Finite Group Databasebeta

← C3×#17577 #10636184

Subgroups — C3×#17577 #10636184

Order 768.

1762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C2×C3×#407C211yesmaximal, characteristic, complemented
3C3×#2280C211yesmaximal, characteristic, complemented
4C3×#1519C214yesmaximal, complemented
5C3×#1510C214yesmaximal, complemented
6C3×#1507C214yesmaximal, complemented
7#17577C311yesmaximal, characteristic, direct product factor, Sylow
8C23×C3×D4—21no—
9C23×C3×D4C411yescharacteristic, complemented
10C24×C3×C4C2211yescharacteristic
11C22×C3×M16—21no—
12C2×C3×#121—21no—
13C2×C3×#121—21no—
14C2×C3×#121—21no—
15C2×C3×#121—21no—
16C2×C3×#121—21no—
17C2×C3×#121—21no—
18C2×C3×#121C412yescomplemented
19C2×C3×#121C412yescomplemented
20C2×C3×#121C412yescomplemented
21C2×C3×#121C2212yes—
22C2×C3×#121C2212yes—
23C2×C3×#121C2212yes—
24C2×C3×#117—21no—
25C22×C3×C4⋊C4C411yescharacteristic, complemented
26C22×C3×C22⋊C4—21no—
27C3×#407—21no—
28C3×#407—21no—
29C3×#407C2212yescomplemented
30C3×#407C2212yescomplemented
31C2×C3×C22⋊C8—21no—
32C2×C3×C22⋊C8C2212yescomplemented
33C3×#381C2212yescomplemented
34C3×#380—21no—
35C3×#380C2212yescomplemented
36C3×#379—21no—
37C3×C4×C22⋊C4—21no—
38C3×C4×C22⋊C4C2212yescomplemented
39C3×#327C22116yescomplemented
40C22×#121C2×C311yescharacteristic
41C2×#407C2×C311yescharacteristic, complemented
42#2280C2×C311yescharacteristic, complemented
43#1519C2×C314yescomplemented
44#1510C2×C314yescomplemented
45#1507C2×C314yescomplemented
46C25×C3—21no—
47C25×C3D411yescharacteristic
48C22×C3×D4—22no—
49C22×C3×D4—22no—
50C22×C3×D4—22no—
51C22×C3×D4—22no—
52C22×C3×D4—22no—
53C22×C3×D4—22no—
54C22×C3×D4—21no—
55C22×C3×D4—21no—
56C22×C3×D4—21no—
57C22×C3×D4—44no—
58C22×C3×D4—48no—
59C22×C3×D4C2×C412yes—
60C22×C3×D4C2×C412yes—
61C22×C3×D4C2×C412yes—
62C23×C3×C4—21no—
63C23×C3×C4—44no—
64C23×C3×C4C2×C411yescharacteristic
65C23×C3×C4C2×C411yescharacteristic
66C23×C3×C4C2×C411yescharacteristic
67C23×C3×C4C2×C411yescharacteristic
68C23×C3×C4D411yescharacteristic
69C23×C3×C4D411yescharacteristic
70C23×C3×C4D411yescharacteristic
71C23×C3×C4D411yescharacteristic
72C23×C3×C4D411yescharacteristic
73C23×C3×C4D411yescharacteristic
74C23×C3×C4D411yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C2×C3×M16—22no—
79C2×C3×M16—22no—
80C2×C3×M16—44no—
81C22×C3×C8—22no—
82C3×#121—22no—
83C3×#121—22no—
84C3×#121—22no—
85C3×#121—22no—
86C3×#121—22no—
87C3×#121—22no—
88C3×#121—22no—
89C3×#121—22no—
90C3×#121—22no—
91C3×#121—22no—
92C3×#121—22no—
93C3×#121—22no—
94C3×#121C2×C414yes—
95C3×#121C2×C414yes—
96C3×#121C2×C414yes—
97C3×#121C2314yes—
98C3×#117—44no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4C2×C412yes—
104C2×C3×C4⋊C4C2×C412yes—
105C2×C3×C4⋊C4C2×C412yes—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C42—22no—
116C3×C22⋊C8—22no—
117C3×C22⋊C8—22no—
118C3×C22⋊C8—22no—
119C3×C22⋊C8C2314yescomplemented
120C3×#95—22no—
121C3×#95C2314yescomplemented
122C23×D4—21no—
123C23×D4C3×C411yescharacteristic, complemented
124C24×C4C22×C311yescharacteristic
125C22×M16—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121—21no—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121C3×C412yescomplemented
133C2×#121C3×C412yescomplemented
134C2×#121C3×C412yescomplemented
135C2×#121C22×C312yes—
136C2×#121C22×C312yes—
137C2×#121C22×C312yes—
138C2×#117—21no—
139C22×C4⋊C4C3×C411yescharacteristic, complemented
140C22×C22⋊C4—21no—
141#407—21no—
142#407—21no—
143#407C22×C312yescomplemented
144#407C22×C312yescomplemented
