Finite Group Databasebeta

← C3×#17592 #10636199

Subgroups — C3×#17592 #10636199

Order 768.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2C2×C3×#407C211yesmaximal, characteristic, complemented
3C2×C3×#380C211yesmaximal, characteristic, complemented
4C3×#1520C212yesmaximal, complemented
5C3×#1519C212yesmaximal, complemented
6C3×#1513C214yesmaximal, complemented
7C3×#1504C214yesmaximal, complemented
8#17592C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×#41C411yescharacteristic, complemented
10C24×C3×C4C2211yescharacteristic
11C22×C3×M16—21no—
12C3×#525—21no—
13C3×#525—21no—
14C3×#525—21no—
15C3×#525—21no—
16C3×#525C412yescomplemented
17C3×#525C412yescomplemented
18C3×#525C2212yes—
19C3×#525C2212yes—
20C2×C3×#123—21no—
21C2×C3×C22⋊Q8C411yescharacteristic, complemented
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×#121C411yescharacteristic, complemented
24C2×C3×#121C2211yescharacteristic
25C2×C3×#120—21no—
26C2×C3×C4×D4—21no—
27C2×C3×C4×D4—21no—
28C2×C3×#117C411yescharacteristic, complemented
29C22×C3×C4⋊C4—21no—
30C22×C3×C22⋊C4—21no—
31C3×#407—21no—
32C3×#407—21no—
33C3×#407C2212yescomplemented
34C3×#407C2212yescomplemented
35C2×C3×C22⋊C8—21no—
36C2×C3×C22⋊C8C2212yes—
37C3×#380—21no—
38C3×#380—21no—
39C3×#380C2212yes—
40C3×#380C2212yescomplemented
41C2×C3×#95C2212yescomplemented
42C3×#328C2218yescomplemented
43C3×#327C2218yescomplemented
44C2×#525C2×C311yescharacteristic
45C2×#407C2×C311yescharacteristic, complemented
46C2×#380C2×C311yescharacteristic, complemented
47#1520C2×C312yescomplemented
48#1519C2×C312yescomplemented
49#1513C2×C314yescomplemented
50#1504C2×C314yescomplemented
51C25×C3D411yescharacteristic
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—44no—
55C2×C3×#41C2×C412yes—
56C2×C3×#41C2×C412yescomplemented
57C22×C3×Q8C2×C411yescharacteristic, complemented
58C22×C3×D4—21no—
59C22×C3×D4—21no—
60C22×C3×D4—21no—
61C22×C3×D4C2×C411yescharacteristic, complemented
62C23×C3×C4—21no—
63C23×C3×C4—22no—
64C23×C3×C4—44no—
65C23×C3×C4C2×C411yescharacteristic
66C23×C3×C4C2×C411yescharacteristic
67C23×C3×C4C2×C411yescharacteristic
68C23×C3×C4C2×C411yescharacteristic
69C23×C3×C4D411yescharacteristic
70C23×C3×C4D411yescharacteristic
71C23×C3×C4D411yescharacteristic
72C23×C3×C4D411yescharacteristic
73C23×C3×C4D411yescharacteristic
74C23×C3×C4D411yescharacteristic
75C23×C3×C4D411yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C2×C3×M16—22no—
80C2×C3×M16—22no—
81C2×C3×M16—44no—
82C22×C3×C8—22no—
83C3×#123—22no—
84C3×#123—22no—
85C3×#123—22no—
86C3×#123—22no—
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8—21no—
91C3×C22⋊Q8C2×C412yes—
92C3×C22⋊Q8C2×C412yescomplemented
93C3×C22⋊Q8C2×C412yescomplemented
94C3×C22⋊Q8C2312yes—
95C3×#121—21no—
96C3×#121—21no—
97C3×#121—21no—
98C3×#121—21no—
99C3×#121C2×C412yes—
100C3×#121C2×C412yescomplemented
101C3×#121C2×C412yescomplemented
102C3×#121C2312yes—
103C3×#120—22no—
104C3×#120—22no—
105C3×#120—22no—
106C3×#120—22no—
107C3×C4×D4—22no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C3×C4×D4—22no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×#117—21no—
