C3×Q8—124no—
485C3×Q8—124no—
486C3×D4—44no—
487C3×D4—44no—
488C3×D4—44no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—48no—
493C3×D4—48no—
494C3×D4—48no—
495C3×D4—124no—
496C3×D4—124no—
497C3×D4—124no—
498C2×C3×C4—24no—
499C2×C3×C4—24no—
500C2×C3×C4—24no—
501C2×C3×C4—24no—
502C2×C3×C4—34no—
503C2×C3×C4—34no—
504C2×C3×C4—34no—
505C2×C3×C4—34no—
506C2×C3×C4—34no—
507C2×C3×C4—34no—
508C2×C3×C4—34no—
509C2×C3×C4—44no—
510C2×C3×C4—41no—
511C2×C3×C4—48no—
512C2×C3×C4—124no—
513C2×C3×C4—124no—
514C2×C3×C4—124no—
515C2×C3×C4C22×C3×D314yes—
516C2×C3×C4C22×C3×D314yes—
517C2×C3×C4C22×C3×D314yes—
518C2×C3×C4C22×C3×D314yes—
519C2×C3×C4C23×C3211yescharacteristic
520C2×C3×C4C23×C3211yescharacteristic
521C2×C3×C4C23×C3211yescharacteristic
522C2×C3×C4C23×C3211yescharacteristic
523#67—41no—
524#67—41no—
525#67—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3C23×C3211yescharacteristic
529C2×Dic3C23×C3211yescharacteristic
530C2×Dic3C23×C3211yescharacteristic
531C2×Dic3C23×C3211yescharacteristic
532C2×Dic3C23×C3211yescharacteristic
533C2×Dic3C23×C3211yescharacteristic
534C2×Dic3C23×C3211yescharacteristic
535C4×D3—41no—
536Dic6—41no—
537Dic6—41no—
538C2×C32—24no—
539C2×C32—24no—
540C2×C32—24no—
541C2×C32—48no—
542C2×C32—44no—
543C2×C32—41no—
544C2×C32—41no—
545C2×C32—41no—
546C2×C32—44no—
547C2×C32—44no—
548C2×C32—84no—
549C2×C32—84no—
550C2×C32—121no—
551C2×C32#100411yescharacteristic
552C2×C32#100411yescharacteristic
553C2×C32#101011yescharacteristic
554C2×C32C3×H(5,𝔽2)14yes—
555C2×C32C3×H(5,𝔽2)14yes—
556C2×C32C3×2−1+414yes—
557C3×D3—44no—
558C2×Q8—31no—
559C2×Q8—31no—
560C2×D4—31no—
561C2×D4—31no—
562C2×D4—31no—
563C2×D4C2×C32×D311yescharacteristic
564C2×D4C2×C32×D311yescharacteristic
565C2×D4C2×C32×D311yescharacteristic
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4C2×C32×D311yescharacteristic
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4C2×C32×D311yescharacteristic
580C22⋊C4—31no—
581C22⋊C4—31no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—31no—
585C22⋊C4—31no—
586C22⋊C4—31no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—31no—
590C22⋊C4C2×C32×D311yescharacteristic
591C22⋊C4C2×C32×D311yescharacteristic
592C42—31no—
593C22×C3—28no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—24no—
613C22×C3—44no—
614C22×C3—44no—
615C22×C3—44no—
616C22×C3—44no—
617C22×C3—44no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—64no—
622C22×C3—64no—
623C22×C3—64no—
624C22×C3C23×C3×D314yes—
625C22×C3C24×C3211yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C3×C4—28no—
630C3×C4—24no—
631C3×C4—24no—
632C3×C4—24no—
633C3×C4—24no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—44no—
639C3×C4—44no—
640C3×C4—44no—
641C3×C4—64no—
642C3×C4—64no—
643C3×C4—64no—
644C3×C4—64no—
645C3×C4—64no—
646C3×C4—64no—
647C3×C4—64no—
648Dic3—21no—
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655C32—24no—
656C32#562111yescharacteristic, direct product factor
657C32C3×#56214yescomplemented
658C23—31no—
659C23C22×C32×D311yescharacteristic
660C23C22×C32×D311yescharacteristic
