Finite Group Databasebeta

← C32×#5615 #13178978

Subgroups — C32×#5615 #13178978

Order 1728.

1816 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#121C211yesmaximal, characteristic, complemented
2C32×#940C211yesmaximal, characteristic, complemented
3C32×#939C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C32×#939C211yesmaximal, characteristic, complemented
6C32×#938C211yesmaximal, characteristic, complemented
7C32×#935C211yesmaximal, characteristic, complemented
8C32×#929C211yesmaximal, characteristic, complemented
9C32×C4×#67C211yesmaximal, characteristic, complemented
10C32×#894C211yesmaximal, characteristic, complemented
11C32×#889C211yesmaximal, characteristic, complemented
12C32×#884C211yesmaximal, characteristic, complemented
13C32×#883C211yesmaximal, characteristic, complemented
14C32×#67⋊C4C211yesmaximal, characteristic, complemented
15C32×#877C211yesmaximal, characteristic, complemented
16C32×#540—31nomaximal
17C3×#5615C314yesmaximal, direct product factor
18C2×C33×D4C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C22×C33×C4C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic
28C22×C32×Dic3C2211yescharacteristic
29C22×C32×Dic3C2211yescharacteristic
30C2×C32×D12C2211yescharacteristic
31C2×C32×C4×D3C2211yescharacteristic
32C2×C32×C4×D3C2211yescharacteristic
33C33×C4⋊C4C2211yescharacteristic
34C33×C22⋊C4C2211yescharacteristic
35C33×C22⋊C4C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×C4⋊Dic3C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×Dic3⋊C4C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#127—31no—
54C32×#125—31no—
55C32×#123—31no—
56C32×#123—31no—
57C32×#123—31no—
58C32×#123—31no—
59C32×#121—24no—
60C32×#121—31no—
61C32×#121—31no—
62C32×#121—31no—
63C32×#121—31no—
64C32×#121—31no—
65C32×#121D311yescharacteristic, complemented
66C32×#121C2×C314yescomplemented
67C32×C4×D4—31no—
68C32×C4×D4—31no—
69C32×#117—31no—
70C3×#940C2×C314yescomplemented
71C3×#939C2×C314yescomplemented
72C3×#939C2×C314yescomplemented
73C3×#939C2×C314yescomplemented
74C3×#938C2×C314yescomplemented
75C3×#935C2×C314yescomplemented
76C3×#929C2×C314yescomplemented
77C3×C4×#67C2×C314yescomplemented
78C3×#894C2×C314yescomplemented
79C3×#889C2×C314yescomplemented
80C3×#884C2×C314yescomplemented
81C3×#883C2×C314yescomplemented
82C3×#67⋊C4C2×C314yescomplemented
83C3×#877C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C23×C33C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C33×D4—41no—
90C33×D4—41no—
91C33×D4—41no—
92C2×C33×C4—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C32×#67—22no—
98C32×#67—22no—
99C32×#67—41no—
100C32×#67—41no—
101C32×#67—41no—
102C32×#67—41no—
103C2×C32×Dic3—22no—
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C32×D12—41no—
112C32×C4×D3—41no—
113C32×C4×D3—41no—
114C3×#540—34no—
115#5615C3211yescharacteristic, direct product factor
116C2×C32×D4—24no—
117C2×C32×D4—24no—
118C2×C32×D4—24no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
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
129C2×C32×D4C22×C314yes—
130C2×C32×D4C22×C314yes—
131C2×C32×D4C22×C314yes—
132C22×C32×C4—24no—
133C22×C32×C4—31no—
134C22×C32×C4—31no—
135C22×C32×C4—31no—
136C22×C32×C4—31no—
137C22×C32×C4C2×D311yescharacteristic
138C22×C32×C4C22×C314yes—
139C2×C3×#67C22×C314yes—
140C2×C3×#67C22×C314yes—
141C2×C3×#67C22×C314yes—
142C2×C3×#67C22×C314yes—
143C2×C3×#67C22×C314yes—
