Finite Group Databasebeta

← C43×#25101 #24945118

Subgroups — C43×#25101 #24945118

Order 11008.

1248 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#463C211yesmaximal, characteristic, complemented
3C2×C43×#447C211yesmaximal, characteristic
4C2×C43×#418C211yesmaximal, characteristic, complemented
5C43×#2435C211yesmaximal, characteristic, complemented
6C43×#2363C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2054C211yesmaximal, characteristic, complemented
9C43×#2042C211yesmaximal, characteristic, complemented
10C43×#2012C211yesmaximal, characteristic, complemented
11C43×#1983C211yesmaximal, characteristic, complemented
12C43×#1925C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1873C211yesmaximal, characteristic, complemented
15C43×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic, complemented
18C22×D8×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×M16×C43C2211yescharacteristic
21C2×#124×C43C2211yescharacteristic
22C2×#124×C43C2211yescharacteristic
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic, complemented
26C2×#117×C43C2211yescharacteristic
27C43×#468—24no—
28C43×#463—24no—
29C43×#447—24no—
30C2×#107×C43C2211yescharacteristic, complemented
31C2×C4⋊C8×C43C2211yescharacteristic, complemented
32C2×C4⋊C8×C43C2211yescharacteristic, complemented
33C43×#418—24no—
34C2×#103×C43C2211yescharacteristic, complemented
35C2×#103×C43C2211yescharacteristic, complemented
36C2×#103×C43C2211yescharacteristic, complemented
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic, complemented
44C2×C22⋊C8×C43C2211yescharacteristic
45C43×#394—21no—
46C43×#394—21no—
47C43×#390—21no—
48C43×#390C2211yescharacteristic
49C43×#390C2211yescharacteristic
50C43×#390C2211yescharacteristic, complemented
51C43×#389C2211yescharacteristic, complemented
52C43×#388—21no—
53C43×#386—21no—
54C43×#379—21no—
55C43×#379—21no—
56C4×C4⋊C4×C43C2211yescharacteristic, complemented
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, complemented
62C43×#336C2211yescharacteristic, complemented
63C25×C43—21no—
64C22×Q8×C43C2311yescharacteristic
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—21no—
68C22×D4×C43—22no—
69C22×D4×C43—21no—
70C22×D4×C43—22no—
71C22×D4×C43—41no—
72C22×D4×C43—41no—
73C22×D4×C43C2311yescharacteristic
74C22×D4×C43C2311yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C23×C4×C43—21no—
77C23×C4×C43C2311yescharacteristic
78C2×SD16×C43—22no—
79C2×SD16×C43—22no—
80C2×SD16×C43—41no—
81C2×D8×C43—22no—
82C2×D8×C43—22no—
83C2×D8×C43—22no—
84C2×D8×C43—22no—
85C2×D8×C43—41no—
86C2×D8×C43—41no—
87C2×M16×C43—22no—
88C2×M16×C43—22no—
89C2×M16×C43—41no—
90C22×C8×C43C2311yescharacteristic
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94#124×C43—22no—
95#124×C43—22no—
96#124×C43—41no—
97#124×C43—41no—
98C22⋊Q8×C43—22no—
99C22⋊Q8×C43—22no—
100#121×C43—22no—
101#121×C43D414yes—
102C4×D4×C43—22no—
103C4×D4×C43—41no—
104#117×C43—22no—
105#117×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#107×C43—22no—
133C4⋊C8×C43—22no—
134C4⋊C8×C43—41no—
135#103×C43—22no—
136#103×C43—22no—
137#103×C43—41no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—22no—
144#102×C43D414yescomplemented
145C22⋊C8×C43—22no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C24×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—42no—
154C24×C43—42no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—81no—
159C24×C43—81no—
160C24×C43C2×D411yescharacteristic
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—24no—
171C2×D4×C43—28no—
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—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—44no—
187C2×D4×C43—44no—
188C2×D4×C43—44no—
189C2×D4×C43—42no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43C2×D412yes—
