Finite Group Databasebeta

← C43×#23975 #24943992

Subgroups — C43×#23975 #24943992

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#553C211yesmaximal, characteristic, complemented
2C2×C43×#449C211yesmaximal, characteristic, complemented
3C2×C43×#417C211yesmaximal, characteristic, complemented
4C43×#2407C211yesmaximal, characteristic, complemented
5C43×#2026C211yesmaximal, characteristic, complemented
6C43×#2025C211yesmaximal, characteristic, complemented
7C43×#2000C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1895C211yesmaximal, characteristic, complemented
10C43×#1879C211yesmaximal, characteristic, complemented
11C43×#1877C211yesmaximal, characteristic, complemented
12C43×#1875C211yesmaximal, characteristic, complemented
13C43×#1873C211yesmaximal, characteristic, complemented
14C43×#1870C211yesmaximal, characteristic, complemented
15C43×#1823C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C43×#553—24no—
21C43×#553—24no—
22C2×#126×C43—21no—
23C2×#125×C43C2211yescharacteristic
24C2×#123×C43—21no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#121×C43—21no—
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×C4×D4×C43—21no—
31C2×C4×D4×C43C2211yescharacteristic
32C2×C4×D4×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C43×#449—24no—
36C43×#417—24no—
37C2×#103×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#394—21no—
49C43×#392—21no—
50C43×#391C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#386—21no—
53C43×#385—21no—
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#41×C43—22no—
64C2×#41×C43—22no—
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—41no—
68C2×#41×C43—41no—
69C22×Q8×C43C2311yescharacteristic
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43D411yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C22×D4×C43C2311yescharacteristic
77C23×C4×C43—21no—
78C23×C4×C43—21no—
79C23×C4×C43—21no—
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C2×SD16×C43—22no—
83C2×SD16×C43—22no—
84C2×SD16×C43—41no—
85C2×D8×C43—22no—
86C2×D8×C43—22no—
87C2×D8×C43—41no—
88C2×M16×C43—22no—
89C2×M16×C43—41no—
90C2×M16×C43—41no—
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95#126×C43—28no—
96#125×C43—22no—
97#125×C43—22no—
98#123×C43—28no—
99C22⋊Q8×C43—22no—
100C22⋊Q8×C43—41no—
101#121×C43—28no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43—22no—
105#121×C43—22no—
106#121×C43—41no—
107#121×C43D414yescomplemented
108C4×D4×C43—28no—
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111C4×D4×C43—22no—
112C4×D4×C43—22no—
113#117×C43—22no—
114#117×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43D414yescomplemented
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C42×C43—21no—
139C2×C42×C43C2311yescharacteristic
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—41no—
147#102×C43—41no—
148C22⋊C8×C43—22no—
149C22⋊C8×C43—41no—
150C22⋊C8×C43—41no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D411yescharacteristic
158#41×C43—28no—
159#41×C43—44no—
160#41×C43—44no—
161#41×C43—44no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43#4112yes—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—22no—
172C2×D4×C43—24no—
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—21no—
180C2×D4×C43—21no—
181C2×D4×C43—41no—
182C2×D4×C43—41no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43—81no—
193C2×D4×C43C2×D412yes—
194C2×D4×C43#4112yes—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—24no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—24no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—42no—
214C22×C4×C43—42no—
215C22×C4×C43—42no—
216C22×C4×C43—81no—
217C22×C4×C43—81no—
218C22×C4×C43—81no—
219C22×C4×C43—81no—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227SD16×C43—44no—
228D8×C43—44no—
229M16×C43—44no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—22no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—42no—
254C4⋊C4×C43C2×D412yes—
255C4⋊C4×C43C2×D412yes—
256C4⋊C4×C43C2×D412yes—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—22no—
262C22⋊C4×C43—22no—
263C22⋊C4×C43—42no—
264C22⋊C4×C43—42no—
265C22⋊C4×C43—42no—
266C22⋊C4×C43—81no—
267C22⋊C4×C43—81no—
