Finite Group Databasebeta

← C43×#17577 #24937594

Subgroups — C43×#17577 #24937594

Order 11008.

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×#121×C43C211yesmaximal, characteristic
2C2×C43×#407C211yesmaximal, characteristic, complemented
3C43×#2280C211yesmaximal, characteristic, complemented
4C43×#1519C214yesmaximal, complemented
5C43×#1510C214yesmaximal, complemented
6C43×#1507C214yesmaximal, complemented
7C23×D4×C43—21no—
8C23×D4×C43C411yescharacteristic, complemented
9C24×C4×C43C2211yescharacteristic
10C22×M16×C43—21no—
11C2×#121×C43—21no—
12C2×#121×C43—21no—
13C2×#121×C43—21no—
14C2×#121×C43—21no—
15C2×#121×C43—21no—
16C2×#121×C43—21no—
17C2×#121×C43C412yescomplemented
18C2×#121×C43C412yescomplemented
19C2×#121×C43C412yescomplemented
20C2×#121×C43C2212yes—
21C2×#121×C43C2212yes—
22C2×#121×C43C2212yes—
23C2×#117×C43—21no—
24C22×C4⋊C4×C43C411yescharacteristic, complemented
25C22×C22⋊C4×C43—21no—
26C43×#407—21no—
27C43×#407—21no—
28C43×#407C2212yescomplemented
29C43×#407C2212yescomplemented
30C2×C22⋊C8×C43—21no—
31C2×C22⋊C8×C43C2212yescomplemented
32C43×#381C2212yescomplemented
33C43×#380—21no—
34C43×#380C2212yescomplemented
35C43×#379—21no—
36C4×C22⋊C4×C43—21no—
37C4×C22⋊C4×C43C2212yescomplemented
38C43×#327C22116yescomplemented
39C25×C43—21no—
40C25×C43D411yescharacteristic
41C22×D4×C43—22no—
42C22×D4×C43—22no—
43C22×D4×C43—22no—
44C22×D4×C43—22no—
45C22×D4×C43—22no—
46C22×D4×C43—22no—
47C22×D4×C43—21no—
48C22×D4×C43—21no—
49C22×D4×C43—21no—
50C22×D4×C43—44no—
51C22×D4×C43—48no—
52C22×D4×C43C2×C412yes—
53C22×D4×C43C2×C412yes—
54C22×D4×C43C2×C412yes—
55C23×C4×C43—21no—
56C23×C4×C43—44no—
57C23×C4×C43C2×C411yescharacteristic
58C23×C4×C43C2×C411yescharacteristic
59C23×C4×C43C2×C411yescharacteristic
60C23×C4×C43C2×C411yescharacteristic
61C23×C4×C43D411yescharacteristic
62C23×C4×C43D411yescharacteristic
63C23×C4×C43D411yescharacteristic
64C23×C4×C43D411yescharacteristic
65C23×C4×C43D411yescharacteristic
66C23×C4×C43D411yescharacteristic
67C23×C4×C43D411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C23×C4×C43C2311yescharacteristic
70C23×C4×C43C2311yescharacteristic
71C2×M16×C43—22no—
72C2×M16×C43—22no—
73C2×M16×C43—44no—
74C22×C8×C43—22no—
75#121×C43—22no—
76#121×C43—22no—
77#121×C43—22no—
78#121×C43—22no—
79#121×C43—22no—
80#121×C43—22no—
81#121×C43—22no—
82#121×C43—22no—
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—22no—
86#121×C43—22no—
87#121×C43C2×C414yes—
88#121×C43C2×C414yes—
89#121×C43C2×C414yes—
90#121×C43C2314yes—
91#117×C43—44no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43C2×C412yes—
97C2×C4⋊C4×C43C2×C412yes—
98C2×C4⋊C4×C43C2×C412yes—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—22no—
108C2×C42×C43—22no—
109C22⋊C8×C43—22no—
110C22⋊C8×C43—22no—
111C22⋊C8×C43—22no—
112C22⋊C8×C43C2314yescomplemented
113#95×C43—22no—
114#95×C43C2314yescomplemented
115C24×C43—24no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—42no—