116C3×#117—21no—
117C3×#117C2×C412yes—
118C3×#117C2×C412yescomplemented
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—44no—
124C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
125C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—44no—
134C2×C3×C42—21no—
135C3×C22⋊C8—22no—
136C3×C22⋊C8—22no—
137C3×C22⋊C8—22no—
138C3×C22⋊C8C2314yes—
139C3×#95—22no—
140C3×#95C2314yes—
141C22×#41C3×C411yescharacteristic, complemented
142C24×C4C22×C311yescharacteristic
143C22×M16—21no—
144#525—21no—
145#525—21no—
146#525—21no—
147#525—21no—
148#525C3×C412yescomplemented
149#525C3×C412yescomplemented
150#525C22×C312yes—
151#525C22×C312yes—
152C2×#123—21no—
153C2×C22⋊Q8C3×C411yescharacteristic, complemented
154C2×C22⋊Q8C22×C311yescharacteristic
155C2×#121C3×C411yescharacteristic, complemented
156C2×#121C22×C311yescharacteristic
157C2×#120—21no—
158C2×C4×D4—21no—
159C2×C4×D4—21no—
160C2×#117C3×C411yescharacteristic, complemented
161C22×C4⋊C4—21no—
162C22×C22⋊C4—21no—
163#407—21no—
164#407—21no—
165#407C22×C312yescomplemented
166#407C22×C312yescomplemented
167C2×C22⋊C8—21no—
168C2×C22⋊C8C22×C312yes—
169#380—21no—
170#380—21no—
171#380C22×C312yes—
172#380C22×C312yescomplemented
173C2×#95C22×C312yescomplemented
174#328C22×C318yescomplemented
175#327C22×C318yescomplemented
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—21no—
179C24×C3—42no—
180C24×C3—42no—
181C24×C3C22⋊C411yescharacteristic
182C24×C3C22⋊C411yescharacteristic
183C24×C3C22⋊C411yescharacteristic
184C24×C3C22⋊C411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C24×C3C2×D411yescharacteristic
187C24×C3C2×D411yescharacteristic
188C3×#41—44no—
189C3×#41—44no—
190C3×#41—44no—
191C3×#41—44no—
192C2×C3×Q8—21no—
193C2×C3×Q8—42no—
194C2×C3×Q8C22×C412yes—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—21no—
202C2×C3×D4—42no—
203C2×C3×D4—44no—
204C2×C3×D4—44no—
205C2×C3×D4—42no—
206C2×C3×D4—42no—
207C2×C3×D4C22×C412yes—
208C22×C3×C4—24no—
209C22×C3×C4—24no—
210C22×C3×C4—24no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—24no—
217C22×C3×C4—42no—
218C22×C3×C4—42no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4—42no—
224C22×C3×C4—42no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—42no—
228C22×C3×C4—44no—
229C22×C3×C4—44no—
230C22×C3×C4—44no—
231C22×C3×C4—44no—
232C22×C3×C4C22⋊C411yescharacteristic
233C22×C3×C4C22⋊C411yescharacteristic
234C22×C3×C4C22⋊C411yescharacteristic
235C22×C3×C4C22⋊C411yescharacteristic
236C22×C3×C4C22⋊C411yescharacteristic
237C22×C3×C4C22⋊C411yescharacteristic
238C22×C3×C4C22⋊C411yescharacteristic
239C22×C3×C4C22⋊C411yescharacteristic
240C22×C3×C4C22⋊C411yescharacteristic
241C22×C3×C4C22⋊C411yescharacteristic
242C22×C3×C4C22⋊C411yescharacteristic
243C22×C3×C4C22⋊C411yescharacteristic
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C22×C411yescharacteristic
247C22×C3×C4C22×C411yescharacteristic
248C22×C3×C4C22×C411yescharacteristic
249C22×C3×C4C22×C411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C3×M16—44no—
261C3×M16—44no—
262C2×C3×C8—24no—