268C42×C43—24no—
269C42×C43—21no—
270C42×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—22no—
279C23×C43—21no—
280C23×C43—22no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43#12012yes—
299C23×C43C22×D411yescharacteristic
300Q8×C43—22no—
301Q8×C43—22no—
302Q8×C43—41no—
303Q8×C43—41no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—44no—
309D4×C43—48no—
310D4×C43—48no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315D4×C43—84no—
316D4×C43—84no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—21no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—48no—
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—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—84no—
356C2×C4×C43—84no—
357C2×C4×C43#12012yes—
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C2×#4111yescharacteristic
361C2×C4×C43C2×#4111yescharacteristic
362C2×C4×C43H(5,𝔽2)11yescharacteristic
363C2×C4×C43H(5,𝔽2)11yescharacteristic
364C8×C43—41no—
365C8×C43—41no—
366C8×C43—41no—
367C8×C43—41no—
368#23975C4311yesmaximal, characteristic, direct product factor, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—41no—
380C22×C43—42no—
381C22×C43—41no—
382C22×C43—42no—
383C22×C43—41no—
384C22×C43—42no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—42no—
388C22×C43—41no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43C2×#12011yescharacteristic
398C22×C43#54611yescharacteristic
399C22×C43#54611yescharacteristic
400C22×C43#57511yescharacteristic
401C22×C43#57511yescharacteristic
402C22×C43#57611yescharacteristic
403C22×C43#57711yescharacteristic
404C4×C43—22no—
405C4×C43—41no—
406C4×C43—42no—
407C4×C43—41no—
408C4×C43—42no—
409C4×C43—41no—
410C4×C43—42no—
411C4×C43—42no—
412C4×C43—81no—
413C4×C43—81no—
414C4×C43#52511yescharacteristic
415C4×C43#53511yescharacteristic
416C4×C43#54611yescharacteristic
417C4×C43#54611yescharacteristic
418C2×#553C2×C4311yescharacteristic, complemented
419C2×#449C2×C4311yescharacteristic, complemented
420C2×#417C2×C4311yescharacteristic, complemented
421#2407C2×C4311yescharacteristic, complemented
422#2026C2×C4311yescharacteristic, complemented
423#2025C2×C4311yescharacteristic, complemented
424#2000C2×C4311yescharacteristic, complemented
425#1999C2×C4311yescharacteristic, complemented
426#1895C2×C4311yescharacteristic, complemented
427#1879C2×C4311yescharacteristic, complemented
428#1877C2×C4311yescharacteristic, complemented
429#1875C2×C4311yescharacteristic, complemented
430#1873C2×C4311yescharacteristic, complemented
431#1870C2×C4311yescharacteristic, complemented
432#1823C2×C4311yescharacteristic, complemented
433C2×C43—42no—
434C2×C43—81no—
435C2×C43—82no—
436C2×C43—82no—
437C2×C43#240411yescharacteristic
438C2×C43#300511yescharacteristic
439C2×C43#301211yescharacteristic
440C2×C43#330711yescharacteristic
441C2×C43#330911yescharacteristic
442C2×C43#332211yescharacteristic
443C2×C43#332611yescharacteristic
444C22×#41C22×C4311yescharacteristic
445C22×SD16C22×C4311yescharacteristic
446C22×D8C22×C4311yescharacteristic
447C22×M16C22×C4311yescharacteristic
448#553—24no—
449#553—24no—
450C2×#126—21no—
451C2×#125C22×C4311yescharacteristic
452C2×#123—21no—
453C2×C22⋊Q8C22×C4311yescharacteristic
454C2×#121—21no—
455C2×#121C22×C4311yescharacteristic
456C2×#121C22×C4311yescharacteristic
457C2×#121C22×C4311yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4C22×C4311yescharacteristic
460C2×C4×D4C22×C4311yescharacteristic
461C2×#117C22×C4311yescharacteristic
462C22×C4⋊C4C22×C4311yescharacteristic
463#449—24no—
464#417—24no—
465C2×#103C22×C4311yescharacteristic
466C2×#103C22×C4311yescharacteristic
467C2×#103C22×C4311yescharacteristic
468C2×#102C22×C4311yescharacteristic
469C2×#102C22×C4311yescharacteristic
470C2×#102C22×C4311yescharacteristic
471C2×#102C22×C4311yescharacteristic
472C2×#102C22×C4311yescharacteristic
473C2×C22⋊C8C22×C4311yescharacteristic
474C2×C22⋊C8C22×C4311yescharacteristic
475C2×C22⋊C8C22×C4311yescharacteristic
476#394—21no—
477#392—21no—
478#391C22×C4311yescharacteristic
479#390C22×C4311yescharacteristic
480#386—21no—
481#385—21no—
482#380C22×C4311yescharacteristic
483#340C22×C4311yescharacteristic
484#340C22×C4311yescharacteristic