145C2×C22⋊C8—21no—
146C2×C22⋊C8C22×C312yescomplemented
147#381C22×C312yescomplemented
148#380—21no—
149#380C22×C312yescomplemented
150#379—21no—
151C4×C22⋊C4—21no—
152C4×C22⋊C4C22×C312yescomplemented
153#327C22×C3116yescomplemented
154C24×C3—24no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—42no—
159C24×C3—42no—
160C24×C3—44no—
161C24×C3—44no—
162C24×C3—44no—
163C24×C3C22⋊C411yescharacteristic
164C24×C3C22⋊C411yescharacteristic
165C24×C3C22⋊C411yescharacteristic
166C24×C3C22⋊C411yescharacteristic
167C24×C3C2×D411yescharacteristic
168C24×C3C2×D411yescharacteristic
169C24×C3C2×D411yescharacteristic
170C2×C3×D4—24no—
171C2×C3×D4—24no—
172C2×C3×D4—24no—
173C2×C3×D4—24no—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—44no—
178C2×C3×D4—44no—
179C2×C3×D4—44no—
180C2×C3×D4—44no—
181C2×C3×D4—44no—
182C2×C3×D4—48no—
183C2×C3×D4—48no—
184C2×C3×D4—48no—
185C2×C3×D4—48no—
186C2×C3×D4—48no—
187C2×C3×D4—48no—
188C2×C3×D4—44no—
189C2×C3×D4C22×C414yes—
190C22×C3×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—24no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—24no—
197C22×C3×C4—42no—
198C22×C3×C4—42no—
199C22×C3×C4—42no—
200C22×C3×C4—42no—
201C22×C3×C4—42no—
202C22×C3×C4—42no—
203C22×C3×C4—42no—
204C22×C3×C4—42no—
205C22×C3×C4—42no—
206C22×C3×C4—42no—
207C22×C3×C4—42no—
208C22×C3×C4—44no—
209C22×C3×C4C22⋊C411yescharacteristic
210C22×C3×C4C22⋊C411yescharacteristic
211C22×C3×C4C22⋊C411yescharacteristic
212C22×C3×C4C22⋊C411yescharacteristic
213C22×C3×C4C22⋊C411yescharacteristic
214C22×C3×C4C22⋊C411yescharacteristic
215C22×C3×C4C22⋊C411yescharacteristic
216C22×C3×C4C22⋊C411yescharacteristic
217C22×C3×C4C22⋊C411yescharacteristic
218C22×C3×C4C22⋊C411yescharacteristic
219C22×C3×C4C22⋊C411yescharacteristic
220C22×C3×C4C22⋊C411yescharacteristic
221C22×C3×C4C22×C411yescharacteristic
222C22×C3×C4C22×C411yescharacteristic
223C22×C3×C4C22×C411yescharacteristic
224C22×C3×C4C22×C411yescharacteristic
225C22×C3×C4C22×C411yescharacteristic
226C22×C3×C4C22×C411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2411yescharacteristic
237C3×M16—44no—
238C3×M16—44no—
239C2×C3×C8—24no—
240C2×C3×C8—44no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—44no—
245C3×C4⋊C4C22×C414yes—
246C3×C22⋊C4—24no—
247C3×C22⋊C4—24no—
248C3×C22⋊C4—24no—
249C3×C22⋊C4—24no—
250C3×C22⋊C4—44no—
251C3×C22⋊C4—44no—
252C3×C22⋊C4—44no—
253C3×C42—44no—
254C25—21no—
255C25C3×D411yescharacteristic
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—44no—
266C22×D4—48no—
267C22×D4C2×C3×C412yes—
268C22×D4C2×C3×C412yes—
269C22×D4C2×C3×C412yes—
270C23×C4—21no—
271C23×C4—44no—
272C23×C4C2×C3×C411yescharacteristic
273C23×C4C2×C3×C411yescharacteristic
274C23×C4C2×C3×C411yescharacteristic
275C23×C4C2×C3×C411yescharacteristic
276C23×C4C3×D411yescharacteristic
277C23×C4C3×D411yescharacteristic
278C23×C4C3×D411yescharacteristic
279C23×C4C3×D411yescharacteristic
280C23×C4C3×D411yescharacteristic
281C23×C4C3×D411yescharacteristic
282C23×C4C3×D411yescharacteristic
283C23×C4C23×C311yescharacteristic
284C23×C4C23×C311yescharacteristic
285C23×C4C23×C311yescharacteristic
286C2×M16—22no—
287C2×M16—22no—
288C2×M16—44no—
289C22×C8—22no—
290#121—22no—
291#121—22no—
292#121—22no—
293#121—22no—
294#121—22no—
295#121—22no—
296#121—22no—
297#121—22no—
298#121—22no—
299#121—22no—
300#121—22no—
301#121—22no—
302#121C2×C3×C414yes—
303#121C2×C3×C414yes—
304#121C2×C3×C414yes—
305#121C23×C314yes—
306#117—44no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4C2×C3×C412yes—