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—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—42no—
205C22×C4×C43—42no—
206C22×C4×C43—81no—
207C22×C4×C43C2×D412yes—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43#4112yes—
214C22×C4×C43C2411yescharacteristic
215SD16×C43—44no—
216D8×C43—44no—
217D8×C43—44no—
218M16×C43—44no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
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×C43C2×D412yes—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—42no—
238C4⋊C4×C43—81no—
239C4⋊C4×C43C2×D412yes—
240C4⋊C4×C43C2×D412yes—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—41no—
243C22⋊C4×C43—41no—
244C22⋊C4×C43—42no—
245C22⋊C4×C43—42no—
246C22⋊C4×C43—42no—
247C22⋊C4×C43—42no—
248C22⋊C4×C43—42no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—81no—
253C22⋊C4×C43—81no—
254C22⋊C4×C43—81no—
255C22⋊C4×C43—81no—
256C22⋊C4×C43—81no—
257C42×C43—21no—
258C42×C43—21no—
259C42×C43—21no—
260C42×C43—21no—
261C42×C43—42no—
262C42×C43—81no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—48no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
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—84no—
292C23×C43—84no—
293C23×C43—84no—
294C23×C43—84no—
295C23×C43—84no—
296C23×C43—84no—
297C23×C43#12112yes—
298C23×C43C22×D411yescharacteristic
299Q8×C43—41no—
300Q8×C43—41no—
301Q8×C43—41no—
302Q8×C43—41no—
303D4×C43—22no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—48no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315D4×C43—41no—
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—22no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
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—84no—
351C2×C4×C43#12112yes—
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—22no—
359C8×C43—41no—
360C8×C43—41no—
361C8×C43—41no—
362#25101C4311yesmaximal, 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—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—816no—
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×C43—81no—
392C22×C43C2×#12111yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43#57511yescharacteristic
396C22×C43#57511yescharacteristic
397C22×C43#57611yescharacteristic
398C22×C43#57611yescharacteristic
399C4×C43—22no—
400C4×C43—41no—
401C4×C43—41no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43—81no—
407C4×C43—81no—
408C4×C43—81no—
409C4×C43#52511yescharacteristic
410C4×C43#53811yescharacteristic
411C4×C43D4211yescharacteristic
412C4×C43#54611yescharacteristic
413C2×#468C2×C4311yescharacteristic, complemented
414C2×#463C2×C4311yescharacteristic, complemented
415C2×#447C2×C4311yescharacteristic
416C2×#418C2×C4311yescharacteristic, complemented
417#2435C2×C4311yescharacteristic, complemented
418#2363C2×C4311yescharacteristic, complemented
419#2067C2×C4311yescharacteristic, complemented
420#2054C2×C4311yescharacteristic, complemented
421#2042C2×C4311yescharacteristic, complemented
422#2012C2×C4311yescharacteristic, complemented
423#1983C2×C4311yescharacteristic, complemented
424#1925C2×C4311yescharacteristic, complemented
425#1879C2×C4311yescharacteristic, complemented
426#1873C2×C4311yescharacteristic, complemented
427#1851C2×C4311yescharacteristic, complemented
428C2×C43—42no—
429C2×C43—82no—
430C2×C43—82no—
431C2×C43—82no—
432C2×C43#242411yescharacteristic
433C2×C43#304011yescharacteristic
434C2×C43#304111yescharacteristic
435C2×C43#326811yescharacteristic
436C2×C43#327311yescharacteristic
437C2×C43#331911yescharacteristic
438C2×C43#332211yescharacteristic
439C23×D4C22×C4311yescharacteristic
440C22×SD16C22×C4311yescharacteristic, complemented
441C22×D8C22×C4311yescharacteristic
442C22×D8C22×C4311yescharacteristic
443C22×M16C22×C4311yescharacteristic
444C2×#124C22×C4311yescharacteristic
445C2×#124C22×C4311yescharacteristic
446C2×C22⋊Q8C22×C4311yescharacteristic