263C2×C3×C8—44no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—44no—
271C3×C4⋊C4—44no—
272C3×C4⋊C4C22×C412yes—
273C3×C4⋊C4C22×C412yes—
274C3×C22⋊C4—22no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—22no—
284C3×C22⋊C4—44no—
285C3×C22⋊C4—44no—
286C3×C42—22no—
287C3×C42—22no—
288C25C3×D411yescharacteristic
289C2×#41—21no—
290C2×#41—21no—
291C2×#41—44no—
292C2×#41C2×C3×C412yes—
293C2×#41C2×C3×C412yescomplemented
294C22×Q8C2×C3×C411yescharacteristic, complemented
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C2×C3×C411yescharacteristic, complemented
299C23×C4—21no—
300C23×C4—22no—
301C23×C4—44no—
302C23×C4C2×C3×C411yescharacteristic
303C23×C4C2×C3×C411yescharacteristic
304C23×C4C2×C3×C411yescharacteristic
305C23×C4C2×C3×C411yescharacteristic
306C23×C4C3×D411yescharacteristic
307C23×C4C3×D411yescharacteristic
308C23×C4C3×D411yescharacteristic
309C23×C4C3×D411yescharacteristic
310C23×C4C3×D411yescharacteristic
311C23×C4C3×D411yescharacteristic
312C23×C4C3×D411yescharacteristic
313C23×C4C23×C311yescharacteristic
314C23×C4C23×C311yescharacteristic
315C23×C4C23×C311yescharacteristic
316C2×M16—22no—
317C2×M16—22no—
318C2×M16—44no—
319C22×C8—22no—
320#123—22no—
321#123—22no—
322#123—22no—
323#123—22no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8C2×C3×C412yes—
329C22⋊Q8C2×C3×C412yescomplemented
330C22⋊Q8C2×C3×C412yescomplemented
331C22⋊Q8C23×C312yes—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121C2×C3×C412yes—
337#121C2×C3×C412yescomplemented
338#121C2×C3×C412yescomplemented
339#121C23×C312yes—
340#120—22no—
341#120—22no—
342#120—22no—
343#120—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—21no—
353#117—21no—
354#117C2×C3×C412yes—
355#117C2×C3×C412yescomplemented
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4C2×C3×C411yescharacteristic, complemented
362C2×C4⋊C4C2×C3×C411yescharacteristic, complemented
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—44no—
371C2×C42—21no—
372C22⋊C8—22no—
373C22⋊C8—22no—
374C22⋊C8—22no—
375C22⋊C8C23×C314yes—
376#95—22no—
377#95C23×C314yes—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—48no—
402C23×C3—48no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3C2×C22⋊C411yescharacteristic
407C23×C3C2×C22⋊C411yescharacteristic
408C23×C3C2×C22⋊C411yescharacteristic
409C23×C3C2×C22⋊C411yescharacteristic
410C23×C3C2×C22⋊C411yescharacteristic
411C23×C3C2×C22⋊C411yescharacteristic
412C23×C3AGL(1,ℤ/8)12yes—
413C23×C3#13712yes—
414C23×C3C22×D411yescharacteristic
415C3×Q8—42no—
416C3×Q8—42no—
417C3×D4—42no—
418C3×D4—44no—
419C3×D4—44no—
420C3×D4—42no—
421C3×D4—42no—
422C3×D4—44no—
423C3×D4—44no—
424C3×D4—44no—
425C3×D4—42no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—44no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—44no—
461C2×C3×C4—44no—
462C2×C3×C4—44no—
463C2×C3×C4—44no—
464C2×C3×C4—88no—
465C2×C3×C4#9914yes—
466C2×C3×C4C2×C22⋊C411yescharacteristic
467C2×C3×C4C2×C22⋊C411yescharacteristic
468C2×C3×C4C2×C22⋊C411yescharacteristic
469C2×C3×C4C2×C22⋊C411yescharacteristic
470C2×C3×C4C2×C22⋊C411yescharacteristic
