Finite Group Databasebeta

← C43×#25144 #24945161

Subgroups — C43×#25144 #24945161

Order 11008.

1114 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×#471C211yesmaximal, characteristic, complemented
2C43×#3056C211yesmaximal, characteristic, complemented
3C43×#3003C211yesmaximal, characteristic
4C2×C43×#450C211yesmaximal, characteristic, complemented
5C43×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C43C211yesmaximal, characteristic, complemented
7C43×#2063C211yesmaximal, characteristic, complemented
8C43×#2051C211yesmaximal, characteristic, complemented
9C43×#2046C211yesmaximal, characteristic, complemented
10C43×#2019C211yesmaximal, characteristic, complemented
11C43×#1977C211yesmaximal, characteristic, complemented
12C43×#1931C211yesmaximal, characteristic, complemented
13C43×#1907C211yesmaximal, characteristic, complemented
14C43×#1901C211yesmaximal, characteristic, complemented
15C43×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C2×#137×C43C2211yescharacteristic, complemented
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C22×SD16×C43C2211yescharacteristic
21C22×SD16×C43C2211yescharacteristic
22C2×#131×C43C2211yescharacteristic, complemented
23C22×M16×C43C2211yescharacteristic
24C22×M16×C43C2211yescharacteristic
25C43×#525C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic
27C43×#471—24no—
28C43×#470—21no—
29C43×#468—21no—
30C43×#467—21no—
31C43×#465—21no—
32C43×#450—21no—
33C43×#450—21no—
34C43×#450—21no—
35C43×#450—21no—
36C43×#450—21no—
37C43×#450—21no—
38C43×#447—21no—
39C43×#447—21no—
40C43×#436—21no—
41C43×#435—21no—
42C43×#435—21no—
43C8×D4×C43—21no—
44C2×#108×C43C2211yescharacteristic, complemented
45C2×#108×C43C2211yescharacteristic, complemented
46C43×#428C2211yescharacteristic, complemented
47C43×#424C2211yescharacteristic, complemented
48C43×#419C2211yescharacteristic, complemented
49C43×#418C2211yescharacteristic
50C43×#418C2211yescharacteristic
51C43×#417C2211yescharacteristic, complemented
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#101×C43C2211yescharacteristic, complemented
55C2×#101×C43C2211yescharacteristic, complemented
56C2×#100×C43—24no—
57C2×#100×C43C2211yescharacteristic
58C2×#100×C43C2211yescharacteristic
59C2×#100×C43C2211yescharacteristic
60C2×#100×C43C2211yescharacteristic
61C43×#408C2211yescharacteristic, complemented
62C43×#407C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic, complemented
65C43×#343C2211yescharacteristic, complemented
66C43×#343C2211yescharacteristic, complemented
67C43×#341C2211yescharacteristic, complemented
68C43×#341C2211yescharacteristic, complemented
69C25×C43—21no—
70C2×#41×C43C2311yescharacteristic
71C22×Q8×C43C2311yescharacteristic
72C22×D4×C43—22no—
73C22×D4×C43—22no—
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—41no—
80C22×D4×C43—41no—
81C22×D4×C43C2311yescharacteristic
82C22×D4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84#137×C43—22no—
85#137×C43—41no—
86AGL(1,ℤ/8)×C43—22no—
87AGL(1,ℤ/8)×C43—22no—
88AGL(1,ℤ/8)×C43—41no—
89AGL(1,ℤ/8)×C43—41no—
90C2×Q16×C43—21no—
91C2×SD16×C43—21no—
92C2×SD16×C43—21no—
93C2×SD16×C43—22no—
94C2×SD16×C43—21no—
95C2×SD16×C43—22no—
96C2×SD16×C43—21no—
97C2×SD16×C43—21no—
98C2×SD16×C43—21no—
99C2×SD16×C43—21no—
100C2×SD16×C43—41no—
101C2×SD16×C43—41no—
102C2×D8×C43—21no—
103C2×D8×C43—21no—
104#131×C43—22no—
105#131×C43—41no—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43—21no—
109C2×M16×C43—22no—
110C2×M16×C43—22no—
111C2×M16×C43—41no—
112C2×M16×C43—41no—