447C2×#121C22×C4311yescharacteristic
448C2×C4×D4C22×C4311yescharacteristic, complemented
449C2×#117C22×C4311yescharacteristic
450#468—24no—
451#463—24no—
452#447—24no—
453C2×#107C22×C4311yescharacteristic, complemented
454C2×C4⋊C8C22×C4311yescharacteristic, complemented
455C2×C4⋊C8C22×C4311yescharacteristic, complemented
456#418—24no—
457C2×#103C22×C4311yescharacteristic, complemented
458C2×#103C22×C4311yescharacteristic, complemented
459C2×#103C22×C4311yescharacteristic, complemented
460C2×#102C22×C4311yescharacteristic
461C2×#102C22×C4311yescharacteristic
462C2×#102C22×C4311yescharacteristic
463C2×#102C22×C4311yescharacteristic
464C2×#102C22×C4311yescharacteristic
465C2×#102C22×C4311yescharacteristic
466C2×#102C22×C4311yescharacteristic, complemented
467C2×C22⋊C8C22×C4311yescharacteristic
468#394—21no—
469#394—21no—
470#390—21no—
471#390C22×C4311yescharacteristic
472#390C22×C4311yescharacteristic
473#390C22×C4311yescharacteristic, complemented
474#389C22×C4311yescharacteristic, complemented
475#388—21no—
476#386—21no—
477#379—21no—
478#379—21no—
479C4×C4⋊C4C22×C4311yescharacteristic, complemented
480C4×C22⋊C4—21no—
481C4×C22⋊C4C22×C4311yescharacteristic
482#340C22×C4311yescharacteristic, complemented
483#340C22×C4311yescharacteristic, complemented
484#336C22×C4311yescharacteristic, complemented
485#336C22×C4311yescharacteristic, complemented
486C43#2510111yescharacteristic, direct product factor, Sylow
487C25—21no—
488C22×Q8C23×C4311yescharacteristic
489C22×D4—22no—
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C23×C4311yescharacteristic
498C22×D4C23×C4311yescharacteristic
499C22×D4C23×C4311yescharacteristic
500C23×C4—21no—
501C23×C4C23×C4311yescharacteristic
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—41no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C22×C8C23×C4311yescharacteristic
515C22×C8C23×C4311yescharacteristic
516C22×C8C23×C4311yescharacteristic
517C22×C8C23×C4311yescharacteristic
518#124—22no—
519#124—22no—
520#124—41no—
521#124—41no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524#121—22no—
525#121D4×C4314yes—
526C4×D4—22no—
527C4×D4—41no—
528#117—22no—
529#117—41no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4C23×C4311yescharacteristic
533C2×C4⋊C4C23×C4311yescharacteristic
534C2×C4⋊C4C23×C4311yescharacteristic
535C2×C4⋊C4C23×C4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C4311yescharacteristic
551C2×C22⋊C4D4×C4311yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C4311yescharacteristic
555C2×C42C23×C4311yescharacteristic
556#107—22no—
557C4⋊C8—22no—
558C4⋊C8—41no—
559#103—22no—
560#103—22no—
561#103—41no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102D4×C4314yescomplemented
569C22⋊C8—22no—
570#95—21no—
571#95—21no—
572#95D4×C4311yescharacteristic
573#95D4×C4311yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24—42no—
578C24—42no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—81no—
583C24—81no—
584C24C2×D4×C4311yescharacteristic
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×D4—28no—
592C2×D4—24no—
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—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—81no—
616C2×D4C2×D4×C4312yes—
617C2×D4C2×D4×C4312yes—
618C2×D4#41×C4312yes—
619C22×C4—21no—
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—42no—
629C22×C4—42no—
630C22×C4—81no—
631C22×C4C2×D4×C4311yescharacteristic
632C22×C4C2×D4×C4311yescharacteristic
633C22×C4C2×D4×C4311yescharacteristic
634C22×C4C2×D4×C4311yescharacteristic
635C22×C4C2×D4×C4311yescharacteristic
636C22×C4C2×D4×C4312yes—
637C22×C4#41×C4312yes—
638C22×C4C24×C4311yescharacteristic
639SD16—44no—
640D8—44no—
641D8—44no—
642M16—44no—
643C2×C8—21no—
644C2×C8—21no—
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×C8C2×D4×C4312yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C4312yes—