661C23C22×C32×D311yescharacteristic
662Q8—121no—
663Q8—121no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—121no—
668D4—121no—
669D4—121no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—31no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—41no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4C22×C32×D311yescharacteristic
682C2×C4C22×C32×D311yescharacteristic
683C2×C4C22×C32×D311yescharacteristic
684C2×C4C22×C32×D311yescharacteristic
685C2×C3—24no—
686C2×C3—24no—
687C2×C3—24no—
688C2×C3—48no—
689C2×C3—41no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—44no—
693C2×C3—44no—
694C2×C3—44no—
695C2×C3—84no—
696C2×C3—84no—
697C2×C3—124no—
698C2×C3C3×#100414yes—
699C2×C3C3×#100414yes—
700C2×C3C3×#101014yes—
701C2×C3C32×H(5,𝔽2)11yescharacteristic
702C2×C3C32×H(5,𝔽2)11yescharacteristic
703C2×C3C32×2−1+411yescharacteristic
704D3—41no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—61no—
715C22—61no—
716C22—61no—
717C22C23×C32×D311yescharacteristic
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—61no—
723C4—61no—
724C4—61no—
725C4—61no—
726C4—61no—
727C4—61no—
728C4—61no—
729C3—24no—
730C3C3×#562114yesdirect product factor
731C3C32×#56211yescharacteristic, complemented
732C2—41no—
733C2—41no—
734C2—41no—
735C2—121no—
736C2C32×#100411yescharacteristic
737C2C32×#100411yescharacteristic
738C2C32×#101011yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#121C2
socleC22×C33C24
hypercenterC32×#121D3
hypocenterC3C32×#562
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×#939C2semidirect
4. C32×#938C2semidirect
5. C32×#936C2semidirect
6. C32×#935C2semidirect
7. C32×#935C2semidirect
8. C32×#929C2semidirect
9. C32×#924C2semidirect
10. C32×#896C2semidirect
11. C32×#889C2semidirect
12. C32×#885C2semidirect
13. C32×#883C2semidirect
14. C32×#878C2semidirect
15. C32×#878C2semidirect
17. C3×#5621C3direct (N × H)
68. C32×#121D3semidirect
69. C32×#121C2×C3semidirect
70. C3×#939C2×C3semidirect
71. C3×#939C2×C3semidirect
72. C3×#938C2×C3semidirect
73. C3×#936C2×C3semidirect
74. C3×#935C2×C3semidirect
75. C3×#935C2×C3semidirect
76. C3×#929C2×C3semidirect
77. C3×#924C2×C3semidirect
78. C3×#896C2×C3semidirect
79. C3×#889C2×C3semidirect
80. C3×#885C2×C3semidirect
81. C3×#883C2×C3semidirect
82. C3×#878C2×C3semidirect
83. C3×#878C2×C3semidirect
112. #5621C32direct (N × H)
229. C3×#121C3×D3semidirect
230. C3×#121C2×C32semidirect
231. #939C2×C32semidirect
232. #939C2×C32semidirect
233. #938C2×C32semidirect
234. #936C2×C32semidirect
235. #935C2×C32semidirect
236. #935C2×C32semidirect
237. #929C2×C32semidirect
238. #924C2×C32semidirect
239. #896C2×C32semidirect
240. #889C2×C32semidirect
241. #885C2×C32semidirect
242. #883C2×C32semidirect
243. #878C2×C32semidirect
244. #878C2×C32semidirect
471. #121C32×D3semidirect
472. C33#562semidirect
656. C32#5621direct (N × H)
657. C32C3×#562semidirect
730. C3C3×#5621direct (N × H)
731. C3C32×#562semidirect

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×#9362
C32×#9352
C32×#9292
C32×#9242
C32×#8962
C32×#8892
C32×#8852
C32×#8832
C32×#8782
C32×#5623
C3×#56213