Finite Group Databasebeta

← C43×#25575 #24945592

Subgroups — C43×#25575 #24945592

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#553C211yesmaximal, characteristic, complemented
2C2×C43×#488C211yesmaximal, characteristic, complemented
3C2×C43×#463C211yesmaximal, characteristic, complemented
4C43×#2540C211yesmaximal, characteristic, complemented
5C43×#2000C211yesmaximal, characteristic, complemented
6C43×#2000C211yesmaximal, characteristic, complemented
7C43×#1999C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1989C211yesmaximal, characteristic, complemented
10C43×#1954C211yesmaximal, characteristic, complemented
11C43×#1875C211yesmaximal, characteristic, complemented
12C43×#1874C211yesmaximal, characteristic, complemented
13C43×#1873C211yesmaximal, characteristic, complemented
14C43×#1872C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C43×#553—24no—
19C43×#553—24no—
20C2×#126×C43—21no—
21C2×#125×C43C2211yescharacteristic
22C2×#124×C43C2211yescharacteristic
23C2×#123×C43—21no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#121×C43—21no—
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×C4×D4×C43—21no—
32C2×C4×D4×C43C2211yescharacteristic
33C2×C4×D4×C43C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#488—24no—
37C43×#463—24no—
38C2×C4⋊C8×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#103×C43C2211yescharacteristic
41C2×#103×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C2×C22⋊C8×C43C2211yescharacteristic
50C2×C22⋊C8×C43C2211yescharacteristic
51C2×C4×C8×C43C2211yescharacteristic
52C43×#399—21no—
53C43×#392—21no—
54C43×#390—21no—
55C43×#390—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Q8×C43C2311yescharacteristic
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43D411yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C22×D4×C43C2311yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C2×SD16×C43—22no—
76C2×SD16×C43—41no—
77C2×SD16×C43—41no—
78C2×D8×C43—22no—
79C2×D8×C43—41no—
80C2×D8×C43—41no—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85#126×C43—28no—
86#125×C43—22no—
87#125×C43D414yescomplemented
88#124×C43—22no—
89#124×C43—22no—
90#123×C43—28no—
91C22⋊Q8×C43—22no—
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—41no—
94C22⋊Q8×C43—41no—
95#121×C43—28no—
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—41no—
103#121×C43—41no—
104C4×D4×C43—28no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43D414yescomplemented
109#117×C43—22no—
110#117×C43—22no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43—22no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139C4⋊C8×C43—22no—
140#103×C43—22no—
141#103×C43—22no—
142#103×C43—22no—
143#102×C43—22no—
144#102×C43—22no—
145#102×C43—22no—
146#102×C43—22no—
147#102×C43—22no—
148C22⋊C8×C43—41no—
149C22⋊C8×C43—41no—
150C22⋊C8×C43—41no—
151C22⋊C8×C43—41no—
152C4×C8×C43—22no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D411yescharacteristic
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×D4×C43—24no—
165C2×D4×C43—24no—
166C2×D4×C43—22no—
167C2×D4×C43—21no—
168C2×D4×C43—22no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—41no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—81no—
187C2×D4×C43—81no—
188C2×D4×C43—81no—
189C2×D4×C43—81no—
190C2×D4×C43C2×D412yes—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—24no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—81no—
212C22×C4×C43—81no—
213C22×C4×C43—81no—
214C22×C4×C43—81no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2411yescharacteristic
220SD16×C43—44no—
221D8×C43—44no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—22no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—42no—
244C4⋊C4×C43—42no—
245C4⋊C4×C43C2×D412yes—
246C4⋊C4×C43C2×D412yes—
247C4⋊C4×C43C2×D412yes—
248C4⋊C4×C43#4112yes—
249C4⋊C4×C43#4112yes—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—24no—
253C22⋊C4×C43—24no—
254C22⋊C4×C43—22no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—42no—
261C22⋊C4×C43—42no—
262C42×C43—24no—
263C42×C43—81no—
264C42×C43C2×D412yes—
265C42×C43C2×D412yes—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—22no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43#13512yes—
