Finite Group Databasebeta

← C3×#17582 #10636189

Subgroups — C3×#17582 #10636189

Order 768.

1438 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
1C2×C3×#525C211yesmaximal, characteristic
2C2×C3×#407C211yesmaximal, characteristic, complemented
3C3×#2280C211yesmaximal, characteristic, complemented
4C3×#1516C214yesmaximal, complemented
5C3×#1513C214yesmaximal, complemented
6C3×#1508C212yesmaximal, complemented
7C3×#1507C212yesmaximal, complemented
8#17582C311yesmaximal, 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×#117—21no—
29C2×C3×#117C411yescharacteristic, complemented
30C3×#407—21no—
31C3×#407—21no—
32C3×#407C2212yes—
33C3×#407C2212yescomplemented
34C2×C3×C22⋊C8—21no—
35C2×C3×C22⋊C8C2212yescomplemented
36C3×#381C2212yescomplemented
37C3×#380—21no—
38C3×#380C2212yescomplemented
39C3×#379—21no—
40C3×C4×C22⋊C4—21no—
41C3×C4×C22⋊C4C2212yes—
42C3×#328C2218yescomplemented
43C3×#327C2218yescomplemented
44C2×#525C2×C311yescharacteristic
45C2×#407C2×C311yescharacteristic, complemented
46#2280C2×C311yescharacteristic, complemented
47#1516C2×C314yescomplemented
48#1513C2×C314yescomplemented
49#1508C2×C312yescomplemented
50#1507C2×C312yescomplemented
51C25×C3D411yescharacteristic
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—44no—
55C2×C3×#41C2×C412yes—
56C2×C3×#41C2×C412yes—
57C22×C3×Q8C2×C411yescharacteristic
58C22×C3×D4—21no—
59C22×C3×D4—21no—
60C22×C3×D4—21no—
61C22×C3×D4C2×C411yescharacteristic
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×#123—22no—
83C3×#123—22no—
84C3×#123—22no—
85C3×#123—22no—
86C3×C22⋊Q8—21no—
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8C2×C412yes—
91C3×C22⋊Q8C2×C412yes—
92C3×C22⋊Q8C2×C412yes—
93C3×C22⋊Q8C2312yes—
94C3×#121—21no—
95C3×#121—21no—
96C3×#121—21no—
97C3×#121—21no—
98C3×#121C2×C412yes—
99C3×#121C2×C412yes—
100C3×#121C2×C412yes—
101C3×#121C2312yes—
102C3×#120—22no—
103C3×#120—22no—
104C3×#120—22no—
105C3×#120—22no—
106C3×C4×D4—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×#117—21no—
115C3×#117—21no—
116C3×#117—44no—
117C3×#117C2×C412yes—
118C3×#117C2×C412yes—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4C2×C411yescharacteristic
123C2×C3×C4⋊C4C2×C411yescharacteristic
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C42—21no—
133C2×C3×C42—22no—
134C3×C22⋊C8—22no—
135C3×C22⋊C8—22no—
136C3×C22⋊C8—22no—
137C3×C22⋊C8C2314yes—
138C3×#95—22no—
139C3×#95C2314yes—
140C22×#41C3×C411yescharacteristic, complemented
141C24×C4C22×C311yescharacteristic
142C22×M16—21no—
143#525—21no—
144#525—21no—
145#525—21no—
146#525—21no—
147#525C3×C412yescomplemented
148#525C3×C412yescomplemented
149#525C22×C312yes—
150#525C22×C312yes—
151C2×#123—21no—
152C2×C22⋊Q8C3×C411yescharacteristic, complemented
153C2×C22⋊Q8C22×C311yescharacteristic
154C2×#121C3×C411yescharacteristic, complemented
155C2×#121C22×C311yescharacteristic
156C2×#120—21no—
157C2×C4×D4—21no—
158C2×C4×D4—21no—
159C2×#117—21no—
160C2×#117C3×C411yescharacteristic, complemented
161#407—21no—
162#407—21no—
163#407C22×C312yes—
164#407C22×C312yescomplemented
165C2×C22⋊C8—21no—
166C2×C22⋊C8C22×C312yescomplemented