120C24×C43—42no—
121C24×C43—44no—
122C24×C43—44no—
123C24×C43—44no—
124C24×C43C22⋊C411yescharacteristic
125C24×C43C22⋊C411yescharacteristic
126C24×C43C22⋊C411yescharacteristic
127C24×C43C22⋊C411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C24×C43C2×D411yescharacteristic
130C24×C43C2×D411yescharacteristic
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—22no—
134C2×D4×C43—24no—
135C2×D4×C43—24no—
136C2×D4×C43—24no—
137C2×D4×C43—24no—
138C2×D4×C43—48no—
139C2×D4×C43—48no—
140C2×D4×C43—48no—
141C2×D4×C43—48no—
142C2×D4×C43—48no—
143C2×D4×C43—44no—
144C2×D4×C43—44no—
145C2×D4×C43—44no—
146C2×D4×C43—44no—
147C2×D4×C43—44no—
148C2×D4×C43—48no—
149C2×D4×C43—44no—
150C2×D4×C43C22×C414yes—
151C22×C4×C43—24no—
152C22×C4×C43—24no—
153C22×C4×C43—24no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—24no—
158C22×C4×C43—42no—
159C22×C4×C43—42no—
160C22×C4×C43—42no—
161C22×C4×C43—44no—
162C22×C4×C43—42no—
163C22×C4×C43—42no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43C22⋊C411yescharacteristic
171C22×C4×C43C22⋊C411yescharacteristic
172C22×C4×C43C22⋊C411yescharacteristic
173C22×C4×C43C22⋊C411yescharacteristic
174C22×C4×C43C22⋊C411yescharacteristic
175C22×C4×C43C22⋊C411yescharacteristic
176C22×C4×C43C22⋊C411yescharacteristic
177C22×C4×C43C22⋊C411yescharacteristic
178C22×C4×C43C22⋊C411yescharacteristic
179C22×C4×C43C22⋊C411yescharacteristic
180C22×C4×C43C22⋊C411yescharacteristic
181C22×C4×C43C22⋊C411yescharacteristic
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198M16×C43—44no—
199M16×C43—44no—
200C2×C8×C43—24no—
201C2×C8×C43—44no—
202C4⋊C4×C43—22no—
203C4⋊C4×C43—22no—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—44no—
206C4⋊C4×C43C22×C414yes—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—24no—
209C22⋊C4×C43—24no—
210C22⋊C4×C43—24no—
211C22⋊C4×C43—44no—
212C22⋊C4×C43—44no—
213C22⋊C4×C43—44no—
214C42×C43—44no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43—24no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—416no—
237C23×C43—44no—
238C23×C43—44no—
239C23×C43—44no—
240C23×C43—44no—
241C23×C43—44no—
242C23×C43—44no—
243C23×C43—44no—
244C23×C43—44no—
245C23×C43—44no—
246C23×C43—816no—
247C23×C43C2×C22⋊C411yescharacteristic
248C23×C43C2×C22⋊C411yescharacteristic
249C23×C43C2×C22⋊C411yescharacteristic
250C23×C43C2×C22⋊C411yescharacteristic
251C23×C43C2×C22⋊C411yescharacteristic
252C23×C43C2×C22⋊C411yescharacteristic
253C23×C43AGL(1,ℤ/8)14yes—
254C23×C43C22×D411yescharacteristic
255D4×C43—44no—
256D4×C43—44no—
257D4×C43—48no—
258D4×C43—48no—
259D4×C43—48no—
260D4×C43—48no—
261D4×C43—44no—
262D4×C43—44no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—24no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—44no—
292C2×C4×C43—44no—
293C2×C4×C43—44no—
294C2×C4×C43—44no—
295C2×C4×C43—44no—
296C2×C4×C43—44no—
297C2×C4×C43#9914yes—
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C2×C4×C43C2×C22⋊C411yescharacteristic