144C2×C3×#67C22×C314yes—
145C22×C3×Dic3C22×C314yes—
146C22×C3×Dic3C22×C314yes—
147C2×C3×D12C22×C314yes—
148C2×C3×C4×D3C22×C314yes—
149C2×C3×C4×D3C22×C314yes—
150C32×C4⋊C4—24no—
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154C32×C4⋊C4—31no—
155C32×C4⋊C4—31no—
156C32×C4⋊C4—31no—
157C32×C4⋊C4—31no—
158C32×C4⋊C4C2×D311yescharacteristic
159C32×C4⋊C4C22×C314yes—
160C32×C22⋊C4—24no—
161C32×C22⋊C4—24no—
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⋊C4—31no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4C2×D311yescharacteristic
171C32×C22⋊C4C2×D311yescharacteristic
172C32×C22⋊C4C22×C314yes—
173C32×C22⋊C4C22×C314yes—
174C32×C42—31no—
175C32×C42—31no—
176C3×#217C22×C314yes—
177C3×#217C22×C314yes—
178C3×#217C22×C314yes—
179C3×#217C22×C314yes—
180C3×(C2×D3)⋊C4C22×C314yes—
181C3×(C2×D3)⋊C4C22×C314yes—
182C3×(C2×D3)⋊C4C22×C314yes—
183C3×(C2×D3)⋊C4C22×C314yes—
184C3×C4⋊Dic3C22×C314yes—
185C3×Dic3⋊C4C22×C314yes—
186C3×Dic3⋊C4C22×C314yes—
187C3×Dic3⋊C4C22×C314yes—
188C3×Dic3⋊C4C22×C314yes—
189C3×Dic3⋊C4C22×C314yes—
190C3×Dic3⋊C4C22×C314yes—
191C3×C4×Dic3C22×C314yes—
192C3×C4×Dic3C22×C314yes—
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—21no—
209C33×C4—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#4112yes—
219C3×#127—34no—
220C3×#125—34no—
221C3×#123—34no—
222C3×#123—34no—
223C3×#123—34no—
224C3×#123—34no—
225C3×#121—24no—
226C3×#121—34no—
227C3×#121—34no—
228C3×#121—34no—
229C3×#121—34no—
230C3×#121—34no—
231C3×#121C3×D314yescomplemented
232C3×#121C2×C3211yescharacteristic, complemented
233C3×C4×D4—34no—
234C3×C4×D4—34no—
235C3×#117—34no—
236#940C2×C3211yescharacteristic, complemented
237#939C2×C3211yescharacteristic, complemented
238#939C2×C3211yescharacteristic, complemented
239#939C2×C3211yescharacteristic, complemented
240#938C2×C3211yescharacteristic, complemented
241#935C2×C3211yescharacteristic, complemented
242#929C2×C3211yescharacteristic, complemented
243C4×#67C2×C3211yescharacteristic, complemented
244#894C2×C3211yescharacteristic, complemented
245#889C2×C3211yescharacteristic, complemented
246#884C2×C3211yescharacteristic, complemented
247#883C2×C3211yescharacteristic, complemented
248#67⋊C4C2×C3211yescharacteristic, complemented
249#877C2×C3211yescharacteristic, complemented
250C23×C32—24no—
251C23×C32—24no—
252C23×C32—24no—
253C23×C32—31no—
254C23×C32—31no—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C23×C32C23×C314yes—
259C23×C32C23×C314yes—
260C23×C32C23×C314yes—
261C22×C3×D3C23×C314yes—
262C22×C3×D3C23×C314yes—
263C32×D4—41no—
264C32×D4—41no—
265C32×D4—41no—
266C32×D4—44no—
267C32×D4—44no—
268C32×D4—44no—
269C32×D4—48no—
270C32×D4—48no—
271C32×D4—48no—
272C32×D4—62no—
273C32×D4—62no—
274C32×D4—121no—
275C32×D4—121no—
276C32×D4—121no—
277C32×D4—121no—
278C32×D4—121no—
279C2×C32×C4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—24no—
283C2×C32×C4—31no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—41no—
290C2×C32×C4—44no—
291C2×C32×C4—48no—
292C2×C32×C4—62no—
293C2×C32×C4—121no—
294C2×C32×C4—121no—
295C2×C32×C4—121no—
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C23×C314yes—
301C2×C32×C4C23×C314yes—
302C2×C32×C4C23×C314yes—
303C2×C32×C4C23×C314yes—
304C3×#67—28no—
305C3×#67—28no—
306C3×#67—44no—
307C3×#67—44no—
308C3×#67—44no—
309C3×#67—44no—
310C2×C3×Dic3—28no—
311C2×C3×Dic3—44no—
312C2×C3×Dic3C23×C314yes—
313C2×C3×Dic3C23×C314yes—