167#381C22×C312yescomplemented
168#380—21no—
169#380C22×C312yescomplemented
170#379—21no—
171C4×C22⋊C4—21no—
172C4×C22⋊C4C22×C312yes—
173#328C22×C318yescomplemented
174#327C22×C318yescomplemented
175C24×C3—21no—
176C24×C3—42no—
177C24×C3—42no—
178C24×C3—42no—
179C24×C3C22⋊C411yescharacteristic
180C24×C3C22⋊C411yescharacteristic
181C24×C3C22⋊C411yescharacteristic
182C24×C3C22⋊C411yescharacteristic
183C24×C3C2×D411yescharacteristic
184C24×C3C2×D411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C3×#41—44no—
187C3×#41—44no—
188C3×#41—44no—
189C3×#41—44no—
190C2×C3×Q8—21no—
191C2×C3×Q8—42no—
192C2×C3×Q8C22×C412yes—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—21no—
200C2×C3×D4—42no—
201C2×C3×D4—44no—
202C2×C3×D4—44no—
203C2×C3×D4—44no—
204C2×C3×D4C22×C412yes—
205C22×C3×C4—24no—
206C22×C3×C4—24no—
207C22×C3×C4—24no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—24no—
214C22×C3×C4—42no—
215C22×C3×C4—42no—
216C22×C3×C4—42no—
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—44no—
226C22×C3×C4C22⋊C411yescharacteristic
227C22×C3×C4C22⋊C411yescharacteristic
228C22×C3×C4C22⋊C411yescharacteristic
229C22×C3×C4C22⋊C411yescharacteristic
230C22×C3×C4C22⋊C411yescharacteristic
231C22×C3×C4C22⋊C411yescharacteristic
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×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2411yescharacteristic
254C3×M16—44no—
255C3×M16—44no—
256C2×C3×C8—24no—
257C2×C3×C8—44no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—44no—
265C3×C4⋊C4C22×C412yes—
266C3×C4⋊C4C22×C412yes—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—22no—
272C3×C22⋊C4—22no—
273C3×C22⋊C4—22no—
274C3×C22⋊C4—22no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—44no—
278C3×C22⋊C4—44no—
279C3×C22⋊C4—44no—
280C3×C42—22no—
281C3×C42—22no—
282C3×C42—44no—
283C25C3×D411yescharacteristic
284C2×#41—21no—
285C2×#41—21no—
286C2×#41—44no—
287C2×#41C2×C3×C412yes—
288C2×#41C2×C3×C412yes—
289C22×Q8C2×C3×C411yescharacteristic
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2×C3×C411yescharacteristic
294C23×C4—21no—
295C23×C4—44no—
296C23×C4C2×C3×C411yescharacteristic
297C23×C4C2×C3×C411yescharacteristic
298C23×C4C2×C3×C411yescharacteristic
299C23×C4C2×C3×C411yescharacteristic
300C23×C4C3×D411yescharacteristic
301C23×C4C3×D411yescharacteristic
302C23×C4C3×D411yescharacteristic
303C23×C4C3×D411yescharacteristic
304C23×C4C3×D411yescharacteristic
305C23×C4C3×D411yescharacteristic
306C23×C4C3×D411yescharacteristic
307C23×C4C23×C311yescharacteristic
308C23×C4C23×C311yescharacteristic
309C23×C4C23×C311yescharacteristic
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—44no—
313C22×C8—22no—
314#123—22no—
315#123—22no—
316#123—22no—
317#123—22no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8C2×C3×C412yes—
323C22⋊Q8C2×C3×C412yes—
324C22⋊Q8C2×C3×C412yes—
325C22⋊Q8C23×C312yes—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121C2×C3×C412yes—
331#121C2×C3×C412yes—
332#121C2×C3×C412yes—
333#121C23×C312yes—
334#120—22no—
335#120—22no—
336#120—22no—
337#120—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346#117—21no—
347#117—21no—
