Finite Group Databasebeta

← C3×#17572 #10636179

Subgroups — C3×#17572 #10636179

Order 768.

1470 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
2C22×C3×C22⋊C8C211yesmaximal, characteristic, complemented
3C3×#2280C211yesmaximal, characteristic, complemented
4C3×#1520C212yesmaximal, complemented
5C3×#1519C212yesmaximal, complemented
6C3×#1516C214yesmaximal, complemented
7C3×#1501C214yesmaximal, complemented
8#17572C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×#41C411yescharacteristic, complemented
10C24×C3×C4C2211yescharacteristic
11C23×C3×C8—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
30C2×C3×C22⋊C8—21no—
31C2×C3×C22⋊C8—21no—
32C2×C3×C22⋊C8—21no—
33C2×C3×C22⋊C8C2212yes—
34C2×C3×C22⋊C8C2212yescomplemented
35C2×C3×C22⋊C8C2212yescomplemented
36C3×#381C2212yescomplemented
37C3×#380—21no—
38C3×#380C2212yes—
39C3×#379—21no—
40C3×C4×C22⋊C4—21no—
41C3×C4×C22⋊C4C2212yescomplemented
42C3×#328C2218yescomplemented
43C3×#327C2218yescomplemented
44C2×#525C2×C311yescharacteristic
45C22×C22⋊C8C2×C311yescharacteristic, complemented
46#2280C2×C311yescharacteristic, complemented
47#1520C2×C312yescomplemented
48#1519C2×C312yescomplemented
49#1516C2×C314yescomplemented
50#1501C2×C314yescomplemented
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
78C22×C3×C8—22no—
79C22×C3×C8—22no—
80C22×C3×C8—22no—
81C22×C3×C8—44no—
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
142C23×C8—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
161C2×C22⋊C8—21no—
162C2×C22⋊C8—21no—
163C2×C22⋊C8—21no—
164C2×C22⋊C8C22×C312yes—
165C2×C22⋊C8C22×C312yescomplemented
166C2×C22⋊C8C22×C312yescomplemented
167#381C22×C312yescomplemented
168#380—21no—
169#380C22×C312yes—
170#379—21no—
171C4×C22⋊C4—21no—
172C4×C22⋊C4C22×C312yescomplemented
173#328C22×C318yescomplemented
174#327C22×C318yescomplemented
175C24×C3—24no—
176C24×C3—21no—
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
254C2×C3×C8—24no—
255C2×C3×C8—44no—
256C2×C3×C8—44no—
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
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—44no—
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—22no—
383C23×C3—22no—
384C23×C3—22no—
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—416no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3C2×C22⋊C411yescharacteristic
398C23×C3C2×C22⋊C411yescharacteristic
399C23×C3C2×C22⋊C411yescharacteristic
400C23×C3C2×C22⋊C411yescharacteristic
401C23×C3C2×C22⋊C411yescharacteristic
402C23×C3C2×C22⋊C411yescharacteristic
403C23×C3#13514yes—
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—24no—
464C24—21no—
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
542C2×C8—24no—
543C2×C8—44no—
544C2×C8—44no—
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—28no—
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—44no—
589C22×C3—44no—
590C22×C3—44no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—84no—
598C22×C3C2×#9912yes—
599C22×C3#41612yes—
600C22×C3#41612yes—
601C22×C3#42112yes—
602C22×C3C22×C22⋊C411yescharacteristic
603C22×C3C2×#13512yes—
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—22no—
627C23—22no—
628C23—22no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—416no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23C2×C3×C22⋊C411yescharacteristic
642C23C2×C3×C22⋊C411yescharacteristic
643C23C2×C3×C22⋊C411yescharacteristic
644C23C2×C3×C22⋊C411yescharacteristic
645C23C2×C3×C22⋊C411yescharacteristic
646C23C2×C3×C22⋊C411yescharacteristic
647C23C3×#13514yes—
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—22no—
711C2×C3—22no—
712C2×C3—41no—
713C2×C3—41no—
714C2×C3—82no—
715C2×C3C22×#9911yescharacteristic
716C2×C3C2×#41611yescharacteristic
717C2×C3C2×#42111yescharacteristic
718C22—28no—
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—44no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—84no—
745C22C2×C3×#9912yes—
746C22C3×#41612yes—
747C22C3×#41612yes—
748C22C3×#42112yes—
749C22C22×C3×C22⋊C411yescharacteristic
750C22C2×C3×#13512yes—
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#1757211yescharacteristic, direct product factor, Sylow
764C2—22no—
765C2—22no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×C3×#9911yescharacteristic
773C2C2×C3×#41611yescharacteristic
774C2C2×C3×#42111yescharacteristic
subgroupG/H
centerC2×C3×C4C2×C22⋊C4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
socleC22×C3C22×C22⋊C4
prime radicalC2×C3×#525C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C3×C4 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊C8C2semidirect
3. C3×#2280C2semidirect
4. C3×#1520C2semidirect
5. C3×#1519C2semidirect
6. C3×#1516C2semidirect
7. C3×#1501C2semidirect
8. #17572C3direct (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
34. C2×C3×C22⋊C8C22semidirect
35. C2×C3×C22⋊C8C22semidirect
36. C3×#381C22semidirect
41. C3×C4×C22⋊C4C22semidirect
42. C3×#328C22semidirect
43. C3×#327C22semidirect
45. C22×C22⋊C8C2×C3semidirect
46. #2280C2×C3semidirect
47. #1520C2×C3semidirect
48. #1519C2×C3semidirect
49. #1516C2×C3semidirect
50. #1501C2×C3semidirect
140. C22×#41C3×C4semidirect
147. #525C3×C4semidirect
148. #525C3×C4semidirect
152. C2×C22⋊Q8C3×C4semidirect
154. C2×#121C3×C4semidirect
160. C2×#117C3×C4semidirect
165. C2×C22⋊C8C22×C3semidirect
166. C2×C22⋊C8C22×C3semidirect
167. #381C22×C3semidirect
172. C4×C22⋊C4C22×C3semidirect
173. #328C22×C3semidirect
174. #327C22×C3semidirect
763. C3#17572direct (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
C22×C3×C22⋊C82
C3×#22802
C3×#15202
C3×#15192
C3×#15162
C3×#15012
#175723