471C2×C3×C4C2×C22⋊C411yescharacteristic
472C2×C3×C4C23×C411yescharacteristic
473C2×C3×C4C22×D411yescharacteristic
474C3×C8—44no—
475C24—22no—
476C24—22no—
477C24—21no—
478C24—42no—
479C24—42no—
480C24C3×C22⋊C411yescharacteristic
481C24C3×C22⋊C411yescharacteristic
482C24C3×C22⋊C411yescharacteristic
483C24C3×C22⋊C411yescharacteristic
484C24C2×C3×D411yescharacteristic
485C24C2×C3×D411yescharacteristic
486C24C2×C3×D411yescharacteristic
487#41—44no—
488#41—44no—
489#41—44no—
490#41—44no—
491C2×Q8—21no—
492C2×Q8—42no—
493C2×Q8C22×C3×C412yes—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4C22×C3×C412yes—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4C3×C22⋊C411yescharacteristic
532C22×C4C3×C22⋊C411yescharacteristic
533C22×C4C3×C22⋊C411yescharacteristic
534C22×C4C3×C22⋊C411yescharacteristic
535C22×C4C3×C22⋊C411yescharacteristic
536C22×C4C3×C22⋊C411yescharacteristic
537C22×C4C3×C22⋊C411yescharacteristic
538C22×C4C3×C22⋊C411yescharacteristic
539C22×C4C3×C22⋊C411yescharacteristic
540C22×C4C3×C22⋊C411yescharacteristic
541C22×C4C3×C22⋊C411yescharacteristic
542C22×C4C3×C22⋊C411yescharacteristic
543C22×C4C22×C3×C411yescharacteristic
544C22×C4C22×C3×C411yescharacteristic
545C22×C4C22×C3×C411yescharacteristic
546C22×C4C22×C3×C411yescharacteristic
547C22×C4C22×C3×C411yescharacteristic
548C22×C4C22×C3×C411yescharacteristic
549C22×C4C2×C3×D411yescharacteristic
550C22×C4C2×C3×D411yescharacteristic
551C22×C4C2×C3×D411yescharacteristic
552C22×C4C2×C3×D411yescharacteristic
553C22×C4C2×C3×D411yescharacteristic
554C22×C4C2×C3×D411yescharacteristic
555C22×C4C2×C3×D411yescharacteristic
556C22×C4C2×C3×D411yescharacteristic
557C22×C4C2×C3×D411yescharacteristic
558C22×C4C24×C311yescharacteristic
559M16—44no—
560M16—44no—
561C2×C8—24no—
562C2×C8—44no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4C22×C3×C412yes—
572C4⋊C4C22×C3×C412yes—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—44no—
584C22⋊C4—44no—
585C42—22no—
586C42—22no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—84no—
617C22×C3C2×#9912yes—
618C22×C3#41712yes—
619C22×C3#41712yes—
620C22×C3#42112yes—
621C22×C3C22×C22⋊C411yescharacteristic
622C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
623C22×C3C2×#13711yescharacteristic
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—42no—
631C3×C4—42no—
632C3×C4—42no—
633C3×C4—84no—
634C3×C4C2×#9912yes—
635C3×C4C2×#9912yes—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—48no—
660C23—48no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23C2×C3×C22⋊C411yescharacteristic
665C23C2×C3×C22⋊C411yescharacteristic
666C23C2×C3×C22⋊C411yescharacteristic
667C23C2×C3×C22⋊C411yescharacteristic
668C23C2×C3×C22⋊C411yescharacteristic
669C23C2×C3×C22⋊C411yescharacteristic
670C23C3×AGL(1,ℤ/8)12yes—
671C23C3×#13712yes—
672C23C22×C3×D411yescharacteristic
673Q8—42no—
674Q8—42no—
675D4—42no—
676D4—44no—
677D4—44no—
678D4—42no—
679D4—42no—
680D4—44no—
681D4—44no—
682D4—44no—
683D4—42no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—88no—
723C2×C4C3×#9914yes—
724C2×C4C2×C3×C22⋊C411yescharacteristic