348#117—44no—
349#117C2×C3×C412yes—
350#117C2×C3×C412yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4C2×C3×C411yescharacteristic
355C2×C4⋊C4C2×C3×C411yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C42—21no—
365C2×C42—22no—
366C22⋊C8—22no—
367C22⋊C8—22no—
368C22⋊C8—22no—
369C22⋊C8C23×C314yes—
370#95—22no—
371#95C23×C314yes—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—416no—
397C23×C3—42no—
398C23×C3C2×C22⋊C411yescharacteristic
399C23×C3C2×C22⋊C411yescharacteristic
400C23×C3C2×C22⋊C411yescharacteristic
401C23×C3C2×C22⋊C411yescharacteristic
402C23×C3C2×C22⋊C411yescharacteristic
403C23×C3C2×C22⋊C411yescharacteristic
404C23×C3C22×D411yescharacteristic
405C3×Q8—42no—
406C3×Q8—42no—
407C3×D4—42no—
408C3×D4—44no—
409C3×D4—44no—
410C3×D4—44no—
411C3×D4—44no—
412C3×D4—44no—
413C3×D4—44no—
414C3×D4—42no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
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—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—44no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—44no—
450C2×C3×C4—44no—
451C2×C3×C4—44no—
452C2×C3×C4—44no—
453C2×C3×C4#9914yes—
454C2×C3×C4C2×C22⋊C411yescharacteristic
455C2×C3×C4C2×C22⋊C411yescharacteristic
456C2×C3×C4C2×C22⋊C411yescharacteristic
457C2×C3×C4C2×C22⋊C411yescharacteristic
458C2×C3×C4C2×C22⋊C411yescharacteristic
459C2×C3×C4C2×C22⋊C411yescharacteristic
460C2×C3×C4C23×C411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C3×C8—44no—
463C24—21no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24C3×C22⋊C411yescharacteristic
468C24C3×C22⋊C411yescharacteristic
469C24C3×C22⋊C411yescharacteristic
470C24C3×C22⋊C411yescharacteristic
471C24C2×C3×D411yescharacteristic
472C24C2×C3×D411yescharacteristic
473C24C2×C3×D411yescharacteristic
474#41—44no—
475#41—44no—
476#41—44no—
477#41—44no—
478C2×Q8—21no—
479C2×Q8—42no—
480C2×Q8C22×C3×C412yes—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—42no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4C22×C3×C412yes—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—44no—
514C22×C4C3×C22⋊C411yescharacteristic
515C22×C4C3×C22⋊C411yescharacteristic
516C22×C4C3×C22⋊C411yescharacteristic
517C22×C4C3×C22⋊C411yescharacteristic
518C22×C4C3×C22⋊C411yescharacteristic
519C22×C4C3×C22⋊C411yescharacteristic
520C22×C4C3×C22⋊C411yescharacteristic
521C22×C4C3×C22⋊C411yescharacteristic
522C22×C4C3×C22⋊C411yescharacteristic
523C22×C4C3×C22⋊C411yescharacteristic
524C22×C4C3×C22⋊C411yescharacteristic
525C22×C4C3×C22⋊C411yescharacteristic
526C22×C4C22×C3×C411yescharacteristic
527C22×C4C22×C3×C411yescharacteristic
528C22×C4C22×C3×C411yescharacteristic
529C22×C4C22×C3×C411yescharacteristic
530C22×C4C22×C3×C411yescharacteristic
531C22×C4C22×C3×C411yescharacteristic
532C22×C4C2×C3×D411yescharacteristic
533C22×C4C2×C3×D411yescharacteristic
534C22×C4C2×C3×D411yescharacteristic
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C24×C311yescharacteristic
542M16—44no—
543M16—44no—
544C2×C8—24no—
545C2×C8—44no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—22no—
552C4⋊C4—44no—
553C4⋊C4C22×C3×C412yes—