113C2×M16×C43C2311yescharacteristic
114C2×M16×C43C2311yescharacteristic
115C2×M16×C43C2311yescharacteristic
116C2×M16×C43C2311yescharacteristic
117C2×M16×C43C2311yescharacteristic
118C2×M16×C43C2311yescharacteristic
119C22×C8×C43—21no—
120C22×C8×C43—21no—
121C22×C8×C43—21no—
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#123×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43D411yescharacteristic
130C22⋊Q8×C43D411yescharacteristic
131#121×C43D411yescharacteristic
132#121×C43D411yescharacteristic
133#120×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136#117×C43C2311yescharacteristic
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140#108×C43—22no—
141#108×C43—41no—
142#107×C43—21no—
143#106×C43—21no—
144C4⋊C8×C43—21no—
145C4⋊C8×C43—21no—
146#103×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#102×C43—21no—
150#102×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157#102×C43—21no—
158#101×C43—22no—
159#101×C43—41no—
160#100×C43—22no—
161#100×C43—22no—
162#100×C43—22no—
163#100×C43D414yescomplemented
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167C22⋊C8×C43—21no—
168C22⋊C8×C43D411yescharacteristic
169C22⋊C8×C43D411yescharacteristic
170C22⋊C8×C43D411yescharacteristic
171C22⋊C8×C43D411yescharacteristic
172#97×C43—21no—
173C4×C8×C43—21no—
174C24×C43—24no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—42no—
178C24×C43—41no—
179C24×C43—41no—
180C24×C43—82no—
181C24×C43—82no—
182C24×C43#4111yescharacteristic
183#41×C43—21no—
184#41×C43—21no—
185#41×C43—21no—
186#41×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×Q8×C43C2×D411yescharacteristic
194C2×D4×C43—24no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—42no—
209C2×D4×C43—42no—
210C2×D4×C43—42no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—42no—
214C2×D4×C43—42no—
215C2×D4×C43—42no—
216C2×D4×C43—42no—
217C2×D4×C43—41no—
218C2×D4×C43—41no—
219C2×D4×C43C2×D412yes—
220C2×D4×C43C2×D411yescharacteristic
221C2×D4×C43#4112yes—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43#4111yescharacteristic
234C22×C4×C43C2411yescharacteristic
235Q16×C43—42no—
236SD16×C43—42no—
237SD16×C43—42no—
238SD16×C43—42no—
239SD16×C43—42no—
240SD16×C43—42no—
241SD16×C43—42no—
242SD16×C43—42no—
243D8×C43—42no—
244D8×C43—42no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43—21no—
252M16×C43—21no—
253M16×C43—21no—
254M16×C43—21no—
255M16×C43—42no—
256M16×C43—42no—
257M16×C43—42no—
258M16×C43C2×D412yes—
259M16×C43C2×D412yes—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—42no—
271C2×C8×C43—42no—
272C2×C8×C43—42no—
273C2×C8×C43C2×D411yescharacteristic
274C2×C8×C43C2×D411yescharacteristic
275C2×C8×C43C2×D411yescharacteristic
276C2×C8×C43C2×D411yescharacteristic
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—41no—
282C4⋊C4×C43—41no—
283C4⋊C4×C43C2×D411yescharacteristic
284C4⋊C4×C43C2×D411yescharacteristic
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—41no—
291C22⋊C4×C43—41no—
292C42×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—22no—
296C23×C43—21no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—41no—
300C23×C43—44no—
301C23×C43—44no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—81no—
307C23×C43—81no—
308C23×C43—81no—
309C23×C43—81no—
310C23×C43—82no—
311C23×C43—82no—
312C23×C43—82no—
313C23×C43—88no—
314C23×C43—88no—
315C23×C43—82no—
316C23×C43#12111yescharacteristic
317C23×C43#12111yescharacteristic
318C23×C43C2×#4111yescharacteristic
319Q8×C43—21no—
320Q8×C43—21no—
321Q8×C43—41no—
322Q8×C43—41no—
323Q8×C43—41no—
324Q8×C43—41no—