294C23×C43C22×D411yescharacteristic
295Q8×C43—41no—
296Q8×C43—41no—
297Q8×C43—41no—
298Q8×C43—41no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—44no—
302D4×C43—48no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—84no—
310D4×C43—84no—
311D4×C43—84no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—84no—
349C2×C4×C43—84no—
350C2×C4×C43#12012yes—
351C2×C4×C43#12012yes—
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43C2×#4111yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C8×C43—41no—
359C8×C43—41no—
360C8×C43—41no—
361C8×C43—41no—
362#25575C4311yesmaximal, characteristic, direct product factor, Sylow
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—42no—
372C22×C43—41no—
373C22×C43—42no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43C2×#12011yescharacteristic
392C22×C43#54611yescharacteristic
393C22×C43#54611yescharacteristic
394C22×C43C2×#13511yescharacteristic
395C22×C43#57511yescharacteristic
396C22×C43#57611yescharacteristic
397C22×C43#57711yescharacteristic
398C4×C43—22no—
399C4×C43—22no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43—42no—
406C4×C43—42no—
407C4×C43—81no—
408C4×C43#53211yescharacteristic
409C4×C43#53511yescharacteristic
410C4×C43#55011yescharacteristic
411C4×C43#55011yescharacteristic
412C2×#553C2×C4311yescharacteristic, complemented
413C2×#488C2×C4311yescharacteristic, complemented
414C2×#463C2×C4311yescharacteristic, complemented
415#2540C2×C4311yescharacteristic, complemented
416#2000C2×C4311yescharacteristic, complemented
417#2000C2×C4311yescharacteristic, complemented
418#1999C2×C4311yescharacteristic, complemented
419#1999C2×C4311yescharacteristic, complemented
420#1989C2×C4311yescharacteristic, complemented
421#1954C2×C4311yescharacteristic, complemented
422#1875C2×C4311yescharacteristic, complemented
423#1874C2×C4311yescharacteristic, complemented
424#1873C2×C4311yescharacteristic, complemented
425#1872C2×C4311yescharacteristic, complemented
426C4×#102C2×C4311yescharacteristic, complemented
427C2×C43—42no—
428C2×C43—81no—
429C2×C43—82no—
430C2×C43—161no—
431C2×C43#243111yescharacteristic
432C2×C43#300211yescharacteristic
433C2×C43#301211yescharacteristic
434C2×C43#329711yescharacteristic
435C2×C43#330111yescharacteristic
436C2×C43#332211yescharacteristic
437C2×C43#332611yescharacteristic
438C22×SD16C22×C4311yescharacteristic
439C22×D8C22×C4311yescharacteristic
440#553—24no—
441#553—24no—
442C2×#126—21no—
443C2×#125C22×C4311yescharacteristic
444C2×#124C22×C4311yescharacteristic
445C2×#123—21no—
446C2×C22⋊Q8C22×C4311yescharacteristic
447C2×C22⋊Q8C22×C4311yescharacteristic
448C2×#121—21no—
449C2×#121C22×C4311yescharacteristic
450C2×#121C22×C4311yescharacteristic
451C2×#121C22×C4311yescharacteristic
452C2×#121C22×C4311yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4C22×C4311yescharacteristic
455C2×C4×D4C22×C4311yescharacteristic
456C2×#117C22×C4311yescharacteristic
457C22×C4⋊C4C22×C4311yescharacteristic
458#488—24no—
459#463—24no—
460C2×C4⋊C8C22×C4311yescharacteristic
461C2×#103C22×C4311yescharacteristic
462C2×#103C22×C4311yescharacteristic
463C2×#103C22×C4311yescharacteristic
464C2×#102C22×C4311yescharacteristic
465C2×#102C22×C4311yescharacteristic
466C2×#102C22×C4311yescharacteristic
467C2×#102C22×C4311yescharacteristic
468C2×#102C22×C4311yescharacteristic
469C2×C22⋊C8C22×C4311yescharacteristic
470C2×C22⋊C8C22×C4311yescharacteristic
471C2×C22⋊C8C22×C4311yescharacteristic
472C2×C22⋊C8C22×C4311yescharacteristic
473C2×C4×C8C22×C4311yescharacteristic
474#399—21no—
475#392—21no—
476#390—21no—
477#390—21no—
478C4×C4⋊C4C22×C4311yescharacteristic
479#340C22×C4311yescharacteristic
480#340C22×C4311yescharacteristic
481#340C22×C4311yescharacteristic
482#340C22×C4311yescharacteristic
483#340C22×C4311yescharacteristic
484#340C22×C4311yescharacteristic
485C43#2557511yescharacteristic, direct product factor, Sylow
486C22×Q8C23×C4311yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4D4×C4311yescharacteristic
492C22×D4C23×C4311yescharacteristic
493C22×D4C23×C4311yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C4311yescharacteristic
497C23×C4C23×C4311yescharacteristic