485#340C22×C4311yescharacteristic
486#340C22×C4311yescharacteristic
487#340C22×C4311yescharacteristic
488#340C22×C4311yescharacteristic
489#336C22×C4311yescharacteristic
490#336C22×C4311yescharacteristic
491C43#2397511yescharacteristic, direct product factor, Sylow
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C4311yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C4311yescharacteristic
504C22×D4C23×C4311yescharacteristic
505C22×D4C23×C4311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C4311yescharacteristic
510C23×C4C23×C4311yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C23×C4311yescharacteristic
521C22×C8C23×C4311yescharacteristic
522C22×C8C23×C4311yescharacteristic
523C22×C8C23×C4311yescharacteristic
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C4314yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C4311yescharacteristic
550C2×C4⋊C4D4×C4314yescomplemented
551C2×C4⋊C4C23×C4311yescharacteristic
552C2×C4⋊C4C23×C4311yescharacteristic
553C2×C4⋊C4C23×C4311yescharacteristic
554C2×C4⋊C4C23×C4311yescharacteristic
555C2×C4⋊C4C23×C4311yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C4311yescharacteristic
566C2×C22⋊C4D4×C4311yescharacteristic
567C2×C42—21no—
568C2×C42C23×C4311yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C4311yescharacteristic
586C24C2×D4×C4311yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C4312yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C4312yes—
623C2×D4#41×C4312yes—
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—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C4311yescharacteristic
650C22×C4C2×D4×C4311yescharacteristic
651C22×C4C2×D4×C4311yescharacteristic
652C22×C4C2×D4×C4311yescharacteristic
653C22×C4C2×D4×C4312yes—
654C22×C4C2×D4×C4312yes—
655C22×C4C24×C4311yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C4312yes—
684C4⋊C4C2×D4×C4312yes—
685C4⋊C4C2×D4×C4312yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C4312yes—
728C23C22×D4×C4311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#120×C4312yes—
787C2×C4C22×D4×C4311yescharacteristic
788C2×C4C22×D4×C4311yescharacteristic
789C2×C4C2×#41×C4311yescharacteristic
790C2×C4C2×#41×C4311yescharacteristic
791C2×C4H(5,𝔽2)×C4311yescharacteristic
792C2×C4H(5,𝔽2)×C4311yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C4311yescharacteristic
826C22C43×#54611yescharacteristic
827C22C43×#54611yescharacteristic
828C22C43×#57511yescharacteristic
829C22C43×#57511yescharacteristic
830C22C43×#57611yescharacteristic
831C22C43×#57711yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4C43×#52511yescharacteristic
843C4C43×#53511yescharacteristic
844C4C43×#54611yescharacteristic
845C4C43×#54611yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C43×#240411yescharacteristic
851C2C43×#300511yescharacteristic
852C2C43×#301211yescharacteristic
853C2C43×#330711yescharacteristic
854C2C43×#330911yescharacteristic
855C2C43×#332211yescharacteristic
856C2C43×#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×#449C2semidirect
3. C2×C43×#417C2semidirect
4. C43×#2407C2semidirect
5. C43×#2026C2semidirect
6. C43×#2025C2semidirect
7. C43×#2000C2semidirect
8. C43×#1999C2semidirect
9. C43×#1895C2semidirect
10. C43×#1879C2semidirect
11. C43×#1877C2semidirect
12. C43×#1875C2semidirect
13. C43×#1873C2semidirect
14. C43×#1870C2semidirect
15. C43×#1823C2semidirect
107. #121×C43D4semidirect
121. C2×C4⋊C4×C43D4semidirect
368. #23975C43direct (N × H)
418. C2×#553C2×C43semidirect
419. C2×#449C2×C43semidirect
420. C2×#417C2×C43semidirect
421. #2407C2×C43semidirect
422. #2026C2×C43semidirect
423. #2025C2×C43semidirect
424. #2000C2×C43semidirect
425. #1999C2×C43semidirect
426. #1895C2×C43semidirect
427. #1879C2×C43semidirect
428. #1877C2×C43semidirect
429. #1875C2×C43semidirect
430. #1873C2×C43semidirect
431. #1870C2×C43semidirect
432. #1823C2×C43semidirect
491. C43#23975direct (N × H)
536. #121D4×C43semidirect
550. C2×C4⋊C4D4×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×#4492
C2×C43×#4172
C43×#24072
C43×#20262
C43×#20252
C43×#20002
C43×#19992
C43×#18952
C43×#18792
C43×#18772
C43×#18752
C43×#18732
C43×#18702
C43×#18232
#2397543