325D4×C43—21no—
326D4×C43—22no—
327D4×C43—22no—
328D4×C43—21no—
329D4×C43—22no—
330D4×C43—22no—
331D4×C43—44no—
332D4×C43—44no—
333D4×C43—41no—
334D4×C43—41no—
335D4×C43—42no—
336D4×C43—41no—
337D4×C43—41no—
338D4×C43—41no—
339D4×C43—41no—
340D4×C43—81no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—81no—
361C2×C4×C43#12111yescharacteristic
362C2×C4×C43#12111yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C2×#4111yescharacteristic
367C2×C4×C43H(5,𝔽2)11yescharacteristic
368C2×C4×C43H(5,𝔽2)11yescharacteristic
369C8×C43—21no—
370C8×C43—21no—
371C8×C43—22no—
372C8×C43—22no—
373C8×C43—21no—
374C8×C43—21no—
375C8×C43—41no—
376C8×C43—41no—
377C8×C43—41no—
378C8×C43—41no—
379#25144C4311yesmaximal, characteristic, direct product factor, Sylow
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—82no—
395C22×C43—82no—
396C22×C43—88no—
397C22×C43—82no—
398C22×C43—82no—
399C22×C43—88no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43#47112yescomplemented
405C22×C43C2×#12111yescharacteristic
406C22×C43#52511yescharacteristic
407C22×C43#53811yescharacteristic
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—41no—
411C4×C43—41no—
412C4×C43—41no—
413C4×C43—81no—
414C4×C43—81no—
415C4×C43D4211yescharacteristic
416C4×C43D4211yescharacteristic
417C4×C43#54611yescharacteristic
418C4×C43#54611yescharacteristic
419C2×#471C2×C4311yescharacteristic, complemented
420#3056C2×C4311yescharacteristic, complemented
421#3003C2×C4311yescharacteristic
422C2×#450C2×C4311yescharacteristic, complemented
423#2933C2×C4311yescharacteristic, complemented
424C22×#100C2×C4311yescharacteristic, complemented
425#2063C2×C4311yescharacteristic, complemented
426#2051C2×C4311yescharacteristic, complemented
427#2046C2×C4311yescharacteristic, complemented
428#2019C2×C4311yescharacteristic, complemented
429#1977C2×C4311yescharacteristic, complemented
430#1931C2×C4311yescharacteristic, complemented
431#1907C2×C4311yescharacteristic, complemented
432#1901C2×C4311yescharacteristic, complemented
433#1855C2×C4311yescharacteristic, complemented
434C2×C43—21no—
435C2×C43—21no—
436C2×C43—22no—
437C2×C43—41no—
438C2×C43—81no—
439C2×C43—82no—
440C2×C43—82no—
441C2×C43#242411yescharacteristic
442C2×C43C2×#47111yescharacteristic
443C2×C43#306811yescharacteristic
444C23×D4C22×C4311yescharacteristic
445C2×#137C22×C4311yescharacteristic, complemented
446C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
447C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
448C22×SD16C22×C4311yescharacteristic
449C22×SD16C22×C4311yescharacteristic
450C2×#131C22×C4311yescharacteristic, complemented
451C22×M16C22×C4311yescharacteristic
452C22×M16C22×C4311yescharacteristic
453#525C22×C4311yescharacteristic
454C2×C22⋊Q8C22×C4311yescharacteristic
455#471—24no—
456#470—21no—
457#468—21no—
458#467—21no—
459#465—21no—
460#450—21no—
461#450—21no—
462#450—21no—
463#450—21no—
464#450—21no—
465#450—21no—
466#447—21no—
467#447—21no—
468#436—21no—
469#435—21no—
470#435—21no—
471C8×D4—21no—
472C2×#108C22×C4311yescharacteristic, complemented
473C2×#108C22×C4311yescharacteristic, complemented
474#428C22×C4311yescharacteristic, complemented
475#424C22×C4311yescharacteristic, complemented
476#419C22×C4311yescharacteristic, complemented
477#418C22×C4311yescharacteristic
478#418C22×C4311yescharacteristic
479#417C22×C4311yescharacteristic, complemented
480C2×#102C22×C4311yescharacteristic
481C2×#102C22×C4311yescharacteristic
482C2×#101C22×C4311yescharacteristic, complemented
483C2×#101C22×C4311yescharacteristic, complemented