314C2×C3×Dic3C23×C314yes—
315C2×C3×Dic3C23×C314yes—
316C2×C3×Dic3C23×C314yes—
317C2×C3×Dic3C23×C314yes—
318C3×D12—44no—
319C3×C4×D3—44no—
320C3×C4×D3—44no—
321#540—31noSylow
322C2×C33—41no—
323C2×C33—41no—
324C2×C33—41no—
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C32×D3—41no—
329C32×D3—41no—
330C2×C3×D4—24no—
331C2×C3×D4—24no—
332C2×C3×D4—24no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—34no—
338C2×C3×D4—34no—
339C2×C3×D4—34no—
340C2×C3×D4C2×C3×D314yes—
341C2×C3×D4C2×C3×D314yes—
342C2×C3×D4C2×C3×D314yes—
343C2×C3×D4C22×C3211yescharacteristic
344C2×C3×D4C22×C3211yescharacteristic
345C2×C3×D4C22×C3211yescharacteristic
346C22×C3×C4—24no—
347C22×C3×C4—34no—
348C22×C3×C4—34no—
349C22×C3×C4—34no—
350C22×C3×C4—34no—
351C22×C3×C4C2×C3×D314yes—
352C22×C3×C4C22×C3211yescharacteristic
353C2×#67C22×C3211yescharacteristic
354C2×#67C22×C3211yescharacteristic
355C2×#67C22×C3211yescharacteristic
356C2×#67C22×C3211yescharacteristic
357C2×#67C22×C3211yescharacteristic
358C2×#67C22×C3211yescharacteristic
359C22×Dic3C22×C3211yescharacteristic
360C22×Dic3C22×C3211yescharacteristic
361C2×D12C22×C3211yescharacteristic
362C2×C4×D3C22×C3211yescharacteristic
363C2×C4×D3C22×C3211yescharacteristic
364C3×C4⋊C4—24no—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4—34no—
368C3×C4⋊C4—34no—
369C3×C4⋊C4—34no—
370C3×C4⋊C4—34no—
371C3×C4⋊C4—34no—
372C3×C4⋊C4C2×C3×D314yes—
373C3×C4⋊C4C22×C3211yescharacteristic
374C3×C22⋊C4—24no—
375C3×C22⋊C4—24no—
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⋊C4—34no—
384C3×C22⋊C4C2×C3×D314yes—
385C3×C22⋊C4C2×C3×D314yes—
386C3×C22⋊C4C22×C3211yescharacteristic
387C3×C22⋊C4C22×C3211yescharacteristic
388C3×C42—34no—
389C3×C42—34no—
390#217C22×C3211yescharacteristic
391#217C22×C3211yescharacteristic
392#217C22×C3211yescharacteristic
393#217C22×C3211yescharacteristic
394(C2×D3)⋊C4C22×C3211yescharacteristic
395(C2×D3)⋊C4C22×C3211yescharacteristic
396(C2×D3)⋊C4C22×C3211yescharacteristic
397(C2×D3)⋊C4C22×C3211yescharacteristic
398C4⋊Dic3C22×C3211yescharacteristic
399Dic3⋊C4C22×C3211yescharacteristic
400Dic3⋊C4C22×C3211yescharacteristic
401Dic3⋊C4C22×C3211yescharacteristic
402Dic3⋊C4C22×C3211yescharacteristic
403Dic3⋊C4C22×C3211yescharacteristic
404Dic3⋊C4C22×C3211yescharacteristic
405C4×Dic3C22×C3211yescharacteristic
406C4×Dic3C22×C3211yescharacteristic
407C22×C32—28no—
408C22×C32—21no—
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—24no—
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—44no—
428C22×C32—44no—
429C22×C32—44no—
430C22×C32—44no—
431C22×C32—44no—
432C22×C32—44no—
433C22×C32—44no—
434C22×C32—44no—
435C22×C32—61no—
436C22×C32—61no—
437C22×C32—61no—
438C22×C32—61no—
439C22×C32—61no—
440C22×C32—61no—
441C22×C32C23×D311yescharacteristic
442C22×C32C24×C314yes—
443C2×C3×D3—24no—
444C2×C3×D3—24no—
445C2×C3×D3—24no—
446C2×C3×D3—24no—
447C2×C3×D3—24no—
448C2×C3×D3—24no—
449C32×C4—28no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—21no—
454C32×C4—24no—
455C32×C4—24no—
456C32×C4—24no—
457C32×C4—24no—
458C32×C4—32no—
459C32×C4—44no—
460C32×C4—44no—
461C32×C4—44no—
462C32×C4—61no—
463C32×C4—61no—
464C32×C4—61no—
465C32×C4—61no—
466C32×C4—61no—
467C3×Dic3—24no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3C3×#4118yes—
473#127—31no—
474#125—31no—
475#123—31no—
476#123—31no—
477#123—31no—
478#123—31no—
479#121—31no—
480#121—31no—
481#121—31no—
482#121—31no—
483#121—31no—