664C4⋊C4C2×D4×C4312yes—
665C22⋊C4—24no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—81no—
677C22⋊C4—81no—
678C22⋊C4—81no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—42no—
686C42—81no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—48no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
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—84no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23#121×C4312yes—
722C23C22×D4×C4311yescharacteristic
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—22no—
733D4—48no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—84no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
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—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4#121×C4312yes—
776C2×C4C22×D4×C4311yescharacteristic
777C2×C4C22×D4×C4311yescharacteristic
778C2×C4C2×#41×C4311yescharacteristic
779C2×C4C2×#41×C4311yescharacteristic
780C2×C4H(5,𝔽2)×C4311yescharacteristic
781C2×C4H(5,𝔽2)×C4311yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—816no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C4311yescharacteristic
816C22D42×C4311yescharacteristic
817C22C43×#54611yescharacteristic
818C22C43×#57511yescharacteristic
819C22C43×#57511yescharacteristic
820C22C43×#57611yescharacteristic
821C22C43×#57611yescharacteristic
822C4—22no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4C43×#52511yescharacteristic
833C4C43×#53811yescharacteristic
834C4D42×C4311yescharacteristic
835C4C43×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—82no—
840C2C43×#242411yescharacteristic
841C2C43×#304011yescharacteristic
842C2C43×#304111yescharacteristic
843C2C43×#326811yescharacteristic
844C2C43×#327311yescharacteristic
845C2C43×#331911yescharacteristic
846C2C43×#332211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#468C2semidirect
2. C2×C43×#463C2semidirect
4. C2×C43×#418C2semidirect
5. C43×#2435C2semidirect
6. C43×#2363C2semidirect
7. C43×#2067C2semidirect
8. C43×#2054C2semidirect
9. C43×#2042C2semidirect
10. C43×#2012C2semidirect
11. C43×#1983C2semidirect
12. C43×#1925C2semidirect
13. C43×#1879C2semidirect
14. C43×#1873C2semidirect
15. C43×#1851C2semidirect
17. C22×SD16×C43C22semidirect
25. C2×C4×D4×C43C22semidirect
30. C2×#107×C43C22semidirect
31. C2×C4⋊C8×C43C22semidirect
32. C2×C4⋊C8×C43C22semidirect
34. C2×#103×C43C22semidirect
35. C2×#103×C43C22semidirect
36. C2×#103×C43C22semidirect
43. C2×#102×C43C22semidirect
50. C43×#390C22semidirect
51. C43×#389C22semidirect
56. C4×C4⋊C4×C43C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
62. C43×#336C22semidirect
144. #102×C43D4semidirect
362. #25101C43direct (N × H)
413. C2×#468C2×C43semidirect
414. C2×#463C2×C43semidirect
416. C2×#418C2×C43semidirect
417. #2435C2×C43semidirect
418. #2363C2×C43semidirect
419. #2067C2×C43semidirect
420. #2054C2×C43semidirect
421. #2042C2×C43semidirect
422. #2012C2×C43semidirect
423. #1983C2×C43semidirect
424. #1925C2×C43semidirect
425. #1879C2×C43semidirect
426. #1873C2×C43semidirect
427. #1851C2×C43semidirect
440. C22×SD16C22×C43semidirect
448. C2×C4×D4C22×C43semidirect
453. C2×#107C22×C43semidirect
454. C2×C4⋊C8C22×C43semidirect
455. C2×C4⋊C8C22×C43semidirect
457. C2×#103C22×C43semidirect
458. C2×#103C22×C43semidirect
459. C2×#103C22×C43semidirect
466. C2×#102C22×C43semidirect
473. #390C22×C43semidirect
474. #389C22×C43semidirect
479. C4×C4⋊C4C22×C43semidirect
482. #340C22×C43semidirect
483. #340C22×C43semidirect
484. #336C22×C43semidirect
485. #336C22×C43semidirect
486. C43#25101direct (N × H)
568. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4682
C2×C43×#4632
C2×C43×#4472
C2×C43×#4182
C43×#24352
C43×#23632
C43×#20672
C43×#20542
C43×#20422
C43×#20122
C43×#19832
C43×#19252
C43×#18792
C43×#18732
C43×#18512
#2510143