484C2×#100—24no—
485C2×#100C22×C4311yescharacteristic
486C2×#100C22×C4311yescharacteristic
487C2×#100C22×C4311yescharacteristic
488C2×#100C22×C4311yescharacteristic
489#408C22×C4311yescharacteristic, complemented
490#407C22×C4311yescharacteristic
491C2×C22⋊C8C22×C4311yescharacteristic
492#405C22×C4311yescharacteristic, complemented
493#343C22×C4311yescharacteristic, complemented
494#343C22×C4311yescharacteristic, complemented
495#341C22×C4311yescharacteristic, complemented
496#341C22×C4311yescharacteristic, complemented
497C43#2514411yescharacteristic, direct product factor, Sylow
498C25—21no—
499C2×#41C23×C4311yescharacteristic
500C22×Q8C23×C4311yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C4311yescharacteristic
511C22×D4C23×C4311yescharacteristic
512C23×C4C23×C4311yescharacteristic
513#137—22no—
514#137—41no—
515AGL(1,ℤ/8)—22no—
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—41no—
518AGL(1,ℤ/8)—41no—
519C2×Q16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—22no—
523C2×SD16—21no—
524C2×SD16—22no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—21no—
532C2×D8—21no—
533#131—22no—
534#131—41no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16C23×C4311yescharacteristic
543C2×M16C23×C4311yescharacteristic
544C2×M16C23×C4311yescharacteristic
545C2×M16C23×C4311yescharacteristic
546C2×M16C23×C4311yescharacteristic
547C2×M16C23×C4311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C4311yescharacteristic
552C22×C8C23×C4311yescharacteristic
553#123—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8D4×C4311yescharacteristic
559C22⋊Q8D4×C4311yescharacteristic
560#121D4×C4311yescharacteristic
561#121D4×C4311yescharacteristic
562#120—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117C23×C4311yescharacteristic
566C2×C4⋊C4—21no—
567C2×C4⋊C4C23×C4311yescharacteristic
568C2×C22⋊C4—21no—
569#108—22no—
570#108—41no—
571#107—21no—
572#106—21no—
573C4⋊C8—21no—
574C4⋊C8—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585#102—21no—
586#102—21no—
587#101—22no—
588#101—41no—
589#100—22no—
590#100—22no—
591#100—22no—
592#100D4×C4314yescomplemented
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597C22⋊C8D4×C4311yescharacteristic
598C22⋊C8D4×C4311yescharacteristic
599C22⋊C8D4×C4311yescharacteristic
600C22⋊C8D4×C4311yescharacteristic
601#97—21no—
602C4×C8—21no—
603C24—24no—
604C24—21no—
605C24—21no—
606C24—42no—
607C24—41no—
608C24—41no—
609C24—82no—
610C24—82no—
611C24#41×C4311yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×D4×C4311yescharacteristic
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4C2×D4×C4312yes—
649C2×D4C2×D4×C4311yescharacteristic
650C2×D4#41×C4312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4C2×D4×C4311yescharacteristic
659C22×C4C2×D4×C4311yescharacteristic
660C22×C4C2×D4×C4311yescharacteristic
661C22×C4C2×D4×C4311yescharacteristic
662C22×C4#41×C4311yescharacteristic
663C22×C4C24×C4311yescharacteristic
664Q16—42no—
665SD16—42no—
666SD16—42no—
667SD16—42no—
668SD16—42no—
669SD16—42no—
670SD16—42no—
671SD16—42no—
672D8—42no—
673D8—42no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C4312yes—
688M16C2×D4×C4312yes—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8C2×D4×C4311yescharacteristic
703C2×C8C2×D4×C4311yescharacteristic
704C2×C8C2×D4×C4311yescharacteristic
705C2×C8C2×D4×C4311yescharacteristic
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C4311yescharacteristic
713C4⋊C4C2×D4×C4311yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—44no—