484#121C32×D311yescharacteristic, complemented
485C4×D4—31no—
486C4×D4—31no—
487#117—31no—
488C33#54011yescharacteristic, complemented, Sylow
489C23×C3—24no—
490C23×C3—24no—
491C23×C3—24no—
492C23×C3—34no—
493C23×C3—34no—
494C23×C3C22×C3×D314yes—
495C23×C3C22×C3×D314yes—
496C23×C3C22×C3×D314yes—
497C23×C3C23×C3211yescharacteristic
498C23×C3C23×C3211yescharacteristic
499C23×C3C23×C3211yescharacteristic
500C22×D3C23×C3211yescharacteristic
501C22×D3C23×C3211yescharacteristic
502C3×D4—44no—
503C3×D4—44no—
504C3×D4—44no—
505C3×D4—41no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—48no—
509C3×D4—48no—
510C3×D4—48no—
511C3×D4—68no—
512C3×D4—68no—
513C3×D4—124no—
514C3×D4—124no—
515C3×D4—124no—
516C3×D4—124no—
517C3×D4—124no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—24no—
522C2×C3×C4—34no—
523C2×C3×C4—34no—
524C2×C3×C4—34no—
525C2×C3×C4—34no—
526C2×C3×C4—34no—
527C2×C3×C4—34no—
528C2×C3×C4—44no—
529C2×C3×C4—41no—
530C2×C3×C4—48no—
531C2×C3×C4—68no—
532C2×C3×C4—124no—
533C2×C3×C4—124no—
534C2×C3×C4—124no—
535C2×C3×C4C22×C3×D314yes—
536C2×C3×C4C22×C3×D314yes—
537C2×C3×C4C22×C3×D314yes—
538C2×C3×C4C22×C3×D314yes—
539C2×C3×C4C23×C3211yescharacteristic
540C2×C3×C4C23×C3211yescharacteristic
541C2×C3×C4C23×C3211yescharacteristic
542C2×C3×C4C23×C3211yescharacteristic
543#67—22no—
544#67—22no—
545#67—41no—
546#67—41no—
547#67—41no—
548#67—41no—
549C2×Dic3—22no—
550C2×Dic3—41no—
551C2×Dic3C23×C3211yescharacteristic
552C2×Dic3C23×C3211yescharacteristic
553C2×Dic3C23×C3211yescharacteristic
554C2×Dic3C23×C3211yescharacteristic
555C2×Dic3C23×C3211yescharacteristic
556C2×Dic3C23×C3211yescharacteristic
557D12—41no—
558C4×D3—41no—
559C4×D3—41no—
560C2×C32—24no—
561C2×C32—24no—
562C2×C32—24no—
563C2×C32—48no—
564C2×C32—44no—
565C2×C32—41no—
566C2×C32—41no—
567C2×C32—41no—
568C2×C32—44no—
569C2×C32—44no—
570C2×C32—84no—
571C2×C32—84no—
572C2×C32—121no—
573C2×C32—121no—
574C2×C32#100411yescharacteristic
575C2×C32#100411yescharacteristic
576C2×C32D3×#4111yescharacteristic
577C2×C32C2×C3×#4114yes—
578C2×C32C3×H(5,𝔽2)14yes—
579C2×C32C3×H(5,𝔽2)14yes—
580C3×D3—44no—
581C3×D3—44no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4C2×C32×D311yescharacteristic
590C2×D4C2×C32×D311yescharacteristic
591C2×D4C2×C32×D311yescharacteristic
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4C2×C32×D311yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4C2×C32×D311yescharacteristic
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⋊C4C2×C32×D311yescharacteristic
614C22⋊C4C2×C32×D311yescharacteristic
615C42—31no—
616C42—31no—
617C22×C3—28no—
618C22×C3—24no—
619C22×C3—24no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—24no—
637C22×C3—44no—
638C22×C3—44no—
639C22×C3—44no—
640C22×C3—44no—
641C22×C3—44no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—44no—
645C22×C3—64no—
646C22×C3—64no—
647C22×C3—64no—
648C22×C3—64no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3C23×C3×D314yes—
652C22×C3C24×C3211yescharacteristic
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C3×C4—28no—
660C3×C4—24no—
661C3×C4—24no—
662C3×C4—24no—
663C3×C4—24no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—38no—
669C3×C4—44no—
670C3×C4—44no—
671C3×C4—44no—
672C3×C4—64no—
673C3×C4—64no—
674C3×C4—64no—
675C3×C4—64no—
676C3×C4—64no—
677Dic3—21no—
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3C32×#4112yes—
683C32—24no—