300C2×C4×C43C2×C22⋊C411yescharacteristic
301C2×C4×C43C2×C22⋊C411yescharacteristic
302C2×C4×C43C2×C22⋊C411yescharacteristic
303C2×C4×C43C2×C22⋊C411yescharacteristic
304C2×C4×C43C23×C411yescharacteristic
305C2×C4×C43C22×D411yescharacteristic
306C8×C43—44no—
307#17577C4311yesmaximal, characteristic, direct product factor, Sylow
308C22×C43—28no—
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—21no—
316C22×C43—21no—
317C22×C43—21no—
318C22×C43—21no—
319C22×C43—21no—
320C22×C43—21no—
321C22×C43—21no—
322C22×C43—21no—
323C22×C43—21no—
324C22×C43—21no—
325C22×C43—44no—
326C22×C43—44no—
327C22×C43—44no—
328C22×C43—44no—
329C22×C43—44no—
330C22×C43—44no—
331C22×C43—44no—
332C22×C43—44no—
333C22×C43—44no—
334C22×C43—88no—
335C22×C43—88no—
336C22×C43—88no—
337C22×C43C2×#9912yes—
338C22×C43#41812yes—
339C22×C43#41812yes—
340C22×C43#42112yes—
341C22×C43C22×C22⋊C411yescharacteristic
342C22×C43C2×AGL(1,ℤ/8)12yes—
343C4×C43—21no—
344C4×C43—21no—
345C4×C43—21no—
346C4×C43—21no—
347C4×C43—21no—
348C4×C43—21no—
349C4×C43—44no—
350C4×C43—84no—
351C4×C43C2×#9912yes—
352C4×C43C2×#9912yes—
353C22×#121C2×C4311yescharacteristic
354C2×#407C2×C4311yescharacteristic, complemented
355#2280C2×C4311yescharacteristic, complemented
356#1519C2×C4314yescomplemented
357#1510C2×C4314yescomplemented
358#1507C2×C4314yescomplemented
359C2×C43—22no—
360C2×C43—22no—
361C2×C43—22no—
362C2×C43—22no—
363C2×C43—22no—
364C2×C43—41no—
365C2×C43—41no—
366C2×C43—84no—
367C2×C43C22×#9911yescharacteristic
368C2×C43C2×#41811yescharacteristic
369C2×C43C2×#42111yescharacteristic
370C23×D4—21no—
371C23×D4C4×C4311yescharacteristic, complemented
372C24×C4C22×C4311yescharacteristic
373C22×M16—21no—
374C2×#121—21no—
375C2×#121—21no—
376C2×#121—21no—
377C2×#121—21no—
378C2×#121—21no—
379C2×#121—21no—
380C2×#121C4×C4312yescomplemented
381C2×#121C4×C4312yescomplemented
382C2×#121C4×C4312yescomplemented
383C2×#121C22×C4312yes—
384C2×#121C22×C4312yes—
385C2×#121C22×C4312yes—
386C2×#117—21no—
387C22×C4⋊C4C4×C4311yescharacteristic, complemented
388C22×C22⋊C4—21no—
389#407—21no—
390#407—21no—
391#407C22×C4312yescomplemented
392#407C22×C4312yescomplemented
393C2×C22⋊C8—21no—
394C2×C22⋊C8C22×C4312yescomplemented
395#381C22×C4312yescomplemented
396#380—21no—
397#380C22×C4312yescomplemented
398#379—21no—
399C4×C22⋊C4—21no—
400C4×C22⋊C4C22×C4312yescomplemented
401#327C22×C43116yescomplemented
402C43#1757711yescharacteristic, direct product factor, Sylow
403C25—21no—
404C25D4×C4311yescharacteristic
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—22no—
408C22×D4—22no—
409C22×D4—22no—
410C22×D4—22no—
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—44no—
415C22×D4—48no—
416C22×D4C2×C4×C4312yes—
417C22×D4C2×C4×C4312yes—
418C22×D4C2×C4×C4312yes—
419C23×C4—21no—
420C23×C4—44no—
421C23×C4C2×C4×C4311yescharacteristic
422C23×C4C2×C4×C4311yescharacteristic