730C23—44no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—88no—
743C23—88no—
744C23—82no—
745C23#121×C4311yescharacteristic
746C23#121×C4311yescharacteristic
747C23C2×#41×C4311yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754D4—21no—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—41no—
763D4—41no—
764D4—42no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—81no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4#121×C4311yescharacteristic
791C2×C4#121×C4311yescharacteristic
792C2×C4C22×D4×C4311yescharacteristic
793C2×C4C22×D4×C4311yescharacteristic
794C2×C4C22×D4×C4311yescharacteristic
795C2×C4C2×#41×C4311yescharacteristic
796C2×C4H(5,𝔽2)×C4311yescharacteristic
797C2×C4H(5,𝔽2)×C4311yescharacteristic
798C8—21no—
799C8—21no—
800C8—22no—
801C8—22no—
802C8—21no—
803C8—21no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—88no—
827C22—88no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22C43×#47112yescomplemented
833C22C2×#121×C4311yescharacteristic
834C22C43×#52511yescharacteristic
835C22C43×#53811yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4D42×C4311yescharacteristic
844C4D42×C4311yescharacteristic
845C4C43×#54611yescharacteristic
846C4C43×#54611yescharacteristic
847C2—21no—
848C2—21no—
849C2—22no—
850C2—41no—
851C2—81no—
852C2—82no—
853C2—82no—
854C2C43×#242411yescharacteristic
855C2C2×C43×#47111yescharacteristic
856C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3003C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#471C2semidirect
2. C43×#3056C2semidirect
4. C2×C43×#450C2semidirect
5. C43×#2933C2semidirect
6. C22×#100×C43C2semidirect
7. C43×#2063C2semidirect
8. C43×#2051C2semidirect
9. C43×#2046C2semidirect
10. C43×#2019C2semidirect
11. C43×#1977C2semidirect
12. C43×#1931C2semidirect
13. C43×#1907C2semidirect
14. C43×#1901C2semidirect
15. C43×#1855C2semidirect
17. C2×#137×C43C22semidirect
22. C2×#131×C43C22semidirect
44. C2×#108×C43C22semidirect
45. C2×#108×C43C22semidirect
46. C43×#428C22semidirect
47. C43×#424C22semidirect
48. C43×#419C22semidirect
51. C43×#417C22semidirect
54. C2×#101×C43C22semidirect
55. C2×#101×C43C22semidirect
61. C43×#408C22semidirect
64. C43×#405C22semidirect
65. C43×#343C22semidirect
66. C43×#343C22semidirect
67. C43×#341C22semidirect
68. C43×#341C22semidirect
163. #100×C43D4semidirect
379. #25144C43direct (N × H)
404. C22×C43#471semidirect
419. C2×#471C2×C43semidirect
420. #3056C2×C43semidirect
422. C2×#450C2×C43semidirect
423. #2933C2×C43semidirect
424. C22×#100C2×C43semidirect
425. #2063C2×C43semidirect
426. #2051C2×C43semidirect
427. #2046C2×C43semidirect
428. #2019C2×C43semidirect
429. #1977C2×C43semidirect
430. #1931C2×C43semidirect
431. #1907C2×C43semidirect
432. #1901C2×C43semidirect
433. #1855C2×C43semidirect
445. C2×#137C22×C43semidirect
450. C2×#131C22×C43semidirect
472. C2×#108C22×C43semidirect
473. C2×#108C22×C43semidirect
474. #428C22×C43semidirect
475. #424C22×C43semidirect
476. #419C22×C43semidirect
479. #417C22×C43semidirect
482. C2×#101C22×C43semidirect
483. C2×#101C22×C43semidirect
489. #408C22×C43semidirect
492. #405C22×C43semidirect
493. #343C22×C43semidirect
494. #343C22×C43semidirect
495. #341C22×C43semidirect
496. #341C22×C43semidirect
497. C43#25144direct (N × H)
592. #100D4×C43semidirect
832. C22C43×#471semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4712
C43×#30562
C43×#30032
C2×C43×#4502
C43×#29332
C22×#100×C432
C43×#20632
C43×#20512
C43×#20462
C43×#20192
C43×#19772
C43×#19312
C43×#19072
C43×#19012
C43×#18552
#2514443