312C2×C4⋊C4C2×C3×C412yes—
313C2×C4⋊C4C2×C3×C412yes—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C42—22no—
324C22⋊C8—22no—
325C22⋊C8—22no—
326C22⋊C8—22no—
327C22⋊C8C23×C314yescomplemented
328#95—22no—
329#95C23×C314yescomplemented
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—24no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—416no—
352C23×C3—44no—
353C23×C3—44no—
354C23×C3—44no—
355C23×C3—44no—
356C23×C3—44no—
357C23×C3—44no—
358C23×C3—44no—
359C23×C3—44no—
360C23×C3—44no—
361C23×C3—816no—
362C23×C3C2×C22⋊C411yescharacteristic
363C23×C3C2×C22⋊C411yescharacteristic
364C23×C3C2×C22⋊C411yescharacteristic
365C23×C3C2×C22⋊C411yescharacteristic
366C23×C3C2×C22⋊C411yescharacteristic
367C23×C3C2×C22⋊C411yescharacteristic
368C23×C3AGL(1,ℤ/8)14yes—
369C23×C3C22×D411yescharacteristic
370C3×D4—44no—
371C3×D4—44no—
372C3×D4—48no—
373C3×D4—48no—
374C3×D4—48no—
375C3×D4—48no—
376C3×D4—44no—
377C3×D4—44no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—44no—
407C2×C3×C4—44no—
408C2×C3×C4—44no—
409C2×C3×C4—44no—
410C2×C3×C4—44no—
411C2×C3×C4—44no—
412C2×C3×C4#9914yes—
413C2×C3×C4C2×C22⋊C411yescharacteristic
414C2×C3×C4C2×C22⋊C411yescharacteristic
415C2×C3×C4C2×C22⋊C411yescharacteristic
416C2×C3×C4C2×C22⋊C411yescharacteristic
417C2×C3×C4C2×C22⋊C411yescharacteristic
418C2×C3×C4C2×C22⋊C411yescharacteristic
419C2×C3×C4C23×C411yescharacteristic
420C2×C3×C4C22×D411yescharacteristic
421C3×C8—44no—
422C24—24no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—42no—
427C24—42no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24C3×C22⋊C411yescharacteristic
432C24C3×C22⋊C411yescharacteristic
433C24C3×C22⋊C411yescharacteristic
434C24C3×C22⋊C411yescharacteristic
435C24C2×C3×D411yescharacteristic
436C24C2×C3×D411yescharacteristic
437C24C2×C3×D411yescharacteristic
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—24no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—44no—
457C2×D4C22×C3×C414yes—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—44no—
477C22×C4C3×C22⋊C411yescharacteristic
478C22×C4C3×C22⋊C411yescharacteristic
479C22×C4C3×C22⋊C411yescharacteristic
480C22×C4C3×C22⋊C411yescharacteristic
481C22×C4C3×C22⋊C411yescharacteristic
482C22×C4C3×C22⋊C411yescharacteristic
483C22×C4C3×C22⋊C411yescharacteristic
484C22×C4C3×C22⋊C411yescharacteristic
485C22×C4C3×C22⋊C411yescharacteristic
486C22×C4C3×C22⋊C411yescharacteristic
487C22×C4C3×C22⋊C411yescharacteristic
488C22×C4C3×C22⋊C411yescharacteristic
489C22×C4C22×C3×C411yescharacteristic
490C22×C4C22×C3×C411yescharacteristic
491C22×C4C22×C3×C411yescharacteristic
492C22×C4C22×C3×C411yescharacteristic
493C22×C4C22×C3×C411yescharacteristic
494C22×C4C22×C3×C411yescharacteristic
495C22×C4C2×C3×D411yescharacteristic
496C22×C4C2×C3×D411yescharacteristic
497C22×C4C2×C3×D411yescharacteristic
498C22×C4C2×C3×D411yescharacteristic
499C22×C4C2×C3×D411yescharacteristic
500C22×C4C2×C3×D411yescharacteristic
501C22×C4C2×C3×D411yescharacteristic
502C22×C4C2×C3×D411yescharacteristic
503C22×C4C2×C3×D411yescharacteristic
504C22×C4C24×C311yescharacteristic
505M16—44no—
506M16—44no—
507C2×C8—24no—
508C2×C8—44no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—44no—
513C4⋊C4C22×C3×C414yes—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—44no—
519C22⋊C4—44no—
520C22⋊C4—44no—
521C42—44no—
522C22×C3—28no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—44no—
542C22×C3—44no—
543C22×C3—44no—
544C22×C3—44no—
545C22×C3—44no—
546C22×C3—44no—
547C22×C3—44no—
548C22×C3—88no—