423C23×C4C2×C4×C4311yescharacteristic
424C23×C4C2×C4×C4311yescharacteristic
425C23×C4D4×C4311yescharacteristic
426C23×C4D4×C4311yescharacteristic
427C23×C4D4×C4311yescharacteristic
428C23×C4D4×C4311yescharacteristic
429C23×C4D4×C4311yescharacteristic
430C23×C4D4×C4311yescharacteristic
431C23×C4D4×C4311yescharacteristic
432C23×C4C23×C4311yescharacteristic
433C23×C4C23×C4311yescharacteristic
434C23×C4C23×C4311yescharacteristic
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—44no—
438C22×C8—22no—
439#121—22no—
440#121—22no—
441#121—22no—
442#121—22no—
443#121—22no—
444#121—22no—
445#121—22no—
446#121—22no—
447#121—22no—
448#121—22no—
449#121—22no—
450#121—22no—
451#121C2×C4×C4314yes—
452#121C2×C4×C4314yes—
453#121C2×C4×C4314yes—
454#121C23×C4314yes—
455#117—44no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4C2×C4×C4312yes—
461C2×C4⋊C4C2×C4×C4312yes—
462C2×C4⋊C4C2×C4×C4312yes—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C42—22no—
473C22⋊C8—22no—
474C22⋊C8—22no—
475C22⋊C8—22no—
476C22⋊C8C23×C4314yescomplemented
477#95—22no—
478#95C23×C4314yescomplemented
479C24—24no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—42no—
484C24—42no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24C22⋊C4×C4311yescharacteristic
489C24C22⋊C4×C4311yescharacteristic
490C24C22⋊C4×C4311yescharacteristic
491C24C22⋊C4×C4311yescharacteristic
492C24C2×D4×C4311yescharacteristic
493C24C2×D4×C4311yescharacteristic
494C24C2×D4×C4311yescharacteristic
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—44no—
514C2×D4C22×C4×C4314yes—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4C22⋊C4×C4311yescharacteristic
535C22×C4C22⋊C4×C4311yescharacteristic
536C22×C4C22⋊C4×C4311yescharacteristic
537C22×C4C22⋊C4×C4311yescharacteristic
538C22×C4C22⋊C4×C4311yescharacteristic
539C22×C4C22⋊C4×C4311yescharacteristic
540C22×C4C22⋊C4×C4311yescharacteristic
541C22×C4C22⋊C4×C4311yescharacteristic
542C22×C4C22⋊C4×C4311yescharacteristic
543C22×C4C22⋊C4×C4311yescharacteristic
544C22×C4C22⋊C4×C4311yescharacteristic
545C22×C4C22⋊C4×C4311yescharacteristic
546C22×C4C22×C4×C4311yescharacteristic
547C22×C4C22×C4×C4311yescharacteristic
548C22×C4C22×C4×C4311yescharacteristic
549C22×C4C22×C4×C4311yescharacteristic
550C22×C4C22×C4×C4311yescharacteristic
551C22×C4C22×C4×C4311yescharacteristic
552C22×C4C2×D4×C4311yescharacteristic
553C22×C4C2×D4×C4311yescharacteristic
554C22×C4C2×D4×C4311yescharacteristic
555C22×C4C2×D4×C4311yescharacteristic
556C22×C4C2×D4×C4311yescharacteristic
557C22×C4C2×D4×C4311yescharacteristic
558C22×C4C2×D4×C4311yescharacteristic
559C22×C4C2×D4×C4311yescharacteristic
560C22×C4C2×D4×C4311yescharacteristic
561C22×C4C24×C4311yescharacteristic
562M16—44no—
563M16—44no—
564C2×C8—24no—
565C2×C8—44no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—44no—
570C4⋊C4C22×C4×C4314yes—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C42—44no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—416no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—816no—