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—41no—
503C2×D8—41no—
504C22×C8C23×C4311yescharacteristic
505C22×C8C23×C4311yescharacteristic
506C22×C8C23×C4311yescharacteristic
507C22×C8C23×C4311yescharacteristic
508#126—28no—
509#125—22no—
510#125D4×C4314yescomplemented
511#124—22no—
512#124—22no—
513#123—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4D4×C4314yescomplemented
532#117—22no—
533#117—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C4311yescharacteristic
542C2×C4⋊C4C23×C4311yescharacteristic
543C2×C4⋊C4C23×C4311yescharacteristic
544C2×C4⋊C4C23×C4311yescharacteristic
545C2×C4⋊C4C23×C4311yescharacteristic
546C2×C4⋊C4C23×C4311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4D4×C4311yescharacteristic
558C2×C22⋊C4D4×C4311yescharacteristic
559C2×C42—21no—
560C2×C42—21no—
561C2×C42C23×C4311yescharacteristic
562C4⋊C8—22no—
563#103—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571C22⋊C8—41no—
572C22⋊C8—41no—
573C22⋊C8—41no—
574C22⋊C8—41no—
575C4×C8—22no—
576#95—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C4311yescharacteristic
580C24C2×D4×C4311yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4C2×D4×C4312yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C2×D4×C4311yescharacteristic
639C22×C4C2×D4×C4311yescharacteristic
640C22×C4C2×D4×C4311yescharacteristic
641C22×C4C2×D4×C4311yescharacteristic
642C22×C4C24×C4311yescharacteristic
643SD16—44no—
644D8—44no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4C2×D4×C4312yes—
669C4⋊C4C2×D4×C4312yes—
670C4⋊C4C2×D4×C4312yes—
671C4⋊C4#41×C4312yes—
672C4⋊C4#41×C4312yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C42—24no—
686C42—81no—
687C42C2×D4×C4312yes—
688C42C2×D4×C4312yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23#135×C4312yes—
717C23C22×D4×C4311yescharacteristic
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—84no—
733D4—84no—
734D4—84no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#120×C4312yes—
774C2×C4#120×C4312yes—
775C2×C4C22×D4×C4311yescharacteristic
776C2×C4C22×D4×C4311yescharacteristic
777C2×C4C2×#41×C4311yescharacteristic
778C2×C4C2×#41×C4311yescharacteristic
779C2×C4H(5,𝔽2)×C4311yescharacteristic
780C2×C4H(5,𝔽2)×C4311yescharacteristic
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C2×#120×C4311yescharacteristic
814C22C43×#54611yescharacteristic
815C22C43×#54611yescharacteristic
816C22C2×#135×C4311yescharacteristic
817C22C43×#57511yescharacteristic
818C22C43×#57611yescharacteristic
819C22C43×#57711yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4C43×#53211yescharacteristic
831C4C43×#53511yescharacteristic
832C4C43×#55011yescharacteristic
833C4C43×#55011yescharacteristic
834C2—42no—
835C2—81no—
836C2—82no—
837C2—161no—
838C2C43×#243111yescharacteristic
839C2C43×#300211yescharacteristic
840C2C43×#301211yescharacteristic
841C2C43×#329711yescharacteristic
842C2C43×#330111yescharacteristic
843C2C43×#332211yescharacteristic
844C2C43×#332611yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#553C2semidirect
2. C2×C43×#488C2semidirect
3. C2×C43×#463C2semidirect
4. C43×#2540C2semidirect
5. C43×#2000C2semidirect
6. C43×#2000C2semidirect
7. C43×#1999C2semidirect
8. C43×#1999C2semidirect
9. C43×#1989C2semidirect
10. C43×#1954C2semidirect
11. C43×#1875C2semidirect
12. C43×#1874C2semidirect
13. C43×#1873C2semidirect
14. C43×#1872C2semidirect
15. C4×#102×C43C2semidirect
87. #125×C43D4semidirect
108. C4×D4×C43D4semidirect
362. #25575C43direct (N × H)
412. C2×#553C2×C43semidirect
413. C2×#488C2×C43semidirect
414. C2×#463C2×C43semidirect
415. #2540C2×C43semidirect
416. #2000C2×C43semidirect
417. #2000C2×C43semidirect
418. #1999C2×C43semidirect
419. #1999C2×C43semidirect
420. #1989C2×C43semidirect
421. #1954C2×C43semidirect
422. #1875C2×C43semidirect
423. #1874C2×C43semidirect
424. #1873C2×C43semidirect
425. #1872C2×C43semidirect
426. C4×#102C2×C43semidirect
485. C43#25575direct (N × H)
510. #125D4×C43semidirect
531. C4×D4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5532
C2×C43×#4882
C2×C43×#4632
C43×#25402
C43×#20002
C43×#19992
C43×#19892
C43×#19542
C43×#18752
C43×#18742
C43×#18732
C43×#18722
C4×#102×C432
#2557543