549C22×C3—88no—
550C22×C3—88no—
551C22×C3C2×#9912yes—
552C22×C3#41812yes—
553C22×C3#41812yes—
554C22×C3#42112yes—
555C22×C3C22×C22⋊C411yescharacteristic
556C22×C3C2×AGL(1,ℤ/8)12yes—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—44no—
564C3×C4—84no—
565C3×C4C2×#9912yes—
566C3×C4C2×#9912yes—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—24no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—416no—
589C23—44no—
590C23—44no—
591C23—44no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—816no—
599C23C2×C3×C22⋊C411yescharacteristic
600C23C2×C3×C22⋊C411yescharacteristic
601C23C2×C3×C22⋊C411yescharacteristic
602C23C2×C3×C22⋊C411yescharacteristic
603C23C2×C3×C22⋊C411yescharacteristic
604C23C2×C3×C22⋊C411yescharacteristic
605C23C3×AGL(1,ℤ/8)14yes—
606C23C22×C3×D411yescharacteristic
607D4—44no—
608D4—44no—
609D4—48no—
610D4—48no—
611D4—48no—
612D4—48no—
613D4—44no—
614D4—44no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4C3×#9914yes—
650C2×C4C2×C3×C22⋊C411yescharacteristic
651C2×C4C2×C3×C22⋊C411yescharacteristic
652C2×C4C2×C3×C22⋊C411yescharacteristic
653C2×C4C2×C3×C22⋊C411yescharacteristic
654C2×C4C2×C3×C22⋊C411yescharacteristic
655C2×C4C2×C3×C22⋊C411yescharacteristic
656C2×C4C23×C3×C411yescharacteristic
657C2×C4C22×C3×D411yescharacteristic
658C8—44no—
659C2×C3—22no—
660C2×C3—22no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—22no—
664C2×C3—41no—
665C2×C3—41no—
666C2×C3—84no—
667C2×C3C22×#9911yescharacteristic
668C2×C3C2×#41811yescharacteristic
669C2×C3C2×#42111yescharacteristic
670C22—28no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—88no—
697C22—88no—
698C22—88no—
699C22C2×C3×#9912yes—
700C22C3×#41812yes—
701C22C3×#41812yes—
702C22C3×#42112yes—
703C22C22×C3×C22⋊C411yescharacteristic
704C22C2×C3×AGL(1,ℤ/8)12yes—
705C4—21no—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—44no—
712C4—84no—
713C4C2×C3×#9912yes—
714C4C2×C3×#9912yes—
715C3#1757711yescharacteristic, direct product factor, Sylow
716C2—22no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—22no—
721C2—41no—
722C2—41no—
723C2—84no—
724C2C22×C3×#9911yescharacteristic
725C2C2×C3×#41811yescharacteristic
726C2C2×C3×#42111yescharacteristic
subgroupG/H
center, socleC22×C3C22×C22⋊C4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#121C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#407C2semidirect
3. C3×#2280C2semidirect
4. C3×#1519C2semidirect
5. C3×#1510C2semidirect
6. C3×#1507C2semidirect
7. #17577C3direct (N × H)
9. C23×C3×D4C4semidirect
18. C2×C3×#121C4semidirect
19. C2×C3×#121C4semidirect
20. C2×C3×#121C4semidirect
25. C22×C3×C4⋊C4C4semidirect
29. C3×#407C22semidirect
30. C3×#407C22semidirect
32. C2×C3×C22⋊C8C22semidirect
33. C3×#381C22semidirect
35. C3×#380C22semidirect
38. C3×C4×C22⋊C4C22semidirect
39. C3×#327C22semidirect
41. C2×#407C2×C3semidirect
42. #2280C2×C3semidirect
43. #1519C2×C3semidirect
44. #1510C2×C3semidirect
45. #1507C2×C3semidirect
119. C3×C22⋊C8C23semidirect
121. C3×#95C23semidirect
123. C23×D4C3×C4semidirect
132. C2×#121C3×C4semidirect
133. C2×#121C3×C4semidirect
134. C2×#121C3×C4semidirect
139. C22×C4⋊C4C3×C4semidirect
143. #407C22×C3semidirect
144. #407C22×C3semidirect
146. C2×C22⋊C8C22×C3semidirect
147. #381C22×C3semidirect
149. #380C22×C3semidirect
152. C4×C22⋊C4C22×C3semidirect
153. #327C22×C3semidirect
327. C22⋊C8C23×C3semidirect
329. #95C23×C3semidirect
715. C3#17577direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C2×C3×#4072
C3×#22802
C3×#15192
C3×#15102
C3×#15072
#175773