554C4⋊C4C22×C3×C412yes—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C42—22no—
569C42—22no—
570C42—44no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—44no—
590C22×C3—44no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—84no—
600C22×C3C2×#9912yes—
601C22×C3#42112yes—
602C22×C3C22×C22⋊C411yescharacteristic
603C22×C3#57512yes—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—42no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—84no—
614C3×C4C2×#9912yes—
615C3×C4C2×#9912yes—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—416no—
641C23—42no—
642C23C2×C3×C22⋊C411yescharacteristic
643C23C2×C3×C22⋊C411yescharacteristic
644C23C2×C3×C22⋊C411yescharacteristic
645C23C2×C3×C22⋊C411yescharacteristic
646C23C2×C3×C22⋊C411yescharacteristic
647C23C2×C3×C22⋊C411yescharacteristic
648C23C22×C3×D411yescharacteristic
649Q8—42no—
650Q8—42no—
651D4—42no—
652D4—44no—
653D4—44no—
654D4—44no—
655D4—44no—
656D4—44no—
657D4—44no—
658D4—42no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4C3×#9914yes—
698C2×C4C2×C3×C22⋊C411yescharacteristic
699C2×C4C2×C3×C22⋊C411yescharacteristic
700C2×C4C2×C3×C22⋊C411yescharacteristic
701C2×C4C2×C3×C22⋊C411yescharacteristic
702C2×C4C2×C3×C22⋊C411yescharacteristic
703C2×C4C2×C3×C22⋊C411yescharacteristic
704C2×C4C23×C3×C411yescharacteristic
705C2×C4C22×C3×D411yescharacteristic
706C8—44no—
707C2×C3—22no—
708C2×C3—22no—
709C2×C3—22no—
710C2×C3—41no—
711C2×C3—41no—
712C2×C3—41no—
713C2×C3—41no—
714C2×C3—82no—
715C2×C3C22×#9911yescharacteristic
716C2×C3#289611yescharacteristic
717C2×C3C2×#42111yescharacteristic
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22C2×C3×#9912yes—
748C22C3×#42112yes—
749C22C22×C3×C22⋊C411yescharacteristic
750C22C3×#57512yes—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—84no—
761C4C2×C3×#9912yes—
762C4C2×C3×#9912yes—
763C3#1758211yescharacteristic, direct product factor, Sylow
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×C3×#9911yescharacteristic
773C2C3×#289611yescharacteristic
774C2C2×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. C3×#2280C2semidirect
4. C3×#1516C2semidirect
5. C3×#1513C2semidirect
6. C3×#1508C2semidirect
7. C3×#1507C2semidirect
8. #17582C3direct (N × H)
9. C22×C3×#41C4semidirect
16. C3×#525C4semidirect
17. C3×#525C4semidirect
21. C2×C3×C22⋊Q8C4semidirect
23. C2×C3×#121C4semidirect
29. C2×C3×#117C4semidirect
33. C3×#407C22semidirect
35. C2×C3×C22⋊C8C22semidirect
36. C3×#381C22semidirect
38. C3×#380C22semidirect
42. C3×#328C22semidirect
43. C3×#327C22semidirect
45. C2×#407C2×C3semidirect
46. #2280C2×C3semidirect
47. #1516C2×C3semidirect
48. #1513C2×C3semidirect
49. #1508C2×C3semidirect
50. #1507C2×C3semidirect
140. C22×#41C3×C4semidirect
147. #525C3×C4semidirect
148. #525C3×C4semidirect
152. C2×C22⋊Q8C3×C4semidirect
154. C2×#121C3×C4semidirect
160. C2×#117C3×C4semidirect
164. #407C22×C3semidirect
166. C2×C22⋊C8C22×C3semidirect
167. #381C22×C3semidirect
169. #380C22×C3semidirect
173. #328C22×C3semidirect
174. #327C22×C3semidirect
763. C3#17582direct (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
C3×#22802
C3×#15162
C3×#15132
C3×#15082
C3×#15072
#175823