684C32#561511yescharacteristic, direct product factor
685C32C3×#54014yescomplemented
686C23—31no—
687C23—31no—
688C23C22×C32×D311yescharacteristic
689C23C22×C32×D311yescharacteristic
690C23C22×C32×D311yescharacteristic
691D4—41no—
692D4—41no—
693D4—41no—
694D4—62no—
695D4—62no—
696D4—121no—
697D4—121no—
698D4—121no—
699D4—121no—
700D4—121no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—41no—
708C2×C4—62no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4C22×C32×D311yescharacteristic
713C2×C4C22×C32×D311yescharacteristic
714C2×C4C22×C32×D311yescharacteristic
715C2×C4C22×C32×D311yescharacteristic
716C2×C3—24no—
717C2×C3—24no—
718C2×C3—24no—
719C2×C3—48no—
720C2×C3—44no—
721C2×C3—44no—
722C2×C3—44no—
723C2×C3—41no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—84no—
727C2×C3—84no—
728C2×C3—124no—
729C2×C3—124no—
730C2×C3C3×#100414yes—
731C2×C3C3×#100414yes—
732C2×C3C3×D3×#4114yes—
733C2×C3C2×C32×#4111yescharacteristic
734C2×C3C32×H(5,𝔽2)11yescharacteristic
735C2×C3C32×H(5,𝔽2)11yescharacteristic
736D3—41no—
737D3—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—61no—
748C22—61no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22C23×C32×D311yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—32no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—61no—
764C3—24no—
765C3C3×#561514yesdirect product factor
766C3C32×#54011yescharacteristic, complemented
767C2—41no—
768C2—41no—
769C2—41no—
770C2—121no—
771C2—121no—
772C2C32×#100411yescharacteristic
773C2C32×#100411yescharacteristic
774C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#121C2
socleC22×C33C24
hypercenterC32×#121D3
hypocenterC3C32×#540
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×#940C2semidirect
3. C32×#939C2semidirect
4. C32×#939C2semidirect
5. C32×#939C2semidirect
6. C32×#938C2semidirect
7. C32×#935C2semidirect
8. C32×#929C2semidirect
9. C32×C4×#67C2semidirect
10. C32×#894C2semidirect
11. C32×#889C2semidirect
12. C32×#884C2semidirect
13. C32×#883C2semidirect
14. C32×#67⋊C4C2semidirect
15. C32×#877C2semidirect
17. C3×#5615C3direct (N × H)
65. C32×#121D3semidirect
66. C32×#121C2×C3semidirect
70. C3×#940C2×C3semidirect
71. C3×#939C2×C3semidirect
72. C3×#939C2×C3semidirect
73. C3×#939C2×C3semidirect
74. C3×#938C2×C3semidirect
75. C3×#935C2×C3semidirect
76. C3×#929C2×C3semidirect
77. C3×C4×#67C2×C3semidirect
78. C3×#894C2×C3semidirect
79. C3×#889C2×C3semidirect
80. C3×#884C2×C3semidirect
81. C3×#883C2×C3semidirect
82. C3×#67⋊C4C2×C3semidirect
83. C3×#877C2×C3semidirect
115. #5615C32direct (N × H)
231. C3×#121C3×D3semidirect
232. C3×#121C2×C32semidirect
236. #940C2×C32semidirect
237. #939C2×C32semidirect
238. #939C2×C32semidirect
239. #939C2×C32semidirect
240. #938C2×C32semidirect
241. #935C2×C32semidirect
242. #929C2×C32semidirect
243. C4×#67C2×C32semidirect
244. #894C2×C32semidirect
245. #889C2×C32semidirect
246. #884C2×C32semidirect
247. #883C2×C32semidirect
248. #67⋊C4C2×C32semidirect
249. #877C2×C32semidirect
484. #121C32×D3semidirect
488. C33#540semidirect
684. C32#5615direct (N × H)
685. C32C3×#540semidirect
765. C3C3×#5615direct (N × H)
766. C3C32×#540semidirect

Maximal subgroups

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

subgroupindex
C33×#1212
C32×#9402
C32×#9392
C32×#9382
C32×#9352
C32×#9292
C32×C4×#672
C32×#8942
C32×#8892
C32×#8842
C32×#8832
C32×#67⋊C42
C32×#8772
C32×#5403
C3×#56153