725C2×C4C2×C3×C22⋊C411yescharacteristic
726C2×C4C2×C3×C22⋊C411yescharacteristic
727C2×C4C2×C3×C22⋊C411yescharacteristic
728C2×C4C2×C3×C22⋊C411yescharacteristic
729C2×C4C2×C3×C22⋊C411yescharacteristic
730C2×C4C23×C3×C411yescharacteristic
731C2×C4C22×C3×D411yescharacteristic
732C8—44no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—22no—
736C2×C3—22no—
737C2×C3—22no—
738C2×C3—22no—
739C2×C3—41no—
740C2×C3—41no—
741C2×C3—82no—
742C2×C3C22×#9911yescharacteristic
743C2×C3C2×#41711yescharacteristic
744C2×C3C2×#42111yescharacteristic
745C22—24no—
746C22—24no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—84no—
775C22C2×C3×#9912yes—
776C22C3×#41712yes—
777C22C3×#41712yes—
778C22C3×#42112yes—
779C22C22×C3×C22⋊C411yescharacteristic
780C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
781C22C2×C3×#13711yescharacteristic
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—84no—
792C4C2×C3×#9912yes—
793C4C2×C3×#9912yes—
794C3#1759211yescharacteristic, direct product factor, Sylow
795C2—21no—
796C2—21no—
797C2—22no—
798C2—22no—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—41no—
803C2—82no—
804C2C22×C3×#9911yescharacteristic
805C2C2×C3×#41711yescharacteristic
806C2C2×C3×#42111yescharacteristic
subgroupG/H
center, socleC22×C3C22×C22⋊C4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#525C2
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. C2×C3×#380C2semidirect
4. C3×#1520C2semidirect
5. C3×#1519C2semidirect
6. C3×#1513C2semidirect
7. C3×#1504C2semidirect
8. #17592C3direct (N × H)
9. C22×C3×#41C4semidirect
16. C3×#525C4semidirect
17. C3×#525C4semidirect
21. C2×C3×C22⋊Q8C4semidirect
23. C2×C3×#121C4semidirect
28. C2×C3×#117C4semidirect
33. C3×#407C22semidirect
34. C3×#407C22semidirect
40. C3×#380C22semidirect
41. C2×C3×#95C22semidirect
42. C3×#328C22semidirect
43. C3×#327C22semidirect
45. C2×#407C2×C3semidirect
46. C2×#380C2×C3semidirect
47. #1520C2×C3semidirect
48. #1519C2×C3semidirect
49. #1513C2×C3semidirect
50. #1504C2×C3semidirect
56. C2×C3×#41C2×C4semidirect
57. C22×C3×Q8C2×C4semidirect
61. C22×C3×D4C2×C4semidirect
92. C3×C22⋊Q8C2×C4semidirect
93. C3×C22⋊Q8C2×C4semidirect
100. C3×#121C2×C4semidirect
101. C3×#121C2×C4semidirect
118. C3×#117C2×C4semidirect
124. C2×C3×C4⋊C4C2×C4semidirect
125. C2×C3×C4⋊C4C2×C4semidirect
141. C22×#41C3×C4semidirect
148. #525C3×C4semidirect
149. #525C3×C4semidirect
153. C2×C22⋊Q8C3×C4semidirect
155. C2×#121C3×C4semidirect
160. C2×#117C3×C4semidirect
165. #407C22×C3semidirect
166. #407C22×C3semidirect
172. #380C22×C3semidirect
173. C2×#95C22×C3semidirect
174. #328C22×C3semidirect
175. #327C22×C3semidirect
293. C2×#41C2×C3×C4semidirect
294. C22×Q8C2×C3×C4semidirect
298. C22×D4C2×C3×C4semidirect
329. C22⋊Q8C2×C3×C4semidirect
330. C22⋊Q8C2×C3×C4semidirect
337. #121C2×C3×C4semidirect
338. #121C2×C3×C4semidirect
355. #117C2×C3×C4semidirect
361. C2×C4⋊C4C2×C3×C4semidirect
362. C2×C4⋊C4C2×C3×C4semidirect
794. C3#17592direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C2×C3×#4072
C2×C3×#3802
C3×#15202
C3×#15192
C3×#15132
C3×#15042
#175923