611C23C2×C22⋊C4×C4311yescharacteristic
612C23C2×C22⋊C4×C4311yescharacteristic
613C23C2×C22⋊C4×C4311yescharacteristic
614C23C2×C22⋊C4×C4311yescharacteristic
615C23C2×C22⋊C4×C4311yescharacteristic
616C23C2×C22⋊C4×C4311yescharacteristic
617C23AGL(1,ℤ/8)×C4314yes—
618C23C22×D4×C4311yescharacteristic
619D4—44no—
620D4—44no—
621D4—48no—
622D4—48no—
623D4—48no—
624D4—48no—
625D4—44no—
626D4—44no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4#99×C4314yes—
662C2×C4C2×C22⋊C4×C4311yescharacteristic
663C2×C4C2×C22⋊C4×C4311yescharacteristic
664C2×C4C2×C22⋊C4×C4311yescharacteristic
665C2×C4C2×C22⋊C4×C4311yescharacteristic
666C2×C4C2×C22⋊C4×C4311yescharacteristic
667C2×C4C2×C22⋊C4×C4311yescharacteristic
668C2×C4C23×C4×C4311yescharacteristic
669C2×C4C22×D4×C4311yescharacteristic
670C8—44no—
671C22—28no—
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—21no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—88no—
698C22—88no—
699C22—88no—
700C22C2×#99×C4312yes—
701C22C43×#41812yes—
702C22C43×#41812yes—
703C22C43×#42112yes—
704C22C22×C22⋊C4×C4311yescharacteristic
705C22C2×AGL(1,ℤ/8)×C4312yes—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—44no—
713C4—84no—
714C4C2×#99×C4312yes—
715C4C2×#99×C4312yes—
716C2—22no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—22no—
721C2—41no—
722C2—41no—
723C2—84no—
724C2C22×#99×C4311yescharacteristic
725C2C2×C43×#41811yescharacteristic
726C2C2×C43×#42111yescharacteristic
subgroupG/H
center, socleC22×C43C22×C22⋊C4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC22×#121×C43C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#407C2semidirect
3. C43×#2280C2semidirect
4. C43×#1519C2semidirect
5. C43×#1510C2semidirect
6. C43×#1507C2semidirect
8. C23×D4×C43C4semidirect
17. C2×#121×C43C4semidirect
18. C2×#121×C43C4semidirect
19. C2×#121×C43C4semidirect
24. C22×C4⋊C4×C43C4semidirect
28. C43×#407C22semidirect
29. C43×#407C22semidirect
31. C2×C22⋊C8×C43C22semidirect
32. C43×#381C22semidirect
34. C43×#380C22semidirect
37. C4×C22⋊C4×C43C22semidirect
38. C43×#327C22semidirect
112. C22⋊C8×C43C23semidirect
114. #95×C43C23semidirect
307. #17577C43direct (N × H)
354. C2×#407C2×C43semidirect
355. #2280C2×C43semidirect
356. #1519C2×C43semidirect
357. #1510C2×C43semidirect
358. #1507C2×C43semidirect
371. C23×D4C4×C43semidirect
380. C2×#121C4×C43semidirect
381. C2×#121C4×C43semidirect
382. C2×#121C4×C43semidirect
387. C22×C4⋊C4C4×C43semidirect
391. #407C22×C43semidirect
392. #407C22×C43semidirect
394. C2×C22⋊C8C22×C43semidirect
395. #381C22×C43semidirect
397. #380C22×C43semidirect
400. C4×C22⋊C4C22×C43semidirect
401. #327C22×C43semidirect
402. C43#17577direct (N × H)
476. C22⋊C8C23×C43semidirect
478. #95C23×C43semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C432
C2×C43×#4072
C43×#22802
C43×#15192
C43×#15102
C43×#15072
#1757743